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)
# --- NEW: placebo & donut settings ---
# Placebo cutoffs (km) to move the cutoff inside treated (-) and control (+) sides
PLACEBO_KM_SEQ <- seq(10, 30, by = 5) # 10,15,20,25,30
# Donut settings (km)
# Full Italy: exclude 5 km around the cutoff -> 2.5 km on either side
DONUT_FULL_SYM_KM <- 2.5
# Lombardia + Square: exclude only 2.5 km on the treated side (keep all control side)
DONUT_TREATED_ONLY_KM <- 2.5
# Outputs (placebo & donut)
placebo_csv_all <- file.path(OUTDIR, "placebo_curve_All_Italy_regFE.csv")
placebo_pdf_all <- file.path(OUTDIR, "placebo_curve_All_Italy_regFE.pdf")
donut_csv_all <- file.path(OUTDIR, "rdrobust_results_All_Italy_regFE_DONUT5km.csv")
donut_csv_lomb <- file.path(OUTDIR, "rdrobust_results_Lombardia_noFE_DONUT_treated2p5.csv")
donut_csv_sq <- file.path(OUTDIR, sprintf("rdrobust_results_LombardiaSquare_area_x%0.2f_noFE_DONUT_treated2p5.csv", TARGET_AREA_SCALE))df0 <- readr::read_csv(DATA_PATH, show_col_types = FALSE)
# key column (municipality id)
KEYCOL <- if ("istat" %in% names(df0)) "istat" else if ("ISTAT" %in% names(df0)) "ISTAT" else stop("No istat/ISTAT column found.")
# ensure expected columns exist
stopifnot(RUNNING %in% names(df0), REGION %in% names(df0))
# region as factor (fixed effects)
df0 <- df0 %>% mutate(.region_fe = factor(.data[[REGION]]))
# convenience alias to match older scripts
if (!("ireg" %in% names(df0))) df0 <- df0 %>% mutate(ireg = as.integer(.data[[REGION]]))
# -----------------------------
# Manual distance corrections
# -----------------------------
manual0 <- readxl::read_excel(MANUAL_DISTANCE_PATH)
# Expected columns in manual file:
# COD_REG, COMUNE, Treated, distance_updated
needed_manual <- c("COD_REG", "COMUNE", "Treated", "distance_updated")
stopifnot(all(needed_manual %in% names(manual0)))
manual <- manual0 %>%
mutate(
COD_REG = as.integer(COD_REG),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE))),
distance_updated = as.numeric(distance_updated)
) %>%
filter(!is.na(distance_updated)) %>%
select(COD_REG, Treated, COMUNE_clean, distance_updated)
df0 <- df0 %>%
mutate(
COD_REG = as.integer(.data[[REGION]]),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE)))
) %>%
left_join(manual, by = c("COD_REG", "Treated", "COMUNE_clean")) %>%
mutate(
.running_original = .data[[RUNNING]],
# overwrite where manual distance exists
"{RUNNING}" := dplyr::if_else(!is.na(distance_updated), distance_updated, .data[[RUNNING]]),
.running_overwritten = !is.na(distance_updated)
)
cat("Manual distance overrides applied:\n")## Manual distance overrides applied:df0 %>%
summarise(
n_rows = n(),
n_overwritten_rows = sum(.running_overwritten, na.rm = TRUE),
n_overwritten_muni = n_distinct(.data[[KEYCOL]][.running_overwritten]),
n_regions = n_distinct(.region_fe),
years = if ("year" %in% names(df0)) paste(sort(unique(year)), collapse = ", ") else NA_character_
) %>%
print()## # A tibble: 1 × 5
## n_rows n_overwritten_rows n_overwritten_muni n_regions years
## <int> <int> <int> <int> <chr>
## 1 7080 68 34 8 2010, 2020# Optional: inspect which municipalities were overwritten
df0 %>%
filter(.running_overwritten) %>%
distinct(COD_REG, COMUNE, Treated, .running_original, !!sym(RUNNING)) %>%
arrange(COD_REG, COMUNE) %>%
head(25) %>%
print()## # A tibble: 25 × 5
## COD_REG COMUNE Treated .running_original distance_treated_positi…¹
## <int> <chr> <int> <dbl> <dbl>
## 1 3 Albiolo 1 -25.3 28.4
## 2 3 Albuzzano 1 -3.67 3.67
## 3 3 Belgioioso 1 -2.67 2.67
## 4 3 Bereguardo 1 -2.76 2.76
## 5 3 Borgo San Siro 0 5.23 -6.67
## 6 3 Campione d'Italia 1 -22.1 22.1
## 7 3 Ceranova 1 -1.91 10.9
## 8 3 Copiano 1 -2.07 8.31
## 9 3 Cura Carpignano 1 -2.55 6.3
## 10 3 Faloppio 1 -27.3 31.6
## # ℹ 15 more rows
## # ℹ abbreviated name: ¹distance_treated_positive_xcollapse_one_row_per_muni <- function(d, keycol, xcol, ycol, keep_year = FALSE) {
# Collapses to one row per municipality (mean across duplicates).
# Also carries Treated (or Treated_num) and COD_PROV when available.
gvars <- c(keycol)
if (keep_year && ("year" %in% names(d))) gvars <- c(gvars, "year")
d %>%
group_by(across(all_of(gvars))) %>%
summarise(
X = mean(.data[[xcol]], na.rm = TRUE),
Y = mean(.data[[ycol]], na.rm = TRUE),
Treated = dplyr::first(
if ("Treated" %in% names(d)) as.integer(.data[["Treated"]])
else if ("Treated_num" %in% names(d)) as.integer(.data[["Treated_num"]])
else NA_integer_
),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(d)) as.integer(.data[["COD_PROV"]]) else NA_integer_),
.region_fe = dplyr::first(if (".region_fe" %in% names(d)) .data[[".region_fe"]] else NA),
.groups = "drop"
)
}
make_sub <- function(d, h) {
# Filter to bandwidth window and drop missing (requires .region_fe).
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.region_fe),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_noFE <- function(d, h) {
# Filter to bandwidth window and drop missing (NO FE requirement).
sub <- d %>%
filter(!is.na(X), !is.na(Y),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; with FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y), !is.na(.region_fe))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full_noFE <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; no FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
region_covs <- function(sub) {
# region dummies (no intercept) for rdrobust(covs=...)
stats::model.matrix(~ .region_fe - 1, data = sub)
}
residualize_region <- function(y, sub) {
# partial out region FE for plotting convenience
stats::residuals(stats::lm(y ~ .region_fe, data = sub))
}
extract_rdrobust <- function(rb, outcome, h, sample, year = NA_integer_, h_type = "MANUAL") {
tibble::tibble(
sample = sample,
outcome = outcome,
year = year,
h_type = h_type, # MANUAL vs AUTO
h_km = h, # manual h, NA for AUTO
p = P,
N = if (!is.null(rb$N)) sum(rb$N) else NA_integer_,
N_left = if (!is.null(rb$N)) rb$N[1] else NA_integer_,
N_right = if (!is.null(rb$N)) rb$N[2] else NA_integer_,
bw_left = if (!is.null(rb$bws)) rb$bws[1] else NA_real_,
bw_right = if (!is.null(rb$bws)) rb$bws[2] else NA_real_,
coef = list(rb$coef),
se = list(rb$se),
pv = list(rb$pv),
ci = list(rb$ci)
)
}
safe_rdrobust <- function(y, x, ..., label = "") {
# Wrapper to avoid hard stops from rdrobust numerical failures (e.g., non-PD matrices).
# Returns NULL on error and prints the error to the current output connection (sink-safe).
tryCatch(
rdrobust::rdrobust(y, x, ...),
error = function(e) {
cat("[Skip rdrobust ERROR] ", label, " : ", conditionMessage(e), "\n", sep = "")
return(NULL)
}
)
