This R Markdown replicates the RD estimations from the Python
workflow using the merged CSV (All_italy_df_merged.csv) and
implements a manual running-variable override for a
specific list of municipalities (via
TreatedControl_Distance_AsCrowFlies_Manual.xlsx).
It then runs the same RD sequence for four samples:
covs= in
rdrobust(); and region-residualized plots).ireg == 3)
without regional fixed effects.square_df_merged.csv, expanded by
TARGET_AREA_SCALE), without regional fixed
effects.Common settings:
distance_treated_positive_x (km)COD_REGrdrobust() without specifying
h (package selects bandwidths)Pillar2_pol is estimated
separately by year (2010, 2020), as in the Python
workflow.# DATA (CSV)
DATA_PATH <- "/Users/murugesana/Dropbox/Research/history_behavior/Experimental_Institutions/R/data/RDD_MERGED_CSVS/All_italy_df_merged.csv"
# MANUAL DISTANCE OVERRIDES (XLSX)
MANUAL_DISTANCE_PATH <- "/Users/murugesana/Dropbox/Research/history_behavior/Experimental_Institutions/R/data/RDD_MERGED_CSVS/TreatedControl_Distance_AsCrowFlies_Manual.xlsx"
# BASELINE SQUARE FOOTPRINT (CSV) for the Lombardia "square" subsample
BASE_SQUARE_PATH <- "/Users/murugesana/Dropbox/Research/history_behavior/Experimental_Institutions/R/data/RDD_MERGED_CSVS/square_df_merged.csv"
# Lombardia constants (region code)
REGION_CODE_LOMBARDIA <- 3
# Lombardia square expansion knob (AREA scale relative to baseline footprint)
TARGET_AREA_SCALE <- 1.25
# CRS for distance-preserving square construction (meters)
UTM_EPSG <- 32632 # UTM zone 32N
OUTDIR <- "output"
dir.create(OUTDIR, showWarnings = FALSE)
RUNNING <- "distance_treated_positive_x" # km
REGION <- "COD_REG"
# Manual bandwidths (requested)
BWS_KM <- c(30, 40, 50)
# Difference-in-means bandwidth (requested)
H_DM <- 40 # km
P <- 1
# Candidate outcomes/placebos/controls to test.
# The script will run only those that exist in DATA_PATH.
OUTCOME_CANDIDATES <- c(
# Main outcomes used in prior versions
"gb_intensity", "gb_reg_rate", "evasione", "services_level",
"marr_civil", "marr_rel", "incomepc", "income",
# Aggregate service / expenditure outcomes
"services_level", "Comp_Serv_lvl", "expend_level", "expenditure", "Comp_Exp_per_cap",
# Central general services
"Admin_Emp", "Admin_Tax_Emp", "Admin_Emp_Tech_O", "Admin_Emp_CivReg",
"Admin_Emp_GenSer", "Admin_SeisRisk", "Admin_Pop65",
# Local police
"pol_serv_lvl", "pol_emp", "pol_pop_dens", "pol_str_markt", "pol_num_school",
"pol_tourist", "pol_mus_vist", "pol_pay_park", "pol_mun_road",
"pol_arrest", "pol_lawsuit", "pol_veh_rem",
# Education
"edu_serv_lvl", "edu_emp_per1000", "edu_muni_schoolpop_perc",
"edu_muni_school_area_per1000", "edu_prvt_schoolpop_perc",
"edu_meal_serv_pop_perc", "edu_sum_camp_pop_perc",
# Public roads and planning
"PublS_Serv_lvl", "PublS_Emp_Serv_per1000", "PublS_Emp_Env_per1000",
"PublS_PopRiskLandslide_perc", "PublS_CyclePath_per", "PublS_lightpoint",
"PublS_PlantPrune_per1000", "PublS_NewTree_per1000", "PublS_RivbedClean_per1000",
"PublS_Project_per1000", "PublS_WorkinProg_per1000", "PublS_Test_per1000",
# Waste management
"waste_coll_recycle", "waste_wasteprod_perpers", "waste_rlandfill", "waste_treated_perc",
# Social care and nursery services
"soccare_user_percpop", "socnurse_user_percpop", "socnurse_emp_per1000",
"socnurse_educators_share", "socnurse_income_mean2017to2019", "socnurse_voucher_share",
"socnurse_foreignpop_share", "socnurse_econdepriv_index",
"socnurse_disabilities_users", "socnurse_mentalhealth_users",
"socnurse_immigrantper1000", "socnurse_povertyusers_per1000",
# Alternate names that can appear in intermediate files
"socnurse_poverty_users", "poverty_users_interventions",
"disabilities_users_interventions", "mentalhealth_users_interventions",
"immigrantsnomads_per1000", "Pillar2_pol"
)
YEARS <- c(2010, 2020)df0 <- readr::read_csv(DATA_PATH, show_col_types = FALSE)
# key column (municipality id)
KEYCOL <- if ("istat" %in% names(df0)) "istat" else if ("ISTAT" %in% names(df0)) "ISTAT" else stop("No istat/ISTAT column found.")
# ensure expected columns exist
stopifnot(RUNNING %in% names(df0), REGION %in% names(df0))
# Keep only requested variables available in the merged dataset.
OUTCOMES <- intersect(OUTCOME_CANDIDATES, names(df0))
MISSING_OUTCOMES <- setdiff(OUTCOME_CANDIDATES, names(df0))
cat("Requested outcomes/placebos/controls: ", length(OUTCOME_CANDIDATES), "\n", sep = "")## Requested outcomes/placebos/controls: 73cat("Available and used in RD: ", length(OUTCOMES), "\n", sep = "")## Available and used in RD: 26if (length(MISSING_OUTCOMES) > 0) {
cat("[Info] Requested but unavailable in data (skipped): ",
paste(MISSING_OUTCOMES, collapse = ", "), "\n", sep = "")
}## [Info] Requested but unavailable in data (skipped): Admin_Emp, Admin_Emp_Tech_O, Admin_Emp_GenSer, Admin_SeisRisk, Admin_Pop65, pol_emp, pol_pop_dens, pol_str_markt, pol_num_school, pol_tourist, pol_mus_vist, pol_pay_park, pol_arrest, pol_lawsuit, pol_veh_rem, PublS_Serv_lvl, PublS_Emp_Serv_per1000, PublS_Emp_Env_per1000, PublS_PopRiskLandslide_perc, PublS_PlantPrune_per1000, PublS_NewTree_per1000, PublS_RivbedClean_per1000, PublS_Project_per1000, PublS_WorkinProg_per1000, PublS_Test_per1000, waste_coll_recycle, waste_wasteprod_perpers, waste_rlandfill, waste_treated_perc, soccare_user_percpop, socnurse_user_percpop, socnurse_emp_per1000, socnurse_educators_share, socnurse_income_mean2017to2019, socnurse_voucher_share, socnurse_foreignpop_share, socnurse_econdepriv_index, socnurse_disabilities_users, socnurse_mentalhealth_users, socnurse_immigrantper1000, socnurse_povertyusers_per1000, socnurse_poverty_users, poverty_users_interventions, disabilities_users_interventions, mentalhealth_users_interventions, immigrantsnomads_per1000# region as factor (fixed effects)
df0 <- df0 %>% mutate(.region_fe = factor(.data[[REGION]]))
# convenience alias to match older scripts
if (!("ireg" %in% names(df0))) df0 <- df0 %>% mutate(ireg = as.integer(.data[[REGION]]))
# -----------------------------
# Manual distance corrections
# -----------------------------
manual0 <- readxl::read_excel(MANUAL_DISTANCE_PATH)
# Expected columns in manual file:
# COD_REG, COMUNE, Treated, distance_updated
needed_manual <- c("COD_REG", "COMUNE", "Treated", "distance_updated")
stopifnot(all(needed_manual %in% names(manual0)))
manual <- manual0 %>%
mutate(
COD_REG = as.integer(COD_REG),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE))),
distance_updated = as.numeric(distance_updated)
) %>%
filter(!is.na(distance_updated)) %>%
select(COD_REG, Treated, COMUNE_clean, distance_updated)
df0 <- df0 %>%
mutate(
COD_REG = as.integer(.data[[REGION]]),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE)))
) %>%
left_join(manual, by = c("COD_REG", "Treated", "COMUNE_clean")) %>%
mutate(
.running_original = .data[[RUNNING]],
# overwrite where manual distance exists
"{RUNNING}" := dplyr::if_else(!is.na(distance_updated), distance_updated, .data[[RUNNING]]),
.running_overwritten = !is.na(distance_updated)
)
# --- Manual correction to distance sign and treated status (user request) ---
# For these municipalities, force the running variable to be NEGATIVE and set Treated = 0:
# (COD_REG, COD_PROV, PRO_COM, COMUNE)
# 8, 36, 36010, Concordia sulla Secchia
# 8, 36, 36022, Mirandola
# 8, 38, 38003, Bondeno
flip_muni <- tibble::tribble(
~COD_REG, ~COD_PROV, ~PRO_COM, ~COMUNE_clean,
8L, 36L, 36010L, "CONCORDIA SULLA SECCHIA",
8L, 36L, 36022L, "MIRANDOLA",
8L, 38L, 38003L, "BONDENO"
)
# Build a robust match indicator depending on which ID columns are available in df0
if (all(c("COD_REG", "COD_PROV") %in% names(df0))) {
# Prefer PRO_COM (municipality/province code) when available; otherwise fall back to COD_UTS/COD_CM/COMUNE_clean matching
if ("PRO_COM" %in% names(df0)) {
df0 <- df0 %>%
mutate(
.flip_flag = (as.integer(COD_REG) == 8L &
as.integer(COD_PROV) %in% c(36L, 38L) &
as.integer(PRO_COM) %in% c(36010L, 36022L, 38003L))
)
} else if ("PRO_COM_T" %in% names(df0)) {
df0 <- df0 %>%
mutate(
.flip_flag = (as.integer(COD_REG) == 8L &
as.integer(COD_PROV) %in% c(36L, 38L) &
as.integer(PRO_COM_T) %in% c(36010L, 36022L, 38003L))
)
} else {
df0 <- df0 %>%
mutate(
.flip_flag = (as.integer(COD_REG) == 8L &
as.integer(COD_PROV) %in% c(36L, 38L) &
COMUNE_clean %in% flip_muni$COMUNE_clean)
)
}
df0 <- df0 %>%
mutate(
Treated = dplyr::if_else(.flip_flag, 0L, as.integer(Treated)),
"{RUNNING}" := dplyr::if_else(.flip_flag, -abs(.data[[RUNNING]]), .data[[RUNNING]])
) %>%
select(-.flip_flag)
} else {
warning("COD_REG/COD_PROV not found in df0; could not apply negative-distance + Treated=0 correction for the three municipalities.")
}
# --- Exclude specific comune from *all* estimations (user request) ---
# Tronzano Lago Maggiore (province code 12)
if ("COD_PROV" %in% names(df0)) {
df0 <- df0 %>%
dplyr::filter(!(COMUNE_clean == "TRONZANO LAGO MAGGIORE" & as.integer(.data[["COD_PROV"]]) == 12))
} else {
warning("COD_PROV not found in df0; could not drop Tronzano Lago Maggiore (province code 12).")
}
# --- User-requested recode: set selected Emilia-Romagna treated comuni to control ---
# Create NEW variables and use them for RDD:
# - Treated_emilia11
# - distance_treated_positive_x_emilia11
EMILIA11_FORCE_CONTROL <- c(
"CALENDASCO",
"CAORSO",
"CASTEL SAN GIOVANNI",
"CASTELVETRO PIACENTINO",
"COLORNO",
"MONTICELLI D'ONGINA",
"PIACENZA",
"ROCCABIANCA",
"ROTTOFRENO",
"SARMATO",
"VILLANOVA SULL'ARDA"
)
RUNNING_NEW <- paste0(RUNNING, "_emilia11")
TREATED_NEW <- "Treated_emilia11"
df0 <- df0 %>%
mutate(
Treated_pre_emilia11 = as.integer(Treated),
"{TREATED_NEW}" := as.integer(Treated),
"{RUNNING_NEW}" := as.numeric(.data[[RUNNING]]),
.emilia11_force = (as.integer(COD_REG) == 8L & COMUNE_clean %in% EMILIA11_FORCE_CONTROL)
) %>%
mutate(
"{TREATED_NEW}" := dplyr::if_else(.emilia11_force, 0L, .data[[TREATED_NEW]]),
"{RUNNING_NEW}" := dplyr::if_else(.emilia11_force, -abs(.data[[RUNNING_NEW]]), .data[[RUNNING_NEW]])
) %>%
mutate(
Treated = .data[[TREATED_NEW]]
) %>%
select(-.emilia11_force)
# Switch downstream RD code to the new running-variable column
RUNNING <- RUNNING_NEW
cat("Emilia-11 recode applied: n_forced_control=",
sum(df0$COMUNE_clean %in% EMILIA11_FORCE_CONTROL & as.integer(df0$COD_REG) == 8L, na.rm = TRUE),
" | using RUNNING=", RUNNING,
" | using treatment column=", TREATED_NEW, "\n", sep = "")## Emilia-11 recode applied: n_forced_control=22 | using RUNNING=distance_treated_positive_x_emilia11 | using treatment column=Treated_emilia11cat("Manual distance overrides applied:\n")## Manual distance overrides applied:df0 %>%
summarise(
n_rows = n(),
n_overwritten_rows = sum(.running_overwritten, na.rm = TRUE),
n_overwritten_muni = n_distinct(.data[[KEYCOL]][.running_overwritten]),
n_regions = n_distinct(.region_fe),
years = if ("year" %in% names(df0)) paste(sort(unique(year)), collapse = ", ") else NA_character_
) %>%
print()## # A tibble: 1 × 5
## n_rows n_overwritten_rows n_overwritten_muni n_regions years
## <int> <int> <int> <int> <chr>
## 1 6984 68 34 7 2010, 2020# Optional: inspect which municipalities were overwritten
df0 %>%
filter(.running_overwritten) %>%
distinct(COD_REG, COMUNE, Treated, .running_original, !!sym(RUNNING)) %>%
arrange(COD_REG, COMUNE) %>%
head(25) %>%
print()## # A tibble: 25 × 5
## COD_REG COMUNE Treated .running_original distance_treated_positi…¹
## <int> <chr> <int> <dbl> <dbl>
## 1 3 Albiolo 1 -25.3 28.4
## 2 3 Albuzzano 1 -3.67 3.67
## 3 3 Belgioioso 1 -2.67 2.67
## 4 3 Bereguardo 1 -2.76 2.76
## 5 3 Borgo San Siro 0 5.23 -6.67
## 6 3 Campione d'Italia 1 -22.1 22.1
## 7 3 Ceranova 1 -1.91 10.9
## 8 3 Copiano 1 -2.07 8.31
## 9 3 Cura Carpignano 1 -2.55 6.3
## 10 3 Faloppio 1 -27.3 31.6
## # ℹ 15 more rows
## # ℹ abbreviated name: ¹distance_treated_positive_x_emilia11collapse_one_row_per_muni <- function(d, keycol, xcol, ycol, keep_year = FALSE) {
# Collapses to one row per municipality (mean across duplicates).
# Also carries Treated (or Treated_num) and COD_PROV when available.
gvars <- c(keycol)
if (keep_year && ("year" %in% names(d))) gvars <- c(gvars, "year")
d %>%
group_by(across(all_of(gvars))) %>%
summarise(
X = mean(.data[[xcol]], na.rm = TRUE),
Y = mean(.data[[ycol]], na.rm = TRUE),
Treated = dplyr::first(
if ("Treated" %in% names(d)) as.integer(.data[["Treated"]])
else if ("Treated_num" %in% names(d)) as.integer(.data[["Treated_num"]])
else NA_integer_
),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(d)) as.integer(.data[["COD_PROV"]]) else NA_integer_),
.region_fe = dplyr::first(if (".region_fe" %in% names(d)) .data[[".region_fe"]] else NA),
.groups = "drop"
)
}
make_sub <- function(d, h) {
# Filter to bandwidth window and drop missing (requires .region_fe).
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.region_fe),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_noFE <- function(d, h) {
# Filter to bandwidth window and drop missing (NO FE requirement).
sub <- d %>%
filter(!is.na(X), !is.na(Y),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; with FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y), !is.na(.region_fe))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full_noFE <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; no FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
region_covs <- function(sub) {
# region dummies (no intercept) for rdrobust(covs=...)
stats::model.matrix(~ .region_fe - 1, data = sub)
}
residualize_region <- function(y, sub) {
# partial out region FE for plotting convenience
stats::residuals(stats::lm(y ~ .region_fe, data = sub))
}
extract_rdrobust <- function(rb, outcome, h, sample, year = NA_integer_, h_type = "MANUAL") {
tibble::tibble(
sample = sample,
outcome = outcome,
year = year,
h_type = h_type, # MANUAL vs AUTO
h_km = h, # manual h, NA for AUTO
p = P,
N = if (!is.null(rb$N)) sum(rb$N) else NA_integer_,
N_left = if (!is.null(rb$N)) rb$N[1] else NA_integer_,
N_right = if (!is.null(rb$N)) rb$N[2] else NA_integer_,
bw_left = if (!is.null(rb$bws)) rb$bws[1] else NA_real_,
bw_right = if (!is.null(rb$bws)) rb$bws[2] else NA_real_,
coef = list(rb$coef),
se = list(rb$se),
pv = list(rb$pv),
ci = list(rb$ci)
)
}
safe_rdrobust <- function(y, x, ..., label = "") {
# Wrapper to avoid hard stops from rdrobust numerical failures (e.g., non-PD matrices).
# Returns NULL on error and prints the error to the current output connection (sink-safe).
tryCatch(
rdrobust::rdrobust(y, x, ...),
error = function(e) {
cat("[Skip rdrobust ERROR] ", label, " : ", conditionMessage(e), "\n", sep = "")
return(NULL)
}
)
}
diff_means_test <- function(d, h, treated_col = "Treated") {
# Difference in means (treated - control) within |X| <= h, using Welch two-sample t-test.
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.data[[treated_col]]),
dplyr::between(X, -h, h)) %>%
mutate(.tr = as.integer(.data[[treated_col]]))
if (!all(c(0L, 1L) %in% unique(sub$.tr))) return(NULL)
y1 <- sub$Y[sub$.tr == 1L]
y0 <- sub$Y[sub$.tr == 0L]
n1 <- sum(sub$.tr == 1L)
n0 <- sum(sub$.tr == 0L)
if (n1 < 5 || n0 < 5) return(NULL)
m1 <- mean(y1, na.rm = TRUE)
m0 <- mean(y0, na.rm = TRUE)
s1 <- stats::var(y1, na.rm = TRUE)
s0 <- stats::var(y0, na.rm = TRUE)
se <- sqrt(s1 / n1 + s0 / n0)
tt <- stats::t.test(Y ~ .tr, data = sub) # Welch by default
tibble::tibble(
h_km = h,
n_treated = n1,
n_control = n0,
mean_treated = m1,
mean_control = m0,
diff_treat_minus_control = m1 - m0,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}
