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 three 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(35, 40, 45)
# Difference-in-means bandwidth (requested)
H_DM <- 40 # km
P <- 1
OUTCOMES <- c(
"gb_intensity","gb_reg_rate","evasione","Admin_Tax_Emp",
"edu_serv_lvl","edu_muni_school_area_per1000", "edu_emp_per1000",
"PublS_CyclePath_per","pol_mun_road","Pillar2_pol",
"marr_civil","marr_rel","incomepc","income",
"expend_level","services_level","expenditure"
)
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))
# 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)
)
cat("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 7080 68 34 8 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_xcollapse_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_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)
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_pavia <- file.path(OUTDIR, "RD_plots_Pavia_noFE_manualDistance.pdf")
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_pavia <- file.path(OUTDIR, "rdrobust_printout_Pavia_noFE_manualDistance.txt")
# 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_pavia40 <- file.path(OUTDIR, "diffmeans_Pavia_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=7080 | 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 (KM) | manual bandwidths=35, 40, 45 | 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 (treated - control) within |X| <= 40 km (Full Italy)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
all_dm40[[length(all_dm40) + 1]] <- dm %>%
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$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "
", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "
", 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$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Full Italy)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
all_dm40[[length(all_dm40) + 1]] <- dm %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = NA_integer_)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "
", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "
", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$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=0.004583 | p=5.036e-05 | N_t=734 N_c=637
##
## ==============================================================================================================
## Outcome: gb_intensity | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=35 km | p=1 | N used=1181 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 533 648
## Eff. Number of Obs. 533 648
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 533 648
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.763 0.006 [-0.010 , -0.002]
## Robust - - -0.993 0.321 [-0.011 , 0.004]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=1316 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 608 708
## Eff. Number of Obs. 608 708
## 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. 608 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.884 0.004 [-0.010 , -0.002]
## Robust - - -1.300 0.193 [-0.011 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=45 km | p=1 | N used=1453 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1453
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 672 781
## Eff. Number of Obs. 672 781
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 672 781
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -3.206 0.001 [-0.010 , -0.002]
## Robust - - -1.276 0.202 [-0.010 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=3513 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3513
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2215 1298
## Eff. Number of Obs. 396 492
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.789 24.789
## BW bias (b) 43.825 43.825
## rho (h/b) 0.566 0.566
## Unique Obs. 2199 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.005 0.003 -1.894 0.058 [-0.010 , 0.000]
## Robust - - -1.265 0.206 [-0.011 , 0.002]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=gb_reg_rate | diff=-0.03899 | p=0.0003641 | N_t=734 N_c=637
##
## ==============================================================================================================
## Outcome: gb_reg_rate | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=35 km | p=1 | N used=1181 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 533 648
## Eff. Number of Obs. 533 648
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 533 648
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.044 0.022 2.052 0.040 [0.002 , 0.087]
## Robust - - 0.888 0.375 [-0.037 , 0.097]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=1316 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 608 708
## Eff. Number of Obs. 608 708
## 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. 608 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.043 0.020 2.112 0.035 [0.003 , 0.082]
## Robust - - 1.261 0.207 [-0.022 , 0.102]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=45 km | p=1 | N used=1453 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1453
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 672 781
## Eff. Number of Obs. 672 781
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 672 781
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.045 0.019 2.381 0.017 [0.008 , 0.083]
## Robust - - 1.248 0.212 [-0.021 , 0.095]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=3513 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3513
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2215 1298
## Eff. Number of Obs. 402 501
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.315 25.315
## BW bias (b) 41.059 41.059
## rho (h/b) 0.617 0.617
## Unique Obs. 2199 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.034 0.025 1.320 0.187 [-0.016 , 0.083]
## Robust - - 0.970 0.332 [-0.032 , 0.093]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=evasione | diff=-2.856 | p=9.763e-11 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: evasione | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.543 0.868 -1.779 0.075 [-3.244 , 0.157]
## Robust - - -0.399 0.690 [-3.408 , 2.255]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.334 0.810 -1.647 0.100 [-2.922 , 0.254]
## Robust - - -0.919 0.358 [-3.790 , 1.370]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.343 0.762 -1.762 0.078 [-2.837 , 0.151]
## Robust - - -0.995 0.320 [-3.599 , 1.175]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 462 580
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.183 30.183
## BW bias (b) 55.582 55.582
## rho (h/b) 0.543 0.543
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.587 0.943 -1.684 0.092 [-3.435 , 0.260]
## Robust - - 0.936 0.349 [-1.966 , 5.561]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1069 | p=0.1179 | N_t=232 N_c=217
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=35 km | p=1 | N used=408 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 408
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 195 213
## Eff. Number of Obs. 195 213
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 195 213
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.064 0.079 0.814 0.416 [-0.090 , 0.218]
## Robust - - 1.254 0.210 [-0.078 , 0.356]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=447 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 447
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 215 232
## Eff. Number of Obs. 215 232
## 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. 215 232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.065 0.059 1.108 0.268 [-0.050 , 0.181]
## Robust - - 0.737 0.461 [-0.159 , 0.351]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=45 km | p=1 | N used=474 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 474
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 225 249
## Eff. Number of Obs. 225 249
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 225 249
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.071 0.047 1.532 0.126 [-0.020 , 0.163]
## Robust - - 0.522 0.602 [-0.195 , 0.336]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=927 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 927
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 574 353
## Eff. Number of Obs. 118 119
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.072 17.072
## BW bias (b) 50.514 50.514
## rho (h/b) 0.338 0.338
## Unique Obs. 569 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.153 0.087 1.756 0.079 [-0.018 , 0.324]
## Robust - - 1.319 0.187 [-0.063 , 0.324]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_serv_lvl | diff=0.6146 | p=0.0001335 | N_t=685 N_c=553
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=35 km | p=1 | N used=1113 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1113
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 485 628
## Eff. Number of Obs. 485 628
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 485 628
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.123 0.342 3.282 0.001 [0.453 , 1.794]
## Robust - - 0.374 0.708 [-0.902 , 1.327]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | 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. 550 685
## Eff. Number of Obs. 550 685
## 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. 550 685
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.301 0.322 4.037 0.000 [0.669 , 1.932]
## Robust - - 0.600 0.548 [-0.701 , 1.319]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=45 km | p=1 | N used=1361 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1361
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 605 756
