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(30, 40, 50)
# Difference-in-means bandwidth (requested)
H_DM <- 40 # km
P <- 1
OUTCOMES <- c(
"gb_intensity","gb_reg_rate","evasione","services_level", "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","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)
)
# --- Exclude specific comune from *all* estimations (user request) ---
# Tronzano Lago Maggiore (province code 12)
if ("COD_PROV" %in% names(df0)) {
df0 <- df0 %>%
dplyr::filter(!(COMUNE_clean == "TRONZANO LAGO MAGGIORE" & as.integer(.data[["COD_PROV"]]) == 12))
} else {
warning("COD_PROV not found in df0; could not drop Tronzano Lago Maggiore (province code 12).")
}
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 6984 68 34 7 2010, 2020# Optional: inspect which municipalities were overwritten
df0 %>%
filter(.running_overwritten) %>%
distinct(COD_REG, COMUNE, Treated, .running_original, !!sym(RUNNING)) %>%
arrange(COD_REG, COMUNE) %>%
head(25) %>%
print()## # A tibble: 25 × 5
## COD_REG COMUNE Treated .running_original distance_treated_positi…¹
## <int> <chr> <int> <dbl> <dbl>
## 1 3 Albiolo 1 -25.3 28.4
## 2 3 Albuzzano 1 -3.67 3.67
## 3 3 Belgioioso 1 -2.67 2.67
## 4 3 Bereguardo 1 -2.76 2.76
## 5 3 Borgo San Siro 0 5.23 -6.67
## 6 3 Campione d'Italia 1 -22.1 22.1
## 7 3 Ceranova 1 -1.91 10.9
## 8 3 Copiano 1 -2.07 8.31
## 9 3 Cura Carpignano 1 -2.55 6.3
## 10 3 Faloppio 1 -27.3 31.6
## # ℹ 15 more rows
## # ℹ abbreviated name: ¹distance_treated_positive_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_test_regFE <- function(d, h, treated_col = "Treated") {
# Difference in means (treated - control) within |X| <= h,
# controlling for region fixed effects via OLS: Y ~ treated + region FE.
# Returns the coefficient on treated (treated-control adjusted for region FE).
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.region_fe), !is.na(.data[[treated_col]]),
dplyr::between(X, -h, h)) %>%
mutate(.tr = as.integer(.data[[treated_col]]))
if (!all(c(0L, 1L) %in% unique(sub$.tr))) return(NULL)
if (sum(sub$.tr == 1L) < 5 || sum(sub$.tr == 0L) < 5) return(NULL)
fit <- stats::lm(Y ~ .tr + .region_fe, data = sub)
coefs <- summary(fit)$coefficients
if (!(".tr" %in% rownames(coefs))) return(NULL)
tibble::tibble(
h_km = h,
diff_fe = as.numeric(coefs[".tr", "Estimate"]),
se_fe = as.numeric(coefs[".tr", "Std. Error"]),
t_fe = as.numeric(coefs[".tr", "t value"]),
df_fe = as.numeric(stats::df.residual(fit)),
p_fe = as.numeric(coefs[".tr", "Pr(>|t|)"])
)
}
diff_means_sign_test <- function(d) {
# Difference in means (X>=0 - X<0) using Welch two-sample t-test.
# Intended for within-square comparisons where "treated" is defined by the sign of the running variable.
sub <- d %>%
filter(!is.na(X), !is.na(Y)) %>%
mutate(.side = if_else(X >= 0, 1L, 0L))
if (!all(c(0L, 1L) %in% unique(sub$.side))) return(NULL)
y_pos <- sub$Y[sub$.side == 1L] # X >= 0
y_neg <- sub$Y[sub$.side == 0L] # X < 0
n_pos <- sum(sub$.side == 1L)
n_neg <- sum(sub$.side == 0L)
if (n_pos < 5 || n_neg < 5) return(NULL)
m_pos <- mean(y_pos, na.rm = TRUE)
m_neg <- mean(y_neg, na.rm = TRUE)
s_pos <- stats::var(y_pos, na.rm = TRUE)
s_neg <- stats::var(y_neg, na.rm = TRUE)
se <- sqrt(s_pos / n_pos + s_neg / n_neg)
tt <- stats::t.test(Y ~ .side, data = sub) # Welch by default
tibble::tibble(
n_pos = n_pos,
n_neg = n_neg,
mean_pos = m_pos,
mean_neg = m_neg,
diff_pos_minus_neg = m_pos - m_neg,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}# Output files (All Italy / Lombardia / Lombardia-square)
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))
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))
# 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")
# accumulator across samples
all_results <- list()# --- FULL ITALY SECTION ---
sink(results_txt_all, split = TRUE)
cat("Using DF: All_italy_df_merged (post manual distance overwrite) | rows=", nrow(df0),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df0), "year", NA),
"\n", sep = "")## Using DF: All_italy_df_merged (post manual distance overwrite) | rows=6984 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, "\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=30, 40, 50 | p=1pdf(plots_pdf_all, width = 6, height = 4.5)
# Difference-in-means accumulator (Full Italy) at h = 40 km
all_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df0))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df0))) {
for (yr in YEARS) {
dY <- df0 %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means within |X| <= 40 km (Full Italy):
# (i) raw Welch t-test
# (ii) OLS controlling for region FE (Y ~ Treated + region dummies)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dplyr::left_join(dm_out, dm_fe, by = "h_km")
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, t_fe = NA_real_, df_fe = NA_real_, p_fe = NA_real_)
}
all_dm40[[length(all_dm40) + 1]] <- dm_out %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = yr)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar, " | year=", yr,
" | diff=", signif(dm_out$diff_treat_minus_control, 4),
" | p=", signif(dm_out$p_value, 4),
" | diff_FE=", signif(dm_out$diff_fe, 4),
" | p_FE=", signif(dm_out$p_fe, 4),
" | N_t=", dm_out$n_treated, " N_c=", dm_out$n_control, "\n", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = yr, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = yr, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means within |X| <= 40 km (Full Italy):
# (i) raw Welch t-test
# (ii) OLS controlling for region FE (Y ~ Treated + region dummies)
dm <- diff_means_test(d1, h = H_DM)
dm_fe <- diff_means_test_regFE(d1, h = H_DM)
if (!is.null(dm)) {
dm_out <- dm
if (!is.null(dm_fe)) {
dm_out <- dplyr::left_join(dm_out, dm_fe, by = "h_km")
} else {
dm_out <- dm_out %>% mutate(diff_fe = NA_real_, se_fe = NA_real_, t_fe = NA_real_, df_fe = NA_real_, p_fe = NA_real_)
}
all_dm40[[length(all_dm40) + 1]] <- dm_out %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = NA_integer_)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm_out$diff_treat_minus_control, 4),
" | p=", signif(dm_out$p_value, 4),
" | diff_FE=", signif(dm_out$diff_fe, 4),
" | p_FE=", signif(dm_out$p_fe, 4),
" | N_t=", dm_out$n_treated, " N_c=", dm_out$n_control, "\n", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = NA_integer_, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = NA_integer_, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}## [Full Italy diff-means] h=40 km | outcome=gb_intensity | diff=0.004363 | p=0.0001711 | diff_FE=-0.01049 | p_FE=4.784e-09 | N_t=708 N_c=607
##
## ==============================================================================================================
## Outcome: gb_intensity | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=1045 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1045
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 463 582
## Eff. Number of Obs. 463 582
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 463 582
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.685 0.007 [-0.011 , -0.002]
## Robust - - -0.499 0.618 [-0.010 , 0.006]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=1315 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 607 708
## Eff. Number of Obs. 607 708
## 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. 607 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.969 0.003 [-0.010 , -0.002]
## Robust - - -1.396 0.163 [-0.011 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=1595 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1595
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 729 866
## Eff. Number of Obs. 729 866
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 729 866
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.002 -3.726 0.000 [-0.011 , -0.003]
## Robust - - -1.362 0.173 [-0.009 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=3512 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3512
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2214 1298
## Eff. Number of Obs. 392 490
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.454 24.454
## BW bias (b) 44.111 44.111
## rho (h/b) 0.554 0.554
## Unique Obs. 2198 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.003 -2.183 0.029 [-0.011 , -0.001]
## Robust - - -1.553 0.120 [-0.012 , 0.001]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=gb_reg_rate | diff=-0.04128 | p=0.000221 | diff_FE=0.04915 | p_FE=0.005687 | N_t=708 N_c=607
##
## ==============================================================================================================
## Outcome: gb_reg_rate | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=1045 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1045
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 463 582
## Eff. Number of Obs. 463 582
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 463 582
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.041 0.023 1.779 0.075 [-0.004 , 0.087]
## Robust - - 0.310 0.757 [-0.062 , 0.086]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=1315 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 607 708
## Eff. Number of Obs. 607 708
## 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. 607 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.041 0.020 2.036 0.042 [0.002 , 0.081]
## Robust - - 1.177 0.239 [-0.025 , 0.099]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=1595 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1595
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 729 866
## Eff. Number of Obs. 729 866
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 729 866
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.052 0.018 2.864 0.004 [0.016 , 0.087]
## Robust - - 0.895 0.371 [-0.030 , 0.079]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=3512 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3512
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2214 1298
## Eff. Number of Obs. 401 504
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.434 25.434