diff_means_test_regFE <- function(d, h, treated_col = "Treated") {
# Difference in means (treated - control) within |X| <= h,
# controlling for region fixed effects via OLS: Y ~ treated + region FE.
# Returns the coefficient on treated (treated-control adjusted for region FE).
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.region_fe), !is.na(.data[[treated_col]]),
dplyr::between(X, -h, h)) %>%
mutate(.tr = as.integer(.data[[treated_col]]))
if (!all(c(0L, 1L) %in% unique(sub$.tr))) return(NULL)
if (sum(sub$.tr == 1L) < 5 || sum(sub$.tr == 0L) < 5) return(NULL)
fit <- stats::lm(Y ~ .tr + .region_fe, data = sub)
coefs <- summary(fit)$coefficients
if (!(".tr" %in% rownames(coefs))) return(NULL)
tibble::tibble(
h_km = h,
diff_fe = as.numeric(coefs[".tr", "Estimate"]),
se_fe = as.numeric(coefs[".tr", "Std. Error"]),
t_fe = as.numeric(coefs[".tr", "t value"]),
df_fe = as.numeric(stats::df.residual(fit)),
p_fe = as.numeric(coefs[".tr", "Pr(>|t|)"])
)
}
diff_means_sign_test <- function(d) {
# Difference in means (X>=0 - X<0) using Welch two-sample t-test.
# Intended for within-square comparisons where "treated" is defined by the sign of the running variable.
sub <- d %>%
filter(!is.na(X), !is.na(Y)) %>%
mutate(.side = if_else(X >= 0, 1L, 0L))
if (!all(c(0L, 1L) %in% unique(sub$.side))) return(NULL)
y_pos <- sub$Y[sub$.side == 1L] # X >= 0
y_neg <- sub$Y[sub$.side == 0L] # X < 0
n_pos <- sum(sub$.side == 1L)
n_neg <- sum(sub$.side == 0L)
if (n_pos < 5 || n_neg < 5) return(NULL)
m_pos <- mean(y_pos, na.rm = TRUE)
m_neg <- mean(y_neg, na.rm = TRUE)
s_pos <- stats::var(y_pos, na.rm = TRUE)
s_neg <- stats::var(y_neg, na.rm = TRUE)
se <- sqrt(s_pos / n_pos + s_neg / n_neg)
tt <- stats::t.test(Y ~ .side, data = sub) # Welch by default
tibble::tibble(
n_pos = n_pos,
n_neg = n_neg,
mean_pos = m_pos,
mean_neg = m_neg,
diff_pos_minus_neg = m_pos - m_neg,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}# Output files (All Italy / Lombardia / Lombardia-square / All-Italy-square)
plots_pdf_all <- file.path(OUTDIR, "RD_plots_All_Italy_regFE_manualDistance.pdf")
plots_pdf_lomb <- file.path(OUTDIR, "RD_plots_Lombardia_noFE_manualDistance.pdf")
plots_pdf_square <- file.path(OUTDIR, sprintf("RD_plots_LombardiaSquare_area_x%0.2f_noFE_manualDistance.pdf", TARGET_AREA_SCALE))
plots_pdf_sq_all <- file.path(OUTDIR, sprintf("RD_plots_AllItalySquare_area_x%0.2f_regFE_manualDistance.pdf", TARGET_AREA_SCALE))
results_csv <- file.path(OUTDIR, "rdrobust_results_All_Italy_Lombardia_Square_manualDistance.csv")
results_txt_all <- file.path(OUTDIR, "rdrobust_printout_All_Italy_regFE_manualDistance.txt")
results_txt_lomb <- file.path(OUTDIR, "rdrobust_printout_Lombardia_noFE_manualDistance.txt")
results_txt_sq <- file.path(OUTDIR, sprintf("rdrobust_printout_LombardiaSquare_area_x%0.2f_noFE_manualDistance.txt", TARGET_AREA_SCALE))
results_txt_sq_all <- file.path(OUTDIR, sprintf("rdrobust_printout_AllItalySquare_area_x%0.2f_regFE_manualDistance.txt", TARGET_AREA_SCALE))
# Difference-in-means outputs (h = 40 km)
dm_csv_all40 <- file.path(OUTDIR, "diffmeans_FullItaly_h40.csv")
dm_csv_lomb40 <- file.path(OUTDIR, "diffmeans_Lombardia_h40.csv")
dm_csv_sq40 <- file.path(OUTDIR, "diffmeans_LombardiaSquare_h40.csv")
dm_csv_sqsign <- file.path(OUTDIR, "diffmeans_LombardiaSquare_sign.csv")
dm_csv_sqall40 <- file.path(OUTDIR, "diffmeans_AllItalySquare_h40.csv")
# accumulator across samples
all_results <- list()# --- FULL ITALY SECTION ---
sink(results_txt_all, split = TRUE)
cat("Using DF: All_italy_df_merged (post manual distance overwrite) | rows=", nrow(df0),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df0), "year", NA),
"\n", sep = "")## Using DF: All_italy_df_merged (post manual distance overwrite) | rows=6984 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, "\n\n", sep = "")## Running var: distance_treated_positive_x_emilia11 (KM) | manual bandwidths=30, 40, 50 | p=1pdf(plots_pdf_all, width = 6, height = 4.5)
# Difference-in-means accumulator (Full Italy) at h = 40 km
all_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df0))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df0))) {
for (yr in YEARS) {
dY <- df0 %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means within |X| <= 40 km (Full Italy):
# (i) raw Welch t-test
# (ii) OLS controlling for region FE (Y ~ Treated + region dummies)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dplyr::left_join(dm_out, dm_fe, by = "h_km")
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, t_fe = NA_real_, df_fe = NA_real_, p_fe = NA_real_)
}
all_dm40[[length(all_dm40) + 1]] <- dm_out %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = yr)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar, " | year=", yr,
" | diff=", signif(dm_out$diff_treat_minus_control, 4),
" | p=", signif(dm_out$p_value, 4),
" | diff_FE=", signif(dm_out$diff_fe, 4),
" | p_FE=", signif(dm_out$p_fe, 4),
" | N_t=", dm_out$n_treated, " N_c=", dm_out$n_control, "\n", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = yr, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = yr, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means within |X| <= 40 km (Full Italy):
# (i) raw Welch t-test
# (ii) OLS controlling for region FE (Y ~ Treated + region dummies)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dplyr::left_join(dm_out, dm_fe, by = "h_km")
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, t_fe = NA_real_, df_fe = NA_real_, p_fe = NA_real_)
}
all_dm40[[length(all_dm40) + 1]] <- dm_out %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = NA_integer_)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm_out$diff_treat_minus_control, 4),
" | p=", signif(dm_out$p_value, 4),
" | diff_FE=", signif(dm_out$diff_fe, 4),
" | p_FE=", signif(dm_out$p_fe, 4),
" | N_t=", dm_out$n_treated, " N_c=", dm_out$n_control, "\n", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = NA_integer_, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = NA_integer_, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}## [Full Italy diff-means] h=40 km | outcome=gb_intensity | diff=0.004012 | p=0.0005553 | diff_FE=-0.01208 | p_FE=1.644e-10 | N_t=694 N_c=621
##
## ==============================================================================================================
## Outcome: gb_intensity | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=1045 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1045
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 477 568
## Eff. Number of Obs. 477 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 477 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.008 0.002 -3.213 0.001 [-0.012 , -0.003]
## Robust - - -0.809 0.418 [-0.012 , 0.005]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=1315 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 621 694
## Eff. Number of Obs. 621 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 621 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.002 -3.541 0.000 [-0.011 , -0.003]
## Robust - - -1.814 0.070 [-0.013 , 0.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=1595 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1595
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 743 852
## Eff. Number of Obs. 743 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 743 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.008 0.002 -4.398 0.000 [-0.012 , -0.005]
## Robust - - -1.886 0.059 [-0.011 , 0.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=3512 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3512
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2228 1284
## Eff. Number of Obs. 408 477
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.737 24.737
## BW bias (b) 43.318 43.318
## rho (h/b) 0.571 0.571
## Unique Obs. 2210 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.003 -2.599 0.009 [-0.012 , -0.002]
## Robust - - -1.890 0.059 [-0.013 , 0.000]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=gb_reg_rate | diff=-0.0416 | p=0.0001927 | diff_FE=0.06671 | p_FE=0.0003745 | N_t=694 N_c=621
##
## ==============================================================================================================
## Outcome: gb_reg_rate | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=1045 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1045
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 477 568
## Eff. Number of Obs. 477 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 477 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.069 0.023 2.946 0.003 [0.023 , 0.114]
## Robust - - 0.887 0.375 [-0.040 , 0.107]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=1315 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 621 694
## Eff. Number of Obs. 621 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 621 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.066 0.020 3.264 0.001 [0.026 , 0.106]
## Robust - - 2.013 0.044 [0.002 , 0.125]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=1595 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1595
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 743 852
## Eff. Number of Obs. 743 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 743 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.075 0.018 4.147 0.000 [0.039 , 0.110]
## Robust - - 1.840 0.066 [-0.003 , 0.106]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=3512 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3512
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2228 1284
## Eff. Number of Obs. 406 476
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.432 24.432
## BW bias (b) 40.603 40.603
## rho (h/b) 0.602 0.602
## Unique Obs. 2210 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.057 0.026 2.226 0.026 [0.007 , 0.107]
## Robust - - 1.743 0.081 [-0.007 , 0.118]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=evasione | diff=-2.716 | p=6.2e-10 | diff_FE=-2.741 | p_FE=0.0001428 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: evasione | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.609 0.946 -1.702 0.089 [-3.463 , 0.244]
## Robust - - 0.059 0.953 [-3.131 , 3.326]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.501 0.810 -1.854 0.064 [-3.088 , 0.086]
## Robust - - -1.004 0.315 [-3.902 , 1.259]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.627 0.721 -2.257 0.024 [-3.039 , -0.214]
## Robust - - -1.209 0.227 [-3.610 , 0.856]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2208 1264
## Eff. Number of Obs. 450 525
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.925 27.925
## BW bias (b) 46.007 46.007
## rho (h/b) 0.607 0.607
## Unique Obs. 2190 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.597 0.984 -1.624 0.104 [-3.525 , 0.330]
## Robust - - -1.272 0.203 [-3.970 , 0.845]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=services_level | diff=0.1767 | p=0.2577 | diff_FE=2.492 | p_FE=1.931e-22 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: services_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.806 0.320 5.637 0.000 [1.178 , 2.434]
## Robust - - 2.336 0.019 [0.205 , 2.337]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.994 0.276 7.235 0.000 [1.454 , 2.535]
## Robust - - 3.488 0.000 [0.679 , 2.419]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.126 0.248 8.571 0.000 [1.640 , 2.612]
## Robust - - 4.506 0.000 [0.971 , 2.466]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 411 479
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.176 25.176
## BW bias (b) 47.448 47.448
## rho (h/b) 0.531 0.531
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.731 0.355 4.879 0.000 [1.036 , 2.426]
## Robust - - 3.722 0.000 [0.743 , 2.397]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_civil | diff=2.725 | p=0.4669 | diff_FE=9.387 | p_FE=0.1563 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: marr_civil | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.221 4.438 0.500 0.617 [-6.477 , 10.919]
## Robust - - 0.764 0.445 [-4.993 , 11.371]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.944 2.511 2.367 0.018 [1.022 , 10.866]
## Robust - - -0.078 0.938 [-14.359 , 13.258]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.689 2.188 3.515 0.000 [3.401 , 11.976]
## Robust - - 0.380 0.704 [-9.423 , 13.950]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 378 441
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 22.172 22.172
## BW bias (b) 42.269 42.269
## rho (h/b) 0.525 0.525
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.854 3.586 0.517 0.605 [-5.175 , 8.882]
## Robust - - -0.032 0.975 [-11.174 , 10.817]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_rel | diff=1.825 | p=0.1333 | diff_FE=4.746 | p_FE=0.02612 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: marr_rel | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.669 1.703 0.393 0.695 [-2.669 , 4.007]
## Robust - - -0.327 0.744 [-5.193 , 3.707]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.215 1.172 1.890 0.059 [-0.082 , 4.511]
## Robust - - -0.461 0.645 [-6.257 , 3.875]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.080 1.050 2.934 0.003 [1.023 , 5.137]
## Robust - - 0.094 0.925 [-4.087 , 4.501]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 381 441
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 22.362 22.362
## BW bias (b) 39.637 39.637
## rho (h/b) 0.564 0.564
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.170 1.671 -0.102 0.919 [-3.446 , 3.105]
## Robust - - -0.596 0.551 [-6.003 , 3.204]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=incomepc | diff=1168 | p=2.453e-11 | diff_FE=2057 | p_FE=5.778e-12 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: incomepc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1760.588 373.916 4.709 0.000 [1027.727 , 2493.450]
## Robust - - 0.868 0.385 [-741.880 , 1921.593]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2048.892 326.858 6.268 0.000 [1408.262 , 2689.521]
## Robust - - 2.170 0.030 [110.453 , 2173.892]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2155.474 295.658 7.290 0.000 [1575.996 , 2734.952]
## Robust - - 3.636 0.000 [747.263 , 2495.290]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 276 330
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 14.898 14.898
## BW bias (b) 48.028 48.028
## rho (h/b) 0.310 0.310
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1287.885 628.022 2.051 0.040 [56.984 , 2518.786]
## Robust - - 1.804 0.071 [-103.210 , 2491.422]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=income | diff=50360000 | p=0.3255 | diff_FE=116200000 | p_FE=0.2041 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: income | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-5975750.67159079235.135 -0.101 0.919[-121768923.769 , 109817422.428]
## Robust - - -0.057 0.954[-82191369.323 , 77512658.649]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional51605877.06826800147.114 1.926 0.054[-921446.056 , 104133200.192]
## Robust - - -0.611 0.541[-245476208.091 , 128839862.573]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional82568424.56523199560.592 3.559 0.000[37098121.348 , 128038727.783]
## Robust - - -0.203 0.839[-173195783.826 , 140658410.876]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 358 413
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.728 20.728
## BW bias (b) 40.826 40.826
## rho (h/b) 0.508 0.508
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional54723085.34947094216.694 1.162 0.245[-37579883.252 , 147026053.950]
## Robust - - -0.086 0.931[-131274862.421 , 120196063.714]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Comp_Serv_lvl | diff=0.1295 | p=0.4129 | diff_FE=2.777 | p_FE=2.406e-27 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: Comp_Serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.326 0.320 7.280 0.000 [1.700 , 2.952]
## Robust - - 1.929 0.054 [-0.017 , 2.110]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.725 0.275 9.898 0.000 [2.186 , 3.265]
## Robust - - 3.768 0.000 [0.799 , 2.532]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.872 0.247 11.609 0.000 [2.387 , 3.357]
## Robust - - 5.824 0.000 [1.472 , 2.965]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 125 149
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.472 6.472
## BW bias (b) 56.004 56.004
## rho (h/b) 0.116 0.116
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.309 1.053 1.243 0.214 [-0.756 , 3.373]
## Robust - - 1.222 0.222 [-0.779 , 3.359]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expend_level | diff=0.3369 | p=0.01049 | diff_FE=0.7444 | p_FE=0.0007855 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: expend_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.481 0.307 1.568 0.117 [-0.120 , 1.083]
## Robust - - 0.341 0.733 [-0.871 , 1.237]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.587 0.261 2.248 0.025 [0.075 , 1.099]
## Robust - - 0.799 0.424 [-0.499 , 1.187]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.672 0.234 2.866 0.004 [0.212 , 1.131]
## Robust - - 1.174 0.240 [-0.286 , 1.142]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 244 288
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 12.599 12.599
## BW bias (b) 27.521 27.521
## rho (h/b) 0.458 0.458
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.238 0.561 0.424 0.672 [-0.861 , 1.336]
## Robust - - 0.182 0.856 [-1.179 , 1.420]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expenditure | diff=240400 | p=0.6328 | diff_FE=1072000 | p_FE=0.226 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: expenditure | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 97352.369542827.680 0.179 0.858[-966570.333 , 1161275.070]
## Robust - - 0.406 0.685[-641449.457 , 976779.533]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional645330.478304183.304 2.122 0.034 [49142.157 , 1241518.798]
## Robust - - -0.350 0.726[-2034258.265 , 1418119.164]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional869818.464250049.506 3.479 0.001[379730.439 , 1359906.490]
## Robust - - 0.185 0.853[-1335330.780 , 1613483.922]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2208 1264
## Eff. Number of Obs. 309 359
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 16.960 16.960
## BW bias (b) 47.258 47.258
## rho (h/b) 0.359 0.359
## Unique Obs. 2190 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional399079.482285937.213 1.396 0.163[-161347.158 , 959506.121]
## Robust - - 0.733 0.463[-434986.636 , 955254.565]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Comp_Exp_per_cap | diff=-160.6 | p=1.155e-40 | diff_FE=-136 | p_FE=6.937e-13 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: Comp_Exp_per_cap | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -87.631 20.526 -4.269 0.000 [-127.861 , -47.402]
## Robust - - -1.434 0.152 [-111.172 , 17.224]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -84.763 18.751 -4.521 0.000 [-121.513 , -48.013]
## Robust - - -3.397 0.001 [-147.605 , -39.600]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -82.484 17.710 -4.657 0.000 [-117.195 , -47.773]
## Robust - - -3.755 0.000 [-141.070 , -44.313]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 223 264
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 11.126 11.126
## BW bias (b) 22.460 22.460
## rho (h/b) 0.495 0.495
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -28.914 37.463 -0.772 0.440 [-102.341 , 44.513]
## Robust - - -0.335 0.738 [-110.416 , 78.218]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1041 | p=0.1372 | diff_FE=0.1416 | p_FE=0.2337 | N_t=226 N_c=220
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=363 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 363
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 177 186
## Eff. Number of Obs. 177 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 177 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.062 0.097 0.640 0.522 [-0.128 , 0.253]
## Robust - - 1.699 0.089 [-0.030 , 0.416]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=446 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 446
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 220 226
## Eff. Number of Obs. 220 226
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 220 226
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.058 0.059 0.991 0.322 [-0.057 , 0.174]
## Robust - - 0.679 0.497 [-0.167 , 0.345]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=499 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 499
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 239 260
## Eff. Number of Obs. 239 260
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 239 260
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.101 0.051 1.986 0.047 [0.001 , 0.200]
## Robust - - -0.149 0.882 [-0.317 , 0.272]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=926 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 926
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 579 347
## Eff. Number of Obs. 125 113
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.161 17.161
## BW bias (b) 50.068 50.068
## rho (h/b) 0.343 0.343
## Unique Obs. 573 346
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.151 0.089 1.701 0.089 [-0.023 , 0.325]
## Robust - - 1.272 0.203 [-0.069 , 0.326]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Admin_Emp_CivReg | diff=-0.05043 | p=0.2952 | diff_FE=-0.0189 | p_FE=0.8086 | N_t=230 N_c=187
##
## ==============================================================================================================
## Outcome: Admin_Emp_CivReg | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=30 km | p=1 | N used=351 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 351
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 150 201
## Eff. Number of Obs. 150 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 150 201
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.035 0.085 -0.413 0.680 [-0.203 , 0.132]
## Robust - - -0.669 0.503 [-0.414 , 0.203]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=40 km | p=1 | N used=417 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 417
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 187 230
## Eff. Number of Obs. 187 230
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 187 230
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.003 0.073 -0.046 0.963 [-0.147 , 0.140]
## Robust - - -0.760 0.447 [-0.347 , 0.153]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=50 km | p=1 | N used=475 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 475
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 208 267
## Eff. Number of Obs. 208 267
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 208 267
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.150 0.138 1.088 0.277 [-0.120 , 0.420]
## Robust - - -1.106 0.269 [-0.976 , 0.272]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | AUTO bandwidth (default) | p=1 | N used=834 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 834
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 489 345
## Eff. Number of Obs. 92 115
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 15.289 15.289
## BW bias (b) 62.107 62.107
## rho (h/b) 0.246 0.246
## Unique Obs. 485 343
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.076 0.146 -0.518 0.604 [-0.363 , 0.211]
## Robust - - -0.914 0.361 [-0.463 , 0.168]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=pol_serv_lvl | diff=-0.2976 | p=0.09841 | diff_FE=-0.1478 | p_FE=0.6414 | N_t=567 N_c=393
##
## ==============================================================================================================
## Outcome: pol_serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=30 km | p=1 | N used=777 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 777
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 315 462