## Eff. Number of Obs. 605 756
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 605 756
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.438 0.306 4.703 0.000 [0.839 , 2.037]
## Robust - - 1.010 0.313 [-0.450 , 1.406]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=3010 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3010
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1760 1250
## Eff. Number of Obs. 299 399
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.993 18.993
## BW bias (b) 42.905 42.905
## rho (h/b) 0.443 0.443
## Unique Obs. 1744 1232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.523 0.493 1.060 0.289 [-0.444 , 1.490]
## Robust - - 0.458 0.647 [-0.844 , 1.358]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=0.796 | p=0.09316 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.963 0.897 3.302 0.001 [1.204 , 4.722]
## Robust - - 0.639 0.523 [-1.920 , 3.780]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.975 0.846 3.517 0.000 [1.317 , 4.634]
## Robust - - 1.190 0.234 [-1.025 , 4.196]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.067 0.803 3.820 0.000 [1.493 , 4.640]
## Robust - - 1.516 0.129 [-0.548 , 4.296]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=3184 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3184
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1906 1278
## Eff. Number of Obs. 437 539
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.855 27.855
## BW bias (b) 50.113 50.113
## rho (h/b) 0.556 0.556
## Unique Obs. 1890 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.455 1.009 2.432 0.015 [0.476 , 4.433]
## Robust - - 1.796 0.073 [-0.199 , 4.560]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_emp_per1000 | diff=-0.01615 | p=0.4388 | N_t=359 N_c=359
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=35 km | p=1 | N used=635 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 635
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 315 320
## Eff. Number of Obs. 315 320
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 315 320
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.061 0.041 1.487 0.137 [-0.019 , 0.141]
## Robust - - -0.639 0.523 [-0.156 , 0.079]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=715 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 715
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 356 359
## Eff. Number of Obs. 356 359
## 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. 356 359
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.069 0.038 1.819 0.069 [-0.005 , 0.144]
## Robust - - -0.165 0.869 [-0.122 , 0.103]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=45 km | p=1 | N used=783 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 783
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 395 388
## Eff. Number of Obs. 395 388
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 395 388
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.073 0.036 2.031 0.042 [0.003 , 0.144]
## Robust - - 0.251 0.802 [-0.093 , 0.121]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=1710 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1710
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1090 620
## Eff. Number of Obs. 185 206
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.952 17.952
## BW bias (b) 35.840 35.840
## rho (h/b) 0.501 0.501
## Unique Obs. 1086 613
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.014 0.052 -0.280 0.780 [-0.116 , 0.087]
## Robust - - -0.755 0.450 [-0.165 , 0.073]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=5.153 | p=9.42e-16 | N_t=694 N_c=602
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=35 km | p=1 | N used=1162 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1162
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 526 636
## Eff. Number of Obs. 526 636
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 526 636
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.838 1.322 4.415 0.000 [3.246 , 8.430]
## Robust - - 2.331 0.020 [0.867 , 10.036]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | 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. 599 694
## Eff. Number of Obs. 599 694
## 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. 599 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.890 1.257 4.685 0.000 [3.426 , 8.353]
## Robust - - 2.680 0.007 [1.488 , 9.590]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=45 km | p=1 | N used=1429 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1429
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 662 767
## Eff. Number of Obs. 662 767
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 662 767
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.048 1.203 5.028 0.000 [3.691 , 8.406]
## Robust - - 2.947 0.003 [1.832 , 9.106]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=3152 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3152
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1886 1266
## Eff. Number of Obs. 496 602
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 32.304 32.304
## BW bias (b) 54.496 54.496
## rho (h/b) 0.593 0.593
## Unique Obs. 1870 1247
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.884 1.372 4.288 0.000 [3.195 , 8.573]
## Robust - - 3.595 0.000 [2.704 , 9.189]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=pol_mun_road | diff=-30.14 | p=9.489e-06 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: pol_mun_road | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 11.053 8.291 1.333 0.183 [-5.198 , 27.304]
## Robust - - -0.464 0.643 [-30.520 , 18.840]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.760 7.793 1.637 0.102 [-2.513 , 28.033]
## Robust - - -0.209 0.835 [-27.186 , 21.957]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 14.082 7.466 1.886 0.059 [-0.551 , 28.715]
## Robust - - 0.099 0.921 [-22.297 , 24.663]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 411 507
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 26.001 26.001
## BW bias (b) 52.086 52.086
## rho (h/b) 0.499 0.499
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.437 9.558 0.255 0.799 [-16.297 , 21.171]
## Robust - - -0.039 0.969 [-23.765 , 22.830]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=1.109 | p=0.01113 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.086 0.905 0.096 0.924 [-1.688 , 1.861]
## Robust - - -1.281 0.200 [-4.778 , 1.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.252 0.850 0.297 0.767 [-1.413 , 1.917]
## Robust - - -0.968 0.333 [-3.948 , 1.337]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.435 0.803 0.541 0.589 [-1.140 , 2.009]
## Robust - - -0.814 0.416 [-3.458 , 1.429]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 321 404
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.852 18.852
## BW bias (b) 36.686 36.686
## rho (h/b) 0.514 0.514
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.567 1.281 -1.223 0.221 [-4.077 , 0.943]
## Robust - - -1.444 0.149 [-5.239 , 0.794]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=3.135 | p=2.144e-09 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.533 1.038 1.477 0.140 [-0.502 , 3.568]
## Robust - - -0.299 0.765 [-3.870 , 2.846]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.837 0.968 1.898 0.058 [-0.060 , 3.733]
## Robust - - -0.108 0.914 [-3.254 , 2.915]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.143 0.911 2.353 0.019 [0.358 , 3.928]
## Robust - - 0.066 0.947 [-2.757 , 2.950]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 303 377
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.276 17.276
## BW bias (b) 29.602 29.602
## rho (h/b) 0.584 0.584
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.562 1.580 0.355 0.722 [-2.535 , 3.659]
## Robust - - 0.087 0.931 [-3.771 , 4.119]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_civil | diff=3.342 | p=0.3658 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: marr_civil | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.331 3.293 1.012 0.312 [-3.124 , 9.786]
## Robust - - -0.576 0.564 [-16.052 , 8.757]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.686 2.548 1.839 0.066 [-0.309 , 9.680]
## Robust - - -0.480 0.632 [-17.209 , 10.443]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.608 2.152 2.606 0.009 [1.390 , 9.825]
## Robust - - -0.276 0.782 [-15.114 , 11.380]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 315 395
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.202 18.202
## BW bias (b) 46.440 46.440
## rho (h/b) 0.392 0.392
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.595 2.860 0.907 0.364 [-3.010 , 8.199]
## Robust - - 0.334 0.739 [-5.674 , 8.002]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_rel | diff=1.971 | p=0.1007 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: marr_rel | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.569 1.389 0.410 0.682 [-2.153 , 3.291]
## Robust - - -1.307 0.191 [-8.200 , 1.640]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.171 1.187 0.986 0.324 [-1.156 , 3.498]
## Robust - - -1.117 0.264 [-7.991 , 2.190]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.665 1.077 1.546 0.122 [-0.445 , 3.775]
## Robust - - -0.901 0.368 [-7.031 , 2.604]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 343 420
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.369 20.369
## BW bias (b) 49.864 49.864
## rho (h/b) 0.408 0.408
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.895 1.535 -0.583 0.560 [-3.904 , 2.114]