## BW bias (b) 41.468 41.468
## rho (h/b) 0.613 0.613
## Unique Obs. 2198 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.037 0.025 1.474 0.140 [-0.012 , 0.087]
## Robust - - 1.096 0.273 [-0.027 , 0.097]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=evasione | diff=-2.867 | p=9.524e-11 | diff_FE=-2.595 | p_FE=0.0001435 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: evasione | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.398 0.946 -1.478 0.139 [-3.252 , 0.456]
## Robust - - 0.167 0.867 [-2.955 , 3.505]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.270 0.810 -1.567 0.117 [-2.858 , 0.319]
## Robust - - -0.844 0.399 [-3.692 , 1.470]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.361 0.722 -1.885 0.059 [-2.775 , 0.054]
## Robust - - -0.993 0.321 [-3.366 , 1.103]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2194 1278
## Eff. Number of Obs. 247 328
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 13.803 13.803
## BW bias (b) 52.249 52.249
## rho (h/b) 0.264 0.264
## Unique Obs. 2178 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.478 1.610 0.297 0.766 [-2.677 , 3.634]
## Robust - - 0.284 0.776 [-2.792 , 3.738]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=services_level | diff=0.2648 | p=0.09143 | diff_FE=2.322 | p_FE=8.993e-22 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: services_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.502 0.324 4.634 0.000 [0.867 , 2.138]
## Robust - - 1.732 0.083 [-0.125 , 2.021]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.717 0.279 6.156 0.000 [1.170 , 2.263]
## Robust - - 2.716 0.007 [0.339 , 2.095]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.864 0.251 7.429 0.000 [1.372 , 2.356]
## Robust - - 3.647 0.000 [0.650 , 2.162]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 435 537
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.714 27.714
## BW bias (b) 57.102 57.102
## rho (h/b) 0.485 0.485
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.670 0.339 4.919 0.000 [1.005 , 2.335]
## Robust - - 3.843 0.000 [0.732 , 2.256]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1055 | p=0.1233 | diff_FE=0.1352 | p_FE=0.2248 | N_t=232 N_c=214
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=363 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 363
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 171 192
## Eff. Number of Obs. 171 192
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 171 192
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.070 0.097 0.718 0.473 [-0.121 , 0.261]
## Robust - - 1.714 0.087 [-0.028 , 0.418]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=446 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 446
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 214 232
## Eff. Number of Obs. 214 232
## 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. 214 232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.064 0.059 1.076 0.282 [-0.052 , 0.179]
## Robust - - 0.719 0.472 [-0.162 , 0.351]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=499 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 499
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 233 266
## Eff. Number of Obs. 233 266
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 233 266
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.104 0.051 2.062 0.039 [0.005 , 0.203]
## Robust - - -0.116 0.907 [-0.313 , 0.278]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=926 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 926
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 573 353
## Eff. Number of Obs. 117 118
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.028 17.028
## BW bias (b) 50.516 50.516
## rho (h/b) 0.337 0.337
## Unique Obs. 568 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.149 0.089 1.676 0.094 [-0.025 , 0.323]
## Robust - - 1.250 0.211 [-0.072 , 0.324]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_serv_lvl | diff=0.6066 | p=0.0001692 | diff_FE=1.223 | p_FE=3.377e-06 | N_t=685 N_c=549
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=991 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 991
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 424 567
## Eff. Number of Obs. 424 567
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 424 567
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.900 0.374 2.404 0.016 [0.166 , 1.633]
## Robust - - 0.362 0.718 [-1.053 , 1.530]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=1234 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1234
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 549 685
## Eff. Number of Obs. 549 685
## 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. 549 685
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.300 0.324 4.015 0.000 [0.665 , 1.934]
## Robust - - 0.587 0.557 [-0.714 , 1.324]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=1496 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1496
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 658 838
## Eff. Number of Obs. 658 838
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 658 838
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.539 0.292 5.268 0.000 [0.966 , 2.112]
## Robust - - 1.539 0.124 [-0.187 , 1.551]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=3009 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3009
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1759 1250
## Eff. Number of Obs. 303 405
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 19.408 19.408
## BW bias (b) 43.994 43.994
## rho (h/b) 0.441 0.441
## Unique Obs. 1743 1232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.557 0.490 1.136 0.256 [-0.404 , 1.517]
## Robust - - 0.530 0.596 [-0.796 , 1.387]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=0.7711 | p=0.1048 | diff_FE=2.905 | p_FE=9.371e-05 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.624 0.971 2.701 0.007 [0.720 , 4.528]
## Robust - - 0.243 0.808 [-2.788 , 3.577]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.930 0.846 3.462 0.001 [1.271 , 4.589]
## Robust - - 1.132 0.258 [-1.103 , 4.119]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=1580 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1580
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 721 859
## Eff. Number of Obs. 721 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 721 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.054 0.765 3.992 0.000 [1.555 , 4.554]
## Robust - - 1.917 0.055 [-0.050 , 4.497]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=3183 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3183
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1905 1278
## Eff. Number of Obs. 441 546
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 28.270 28.270
## BW bias (b) 50.396 50.396
## rho (h/b) 0.561 0.561
## Unique Obs. 1889 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.160 1.003 2.154 0.031 [0.194 , 4.125]
## Robust - - 1.586 0.113 [-0.453 , 4.291]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_emp_per1000 | diff=-0.01374 | p=0.5075 | diff_FE=0.05362 | p_FE=0.07314 | N_t=359 N_c=355
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=568 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 568
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 275 293
## Eff. Number of Obs. 275 293
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 275 293
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.045 0.045 0.998 0.318 [-0.043 , 0.132]
## Robust - - -1.039 0.299 [-0.187 , 0.057]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=714 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 714
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 355 359
## Eff. Number of Obs. 355 359
## 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. 355 359
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.069 0.038 1.798 0.072 [-0.006 , 0.145]
## Robust - - -0.177 0.860 [-0.125 , 0.104]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=849 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 849
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 431 418
## Eff. Number of Obs. 431 418
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 431 418
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.081 0.035 2.305 0.021 [0.012 , 0.150]
## Robust - - 0.358 0.720 [-0.088 , 0.127]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=1709 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1709
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1089 620
## Eff. Number of Obs. 184 206
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.020 18.020
## BW bias (b) 36.084 36.084
## rho (h/b) 0.499 0.499
## Unique Obs. 1085 613
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.035 0.053 -0.658 0.510 [-0.138 , 0.068]
## Robust - - -1.091 0.275 [-0.188 , 0.054]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=5.137 | p=1.388e-15 | diff_FE=6.071 | p_FE=4.831e-09 | N_t=694 N_c=598
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=1028 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1028
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 456 572
## Eff. Number of Obs. 456 572
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 456 572
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.704 1.439 3.964 0.000 [2.884 , 8.525]
## Robust - - 1.940 0.052 [-0.054 , 10.594]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=1292 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1292
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 598 694
## Eff. Number of Obs. 598 694
## 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. 598 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.851 1.261 4.642 0.000 [3.381 , 8.322]
## Robust - - 2.640 0.008 [1.411 , 9.545]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=1568 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1568
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 718 850
## Eff. Number of Obs. 718 850
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 718 850
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.022 1.157 5.206 0.000 [3.755 , 8.289]
## Robust - - 3.383 0.001 [2.432 , 9.130]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=3151 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3151
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1885 1266
## Eff. Number of Obs. 486 591
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 31.527 31.527
## BW bias (b) 54.363 54.363
## rho (h/b) 0.580 0.580
## Unique Obs. 1869 1247
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.724 1.395 4.103 0.000 [2.989 , 8.459]