## Eff. Number of Obs. 315 462
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 315 462
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.697 0.442 -1.579 0.114 [-1.563 , 0.168]
## Robust - - -1.393 0.164 [-2.736 , 0.463]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=40 km | p=1 | N used=960 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 960
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 393 567
## Eff. Number of Obs. 393 567
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 393 567
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.554 0.371 -1.495 0.135 [-1.281 , 0.173]
## Robust - - -1.412 0.158 [-2.145 , 0.348]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=50 km | p=1 | N used=1158 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1158
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 699
## Eff. Number of Obs. 459 699
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 699
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.507 0.330 -1.535 0.125 [-1.153 , 0.140]
## Robust - - -1.271 0.204 [-1.722 , 0.368]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | AUTO bandwidth (default) | p=1 | N used=2272 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 2272
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1246 1026
## Eff. Number of Obs. 374 549
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 38.070 38.070
## BW bias (b) 64.393 64.393
## rho (h/b) 0.591 0.591
## Unique Obs. 1233 1013
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.588 0.381 -1.542 0.123 [-1.335 , 0.160]
## Robust - - -0.708 0.479 [-1.235 , 0.579]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=pol_mun_road | diff=-36.35 | p=9.034e-08 | diff_FE=12.91 | p_FE=0.2166 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: pol_mun_road | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.195 9.023 1.352 0.176 [-5.489 , 29.879]
## Robust - - 0.815 0.415 [-14.948 , 36.243]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 15.863 7.741 2.049 0.040 [0.691 , 31.034]
## Robust - - 0.677 0.498 [-16.027 , 32.941]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 17.793 7.244 2.456 0.014 [3.594 , 31.991]
## Robust - - 1.101 0.271 [-9.540 , 34.009]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1923 1264
## Eff. Number of Obs. 294 345
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 16.123 16.123
## BW bias (b) 32.362 32.362
## rho (h/b) 0.498 0.498
## Unique Obs. 1905 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 24.257 11.234 2.159 0.031 [2.240 , 46.275]
## Robust - - 1.694 0.090 [-3.855 , 53.011]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_serv_lvl | diff=0.6012 | p=0.0001856 | diff_FE=1.401 | p_FE=5.188e-07 | N_t=671 N_c=563
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=991 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 991
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 438 553
## Eff. Number of Obs. 438 553
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 438 553
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.093 0.370 2.958 0.003 [0.369 , 1.817]
## Robust - - 0.639 0.523 [-0.866 , 1.703]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=1234 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1234
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 563 671
## Eff. Number of Obs. 563 671
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 563 671
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.510 0.319 4.731 0.000 [0.884 , 2.135]
## Robust - - 1.046 0.296 [-0.471 , 1.549]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=1496 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1496
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 672 824
## Eff. Number of Obs. 672 824
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 672 824
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.759 0.288 6.115 0.000 [1.196 , 2.323]
## Robust - - 2.130 0.033 [0.075 , 1.793]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=3009 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3009
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1773 1236
## Eff. Number of Obs. 310 378
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.547 18.547
## BW bias (b) 41.762 41.762
## rho (h/b) 0.444 0.444
## Unique Obs. 1755 1221
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.606 0.504 1.204 0.229 [-0.381 , 1.594]
## Robust - - 0.587 0.557 [-0.790 , 1.467]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_emp_per1000 | diff=-0.02498 | p=0.2261 | diff_FE=0.06313 | p_FE=0.04538 | N_t=351 N_c=363
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=568 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 568
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 283 285
## Eff. Number of Obs. 283 285
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 283 285
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.039 0.043 0.900 0.368 [-0.046 , 0.124]
## Robust - - -1.283 0.200 [-0.199 , 0.042]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=714 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 714
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 363 351
## Eff. Number of Obs. 363 351
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 363 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.072 0.037 1.922 0.055 [-0.001 , 0.145]
## Robust - - -0.245 0.806 [-0.126 , 0.098]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=849 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 849
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 439 410
## Eff. Number of Obs. 439 410
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 439 410
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.087 0.034 2.528 0.011 [0.019 , 0.154]
## Robust - - 0.382 0.703 [-0.084 , 0.125]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=1709 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1709
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1097 612
## Eff. Number of Obs. 195 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.479 18.479
## BW bias (b) 38.056 38.056
## rho (h/b) 0.486 0.486
## Unique Obs. 1093 606
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.044 0.051 -0.867 0.386 [-0.144 , 0.056]
## Robust - - -1.253 0.210 [-0.191 , 0.042]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_muni_schoolpop_perc | diff=0.3971 | p=0.005979 | diff_FE=0.3041 | p_FE=0.2285 | N_t=684 N_c=609
##
## ==============================================================================================================
## Outcome: edu_muni_schoolpop_perc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=30 km | p=1 | N used=1028 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1028
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 468 560
## Eff. Number of Obs. 468 560
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 468 560
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.192 0.276 0.695 0.487 [-0.349 , 0.732]
## Robust - - 0.221 0.825 [-0.869 , 1.089]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=40 km | p=1 | N used=1293 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1293
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 609 684
## Eff. Number of Obs. 609 684
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 609 684
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.172 0.240 0.714 0.475 [-0.299 , 0.642]
## Robust - - 0.615 0.538 [-0.531 , 1.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=50 km | p=1 | N used=1569 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1569
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 728 841
## Eff. Number of Obs. 728 841
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 728 841
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.126 0.218 0.576 0.564 [-0.302 , 0.554]
## Robust - - 0.852 0.394 [-0.371 , 0.941]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=3161 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3161
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1903 1258
## Eff. Number of Obs. 593 665
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 38.458 38.458
## BW bias (b) 69.686 69.686
## rho (h/b) 0.552 0.552
## Unique Obs. 1886 1242
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.178 0.244 0.729 0.466 [-0.301 , 0.657]
## Robust - - 0.659 0.510 [-0.378 , 0.760]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=0.6042 | p=0.2007 | diff_FE=3.213 | p_FE=4.274e-05 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.960 0.961 3.082 0.002 [1.078 , 4.843]
## Robust - - 0.475 0.635 [-2.389 , 3.918]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.289 0.837 3.929 0.000 [1.648 , 4.930]
## Robust - - 1.462 0.144 [-0.657 , 4.516]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=1580 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1580
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 735 845
## Eff. Number of Obs. 735 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 735 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.443 0.757 4.550 0.000 [1.960 , 4.926]
## Robust - - 2.329 0.020 [0.423 , 4.923]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=3183 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3183
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1919 1264
## Eff. Number of Obs. 457 533
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 28.363 28.363
## BW bias (b) 50.544 50.544
## rho (h/b) 0.561 0.561
## Unique Obs. 1901 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.357 0.991 2.378 0.017 [0.414 , 4.300]
## Robust - - 1.634 0.102 [-0.391 , 4.308]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_prvt_schoolpop_perc | diff=4.586 | p=1.055e-19 | diff_FE=6.364 | p_FE=1.197e-13 | N_t=684 N_c=615
##
## ==============================================================================================================
## Outcome: edu_prvt_schoolpop_perc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=30 km | p=1 | N used=1033 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1033
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 560
## Eff. Number of Obs. 473 560
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 560
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.462 1.096 4.985 0.000 [3.315 , 7.610]
## Robust - - 2.554 0.011 [1.149 , 8.733]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=40 km | p=1 | N used=1299 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1299
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 684
## Eff. Number of Obs. 615 684
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 684
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.225 0.942 5.547 0.000 [3.378 , 7.071]
## Robust - - 3.475 0.001 [2.333 , 8.368]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=50 km | p=1 | N used=1575 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1575
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 734 841
## Eff. Number of Obs. 734 841
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 734 841
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.017 0.847 5.923 0.000 [3.357 , 6.678]
## Robust - - 4.222 0.000 [2.948 , 8.056]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=3144 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3144
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1892 1252
## Eff. Number of Obs. 392 446
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 23.001 23.001
## BW bias (b) 40.059 40.059
## rho (h/b) 0.574 0.574
## Unique Obs. 1874 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.703 1.291 4.418 0.000 [3.173 , 8.233]
## Robust - - 3.625 0.000 [2.674 , 8.969]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_meal_serv_pop_perc | diff=5.224 | p=2.618e-08 | diff_FE=11.05 | p_FE=3.804e-12 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: edu_meal_serv_pop_perc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 11.058 2.106 5.252 0.000 [6.931 , 15.185]
## Robust - - 1.627 0.104 [-1.302 , 14.006]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.087 1.795 6.734 0.000 [8.569 , 15.606]
## Robust - - 2.892 0.004 [2.817 , 14.659]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=50 km | p=1 | N used=1580 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1580
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 735 845
## Eff. Number of Obs. 735 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 735 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.803 1.615 7.929 0.000 [9.638 , 15.967]
## Robust - - 4.006 0.000 [5.187 , 15.125]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | AUTO bandwidth (default) | p=1 | N used=3183 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3183
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1919 1264
## Eff. Number of Obs. 405 472
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.615 24.615
## BW bias (b) 48.570 48.570
## rho (h/b) 0.507 0.507
## Unique Obs. 1901 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 10.073 2.400 4.198 0.000 [5.370 , 14.776]
## Robust - - 3.269 0.001 [3.701 , 14.785]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_sum_camp_pop_perc | diff=-1.109 | p=0.2762 | diff_FE=2.09 | p_FE=0.2299 | N_t=659 N_c=576
##
## ==============================================================================================================
## Outcome: edu_sum_camp_pop_perc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=30 km | p=1 | N used=986 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 986
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 447 539
## Eff. Number of Obs. 447 539
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 447 539
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.992 2.452 1.628 0.104 [-0.814 , 8.799]
## Robust - - -0.118 0.906 [-9.219 , 8.172]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=40 km | p=1 | N used=1235 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1235
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 576 659
## Eff. Number of Obs. 576 659
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 576 659
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.832 2.047 2.360 0.018 [0.820 , 8.845]
## Robust - - 0.455 0.649 [-5.276 , 8.466]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=50 km | p=1 | N used=1497 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1497
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 686 811
## Eff. Number of Obs. 686 811
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 686 811
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.270 1.795 2.936 0.003 [1.752 , 8.788]
## Robust - - 0.970 0.332 [-2.927 , 8.665]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | AUTO bandwidth (default) | p=1 | N used=2955 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 2955
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1758 1197
## Eff. Number of Obs. 502 589
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 34.002 34.002
## BW bias (b) 58.385 58.385
## rho (h/b) 0.582 0.582
## Unique Obs. 1740 1185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.462 2.252 1.981 0.048 [0.048 , 8.876]
## Robust - - 1.439 0.150 [-1.439 , 9.387]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=5.064 | p=3.765e-15 | diff_FE=6.721 | p_FE=8.361e-10 | N_t=680 N_c=612
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=1028 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1028
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 470 558
## Eff. Number of Obs. 470 558
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 470 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.519 1.451 4.492 0.000 [3.674 , 9.363]
## Robust - - 2.084 0.037 [0.338 , 11.030]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=1292 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1292
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 612 680
## Eff. Number of Obs. 612 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 612 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.674 1.267 5.268 0.000 [4.190 , 9.157]
## Robust - - 2.954 0.003 [2.079 , 10.274]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=1568 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1568
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 732 836
## Eff. Number of Obs. 732 836
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 732 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.812 1.159 5.878 0.000 [4.540 , 9.083]
## Robust - - 3.792 0.000 [3.157 , 9.909]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=3151 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3151
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1899 1252
## Eff. Number of Obs. 521 598
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 33.227 33.227
## BW bias (b) 55.455 55.455
## rho (h/b) 0.599 0.599
## Unique Obs. 1881 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.465 1.366 4.731 0.000 [3.787 , 9.143]
## Robust - - 3.949 0.000 [3.277 , 9.737]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=PublS_lightpoint | diff=-73.05 | p=5.641e-13 | diff_FE=-20.94 | p_FE=0.2117 | N_t=680 N_c=612
##
## ==============================================================================================================
## Outcome: PublS_lightpoint | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=30 km | p=1 | N used=1028 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1028
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 470 558
## Eff. Number of Obs. 470 558
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 470 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 33.545 25.338 1.324 0.186 [-16.116 , 83.206]
## Robust - - 1.119 0.263 [-37.502 , 137.398]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=40 km | p=1 | N used=1292 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1292
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 612 680
## Eff. Number of Obs. 612 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 612 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 16.532 21.377 0.773 0.439 [-25.365 , 58.430]
## Robust - - 1.331 0.183 [-22.623 , 118.437]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=50 km | p=1 | N used=1568 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1568
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 732 836
## Eff. Number of Obs. 732 836
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 732 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.374 19.019 0.125 0.901 [-34.901 , 39.650]
## Robust - - 1.438 0.151 [-15.786 , 102.655]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | AUTO bandwidth (default) | p=1 | N used=3151 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3151
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1899 1252
## Eff. Number of Obs. 398 457
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 23.843 23.843
## BW bias (b) 48.460 48.460
## rho (h/b) 0.492 0.492
## Unique Obs. 1881 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 45.064 29.786 1.513 0.130 [-13.316 , 103.444]
## Robust - - 1.649 0.099 [-10.716 , 124.382]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=0.9698 | p=0.02662 | diff_FE=2.055 | p_FE=0.004465 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.279 0.982 0.284 0.776 [-1.646 , 2.204]
## Robust - - -0.898 0.369 [-4.775 , 1.774]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.808 0.845 0.956 0.339 [-0.848 , 2.464]
## Robust - - -0.434 0.664 [-3.252 , 2.073]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.130 0.758 1.491 0.136 [-0.355 , 2.616]
## Robust - - -0.104 0.917 [-2.410 , 2.167]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2208 1264
## Eff. Number of Obs. 370 426
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 21.503 21.503
## BW bias (b) 40.083 40.083
## rho (h/b) 0.536 0.536
## Unique Obs. 2190 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.714 1.199 -0.596 0.551 [-3.064 , 1.636]
## Robust - - -0.830 0.407 [-4.050 , 1.640]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=2.891 | p=3.293e-08 | diff_FE=4.756 | p_FE=2.575e-08 | N_t=688 N_c=615
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 473 564
## Eff. Number of Obs. 473 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 473 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.577 1.138 1.387 0.166 [-0.652 , 3.807]
## Robust - - 0.168 0.866 [-3.449 , 4.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 615 688
## Eff. Number of Obs. 615 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 615 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.383 0.968 2.462 0.014 [0.486 , 4.281]
## Robust - - 0.300 0.764 [-2.617 , 3.561]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 736 845
## Eff. Number of Obs. 736 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 736 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.882 0.862 3.345 0.001 [1.194 , 4.571]
## Robust - - 0.844 0.399 [-1.513 , 3.803]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2208 1264
## Eff. Number of Obs. 398 455
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 23.405 23.405
## BW bias (b) 47.859 47.859
## rho (h/b) 0.489 0.489
## Unique Obs. 2190 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.755 1.309 0.577 0.564 [-1.811 , 3.321]
## Robust - - 0.178 0.859 [-2.703 , 3.243]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2# Export Full-Italy diff-means results at 40 km
dm_all40 <- dplyr::bind_rows(all_dm40)
if (nrow(dm_all40) > 0) {
readr::write_csv(dm_all40, dm_csv_all40)
cat("
[Full Italy diff-means] Wrote: ", dm_csv_all40, " | rows=", nrow(dm_all40), "
", sep = "")
print(dm_all40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, p_value,
diff_fe, se_fe, p_fe) %>%
head(10))
} else {
cat("
[Full Italy diff-means] No usable data within ±40 km for any outcome; skipping export.
", sep = "")
}##
## [Full Italy diff-means] Wrote: output/diffmeans_FullItaly_h40.csv | rows=27
## # A tibble: 10 × 12
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 FULL_… gb_int… NA 40 694 621 4.01e-3 1.16e-3
## 2 FULL_… gb_reg… NA 40 694 621 -4.16e-2 1.11e-2
## 3 FULL_… evasio… NA 40 688 615 -2.72e+0 4.35e-1
## 4 FULL_… servic… NA 40 688 615 1.77e-1 1.56e-1
## 5 FULL_… marr_c… NA 40 688 615 2.72e+0 3.74e+0
## 6 FULL_… marr_r… NA 40 688 615 1.83e+0 1.21e+0
## 7 FULL_… income… NA 40 688 615 1.17e+3 1.73e+2
## 8 FULL_… income NA 40 688 615 5.04e+7 5.12e+7
## 9 FULL_… Comp_S… NA 40 688 615 1.29e-1 1.58e-1
## 10 FULL_… expend… NA 40 688 615 3.37e-1 1.31e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 4 more variables: p_value <dbl>, diff_fe <dbl>, se_fe <dbl>, p_fe <dbl>sink()df_lombardia <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
# --- LIST: Lombardia control-side municipalities (distance < 0) ---
# pick name column robustly
NAMECOL <- if ("COMUNE" %in% names(df_lombardia)) "COMUNE" else stop("COMUNE column not found in df_lombardia")
lomb_control_muni <- df_lombardia %>%
mutate(X = as.numeric(.data[[RUNNING]])) %>%
filter(!is.na(.data[[KEYCOL]]), !is.na(X), !is.na(.data[[NAMECOL]])) %>%
group_by(.data[[KEYCOL]]) %>%
summarise(
COMUNE = dplyr::first(.data[[NAMECOL]]),
X_km = mean(X, na.rm = TRUE), # one distance per municipality
Treated = dplyr::first(as.integer(Treated)),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(df_lombardia)) as.integer(COD_PROV) else NA_integer_),
.groups = "drop"
) %>%
filter(X_km < 0) %>%
arrange(X_km, COMUNE)
cat("\n=== Lombardia (ireg==3): CONTROL side municipalities (X < 0) ===\n")##
## === Lombardia (ireg==3): CONTROL side municipalities (X < 0) ===cat("Count (unique comuni): ", nrow(lomb_control_muni), "\n", sep = "")## Count (unique comuni): 132cat("[Suppressed] Municipality name list omitted (Lombardia control side).