## Robust - - -0.909 0.363 [-5.046 , 1.848]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=incomepc | diff=1195 | p=7.211e-12 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: incomepc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1585.445 342.609 4.628 0.000 [913.944 , 2256.946]
## Robust - - 0.872 0.383 [-640.180 , 1666.772]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1692.075 323.124 5.237 0.000 [1058.764 , 2325.386]
## Robust - - 1.454 0.146 [-266.344 , 1797.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1787.925 306.585 5.832 0.000 [1187.029 , 2388.821]
## Robust - - 1.989 0.047 [14.012 , 1892.207]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 398 496
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.262 25.262
## BW bias (b) 49.368 49.368
## rho (h/b) 0.512 0.512
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1160.257 409.920 2.830 0.005 [356.829 , 1963.686]
## Robust - - 1.983 0.047 [11.110 , 1899.471]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=income | diff=56250000 | p=0.2643 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: income | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional15099800.13240399986.805 0.374 0.709[-64082718.983 , 94282319.246]
## Robust - - -1.079 0.280[-248621994.722 , 72044352.624]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional37518175.34027343895.986 1.372 0.170[-16074875.989 , 91111226.669]
## Robust - - -0.922 0.356[-275480655.714 , 99196550.975]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional54136540.20720772809.466 2.606 0.009[13422581.796 , 94850498.618]
## Robust - - -0.739 0.460[-248478893.487 , 112397241.577]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 275 350
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 15.659 15.659
## BW bias (b) 42.346 42.346
## rho (h/b) 0.370 0.370
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional7125288.58029378229.905 0.243 0.808[-50454983.963 , 64705561.122]
## Robust - - -0.490 0.624[-92551405.010 , 55536652.758]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expend_level | diff=0.365 | p=0.005602 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: expend_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.388 0.280 1.383 0.167 [-0.162 , 0.937]
## Robust - - 0.064 0.949 [-0.904 , 0.965]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.437 0.262 1.669 0.095 [-0.076 , 0.950]
## Robust - - 0.278 0.781 [-0.728 , 0.968]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.486 0.247 1.964 0.050 [0.001 , 0.970]
## Robust - - 0.443 0.658 [-0.601 , 0.951]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 436 537
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.692 27.692
## BW bias (b) 51.264 51.264
## rho (h/b) 0.540 0.540
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.337 0.324 1.040 0.298 [-0.298 , 0.971]
## Robust - - 0.596 0.551 [-0.524 , 0.983]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=services_level | diff=0.2873 | p=0.0668 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: services_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.603 0.296 5.419 0.000 [1.023 , 2.183]
## Robust - - 2.347 0.019 [0.188 , 2.091]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.710 0.278 6.159 0.000 [1.166 , 2.254]
## Robust - - 2.717 0.007 [0.337 , 2.081]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.803 0.263 6.856 0.000 [1.287 , 2.318]
## Robust - - 3.111 0.002 [0.473 , 2.084]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 361 442
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 21.848 21.848
## BW bias (b) 43.443 43.443
## rho (h/b) 0.503 0.503
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.222 0.388 3.153 0.002 [0.462 , 1.982]
## Robust - - 2.284 0.022 [0.148 , 1.936]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expenditure | diff=314600 | p=0.527 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: expenditure | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=35 km | p=1 | N used=1172 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1172
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 529 643
## Eff. Number of Obs. 529 643
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 529 643
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional317138.339400675.991 0.792 0.429[-468172.173 , 1102448.852]
## Robust - - -0.929 0.353[-2279596.243 , 814019.059]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## 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. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional502204.049308425.201 1.628 0.103[-102298.237 , 1106706.334]
## Robust - - -0.730 0.466[-2369395.251 , 1083933.670]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=45 km | p=1 | N used=1441 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1441
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 666 775
## Eff. Number of Obs. 666 775
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 666 775
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional620927.862248209.916 2.502 0.012[134445.366 , 1107410.358]
## Robust - - -0.468 0.640[-2052491.956 , 1261724.375]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 289 363
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 16.466 16.466
## BW bias (b) 46.308 46.308
## rho (h/b) 0.356 0.356
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional122100.132288686.482 0.423 0.672[-443714.975 , 687915.239]
## Robust - - -0.149 0.881[-754025.561 , 647161.365]
## =============================================================================
## 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) %>%
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=18
## # 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 FULL_… gb_int… NA 40 734 637 0.00458 0.00113
## 2 FULL_… gb_reg… NA 40 734 637 -0.0390 0.0109
## 3 FULL_… evasio… NA 40 702 605 -2.86 0.437
## 4 FULL_… Admin_… NA 40 232 217 0.107 0.0681
## 5 FULL_… edu_se… NA 40 685 553 0.615 0.160
## 6 FULL_… edu_mu… NA 40 702 605 0.796 0.474
## 7 FULL_… edu_em… NA 40 359 359 -0.0161 0.0208
## 8 FULL_… PublS_… NA 40 694 602 5.15 0.633
## 9 FULL_… pol_mu… NA 40 702 605 -30.1 6.77
## 10 FULL_… Pillar… 2010 40 702 605 1.11 0.436
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()df_lombardia <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
sink(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=2814 | 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 (KM) | manual bandwidths=35, 40, 45 | 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=-0.01197 | p=2.908e-07 | N_t=694 N_c=133
##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=35 km | p=1 | N used=767 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 767
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 634
## Eff. Number of Obs. 133 634
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 634
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.008 0.004 -2.300 0.021 [-0.015 , -0.001]
## Robust - - 0.713 0.476 [-0.008 , 0.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=827 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 827
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 694
## Eff. Number of Obs. 133 694
## 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. 133 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.009 0.003 -2.605 0.009 [-0.016 , -0.002]
## Robust - - 0.719 0.472 [-0.007 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=45 km | p=1 | N used=900 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 900
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 767
## Eff. Number of Obs. 133 767
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 767
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.010 0.003 -2.939 0.003 [-0.017 , -0.003]
## Robust - - 0.846 0.397 [-0.006 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=1417 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1417
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1284
## Eff. Number of Obs. 26 131
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.565 5.565
## BW bias (b) 12.381 12.381
## rho (h/b) 0.449 0.449
## Unique Obs. 130 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.051 0.011 4.686 0.000 [0.030 , 0.073]
## Robust - - 4.349 0.000 [0.032 , 0.085]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=gb_reg_rate | diff=0.06762 | p=9.281e-09 | N_t=694 N_c=133
##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=35 km | p=1 | N used=767 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 767
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 634
## Eff. Number of Obs. 133 634
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 634
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.069 0.023 2.982 0.003 [0.024 , 0.114]
## Robust - - 2.194 0.028 [0.008 , 0.148]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=827 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 827
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 694
## Eff. Number of Obs. 133 694
## 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. 133 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.068 0.022 3.051 0.002 [0.024 , 0.111]
## Robust - - 2.552 0.011 [0.020 , 0.154]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=45 km | p=1 | N used=900 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 900
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 767
## Eff. Number of Obs. 133 767
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 767
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.070 0.022 3.232 0.001 [0.027 , 0.112]
## Robust - - 2.706 0.007 [0.025 , 0.154]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=1417 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1417
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1284