## Robust - - 3.424 0.001 [2.449 , 9.006]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=pol_mun_road | diff=-30.58 | p=7.577e-06 | diff_FE=11.52 | p_FE=0.2444 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: pol_mun_road | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.081 9.150 0.774 0.439 [-10.853 , 25.015]
## Robust - - -0.464 0.642 [-31.392 , 19.364]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.452 7.829 1.591 0.112 [-2.892 , 27.796]
## Robust - - -0.250 0.803 [-27.868 , 21.568]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 15.079 7.286 2.070 0.038 [0.799 , 29.360]
## Robust - - 0.347 0.729 [-18.150 , 25.961]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 397 496
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.250 25.250
## BW bias (b) 52.146 52.146
## rho (h/b) 0.484 0.484
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -24.429 9.646 -2.533 0.011 [-43.335 , -5.523]
## Robust - - -2.589 0.010 [-54.234 , -7.503]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=1.099 | p=0.01216 | diff_FE=1.672 | p_FE=0.01458 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.360 0.995 -0.362 0.718 [-2.311 , 1.591]
## Robust - - -1.345 0.179 [-5.549 , 1.033]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.213 0.857 0.249 0.803 [-1.466 , 1.893]
## Robust - - -1.009 0.313 [-4.066 , 1.303]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.584 0.769 0.759 0.448 [-0.924 , 2.092]
## Robust - - -0.730 0.465 [-3.176 , 1.451]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2194 1278
## Eff. Number of Obs. 319 402
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.792 18.792
## BW bias (b) 34.996 34.996
## rho (h/b) 0.537 0.537
## Unique Obs. 2178 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.560 1.307 -1.194 0.232 [-4.122 , 1.001]
## Robust - - -1.445 0.148 [-5.442 , 0.823]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=3.125 | p=2.664e-09 | diff_FE=4.311 | p_FE=9.961e-08 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.978 1.142 0.856 0.392 [-1.262 , 3.217]
## Robust - - -0.159 0.873 [-4.088 , 3.473]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.815 0.970 1.870 0.061 [-0.087 , 3.717]
## Robust - - -0.135 0.893 [-3.316 , 2.889]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.338 0.863 2.708 0.007 [0.646 , 4.029]
## Robust - - 0.354 0.723 [-2.188 , 3.152]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2194 1278
## Eff. Number of Obs. 441 546
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 28.278 28.278
## BW bias (b) 55.745 55.745
## rho (h/b) 0.507 0.507
## Unique Obs. 2178 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.065 1.199 -0.054 0.957 [-2.415 , 2.286]
## Robust - - -0.417 0.676 [-3.309 , 2.147]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_civil | diff=3.3 | p=0.3724 | diff_FE=8.114 | p_FE=0.1956 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: marr_civil | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.935 4.466 0.209 0.834 [-7.817 , 9.688]
## Robust - - -0.054 0.957 [-8.293 , 7.851]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.630 2.557 1.811 0.070 [-0.381 , 9.642]
## Robust - - -0.494 0.621 [-17.335 , 10.356]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.362 2.168 2.935 0.003 [2.113 , 10.611]
## Robust - - -0.033 0.974 [-11.982 , 11.584]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 313 394
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.169 18.169
## BW bias (b) 46.499 46.499
## rho (h/b) 0.391 0.391
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.172 2.884 0.753 0.451 [-3.481 , 7.826]
## Robust - - 0.209 0.834 [-6.143 , 7.612]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_rel | diff=1.959 | p=0.1032 | diff_FE=3.858 | p_FE=0.05621 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: marr_rel | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.466 1.726 -0.270 0.787 [-3.848 , 2.917]
## Robust - - -1.154 0.248 [-7.111 , 1.840]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.130 1.193 0.947 0.344 [-1.208 , 3.467]
## Robust - - -1.142 0.253 [-8.094 , 2.134]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.023 1.054 1.919 0.055 [-0.043 , 4.088]
## Robust - - -0.636 0.525 [-5.763 , 2.941]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 343 426
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.634 20.634
## BW bias (b) 50.608 50.608
## rho (h/b) 0.408 0.408
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.253 1.541 -0.164 0.869 [-3.273 , 2.767]
## Robust - - -0.579 0.562 [-4.499 , 2.447]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=incomepc | diff=1180 | p=1.396e-11 | diff_FE=1777 | p_FE=3.574e-10 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: incomepc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1336.554 370.108 3.611 0.000 [611.156 , 2061.953]
## Robust - - 0.262 0.793 [-1153.677 , 1510.074]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1641.987 322.474 5.092 0.000 [1009.950 , 2274.024]
## Robust - - 1.276 0.202 [-358.759 , 1696.667]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1767.131 291.458 6.063 0.000 [1195.884 , 2338.378]
## Robust - - 2.605 0.009 [285.253 , 2019.801]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 343 426
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.622 20.622
## BW bias (b) 45.226 45.226
## rho (h/b) 0.456 0.456
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 829.953 470.276 1.765 0.078 [-91.772 , 1751.677]
## Robust - - 1.118 0.264 [-454.011 , 1659.753]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=income | diff=55690000 | p=0.2694 | diff_FE=101300000 | p_FE=0.2427 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: income | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-20111931.52059333139.814 -0.339 0.735[-136402748.646 , 96178885.606]
## Robust - - -0.927 0.354[-114885670.601 , 41117169.917]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional37157819.16227424077.798 1.355 0.175[-16592385.632 , 90908023.956]
## Robust - - -0.929 0.353[-276242165.414 , 98643160.190]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional67693302.41022613263.074 2.994 0.003[23372121.213 , 112014483.607]
## Robust - - -0.524 0.600[-200309985.933 , 115794515.407]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 275 350
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 15.678 15.678
## BW bias (b) 42.352 42.352
## rho (h/b) 0.370 0.370
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional4402065.82529614467.657 0.149 0.882[-53641224.204 , 62445355.854]
## Robust - - -0.563 0.574[-95914988.068 , 53134345.366]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expend_level | diff=0.3745 | p=0.004514 | diff_FE=0.666 | p_FE=0.001511 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: expend_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.403 0.307 1.311 0.190 [-0.199 , 1.005]
## Robust - - 0.180 0.857 [-0.960 , 1.153]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.510 0.261 1.951 0.051 [-0.002 , 1.022]
## Robust - - 0.586 0.558 [-0.592 , 1.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.590 0.234 2.518 0.012 [0.131 , 1.049]
## Robust - - 0.917 0.359 [-0.380 , 1.049]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=3187 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3187
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1909 1278
## Eff. Number of Obs. 464 586
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.453 30.453
## BW bias (b) 59.733 59.733
## rho (h/b) 0.510 0.510
## Unique Obs. 1893 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.358 0.304 1.176 0.240 [-0.239 , 0.955]
## Robust - - 1.262 0.207 [-0.247 , 1.139]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expenditure | diff=309000 | p=0.535 | diff_FE=918900 | p_FE=0.2732 | N_t=702 N_c=601
##
## ==============================================================================================================
## Outcome: expenditure | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=1037 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1037
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 459 578
## Eff. Number of Obs. 459 578
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 459 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-36395.620545081.960 -0.067 0.947[-1104736.629 , 1031945.389]
## Robust - - -0.539 0.590[-998169.501 , 567758.205]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=1303 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 601 702
## Eff. Number of Obs. 601 702
## 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. 601 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional502095.497309616.297 1.622 0.105[-104741.293 , 1108932.288]
## Robust - - -0.729 0.466[-2371163.128 , 1085119.680]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=1581 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1581
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 722 859
## Eff. Number of Obs. 722 859
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 722 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional723886.004245333.280 2.951 0.003[243041.611 , 1204730.398]
## Robust - - -0.183 0.855[-1623781.665 , 1346749.665]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=3472 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3472
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2194 1278
## Eff. Number of Obs. 306 378
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.381 17.381
## BW bias (b) 46.504 46.504
## rho (h/b) 0.374 0.374
## Unique Obs. 2178 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 63453.103263802.004 0.241 0.810[-453589.324 , 580495.530]
## Robust - - -0.363 0.717[-794991.520 , 546530.498]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2# Export Full-Italy diff-means results at 40 km
dm_all40 <- dplyr::bind_rows(all_dm40)
if (nrow(dm_all40) > 0) {
readr::write_csv(dm_all40, dm_csv_all40)
cat("
[Full Italy diff-means] Wrote: ", dm_csv_all40, " | rows=", nrow(dm_all40), "
", sep = "")
print(dm_all40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, p_value,
diff_fe, se_fe, p_fe) %>%
head(10))
} else {
cat("
[Full Italy diff-means] No usable data within ±40 km for any outcome; skipping export.