")## [Suppressed] Municipality name list omitted (Lombardia control side).# optional export
lomb_control_out <- file.path(OUTDIR, "lombardia_control_municipalities_distance_lt_0.csv")
readr::write_csv(lomb_control_muni, lomb_control_out)
cat("Wrote: ", lomb_control_out, "\n", sep = "")## Wrote: output/lombardia_control_municipalities_distance_lt_0.csvsink(results_txt_lomb, split = TRUE)
cat("Using DF: Lombardia only (ireg==3) | rows=", nrow(df_lombardia),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_lombardia), "year", NA),
"\n", sep = "")## Using DF: Lombardia only (ireg==3) | rows=2812 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x_emilia11 (KM) | manual bandwidths=30, 40, 50 | p=1 | NO regional FEpdf(plots_pdf_lomb, width = 6, height = 4.5)
# Difference-in-means accumulator (Lombardia) at h = 40 km
lomb_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lombardia))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_lombardia))) {
for (yr in YEARS) {
dY <- df_lombardia %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Lombardia)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
lomb_dm40[[length(lomb_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_noFE", outcome = yvar, year = yr)
cat("[Lombardia diff-means] h=", H_DM, " km | outcome=", yvar, " | year=", yr,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Lombardia diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | LOMBARDIA ONLY | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_noFE", year = yr, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_noFE", year = yr, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df_lombardia, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Lombardia)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
lomb_dm40[[length(lomb_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_noFE", outcome = yvar, year = NA_integer_)
cat("[Lombardia diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Lombardia diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | LOMBARDIA ONLY | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_noFE", year = NA_integer_, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_noFE", year = NA_integer_, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}## [Lombardia diff-means] h=40 km | outcome=gb_intensity | diff=-0.01208 | p=2.724e-07 | N_t=694 N_c=132
##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=699 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 699
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 568
## Eff. Number of Obs. 131 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.008 0.004 -2.011 0.044 [-0.015 , -0.000]
## Robust - - 0.792 0.429 [-0.008 , 0.019]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=826 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 826
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 694
## Eff. Number of Obs. 132 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.010 0.004 -2.711 0.007 [-0.016 , -0.003]
## Robust - - 0.567 0.571 [-0.009 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=984 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 984
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 852
## Eff. Number of Obs. 132 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.012 0.003 -3.418 0.001 [-0.019 , -0.005]
## Robust - - 0.796 0.426 [-0.007 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=1416 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1416
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1284
## Eff. Number of Obs. 26 133
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.633 5.633
## BW bias (b) 12.285 12.285
## rho (h/b) 0.459 0.459
## Unique Obs. 129 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.049 0.012 4.234 0.000 [0.026 , 0.072]
## Robust - - 3.893 0.000 [0.028 , 0.085]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=gb_reg_rate | diff=0.06671 | p=1.486e-08 | N_t=694 N_c=132
##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=699 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 699
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 568
## Eff. Number of Obs. 131 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.066 0.025 2.693 0.007 [0.018 , 0.115]
## Robust - - 1.375 0.169 [-0.023 , 0.131]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=826 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 826
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 694
## Eff. Number of Obs. 132 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.064 0.022 2.856 0.004 [0.020 , 0.108]
## Robust - - 2.317 0.020 [0.012 , 0.149]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=984 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 984
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 852
## Eff. Number of Obs. 132 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.071 0.021 3.380 0.001 [0.030 , 0.113]
## Robust - - 2.461 0.014 [0.016 , 0.144]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=1416 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1416
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1284
## Eff. Number of Obs. 51 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.506 8.506
## BW bias (b) 17.131 17.131
## rho (h/b) 0.497 0.497
## Unique Obs. 129 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.023 0.052 0.431 0.666 [-0.080 , 0.125]
## Robust - - 0.035 0.972 [-0.128 , 0.133]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=evasione | diff=-2.741 | p=0.0003199 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.091 1.487 -0.734 0.463 [-4.006 , 1.823]
## Robust - - 0.751 0.452 [-2.892 , 6.488]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.512 1.425 -1.061 0.289 [-4.304 , 1.281]
## Robust - - -0.031 0.975 [-4.277 , 4.144]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.970 1.404 -1.403 0.161 [-4.722 , 0.782]
## Robust - - -0.511 0.609 [-5.147 , 3.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 25 128
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.479 5.479
## BW bias (b) 12.061 12.061
## rho (h/b) 0.454 0.454
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.918 5.172 1.144 0.252 [-4.218 , 16.055]
## Robust - - 1.312 0.189 [-4.061 , 20.522]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=services_level | diff=2.492 | p=2.681e-16 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.383 0.621 2.228 0.026 [0.167 , 2.600]
## Robust - - 0.966 0.334 [-1.096 , 3.225]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.469 0.570 2.578 0.010 [0.352 , 2.586]
## Robust - - 1.093 0.274 [-0.859 , 3.023]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.531 0.551 2.778 0.005 [0.451 , 2.612]
## Robust - - 1.162 0.245 [-0.767 , 3.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 160
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.827 6.827
## BW bias (b) 13.997 13.997
## rho (h/b) 0.488 0.488
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.559 2.270 1.127 0.260 [-1.890 , 7.007]
## Robust - - 0.908 0.364 [-3.083 , 8.406]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_civil | diff=9.387 | p=0.007798 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.030 5.177 -0.392 0.695 [-12.176 , 8.117]
## Robust - - -1.181 0.238 [-20.648 , 5.121]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.930 3.324 0.581 0.562 [-4.585 , 8.445]
## Robust - - -1.199 0.231 [-26.655 , 6.420]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.830 3.124 1.546 0.122 [-1.294 , 10.953]
## Robust - - -1.096 0.273 [-22.874 , 6.469]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 31 140
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.175 6.175
## BW bias (b) 10.511 10.511
## rho (h/b) 0.587 0.587
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.220 5.834 1.580 0.114 [-2.215 , 20.655]
## Robust - - 1.892 0.059 [-0.544 , 30.781]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_rel | diff=4.746 | p=0.0001261 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.522 2.395 -0.218 0.827 [-5.216 , 4.171]
## Robust - - -1.409 0.159 [-13.141 , 2.148]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.264 1.912 0.661 0.509 [-2.484 , 5.011]
## Robust - - -1.283 0.199 [-12.770 , 2.664]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.439 1.820 1.340 0.180 [-1.129 , 6.006]
## Robust - - -1.013 0.311 [-10.929 , 3.483]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 54 214
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.990 8.990
## BW bias (b) 15.465 15.465
## rho (h/b) 0.581 0.581
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -5.729 4.861 -1.179 0.239 [-15.256 , 3.798]
## Robust - - -1.196 0.232 [-19.492 , 4.715]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=incomepc | diff=2057 | p=6.337e-17 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2069.766 502.824 4.116 0.000 [1084.250 , 3055.282]
## Robust - - 0.489 0.625 [-1300.929 , 2165.776]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2242.528 463.632 4.837 0.000 [1333.826 , 3151.231]
## Robust - - 1.692 0.091 [-204.071 , 2781.606]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2264.596 446.058 5.077 0.000 [1390.338 , 3138.855]
## Robust - - 2.378 0.017 [301.705 , 3128.437]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 37 146
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.359 6.359
## BW bias (b) 14.195 14.195
## rho (h/b) 0.448 0.448
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5866.597 2668.545 2.198 0.028 [636.345 , 11096.849]
## Robust - - 2.015 0.044 [173.182 , 12591.286]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=income | diff=116200000 | p=0.01815 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: income | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-54634900.59763118994.341 -0.866 0.387[-178345856.245 , 69076055.052]
## Robust - - -2.078 0.038[-229386511.964 , -6684876.697]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional6274501.31231383630.427 0.200 0.842[-55236284.030 , 67785286.654]
## Robust - - -1.557 0.119[-360907701.698 , 41318881.510]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional49398800.15029014936.088 1.703 0.089[-7469429.597 , 106267029.896]
## Robust - - -1.439 0.150[-298748104.659 , 45773473.771]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 47 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.295 8.295
## BW bias (b) 12.415 12.415
## rho (h/b) 0.668 0.668
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-81627087.40064825227.005 -1.259 0.208[-208682197.619 , 45428022.820]
## Robust - - -1.141 0.254[-255907649.373 , 67584919.999]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Comp_Serv_lvl | diff=2.777 | p=3.49e-21 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Comp_Serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.134 0.526 4.055 0.000 [1.103 , 3.166]
## Robust - - 1.964 0.049 [0.004 , 3.397]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.365 0.494 4.791 0.000 [1.398 , 3.333]
## Robust - - 2.087 0.037 [0.102 , 3.254]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.474 0.482 5.128 0.000 [1.528 , 3.419]
## Robust - - 2.420 0.016 [0.362 , 3.443]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 11 78
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.745 3.745
## BW bias (b) 9.969 9.969
## rho (h/b) 0.376 0.376
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.671 5.167 1.098 0.272 [-4.457 , 15.799]
## Robust - - 1.424 0.154 [-2.854 , 18.033]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expend_level | diff=0.7444 | p=0.00238 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.432 0.533 0.810 0.418 [-0.613 , 1.478]
## Robust - - 0.744 0.457 [-1.114 , 2.478]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.394 0.495 0.797 0.426 [-0.575 , 1.363]
## Robust - - 0.933 0.351 [-0.834 , 2.348]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.433 0.480 0.902 0.367 [-0.507 , 1.373]
## Robust - - 0.934 0.350 [-0.800 , 2.257]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 55 220
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.483 9.483
## BW bias (b) 18.870 18.870
## rho (h/b) 0.503 0.503
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.924 1.188 0.777 0.437 [-1.405 , 3.253]
## Robust - - 0.734 0.463 [-1.850 , 4.066]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expenditure | diff=1072000 | p=0.01563 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-441090.599562715.756 -0.784 0.433[-1543993.215 , 661812.017]
## Robust - - -1.917 0.055[-1905686.366 , 21211.531]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 77434.050271158.180 0.286 0.775[-454026.216 , 608894.317]
## Robust - - -1.411 0.158[-3093908.706 , 504301.089]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional462535.560249037.393 1.857 0.063[-25568.761 , 950639.880]
## Robust - - -1.305 0.192[-2559444.722 , 513200.363]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 21 118
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.170 5.170
## BW bias (b) 9.340 9.340
## rho (h/b) 0.554 0.554
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional1079991.984717943.484 1.504 0.133[-327151.387 , 2487135.355]
## Robust - - 1.497 0.134[-466829.974 , 3485346.116]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Comp_Exp_per_cap | diff=-136 | p=4.218e-10 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Comp_Exp_per_cap | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -34.113 26.274 -1.298 0.194 [-85.609 , 17.383]
## Robust - - 1.132 0.257 [-35.376 , 132.176]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -38.078 26.691 -1.427 0.154 [-90.390 , 14.235]
## Robust - - 0.195 0.845 [-69.017 , 84.295]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -40.559 27.211 -1.491 0.136 [-93.892 , 12.773]
## Robust - - -0.188 0.851 [-85.002 , 70.108]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 37 149
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.453 6.453
## BW bias (b) 13.344 13.344
## rho (h/b) 0.484 0.484
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -73.537 41.593 -1.768 0.077 [-155.057 , 7.983]
## Robust - - -1.143 0.253 [-186.329 , 49.079]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1416 | p=0.0586 | N_t=226 N_c=48
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=234 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 234
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 186
## Eff. Number of Obs. 48 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.056 0.102 0.550 0.583 [-0.144 , 0.255]
## Robust - - 0.614 0.539 [-0.163 , 0.312]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=274 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 274
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 226
## Eff. Number of Obs. 48 226
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 226
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.102 0.075 1.359 0.174 [-0.045 , 0.250]
## Robust - - -0.347 0.729 [-0.352 , 0.246]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=308 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 308
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 260
## Eff. Number of Obs. 48 260
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 260
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.138 0.068 2.025 0.043 [0.004 , 0.271]
## Robust - - -0.474 0.635 [-0.384 , 0.234]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=395 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 395
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 347
## Eff. Number of Obs. 17 38
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.701 6.701
## BW bias (b) 12.013 12.013
## rho (h/b) 0.558 0.558
## Unique Obs. 48 346
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.126 0.192 0.655 0.512 [-0.250 , 0.502]
## Robust - - 0.678 0.498 [-0.325 , 0.667]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Admin_Emp_CivReg | diff=-0.0189 | p=0.8301 | N_t=230 N_c=40
##
## ==============================================================================================================
## Outcome: Admin_Emp_CivReg | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=30 km | p=1 | N used=241 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 241
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 201
## Eff. Number of Obs. 40 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 201
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.031 0.195 -0.158 0.874 [-0.413 , 0.351]
## Robust - - 0.472 0.637 [-0.407 , 0.666]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=40 km | p=1 | N used=270 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 270
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 230
## Eff. Number of Obs. 40 230
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 230
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.041 0.189 -0.216 0.829 [-0.410 , 0.329]
## Robust - - 0.368 0.713 [-0.392 , 0.573]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=50 km | p=1 | N used=307 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 307
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 267
## Eff. Number of Obs. 40 267
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 267
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.044 0.186 -0.236 0.814 [-0.408 , 0.321]
## Robust - - 0.371 0.711 [-0.383 , 0.562]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | AUTO bandwidth (default) | p=1 | N used=385 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 385
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 345
## Eff. Number of Obs. 4 26
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.443 4.443
## BW bias (b) 11.826 11.826
## rho (h/b) 0.376 0.376
## Unique Obs. 40 343
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.746 1.687 1.035 0.301 [-1.560 , 5.053]
## Robust - - 0.986 0.324 [-1.749 , 5.292]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=pol_serv_lvl | diff=-0.1478 | p=0.6845 | N_t=567 N_c=83
##
## ==============================================================================================================
## Outcome: pol_serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=30 km | p=1 | N used=544 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 544
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 82 462
## Eff. Number of Obs. 82 462
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 82 462
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.821 0.773 -1.063 0.288 [-2.336 , 0.694]
## Robust - - -0.105 0.916 [-3.013 , 2.706]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=40 km | p=1 | N used=650 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 650
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 567
## Eff. Number of Obs. 83 567
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 83 567
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.817 0.712 -1.148 0.251 [-2.213 , 0.578]
## Robust - - -0.274 0.784 [-2.887 , 2.179]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=50 km | p=1 | N used=782 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 782
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 699
## Eff. Number of Obs. 83 699
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 83 699
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.800 0.695 -1.152 0.250 [-2.163 , 0.562]
## Robust - - -0.206 0.837 [-2.708 , 2.193]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | AUTO bandwidth (default) | p=1 | N used=1109 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1109
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 1026
## Eff. Number of Obs. 41 175
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.180 9.180
## BW bias (b) 18.385 18.385
## rho (h/b) 0.499 0.499
## Unique Obs. 80 1013
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.440 2.076 0.212 0.832 [-3.628 , 4.508]
## Robust - - 0.317 0.751 [-4.291 , 5.950]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=pol_mun_road | diff=12.91 | p=0.02747 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.302 13.873 -0.310 0.756 [-31.492 , 22.887]
## Robust - - -1.835 0.067 [-90.842 , 3.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.025 12.200 0.494 0.621 [-17.887 , 29.937]
## Robust - - -1.711 0.087 [-81.147 , 5.502]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 11.460 11.751 0.975 0.329 [-11.572 , 34.493]
## Robust - - -1.481 0.139 [-72.617 , 10.105]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 45 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.953 7.953
## BW bias (b) 12.130 12.130
## rho (h/b) 0.656 0.656
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -43.609 29.314 -1.488 0.137 [-101.064 , 13.846]
## Robust - - -1.502 0.133 [-126.689 , 16.744]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_serv_lvl | diff=1.401 | p=1.978e-07 | N_t=671 N_c=120
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=672 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 672
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 553
## Eff. Number of Obs. 119 553
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 553
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.746 0.513 1.454 0.146 [-0.260 , 1.752]
## Robust - - 0.031 0.976 [-1.717 , 1.772]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=791 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 791
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 671
## Eff. Number of Obs. 120 671
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 671
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.049 0.476 2.203 0.028 [0.116 , 1.982]
## Robust - - 0.147 0.883 [-1.424 , 1.655]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=944 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 944
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 824
## Eff. Number of Obs. 120 824
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 824
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.211 0.461 2.625 0.009 [0.307 , 2.115]
## Robust - - 0.548 0.584 [-1.062 , 1.886]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=1356 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1356
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 1236
## Eff. Number of Obs. 42 192
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.354 8.354
## BW bias (b) 16.699 16.699
## rho (h/b) 0.500 0.500
## Unique Obs. 117 1221
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.927 1.348 0.688 0.492 [-1.715 , 3.570]
## Robust - - 0.669 0.504 [-2.192 , 4.463]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_emp_per1000 | diff=0.06313 | p=0.0003043 | N_t=351 N_c=80
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=365 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 365
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 285
## Eff. Number of Obs. 80 285
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 285
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.009 0.053 -0.174 0.862 [-0.113 , 0.095]