## Eff. Number of Obs. 45 174
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.633 7.633
## BW bias (b) 15.428 15.428
## rho (h/b) 0.495 0.495
## Unique Obs. 130 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.055 0.398 0.690 [-0.086 , 0.130]
## Robust - - 0.005 0.996 [-0.141 , 0.142]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=evasione | diff=-2.774 | p=0.0002511 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.492 1.420 -1.051 0.293 [-4.274 , 1.291]
## Robust - - 0.115 0.908 [-3.987 , 4.484]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.675 1.401 -1.196 0.232 [-4.422 , 1.071]
## Robust - - -0.192 0.848 [-4.514 , 3.709]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.931 1.390 -1.389 0.165 [-4.655 , 0.794]
## Robust - - -0.401 0.689 [-4.859 , 3.209]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 31 136
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.976 5.976
## BW bias (b) 13.060 13.060
## rho (h/b) 0.458 0.458
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.834 4.301 0.659 0.510 [-5.596 , 11.264]
## Robust - - 0.929 0.353 [-5.483 , 15.358]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.143 | p=0.05524 | N_t=226 N_c=49
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=35 km | p=1 | N used=256 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 256
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 207
## Eff. Number of Obs. 49 207
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 49 207
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.082 0.087 0.943 0.346 [-0.088 , 0.251]
## Robust - - 0.059 0.953 [-0.236 , 0.251]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=275 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 275
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 226
## Eff. Number of Obs. 49 226
## 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. 49 226
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.104 0.073 1.428 0.153 [-0.039 , 0.247]
## Robust - - -0.256 0.798 [-0.326 , 0.250]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=45 km | p=1 | N used=292 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 292
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 243
## Eff. Number of Obs. 49 243
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 49 243
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.123 0.066 1.859 0.063 [-0.007 , 0.253]
## Robust - - -0.369 0.712 [-0.360 , 0.246]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 347
## Eff. Number of Obs. 12 34
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.390 5.390
## BW bias (b) 10.035 10.035
## rho (h/b) 0.537 0.537
## Unique Obs. 49 346
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.104 0.243 0.426 0.670 [-0.373 , 0.580]
## Robust - - 0.459 0.646 [-0.484 , 0.780]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_serv_lvl | diff=1.399 | p=1.68e-07 | N_t=671 N_c=121
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=35 km | p=1 | N used=735 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 735
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 614
## Eff. Number of Obs. 121 614
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 121 614
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.921 0.478 1.925 0.054 [-0.017 , 1.859]
## Robust - - 0.114 0.909 [-1.456 , 1.636]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=792 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 792
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 671
## Eff. Number of Obs. 121 671
## 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. 121 671
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.059 0.467 2.269 0.023 [0.144 , 1.973]
## Robust - - 0.189 0.850 [-1.345 , 1.632]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=45 km | p=1 | N used=863 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 863
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 742
## Eff. Number of Obs. 121 742
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 121 742
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.146 0.459 2.500 0.012 [0.247 , 2.045]
## Robust - - 0.401 0.689 [-1.154 , 1.747]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=1357 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1357
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 1236
## Eff. Number of Obs. 49 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.586 8.586
## BW bias (b) 17.004 17.004
## rho (h/b) 0.505 0.505
## Unique Obs. 118 1221
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.767 1.226 0.626 0.531 [-1.635 , 3.169]
## Robust - - 0.633 0.527 [-2.064 , 4.034]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=3.24 | p=0.0001055 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.260 1.515 2.813 0.005 [1.291 , 7.228]
## Robust - - 0.530 0.596 [-3.835 , 6.680]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.518 1.475 3.063 0.002 [1.627 , 7.410]
## Robust - - 0.794 0.427 [-3.046 , 7.193]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.719 1.451 3.252 0.001 [1.875 , 7.563]
## Robust - - 1.043 0.297 [-2.359 , 7.728]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 31 136
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.957 5.957
## BW bias (b) 12.785 12.785
## rho (h/b) 0.466 0.466
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.663 5.988 0.111 0.912 [-11.074 , 12.400]
## Robust - - -0.241 0.809 [-16.264 , 12.701]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_emp_per1000 | diff=0.06333 | p=0.0002704 | N_t=351 N_c=81
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=35 km | p=1 | N used=393 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 393
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 312
## Eff. Number of Obs. 81 312
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 81 312
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.010 0.048 0.203 0.839 [-0.084 , 0.103]
## Robust - - -1.123 0.261 [-0.247 , 0.067]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=432 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 432
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 351
## Eff. Number of Obs. 81 351
## 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. 81 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.046 0.485 0.627 [-0.068 , 0.112]
## Robust - - -1.009 0.313 [-0.231 , 0.074]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=45 km | p=1 | N used=461 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 461
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 380
## Eff. Number of Obs. 81 380
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 81 380
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.031 0.045 0.700 0.484 [-0.056 , 0.119]
## Robust - - -0.884 0.377 [-0.217 , 0.082]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=693 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 693
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 612
## Eff. Number of Obs. 33 107
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.000 9.000
## BW bias (b) 14.251 14.251
## rho (h/b) 0.632 0.632
## Unique Obs. 80 606
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.105 0.095 -1.111 0.266 [-0.291 , 0.080]
## Robust - - -1.050 0.294 [-0.373 , 0.113]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=6.738 | p=7.322e-17 | N_t=680 N_c=133
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=35 km | p=1 | N used=755 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 755
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 622
## Eff. Number of Obs. 133 622
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 622
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.907 2.368 2.072 0.038 [0.265 , 9.549]
## Robust - - 0.173 0.863 [-7.411 , 8.846]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=813 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 813
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 680
## Eff. Number of Obs. 133 680
## 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. 133 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.229 2.270 2.303 0.021 [0.780 , 9.678]
## Robust - - 0.290 0.772 [-6.636 , 8.939]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=45 km | p=1 | N used=886 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 886
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 753
## Eff. Number of Obs. 133 753
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 753
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.492 2.202 2.493 0.013 [1.175 , 9.808]
## Robust - - 0.387 0.699 [-6.056 , 9.037]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=1385 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1385
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1252
## Eff. Number of Obs. 60 234
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.167 10.167
## BW bias (b) 16.241 16.241
## rho (h/b) 0.626 0.626
## Unique Obs. 130 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.064 5.088 -0.012 0.990 [-10.037 , 9.910]
## Robust - - -0.200 0.842 [-14.054 , 11.453]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=pol_mun_road | diff=13.15 | p=0.02435 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.268 12.456 0.262 0.793 [-21.146 , 27.682]
## Robust - - -1.757 0.079 [-79.927 , 4.368]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.026 11.908 0.590 0.555 [-16.312 , 30.364]
## Robust - - -1.631 0.103 [-76.033 , 6.954]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.923 11.620 0.854 0.393 [-12.852 , 32.698]
## Robust - - -1.509 0.131 [-71.869 , 9.350]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 46 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.960 7.960
## BW bias (b) 11.577 11.577
## rho (h/b) 0.688 0.688
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -35.434 26.172 -1.354 0.176 [-86.730 , 15.862]