}
diff_means_test <- function(d, h, treated_col = "Treated") {
# Difference in means (treated - control) within |X| <= h, using Welch two-sample t-test.
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.data[[treated_col]]),
dplyr::between(X, -h, h)) %>%
mutate(.tr = as.integer(.data[[treated_col]]))
if (!all(c(0L, 1L) %in% unique(sub$.tr))) return(NULL)
y1 <- sub$Y[sub$.tr == 1L]
y0 <- sub$Y[sub$.tr == 0L]
n1 <- sum(sub$.tr == 1L)
n0 <- sum(sub$.tr == 0L)
if (n1 < 5 || n0 < 5) return(NULL)
m1 <- mean(y1, na.rm = TRUE)
m0 <- mean(y0, na.rm = TRUE)
s1 <- stats::var(y1, na.rm = TRUE)
s0 <- stats::var(y0, na.rm = TRUE)
se <- sqrt(s1 / n1 + s0 / n0)
tt <- stats::t.test(Y ~ .tr, data = sub) # Welch by default
tibble::tibble(
h_km = h,
n_treated = n1,
n_control = n0,
mean_treated = m1,
mean_control = m0,
diff_treat_minus_control = m1 - m0,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}
diff_means_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
)
}
# --- NEW: Donut filters ---
apply_donut_symmetric <- function(d, donut_km) {
# Drop observations with |X| < donut_km on BOTH sides
d %>% filter(!is.na(X), abs(X) >= donut_km)
}
apply_donut_treated_only <- function(d, donut_km) {
# Drop only treated-side observations close to cutoff: X in [-donut_km, 0)
d %>% filter(!is.na(X), !(X < 0 & X > -donut_km))
}
# --- NEW: Placebo curve runner (continuity-based) ---
run_placebo_curve <- function(y, x, covs = NULL, placebo_km_seq = seq(10, 30, by = 5),
p = 1, label_prefix = "") {
cutoffs <- c(-placebo_km_seq, placebo_km_seq) %>% sort()
res <- lapply(cutoffs, function(c0) {
rb <- safe_rdrobust(y, x, c = c0, p = p,
covs = covs,
label = paste0(label_prefix, " c=", c0))
if (is.null(rb)) return(NULL)
# rdrobust stores coef/se/pv/ci as vectors/matrices; we use the first (conventional) entry
est <- as.numeric(rb$coef[1])
se <- as.numeric(rb$se[1])
pv <- as.numeric(rb$pv[1])
ci_low <- NA_real_
ci_high <- NA_real_
if (!is.null(rb$ci)) {
ci_low <- as.numeric(rb$ci[1, 1])
ci_high <- as.numeric(rb$ci[1, 2])
}
tibble::tibble(
placebo_cutoff_km = c0,
estimate = est,
se = se,
p_value = pv,
ci_low = ci_low,
ci_high = ci_high,
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_
)
})
out <- dplyr::bind_rows(res)
if (nrow(out) == 0) return(out)
# Multiple-testing adjustments across placebo cutoffs (within this outcome/year/spec)
out <- out %>%
mutate(
p_holm = p.adjust(p_value, method = "holm"),
p_bh = p.adjust(p_value, method = "BH")
) %>%
arrange(placebo_cutoff_km)
out
}
plot_placebo_curve <- function(placebo_df, outcome, year = NA, sample = "FULL_ITALY",
subtitle = "Placebo cutoffs: ±10–30 km") {
if (nrow(placebo_df) == 0) return(NULL)
ttl <- if (!is.na(year)) {
paste0(outcome, " | Year=", year, " | ", sample, " | Placebo curve")
} else {
paste0(outcome, " | ", sample, " | Placebo curve")
}
ggplot(placebo_df, aes(x = placebo_cutoff_km, y = estimate)) +
geom_hline(yintercept = 0) +
geom_vline(xintercept = 0, linetype = 2) +
geom_errorbar(aes(ymin = ci_low, ymax = ci_high), width = 0) +
geom_point() +
labs(
title = ttl,
subtitle = subtitle,
x = "Artificial cutoff (km; 0 = true cutoff)",
y = "Estimated discontinuity (rdrobust)"
) +
theme_minimal()
}# 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=7080 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, "\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=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=0.004583 | p=5.036e-05 | diff_FE=-0.0104 | p_FE=5.651e-09 | N_t=734 N_c=637
##
## ==============================================================================================================
## Outcome: gb_intensity | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=1046 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1046
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 464 582
## Eff. Number of Obs. 464 582
## 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. 464 582
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.583 0.010 [-0.011 , -0.001]
## Robust - - -0.393 0.694 [-0.010 , 0.007]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=1316 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 608 708
## Eff. Number of Obs. 608 708
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 608 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.002 -2.884 0.004 [-0.010 , -0.002]
## Robust - - -1.300 0.193 [-0.011 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=1596 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1596
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 730 866
## Eff. Number of Obs. 730 866
## 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. 730 866
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.002 -3.651 0.000 [-0.011 , -0.003]
## Robust - - -1.271 0.204 [-0.009 , 0.002]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=3513 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3513
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2215 1298
## Eff. Number of Obs. 396 492
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 24.789 24.789
## BW bias (b) 43.825 43.825
## rho (h/b) 0.566 0.566
## Unique Obs. 2199 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.005 0.003 -1.894 0.058 [-0.010 , 0.000]
## Robust - - -1.265 0.206 [-0.011 , 0.002]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=gb_reg_rate | diff=-0.03899 | p=0.0003641 | diff_FE=0.05006 | p_FE=0.004728 | N_t=734 N_c=637
##
## ==============================================================================================================
## Outcome: gb_reg_rate | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=1046 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1046
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 464 582
## Eff. Number of Obs. 464 582
## 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. 464 582
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.044 0.023 1.865 0.062 [-0.002 , 0.089]
## Robust - - 0.413 0.680 [-0.059 , 0.090]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=1316 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1316
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 608 708
## Eff. Number of Obs. 608 708
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 608 708
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.043 0.020 2.112 0.035 [0.003 , 0.082]
## Robust - - 1.261 0.207 [-0.022 , 0.102]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=1596 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1596
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 730 866
## Eff. Number of Obs. 730 866
## 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. 730 866
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.053 0.018 2.936 0.003 [0.018 , 0.088]
## Robust - - 0.974 0.330 [-0.028 , 0.082]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=3513 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3513
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2215 1298
## Eff. Number of Obs. 402 501
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.315 25.315
## BW bias (b) 41.059 41.059
## rho (h/b) 0.617 0.617
## Unique Obs. 2199 1279
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.034 0.025 1.320 0.187 [-0.016 , 0.083]
## Robust - - 0.970 0.332 [-0.032 , 0.093]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=evasione | diff=-2.856 | p=9.763e-11 | diff_FE=-2.625 | p_FE=0.0001142 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: evasione | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.475 0.946 -1.559 0.119 [-3.329 , 0.379]
## Robust - - 0.079 0.937 [-3.098 , 3.358]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.334 0.810 -1.647 0.100 [-2.922 , 0.254]
## Robust - - -0.919 0.358 [-3.790 , 1.370]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.419 0.722 -1.966 0.049 [-2.833 , -0.004]
## Robust - - -1.067 0.286 [-3.449 , 1.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 462 580
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.183 30.183
## BW bias (b) 55.582 55.582
## rho (h/b) 0.543 0.543
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.587 0.943 -1.684 0.092 [-3.435 , 0.260]
## Robust - - 0.936 0.349 [-1.966 , 5.561]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=services_level | diff=0.2873 | p=0.0668 | diff_FE=2.314 | p_FE=9.321e-22 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: services_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.496 0.322 4.639 0.000 [0.864 , 2.128]
## Robust - - 1.738 0.082 [-0.120 , 2.004]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.710 0.278 6.159 0.000 [1.166 , 2.254]
## Robust - - 2.717 0.007 [0.337 , 2.081]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.858 0.250 7.430 0.000 [1.368 , 2.348]
## Robust - - 3.648 0.000 [0.647 , 2.149]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 361 442
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 21.848 21.848
## BW bias (b) 43.443 43.443
## rho (h/b) 0.503 0.503
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.222 0.388 3.153 0.002 [0.462 , 1.982]
## Robust - - 2.284 0.022 [0.148 , 1.936]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.1069 | p=0.1179 | diff_FE=0.1366 | p_FE=0.2162 | N_t=232 N_c=217
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=364 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 364
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 172 192
## Eff. Number of Obs. 172 192
## 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. 172 192
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.071 0.097 0.732 0.464 [-0.119 , 0.261]
## Robust - - 1.774 0.076 [-0.021 , 0.416]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=447 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 447
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 215 232
## Eff. Number of Obs. 215 232
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 215 232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.065 0.059 1.108 0.268 [-0.050 , 0.181]
## Robust - - 0.737 0.461 [-0.159 , 0.351]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=500 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 500
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 234 266
## Eff. Number of Obs. 234 266
## 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. 234 266
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.105 0.050 2.101 0.036 [0.007 , 0.203]
## Robust - - -0.096 0.924 [-0.308 , 0.279]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=927 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 927
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 574 353
## Eff. Number of Obs. 118 119
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.072 17.072
## BW bias (b) 50.514 50.514
## rho (h/b) 0.338 0.338
## Unique Obs. 569 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.153 0.087 1.756 0.079 [-0.018 , 0.324]
## Robust - - 1.319 0.187 [-0.063 , 0.324]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_serv_lvl | diff=0.6146 | p=0.0001335 | diff_FE=1.223 | p_FE=3.134e-06 | N_t=685 N_c=553
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=992 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 992