", sep = "")
}##
## [Full Italy diff-means] Wrote: output/diffmeans_FullItaly_h40.csv | rows=18
## # A tibble: 10 × 12
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 FULL_… gb_int… NA 40 708 607 0.00436 0.00116
## 2 FULL_… gb_reg… NA 40 708 607 -0.0413 0.0111
## 3 FULL_… evasio… NA 40 702 601 -2.87 0.438
## 4 FULL_… servic… NA 40 702 601 0.265 0.157
## 5 FULL_… Admin_… NA 40 232 214 0.105 0.0682
## 6 FULL_… edu_se… NA 40 685 549 0.607 0.161
## 7 FULL_… edu_mu… NA 40 702 601 0.771 0.475
## 8 FULL_… edu_em… NA 40 359 355 -0.0137 0.0207
## 9 FULL_… PublS_… NA 40 694 598 5.14 0.635
## 10 FULL_… pol_mu… NA 40 702 601 -30.6 6.80
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 4 more variables: p_value <dbl>, diff_fe <dbl>, se_fe <dbl>, p_fe <dbl>sink()df_lombardia <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
# --- LIST: Lombardia control-side municipalities (distance < 0) ---
# pick name column robustly
NAMECOL <- if ("COMUNE" %in% names(df_lombardia)) "COMUNE" else stop("COMUNE column not found in df_lombardia")
lomb_control_muni <- df_lombardia %>%
mutate(X = as.numeric(.data[[RUNNING]])) %>%
filter(!is.na(.data[[KEYCOL]]), !is.na(X), !is.na(.data[[NAMECOL]])) %>%
group_by(.data[[KEYCOL]]) %>%
summarise(
COMUNE = dplyr::first(.data[[NAMECOL]]),
X_km = mean(X, na.rm = TRUE), # one distance per municipality
Treated = dplyr::first(as.integer(Treated)),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(df_lombardia)) as.integer(COD_PROV) else NA_integer_),
.groups = "drop"
) %>%
filter(X_km < 0) %>%
arrange(X_km, COMUNE)
cat("\n=== Lombardia (ireg==3): CONTROL side municipalities (X < 0) ===\n")##
## === Lombardia (ireg==3): CONTROL side municipalities (X < 0) ===cat("Count (unique comuni): ", nrow(lomb_control_muni), "\n", sep = "")## Count (unique comuni): 132cat("[Suppressed] Municipality name list omitted (Lombardia control side).
")## [Suppressed] Municipality name list omitted (Lombardia control side).# optional export
lomb_control_out <- file.path(OUTDIR, "lombardia_control_municipalities_distance_lt_0.csv")
readr::write_csv(lomb_control_muni, lomb_control_out)
cat("Wrote: ", lomb_control_out, "\n", sep = "")## Wrote: output/lombardia_control_municipalities_distance_lt_0.csvsink(results_txt_lomb, split = TRUE)
cat("Using DF: Lombardia only (ireg==3) | rows=", nrow(df_lombardia),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_lombardia), "year", NA),
"\n", sep = "")## Using DF: Lombardia only (ireg==3) | rows=2812 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=30, 40, 50 | p=1 | NO regional FEpdf(plots_pdf_lomb, width = 6, height = 4.5)
# Difference-in-means accumulator (Lombardia) at h = 40 km
lomb_dm40 <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lombardia))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_lombardia))) {
for (yr in YEARS) {
dY <- df_lombardia %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Lombardia)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
lomb_dm40[[length(lomb_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_noFE", outcome = yvar, year = yr)
cat("[Lombardia diff-means] h=", H_DM, " km | outcome=", yvar, " | year=", yr,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Lombardia diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | LOMBARDIA ONLY | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_noFE", year = yr, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_noFE", year = yr, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df_lombardia, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Lombardia)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
lomb_dm40[[length(lomb_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_noFE", outcome = yvar, year = NA_integer_)
cat("[Lombardia diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Lombardia diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "\n", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | LOMBARDIA ONLY | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_noFE", year = NA_integer_, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_noFE", year = NA_integer_, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}## [Lombardia diff-means] h=40 km | outcome=gb_intensity | diff=-0.01208 | p=2.724e-07 | N_t=694 N_c=132
##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=699 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 699
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 568
## Eff. Number of Obs. 131 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.008 0.004 -2.011 0.044 [-0.015 , -0.000]
## Robust - - 0.792 0.429 [-0.008 , 0.019]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=826 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 826
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 694
## Eff. Number of Obs. 132 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.010 0.004 -2.711 0.007 [-0.016 , -0.003]
## Robust - - 0.567 0.571 [-0.009 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=984 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 984
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 852
## Eff. Number of Obs. 132 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.012 0.003 -3.418 0.001 [-0.019 , -0.005]
## Robust - - 0.796 0.426 [-0.007 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=1416 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1416
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1284
## Eff. Number of Obs. 26 133
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.633 5.633
## BW bias (b) 12.285 12.285
## rho (h/b) 0.459 0.459
## Unique Obs. 129 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.049 0.012 4.234 0.000 [0.026 , 0.072]
## Robust - - 3.893 0.000 [0.028 , 0.085]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=gb_reg_rate | diff=0.06671 | p=1.486e-08 | N_t=694 N_c=132
##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=699 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 699
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 568
## Eff. Number of Obs. 131 568
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.066 0.025 2.693 0.007 [0.018 , 0.115]
## Robust - - 1.375 0.169 [-0.023 , 0.131]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=826 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 826
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 694
## Eff. Number of Obs. 132 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.064 0.022 2.856 0.004 [0.020 , 0.108]
## Robust - - 2.317 0.020 [0.012 , 0.149]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=984 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 984
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 852
## Eff. Number of Obs. 132 852
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.071 0.021 3.380 0.001 [0.030 , 0.113]
## Robust - - 2.461 0.014 [0.016 , 0.144]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=1416 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1416
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1284
## Eff. Number of Obs. 51 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.506 8.506
## BW bias (b) 17.131 17.131
## rho (h/b) 0.497 0.497
## Unique Obs. 129 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.023 0.052 0.431 0.666 [-0.080 , 0.125]
## Robust - - 0.035 0.972 [-0.128 , 0.133]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=evasione | diff=-2.741 | p=0.0003199 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.091 1.487 -0.734 0.463 [-4.006 , 1.823]
## Robust - - 0.751 0.452 [-2.892 , 6.488]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.512 1.425 -1.061 0.289 [-4.304 , 1.281]
## Robust - - -0.031 0.975 [-4.277 , 4.144]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.970 1.404 -1.403 0.161 [-4.722 , 0.782]
## Robust - - -0.511 0.609 [-5.147 , 3.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 25 128
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.479 5.479
## BW bias (b) 12.061 12.061
## rho (h/b) 0.454 0.454
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.918 5.172 1.144 0.252 [-4.218 , 16.055]
## Robust - - 1.312 0.189 [-4.061 , 20.522]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=services_level | diff=2.492 | p=2.681e-16 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.383 0.621 2.228 0.026 [0.167 , 2.600]
## Robust - - 0.966 0.334 [-1.096 , 3.225]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.469 0.570 2.578 0.010 [0.352 , 2.586]
## Robust - - 1.093 0.274 [-0.859 , 3.023]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.531 0.551 2.778 0.005 [0.451 , 2.612]
## Robust - - 1.162 0.245 [-0.767 , 3.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 160
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.827 6.827
## BW bias (b) 13.997 13.997
## rho (h/b) 0.488 0.488
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.559 2.270 1.127 0.260 [-1.890 , 7.007]
## Robust - - 0.908 0.364 [-3.083 , 8.406]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1416 | p=0.0586 | N_t=226 N_c=48
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=234 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 234
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 186
## Eff. Number of Obs. 48 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.056 0.102 0.550 0.583 [-0.144 , 0.255]
## Robust - - 0.614 0.539 [-0.163 , 0.312]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=274 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 274
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 226
## Eff. Number of Obs. 48 226
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 226
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.102 0.075 1.359 0.174 [-0.045 , 0.250]
## Robust - - -0.347 0.729 [-0.352 , 0.246]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=308 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 308
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 260
## Eff. Number of Obs. 48 260
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 260