## Robust - - -1.177 0.239 [-98.638 , 24.628]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=2.07 | p=0.003646 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.351 1.492 0.235 0.814 [-2.574 , 3.275]
## Robust - - -1.057 0.291 [-6.828 , 2.044]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.501 1.458 0.344 0.731 [-2.356 , 3.358]
## Robust - - -0.852 0.394 [-6.177 , 2.435]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.624 1.434 0.435 0.663 [-2.187 , 3.435]
## Robust - - -0.730 0.466 [-5.797 , 2.652]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 161
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.862 6.862
## BW bias (b) 13.851 13.851
## rho (h/b) 0.495 0.495
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.201 4.441 -0.045 0.964 [-8.905 , 8.503]
## Robust - - -0.076 0.939 [-12.023 , 11.121]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=4.76 | p=3.93e-08 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.597 1.653 0.966 0.334 [-1.643 , 4.837]
## Robust - - -0.247 0.805 [-5.519 , 4.282]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.881 1.626 1.156 0.248 [-1.307 , 5.068]
## Robust - - -0.181 0.856 [-5.218 , 4.336]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.143 1.609 1.332 0.183 [-1.010 , 5.296]
## Robust - - -0.122 0.903 [-4.993 , 4.407]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.957 6.957
## BW bias (b) 13.924 13.924
## rho (h/b) 0.500 0.500
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.818 4.529 0.622 0.534 [-6.058 , 11.695]
## Robust - - 0.507 0.612 [-8.800 , 14.944]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_civil | diff=9.426 | p=0.00751 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.430 3.942 0.109 0.913 [-7.295 , 8.155]
## Robust - - -1.184 0.236 [-23.953 , 5.912]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.150 3.257 0.660 0.509 [-4.234 , 8.533]
## Robust - - -1.141 0.254 [-25.662 , 6.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.692 2.997 1.232 0.218 [-2.182 , 9.566]
## Robust - - -1.108 0.268 [-24.575 , 6.824]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 38 148
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.444 6.444
## BW bias (b) 10.938 10.938
## rho (h/b) 0.589 0.589
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.567 5.848 1.294 0.196 [-3.895 , 19.028]
## Robust - - 1.699 0.089 [-1.999 , 28.047]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_rel | diff=4.766 | p=0.0001148 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.625 2.034 0.307 0.759 [-3.361 , 4.611]
## Robust - - -1.336 0.182 [-12.337 , 2.337]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.373 1.868 0.735 0.462 [-2.289 , 5.034]
## Robust - - -1.238 0.216 [-12.154 , 2.744]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.012 1.795 1.121 0.262 [-1.505 , 5.529]
## Robust - - -1.121 0.262 [-11.420 , 3.110]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 55 206
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.640 8.640
## BW bias (b) 11.967 11.967
## rho (h/b) 0.722 0.722
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.852 4.437 -1.093 0.274 [-13.548 , 3.845]
## Robust - - -1.091 0.275 [-16.298 , 4.641]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=incomepc | diff=2084 | p=3.064e-17 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2325.767 481.612 4.829 0.000 [1381.824 , 3269.710]
## Robust - - 1.519 0.129 [-359.650 , 2834.472]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2360.419 467.447 5.050 0.000 [1444.239 , 3276.599]
## Robust - - 2.019 0.043 [45.839 , 3084.349]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2386.042 457.397 5.217 0.000 [1489.560 , 3282.525]
## Robust - - 2.370 0.018 [307.247 , 3244.984]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 21 112
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.967 4.967
## BW bias (b) 12.251 12.251
## rho (h/b) 0.405 0.405
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7828.024 5123.781 1.528 0.127 [-2214.403 , 17870.451]
## Robust - - 1.551 0.121 [-2323.064 , 19946.656]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=income | diff=116500000 | p=0.01785 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: income | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-18511178.47443493701.278 -0.426 0.670[-103757266.533 , 66734909.586]
## Robust - - -1.680 0.093[-320712099.175 , 24696941.440]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional8065490.62030865204.834 0.261 0.794[-52429199.230 , 68560180.469]
## Robust - - -1.516 0.130[-353449243.591 , 45193458.674]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional31179277.02426037341.643 1.197 0.231[-19852974.849 , 82211528.898]
## Robust - - -1.453 0.146[-335337061.025 , 49849650.925]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 47 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.999 7.999
## BW bias (b) 11.726 11.726
## rho (h/b) 0.682 0.682
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-65598987.39857953638.311 -1.132 0.258[-179186031.260 , 47988056.464]
## Robust - - -0.868 0.386[-202067074.138 , 78056884.815]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expend_level | diff=0.6987 | p=0.004729 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.216 0.553 0.391 0.696 [-0.867 , 1.299]
## Robust - - 0.258 0.796 [-1.657 , 2.160]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.206 0.536 0.385 0.700 [-0.844 , 1.257]
## Robust - - 0.347 0.729 [-1.507 , 2.155]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.222 0.525 0.422 0.673 [-0.808 , 1.251]
## Robust - - 0.363 0.717 [-1.454 , 2.115]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 44 171
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.318 7.318
## BW bias (b) 14.949 14.949
## rho (h/b) 0.490 0.490
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.376 1.951 -0.193 0.847 [-4.199 , 3.447]
## Robust - - -0.264 0.792 [-5.547 , 4.230]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=services_level | diff=2.481 | p=2.27e-16 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.420 0.564 2.518 0.012 [0.315 , 2.525]
## Robust - - 1.130 0.258 [-0.789 , 2.937]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.459 0.549 2.659 0.008 [0.383 , 2.534]
## Robust - - 1.157 0.247 [-0.743 , 2.883]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.498 0.539 2.780 0.005 [0.442 , 2.554]
## Robust - - 1.175 0.240 [-0.714 , 2.851]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.960 6.960
## BW bias (b) 13.946 13.946
## rho (h/b) 0.499 0.499
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.342 1.867 1.254 0.210 [-1.318 , 6.001]
## Robust - - 0.979 0.328 [-2.422 , 7.253]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expenditure | diff=1074000 | p=0.01547 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=35 km | p=1 | N used=762 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 762
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 629
## Eff. Number of Obs. 133 629
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 629
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-137862.833383767.457 -0.359 0.719[-890033.228 , 614307.561]
## Robust - - -1.538 0.124[-2749767.542 , 331778.798]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## 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. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 89112.810267018.946 0.334 0.739[-434234.708 , 612460.328]
## Robust - - -1.381 0.167[-3041870.279 , 527107.272]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=45 km | p=1 | N used=894 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 894
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 761
## Eff. Number of Obs. 133 761
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 761
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional292518.858221536.326 1.320 0.187[-141684.362 , 726722.079]
## Robust - - -1.326 0.185[-2888371.139 , 557685.447]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 10 49
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.116 3.116
## BW bias (b) 8.022 8.022
## rho (h/b) 0.388 0.388
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional862313.164444987.329 1.938 0.053 [-9845.975 , 1734472.303]
## Robust - - 2.537 0.011[434665.445 , 3389359.790]
## =============================================================================
## 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=18
## # 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 40 694 133 -0.0120 0.00225
## 2 LOMBA… gb_reg… NA 40 694 133 0.0676 0.0115
## 3 LOMBA… evasio… NA 40 688 133 -2.77 0.741
## 4 LOMBA… Admin_… NA 40 226 49 0.143 0.0743
## 5 LOMBA… edu_se… NA 40 671 121 1.40 0.257
## 6 LOMBA… edu_mu… NA 40 688 133 3.24 0.816
## 7 LOMBA… edu_em… NA 40 351 81 0.0633 0.0172
## 8 LOMBA… PublS_… NA 40 680 133 6.74 0.764
## 9 LOMBA… pol_mu… NA 40 688 133 13.1 5.82
## 10 LOMBA… Pillar… 2010 40 688 133 2.07 0.703
## # 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$poly)
df_lomb_square <- lomb_sf_utm %>%
mutate(in_expanded_square = in_sq) %>%
filter(in_expanded_square) %>%
st_drop_geometry()
# 6) Write square dataset + metadata
square_out_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f.csv", TARGET_AREA_SCALE))
square_meta_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_metadata.csv", TARGET_AREA_SCALE))
readr::write_csv(df_lomb_square, square_out_file)