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 425 567
## Eff. Number of Obs. 425 567
## 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. 425 567
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.903 0.372 2.428 0.015 [0.174 , 1.632]
## Robust - - 0.376 0.707 [-1.033 , 1.523]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=1235 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1235
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 550 685
## Eff. Number of Obs. 550 685
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 550 685
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.301 0.322 4.037 0.000 [0.669 , 1.932]
## Robust - - 0.600 0.548 [-0.701 , 1.319]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=1497 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1497
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 659 838
## Eff. Number of Obs. 659 838
## 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. 659 838
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.539 0.291 5.289 0.000 [0.969 , 2.109]
## Robust - - 1.555 0.120 [-0.178 , 1.547]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=3010 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3010
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1760 1250
## Eff. Number of Obs. 299 399
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.993 18.993
## BW bias (b) 42.905 42.905
## rho (h/b) 0.443 0.443
## Unique Obs. 1744 1232
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.523 0.493 1.060 0.289 [-0.444 , 1.490]
## Robust - - 0.458 0.647 [-0.844 , 1.358]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=0.796 | p=0.09316 | diff_FE=2.931 | p_FE=7.685e-05 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.679 0.971 2.759 0.006 [0.776 , 4.582]
## Robust - - 0.314 0.754 [-2.671 , 3.690]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.975 0.846 3.517 0.000 [1.317 , 4.634]
## Robust - - 1.190 0.234 [-1.025 , 4.196]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=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 3.094 0.765 4.045 0.000 [1.595 , 4.593]
## Robust - - 1.972 0.049 [0.014 , 4.560]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=3184 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3184
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1906 1278
## Eff. Number of Obs. 437 539
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.855 27.855
## BW bias (b) 50.113 50.113
## rho (h/b) 0.556 0.556
## Unique Obs. 1890 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.455 1.009 2.432 0.015 [0.476 , 4.433]
## Robust - - 1.796 0.073 [-0.199 , 4.560]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=edu_emp_per1000 | diff=-0.01615 | p=0.4388 | diff_FE=0.05389 | p_FE=0.07027 | N_t=359 N_c=359
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=569 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 569
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 276 293
## Eff. Number of Obs. 276 293
## 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. 276 293
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.045 0.044 1.019 0.308 [-0.042 , 0.132]
## Robust - - -1.027 0.304 [-0.182 , 0.057]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=715 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 715
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 356 359
## Eff. Number of Obs. 356 359
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 356 359
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.069 0.038 1.819 0.069 [-0.005 , 0.144]
## Robust - - -0.165 0.869 [-0.122 , 0.103]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=850 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 850
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 432 418
## Eff. Number of Obs. 432 418
## 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. 432 418
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.082 0.035 2.326 0.020 [0.013 , 0.150]
## Robust - - 0.373 0.709 [-0.086 , 0.126]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=1710 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1710
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1090 620
## Eff. Number of Obs. 185 206
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.952 17.952
## BW bias (b) 35.840 35.840
## rho (h/b) 0.501 0.501
## Unique Obs. 1086 613
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.014 0.052 -0.280 0.780 [-0.116 , 0.087]
## Robust - - -0.755 0.450 [-0.165 , 0.073]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=5.153 | p=9.42e-16 | diff_FE=6.09 | p_FE=3.876e-09 | N_t=694 N_c=602
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=1029 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1029
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 457 572
## Eff. Number of Obs. 457 572
## 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. 457 572
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.753 1.435 4.010 0.000 [2.941 , 8.565]
## Robust - - 1.981 0.048 [0.058 , 10.644]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=1293 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1293
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 599 694
## Eff. Number of Obs. 599 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 599 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.890 1.257 4.685 0.000 [3.426 , 8.353]
## Robust - - 2.680 0.007 [1.488 , 9.590]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=1569 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1569
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 719 850
## Eff. Number of Obs. 719 850
## 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. 719 850
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.054 1.154 5.247 0.000 [3.793 , 8.316]
## Robust - - 3.425 0.001 [2.494 , 9.169]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=3152 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3152
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1886 1266
## Eff. Number of Obs. 496 602
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 32.304 32.304
## BW bias (b) 54.496 54.496
## rho (h/b) 0.593 0.593
## Unique Obs. 1870 1247
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.884 1.372 4.288 0.000 [3.195 , 8.573]
## Robust - - 3.595 0.000 [2.704 , 9.189]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=pol_mun_road | diff=-30.14 | p=9.489e-06 | diff_FE=11.74 | p_FE=0.2341 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: pol_mun_road | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.480 9.104 0.822 0.411 [-10.364 , 25.324]
## Robust - - -0.410 0.682 [-30.390 , 19.867]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.760 7.793 1.637 0.102 [-2.513 , 28.033]
## Robust - - -0.209 0.835 [-27.186 , 21.957]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 15.352 7.258 2.115 0.034 [1.127 , 29.577]
## Robust - - 0.387 0.699 [-17.608 , 26.267]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 411 507
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 26.001 26.001
## BW bias (b) 52.086 52.086
## rho (h/b) 0.499 0.499
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.437 9.558 0.255 0.799 [-16.297 , 21.171]
## Robust - - -0.039 0.969 [-23.765 , 22.830]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=1.109 | p=0.01113 | diff_FE=1.688 | p_FE=0.01337 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.305 0.984 -0.310 0.757 [-2.233 , 1.623]
## Robust - - -1.305 0.192 [-5.364 , 1.076]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.252 0.850 0.297 0.767 [-1.413 , 1.917]
## Robust - - -0.968 0.333 [-3.948 , 1.337]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.615 0.764 0.805 0.421 [-0.882 , 2.112]
## Robust - - -0.689 0.491 [-3.087 , 1.481]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 321 404
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.852 18.852
## BW bias (b) 36.686 36.686
## rho (h/b) 0.514 0.514
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.567 1.281 -1.223 0.221 [-4.077 , 0.943]
## Robust - - -1.444 0.149 [-5.239 , 0.794]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=3.135 | p=2.144e-09 | diff_FE=4.317 | p_FE=8.705e-08 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.010 1.138 0.888 0.375 [-1.220 , 3.241]
## Robust - - -0.130 0.897 [-4.001 , 3.504]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.837 0.968 1.898 0.058 [-0.060 , 3.733]
## Robust - - -0.108 0.914 [-3.254 , 2.915]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.355 0.861 2.735 0.006 [0.667 , 4.042]
## Robust - - 0.381 0.704 [-2.142 , 3.174]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 303 377
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 17.276 17.276
## BW bias (b) 29.602 29.602
## rho (h/b) 0.584 0.584
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.562 1.580 0.355 0.722 [-2.535 , 3.659]
## Robust - - 0.087 0.931 [-3.771 , 4.119]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_civil | diff=3.342 | p=0.3658 | diff_FE=8.156 | p_FE=0.1919 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: marr_civil | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.013 4.459 0.227 0.820 [-7.727 , 9.754]
## Robust - - -0.013 0.989 [-8.068 , 7.959]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.686 2.548 1.839 0.066 [-0.309 , 9.680]
## Robust - - -0.480 0.632 [-17.209 , 10.443]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 6.417 2.161 2.969 0.003 [2.181 , 10.653]
## Robust - - -0.021 0.983 [-11.890 , 11.640]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 315 395
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 18.202 18.202
## BW bias (b) 46.440 46.440
## rho (h/b) 0.392 0.392
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.595 2.860 0.907 0.364 [-3.010 , 8.199]
## Robust - - 0.334 0.739 [-5.674 , 8.002]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=marr_rel | diff=1.971 | p=0.1007 | diff_FE=3.881 | p_FE=0.05396 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: marr_rel | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.409 1.719 -0.238 0.812 [-3.777 , 2.960]
## Robust - - -1.118 0.264 [-6.930 , 1.897]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.171 1.187 0.986 0.324 [-1.156 , 3.498]
## Robust - - -1.117 0.264 [-7.991 , 2.190]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.059 1.050 1.961 0.050 [0.001 , 4.117]
## Robust - - -0.611 0.541 [-5.687 , 2.984]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 343 420
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.369 20.369
## BW bias (b) 49.864 49.864
## rho (h/b) 0.408 0.408
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.895 1.535 -0.583 0.560 [-3.904 , 2.114]