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.138 0.068 2.025 0.043 [0.004 , 0.271]
## Robust - - -0.474 0.635 [-0.384 , 0.234]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=395 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 395
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 347
## Eff. Number of Obs. 17 38
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.701 6.701
## BW bias (b) 12.013 12.013
## rho (h/b) 0.558 0.558
## Unique Obs. 48 346
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.126 0.192 0.655 0.512 [-0.250 , 0.502]
## Robust - - 0.678 0.498 [-0.325 , 0.667]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_serv_lvl | diff=1.401 | p=1.978e-07 | N_t=671 N_c=120
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=672 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 672
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 553
## Eff. Number of Obs. 119 553
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 553
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.746 0.513 1.454 0.146 [-0.260 , 1.752]
## Robust - - 0.031 0.976 [-1.717 , 1.772]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=791 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 791
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 671
## Eff. Number of Obs. 120 671
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 671
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.049 0.476 2.203 0.028 [0.116 , 1.982]
## Robust - - 0.147 0.883 [-1.424 , 1.655]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=944 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 944
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 824
## Eff. Number of Obs. 120 824
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 824
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.211 0.461 2.625 0.009 [0.307 , 2.115]
## Robust - - 0.548 0.584 [-1.062 , 1.886]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=1356 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1356
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 1236
## Eff. Number of Obs. 42 192
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.354 8.354
## BW bias (b) 16.699 16.699
## rho (h/b) 0.500 0.500
## Unique Obs. 117 1221
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.927 1.348 0.688 0.492 [-1.715 , 3.570]
## Robust - - 0.669 0.504 [-2.192 , 4.463]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=3.213 | p=0.0001319 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.758 1.661 2.262 0.024 [0.502 , 7.013]
## Robust - - 0.092 0.927 [-5.783 , 6.354]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.435 1.527 2.905 0.004 [1.442 , 7.427]
## Robust - - 0.673 0.501 [-3.575 , 7.314]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.722 1.482 3.187 0.001 [1.818 , 7.626]
## Robust - - 1.176 0.239 [-2.118 , 8.480]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 27 133
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.721 5.721
## BW bias (b) 12.498 12.498
## rho (h/b) 0.458 0.458
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.612 8.238 0.074 0.941 [-15.534 , 16.757]
## Robust - - -0.201 0.841 [-21.337 , 17.375]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_emp_per1000 | diff=0.06313 | p=0.0003043 | N_t=351 N_c=80
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=365 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 365
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 285
## Eff. Number of Obs. 80 285
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 285
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.009 0.053 -0.174 0.862 [-0.113 , 0.095]
## Robust - - -1.221 0.222 [-0.299 , 0.069]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=431 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 431
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 351
## Eff. Number of Obs. 80 351
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.019 0.048 0.409 0.683 [-0.074 , 0.113]
## Robust - - -1.042 0.297 [-0.254 , 0.078]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=490 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 490
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 410
## Eff. Number of Obs. 80 410
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 410
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.035 0.046 0.764 0.445 [-0.055 , 0.125]
## Robust - - -0.777 0.437 [-0.223 , 0.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=692 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 692
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 612
## Eff. Number of Obs. 32 110
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.411 9.411
## BW bias (b) 15.473 15.473
## rho (h/b) 0.608 0.608
## Unique Obs. 79 606
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.122 0.111 -1.098 0.272 [-0.340 , 0.096]
## Robust - - -1.074 0.283 [-0.435 , 0.127]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=6.721 | p=1.202e-16 | N_t=680 N_c=132
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=689 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 689
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 558
## Eff. Number of Obs. 131 558
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.257 2.606 1.633 0.102 [-0.852 , 9.365]
## Robust - - -0.127 0.899 [-9.811 , 8.621]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=812 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 812
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 680
## Eff. Number of Obs. 132 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.109 2.321 2.202 0.028 [0.561 , 9.657]
## Robust - - 0.187 0.851 [-7.343 , 8.896]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=968 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 968
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 836
## Eff. Number of Obs. 132 836
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.489 2.197 2.498 0.012 [1.182 , 9.795]
## Robust - - 0.421 0.674 [-6.044 , 9.346]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=1384 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1384
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1252
## Eff. Number of Obs. 61 252
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.787 10.787
## BW bias (b) 17.913 17.913
## rho (h/b) 0.602 0.602
## Unique Obs. 129 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.728 5.318 -0.137 0.891 [-11.151 , 9.694]
## Robust - - -0.342 0.732 [-15.433 , 10.842]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=pol_mun_road | diff=12.91 | p=0.02747 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.302 13.873 -0.310 0.756 [-31.492 , 22.887]
## Robust - - -1.835 0.067 [-90.842 , 3.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.025 12.200 0.494 0.621 [-17.887 , 29.937]
## Robust - - -1.711 0.087 [-81.147 , 5.502]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 11.460 11.751 0.975 0.329 [-11.572 , 34.493]
## Robust - - -1.481 0.139 [-72.617 , 10.105]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 45 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.953 7.953
## BW bias (b) 12.130 12.130
## rho (h/b) 0.656 0.656
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -43.609 29.314 -1.488 0.137 [-101.064 , 13.846]
## Robust - - -1.502 0.133 [-126.689 , 16.744]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=2.055 | p=0.004121 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.162 1.587 -0.102 0.919 [-3.273 , 2.949]
## Robust - - -1.272 0.203 [-8.102 , 1.724]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.402 1.483 0.271 0.786 [-2.505 , 3.309]
## Robust - - -0.950 0.342 [-6.577 , 2.281]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.629 1.441 0.437 0.662 [-2.194 , 3.453]
## Robust - - -0.729 0.466 [-5.889 , 2.697]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 167
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.137 7.137
## BW bias (b) 14.500 14.500
## rho (h/b) 0.492 0.492
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.189 4.403 -0.270 0.787 [-9.820 , 7.441]
## Robust - - -0.264 0.792 [-12.941 , 9.873]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=4.756 | p=4.897e-08 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.969 1.745 0.555 0.579 [-2.451 , 4.389]
## Robust - - -0.116 0.908 [-5.757 , 5.116]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.822 1.658 1.099 0.272 [-1.427 , 5.070]
## Robust - - -0.239 0.811 [-5.533 , 4.332]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.270 1.624 1.397 0.162 [-0.914 , 5.453]
## Robust - - -0.074 0.941 [-4.983 , 4.620]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 42 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.962 6.962
## BW bias (b) 14.101 14.101
## rho (h/b) 0.494 0.494
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.761 4.827 0.572 0.567 [-6.699 , 12.222]
## Robust - - 0.478 0.633 [-9.473 , 15.586]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_civil | diff=9.387 | p=0.007798 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.030 5.177 -0.392 0.695 [-12.176 , 8.117]
## Robust - - -1.181 0.238 [-20.648 , 5.121]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.930 3.324 0.581 0.562 [-4.585 , 8.445]
## Robust - - -1.199 0.231 [-26.655 , 6.420]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.830 3.124 1.546 0.122 [-1.294 , 10.953]
## Robust - - -1.096 0.273 [-22.874 , 6.469]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 31 140
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.175 6.175
## BW bias (b) 10.511 10.511
## rho (h/b) 0.587 0.587
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.220 5.834 1.580 0.114 [-2.215 , 20.655]