meta <- tibble::tibble(
baseline_n = nrow(base),
expanded_n = nrow(df_lomb_square),
target_area_scale = TARGET_AREA_SCALE,
side_multiplier = sq$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)
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>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 (KM) | manual bandwidths=35, 40, 45 | 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.009 0.004 -2.256 0.024 [-0.018 , -0.001]
## Robust - - 1.756 0.079 [-0.001 , 0.027]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.012 0.004 -3.107 0.002 [-0.020 , -0.005]
## Robust - - 1.600 0.110 [-0.002 , 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.119 0.033 3.630 0.000 [0.055 , 0.183]
## Robust - - 2.196 0.028 [0.011 , 0.200]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.123 0.031 3.941 0.000 [0.062 , 0.185]
## Robust - - 2.414 0.016 [0.021 , 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.169 1.597 0.106 0.916 [-2.960 , 3.298]
## Robust - - 0.397 0.692 [-3.857 , 5.814]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.311 1.558 0.200 0.842 [-2.741 , 3.364]
## Robust - - 0.003 0.998 [-4.637 , 4.649]
## =============================================================================
## 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: Admin_Tax_Emp | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=35 km | p=1 | N used=116 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 116
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 68
## Eff. Number of Obs. 48 68
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 68
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.147 0.078 1.891 0.059 [-0.005 , 0.300]
## Robust - - 0.256 0.798 [-0.221 , 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.160 0.079 2.033 0.042 [0.006 , 0.315]
## Robust - - 0.176 0.860 [-0.235 , 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: edu_serv_lvl | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=35 km | p=1 | N used=312 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 312
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 192
## Eff. Number of Obs. 120 192
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 192
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.942 0.568 3.419 0.001 [0.829 , 3.055]
## Robust - - 0.834 0.404 [-1.070 , 2.653]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.176 0.545 3.991 0.000 [1.108 , 3.245]
## Robust - - 0.926 0.354 [-0.927 , 2.588]
## =============================================================================
## 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_muni_school_area_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.032 1.723 1.760 0.078 [-0.345 , 6.410]
## Robust - - -0.182 0.856 [-6.597 , 5.475]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.541 1.656 2.138 0.032 [0.295 , 6.787]
## Robust - - 0.049 0.961 [-5.608 , 5.895]
## =============================================================================
## 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_emp_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=35 km | p=1 | N used=171 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 171
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 91
## Eff. Number of Obs. 80 91
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 91
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.000 0.060 -0.004 0.996 [-0.119 , 0.118]
## Robust - - -1.178 0.239 [-0.305 , 0.076]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.017 0.057 0.295 0.768 [-0.095 , 0.128]
## Robust - - -1.143 0.253 [-0.294 , 0.077]
## =============================================================================
## 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: PublS_CyclePath_per | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=35 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) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 193
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.077 3.032 2.334 0.020 [1.135 , 13.019]
## Robust - - 0.691 0.490 [-6.644 , 13.872]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.467 2.851 2.619 0.009 [1.879 , 13.055]
## Robust - - 0.777 0.437 [-5.834 , 13.491]
## =============================================================================
## 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: pol_mun_road | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -20.056 16.396 -1.223 0.221 [-52.192 , 12.079]
## Robust - - -2.366 0.018 [-105.557 , -9.910]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -12.506 13.970 -0.895 0.371 [-39.886 , 14.874]
## Robust - - -2.245 0.025 [-114.581 , -7.761]
## =============================================================================
## 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: Pillar2_pol | Year=2010 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.524 1.677 -0.312 0.755 [-3.812 , 2.764]
## Robust - - -1.499 0.134 [-8.967 , 1.196]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.139 1.618 -0.086 0.931 [-3.311 , 3.032]
## Robust - - -1.337 0.181 [-8.201 , 1.548]
## =============================================================================
## 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.415 1.834 0.226 0.821 [-3.179 , 4.009]
## Robust - - -0.822 0.411 [-7.898 , 3.229]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.922 1.790 0.515 0.606 [-2.585 , 4.430]
## Robust - - -0.848 0.397 [-7.671 , 3.039]
## =============================================================================
## 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]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -9.243 10.394 -0.889 0.374 [-29.614 , 11.128]
## Robust - - -1.251 0.211 [-37.423 , 8.256]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -5.404 7.421 -0.728 0.466 [-19.949 , 9.140]
## Robust - - -1.203 0.229 [-55.118 , 13.197]
## =============================================================================
## 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -3.098 3.624 -0.855 0.393 [-10.202 , 4.006]
## Robust - - -1.544 0.123 [-16.611 , 1.972]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.661 2.806 -0.592 0.554 [-7.160 , 3.838]
## Robust - - -1.439 0.150 [-20.725 , 3.176]
## =============================================================================
## 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2789.323 581.645 4.796 0.000 [1649.319 , 3929.327]
## Robust - - 1.522 0.128 [-449.829 , 3575.417]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2971.105 555.290 5.351 0.000 [1882.756 , 4059.454]
## Robust - - 1.835 0.067 [-117.674 , 3560.775]
## =============================================================================
## 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=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-156469186.925144617994.236 -1.082 0.279[-439915247.143 , 126976873.294]
## Robust - - -1.576 0.115[-535444833.334 , 58200130.583]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-95630431.30699633611.816 -0.960 0.337[-290908722.115 , 99647859.503]
## Robust - - -1.374 0.170[-809866244.787 , 142471331.644]
## =============================================================================
## 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: expend_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.274 0.575 0.477 0.633 [-0.853 , 1.402]
## Robust - - 0.489 0.625 [-1.360 , 2.265]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.325 0.554 0.587 0.557 [-0.760 , 1.410]
## Robust - - 0.418 0.676 [-1.357 , 2.094]
## =============================================================================
## 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: services_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.585 0.668 0.875 0.381 [-0.725 , 1.894]
## Robust - - -0.002 0.998 [-2.218 , 2.213]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.679 0.637 1.067 0.286 [-0.569 , 1.927]
## Robust - - 0.028 0.978 [-2.087 , 2.147]
## =============================================================================
## 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: expenditure | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=35 km | p=1 | N used=326 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 326
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 194
## Eff. Number of Obs. 132 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 35.000 35.000
## BW bias (b) 35.000 35.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 194
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1421408.1291304038.731 -1.090 0.276[-3977277.076 , 1134460.818]
## Robust - - -1.507 0.132[-4721343.929 , 617003.804]
## =============================================================================
## 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=45 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) 45.000 45.000
## BW bias (b) 45.000 45.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-887757.792897016.501 -0.990 0.322[-2645877.827 , 870362.243]
## Robust - - -1.328 0.184[-7204687.015 , 1384127.672]
## =============================================================================
## 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]
## =============================================================================
## 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("
[Square diff-means] Wrote: ", dm_csv_sq40, " | rows=", nrow(dm_sq40), "
", sep = "")
print(dm_sq40 %>% dplyr::select(sample, outcome, year, h_km, n_treated, n_control, diff_treat_minus_control, se_diff, p_value) %>% head(10))
} else {
cat("
[Square diff-means] No usable data within ±40 km for any outcome; skipping export.