## Robust - - -0.909 0.363 [-5.046 , 1.848]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=incomepc | diff=1195 | p=7.211e-12 | diff_FE=1802 | p_FE=1.797e-10 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: incomepc | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1405.997 371.068 3.789 0.000 [678.718 , 2133.276]
## Robust - - 0.464 0.643 [-1020.870 , 1654.459]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1692.075 323.124 5.237 0.000 [1058.764 , 2325.386]
## Robust - - 1.454 0.146 [-266.344 , 1797.202]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1808.611 291.953 6.195 0.000 [1236.395 , 2380.828]
## Robust - - 2.763 0.006 [356.521 , 2097.068]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 398 496
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 25.262 25.262
## BW bias (b) 49.368 49.368
## rho (h/b) 0.512 0.512
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1160.257 409.920 2.830 0.005 [356.829 , 1963.686]
## Robust - - 1.983 0.047 [11.110 , 1899.471]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=income | diff=56250000 | p=0.2643 | diff_FE=101600000 | p_FE=0.2396 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: income | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-19595546.75759296979.526 -0.330 0.741[-135815491.021 , 96624397.507]
## Robust - - -0.907 0.364[-113409225.489 , 41629913.286]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional37518175.34027343895.986 1.372 0.170[-16074875.989 , 91111226.669]
## Robust - - -0.922 0.356[-275480655.714 , 99196550.975]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional68082107.31322550633.319 3.019 0.003[23883678.179 , 112280536.446]
## Robust - - -0.519 0.604[-199756847.263 , 116129605.662]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 275 350
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 15.659 15.659
## BW bias (b) 42.346 42.346
## rho (h/b) 0.370 0.370
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional7125288.58029378229.905 0.243 0.808[-50454983.963 , 64705561.122]
## Robust - - -0.490 0.624[-92551405.010 , 55536652.758]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expend_level | diff=0.365 | p=0.005602 | diff_FE=0.6255 | p_FE=0.002862 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: expend_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.306 0.308 0.993 0.321 [-0.298 , 0.910]
## Robust - - -0.169 0.865 [-1.153 , 0.970]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.437 0.262 1.669 0.095 [-0.076 , 0.950]
## Robust - - 0.278 0.781 [-0.728 , 0.968]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.529 0.235 2.251 0.024 [0.068 , 0.989]
## Robust - - 0.628 0.530 [-0.488 , 0.947]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=3188 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3188
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 1910 1278
## Eff. Number of Obs. 436 537
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 27.692 27.692
## BW bias (b) 51.264 51.264
## rho (h/b) 0.540 0.540
## Unique Obs. 1894 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.337 0.324 1.040 0.298 [-0.298 , 0.971]
## Robust - - 0.596 0.551 [-0.524 , 0.983]
## =============================================================================
## NULL## [Full Italy diff-means] h=40 km | outcome=expenditure | diff=314600 | p=0.527 | diff_FE=921100 | p_FE=0.2705 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: expenditure | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=1038 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1038
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 460 578
## Eff. Number of Obs. 460 578
## 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. 460 578
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-35484.778544630.276 -0.065 0.948[-1102940.503 , 1031970.947]
## Robust - - -0.539 0.590[-992015.240 , 563864.524]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=1304 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1304
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 602 702
## Eff. Number of Obs. 602 702
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 602 702
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional502204.049308425.201 1.628 0.103[-102298.237 , 1106706.334]
## Robust - - -0.730 0.466[-2369395.251 , 1083933.670]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=1582 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1582
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 723 859
## Eff. Number of Obs. 723 859
## 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. 723 859
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional725178.708244532.771 2.966 0.003[245903.283 , 1204454.132]
## Robust - - -0.184 0.854[-1622881.812 , 1343873.024]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=3473 | + REGION FE
## ------------------------------------------------------------------------------------------## Covariate-adjusted Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 3473
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2195 1278
## Eff. Number of Obs. 289 363
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 16.466 16.466
## BW bias (b) 46.308 46.308
## rho (h/b) 0.356 0.356
## Unique Obs. 2179 1259
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional122100.132288686.482 0.423 0.672[-443714.975 , 687915.239]
## Robust - - -0.149 0.881[-754025.561 , 647161.365]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2# Export Full-Italy diff-means results at 40 km
dm_all40 <- dplyr::bind_rows(all_dm40)
if (nrow(dm_all40) > 0) {
readr::write_csv(dm_all40, dm_csv_all40)
cat("
[Full Italy diff-means] Wrote: ", dm_csv_all40, " | rows=", nrow(dm_all40), "
", sep = "")
print(dm_all40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, p_value,
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 40 734 637 0.00458 0.00113
## 2 FULL_… gb_reg… NA 40 734 637 -0.0390 0.0109
## 3 FULL_… evasio… NA 40 702 605 -2.86 0.437
## 4 FULL_… servic… NA 40 702 605 0.287 0.157
## 5 FULL_… Admin_… NA 40 232 217 0.107 0.0681
## 6 FULL_… edu_se… NA 40 685 553 0.615 0.160
## 7 FULL_… edu_mu… NA 40 702 605 0.796 0.474
## 8 FULL_… edu_em… NA 40 359 359 -0.0161 0.0208
## 9 FULL_… PublS_… NA 40 694 602 5.15 0.633
## 10 FULL_… pol_mu… NA 40 702 605 -30.1 6.77
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 4 more variables: p_value <dbl>, diff_fe <dbl>, se_fe <dbl>, p_fe <dbl>sink()# ------------------------------------------------------------
# Placebo curve (Full Italy, region FE)
# Artificial cutoffs: move inside treated (-) and control (+) sides, 10–30 km
# ------------------------------------------------------------
placebo_all <- list()
pdf(placebo_pdf_all, width = 7, height = 4.5)
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df0))) next
# Pillar2_pol: run by year
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)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) next
covs_full <- region_covs(sub_full)
plc <- run_placebo_curve(
y = sub_full$Y,
x = sub_full$X,
covs = covs_full,
placebo_km_seq = PLACEBO_KM_SEQ,
p = P,
label_prefix = paste0("PLACEBO | ", yvar, " | Year=", yr)
)
if (nrow(plc) > 0) {
plc <- plc %>% mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = yr)
placebo_all[[length(placebo_all) + 1]] <- plc
g <- plot_placebo_curve(plc, outcome = yvar, year = yr, sample = "FULL_ITALY_regFE",
subtitle = "Artificial cutoffs: -30..-10 km (treated side) and +10..+30 km (control side)")
print(g)
}
}
} else {
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) next
covs_full <- region_covs(sub_full)
plc <- run_placebo_curve(
y = sub_full$Y,
x = sub_full$X,
covs = covs_full,
placebo_km_seq = PLACEBO_KM_SEQ,
p = P,
label_prefix = paste0("PLACEBO | ", yvar)
)
if (nrow(plc) > 0) {
plc <- plc %>% mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = NA_integer_)
placebo_all[[length(placebo_all) + 1]] <- plc
g <- plot_placebo_curve(plc, outcome = yvar, year = NA, sample = "FULL_ITALY_regFE",
subtitle = "Artificial cutoffs: -30..-10 km (treated side) and +10..+30 km (control side)")
print(g)
}
}
}
dev.off()## quartz_off_screen
## 2placebo_all_df <- dplyr::bind_rows(placebo_all)
if (nrow(placebo_all_df) > 0) {
readr::write_csv(placebo_all_df, placebo_csv_all)
cat("[Placebo curve] Wrote: ", placebo_csv_all, " | rows=", nrow(placebo_all_df), "
", sep = "")
cat("[Placebo curve] Plots: ", placebo_pdf_all, "
", sep = "")
} else {
cat("[Placebo curve] No placebo results (insufficient data around placebo cutoffs for all outcomes).
")
}## [Placebo curve] Wrote: output/placebo_curve_All_Italy_regFE.csv | rows=180
## [Placebo curve] Plots: output/placebo_curve_All_Italy_regFE.pdf# ------------------------------------------------------------
# Donut RD (Full Italy, region FE)
# Exclude 5 km around cutoff => drop |X| < 2.5 km
# ------------------------------------------------------------
donut_all <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df0))) next
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)
d1_donut <- apply_donut_symmetric(d1, donut_km = DONUT_FULL_SYM_KM)
# MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1_donut, h)
if (is.null(sub)) next
covs <- region_covs(sub)
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs,
label = paste0("DONUT FullItaly | ", yvar, " | Year=", yr, " | h=", h))
if (is.null(rb)) next
donut_all[[length(donut_all) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY_DONUT5km", year = yr, h_type = "MANUAL")
}
# AUTO bandwidth
sub_full <- make_sub_full(d1_donut)
if (!is.null(sub_full)) {
covs_full <- region_covs(sub_full)
rb_auto <- safe_rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full,
label = paste0("DONUT FullItaly AUTO | ", yvar, " | Year=", yr))
if (!is.null(rb_auto)) {
donut_all[[length(donut_all) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY_DONUT5km", year = yr, h_type = "AUTO")
}
}
}
} else {
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
d1_donut <- apply_donut_symmetric(d1, donut_km = DONUT_FULL_SYM_KM)
for (h in BWS_KM) {
sub <- make_sub(d1_donut, h)
if (is.null(sub)) next
covs <- region_covs(sub)
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs,
label = paste0("DONUT FullItaly | ", yvar, " | h=", h))
if (is.null(rb)) next
donut_all[[length(donut_all) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY_DONUT5km", year = NA_integer_, h_type = "MANUAL")
}
sub_full <- make_sub_full(d1_donut)
if (!is.null(sub_full)) {
covs_full <- region_covs(sub_full)
rb_auto <- safe_rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full,
label = paste0("DONUT FullItaly AUTO | ", yvar))
if (!is.null(rb_auto)) {
donut_all[[length(donut_all) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY_DONUT5km", year = NA_integer_, h_type = "AUTO")
}
}
}
}
donut_all_df <- dplyr::bind_rows(donut_all)
if (nrow(donut_all_df) > 0) {
readr::write_csv(donut_all_df, donut_csv_all)
cat("[Donut RD | Full Italy] Wrote: ", donut_csv_all, " | rows=", nrow(donut_all_df), "
", sep = "")
} else {
cat("[Donut RD | Full Italy] No donut RD results produced (insufficient data after donut exclusion).