## Robust - - 1.892 0.059 [-0.544 , 30.781]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_rel | diff=4.746 | p=0.0001261 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.522 2.395 -0.218 0.827 [-5.216 , 4.171]
## Robust - - -1.409 0.159 [-13.141 , 2.148]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.264 1.912 0.661 0.509 [-2.484 , 5.011]
## Robust - - -1.283 0.199 [-12.770 , 2.664]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.439 1.820 1.340 0.180 [-1.129 , 6.006]
## Robust - - -1.013 0.311 [-10.929 , 3.483]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 54 214
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.990 8.990
## BW bias (b) 15.465 15.465
## rho (h/b) 0.581 0.581
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -5.729 4.861 -1.179 0.239 [-15.256 , 3.798]
## Robust - - -1.196 0.232 [-19.492 , 4.715]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=incomepc | diff=2057 | p=6.337e-17 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2069.766 502.824 4.116 0.000 [1084.250 , 3055.282]
## Robust - - 0.489 0.625 [-1300.929 , 2165.776]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2242.528 463.632 4.837 0.000 [1333.826 , 3151.231]
## Robust - - 1.692 0.091 [-204.071 , 2781.606]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2264.596 446.058 5.077 0.000 [1390.338 , 3138.855]
## Robust - - 2.378 0.017 [301.705 , 3128.437]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 37 146
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.359 6.359
## BW bias (b) 14.195 14.195
## rho (h/b) 0.448 0.448
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5866.597 2668.545 2.198 0.028 [636.345 , 11096.849]
## Robust - - 2.015 0.044 [173.182 , 12591.286]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=income | diff=116200000 | p=0.01815 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: income | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-54634900.59763118994.341 -0.866 0.387[-178345856.245 , 69076055.052]
## Robust - - -2.078 0.038[-229386511.964 , -6684876.697]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional6274501.31231383630.427 0.200 0.842[-55236284.030 , 67785286.654]
## Robust - - -1.557 0.119[-360907701.698 , 41318881.510]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional49398800.15029014936.088 1.703 0.089[-7469429.597 , 106267029.896]
## Robust - - -1.439 0.150[-298748104.659 , 45773473.771]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 47 194
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.295 8.295
## BW bias (b) 12.415 12.415
## rho (h/b) 0.668 0.668
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-81627087.40064825227.005 -1.259 0.208[-208682197.619 , 45428022.820]
## Robust - - -1.141 0.254[-255907649.373 , 67584919.999]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expend_level | diff=0.7444 | p=0.00238 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.432 0.533 0.810 0.418 [-0.613 , 1.478]
## Robust - - 0.744 0.457 [-1.114 , 2.478]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.394 0.495 0.797 0.426 [-0.575 , 1.363]
## Robust - - 0.933 0.351 [-0.834 , 2.348]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.433 0.480 0.902 0.367 [-0.507 , 1.373]
## Robust - - 0.934 0.350 [-0.800 , 2.257]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 55 220
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.483 9.483
## BW bias (b) 18.870 18.870
## rho (h/b) 0.503 0.503
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.924 1.188 0.777 0.437 [-1.405 , 3.253]
## Robust - - 0.734 0.463 [-1.850 , 4.066]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expenditure | diff=1072000 | p=0.01563 | N_t=688 N_c=132
##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=695 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 695
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 564
## Eff. Number of Obs. 131 564
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-441090.599562715.756 -0.784 0.433[-1543993.215 , 661812.017]
## Robust - - -1.917 0.055[-1905686.366 , 21211.531]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=820 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 820
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 688
## Eff. Number of Obs. 132 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 77434.050271158.180 0.286 0.775[-454026.216 , 608894.317]
## Robust - - -1.411 0.158[-3093908.706 , 504301.089]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=977 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 977
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 845
## Eff. Number of Obs. 132 845
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional462535.560249037.393 1.857 0.063[-25568.761 , 950639.880]
## Robust - - -1.305 0.192[-2559444.722 , 513200.363]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=1396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 1264
## Eff. Number of Obs. 21 118
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.170 5.170
## BW bias (b) 9.340 9.340
## rho (h/b) 0.554 0.554
## Unique Obs. 129 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional1079991.984717943.484 1.504 0.133[-327151.387 , 2487135.355]
## Robust - - 1.497 0.134[-466829.974 , 3485346.116]
## =============================================================================
## 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 40 694 132 -0.0121 0.00226
## 2 LOMBA… gb_reg… NA 40 694 132 0.0667 0.0115
## 3 LOMBA… evasio… NA 40 688 132 -2.74 0.746
## 4 LOMBA… servic… NA 40 688 132 2.49 0.274
## 5 LOMBA… Admin_… NA 40 226 48 0.142 0.0746
## 6 LOMBA… edu_se… NA 40 671 120 1.40 0.259
## 7 LOMBA… edu_mu… NA 40 688 132 3.21 0.821
## 8 LOMBA… edu_em… NA 40 351 80 0.0631 0.0173
## 9 LOMBA… PublS_… NA 40 680 132 6.72 0.767
## 10 LOMBA… pol_mu… NA 40 688 132 12.9 5.84
## # 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$poly)
df_lomb_square <- lomb_sf_utm %>%
mutate(in_expanded_square = in_sq) %>%
filter(in_expanded_square) %>%
st_drop_geometry()
# --- LIST: Lombardia-square control-side municipalities (distance < 0) ---
NAMECOL_SQ <- if ("COMUNE" %in% names(df_lomb_square)) "COMUNE" else stop("COMUNE column not found in df_lomb_square")
sq_control_muni <- df_lomb_square %>%
mutate(X = as.numeric(.data[[RUNNING]])) %>%
filter(!is.na(.data[[KEYCOL]]), !is.na(X), !is.na(.data[[NAMECOL_SQ]])) %>%
group_by(.data[[KEYCOL]]) %>%
summarise(
COMUNE = dplyr::first(.data[[NAMECOL_SQ]]),
X_km = mean(X, na.rm = TRUE),
Treated = dplyr::first(as.integer(Treated)),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(df_lomb_square)) as.integer(COD_PROV) else NA_integer_),
.groups = "drop"
) %>%
filter(X_km < 0) %>%
arrange(X_km, COMUNE)
cat("\n=== Lombardia SQUARE: CONTROL side municipalities (X < 0) ===\n")##
## === Lombardia SQUARE: CONTROL side municipalities (X < 0) ===cat("Count (unique comuni): ", nrow(sq_control_muni), "\n", sep = "")## Count (unique comuni): 132cat("[Suppressed] Municipality name list omitted (Lombardia square control side).
")## [Suppressed] Municipality name list omitted (Lombardia square control side).# optional export
sq_control_out <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_control_municipalities_distance_lt_0.csv", TARGET_AREA_SCALE))
readr::write_csv(sq_control_muni, sq_control_out)
cat("Wrote: ", sq_control_out, "\n", sep = "")## Wrote: output/lombardia_square_area_x1.25_control_municipalities_distance_lt_0.csv# 6) Write square dataset + metadata
square_out_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f.csv", TARGET_AREA_SCALE))
square_meta_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_metadata.csv", TARGET_AREA_SCALE))
readr::write_csv(df_lomb_square, square_out_file)
meta <- tibble::tibble(
baseline_n = nrow(base),
expanded_n = nrow(df_lomb_square),
target_area_scale = TARGET_AREA_SCALE,
side_multiplier = sq$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=30, 40, 50 | p=1 | NO regional FEpdf(plots_pdf_square, width = 6, height = 4.5)
# Difference-in-means accumulator (Square sample only) at h = 40 km
sq_dm40 <- list()
# Difference-in-means accumulator (Square sample only): sign-based split (X>=0 vs X<0), no bandwidth trim
sq_sign_dm <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lomb_square))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_lomb_square))) {
for (yr in YEARS) {
dY <- df_lomb_square %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Square sample only)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
sq_dm40[[length(sq_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = yr)
}
# Difference in means by sign (X>=0 - X<0) within square (no bandwidth trim)
dm_sign <- diff_means_sign_test(d1)
if (!is.null(dm_sign)) {
sq_sign_dm[[length(sq_sign_dm) + 1]] <- dm_sign %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = yr)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | LOMBARDIA SQUARE | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia-square | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE", year = yr, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE", year = yr, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | Lombardia-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df_lomb_square, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Square sample only)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
sq_dm40[[length(sq_dm40) + 1]] <- dm %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = NA_integer_)
}
# Difference in means by sign (X>=0 - X<0) within square (no bandwidth trim)
dm_sign <- diff_means_sign_test(d1)
if (!is.null(dm_sign)) {
sq_sign_dm[[length(sq_sign_dm) + 1]] <- dm_sign %>%
mutate(sample = "LOMBARDIA_SQUARE_noFE", outcome = yvar, year = NA_integer_)
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | LOMBARDIA SQUARE | p=", P, " | X in KM | NO region FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# RD plots (raw only) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia-square | raw | h=", h, " km"))
}
# RD tables (MANUAL bandwidths)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE", year = NA_integer_, h_type = "MANUAL")
}
# RD table (AUTO bandwidth)
sub_full <- make_sub_full_noFE(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | NO region FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE", year = NA_integer_, h_type = "AUTO")