", sep = "")# 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("
[Square diff-means SIGN] Wrote: ", dm_csv_sqsign, " | rows=", nrow(dm_sqsign), "
", sep = "")
print(dm_sqsign %>%
dplyr::select(sample, outcome, year, n_pos, n_neg, diff_pos_minus_neg, se_diff, p_value) %>%
head(10))
} else {
cat("
[Square diff-means SIGN] No usable data in square for any outcome; skipping export.
", sep = "")
}
}##
## [Square diff-means] Wrote: output/diffmeans_LombardiaSquare_h40.csv | rows=18
## # 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 40 197 132 -0.0148 2.49e-3
## 2 LOMBA… gb_reg… NA 40 197 132 0.135 1.66e-2
## 3 LOMBA… evasio… NA 40 197 132 -0.845 8.22e-1
## 4 LOMBA… Admin_… NA 40 70 48 0.0854 3.92e-2
## 5 LOMBA… edu_se… NA 40 195 120 3.08 2.97e-1
## 6 LOMBA… edu_mu… NA 40 197 132 3.89 9.31e-1
## 7 LOMBA… edu_em… NA 40 93 80 0.105 3.29e-2
## 8 LOMBA… PublS_… NA 40 196 132 10.9 1.29e+0
## 9 LOMBA… pol_mu… NA 40 197 132 18.5 1.32e+1
## 10 LOMBA… Pillar… 2010 40 197 132 1.67 8.35e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>if (!("COD_PROV" %in% names(df0))) {
warning("COD_PROV not found in df0; skipping Pavia-province estimates (COD_PROV=18).")
} else {
# Province of Pavia within Lombardia: COD_REG == 3 & COD_PROV == 18
df_pavia <- df0 %>%
filter(
as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA,
as.integer(.data[["COD_PROV"]]) == 18
)
H_PAVIA <- H_DM # km bandwidth requested for BOTH RD and diff-means in Pavia
# ---- logging (sink-safe) ----
sink(results_txt_pavia, split = TRUE)
on.exit({ while (sink.number() > 0) sink() }, add = TRUE)
cat("Using DF: Pavia province only (COD_REG==3 & COD_PROV==18) | rows=", nrow(df_pavia),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_pavia), "year", NA),
"\n", sep = "")
cat("Running var: ", RUNNING, " (KM) | h=", H_PAVIA, " km | p=", P, " | NO regional FE\n\n", sep = "")
# ---- treated/control counts (unique municipalities) ----
tcol_raw <- if ("Treated" %in% names(df_pavia)) "Treated" else if ("Treated_num" %in% names(df_pavia)) "Treated_num" else NA_character_
if (is.na(tcol_raw)) {
cat("[WARN] Neither Treated nor Treated_num found in df_pavia; cannot tabulate treated/control counts from the raw DF.\n")
} else {
tc_pavia <- df_pavia %>%
distinct(.data[[KEYCOL]], Treated = as.integer(.data[[tcol_raw]])) %>%
count(Treated, name = "n_muni") %>%
arrange(Treated)
cat("Treated/control counts (unique municipalities) in Pavia province:\n")
print(tc_pavia)
if (nrow(tc_pavia) < 2) {
cat("[WARN] Only one Treated status present in Pavia province after filtering.\n")
}
}
# ---- local helper: subsetting to h and basic checks ----
make_sub_pavia_h <- function(d, h) {
sub <- d %>%
filter(!is.na(X), !is.na(Y),
dplyr::between(X, -h, h))
if (nrow(sub) < 20) return(NULL)
if (!is.finite(stats::sd(sub$X, na.rm = TRUE)) || stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0, na.rm = TRUE) < 5 || sum(sub$X >= 0, na.rm = TRUE) < 5) return(NULL)
sub
}
# ---- Pavia: diff-in-means + rdrobust at h=40 km ----
pavia_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_pavia))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_pavia))) {
for (yr in YEARS) {
dY <- df_pavia %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | PAVIA PROVINCE | h=", H_PAVIA, " km | p=", P, " | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# Difference-in-means within |X|<=40 km (treated - control)
dm <- diff_means_test(d1, h = H_PAVIA, treated_col = "Treated")
if (!is.null(dm)) {
pavia_dm40[[length(pavia_dm40) + 1]] <- dm %>%
mutate(sample = "PAVIA_noFE", outcome = yvar, year = yr)
cat("[Pavia diff-means] h=", H_PAVIA, " km | diff=",
signif(dm$diff_treat_minus_control, 4), " | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Pavia diff-means] Skip: insufficient treated/control data within ±", H_PAVIA, " km.\n", sep = "")
}
# RDROBUST at h=40 km (if it fails, continue)
sub <- make_sub_pavia_h(d1, H_PAVIA)
if (is.null(sub)) {
cat("[Pavia rdrobust] Skip: too little usable data/variation within ±", H_PAVIA, " km.\n", sep = "")
next
}
rb <- safe_rdrobust(sub$Y, sub$X, h = H_PAVIA, p = P,
label = paste0("PAVIA|", yvar, "|Year=", yr, "|h=40"))
if (is.null(rb)) next
print(summary(rb))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = H_PAVIA, sample = "PAVIA_noFE", year = yr, h_type = "H40")
}
next
}
# --- All other outcomes ---
d1 <- collapse_one_row_per_muni(df_pavia, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | PAVIA PROVINCE | h=", H_PAVIA, " km | p=", P, " | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# Difference-in-means within |X|<=40 km (treated - control)
dm <- diff_means_test(d1, h = H_PAVIA, treated_col = "Treated")
if (!is.null(dm)) {
pavia_dm40[[length(pavia_dm40) + 1]] <- dm %>%
mutate(sample = "PAVIA_noFE", outcome = yvar, year = NA_integer_)
cat("[Pavia diff-means] h=", H_PAVIA, " km | diff=",
signif(dm$diff_treat_minus_control, 4), " | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Pavia diff-means] Skip: insufficient treated/control data within ±", H_PAVIA, " km.\n", sep = "")
}
# RDROBUST at h=40 km (if it fails, continue)
sub <- make_sub_pavia_h(d1, H_PAVIA)
if (is.null(sub)) {
cat("[Pavia rdrobust] Skip: too little usable data/variation within ±", H_PAVIA, " km.\n", sep = "")
next
}
rb <- safe_rdrobust(sub$Y, sub$X, h = H_PAVIA, p = P,
label = paste0("PAVIA|", yvar, "|h=40"))
if (is.null(rb)) next
print(summary(rb))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = H_PAVIA, sample = "PAVIA_noFE", year = NA_integer_, h_type = "H40")
}
# Export Pavia diff-means results at 40 km
dm_pavia40 <- dplyr::bind_rows(pavia_dm40)
dm_pavia40_csv <- dm_csv_pavia40
if (nrow(dm_pavia40) > 0) {
readr::write_csv(dm_pavia40, dm_pavia40_csv)
cat("\n[Pavia diff-means] Wrote: ", dm_pavia40_csv, " | rows=", nrow(dm_pavia40), "\n", sep = "")
print(dm_pavia40 %>% dplyr::select(sample, outcome, year, h_km, n_treated, n_control, diff_treat_minus_control, se_diff, p_value) %>% head(10))
} else {
cat("\n[Pavia diff-means] No usable outcomes for diff-means export.\n", sep = "")
}
# close sink explicitly (also covered by on.exit)
sink()
}## Using DF: Pavia province only (COD_REG==3 & COD_PROV==18) | rows=364 | key=istat | yearcol=year