")
}## [Donut RD | Full Italy] Wrote: output/rdrobust_results_All_Italy_regFE_DONUT5km.csv | rows=72df_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): 133print(lomb_control_muni %>% dplyr::select(COMUNE, X_km, Treated, COD_PROV), n = Inf)## # A tibble: 133 × 4
## COMUNE X_km Treated COD_PROV
## <chr> <dbl> <int> <int>
## 1 Brallo di Pregola -31.0 0 18
## 2 Santa Margherita di Staffora -29.9 0 18
## 3 Cecima -28.3 0 18
## 4 Rivanazzano Terme -27.5 0 18
## 5 Bagnaria -26.6 0 18
## 6 Godiasco Salice Terme -26.0 0 18
## 7 Ponte Nizza -25.1 0 18
## 8 Retorbido -25.0 0 18
## 9 Varzi -24.2 0 18
## 10 Codevilla -23.2 0 18
## 11 Menconico -22.8 0 18
## 12 Voghera -22.6 0 18
## 13 Rocca Susella -22.4 0 18
## 14 Frascarolo -22.3 0 18
## 15 Suardi -21.7 0 18
## 16 Casei Gerola -21.3 0 18
## 17 Montesegale -21.0 0 18
## 18 Torrazza Coste -20.9 0 18
## 19 Montebello della Battaglia -20.0 0 18
## 20 Val di Nizza -20.0 0 18
## 21 Torre Beretti e Castellaro -19.9 0 18
## 22 Gambarana -19.9 0 18
## 23 Lungavilla -19.1 0 18
## 24 Pizzale -19.0 0 18
## 25 Romagnese -18.0 0 18
## 26 Verretto -17.9 0 18
## 27 Silvano Pietra -17.4 0 18
## 28 Sartirana Lomellina -17.2 0 18
## 29 Borgo Priolo -17.1 0 18
## 30 Casteggio -17.1 0 18
## 31 Pieve del Cairo -17.0 0 18
## 32 Fortunago -16.9 0 18
## 33 Palestro -16.8 0 18
## 34 Cervesina -16.4 0 18
## 35 Casatisma -16.4 0 18
## 36 Breme -16.3 0 18
## 37 Robecco Pavese -16.2 0 18
## 38 Zavattarello -16.1 0 18
## 39 Mezzana Bigli -15.8 0 18
## 40 Castelletto di Branduzzo -15.7 0 18
## 41 Pancarana -15.5 0 18
## 42 Corana -15.5 0 18
## 43 Mede -15.5 0 18
## 44 Langosco -15.4 0 18
## 45 Corvino San Quirico -15.3 0 18
## 46 Candia Lomellina -15.2 0 18
## 47 Calvignano -14.8 0 18
## 48 Villa Biscossi -14.5 0 18
## 49 Rosasco -14.3 0 18
## 50 Torricella Verzate -14.2 0 18
## 51 Confienza -13.9 0 18
## 52 Borgoratto Mormorolo -13.9 0 18
## 53 Santa Giuletta -13.2 0 18
## 54 Bressana Bottarone -13.1 0 18
## 55 Oliva Gessi -13.1 0 18
## 56 Galliavola -12.9 0 18
## 57 Pinarolo Po -12.9 0 18
## 58 Mezzana Rabattone -12.8 0 18
## 59 Bastida Pancarana -12.7 0 18
## 60 Semiana -12.5 0 18
## 61 Sannazzaro de' Burgondi -11.9 0 18
## 62 Valle Lomellina -11.9 0 18
## 63 Redavalle -11.7 0 18
## 64 Ferrera Erbognone -11.7 0 18
## 65 Pieve Albignola -11.4 0 18
## 66 Cozzo -11.4 0 18
## 67 Barbianello -11.2 0 18
## 68 Lomello -10.9 0 18
## 69 Montalto Pavese -10.9 0 18
## 70 Mornico Losana -10.9 0 18
## 71 Robbio -10.8 0 18
## 72 Sommo -10.7 0 18
## 73 Zinasco -10.4 0 18
## 74 Velezzo Lomellina -10.1 0 18
## 75 Castelnovetto -9.74 0 18
## 76 Verrua Po -9.64 0 18
## 77 Rocca de' Giorgi -9.57 0 18
## 78 Casanova Lonati -9.26 0 18
## 79 Cava Manara -8.60 0 18
## 80 Pietra de' Giorgi -8.55 0 18
## 81 Zeme -8.55 0 18
## 82 Rea -8.50 0 18
## 83 Broni -8.47 0 18
## 84 Cigognola -8.44 0 18
## 85 Scaldasole -8.36 0 18
## 86 Sant'Angelo Lomellina -8.22 0 18
## 87 Mezzanino -8.00 0 18
## 88 Volpara -7.71 0 18
## 89 Campospinoso Albaredo -7.33 0 18
## 90 Lirio -7.27 0 18
## 91 Montecalvo Versiggia -6.73 0 18
## 92 Nicorvo -6.67 0 18
## 93 Borgo San Siro -6.67 0 18
## 94 Valeggio -6.64 0 18
## 95 San Giorgio di Lomellina -6.58 0 18
## 96 Ottobiano -6.35 0 18
## 97 Golferenzo -6.35 0 18
## 98 Dorno -6.32 0 18
## 99 Garlasco -6.30 0 18
## 100 Tromello -6.30 0 18
## 101 Carbonara al Ticino -6.30 0 18
## 102 Ceretto Lomellina -6.14 0 18
## 103 Cergnago -5.86 0 18
## 104 Castana -5.83 0 18
## 105 Canneto Pavese -5.77 0 18
## 106 San Martino Siccomario -5.66 0 18
## 107 Villanova d'Ardenghi -5.58 0 18
## 108 Travacò Siccomario -5.32 0 18
## 109 Castello d'Agogna -5.28 0 18
## 110 Alagna -5.25 0 18
## 111 Stradella -5.19 0 18
## 112 Olevano di Lomellina -5.08 0 18
## 113 Montescano -4.94 0 18
## 114 Gropello Cairoli -4.70 0 18
## 115 Gambolò -4.62 0 18
## 116 Zerbolò -4.39 0 18
## 117 Cassolnovo -4.11 0 18
## 118 Gravellona Lomellina -3.95 0 18
## 119 Santa Maria della Versa -3.88 0 18
## 120 San Cipriano Po -3.86 0 18
## 121 Mortara -3.83 0 18
## 122 Albonese -3.74 0 18
## 123 Vigevano -3.57 0 18
## 124 Arena Po -3.08 0 18
## 125 Bosnasco -3.03 0 18
## 126 Cilavegna -2.76 0 18
## 127 Parona -2.76 0 18
## 128 Portalbera -2.68 0 18
## 129 Montù Beccaria -2.65 0 18
## 130 Rovescala -2.55 0 18
## 131 San Damiano al Colle -2.55 0 18
## 132 Tronzano Lago Maggiore -2.42 0 12
## 133 Zenevredo -2.19 0 18# 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=2814 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=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=-0.01197 | p=2.908e-07 | N_t=694 N_c=133
##
## ==============================================================================================================
## Outcome: gb_intensity | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=30 km | p=1 | N used=700 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 700
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 568
## Eff. Number of Obs. 132 568
## 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. 132 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.007 0.004 -1.895 0.058 [-0.014 , 0.000]
## Robust - - 0.951 0.342 [-0.007 , 0.020]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=40 km | p=1 | N used=827 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 827
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 694
## Eff. Number of Obs. 133 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.009 0.003 -2.605 0.009 [-0.016 , -0.002]
## Robust - - 0.719 0.472 [-0.007 , 0.016]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=50 km | p=1 | N used=985 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 985
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 852
## Eff. Number of Obs. 133 852
## 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. 133 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.011 0.003 -3.326 0.001 [-0.018 , -0.005]
## Robust - - 0.959 0.338 [-0.006 , 0.017]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | AUTO bandwidth (default) | p=1 | N used=1417 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1417
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1284
## Eff. Number of Obs. 26 131
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.565 5.565
## BW bias (b) 12.381 12.381
## rho (h/b) 0.449 0.449
## Unique Obs. 130 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.051 0.011 4.686 0.000 [0.030 , 0.073]
## Robust - - 4.349 0.000 [0.032 , 0.085]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=gb_reg_rate | diff=0.06762 | p=9.281e-09 | N_t=694 N_c=133
##
## ==============================================================================================================
## Outcome: gb_reg_rate | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=30 km | p=1 | N used=700 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 700
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 568
## Eff. Number of Obs. 132 568
## 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. 132 568
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.070 0.024 2.888 0.004 [0.023 , 0.118]
## Robust - - 1.606 0.108 [-0.014 , 0.137]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=40 km | p=1 | N used=827 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 827
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 694
## Eff. Number of Obs. 133 694
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 694
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.068 0.022 3.051 0.002 [0.024 , 0.111]
## Robust - - 2.552 0.011 [0.020 , 0.154]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | h=50 km | p=1 | N used=985 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 985
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 852
## Eff. Number of Obs. 133 852
## 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. 133 852
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.075 0.021 3.585 0.000 [0.034 , 0.116]
## Robust - - 2.705 0.007 [0.024 , 0.150]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_reg_rate | AUTO bandwidth (default) | p=1 | N used=1417 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1417
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1284
## Eff. Number of Obs. 45 174
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.633 7.633
## BW bias (b) 15.428 15.428
## rho (h/b) 0.495 0.495
## Unique Obs. 130 1268
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.055 0.398 0.690 [-0.086 , 0.130]
## Robust - - 0.005 0.996 [-0.141 , 0.142]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=evasione | diff=-2.774 | p=0.0002511 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: evasione | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.272 1.462 -0.870 0.384 [-4.137 , 1.593]
## Robust - - 0.578 0.563 [-3.230 , 5.930]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.675 1.401 -1.196 0.232 [-4.422 , 1.071]
## Robust - - -0.192 0.848 [-4.514 , 3.709]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.127 1.381 -1.540 0.123 [-4.833 , 0.579]
## Robust - - -0.676 0.499 [-5.356 , 2.608]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — evasione | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 31 136
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.976 5.976
## BW bias (b) 13.060 13.060
## rho (h/b) 0.458 0.458
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.834 4.301 0.659 0.510 [-5.596 , 11.264]
## Robust - - 0.929 0.353 [-5.483 , 15.358]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=services_level | diff=2.481 | p=2.27e-16 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: services_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.373 0.595 2.308 0.021 [0.207 , 2.538]
## Robust - - 1.033 0.302 [-0.945 , 3.049]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.459 0.549 2.659 0.008 [0.383 , 2.534]
## Robust - - 1.157 0.247 [-0.743 , 2.883]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.521 0.531 2.862 0.004 [0.480 , 2.563]
## Robust - - 1.228 0.220 [-0.659 , 2.868]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.960 6.960
## BW bias (b) 13.946 13.946
## rho (h/b) 0.499 0.499
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.342 1.867 1.254 0.210 [-1.318 , 6.001]
## Robust - - 0.979 0.328 [-2.422 , 7.253]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Admin_Tax_Emp | diff=0.143 | p=0.05524 | N_t=226 N_c=49
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=30 km | p=1 | N used=235 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 235