## Robust - - -1.221 0.222 [-0.299 , 0.069]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=431 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 431
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 351
## Eff. Number of Obs. 80 351
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.019 0.048 0.409 0.683 [-0.074 , 0.113]
## Robust - - -1.042 0.297 [-0.254 , 0.078]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=490 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 490
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 410
## Eff. Number of Obs. 80 410
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 410
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.035 0.046 0.764 0.445 [-0.055 , 0.125]
## Robust - - -0.777 0.437 [-0.223 , 0.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=692 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 692
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 612
## Eff. Number of Obs. 32 110
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.411 9.411
## BW bias (b) 15.473 15.473
## rho (h/b) 0.608 0.608
## Unique Obs. 79 606
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.122 0.111 -1.098 0.272 [-0.340 , 0.096]
## Robust - - -1.074 0.283 [-0.435 , 0.127]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_muni_schoolpop_perc | diff=0.3041 | p=0.2012 | N_t=684 N_c=132
##
## ==============================================================================================================
## Outcome: edu_muni_schoolpop_perc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=30 km | p=1 | N used=691 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 691
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 560
## Eff. Number of Obs. 131 560
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 560
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.066 0.507 -0.130 0.897 [-1.060 , 0.928]
## Robust - - -0.568 0.570 [-2.299 , 1.265]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=40 km | p=1 | N used=816 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 816
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 684
## Eff. Number of Obs. 132 684
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 684
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.037 0.456 -0.082 0.935 [-0.932 , 0.857]
## Robust - - -0.360 0.719 [-1.824 , 1.258]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=50 km | p=1 | N used=973 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 973
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 841
## Eff. Number of Obs. 132 841
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 841
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.019 0.435 -0.043 0.966 [-0.871 , 0.833]
## Robust - - -0.263 0.793 [-1.673 , 1.278]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=1390 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1390
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1258
## Eff. Number of Obs. 44 171
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.635 7.635
## BW bias (b) 15.077 15.077
## rho (h/b) 0.506 0.506
## Unique Obs. 129 1242
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.324 1.595 -0.830 0.406 [-4.450 , 1.802]
## Robust - - -0.660 0.509 [-5.326 , 2.643]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=3.213 | p=0.0001319 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.758 1.661 2.262 0.024 [0.502 , 7.013]
## Robust - - 0.092 0.927 [-5.783 , 6.354]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.435 1.527 2.905 0.004 [1.442 , 7.427]
## Robust - - 0.673 0.501 [-3.575 , 7.314]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.722 1.482 3.187 0.001 [1.818 , 7.626]
## Robust - - 1.176 0.239 [-2.118 , 8.480]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 27 133
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.721 5.721
## BW bias (b) 12.498 12.498
## rho (h/b) 0.458 0.458
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.612 8.238 0.074 0.941 [-15.534 , 16.757]
## Robust - - -0.201 0.841 [-21.337 , 17.375]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_prvt_schoolpop_perc | diff=6.364 | p=1.23e-19 | N_t=684 N_c=132
##
## ==============================================================================================================
## Outcome: edu_prvt_schoolpop_perc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=30 km | p=1 | N used=691 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 691
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 560
## Eff. Number of Obs. 131 560
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 560
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.931 1.293 4.588 0.000 [3.397 , 8.465]
## Robust - - 2.817 0.005 [1.642 , 9.152]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=40 km | p=1 | N used=816 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 816
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 684
## Eff. Number of Obs. 132 684
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 684
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.051 1.202 5.036 0.000 [3.696 , 8.406]
## Robust - - 3.583 0.000 [2.822 , 9.637]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=50 km | p=1 | N used=973 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 973
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 841
## Eff. Number of Obs. 132 841
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 841
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.879 1.154 5.093 0.000 [3.617 , 8.142]
## Robust - - 4.245 0.000 [3.756 , 10.201]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=1384 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1384
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1252
## Eff. Number of Obs. 26 131
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.630 5.630
## BW bias (b) 11.844 11.844
## rho (h/b) 0.475 0.475
## Unique Obs. 129 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.934 4.636 2.143 0.032 [0.849 , 19.020]
## Robust - - 1.929 0.054 [-0.180 , 22.379]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_meal_serv_pop_perc | diff=11.05 | p=1.885e-14 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: edu_meal_serv_pop_perc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 10.471 2.801 3.738 0.000 [4.980 , 15.962]
## Robust - - 0.845 0.398 [-5.755 , 14.473]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.001 2.562 4.684 0.000 [6.980 , 17.022]
## Robust - - 1.442 0.149 [-2.324 , 15.281]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.525 2.461 5.090 0.000 [7.702 , 17.349]
## Robust - - 2.054 0.040 [0.401 , 17.183]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 46 188
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.049 8.049
## BW bias (b) 15.823 15.823
## rho (h/b) 0.509 0.509
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.510 8.158 0.430 0.667 [-12.479 , 19.500]
## Robust - - 0.223 0.824 [-18.063 , 22.697]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_sum_camp_pop_perc | diff=2.09 | p=0.1953 | N_t=659 N_c=120
##
## ==============================================================================================================
## Outcome: edu_sum_camp_pop_perc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=30 km | p=1 | N used=658 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 658
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 539
## Eff. Number of Obs. 119 539
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 539
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.917 3.208 1.844 0.065 [-0.371 , 12.205]
## Robust - - -0.271 0.786 [-12.206 , 9.241]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=40 km | p=1 | N used=779 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 779
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 659
## Eff. Number of Obs. 120 659
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 659
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.268 3.052 2.381 0.017 [1.286 , 13.250]
## Robust - - -0.001 0.999 [-9.941 , 9.934]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=50 km | p=1 | N used=931 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 931
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 811
## Eff. Number of Obs. 120 811
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 811
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 8.058 3.019 2.669 0.008 [2.141 , 13.975]
## Robust - - 0.081 0.935 [-9.363 , 10.172]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | AUTO bandwidth (default) | p=1 | N used=1317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1317
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 1197
## Eff. Number of Obs. 36 142
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.521 6.521
## BW bias (b) 13.517 13.517
## rho (h/b) 0.482 0.482
## Unique Obs. 117 1185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.164 12.655 0.092 0.927 [-23.639 , 25.967]
## Robust - - 0.018 0.986 [-31.208 , 31.788]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=6.721 | p=1.202e-16 | N_t=680 N_c=132
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=689 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 689
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 558
## Eff. Number of Obs. 131 558
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.257 2.606 1.633 0.102 [-0.852 , 9.365]
## Robust - - -0.127 0.899 [-9.811 , 8.621]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=812 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 812
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 680
## Eff. Number of Obs. 132 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.109 2.321 2.202 0.028 [0.561 , 9.657]
## Robust - - 0.187 0.851 [-7.343 , 8.896]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=968 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 968
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 836
## Eff. Number of Obs. 132 836
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.489 2.197 2.498 0.012 [1.182 , 9.795]
## Robust - - 0.421 0.674 [-6.044 , 9.346]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=1384 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1384
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1252
## Eff. Number of Obs. 61 252
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.787 10.787
## BW bias (b) 17.913 17.913
## rho (h/b) 0.602 0.602
## Unique Obs. 129 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.728 5.318 -0.137 0.891 [-11.151 , 9.694]
## Robust - - -0.342 0.732 [-15.433 , 10.842]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=PublS_lightpoint | diff=-20.94 | p=0.1314 | N_t=680 N_c=132
##
## ==============================================================================================================
## Outcome: PublS_lightpoint | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=30 km | p=1 | N used=689 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 689
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 558
## Eff. Number of Obs. 131 558
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 53.200 29.371 1.811 0.070 [-4.367 , 110.767]
## Robust - - 0.621 0.535 [-69.409 , 133.785]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=40 km | p=1 | N used=812 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 812
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 680
## Eff. Number of Obs. 132 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 46.017 27.269 1.687 0.092 [-7.430 , 99.464]
## Robust - - 0.969 0.333 [-46.486 , 137.325]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=50 km | p=1 | N used=968 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 968
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 836
## Eff. Number of Obs. 132 836
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 37.691 26.417 1.427 0.154 [-14.084 , 89.467]
## Robust - - 0.917 0.359 [-47.418 , 130.840]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | AUTO bandwidth (default) | p=1 | N used=1384 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1384
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1252
## Eff. Number of Obs. 42 162
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.994 6.994
## BW bias (b) 14.467 14.467
## rho (h/b) 0.483 0.483
## Unique Obs. 129 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 59.014 109.252 0.540 0.589 [-155.115 , 273.143]
## Robust - - 0.584 0.559 [-189.706 , 350.602]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=2.055 | p=0.004121 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.162 1.587 -0.102 0.919 [-3.273 , 2.949]
## Robust - - -1.272 0.203 [-8.102 , 1.724]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.402 1.483 0.271 0.786 [-2.505 , 3.309]
## Robust - - -0.950 0.342 [-6.577 , 2.281]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.629 1.441 0.437 0.662 [-2.194 , 3.453]
## Robust - - -0.729 0.466 [-5.889 , 2.697]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 167
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.137 7.137
## BW bias (b) 14.500 14.500
## rho (h/b) 0.492 0.492
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.189 4.403 -0.270 0.787 [-9.820 , 7.441]
## Robust - - -0.264 0.792 [-12.941 , 9.873]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=4.756 | p=4.897e-08 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.969 1.745 0.555 0.579 [-2.451 , 4.389]
## Robust - - -0.116 0.908 [-5.757 , 5.116]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.822 1.658 1.099 0.272 [-1.427 , 5.070]
## Robust - - -0.239 0.811 [-5.533 , 4.332]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.270 1.624 1.397 0.162 [-0.914 , 5.453]
## Robust - - -0.074 0.941 [-4.983 , 4.620]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.962 6.962
## BW bias (b) 14.101 14.101
## rho (h/b) 0.494 0.494
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.761 4.827 0.572 0.567 [-6.699 , 12.222]
## Robust - - 0.478 0.633 [-9.473 , 15.586]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2# Export Lombardia diff-means results at 40 km
dm_lomb40 <- dplyr::bind_rows(lomb_dm40)
if (nrow(dm_lomb40) > 0) {
readr::write_csv(dm_lomb40, dm_csv_lomb40)
cat("
[Lombardia diff-means] Wrote: ", dm_csv_lomb40, " | rows=", nrow(dm_lomb40), "
", sep = "")
print(dm_lomb40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, p_value) %>%
head(10))
} else {
cat("
[Lombardia diff-means] No usable data within ±40 km for any outcome; skipping export.
", sep = "")
}##
## [Lombardia diff-means] Wrote: output/diffmeans_Lombardia_h40.csv | rows=27
## # A tibble: 10 × 9
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 694 132 -1.21e-2 2.26e-3
## 2 LOMBA… gb_reg… NA 40 694 132 6.67e-2 1.15e-2
## 3 LOMBA… evasio… NA 40 688 132 -2.74e+0 7.46e-1
## 4 LOMBA… servic… NA 40 688 132 2.49e+0 2.74e-1
## 5 LOMBA… marr_c… NA 40 688 132 9.39e+0 3.52e+0
## 6 LOMBA… marr_r… NA 40 688 132 4.75e+0 1.23e+0
## 7 LOMBA… income… NA 40 688 132 2.06e+3 2.31e+2
## 8 LOMBA… income NA 40 688 132 1.16e+8 4.91e+7
## 9 LOMBA… Comp_S… NA 40 688 132 2.78e+0 2.57e-1
## 10 LOMBA… expend… NA 40 688 132 7.44e-1 2.41e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()# Columns (adjust only if your file differs)
COL_NAME <- "COMUNE"
COL_TREATED <- "Treated"
COL_BORDER <- "treated_border_municipality"
# Numerical tolerance to avoid boundary issues (meters)
EPS_M <- 1
guess_col <- function(df, candidates, label = "column") {
hit <- candidates[candidates %in% names(df)]
if (length(hit) == 0) stop("Could not find ", label, ". Tried: ", paste(candidates, collapse = ", "))
hit[[1]]
}
# Robust name normalization: lowercase, strip accents, drop punctuation, collapse whitespace
norm_name <- function(x) {
x <- as.character(x)
x <- str_trim(x)
fixed <- suppressWarnings(iconv(x, from = "latin1", to = "UTF-8"))
x[!is.na(fixed)] <- fixed[!is.na(fixed)]
x <- tolower(x)
x <- stringi::stri_trans_general(x, "NFD; [:Nonspacing Mark:] Remove; NFC")
x <- str_replace_all(x, "[’'`]", "")
x <- str_replace_all(x, "[^a-z0-9\\s]", " ")
x <- str_replace_all(x, "\\s+", " ")
str_trim(x)
}
inside_square <- function(points_sf, square_sfc) {
as.logical(sf::st_intersects(points_sf, square_sfc, sparse = FALSE)[, 1])
}
build_square_from_bbox_utm <- function(bbox_utm, area_scale = 1.25, eps = 1, utm_epsg = 32632) {
if (!is.finite(area_scale) || area_scale <= 0) stop("area_scale must be > 0.")
xmin <- bbox_utm[["xmin"]]; xmax <- bbox_utm[["xmax"]]
ymin <- bbox_utm[["ymin"]]; ymax <- bbox_utm[["ymax"]]
dx <- xmax - xmin
dy <- ymax - ymin
side_base <- max(dx, dy)
side_inflated <- side_base * sqrt(area_scale)
cx <- (xmin + xmax) / 2
cy <- (ymin + ymax) / 2
half <- (side_inflated / 2) + eps
sq <- sf::st_polygon(list(matrix(
c(cx - half, cy - half,
cx + half, cy - half,
cx + half, cy + half,
cx - half, cy + half,
cx - half, cy - half),
ncol = 2, byrow = TRUE
)))
list(
poly = sf::st_sfc(sq, crs = utm_epsg),
meta = list(
cx = cx, cy = cy,
side_base_m = side_base,
side_expanded_m = 2 * half,
side_multiplier = sqrt(area_scale),
area_scale = area_scale
)
)
}
# 1) Filter Lombardia from in-memory df0 (post distance overwrite)
lomb0 <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
# 2) Determine coordinate column names
LATCOL_ALL <- guess_col(lomb0, c("lat", "LAT", "latitude", "Latitude"), "Lombardia latitude column")
LNGCOL_ALL <- guess_col(lomb0, c("lng", "LNG", "lon", "longitude", "Longitude"), "Lombardia longitude column")
# 3) Prep Lombardia points (WGS84)
lomb <- lomb0 %>%
mutate(
lat_num = suppressWarnings(as.numeric(.data[[LATCOL_ALL]])),
lng_num = suppressWarnings(as.numeric(.data[[LNGCOL_ALL]]))
) %>%
filter(!is.na(lat_num), !is.na(lng_num))
if (nrow(lomb) == 0) stop("Lombardia subset is empty after dropping missing coordinates.")
# Ensure border column exists (for compatibility with attached script)
if (!COL_BORDER %in% names(lomb)) lomb[[COL_BORDER]] <- 0L
# Optional hard-coding (ported from the attached script; affects only Treated_num and border flag)
APPLY_HARDCODING <- TRUE
if (isTRUE(APPLY_HARDCODING) && (COL_NAME %in% names(lomb)) && (COL_TREATED %in% names(lomb))) {
force_treated_raw <- c(
"Ceranoval", "Ceranova", "Lardirago", "Roncaro",
"Sant'Aleesio con Vialone", "Sant'Alessio con Vialone",
"Vistarino", "Cura Carpignano", "Albuzzano", "Copiano",
"Filighera", "Trivolzio", "Marcignago",
"Nosate", "Turbigo", "Vizzola Ticino", "Campione d'Italia",
"Ranco", "Sangiano", "Monvalle", "Faloppio", "Leggiuno", "Albiolo"
)
force_control_raw <- c(
"Vivegano", "Vigevano",
"Gambolò", "Gambolò",
"Borgo San Siro"
)
force_treated_border_raw <- c(
"Bereguardo", "Torre d'Isola", "Pavia", "Valle Salimbene", "Linarolo",
"Belgioioso", "Belgioso", "Belgioiso",
"Tosce de' Negri", "Torre de' Negri",
"Spessa",
"San Zenone al Po", "San Zenone Al Po",
"Zerbo"
)
force_border1_raw <- c("Vivegano", "Vigevano", "Borgo San Siro")
lomb <- lomb %>% mutate(
name_norm = norm_name(.data[[COL_NAME]]),
Treated_num = suppressWarnings(as.integer(.data[[COL_TREATED]]))
)
force_treated <- unique(norm_name(force_treated_raw))
force_control <- unique(norm_name(force_control_raw))
force_treated_border <- unique(norm_name(force_treated_border_raw))
force_border1 <- unique(norm_name(force_border1_raw))
lomb <- lomb %>%
mutate(
Treated_num = if_else(name_norm %in% force_treated, 1L, Treated_num),
Treated_num = if_else(name_norm %in% force_control, 0L, Treated_num),
Treated_num = if_else(name_norm %in% force_treated_border, 1L, Treated_num),
!!COL_BORDER := if_else(name_norm %in% force_treated_border, 1L, .data[[COL_BORDER]]),
!!COL_BORDER := if_else(name_norm %in% force_border1, 1L, .data[[COL_BORDER]])
) %>%
select(-name_norm)
}
# 4) Read the baseline square dataset to infer the footprint bbox
base0 <- readr::read_csv(BASE_SQUARE_PATH, show_col_types = FALSE)
# If baseline has the region column, enforce Lombardia-only footprint; else use all rows.
if (REGION %in% names(base0)) {
base0 <- base0 %>% filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
}
LATCOL_BASE <- guess_col(base0, c("lat", "LAT", "latitude", "Latitude"), "baseline square latitude column")
LNGCOL_BASE <- guess_col(base0, c("lng", "LNG", "lon", "longitude", "Longitude"), "baseline square longitude column")
base <- base0 %>%
mutate(
lat_num = suppressWarnings(as.numeric(.data[[LATCOL_BASE]])),
lng_num = suppressWarnings(as.numeric(.data[[LNGCOL_BASE]]))
) %>%
filter(!is.na(lat_num), !is.na(lng_num))
if (nrow(base) == 0) stop("Baseline square dataset has no valid coordinates after filtering.")
# 5) Build SF points and infer baseline square footprint in UTM
lomb_sf_wgs <- st_as_sf(lomb, coords = c("lng_num", "lat_num"), crs = 4326, remove = FALSE)
lomb_sf_utm <- st_transform(lomb_sf_wgs, UTM_EPSG)
base_sf_wgs <- st_as_sf(base, coords = c("lng_num", "lat_num"), crs = 4326, remove = FALSE)
base_sf_utm <- st_transform(base_sf_wgs, UTM_EPSG)
bbox_base <- st_bbox(base_sf_utm)
sq <- build_square_from_bbox_utm(bbox_base, area_scale = TARGET_AREA_SCALE, eps = EPS_M, utm_epsg = UTM_EPSG)
in_sq <- inside_square(lomb_sf_utm, sq$poly)
df_lomb_square <- lomb_sf_utm %>%
mutate(in_expanded_square = in_sq) %>%
filter(in_expanded_square) %>%
st_drop_geometry()
# 5b) Build full-Italy points and clip to the SAME square geometry
LATCOL_FULL <- guess_col(df0, c("lat", "LAT", "latitude", "Latitude"), "All-Italy latitude column")
LNGCOL_FULL <- guess_col(df0, c("lng", "LNG", "lon", "longitude", "Longitude"), "All-Italy longitude column")
all_pts <- df0 %>%
mutate(
lat_num = suppressWarnings(as.numeric(.data[[LATCOL_FULL]])),
lng_num = suppressWarnings(as.numeric(.data[[LNGCOL_FULL]]))
) %>%
filter(!is.na(lat_num), !is.na(lng_num))
if (nrow(all_pts) == 0) stop("All-Italy sample is empty after dropping missing coordinates.")
all_sf_wgs <- st_as_sf(all_pts, coords = c("lng_num", "lat_num"), crs = 4326, remove = FALSE)
all_sf_utm <- st_transform(all_sf_wgs, UTM_EPSG)
in_sq_all <- inside_square(all_sf_utm, sq$poly)
df_all_square <- all_sf_utm %>%
mutate(in_expanded_square = in_sq_all) %>%
filter(in_expanded_square) %>%
st_drop_geometry()
# --- LIST: Lombardia-square control-side municipalities (distance < 0) ---
NAMECOL_SQ <- if ("COMUNE" %in% names(df_lomb_square)) "COMUNE" else stop("COMUNE column not found in df_lomb_square")
sq_control_muni <- df_lomb_square %>%
mutate(X = as.numeric(.data[[RUNNING]])) %>%
filter(!is.na(.data[[KEYCOL]]), !is.na(X), !is.na(.data[[NAMECOL_SQ]])) %>%
group_by(.data[[KEYCOL]]) %>%
summarise(
COMUNE = dplyr::first(.data[[NAMECOL_SQ]]),
X_km = mean(X, na.rm = TRUE),
Treated = dplyr::first(as.integer(Treated)),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(df_lomb_square)) as.integer(COD_PROV) else NA_integer_),
.groups = "drop"
) %>%
filter(X_km < 0) %>%
arrange(X_km, COMUNE)
cat("\n=== Lombardia SQUARE: CONTROL side municipalities (X < 0) ===\n")##
## === Lombardia SQUARE: CONTROL side municipalities (X < 0) ===cat("Count (unique comuni): ", nrow(sq_control_muni), "\n", sep = "")## Count (unique comuni): 132cat("[Suppressed] Municipality name list omitted (Lombardia square control side).