## Running var: distance_treated_positive_x (KM) | h=40 km | p=1 | NO regional FE
##
## Treated/control counts (unique municipalities) in Pavia province:
## # A tibble: 2 × 2
## Treated n_muni
## <int> <int>
## 1 0 132
## 2 1 50
##
## ==============================================================================================================
## Outcome: gb_intensity | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=0.007483 | p=0.02422 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.007 0.006 1.139 0.255 [-0.005 , 0.018]
## Robust - - 1.562 0.118 [-0.004 , 0.039]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: gb_reg_rate | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=-0.04613 | p=0.0003289 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.048 0.025 -1.896 0.058 [-0.097 , 0.002]
## Robust - - -0.038 0.970 [-0.117 , 0.113]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: evasione | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=1.413 | p=0.2435 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.860 2.294 1.683 0.092 [-0.636 , 8.356]
## Robust - - 2.903 0.004 [3.923 , 20.234]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=0.09142 | p=0.3671 | N_t=8 N_c=48
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 56
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 8
## Eff. Number of Obs. 48 8
## 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 8
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.049 0.153 0.319 0.750 [-0.251 , 0.348]
## Robust - - -1.515 0.130 [-1.129 , 0.145]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=1.265 | p=0.009716 | N_t=49 N_c=120
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 169
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 49
## Eff. Number of Obs. 120 49
## 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 49
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.591 1.017 1.564 0.118 [-0.403 , 3.585]
## Robust - - -0.227 0.820 [-5.291 , 4.191]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=-0.8592 | p=0.5044 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.421 2.500 -0.169 0.866 [-5.321 , 4.478]
## Robust - - -0.762 0.446 [-17.608 , 7.751]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=0.02731 | p=0.547 | N_t=24 N_c=80
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 104
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 24
## Eff. Number of Obs. 80 24
## 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 24
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.069 0.045 -1.549 0.121 [-0.157 , 0.018]
## Robust - - -1.448 0.148 [-0.893 , 0.134]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=8.554 | p=0.0005305 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.289 3.887 0.846 0.397 [-4.329 , 10.906]
## Robust - - -0.330 0.742 [-30.497 , 21.711]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: pol_mun_road | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=-10.79 | p=0.1625 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -15.809 12.469 -1.268 0.205 [-40.247 , 8.629]
## Robust - - -2.075 0.038 [-175.602 , -5.002]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=-0.4465 | p=0.703 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.497 2.224 -0.673 0.501 [-5.856 , 2.862]
## Robust - - -0.861 0.389 [-12.741 , 4.966]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=1.87 | p=0.171 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.013 2.624 -0.767 0.443 [-7.156 , 3.131]
## Robust - - -0.954 0.340 [-15.279 , 5.274]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: marr_civil | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=3.415 | p=0.2839 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.503 4.318 0.117 0.907 [-7.960 , 8.966]
## Robust - - -0.835 0.404 [-53.503 , 21.538]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: marr_rel | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=0.7479 | p=0.6457 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.279 2.002 -0.639 0.523 [-5.203 , 2.645]
## Robust - - -1.095 0.274 [-29.922 , 8.478]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: incomepc | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=2461 | p=5.378e-06 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3682.804 1297.291 2.839 0.005 [1140.161 , 6225.447]
## Robust - - 1.402 0.161 [-2659.923 , 16043.871]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: income | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=29040000 | p=0.335 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-26450456.91928950626.151 -0.914 0.361[-83192641.505 , 30291727.667]
## Robust - - -1.318 0.187[-586973410.969 , 114898572.764]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: expend_level | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=-0.5242 | p=0.1928 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.649 0.822 -0.790 0.429 [-2.259 , 0.961]
## Robust - - 0.266 0.790 [-3.034 , 3.987]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: services_level | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=0.8236 | p=0.09342 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.283 1.010 0.280 0.780 [-1.696 , 2.261]
## Robust - - 0.228 0.820 [-4.153 , 5.244]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: expenditure | PAVIA PROVINCE | h=40 km | p=1 | NO region FE
## ==============================================================================================================
## [Pavia diff-means] h=40 km | diff=247800 | p=0.3754 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-303951.854244380.481 -1.244 0.214[-782928.794 , 175025.087]
## Robust - - -1.288 0.198[-5427355.180 , 1122000.182]
## =============================================================================
## NULL
##
## [Pavia diff-means] Wrote: output/diffmeans_Pavia_h40.csv | rows=18
## # 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 PAVIA… gb_int… NA 40 50 132 0.00748 0.00328
## 2 PAVIA… gb_reg… NA 40 50 132 -0.0461 0.0125
## 3 PAVIA… evasio… NA 40 50 132 1.41 1.20
## 4 PAVIA… Admin_… NA 40 8 48 0.0914 0.0961
## 5 PAVIA… edu_se… NA 40 49 120 1.26 0.477
## 6 PAVIA… edu_mu… NA 40 50 132 -0.859 1.28
## 7 PAVIA… edu_em… NA 40 24 80 0.0273 0.0448
## 8 PAVIA… PublS_… NA 40 50 132 8.55 2.33
## 9 PAVIA… pol_mu… NA 40 50 132 -10.8 7.66
## 10 PAVIA… Pillar… 2010 40 50 132 -0.447 1.17
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>results_df <- dplyr::bind_rows(all_results)
# save as CSV (keeps list-columns)
readr::write_csv(results_df, results_csv)
results_df %>%
dplyr::select(sample, outcome, year, h_type, h_km, p, N, N_left, N_right, bw_left, bw_right) %>%
head(20)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.pdflombardia_square_area_x<scale>.csvlombardia_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.txtRD_plots_Pavia_noFE_manualDistance.pdfrdrobust_printout_Pavia_noFE_manualDistance.txtdiffmeans_FullItaly_h40.csvdiffmeans_Lombardia_h40.csvdiffmeans_LombardiaSquare_h40.csvdiffmeans_Pavia_h40.csv