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 186
## Eff. Number of Obs. 49 186
## 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. 49 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.059 0.100 0.589 0.556 [-0.137 , 0.256]
## Robust - - 0.802 0.422 [-0.132 , 0.316]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=40 km | p=1 | N used=275 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 275
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 226
## Eff. Number of Obs. 49 226
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 49 226
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.104 0.073 1.428 0.153 [-0.039 , 0.247]
## Robust - - -0.256 0.798 [-0.326 , 0.250]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=50 km | p=1 | N used=309 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 309
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 260
## Eff. Number of Obs. 49 260
## 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. 49 260
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.139 0.065 2.138 0.033 [0.012 , 0.267]
## Robust - - -0.396 0.692 [-0.358 , 0.238]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | AUTO bandwidth (default) | p=1 | N used=396 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 396
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 49 347
## Eff. Number of Obs. 12 34
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.390 5.390
## BW bias (b) 10.035 10.035
## rho (h/b) 0.537 0.537
## Unique Obs. 49 346
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.104 0.243 0.426 0.670 [-0.373 , 0.580]
## Robust - - 0.459 0.646 [-0.484 , 0.780]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_serv_lvl | diff=1.399 | p=1.68e-07 | N_t=671 N_c=121
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=30 km | p=1 | N used=673 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 673
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 553
## Eff. Number of Obs. 120 553
## 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. 120 553
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.758 0.502 1.511 0.131 [-0.226 , 1.743]
## Robust - - 0.065 0.948 [-1.626 , 1.739]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=40 km | p=1 | N used=792 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 792
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 671
## Eff. Number of Obs. 121 671
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 121 671
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.059 0.467 2.269 0.023 [0.144 , 1.973]
## Robust - - 0.189 0.850 [-1.345 , 1.632]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | h=50 km | p=1 | N used=945 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 945
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 824
## Eff. Number of Obs. 121 824
## 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. 121 824
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.220 0.452 2.698 0.007 [0.334 , 2.106]
## Robust - - 0.604 0.546 [-0.986 , 1.864]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_serv_lvl | AUTO bandwidth (default) | p=1 | N used=1357 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1357
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 121 1236
## Eff. Number of Obs. 49 201
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.586 8.586
## BW bias (b) 17.004 17.004
## rho (h/b) 0.505 0.505
## Unique Obs. 118 1221
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.767 1.226 0.626 0.531 [-1.635 , 3.169]
## Robust - - 0.633 0.527 [-2.064 , 4.034]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_muni_school_area_per1000 | diff=3.24 | p=0.0001055 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.852 1.598 2.411 0.016 [0.721 , 6.983]
## Robust - - 0.200 0.842 [-5.073 , 6.223]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.518 1.475 3.063 0.002 [1.627 , 7.410]
## Robust - - 0.794 0.427 [-3.046 , 7.193]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.801 1.434 3.348 0.001 [1.991 , 7.611]
## Robust - - 1.320 0.187 [-1.632 , 8.359]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_muni_school_area_per1000 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 31 136
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 5.957 5.957
## BW bias (b) 12.785 12.785
## rho (h/b) 0.466 0.466
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.663 5.988 0.111 0.912 [-11.074 , 12.400]
## Robust - - -0.241 0.809 [-16.264 , 12.701]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=edu_emp_per1000 | diff=0.06333 | p=0.0002704 | N_t=351 N_c=81
##
## ==============================================================================================================
## Outcome: edu_emp_per1000 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=30 km | p=1 | N used=366 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 366
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 285
## Eff. Number of Obs. 81 285
## 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. 81 285
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.006 0.051 -0.113 0.910 [-0.105 , 0.094]
## Robust - - -1.200 0.230 [-0.270 , 0.065]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=40 km | p=1 | N used=432 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 432
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 351
## Eff. Number of Obs. 81 351
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 81 351
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.046 0.485 0.627 [-0.068 , 0.112]
## Robust - - -1.009 0.313 [-0.231 , 0.074]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | h=50 km | p=1 | N used=491 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 491
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 410
## Eff. Number of Obs. 81 410
## 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. 81 410
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.037 0.044 0.850 0.395 [-0.049 , 0.124]
## Robust - - -0.723 0.470 [-0.202 , 0.093]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — edu_emp_per1000 | AUTO bandwidth (default) | p=1 | N used=693 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 693
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 81 612
## Eff. Number of Obs. 33 107
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 9.000 9.000
## BW bias (b) 14.251 14.251
## rho (h/b) 0.632 0.632
## Unique Obs. 80 606
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.105 0.095 -1.111 0.266 [-0.291 , 0.080]
## Robust - - -1.050 0.294 [-0.373 , 0.113]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=PublS_CyclePath_per | diff=6.738 | p=7.322e-17 | N_t=680 N_c=133
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=30 km | p=1 | N used=690 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 690
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 558
## Eff. Number of Obs. 132 558
## 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. 132 558
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.406 2.544 1.732 0.083 [-0.579 , 9.392]
## Robust - - -0.028 0.978 [-8.923 , 8.674]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=40 km | p=1 | N used=813 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 813
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 680
## Eff. Number of Obs. 133 680
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 680
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.229 2.270 2.303 0.021 [0.780 , 9.678]
## Robust - - 0.290 0.772 [-6.636 , 8.939]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=50 km | p=1 | N used=969 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 969
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 836
## Eff. Number of Obs. 133 836
## 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. 133 836
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.598 2.150 2.603 0.009 [1.383 , 9.812]
## Robust - - 0.532 0.595 [-5.378 , 9.380]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | AUTO bandwidth (default) | p=1 | N used=1385 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1385
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1252
## Eff. Number of Obs. 60 234
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 10.167 10.167
## BW bias (b) 16.241 16.241
## rho (h/b) 0.626 0.626
## Unique Obs. 130 1236
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.064 5.088 -0.012 0.990 [-10.037 , 9.910]
## Robust - - -0.200 0.842 [-14.054 , 11.453]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=pol_mun_road | diff=13.15 | p=0.02435 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: pol_mun_road | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -3.033 13.519 -0.224 0.822 [-29.530 , 23.464]
## Robust - - -1.755 0.079 [-84.260 , 4.638]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.026 11.908 0.590 0.555 [-16.312 , 30.364]
## Robust - - -1.631 0.103 [-76.033 , 6.954]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 12.367 11.483 1.077 0.282 [-10.140 , 34.874]
## Robust - - -1.394 0.163 [-67.818 , 11.450]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — pol_mun_road | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 46 184
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.960 7.960
## BW bias (b) 11.577 11.577
## rho (h/b) 0.688 0.688
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -35.434 26.172 -1.354 0.176 [-86.730 , 15.862]
## Robust - - -1.177 0.239 [-98.638 , 24.628]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2010 | diff=2.07 | p=0.003646 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.042 1.558 -0.027 0.979 [-3.095 , 3.011]
## Robust - - -1.169 0.243 [-7.616 , 1.926]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.501 1.458 0.344 0.731 [-2.356 , 3.358]
## Robust - - -0.852 0.394 [-6.177 , 2.435]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.721 1.416 0.509 0.611 [-2.055 , 3.496]
## Robust - - -0.628 0.530 [-5.507 , 2.835]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2010 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 161
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.862 6.862
## BW bias (b) 13.851 13.851
## rho (h/b) 0.495 0.495
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.201 4.441 -0.045 0.964 [-8.905 , 8.503]