")## [Suppressed] Municipality name list omitted (Lombardia square control side).# optional export
sq_control_out <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_control_municipalities_distance_lt_0.csv", TARGET_AREA_SCALE))
readr::write_csv(sq_control_muni, sq_control_out)
cat("Wrote: ", sq_control_out, "\n", sep = "")## Wrote: output/lombardia_square_area_x1.25_control_municipalities_distance_lt_0.csv# 6) Write square dataset + metadata
square_out_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f.csv", TARGET_AREA_SCALE))
square_meta_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_metadata.csv", TARGET_AREA_SCALE))
square_all_out_file <- file.path(OUTDIR, sprintf("allitaly_square_area_x%0.2f.csv", TARGET_AREA_SCALE))
square_all_meta_file <- file.path(OUTDIR, sprintf("allitaly_square_area_x%0.2f_metadata.csv", TARGET_AREA_SCALE))
readr::write_csv(df_lomb_square, square_out_file)
readr::write_csv(df_all_square, square_all_out_file)
meta <- tibble::tibble(
baseline_n = nrow(base),
expanded_n = nrow(df_lomb_square),
target_area_scale = TARGET_AREA_SCALE,
side_multiplier = sq$meta$side_multiplier,
side_base_m = sq$meta$side_base_m,
side_expanded_m = sq$meta$side_expanded_m
)
readr::write_csv(meta, square_meta_file)
meta_all <- tibble::tibble(
baseline_n = nrow(base),
expanded_n = nrow(df_all_square),
target_area_scale = TARGET_AREA_SCALE,
side_multiplier = sq$meta$side_multiplier,
side_base_m = sq$meta$side_base_m,
side_expanded_m = sq$meta$side_expanded_m
)
readr::write_csv(meta_all, square_all_meta_file)
cat("\n=== Lombardia square constructed ===\n")##
## === Lombardia square constructed ===cat("Square dataset: ", square_out_file, "\n", sep = "")## Square dataset: output/lombardia_square_area_x1.25.csvcat("Square metadata: ", square_meta_file, "\n", sep = "")## Square metadata: output/lombardia_square_area_x1.25_metadata.csvprint(meta)## # A tibble: 1 × 6
## baseline_n expanded_n target_area_scale side_multiplier side_base_m
## <int> <int> <dbl> <dbl> <dbl>
## 1 546 658 1.25 1.12 83583.
## # ℹ 1 more variable: side_expanded_m <dbl>cat("\n=== All-Italy square constructed (same geometry) ===\n")##
## === All-Italy square constructed (same geometry) ===cat("Square dataset: ", square_all_out_file, "\n", sep = "")## Square dataset: output/allitaly_square_area_x1.25.csvcat("Square metadata: ", square_all_meta_file, "\n", sep = "")## Square metadata: output/allitaly_square_area_x1.25_metadata.csvprint(meta_all)## # A tibble: 1 × 6
## baseline_n expanded_n target_area_scale side_multiplier side_base_m
## <int> <int> <dbl> <dbl> <dbl>
## 1 546 970 1.25 1.12 83583.
## # ℹ 1 more variable: side_expanded_m <dbl>sink(results_txt_sq, split = TRUE)
cat("Using DF: Lombardia square subsample | rows=", nrow(df_lomb_square),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_lomb_square), "year", NA),
"\n", sep = "")## Using DF: Lombardia square subsample | rows=658 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x_emilia11 (KM) | manual bandwidths=30, 40, 50 | p=1 | NO regional FEpdf(plots_pdf_square, width = 6, height = 4.5)
# Difference-in-means accumulator (Square sample only) at h = 40 km
sq_dm40 <- list()
# Difference-in-means accumulator (Square sample only): sign-based split (X>=0 vs X<0), no bandwidth trim
sq_sign_dm <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lomb_square))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_lomb_square))) {
for (yr in YEARS) {
dY <- df_lomb_square %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Square sample only)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
sq_dm40[[length(sq_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = yr)
}
# Difference in means by sign (X>=0 - X<0) within square (no bandwidth trim)
dm_sign <- diff_means_sign_test(d1)
if (!is.null(dm_sign)) {
sq_sign_dm[[length(sq_sign_dm) + 1]] <- dm_sign %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = yr)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | LOMBARDIA SQUARE | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia-square | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE", year = yr, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE", year = yr, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df_lomb_square, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Square sample only)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
sq_dm40[[length(sq_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = NA_integer_)
}
# Difference in means by sign (X>=0 - X<0) within square (no bandwidth trim)
dm_sign <- diff_means_sign_test(d1)
if (!is.null(dm_sign)) {
sq_sign_dm[[length(sq_sign_dm) + 1]] <- dm_sign %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = NA_integer_)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | LOMBARDIA SQUARE | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia-square | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE", year = NA_integer_, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE", year = NA_integer_, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.004 -1.523 0.128 [-0.015 , 0.002]
## Robust - - 1.983 0.047 [0.000 , 0.030]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.011 0.004 -2.786 0.005 [-0.019 , -0.003]
## Robust - - 1.673 0.094 [-0.002 , 0.025]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.013 0.004 -3.317 0.001 [-0.021 , -0.005]
## Robust - - 1.552 0.121 [-0.003 , 0.024]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 18 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.655 4.655
## BW bias (b) 10.989 10.989
## rho (h/b) 0.424 0.424
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.057 0.020 2.921 0.003 [0.019 , 0.096]
## Robust - - 2.935 0.003 [0.022 , 0.108]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.118 0.034 3.448 0.001 [0.051 , 0.186]
## Robust - - 1.748 0.080 [-0.011 , 0.189]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.121 0.032 3.816 0.000 [0.059 , 0.183]
## Robust - - 2.364 0.018 [0.019 , 0.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.124 0.031 4.014 0.000 [0.064 , 0.185]
## Robust - - 2.437 0.015 [0.022 , 0.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 20 54
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.978 4.978
## BW bias (b) 11.309 11.309
## rho (h/b) 0.440 0.440
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.047 0.123 -0.385 0.700 [-0.289 , 0.194]
## Robust - - -0.510 0.610 [-0.361 , 0.212]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.039 1.655 0.024 0.981 [-3.205 , 3.284]
## Robust - - 0.900 0.368 [-2.816 , 7.597]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.252 1.569 0.161 0.872 [-2.824 , 3.328]
## Robust - - 0.146 0.884 [-4.350 , 5.048]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.353 1.552 0.227 0.820 [-2.690 , 3.395]
## Robust - - -0.087 0.931 [-4.823 , 4.413]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 25 60
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.462 5.462
## BW bias (b) 13.223 13.223
## rho (h/b) 0.413 0.413
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.593 5.778 1.660 0.097 [-1.731 , 20.917]
## Robust - - 1.889 0.059 [-0.466 , 25.267]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.509 0.707 0.720 0.472 [-0.878 , 1.896]
## Robust - - -0.058 0.954 [-2.452 , 2.312]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.645 0.648 0.995 0.320 [-0.625 , 1.914]
## Robust - - 0.012 0.991 [-2.136 , 2.162]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.701 0.630 1.114 0.265 [-0.533 , 1.936]
## Robust - - 0.038 0.969 [-2.058 , 2.140]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 77
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.064 7.064
## BW bias (b) 14.698 14.698
## rho (h/b) 0.481 0.481
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.082 2.360 0.882 0.378 [-2.544 , 6.708]
## Robust - - 0.713 0.476 [-3.777 , 8.101]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -12.122 12.715 -0.953 0.340 [-37.042 , 12.799]
## Robust - - -0.822 0.411 [-19.008 , 7.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -6.847 8.526 -0.803 0.422 [-23.557 , 9.864]
## Robust - - -1.225 0.221 [-49.635 , 11.460]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.487 6.742 -0.666 0.506 [-17.701 , 8.727]
## Robust - - -1.189 0.234 [-58.228 , 14.245]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 19 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.771 4.771
## BW bias (b) 9.318 9.318
## rho (h/b) 0.512 0.512
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 43.780 20.696 2.115 0.034 [3.217 , 84.343]
## Robust - - 2.021 0.043 [1.551 , 100.351]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.260 4.308 -0.989 0.323 [-12.703 , 4.183]
## Robust - - -1.286 0.199 [-12.867 , 2.673]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.183 3.104 -0.703 0.482 [-8.267 , 3.901]
## Robust - - -1.494 0.135 [-19.488 , 2.630]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.327 2.626 -0.505 0.613 [-6.473 , 3.820]
## Robust - - -1.406 0.160 [-21.430 , 3.525]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 76
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.938 6.938
## BW bias (b) 11.750 11.750
## rho (h/b) 0.590 0.590
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -6.662 4.999 -1.333 0.183 [-16.460 , 3.136]
## Robust - - -1.190 0.234 [-21.358 , 5.219]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2611.088 616.338 4.236 0.000 [1403.087 , 3819.088]
## Robust - - 1.256 0.209 [-809.458 , 3694.875]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2906.803 564.059 5.153 0.000 [1801.268 , 4012.339]
## Robust - - 1.706 0.088 [-245.731 , 3541.413]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3012.067 550.454 5.472 0.000 [1933.197 , 4090.936]
## Robust - - 1.913 0.056 [-43.239 , 3579.641]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 55 96
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.348 9.348
## BW bias (b) 19.922 19.922
## rho (h/b) 0.469 0.469
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2955.607 1813.800 1.630 0.103 [-599.377 , 6510.591]
## Robust - - 1.410 0.158 [-1243.473 , 7624.355]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: income | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-203086417.400178913009.220 -1.135 0.256[-553749471.837 , 147576637.038]
## Robust - - -1.736 0.083[-207615414.107 , 12571791.460]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-118185955.185116520885.608 -1.014 0.310[-346562694.423 , 110190784.053]
## Robust - - -1.429 0.153[-726696123.362 , 113801001.714]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-81323204.54189117008.244 -0.913 0.361[-255989331.108 , 93342922.027]
## Robust - - -1.346 0.178[-856989877.868 , 159120640.815]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 17 51
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.481 4.481
## BW bias (b) 8.919 8.919
## rho (h/b) 0.502 0.502
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional303656334.545199890447.930 1.519 0.129[-88121744.252 , 695434413.341]
## Robust - - 1.562 0.118[-95526124.582 , 845977760.830]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Comp_Serv_lvl | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.130 0.631 1.789 0.074 [-0.108 , 2.367]
## Robust - - 0.006 0.995 [-1.977 , 1.990]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.412 0.585 2.411 0.016 [0.264 , 2.559]
## Robust - - 0.259 0.796 [-1.597 , 2.083]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.516 0.574 2.643 0.008 [0.392 , 2.640]
## Robust - - 0.369 0.712 [-1.472 , 2.154]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 10 45
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.698 3.698
## BW bias (b) 10.590 10.590
## rho (h/b) 0.349 0.349
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.417 6.414 0.845 0.398 [-7.154 , 17.988]
## Robust - - 1.106 0.269 [-5.668 , 20.352]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.255 0.602 0.423 0.672 [-0.926 , 1.436]
## Robust - - 0.555 0.579 [-1.406 , 2.518]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.302 0.561 0.539 0.590 [-0.797 , 1.402]
## Robust - - 0.455 0.649 [-1.346 , 2.160]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.338 0.549 0.616 0.538 [-0.738 , 1.415]
## Robust - - 0.394 0.693 [-1.366 , 2.055]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 54 94
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.026 9.026
## BW bias (b) 18.572 18.572
## rho (h/b) 0.486 0.486
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.837 1.329 0.630 0.529 [-1.767 , 3.441]
## Robust - - 0.609 0.543 [-2.263 , 4.303]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1826407.3501613902.328 -1.132 0.258[-4989597.788 , 1336783.087]
## Robust - - -1.615 0.106[-1730029.922 , 166742.297]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1085395.0961049889.006 -1.034 0.301[-3143139.735 , 972349.544]
## Robust - - -1.378 0.168[-6451852.084 , 1124291.563]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-762565.683801757.625 -0.951 0.342[-2333981.753 , 808850.387]
## Robust - - -1.304 0.192[-7631610.569 , 1534500.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 10 43
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.574 3.574
## BW bias (b) 8.478 8.478
## rho (h/b) 0.422 0.422
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional415457.424446302.935 0.931 0.352[-459280.254 , 1290195.103]
## Robust - - 1.641 0.101[-230817.238 , 2607050.435]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Comp_Exp_per_cap | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -73.620 26.211 -2.809 0.005 [-124.994 , -22.247]
## Robust - - 0.157 0.875 [-76.878 , 90.240]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -69.612 26.619 -2.615 0.009 [-121.784 , -17.440]
## Robust - - -1.121 0.262 [-121.257 , 33.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -67.979 27.315 -2.489 0.013 [-121.515 , -14.443]
## Robust - - -1.396 0.163 [-134.980 , 22.695]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 26 63
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.612 5.612
## BW bias (b) 12.380 12.380
## rho (h/b) 0.453 0.453
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -46.638 60.145 -0.775 0.438 [-164.520 , 71.244]
## Robust - - -0.591 0.554 [-195.904 , 105.081]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=113 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 113
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 65
## Eff. Number of Obs. 48 65
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 65
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.135 0.079 1.718 0.086 [-0.019 , 0.289]
## Robust - - 0.322 0.747 [-0.207 , 0.288]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 48 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.155 0.078 1.982 0.047 [0.002 , 0.308]
## Robust - - 0.204 0.839 [-0.230 , 0.283]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 48 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.164 0.079 2.059 0.039 [0.008 , 0.319]
## Robust - - 0.161 0.872 [-0.238 , 0.281]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 20 17
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.795 7.795
## BW bias (b) 12.695 12.695
## rho (h/b) 0.614 0.614
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.002 0.101 -0.017 0.987 [-0.200 , 0.196]
## Robust - - -0.035 0.972 [-0.268 , 0.258]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Admin_Emp_CivReg | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=30 km | p=1 | N used=110 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 110
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 70
## Eff. Number of Obs. 40 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.026 0.229 0.113 0.910 [-0.422 , 0.474]
## Robust - - 0.345 0.730 [-0.576 , 0.822]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=40 km | p=1 | N used=114 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 114
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 74
## Eff. Number of Obs. 40 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.027 0.213 0.128 0.898 [-0.391 , 0.445]
## Robust - - 0.349 0.727 [-0.508 , 0.729]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=50 km | p=1 | N used=114 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 114
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 74
## Eff. Number of Obs. 40 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 40 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.026 0.208 0.127 0.899 [-0.382 , 0.435]
## Robust - - 0.377 0.706 [-0.481 , 0.710]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | AUTO bandwidth (default) | p=1 | N used=114 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 114
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 40 74
## Eff. Number of Obs. 6 9
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.046 5.046
## BW bias (b) 12.445 12.445
## rho (h/b) 0.405 0.405
## Unique Obs. 40 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.300 1.060 0.283 0.777 [-1.777 , 2.378]
## Robust - - 0.207 0.836 [-2.130 , 2.633]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: pol_serv_lvl | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=30 km | p=1 | N used=245 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 245
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 82 163
## Eff. Number of Obs. 82 163
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 82 163
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.088 0.845 -1.287 0.198 [-2.745 , 0.569]
## Robust - - -1.033 0.302 [-4.620 , 1.431]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=40 km | p=1 | N used=255 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 255
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 172
## Eff. Number of Obs. 83 172
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 83 172
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.961 0.780 -1.233 0.217 [-2.489 , 0.566]
## Robust - - -0.922 0.357 [-3.963 , 1.427]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=50 km | p=1 | N used=255 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 255
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 172
## Eff. Number of Obs. 83 172
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 83 172
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.936 0.764 -1.226 0.220 [-2.433 , 0.561]
## Robust - - -0.813 0.416 [-3.719 , 1.537]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | AUTO bandwidth (default) | p=1 | N used=255 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 255
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 83 172
## Eff. Number of Obs. 41 84
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.116 9.116
## BW bias (b) 18.140 18.140
## rho (h/b) 0.503 0.503
## Unique Obs. 80 165
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.484 2.159 -0.224 0.823 [-4.717 , 3.748]
## Robust - - -0.079 0.937 [-5.576 , 5.142]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -27.026 18.635 -1.450 0.147 [-63.549 , 9.497]
## Robust - - -2.125 0.034 [-98.065 , -3.952]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -15.200 14.835 -1.025 0.306 [-44.276 , 13.877]
## Robust - - -2.319 0.020 [-112.217 , -9.426]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -10.745 13.457 -0.799 0.425 [-37.120 , 15.629]
## Robust - - -2.198 0.028 [-115.957 , -6.646]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 15 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.108 4.108
## BW bias (b) 8.933 8.933
## rho (h/b) 0.460 0.460
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 209.952 136.695 1.536 0.125 [-57.965 , 477.869]
## Robust - - 1.633 0.102 [-50.313 , 553.350]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=303 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 184
## Eff. Number of Obs. 119 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 184
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.730 0.599 2.890 0.004 [0.557 , 2.904]
## Robust - - 0.809 0.419 [-1.186 , 2.853]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 120 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.093 0.553 3.786 0.000 [1.009 , 3.176]
## Robust - - 0.875 0.382 [-0.991 , 2.590]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 120 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.229 0.541 4.119 0.000 [1.169 , 3.290]
## Robust - - 0.953 0.340 [-0.894 , 2.589]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 40 83
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.901 7.901
## BW bias (b) 16.151 16.151
## rho (h/b) 0.489 0.489
## Unique Obs. 117 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.364 1.668 1.417 0.156 [-0.906 , 5.634]
## Robust - - 1.160 0.246 [-1.685 , 6.574]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=169 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 169
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 89
## Eff. Number of Obs. 80 89
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 89
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.016 0.064 -0.243 0.808 [-0.141 , 0.110]
## Robust - - -1.176 0.239 [-0.323 , 0.081]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 80 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.010 0.058 0.178 0.859 [-0.104 , 0.124]
## Robust - - -1.157 0.247 [-0.298 , 0.077]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 80 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.021 0.056 0.376 0.707 [-0.089 , 0.131]
## Robust - - -1.133 0.257 [-0.291 , 0.078]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 24 35
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.093 7.093
## BW bias (b) 12.686 12.686
## rho (h/b) 0.559 0.559
## Unique Obs. 79 91
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.126 0.129 -0.975 0.330 [-0.380 , 0.127]
## Robust - - -0.778 0.437 [-0.480 , 0.207]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_muni_schoolpop_perc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=30 km | p=1 | N used=313 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 313
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 182
## Eff. Number of Obs. 131 182
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 182
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.222 0.657 0.337 0.736 [-1.066 , 1.510]
## Robust - - -0.032 0.974 [-2.211 , 2.140]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=40 km | p=1 | N used=325 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 325
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 193
## Eff. Number of Obs. 132 193
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 193
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.235 0.599 0.393 0.694 [-0.938 , 1.408]
## Robust - - 0.065 0.948 [-1.849 , 1.975]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=50 km | p=1 | N used=325 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 325
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 193
## Eff. Number of Obs. 132 193
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 193
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.251 0.579 0.433 0.665 [-0.883 , 1.385]
## Robust - - 0.079 0.937 [-1.777 , 1.926]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=325 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 325
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 193
## Eff. Number of Obs. 44 76
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.422 7.422
## BW bias (b) 14.188 14.188
## rho (h/b) 0.523 0.523
## Unique Obs. 129 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.811 1.771 -0.458 0.647 [-4.283 , 2.661]
## Robust - - -0.395 0.693 [-5.462 , 3.631]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.588 1.820 1.422 0.155 [-0.978 , 6.154]
## Robust - - -0.427 0.669 [-7.964 , 5.114]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.352 1.679 1.997 0.046 [0.062 , 6.642]
## Robust - - -0.041 0.967 [-5.965 , 5.720]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.660 1.643 2.227 0.026 [0.439 , 6.880]
## Robust - - 0.107 0.914 [-5.389 , 6.014]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 38 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.579 6.579
## BW bias (b) 13.954 13.954
## rho (h/b) 0.471 0.471
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.159 6.805 0.023 0.981 [-13.179 , 13.498]
## Robust - - -0.185 0.853 [-18.203 , 15.062]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_prvt_schoolpop_perc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=30 km | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 184
## Eff. Number of Obs. 131 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 184
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.834 1.350 2.099 0.036 [0.188 , 5.480]
## Robust - - 0.974 0.330 [-1.842 , 5.482]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=40 km | p=1 | N used=327 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 327
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 195
## Eff. Number of Obs. 132 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.268 1.279 2.556 0.011 [0.762 , 5.774]
## Robust - - 1.141 0.254 [-1.481 , 5.609]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=50 km | p=1 | N used=327 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 327
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 195