# Optional plot using h_plot = max(bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub_noFE(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Lombardia-square | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
}
}
}
}##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.004 -1.523 0.128 [-0.015 , 0.002]
## Robust - - 1.983 0.047 [0.000 , 0.030]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.011 0.004 -2.786 0.005 [-0.019 , -0.003]
## Robust - - 1.673 0.094 [-0.002 , 0.025]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.013 0.004 -3.317 0.001 [-0.021 , -0.005]
## Robust - - 1.552 0.121 [-0.003 , 0.024]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 18 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.655 4.655
## BW bias (b) 10.989 10.989
## rho (h/b) 0.424 0.424
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.057 0.020 2.921 0.003 [0.019 , 0.096]
## Robust - - 2.935 0.003 [0.022 , 0.108]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.118 0.034 3.448 0.001 [0.051 , 0.186]
## Robust - - 1.748 0.080 [-0.011 , 0.189]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.121 0.032 3.816 0.000 [0.059 , 0.183]
## Robust - - 2.364 0.018 [0.019 , 0.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.124 0.031 4.014 0.000 [0.064 , 0.185]
## Robust - - 2.437 0.015 [0.022 , 0.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 20 54
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.978 4.978
## BW bias (b) 11.309 11.309
## rho (h/b) 0.440 0.440
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.047 0.123 -0.385 0.700 [-0.289 , 0.194]
## Robust - - -0.510 0.610 [-0.361 , 0.212]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.039 1.655 0.024 0.981 [-3.205 , 3.284]
## Robust - - 0.900 0.368 [-2.816 , 7.597]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.252 1.569 0.161 0.872 [-2.824 , 3.328]
## Robust - - 0.146 0.884 [-4.350 , 5.048]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.353 1.552 0.227 0.820 [-2.690 , 3.395]
## Robust - - -0.087 0.931 [-4.823 , 4.413]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 25 60
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.462 5.462
## BW bias (b) 13.223 13.223
## rho (h/b) 0.413 0.413
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 9.593 5.778 1.660 0.097 [-1.731 , 20.917]
## Robust - - 1.889 0.059 [-0.466 , 25.267]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.509 0.707 0.720 0.472 [-0.878 , 1.896]
## Robust - - -0.058 0.954 [-2.452 , 2.312]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.645 0.648 0.995 0.320 [-0.625 , 1.914]
## Robust - - 0.012 0.991 [-2.136 , 2.162]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.701 0.630 1.114 0.265 [-0.533 , 1.936]
## Robust - - 0.038 0.969 [-2.058 , 2.140]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 77
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.064 7.064
## BW bias (b) 14.698 14.698
## rho (h/b) 0.481 0.481
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.082 2.360 0.882 0.378 [-2.544 , 6.708]
## Robust - - 0.713 0.476 [-3.777 , 8.101]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=113 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 113
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 65
## Eff. Number of Obs. 48 65
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 65
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.135 0.079 1.718 0.086 [-0.019 , 0.289]
## Robust - - 0.322 0.747 [-0.207 , 0.288]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 48 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.155 0.078 1.982 0.047 [0.002 , 0.308]
## Robust - - 0.204 0.839 [-0.230 , 0.283]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 48 70
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.164 0.079 2.059 0.039 [0.008 , 0.319]
## Robust - - 0.161 0.872 [-0.238 , 0.281]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=118 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 118
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 70
## Eff. Number of Obs. 20 17
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.795 7.795
## BW bias (b) 12.695 12.695
## rho (h/b) 0.614 0.614
## Unique Obs. 48 70
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.002 0.101 -0.017 0.987 [-0.200 , 0.196]
## Robust - - -0.035 0.972 [-0.268 , 0.258]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=303 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 303
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 184
## Eff. Number of Obs. 119 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 119 184
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.730 0.599 2.890 0.004 [0.557 , 2.904]
## Robust - - 0.809 0.419 [-1.186 , 2.853]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 120 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.093 0.553 3.786 0.000 [1.009 , 3.176]
## Robust - - 0.875 0.382 [-0.991 , 2.590]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 120 195
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 195
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.229 0.541 4.119 0.000 [1.169 , 3.290]
## Robust - - 0.953 0.340 [-0.894 , 2.589]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=315 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 315
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 195
## Eff. Number of Obs. 40 83
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.901 7.901
## BW bias (b) 16.151 16.151
## rho (h/b) 0.489 0.489
## Unique Obs. 117 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.364 1.668 1.417 0.156 [-0.906 , 5.634]
## Robust - - 1.160 0.246 [-1.685 , 6.574]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.588 1.820 1.422 0.155 [-0.978 , 6.154]
## Robust - - -0.427 0.669 [-7.964 , 5.114]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.352 1.679 1.997 0.046 [0.062 , 6.642]
## Robust - - -0.041 0.967 [-5.965 , 5.720]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.660 1.643 2.227 0.026 [0.439 , 6.880]
## Robust - - 0.107 0.914 [-5.389 , 6.014]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 38 74
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.579 6.579
## BW bias (b) 13.954 13.954
## rho (h/b) 0.471 0.471
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.159 6.805 0.023 0.981 [-13.179 , 13.498]
## Robust - - -0.185 0.853 [-18.203 , 15.062]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=169 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 169
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 89
## Eff. Number of Obs. 80 89
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 89
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.016 0.064 -0.243 0.808 [-0.141 , 0.110]
## Robust - - -1.176 0.239 [-0.323 , 0.081]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 80 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.010 0.058 0.178 0.859 [-0.104 , 0.124]
## Robust - - -1.157 0.247 [-0.298 , 0.077]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 80 93
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 80 93
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.021 0.056 0.376 0.707 [-0.089 , 0.131]
## Robust - - -1.133 0.257 [-0.291 , 0.078]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=173 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 173
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 80 93
## Eff. Number of Obs. 24 35
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.093 7.093
## BW bias (b) 12.686 12.686
## rho (h/b) 0.559 0.559
## Unique Obs. 79 91
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.126 0.129 -0.975 0.330 [-0.380 , 0.127]
## Robust - - -0.778 0.437 [-0.480 , 0.207]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=316 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 185
## Eff. Number of Obs. 131 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 185
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.602 3.253 2.030 0.042 [0.227 , 12.977]
## Robust - - 0.617 0.537 [-7.564 , 14.513]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.318 2.915 2.510 0.012 [1.605 , 13.032]
## Robust - - 0.743 0.457 [-6.127 , 13.611]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 132 196
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 196
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.567 2.812 2.691 0.007 [2.057 , 13.078]
## Robust - - 0.798 0.425 [-5.658 , 13.429]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=328 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 328
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 196
## Eff. Number of Obs. 62 109
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.820 10.820
## BW bias (b) 19.866 19.866
## rho (h/b) 0.545 0.545
## Unique Obs. 129 188
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.782 6.323 0.598 0.550 [-8.611 , 16.174]
## Robust - - 0.429 0.668 [-12.190 , 19.018]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -27.026 18.635 -1.450 0.147 [-63.549 , 9.497]
## Robust - - -2.125 0.034 [-98.065 , -3.952]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -15.200 14.835 -1.025 0.306 [-44.276 , 13.877]
## Robust - - -2.319 0.020 [-112.217 , -9.426]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -10.745 13.457 -0.799 0.425 [-37.120 , 15.629]
## Robust - - -2.198 0.028 [-115.957 , -6.646]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 15 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.108 4.108
## BW bias (b) 8.933 8.933
## rho (h/b) 0.460 0.460
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 209.952 136.695 1.536 0.125 [-57.965 , 477.869]
## Robust - - 1.633 0.102 [-50.313 , 553.350]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.004 1.756 -0.572 0.568 [-4.446 , 2.439]
## Robust - - -1.478 0.139 [-9.568 , 1.340]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.257 1.638 -0.157 0.875 [-3.467 , 2.954]
## Robust - - -1.431 0.152 [-8.534 , 1.331]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.062 1.607 -0.039 0.969 [-3.212 , 3.088]
## Robust - - -1.279 0.201 [-8.017 , 1.685]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 46 86
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.211 8.211