## Robust - - -0.076 0.939 [-12.023 , 11.121]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=Pillar2_pol | year=2020 | diff=4.76 | p=3.93e-08 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.044 1.709 0.611 0.541 [-2.306 , 4.394]
## Robust - - -0.062 0.951 [-5.420 , 5.088]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.881 1.626 1.156 0.248 [-1.307 , 5.068]
## Robust - - -0.181 0.856 [-5.218 , 4.336]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.323 1.594 1.457 0.145 [-0.802 , 5.447]
## Robust - - -0.009 0.993 [-4.670 , 4.628]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — Pillar2_pol | Year=2020 | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 43 164
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.957 6.957
## BW bias (b) 13.924 13.924
## rho (h/b) 0.500 0.500
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.818 4.529 0.622 0.534 [-6.058 , 11.695]
## Robust - - 0.507 0.612 [-8.800 , 14.944]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_civil | diff=9.426 | p=0.00751 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: marr_civil | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.760 5.116 -0.344 0.731 [-11.788 , 8.268]
## Robust - - -1.098 0.272 [-19.159 , 5.404]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.150 3.257 0.660 0.509 [-4.234 , 8.533]
## Robust - - -1.141 0.254 [-25.662 , 6.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 5.032 3.062 1.643 0.100 [-0.969 , 11.034]
## Robust - - -1.036 0.300 [-21.931 , 6.766]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_civil | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 38 148
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 6.444 6.444
## BW bias (b) 10.938 10.938
## rho (h/b) 0.589 0.589
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7.567 5.848 1.294 0.196 [-3.895 , 19.028]
## Robust - - 1.699 0.089 [-1.999 , 28.047]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=marr_rel | diff=4.766 | p=0.0001148 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: marr_rel | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.387 2.345 -0.165 0.869 [-4.984 , 4.209]
## Robust - - -1.361 0.173 [-12.284 , 2.214]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.373 1.868 0.735 0.462 [-2.289 , 5.034]
## Robust - - -1.238 0.216 [-12.154 , 2.744]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.539 1.780 1.426 0.154 [-0.950 , 6.028]
## Robust - - -0.960 0.337 [-10.352 , 3.545]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — marr_rel | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 55 206
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 8.640 8.640
## BW bias (b) 11.967 11.967
## rho (h/b) 0.722 0.722
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -4.852 4.437 -1.093 0.274 [-13.548 , 3.845]
## Robust - - -1.091 0.275 [-16.298 , 4.641]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=incomepc | diff=2084 | p=3.064e-17 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: incomepc | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2206.598 507.983 4.344 0.000 [1210.970 , 3202.226]
## Robust - - 0.858 0.391 [-995.370 , 2544.790]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2360.419 467.447 5.050 0.000 [1444.239 , 3276.599]
## Robust - - 2.019 0.043 [45.839 , 3084.349]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2375.555 449.294 5.287 0.000 [1494.955 , 3256.155]
## Robust - - 2.694 0.007 [537.733 , 3410.536]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — incomepc | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 21 112
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 4.967 4.967
## BW bias (b) 12.251 12.251
## rho (h/b) 0.405 0.405
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 7828.024 5123.781 1.528 0.127 [-2214.403 , 17870.451]
## Robust - - 1.551 0.121 [-2323.064 , 19946.656]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=income | diff=116500000 | p=0.01785 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: income | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-52407006.83862765696.903 -0.835 0.404[-175425512.233 , 70611498.557]
## Robust - - -2.038 0.042[-217242506.256 , -4229898.356]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional8065490.62030865204.834 0.261 0.794[-52429199.230 , 68560180.469]
## Robust - - -1.516 0.130[-353449243.591 , 45193458.674]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional51036928.19428521863.830 1.789 0.074[-4864897.685 , 106938754.073]
## Robust - - -1.395 0.163[-291619227.423 , 49145216.763]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — income | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 47 185
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.999 7.999
## BW bias (b) 11.726 11.726
## rho (h/b) 0.682 0.682
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-65598987.39857953638.311 -1.132 0.258[-179186031.260 , 47988056.464]
## Robust - - -0.868 0.386[-202067074.138 , 78056884.815]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expend_level | diff=0.6987 | p=0.004729 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: expend_level | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.214 0.585 0.366 0.714 [-0.932 , 1.360]
## Robust - - 0.148 0.882 [-1.943 , 2.261]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.206 0.536 0.385 0.700 [-0.844 , 1.257]
## Robust - - 0.347 0.729 [-1.507 , 2.155]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.256 0.517 0.495 0.621 [-0.758 , 1.270]
## Robust - - 0.357 0.721 [-1.433 , 2.072]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expend_level | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 44 171
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 7.318 7.318
## BW bias (b) 14.949 14.949
## rho (h/b) 0.490 0.490
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.376 1.951 -0.193 0.847 [-4.199 , 3.447]
## Robust - - -0.264 0.792 [-5.547 , 4.230]
## =============================================================================
## NULL## [Lombardia diff-means] h=40 km | outcome=expenditure | diff=1074000 | p=0.01547 | N_t=688 N_c=133
##
## ==============================================================================================================
## Outcome: expenditure | LOMBARDIA ONLY | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=696 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 696
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 564
## Eff. Number of Obs. 132 564
## 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. 132 564
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-426528.558559928.373 -0.762 0.446[-1523968.003 , 670910.887]
## Robust - - -1.898 0.058[-1816684.760 , 28990.212]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=821 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 821
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 688
## Eff. Number of Obs. 133 688
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 133 688
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 89112.810267018.946 0.334 0.739[-434234.708 , 612460.328]
## Robust - - -1.381 0.167[-3041870.279 , 527107.272]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=978 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 978
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 845
## Eff. Number of Obs. 133 845
## 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. 133 845
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional473204.914245111.504 1.931 0.054 [-7204.806 , 953614.634]
## Robust - - -1.274 0.203[-2509457.397 , 532493.162]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=1397 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 1397
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 133 1264
## Eff. Number of Obs. 10 49
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.116 3.116
## BW bias (b) 8.022 8.022
## rho (h/b) 0.388 0.388
## Unique Obs. 130 1248
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional862313.164444987.329 1.938 0.053 [-9845.975 , 1734472.303]
## Robust - - 2.537 0.011[434665.445 , 3389359.790]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2# Export Lombardia diff-means results at 40 km
dm_lomb40 <- dplyr::bind_rows(lomb_dm40)
if (nrow(dm_lomb40) > 0) {
readr::write_csv(dm_lomb40, dm_csv_lomb40)
cat("
[Lombardia diff-means] Wrote: ", dm_csv_lomb40, " | rows=", nrow(dm_lomb40), "
", sep = "")
print(dm_lomb40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, p_value) %>%
head(10))
} else {
cat("
[Lombardia diff-means] No usable data within ±40 km for any outcome; skipping export.
", sep = "")
}##
## [Lombardia diff-means] Wrote: output/diffmeans_Lombardia_h40.csv | rows=18
## # A tibble: 10 × 9
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 694 133 -0.0120 0.00225
## 2 LOMBA… gb_reg… NA 40 694 133 0.0676 0.0115
## 3 LOMBA… evasio… NA 40 688 133 -2.77 0.741
## 4 LOMBA… servic… NA 40 688 133 2.48 0.273
## 5 LOMBA… Admin_… NA 40 226 49 0.143 0.0743
## 6 LOMBA… edu_se… NA 40 671 121 1.40 0.257
## 7 LOMBA… edu_mu… NA 40 688 133 3.24 0.816
## 8 LOMBA… edu_em… NA 40 351 81 0.0633 0.0172
## 9 LOMBA… PublS_… NA 40 680 133 6.74 0.764
## 10 LOMBA… pol_mu… NA 40 688 133 13.1 5.82
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()donut_lomb <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lombardia))) next
d1 <- collapse_one_row_per_muni(df_lombardia, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
d1_donut <- apply_donut_treated_only(d1, donut_km = DONUT_TREATED_ONLY_KM)
# MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub_noFE(d1_donut, h)
if (is.null(sub)) next
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P,
label = paste0("DONUT Lombardia | ", yvar, " | h=", h))
if (is.null(rb)) next
donut_lomb[[length(donut_lomb) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_noFE_DONUT_treated2p5", year = NA_integer_, h_type = "MANUAL")
}
# AUTO bandwidth
sub_full <- make_sub_full_noFE(d1_donut)
if (!is.null(sub_full)) {
rb_auto <- safe_rdrobust(sub_full$Y, sub_full$X, p = P,
label = paste0("DONUT Lombardia AUTO | ", yvar))
if (!is.null(rb_auto)) {
donut_lomb[[length(donut_lomb) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_noFE_DONUT_treated2p5", year = NA_integer_, h_type = "AUTO")
}
}
}
donut_lomb_df <- dplyr::bind_rows(donut_lomb)
if (nrow(donut_lomb_df) > 0) {
readr::write_csv(donut_lomb_df, donut_csv_lomb)
cat("[Donut RD | Lombardia] Wrote: ", donut_csv_lomb, " | rows=", nrow(donut_lomb_df), "
", sep = "")
} else {
cat("[Donut RD | Lombardia] No donut RD results produced.