## Eff. Number of Obs. 132 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.384 1.265 2.675 0.007 [0.905 , 5.863]
## Robust - - 1.299 0.194 [-1.197 , 5.899]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=327 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 327
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 195
## Eff. Number of Obs. 19 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.785 4.785
## BW bias (b) 11.308 11.308
## rho (h/b) 0.423 0.423
## Unique Obs. 129 187
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.244 4.073 0.060 0.952 [-7.740 , 8.228]
## Robust - - -0.060 0.952 [-9.513 , 8.947]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_meal_serv_pop_perc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 14.552 3.456 4.211 0.000 [7.779 , 21.326]
## Robust - - 0.968 0.333 [-6.044 , 17.846]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 16.704 3.157 5.291 0.000 [10.516 , 22.892]
## Robust - - 1.455 0.146 [-2.703 , 18.284]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 17.507 3.070 5.703 0.000 [11.490 , 23.524]
## Robust - - 1.667 0.095 [-1.515 , 18.770]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 54 91
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.735 8.735
## BW bias (b) 17.451 17.451
## rho (h/b) 0.501 0.501
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.025 8.807 0.571 0.568 [-12.237 , 22.287]
## Robust - - 0.286 0.775 [-18.473 , 24.788]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_sum_camp_pop_perc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=30 km | p=1 | N used=299 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 299
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 180
## Eff. Number of Obs. 119 180
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 180
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.947 3.724 1.866 0.062 [-0.352 , 14.247]
## Robust - - 0.034 0.973 [-11.926 , 12.343]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=40 km | p=1 | N used=311 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 311
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 191
## Eff. Number of Obs. 120 191
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 191
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 8.700 3.513 2.477 0.013 [1.816 , 15.585]
## Robust - - 0.073 0.942 [-10.799 , 11.637]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=50 km | p=1 | N used=311 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 311
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 191
## Eff. Number of Obs. 120 191
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 191
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.407 3.490 2.696 0.007 [2.567 , 16.247]
## Robust - - 0.094 0.925 [-10.614 , 11.678]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | AUTO bandwidth (default) | p=1 | N used=311 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 311
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 191
## Eff. Number of Obs. 41 71
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.759 6.759
## BW bias (b) 14.434 14.434
## rho (h/b) 0.468 0.468
## Unique Obs. 117 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.826 12.535 0.784 0.433 [-14.742 , 34.393]
## Robust - - 0.720 0.471 [-19.651 , 42.493]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=316 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 185
## Eff. Number of Obs. 131 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.602 3.253 2.030 0.042 [0.227 , 12.977]
## Robust - - 0.617 0.537 [-7.564 , 14.513]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.318 2.915 2.510 0.012 [1.605 , 13.032]
## Robust - - 0.743 0.457 [-6.127 , 13.611]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.567 2.812 2.691 0.007 [2.057 , 13.078]
## Robust - - 0.798 0.425 [-5.658 , 13.429]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 62 109
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.820 10.820
## BW bias (b) 19.866 19.866
## rho (h/b) 0.545 0.545
## Unique Obs. 129 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.782 6.323 0.598 0.550 [-8.611 , 16.174]
## Robust - - 0.429 0.668 [-12.190 , 19.018]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: PublS_lightpoint | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=30 km | p=1 | N used=316 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 185
## Eff. Number of Obs. 131 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 18.585 25.146 0.739 0.460 [-30.700 , 67.870]
## Robust - - -0.666 0.506 [-124.192 , 61.210]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=40 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 24.804 24.431 1.015 0.310 [-23.081 , 72.688]
## Robust - - -0.349 0.727 [-99.214 , 69.257]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=50 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 26.372 24.702 1.068 0.286 [-22.042 , 74.787]
## Robust - - -0.200 0.841 [-92.727 , 75.535]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | AUTO bandwidth (default) | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 42 77
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.008 7.008
## BW bias (b) 14.947 14.947
## rho (h/b) 0.469 0.469
## Unique Obs. 129 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 25.173 85.091 0.296 0.767 [-141.602 , 191.948]
## Robust - - 0.456 0.649 [-160.436 , 257.670]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.004 1.756 -0.572 0.568 [-4.446 , 2.439]
## Robust - - -1.478 0.139 [-9.568 , 1.340]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.257 1.638 -0.157 0.875 [-3.467 , 2.954]
## Robust - - -1.431 0.152 [-8.534 , 1.331]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.062 1.607 -0.039 0.969 [-3.212 , 3.088]
## Robust - - -1.279 0.201 [-8.017 , 1.685]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 46 86
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.211 8.211
## BW bias (b) 16.911 16.911
## rho (h/b) 0.486 0.486
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.349 4.100 -0.329 0.742 [-9.384 , 6.686]
## Robust - - -0.367 0.713 [-11.967 , 8.191]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.102 1.901 -0.054 0.957 [-3.828 , 3.623]
## Robust - - -0.666 0.506 [-7.984 , 3.936]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.731 1.803 0.406 0.685 [-2.803 , 4.265]
## Robust - - -0.839 0.401 [-7.733 , 3.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.047 1.783 0.587 0.557 [-2.449 , 4.542]
## Robust - - -0.857 0.392 [-7.660 , 3.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 77
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.035 7.035
## BW bias (b) 14.652 14.652
## rho (h/b) 0.480 0.480
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.334 5.062 -0.066 0.947 [-10.255 , 9.586]
## Robust - - -0.066 0.947 [-13.320 , 12.452]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2sink()
# Export square-sample difference-in-means results at 40 km
dm_sq40 <- dplyr::bind_rows(sq_dm40)
if (nrow(dm_sq40) > 0) {
readr::write_csv(dm_sq40, dm_csv_sq40)
cat("\n[Square diff-means] Wrote: ", dm_csv_sq40, " | rows=", nrow(dm_sq40), "\n", sep = "")
print(
dm_sq40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means] No usable data within ±40 km for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means] Wrote: output/diffmeans_LombardiaSquare_h40.csv | rows=27
## # A tibble: 10 × 11
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 197 132 -1.48e-2 2.49e-3
## 2 LOMBA… gb_reg… NA 40 197 132 1.35e-1 1.66e-2
## 3 LOMBA… evasio… NA 40 197 132 -8.45e-1 8.22e-1
## 4 LOMBA… servic… NA 40 197 132 2.38e+0 3.13e-1
## 5 LOMBA… marr_c… NA 40 197 132 2.02e+1 1.16e+1
## 6 LOMBA… marr_r… NA 40 197 132 7.70e+0 3.60e+0
## 7 LOMBA… income… NA 40 197 132 3.61e+3 3.13e+2
## 8 LOMBA… income NA 40 197 132 2.71e+8 1.67e+8
## 9 LOMBA… Comp_S… NA 40 197 132 2.88e+0 3.03e-1
## 10 LOMBA… expend… NA 40 197 132 1.01e+0 2.85e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 3 more variables: t_stat <dbl>, df <dbl>, p_value <dbl># Export square-sample sign-based difference-in-means results (X>=0 vs X<0; no bandwidth trim)
dm_sqsign <- dplyr::bind_rows(sq_sign_dm)
if (nrow(dm_sqsign) > 0) {
readr::write_csv(dm_sqsign, dm_csv_sqsign)
cat("\n[Square diff-means SIGN] Wrote: ", dm_csv_sqsign, " | rows=", nrow(dm_sqsign), "\n", sep = "")
print(
dm_sqsign %>%
dplyr::select(sample, outcome, year, n_pos, n_neg,
diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means SIGN] No usable data in square for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means SIGN] Wrote: output/diffmeans_LombardiaSquare_sign.csv | rows=27
## # A tibble: 10 × 10
## sample outcome year n_pos n_neg diff_pos_minus_neg se_diff t_stat df
## <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 LOMBARDIA_… gb_int… NA 197 132 -1.48e-2 2.49e-3 5.95 236.
## 2 LOMBARDIA_… gb_reg… NA 197 132 1.35e-1 1.66e-2 -8.14 302.
## 3 LOMBARDIA_… evasio… NA 197 132 -8.45e-1 8.22e-1 1.03 224.
## 4 LOMBARDIA_… servic… NA 197 132 2.38e+0 3.13e-1 -7.61 250.
## 5 LOMBARDIA_… marr_c… NA 197 132 2.02e+1 1.16e+1 -1.74 199.
## 6 LOMBARDIA_… marr_r… NA 197 132 7.70e+0 3.60e+0 -2.14 208.
## 7 LOMBARDIA_… income… NA 197 132 3.61e+3 3.13e+2 -11.5 325.
## 8 LOMBARDIA_… income NA 197 132 2.71e+8 1.67e+8 -1.62 197.
## 9 LOMBARDIA_… Comp_S… NA 197 132 2.88e+0 3.03e-1 -9.51 273.
## 10 LOMBARDIA_… expend… NA 197 132 1.01e+0 2.85e-1 -3.57 272.
## # ℹ 1 more variable: p_value <dbl># Run RD on the All-Italy square subsample (with regional fixed effects)
sink(results_txt_sq_all, split = TRUE)
cat("Using DF: All-Italy square subsample | rows=", nrow(df_all_square),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_all_square), "year", NA),
"\n", sep = "")## Using DF: All-Italy square subsample | rows=970 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | + regional FE\n\n", sep = "")## Running var: distance_treated_positive_x_emilia11 (KM) | manual bandwidths=30, 40, 50 | p=1 | + regional FEpdf(plots_pdf_sq_all, width = 6, height = 4.5)
# Difference-in-means accumulator (All-Italy square) at h = 40 km
sqall_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_all_square))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_all_square))) {
for (yr in YEARS) {
dY <- df_all_square %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means within |X| <= 40 km (All-Italy square):
# (i) raw Welch t-test
# (ii) OLS controlling for region FE (Y ~ Treated + region dummies)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dm_out %>% mutate(
diff_fe = dm_fe$diff_treat_minus_control_fe,
se_fe = dm_fe$se_diff_fe,
p_fe = dm_fe$p_value_fe
)
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, p_fe = NA_real_)
}
sqall_dm40[[length(sqall_dm40) + 1]] <- dm_out %>%
mutate(sample = "ALL_ITALY_SQUARE_regFE", outcome = yvar, year = yr)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | ALL-ITALY SQUARE | p=", P, " | X in KM | + REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw + region-residualized) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | All-Italy-square | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | All-Italy-square | region FE residual | h=", h, " km"))
}
# RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(
rb, outcome = yvar, h = h, sample = "ALL_ITALY_SQUARE_regFE", year = yr, h_type = "MANUAL"
)
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "ALL_ITALY_SQUARE_regFE", year = yr, h_type = "AUTO")
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | All-Italy-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | All-Italy-square | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df_all_square, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dm_out %>% mutate(
diff_fe = dm_fe$diff_treat_minus_control_fe,
se_fe = dm_fe$se_diff_fe,
p_fe = dm_fe$p_value_fe
)
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, p_fe = NA_real_)
}
sqall_dm40[[length(sqall_dm40) + 1]] <- dm_out %>%
mutate(sample = "ALL_ITALY_SQUARE_regFE", outcome = yvar, year = NA_integer_)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | ALL-ITALY SQUARE | p=", P, " | X in KM | + REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw + region-residualized) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | All-Italy-square | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | All-Italy-square | region FE residual | h=", h, " km"))
}
# RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(
rb, outcome = yvar, h = h, sample = "ALL_ITALY_SQUARE_regFE", year = NA_integer_, h_type = "MANUAL"
)
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "ALL_ITALY_SQUARE_regFE", year = NA_integer_, h_type = "AUTO")
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | All-Italy-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | All-Italy-square | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}##
## ==============================================================================================================
## Outcome: gb_intensity | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=392 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 392
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 206 186
## Eff. Number of Obs. 206 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 206 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.004 -1.695 0.090 [-0.014 , 0.001]
## Robust - - 1.766 0.077 [-0.001 , 0.024]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=440 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 440
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 243 197
## Eff. Number of Obs. 243 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 243 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.010 0.003 -2.960 0.003 [-0.017 , -0.003]
## Robust - - 0.738 0.461 [-0.007 , 0.014]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=464 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 464
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 267 197
## Eff. Number of Obs. 267 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 267 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.011 0.003 -3.481 0.001 [-0.018 , -0.005]
## Robust - - 0.189 0.850 [-0.009 , 0.011]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=486 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 486
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 289 197
## Eff. Number of Obs. 60 75
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.786 6.786
## BW bias (b) 14.035 14.035
## rho (h/b) 0.484 0.484
## Unique Obs. 282 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.025 0.010 2.564 0.010 [0.006 , 0.044]
## Robust - - 2.330 0.020 [0.005 , 0.054]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: gb_reg_rate | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=392 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 392
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 206 186
## Eff. Number of Obs. 206 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 206 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.108 0.033 3.240 0.001 [0.043 , 0.174]
## Robust - - 1.848 0.065 [-0.006 , 0.189]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=440 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 440
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 243 197
## Eff. Number of Obs. 243 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 243 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.098 0.030 3.219 0.001 [0.038 , 0.158]
## Robust - - 2.344 0.019 [0.017 , 0.191]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=464 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 464
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 267 197
## Eff. Number of Obs. 267 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 267 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.096 0.029 3.291 0.001 [0.039 , 0.154]
## Robust - - 1.933 0.053 [-0.001 , 0.166]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=486 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 486
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 289 197
## Eff. Number of Obs. 39 62
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.595 5.595
## BW bias (b) 11.912 11.912
## rho (h/b) 0.470 0.470
## Unique Obs. 282 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.070 0.103 -0.684 0.494 [-0.271 , 0.131]
## Robust - - -0.974 0.330 [-0.380 , 0.128]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: evasione | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.167 1.344 0.124 0.901 [-2.468 , 2.802]
## Robust - - 1.343 0.179 [-1.380 , 7.390]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.979 1.214 0.807 0.420 [-1.399 , 3.358]
## Robust - - 0.028 0.978 [-3.619 , 3.723]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.466 1.147 1.278 0.201 [-0.783 , 3.714]
## Robust - - 0.226 0.822 [-3.050 , 3.843]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 39 63
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.613 5.613
## BW bias (b) 13.051 13.051
## rho (h/b) 0.430 0.430
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 8.560 4.941 1.732 0.083 [-1.124 , 18.245]
## Robust - - 1.909 0.056 [-0.292 , 22.340]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: services_level | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.662 0.583 1.135 0.256 [-0.481 , 1.804]
## Robust - - 0.259 0.796 [-1.707 , 2.227]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.480 0.511 0.939 0.348 [-0.522 , 1.481]
## Robust - - 0.867 0.386 [-0.900 , 2.329]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.344 0.478 0.721 0.471 [-0.592 , 1.281]
## Robust - - 0.789 0.430 [-0.876 , 2.056]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 100 118
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 12.448 12.448
## BW bias (b) 25.354 25.354
## rho (h/b) 0.491 0.491
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.092 1.082 -0.085 0.932 [-2.212 , 2.028]
## Robust - - -0.274 0.784 [-2.972 , 2.242]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_civil | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -13.444 12.596 -1.067 0.286 [-38.132 , 11.243]
## Robust - - -0.626 0.531 [-15.780 , 8.139]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -8.105 8.352 -0.970 0.332 [-24.475 , 8.265]
## Robust - - -1.195 0.232 [-47.783 , 11.594]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -5.417 6.506 -0.833 0.405 [-18.168 , 7.335]
## Robust - - -1.148 0.251 [-56.132 , 14.666]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 31 56
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.191 5.191
## BW bias (b) 10.958 10.958
## rho (h/b) 0.474 0.474
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 23.504 10.256 2.292 0.022 [3.403 , 43.605]
## Robust - - 1.611 0.107 [-4.448 , 45.582]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_rel | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.965 4.121 -1.205 0.228 [-13.041 , 3.111]
## Robust - - -1.265 0.206 [-10.406 , 2.242]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.947 2.858 -1.031 0.302 [-8.549 , 2.654]
## Robust - - -1.516 0.130 [-17.576 , 2.247]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.972 2.317 -0.851 0.395 [-6.513 , 2.569]
## Robust - - -1.400 0.162 [-19.476 , 3.246]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 40 63
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.657 5.657
## BW bias (b) 11.624 11.624
## rho (h/b) 0.487 0.487
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.583 3.776 -0.419 0.675 [-8.984 , 5.817]
## Robust - - -0.946 0.344 [-14.918 , 5.202]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: incomepc | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2214.829 563.045 3.934 0.000 [1111.280 , 3318.378]
## Robust - - 1.851 0.064 [-115.548 , 4030.919]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2465.191 498.823 4.942 0.000 [1487.515 , 3442.866]
## Robust - - 1.853 0.064 [-90.598 , 3222.730]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2696.451 472.260 5.710 0.000 [1770.839 , 3622.064]
## Robust - - 1.784 0.074 [-136.711 , 2909.257]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 48 67
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.191 6.191
## BW bias (b) 15.073 15.073
## rho (h/b) 0.411 0.411
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 8444.849 4248.813 1.988 0.047 [117.328 , 16772.370]
## Robust - - 1.968 0.049 [38.140 , 18968.311]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: income | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-215988372.431178465743.243 -1.210 0.226[-565774801.662 , 133798056.800]
## Robust - - -1.522 0.128[-176298537.104 , 22189713.167]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-130163345.101115883685.176 -1.123 0.261[-357291194.441 , 96964504.239]
## Robust - - -1.403 0.161[-714106385.298 , 118301964.168]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-90028766.28788209429.654 -1.021 0.307[-262916071.505 , 82858538.932]
## Robust - - -1.311 0.190[-841446202.000 , 167097299.550]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 15 46
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.802 3.802
## BW bias (b) 7.983 7.983
## rho (h/b) 0.476 0.476
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional597749324.364242558093.252 2.464 0.014[122344197.431 , 1073154451.298]
## Robust - - 2.799 0.005[237387766.254 , 1346277997.735]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Comp_Serv_lvl | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.124 0.546 2.057 0.040 [0.053 , 2.195]
## Robust - - -0.323 0.747 [-2.028 , 1.455]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.168 0.485 2.410 0.016 [0.218 , 2.117]
## Robust - - 0.696 0.486 [-0.961 , 2.021]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.059 0.455 2.329 0.020 [0.168 , 1.950]
## Robust - - 0.951 0.342 [-0.711 , 2.052]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Serv_lvl | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 80 96
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.345 9.345
## BW bias (b) 18.030 18.030
## rho (h/b) 0.518 0.518
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.137 1.188 0.957 0.338 [-1.191 , 3.465]
## Robust - - 0.663 0.507 [-2.011 , 4.066]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expend_level | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.393 0.491 0.802 0.423 [-0.568 , 1.355]
## Robust - - 0.951 0.342 [-0.838 , 2.418]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.339 0.443 0.766 0.444 [-0.529 , 1.208]
## Robust - - 0.739 0.460 [-0.833 , 1.842]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.253 0.421 0.600 0.548 [-0.573 , 1.078]
## Robust - - 0.521 0.602 [-0.902 , 1.555]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 91 111
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.945 10.945
## BW bias (b) 22.432 22.432
## rho (h/b) 0.488 0.488
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.369 0.999 0.369 0.712 [-1.589 , 2.326]
## Robust - - 0.384 0.701 [-1.973 , 2.934]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expenditure | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1947617.7541611109.542 -1.209 0.227[-5105334.433 , 1210098.924]
## Robust - - -1.398 0.162[-1480102.266 , 247551.778]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1199809.3581046555.021 -1.146 0.252[-3251019.508 , 851400.792]
## Robust - - -1.374 0.169[-6388204.243 , 1121760.935]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-846202.191797039.809 -1.062 0.288[-2408371.512 , 715967.130]
## Robust - - -1.297 0.195[-7563732.524 , 1540855.652]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 26 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.617 4.617
## BW bias (b) 8.360 8.360
## rho (h/b) 0.552 0.552
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional1436273.627848801.544 1.692 0.091[-227346.829 , 3099894.083]
## Robust - - 2.010 0.044 [59054.296 , 4686504.779]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Comp_Exp_per_cap | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -79.923 20.681 -3.865 0.000 [-120.457 , -39.389]
## Robust - - 0.334 0.739 [-55.918 , 78.868]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -72.808 20.442 -3.562 0.000 [-112.873 , -32.742]
## Robust - - -2.510 0.012 [-122.888 , -15.126]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -72.907 20.457 -3.564 0.000 [-113.002 , -32.811]
## Robust - - -2.729 0.006 [-119.587 , -19.611]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Comp_Exp_per_cap | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 63 79
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.459 7.459
## BW bias (b) 20.051 20.051
## rho (h/b) 0.372 0.372
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -31.431 43.311 -0.726 0.468 [-116.318 , 53.456]
## Robust - - -0.174 0.862 [-109.134 , 91.358]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=137 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 137
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 72 65
## Eff. Number of Obs. 72 65
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 72 65
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.087 0.078 1.112 0.266 [-0.066 , 0.239]
## Robust - - 0.173 0.862 [-0.223 , 0.266]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=151 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 151
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 70
## Eff. Number of Obs. 81 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 81 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.090 0.069 1.304 0.192 [-0.045 , 0.225]
## Robust - - 0.527 0.598 [-0.154 , 0.268]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=157 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 157
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 87 70