## BW bias (b) 16.911 16.911
## rho (h/b) 0.486 0.486
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.349 4.100 -0.329 0.742 [-9.384 , 6.686]
## Robust - - -0.367 0.713 [-11.967 , 8.191]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.102 1.901 -0.054 0.957 [-3.828 , 3.623]
## Robust - - -0.666 0.506 [-7.984 , 3.936]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.731 1.803 0.406 0.685 [-2.803 , 4.265]
## Robust - - -0.839 0.401 [-7.733 , 3.096]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.047 1.783 0.587 0.557 [-2.449 , 4.542]
## Robust - - -0.857 0.392 [-7.660 , 3.000]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 77
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.035 7.035
## BW bias (b) 14.652 14.652
## rho (h/b) 0.480 0.480
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.334 5.062 -0.066 0.947 [-10.255 , 9.586]
## Robust - - -0.066 0.947 [-13.320 , 12.452]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -12.122 12.715 -0.953 0.340 [-37.042 , 12.799]
## Robust - - -0.822 0.411 [-19.008 , 7.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -6.847 8.526 -0.803 0.422 [-23.557 , 9.864]
## Robust - - -1.225 0.221 [-49.635 , 11.460]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.487 6.742 -0.666 0.506 [-17.701 , 8.727]
## Robust - - -1.189 0.234 [-58.228 , 14.245]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 19 53
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.771 4.771
## BW bias (b) 9.318 9.318
## rho (h/b) 0.512 0.512
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 43.780 20.696 2.115 0.034 [3.217 , 84.343]
## Robust - - 2.021 0.043 [1.551 , 100.351]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.260 4.308 -0.989 0.323 [-12.703 , 4.183]
## Robust - - -1.286 0.199 [-12.867 , 2.673]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.183 3.104 -0.703 0.482 [-8.267 , 3.901]
## Robust - - -1.494 0.135 [-19.488 , 2.630]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.327 2.626 -0.505 0.613 [-6.473 , 3.820]
## Robust - - -1.406 0.160 [-21.430 , 3.525]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 42 76
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.938 6.938
## BW bias (b) 11.750 11.750
## rho (h/b) 0.590 0.590
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -6.662 4.999 -1.333 0.183 [-16.460 , 3.136]
## Robust - - -1.190 0.234 [-21.358 , 5.219]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2611.088 616.338 4.236 0.000 [1403.087 , 3819.088]
## Robust - - 1.256 0.209 [-809.458 , 3694.875]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2906.803 564.059 5.153 0.000 [1801.268 , 4012.339]
## Robust - - 1.706 0.088 [-245.731 , 3541.413]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3012.067 550.454 5.472 0.000 [1933.197 , 4090.936]
## Robust - - 1.913 0.056 [-43.239 , 3579.641]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 55 96
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.348 9.348
## BW bias (b) 19.922 19.922
## rho (h/b) 0.469 0.469
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2955.607 1813.800 1.630 0.103 [-599.377 , 6510.591]
## Robust - - 1.410 0.158 [-1243.473 , 7624.355]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: income | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-203086417.400178913009.220 -1.135 0.256[-553749471.837 , 147576637.038]
## Robust - - -1.736 0.083[-207615414.107 , 12571791.460]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-118185955.185116520885.608 -1.014 0.310[-346562694.423 , 110190784.053]
## Robust - - -1.429 0.153[-726696123.362 , 113801001.714]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-81323204.54189117008.244 -0.913 0.361[-255989331.108 , 93342922.027]
## Robust - - -1.346 0.178[-856989877.868 , 159120640.815]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 17 51
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.481 4.481
## BW bias (b) 8.919 8.919
## rho (h/b) 0.502 0.502
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional303656334.545199890447.930 1.519 0.129[-88121744.252 , 695434413.341]
## Robust - - 1.562 0.118[-95526124.582 , 845977760.830]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.255 0.602 0.423 0.672 [-0.926 , 1.436]
## Robust - - 0.555 0.579 [-1.406 , 2.518]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.302 0.561 0.539 0.590 [-0.797 , 1.402]
## Robust - - 0.455 0.649 [-1.346 , 2.160]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.338 0.549 0.616 0.538 [-0.738 , 1.415]
## Robust - - 0.394 0.693 [-1.366 , 2.055]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 54 94
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.026 9.026
## BW bias (b) 18.572 18.572
## rho (h/b) 0.486 0.486
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.837 1.329 0.630 0.529 [-1.767 , 3.441]
## Robust - - 0.609 0.543 [-2.263 , 4.303]
## =============================================================================
## NULL##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1826407.3501613902.328 -1.132 0.258[-4989597.788 , 1336783.087]
## Robust - - -1.615 0.106[-1730029.922 , 166742.297]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1085395.0961049889.006 -1.034 0.301[-3143139.735 , 972349.544]
## Robust - - -1.378 0.168[-6451852.084 , 1124291.563]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-762565.683801757.625 -0.951 0.342[-2333981.753 , 808850.387]
## Robust - - -1.304 0.192[-7631610.569 , 1534500.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 10 43
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.574 3.574
## BW bias (b) 8.478 8.478
## rho (h/b) 0.422 0.422
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional415457.424446302.935 0.931 0.352[-459280.254 , 1290195.103]
## Robust - - 1.641 0.101[-230817.238 , 2607050.435]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2sink()
# Export square-sample difference-in-means results at 40 km
dm_sq40 <- dplyr::bind_rows(sq_dm40)
if (nrow(dm_sq40) > 0) {
readr::write_csv(dm_sq40, dm_csv_sq40)
cat("\n[Square diff-means] Wrote: ", dm_csv_sq40, " | rows=", nrow(dm_sq40), "\n", sep = "")
print(
dm_sq40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means] No usable data within ±40 km for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means] Wrote: output/diffmeans_LombardiaSquare_h40.csv | rows=18
## # A tibble: 10 × 11
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 197 132 -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… servic… NA 40 197 132 2.38 3.13e-1
## 5 LOMBA… Admin_… NA 40 70 48 0.0854 3.92e-2
## 6 LOMBA… edu_se… NA 40 195 120 3.08 2.97e-1
## 7 LOMBA… edu_mu… NA 40 197 132 3.89 9.31e-1
## 8 LOMBA… edu_em… NA 40 93 80 0.105 3.29e-2
## 9 LOMBA… PublS_… NA 40 196 132 10.9 1.29e+0
## 10 LOMBA… pol_mu… NA 40 197 132 18.5 1.32e+1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 3 more variables: t_stat <dbl>, df <dbl>, p_value <dbl># Export square-sample sign-based difference-in-means results (X>=0 vs X<0; no bandwidth trim)
dm_sqsign <- dplyr::bind_rows(sq_sign_dm)
if (nrow(dm_sqsign) > 0) {
readr::write_csv(dm_sqsign, dm_csv_sqsign)
cat("\n[Square diff-means SIGN] Wrote: ", dm_csv_sqsign, " | rows=", nrow(dm_sqsign), "\n", sep = "")
print(
dm_sqsign %>%
dplyr::select(sample, outcome, year, n_pos, n_neg,
diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means SIGN] No usable data in square for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means SIGN] Wrote: output/diffmeans_LombardiaSquare_sign.csv | rows=18
## # A tibble: 10 × 10
## sample outcome year n_pos n_neg diff_pos_minus_neg se_diff t_stat df
## <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 LOMBARDIA_… gb_int… NA 197 132 -0.0148 2.49e-3 5.95 236.
## 2 LOMBARDIA_… gb_reg… NA 197 132 0.135 1.66e-2 -8.14 302.
## 3 LOMBARDIA_… evasio… NA 197 132 -0.845 8.22e-1 1.03 224.
## 4 LOMBARDIA_… servic… NA 197 132 2.38 3.13e-1 -7.61 250.
## 5 LOMBARDIA_… Admin_… NA 70 48 0.0854 3.92e-2 -2.18 93.1
## 6 LOMBARDIA_… edu_se… NA 195 120 3.08 2.97e-1 -10.3 252.
## 7 LOMBARDIA_… edu_mu… NA 197 132 3.89 9.31e-1 -4.18 245.
## 8 LOMBARDIA_… edu_em… NA 93 80 0.105 3.29e-2 -3.20 116.
## 9 LOMBARDIA_… PublS_… NA 196 132 10.9 1.29e+0 -8.42 286.
## 10 LOMBARDIA_… pol_mu… NA 197 132 18.5 1.32e+1 -1.40 239.
## # ℹ 1 more variable: p_value <dbl>{r} read_if_exists <- function(path) { if (file.exists(path)) readr::read_csv(path, show_col_types = FALSE) else NULL }
dm_all40_tbl <- read_if_exists(dm_csv_all40) dm_lomb40_tbl <- read_if_exists(dm_csv_lomb40) dm_sq40_tbl <- read_if_exists(dm_csv_sq40) dm_sqsign_tbl <- read_if_exists(dm_csv_sqsign)
dm_band <- dplyr::bind_rows(dm_all40_tbl, dm_lomb40_tbl, dm_sq40_tbl)
if (!is.null(dm_band) && nrow(dm_band) > 0) { dm_band_out <- dm_band %>% dplyr::select(sample, outcome, year, h_km, n_treated, n_control, mean_treated, mean_control, diff_treat_minus_control, se_diff, t_stat, df, p_value) %>% dplyr::arrange(sample, outcome, year)
knitr::kable(dm_band_out, digits = 4) } else { cat(“No bandwidth-based diff-in-means table was created (no rows found).”) }
cat(“”)
if (!is.null(dm_sqsign_tbl) && nrow(dm_sqsign_tbl) > 0) { dm_sqsign_out <- dm_sqsign_tbl %>% dplyr::select(sample, outcome, year, n_pos, n_neg, mean_pos, mean_neg, diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>% dplyr::arrange(sample, outcome, year)
knitr::kable(dm_sqsign_out, digits = 4) } else { cat(“No within-square sign-based diff-in-means table was created (no rows found).”) } ```
This Rmd writes the following files to output/:
RD_plots_All_Italy_regFE_manualDistance.pdfRD_plots_Lombardia_noFE_manualDistance.pdfRD_plots_LombardiaSquare_area_x<scale>_noFE_manualDistance.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.txtdiffmeans_FullItaly_h40.csvdiffmeans_Lombardia_h40.csvdiffmeans_LombardiaSquare_h40.csv