## Eff. Number of Obs. 87 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 87 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.087 0.063 1.376 0.169 [-0.037 , 0.212]
## Robust - - 0.723 0.470 [-0.127 , 0.275]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=158 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 158
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 88 70
## Eff. Number of Obs. 29 17
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.361 8.361
## BW bias (b) 13.752 13.752
## rho (h/b) 0.608 0.608
## Unique Obs. 87 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.030 0.124 -0.245 0.807 [-0.274 , 0.214]
## Robust - - -0.429 0.668 [-0.386 , 0.247]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Admin_Emp_CivReg | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=30 km | p=1 | N used=126 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 126
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 56 70
## Eff. Number of Obs. 56 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 56 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.172 -0.041 0.967 [-0.344 , 0.330]
## Robust - - -0.072 0.943 [-0.616 , 0.572]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=40 km | p=1 | N used=137 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 137
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 63 74
## Eff. Number of Obs. 63 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 63 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.012 0.149 0.079 0.937 [-0.280 , 0.303]
## Robust - - -0.197 0.844 [-0.555 , 0.454]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | h=50 km | p=1 | N used=142 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 142
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 68 74
## Eff. Number of Obs. 68 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 68 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.138 0.162 0.871 [-0.247 , 0.292]
## Robust - - -0.187 0.852 [-0.513 , 0.424]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Emp_CivReg | AUTO bandwidth (default) | p=1 | N used=142 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 142
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 68 74
## Eff. Number of Obs. 30 33
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 11.883 11.883
## BW bias (b) 25.219 25.219
## rho (h/b) 0.471 0.471
## Unique Obs. 67 74
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.187 0.339 0.550 0.582 [-0.478 , 0.852]
## Robust - - 0.537 0.591 [-0.599 , 1.051]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: pol_serv_lvl | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=30 km | p=1 | N used=293 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 293
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 130 163
## Eff. Number of Obs. 130 163
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 130 163
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.053 0.691 -1.524 0.128 [-2.407 , 0.302]
## Robust - - -1.705 0.088 [-4.574 , 0.318]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=40 km | p=1 | N used=321 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 321
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 149 172
## Eff. Number of Obs. 149 172
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 149 172
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.983 0.605 -1.625 0.104 [-2.168 , 0.202]
## Robust - - -1.500 0.134 [-3.541 , 0.470]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | h=50 km | p=1 | N used=333 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 333
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 161 172
## Eff. Number of Obs. 161 172
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 161 172
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.035 0.567 -1.827 0.068 [-2.146 , 0.076]
## Robust - - -1.575 0.115 [-3.176 , 0.346]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_serv_lvl | AUTO bandwidth (default) | p=1 | N used=349 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 349
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 177 172
## Eff. Number of Obs. 63 95
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.654 10.654
## BW bias (b) 21.346 21.346
## rho (h/b) 0.499 0.499
## Unique Obs. 171 165
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.632 1.609 -1.014 0.310 [-4.785 , 1.521]
## Robust - - -0.887 0.375 [-5.780 , 2.177]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: pol_mun_road | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -25.182 17.331 -1.453 0.146 [-59.150 , 8.786]
## Robust - - -2.036 0.042 [-83.897 , -1.586]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -11.458 13.192 -0.869 0.385 [-37.313 , 14.397]
## Robust - - -2.074 0.038 [-92.169 , -2.605]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -6.940 11.802 -0.588 0.557 [-30.072 , 16.193]
## Robust - - -1.603 0.109 [-84.781 , 8.499]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 69 85
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.040 8.040
## BW bias (b) 14.492 14.492
## rho (h/b) 0.555 0.555
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -51.063 30.966 -1.649 0.099 [-111.756 , 9.630]
## Robust - - -1.355 0.175 [-135.813 , 24.764]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_serv_lvl | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=369 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 369
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 185 184
## Eff. Number of Obs. 185 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 185 184
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.952 0.519 3.761 0.000 [0.935 , 2.969]
## Robust - - 1.034 0.301 [-0.853 , 2.757]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=413 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 413
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 218 195
## Eff. Number of Obs. 218 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 218 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.448 0.464 5.279 0.000 [1.539 , 3.357]
## Robust - - 1.286 0.198 [-0.507 , 2.445]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=432 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 432
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 237 195
## Eff. Number of Obs. 237 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 237 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.619 0.442 5.921 0.000 [1.752 , 3.487]
## Robust - - 1.718 0.086 [-0.168 , 2.554]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=452 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 452
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 257 195
## Eff. Number of Obs. 77 99
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.878 9.878
## BW bias (b) 19.620 19.620
## rho (h/b) 0.503 0.503
## Unique Obs. 250 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.120 1.208 0.927 0.354 [-1.247 , 3.488]
## Robust - - 0.580 0.562 [-2.125 , 3.912]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=206 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 206
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 117 89
## Eff. Number of Obs. 117 89
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 117 89
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.037 0.064 -0.575 0.566 [-0.161 , 0.088]
## Robust - - -1.451 0.147 [-0.337 , 0.050]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=231 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 231
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 138 93
## Eff. Number of Obs. 138 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 138 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.004 0.055 -0.078 0.937 [-0.112 , 0.103]
## Robust - - -1.446 0.148 [-0.293 , 0.044]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=247 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 247
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 154 93
## Eff. Number of Obs. 154 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 154 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.014 0.050 0.271 0.786 [-0.085 , 0.112]
## Robust - - -1.406 0.160 [-0.269 , 0.044]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=255 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 255
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 162 93
## Eff. Number of Obs. 42 40
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.291 9.291
## BW bias (b) 16.354 16.354
## rho (h/b) 0.568 0.568
## Unique Obs. 161 91
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.108 0.117 -0.928 0.353 [-0.337 , 0.121]
## Robust - - -0.931 0.352 [-0.438 , 0.156]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_muni_schoolpop_perc | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=30 km | p=1 | N used=386 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 386
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 182
## Eff. Number of Obs. 204 182
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 182
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.244 0.563 0.433 0.665 [-0.860 , 1.349]
## Robust - - 0.128 0.898 [-1.749 , 1.993]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=40 km | p=1 | N used=434 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 434
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 193
## Eff. Number of Obs. 241 193
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 193
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.275 0.500 0.550 0.582 [-0.705 , 1.256]
## Robust - - 0.212 0.832 [-1.399 , 1.737]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | h=50 km | p=1 | N used=458 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 458
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 193
## Eff. Number of Obs. 265 193
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 193
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.303 0.476 0.637 0.524 [-0.629 , 1.236]
## Robust - - 0.234 0.815 [-1.275 , 1.621]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=480 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 480
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 193
## Eff. Number of Obs. 85 98
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.189 10.189
## BW bias (b) 19.949 19.949
## rho (h/b) 0.511 0.511
## Unique Obs. 280 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.005 1.289 0.004 0.997 [-2.521 , 2.531]
## Robust - - -0.071 0.943 [-3.331 , 3.097]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.801 1.542 1.817 0.069 [-0.221 , 5.824]
## Robust - - -0.283 0.778 [-6.192 , 4.631]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.033 1.360 2.230 0.026 [0.367 , 5.700]
## Robust - - 0.648 0.517 [-2.913 , 5.787]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.762 1.278 2.161 0.031 [0.256 , 5.268]
## Robust - - 0.848 0.397 [-2.208 , 5.575]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 79 95
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.164 9.164
## BW bias (b) 21.191 21.191
## rho (h/b) 0.432 0.432
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.946 4.044 -0.481 0.630 [-9.872 , 5.981]
## Robust - - -0.742 0.458 [-13.008 , 5.865]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_prvt_schoolpop_perc | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=30 km | p=1 | N used=388 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 388
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 184
## Eff. Number of Obs. 204 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 184
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.581 1.348 0.431 0.666 [-2.061 , 3.223]
## Robust - - -0.611 0.541 [-5.337 , 2.799]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=40 km | p=1 | N used=436 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 436
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 195
## Eff. Number of Obs. 241 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.247 1.218 1.024 0.306 [-1.140 , 3.633]
## Robust - - -0.782 0.434 [-4.996 , 2.146]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | h=50 km | p=1 | N used=459 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 459
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 264 195
## Eff. Number of Obs. 264 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 264 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.588 1.157 1.373 0.170 [-0.679 , 3.855]
## Robust - - -0.708 0.479 [-4.569 , 2.143]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_prvt_schoolpop_perc | AUTO bandwidth (default) | p=1 | N used=477 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 477
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 282 195
## Eff. Number of Obs. 74 89
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.476 8.476
## BW bias (b) 17.221 17.221
## rho (h/b) 0.492 0.492
## Unique Obs. 275 187
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.116 2.565 -0.435 0.664 [-6.144 , 3.912]
## Robust - - -0.456 0.648 [-8.235 , 5.126]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_meal_serv_pop_perc | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 14.935 3.044 4.906 0.000 [8.968 , 20.902]
## Robust - - 1.125 0.260 [-4.437 , 16.402]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 16.859 2.727 6.181 0.000 [11.513 , 22.204]
## Robust - - 2.178 0.029 [0.951 , 18.058]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 17.403 2.593 6.711 0.000 [12.320 , 22.486]
## Robust - - 2.582 0.010 [2.507 , 18.305]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_meal_serv_pop_perc | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 82 97
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.664 9.664
## BW bias (b) 21.041 21.041
## rho (h/b) 0.459 0.459
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.417 7.202 0.752 0.452 [-8.698 , 19.533]
## Robust - - 0.298 0.766 [-14.489 , 19.687]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_sum_camp_pop_perc | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=30 km | p=1 | N used=365 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 365
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 185 180
## Eff. Number of Obs. 185 180
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 185 180
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 8.438 3.265 2.584 0.010 [2.038 , 14.838]
## Robust - - 0.281 0.779 [-8.980 , 11.984]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=40 km | p=1 | N used=407 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 407
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 216 191
## Eff. Number of Obs. 216 191
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 216 191
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.536 2.886 3.304 0.001 [3.879 , 15.193]
## Robust - - 1.138 0.255 [-3.802 , 14.327]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | h=50 km | p=1 | N used=430 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 430
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 239 191
## Eff. Number of Obs. 239 191
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 239 191
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.034 2.696 3.351 0.001 [3.750 , 14.318]
## Robust - - 1.754 0.079 [-0.885 , 15.937]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_sum_camp_pop_perc | AUTO bandwidth (default) | p=1 | N used=449 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 449
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 258 191
## Eff. Number of Obs. 75 90
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.838 8.838
## BW bias (b) 17.424 17.424
## rho (h/b) 0.507 0.507
## Unique Obs. 251 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.876 8.129 0.846 0.398 [-9.056 , 22.808]
## Robust - - 0.786 0.432 [-12.281 , 28.739]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=389 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 389
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 185
## Eff. Number of Obs. 204 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.539 2.731 2.394 0.017 [1.186 , 11.891]
## Robust - - 0.801 0.423 [-5.458 , 12.996]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=437 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 437
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 196
## Eff. Number of Obs. 241 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.341 2.368 3.100 0.002 [2.700 , 11.982]
## Robust - - 1.194 0.232 [-3.059 , 12.596]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=461 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 461
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 196
## Eff. Number of Obs. 265 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.880 2.231 3.532 0.000 [3.507 , 12.252]
## Robust - - 1.406 0.160 [-2.058 , 12.493]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=483 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 483
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 196
## Eff. Number of Obs. 86 107
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.472 10.472
## BW bias (b) 18.965 18.965
## rho (h/b) 0.552 0.552
## Unique Obs. 280 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.743 5.700 0.657 0.511 [-7.428 , 14.915]
## Robust - - 0.429 0.668 [-11.339 , 17.701]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: PublS_lightpoint | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=30 km | p=1 | N used=389 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 389
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 185
## Eff. Number of Obs. 204 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 21.324 19.854 1.074 0.283 [-17.589 , 60.237]
## Robust - - 0.122 0.903 [-75.740 , 85.832]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=40 km | p=1 | N used=437 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 437
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 196
## Eff. Number of Obs. 241 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 20.971 17.580 1.193 0.233 [-13.485 , 55.427]
## Robust - - 0.415 0.678 [-50.287 , 77.285]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | h=50 km | p=1 | N used=461 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 461
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 196
## Eff. Number of Obs. 265 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 13.386 17.175 0.779 0.436 [-20.276 , 47.048]
## Robust - - 1.113 0.266 [-23.102 , 83.800]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_lightpoint | AUTO bandwidth (default) | p=1 | N used=483 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 483
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 196
## Eff. Number of Obs. 80 96
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.351 9.351
## BW bias (b) 20.406 20.406
## rho (h/b) 0.458 0.458
## Unique Obs. 280 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 23.771 53.599 0.444 0.657 [-81.281 , 128.824]
## Robust - - 0.183 0.855 [-116.960 , 141.063]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.030 1.465 -0.703 0.482 [-3.901 , 1.841]
## Robust - - -1.726 0.084 [-9.077 , 0.576]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.577 1.305 -0.442 0.658 [-3.134 , 1.980]
## Robust - - -1.382 0.167 [-6.887 , 1.190]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.247 1.234 -0.200 0.842 [-2.665 , 2.172]
## Robust - - -1.390 0.165 [-6.382 , 1.086]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 78 94
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.996 8.996
## BW bias (b) 17.555 17.555
## rho (h/b) 0.512 0.512
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.203 3.386 -0.651 0.515 [-8.840 , 4.434]
## Robust - - -0.613 0.540 [-11.301 , 5.913]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | ALL-ITALY SQUARE | p=1 | X in KM | + REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=390 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 390
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 204 186
## Eff. Number of Obs. 204 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 204 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.799 1.600 -0.499 0.617 [-3.935 , 2.337]
## Robust - - -1.393 0.164 [-8.655 , 1.465]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=438 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 438
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 241 197
## Eff. Number of Obs. 241 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 241 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.369 1.423 0.259 0.795 [-2.420 , 3.158]
## Robust - - -1.550 0.121 [-7.812 , 0.913]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=462 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 462
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 265 197
## Eff. Number of Obs. 265 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 265 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.839 1.336 0.628 0.530 [-1.780 , 3.458]
## Robust - - -1.294 0.196 [-6.788 , 1.389]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=484 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 484
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 287 197
## Eff. Number of Obs. 87 108
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.730 10.730
## BW bias (b) 21.904 21.904
## rho (h/b) 0.490 0.490
## Unique Obs. 280 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.987 3.201 -0.308 0.758 [-7.262 , 5.287]
## Robust - - -0.189 0.850 [-8.645 , 7.123]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2dm_sqall40 <- dplyr::bind_rows(sqall_dm40)
if (nrow(dm_sqall40) > 0) {
readr::write_csv(dm_sqall40, dm_csv_sqall40)
cat("\n[All-Italy-square diff-means] Wrote: ", dm_csv_sqall40, " | rows=", nrow(dm_sqall40), "\n", sep = "")
print(
dm_sqall40 %>%
dplyr::select(dplyr::any_of(c(
"sample", "outcome", "year", "h_km", "n_treated", "n_control",
"diff_treat_minus_control", "se_diff", "p_value",
"diff_fe", "se_fe", "p_fe"
))) %>%
head(10)
)
} else {
cat("\n[All-Italy-square diff-means] No usable data within ±40 km for any outcome; skipping export.\n", sep = "")
}##
## [All-Italy-square diff-means] Wrote: output/diffmeans_AllItalySquare_h40.csv | rows=27
## # A tibble: 10 × 9
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 ALL_I… gb_int… NA 40 197 243 -8.12e-3 1.97e-3
## 2 ALL_I… gb_reg… NA 40 197 243 7.61e-2 1.66e-2
## 3 ALL_I… evasio… NA 40 197 241 -1.82e+0 6.86e-1
## 4 ALL_I… servic… NA 40 197 241 1.30e+0 2.76e-1
## 5 ALL_I… marr_c… NA 40 197 241 1.89e+1 1.16e+1
## 6 ALL_I… marr_r… NA 40 197 241 7.27e+0 3.58e+0
## 7 ALL_I… income… NA 40 197 241 3.18e+3 2.90e+2
## 8 ALL_I… income NA 40 197 241 2.56e+8 1.68e+8
## 9 ALL_I… Comp_S… NA 40 197 241 1.56e+0 2.79e-1
## 10 ALL_I… expend… NA 40 197 241 1.04e+0 2.34e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()
# Export pooled rdrobust estimates across all samples
rd_all_tbl <- dplyr::bind_rows(all_results)
if (nrow(rd_all_tbl) > 0) {
readr::write_csv(rd_all_tbl, results_csv)
cat("\n[RD results] Wrote: ", results_csv, " | rows=", nrow(rd_all_tbl), "\n", sep = "")
} else {
cat("\n[RD results] No rdrobust rows to export; skipping ", results_csv, "\n", sep = "")
}##
## [RD results] Wrote: output/rdrobust_results_All_Italy_Lombardia_Square_manualDistance.csv | rows=432{r} read_if_exists <- function(path) { if (file.exists(path)) readr::read_csv(path, show_col_types = FALSE) else NULL }
dm_all40_tbl <- read_if_exists(dm_csv_all40) dm_lomb40_tbl <- read_if_exists(dm_csv_lomb40) dm_sq40_tbl <- read_if_exists(dm_csv_sq40) dm_sqall40_tbl <- read_if_exists(dm_csv_sqall40) dm_sqsign_tbl <- read_if_exists(dm_csv_sqsign)
dm_band <- dplyr::bind_rows(dm_all40_tbl, dm_lomb40_tbl, dm_sq40_tbl, dm_sqall40_tbl)
if (!is.null(dm_band) && nrow(dm_band) > 0) { dm_band_out <- dm_band %>% dplyr::select(sample, outcome, year, h_km, n_treated, n_control, mean_treated, mean_control, diff_treat_minus_control, se_diff, t_stat, df, p_value) %>% dplyr::arrange(sample, outcome, year)
knitr::kable(dm_band_out, digits = 4) } else { cat(“No bandwidth-based diff-in-means table was created (no rows found).”) }
cat(“”)
if (!is.null(dm_sqsign_tbl) && nrow(dm_sqsign_tbl) > 0) { dm_sqsign_out <- dm_sqsign_tbl %>% dplyr::select(sample, outcome, year, n_pos, n_neg, mean_pos, mean_neg, diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>% dplyr::arrange(sample, outcome, year)
knitr::kable(dm_sqsign_out, digits = 4) } else { cat(“No within-square sign-based diff-in-means table was created (no rows found).”) } ```
This Rmd writes the following files to output/:
RD_plots_All_Italy_regFE_manualDistance.pdfRD_plots_Lombardia_noFE_manualDistance.pdfRD_plots_LombardiaSquare_area_x<scale>_noFE_manualDistance.pdfRD_plots_AllItalySquare_area_x<scale>_regFE_manualDistance.pdflombardia_square_area_x<scale>.csvlombardia_square_area_x<scale>_metadata.csvallitaly_square_area_x<scale>.csvallitaly_square_area_x<scale>_metadata.csvrdrobust_results_All_Italy_Lombardia_Square_manualDistance.csvrdrobust_printout_All_Italy_regFE_manualDistance.txtrdrobust_printout_Lombardia_noFE_manualDistance.txtrdrobust_printout_LombardiaSquare_area_x<scale>_noFE_manualDistance.txtrdrobust_printout_AllItalySquare_area_x<scale>_regFE_manualDistance.txtdiffmeans_FullItaly_h40.csvdiffmeans_Lombardia_h40.csvdiffmeans_LombardiaSquare_h40.csvdiffmeans_AllItalySquare_h40.csv