")
}## [Donut RD | Lombardia] Wrote: output/rdrobust_results_Lombardia_noFE_DONUT_treated2p5.csv | rows=68# 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): 132print(sq_control_muni %>% dplyr::select(COMUNE, X_km, Treated, COD_PROV), n = Inf)## # A tibble: 132 × 4
## COMUNE X_km Treated COD_PROV
## <chr> <dbl> <int> <int>
## 1 Brallo di Pregola -31.0 0 18
## 2 Santa Margherita di Staffora -29.9 0 18
## 3 Cecima -28.3 0 18
## 4 Rivanazzano Terme -27.5 0 18
## 5 Bagnaria -26.6 0 18
## 6 Godiasco Salice Terme -26.0 0 18
## 7 Ponte Nizza -25.1 0 18
## 8 Retorbido -25.0 0 18
## 9 Varzi -24.2 0 18
## 10 Codevilla -23.2 0 18
## 11 Menconico -22.8 0 18
## 12 Voghera -22.6 0 18
## 13 Rocca Susella -22.4 0 18
## 14 Frascarolo -22.3 0 18
## 15 Suardi -21.7 0 18
## 16 Casei Gerola -21.3 0 18
## 17 Montesegale -21.0 0 18
## 18 Torrazza Coste -20.9 0 18
## 19 Montebello della Battaglia -20.0 0 18
## 20 Val di Nizza -20.0 0 18
## 21 Torre Beretti e Castellaro -19.9 0 18
## 22 Gambarana -19.9 0 18
## 23 Lungavilla -19.1 0 18
## 24 Pizzale -19.0 0 18
## 25 Romagnese -18.0 0 18
## 26 Verretto -17.9 0 18
## 27 Silvano Pietra -17.4 0 18
## 28 Sartirana Lomellina -17.2 0 18
## 29 Borgo Priolo -17.1 0 18
## 30 Casteggio -17.1 0 18
## 31 Pieve del Cairo -17.0 0 18
## 32 Fortunago -16.9 0 18
## 33 Palestro -16.8 0 18
## 34 Cervesina -16.4 0 18
## 35 Casatisma -16.4 0 18
## 36 Breme -16.3 0 18
## 37 Robecco Pavese -16.2 0 18
## 38 Zavattarello -16.1 0 18
## 39 Mezzana Bigli -15.8 0 18
## 40 Castelletto di Branduzzo -15.7 0 18
## 41 Pancarana -15.5 0 18
## 42 Corana -15.5 0 18
## 43 Mede -15.5 0 18
## 44 Langosco -15.4 0 18
## 45 Corvino San Quirico -15.3 0 18
## 46 Candia Lomellina -15.2 0 18
## 47 Calvignano -14.8 0 18
## 48 Villa Biscossi -14.5 0 18
## 49 Rosasco -14.3 0 18
## 50 Torricella Verzate -14.2 0 18
## 51 Confienza -13.9 0 18
## 52 Borgoratto Mormorolo -13.9 0 18
## 53 Santa Giuletta -13.2 0 18
## 54 Bressana Bottarone -13.1 0 18
## 55 Oliva Gessi -13.1 0 18
## 56 Galliavola -12.9 0 18
## 57 Pinarolo Po -12.9 0 18
## 58 Mezzana Rabattone -12.8 0 18
## 59 Bastida Pancarana -12.7 0 18
## 60 Semiana -12.5 0 18
## 61 Sannazzaro de' Burgondi -11.9 0 18
## 62 Valle Lomellina -11.9 0 18
## 63 Redavalle -11.7 0 18
## 64 Ferrera Erbognone -11.7 0 18
## 65 Pieve Albignola -11.4 0 18
## 66 Cozzo -11.4 0 18
## 67 Barbianello -11.2 0 18
## 68 Lomello -10.9 0 18
## 69 Montalto Pavese -10.9 0 18
## 70 Mornico Losana -10.9 0 18
## 71 Robbio -10.8 0 18
## 72 Sommo -10.7 0 18
## 73 Zinasco -10.4 0 18
## 74 Velezzo Lomellina -10.1 0 18
## 75 Castelnovetto -9.74 0 18
## 76 Verrua Po -9.64 0 18
## 77 Rocca de' Giorgi -9.57 0 18
## 78 Casanova Lonati -9.26 0 18
## 79 Cava Manara -8.60 0 18
## 80 Pietra de' Giorgi -8.55 0 18
## 81 Zeme -8.55 0 18
## 82 Rea -8.50 0 18
## 83 Broni -8.47 0 18
## 84 Cigognola -8.44 0 18
## 85 Scaldasole -8.36 0 18
## 86 Sant'Angelo Lomellina -8.22 0 18
## 87 Mezzanino -8.00 0 18
## 88 Volpara -7.71 0 18
## 89 Campospinoso Albaredo -7.33 0 18
## 90 Lirio -7.27 0 18
## 91 Montecalvo Versiggia -6.73 0 18
## 92 Nicorvo -6.67 0 18
## 93 Borgo San Siro -6.67 0 18
## 94 Valeggio -6.64 0 18
## 95 San Giorgio di Lomellina -6.58 0 18
## 96 Ottobiano -6.35 0 18
## 97 Golferenzo -6.35 0 18
## 98 Dorno -6.32 0 18
## 99 Garlasco -6.30 0 18
## 100 Tromello -6.30 0 18
## 101 Carbonara al Ticino -6.30 0 18
## 102 Ceretto Lomellina -6.14 0 18
## 103 Cergnago -5.86 0 18
## 104 Castana -5.83 0 18
## 105 Canneto Pavese -5.77 0 18
## 106 San Martino Siccomario -5.66 0 18
## 107 Villanova d'Ardenghi -5.58 0 18
## 108 Travacò Siccomario -5.32 0 18
## 109 Castello d'Agogna -5.28 0 18
## 110 Alagna -5.25 0 18
## 111 Stradella -5.19 0 18
## 112 Olevano di Lomellina -5.08 0 18
## 113 Montescano -4.94 0 18
## 114 Gropello Cairoli -4.70 0 18
## 115 Gambolò -4.62 0 18
## 116 Zerbolò -4.39 0 18
## 117 Cassolnovo -4.11 0 18
## 118 Gravellona Lomellina -3.95 0 18
## 119 Santa Maria della Versa -3.88 0 18
## 120 San Cipriano Po -3.86 0 18
## 121 Mortara -3.83 0 18
## 122 Albonese -3.74 0 18
## 123 Vigevano -3.57 0 18
## 124 Arena Po -3.08 0 18
## 125 Bosnasco -3.03 0 18
## 126 Cilavegna -2.76 0 18
## 127 Parona -2.76 0 18
## 128 Portalbera -2.68 0 18
## 129 Montù Beccaria -2.65 0 18
## 130 Rovescala -2.55 0 18
## 131 San Damiano al Colle -2.55 0 18
## 132 Zenevredo -2.19 0 18# 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()
# NEW: Donut RD (Lombardia square + no FE)
# Drop only treated-side observations within 2.5 km of the cutoff (keep all control-side)donut_sq <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_lomb_square))) next
# Pillar2_pol in square: if year exists, keep as in main section
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)
d1_donut <- apply_donut_treated_only(d1, donut_km = DONUT_TREATED_ONLY_KM)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1_donut, h)
if (is.null(sub)) next
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P,
label = paste0("DONUT Square | ", yvar, " | Year=", yr, " | h=", h))
if (is.null(rb)) next
donut_sq[[length(donut_sq) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE_DONUT_treated2p5", year = yr, h_type = "MANUAL")
}
sub_full <- make_sub_full_noFE(d1_donut)
if (!is.null(sub_full)) {
rb_auto <- safe_rdrobust(sub_full$Y, sub_full$X, p = P,
label = paste0("DONUT Square AUTO | ", yvar, " | Year=", yr))
if (!is.null(rb_auto)) {
donut_sq[[length(donut_sq) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE_DONUT_treated2p5", year = yr, h_type = "AUTO")
}
}
}
} else {
d1 <- collapse_one_row_per_muni(df_lomb_square, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
d1_donut <- apply_donut_treated_only(d1, donut_km = DONUT_TREATED_ONLY_KM)
for (h in BWS_KM) {
sub <- make_sub_noFE(d1_donut, h)
if (is.null(sub)) next
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P,
label = paste0("DONUT Square | ", yvar, " | h=", h))
if (is.null(rb)) next
donut_sq[[length(donut_sq) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "LOMBARDIA_SQUARE_noFE_DONUT_treated2p5", year = NA_integer_, h_type = "MANUAL")
}
sub_full <- make_sub_full_noFE(d1_donut)
if (!is.null(sub_full)) {
rb_auto <- safe_rdrobust(sub_full$Y, sub_full$X, p = P,
label = paste0("DONUT Square AUTO | ", yvar))
if (!is.null(rb_auto)) {
donut_sq[[length(donut_sq) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "LOMBARDIA_SQUARE_noFE_DONUT_treated2p5", year = NA_integer_, h_type = "AUTO")
}
}
}
}
donut_sq_df <- dplyr::bind_rows(donut_sq)
if (nrow(donut_sq_df) > 0) {
readr::write_csv(donut_sq_df, donut_csv_sq)
cat("[Donut RD | Square] Wrote: ", donut_csv_sq, " | rows=", nrow(donut_sq_df), "
", sep = "")
} else {
cat("[Donut RD | Square] No donut RD results produced.
")
}## [Donut RD | Square] Wrote: output/rdrobust_results_LombardiaSquare_area_x1.25_noFE_DONUT_treated2p5.csv | rows=72dm_sq40 <- dplyr::bind_rows(sq_dm40) if (nrow(dm_sq40) > 0) { readr::write_csv(dm_sq40, dm_csv_sq40) cat(“Wrote:”, dm_csv_sq40, ” | rows=“, nrow(dm_sq40),”“, sep =”“) print( dm_sq40 %>% dplyr::select(sample, outcome, year, h_km, n_treated, n_control, diff_treat_minus_control, se_diff, t_stat, df, p_value) %>% head(10) ) } else { cat(”No usable data within ±40 km for any outcome; skipping export.“, sep =”“) }
dm_sqsign <- dplyr::bind_rows(sq_sign_dm) if (nrow(dm_sqsign) > 0) { readr::write_csv(dm_sqsign, dm_csv_sqsign) cat(“Wrote:”, dm_csv_sqsign, ” | rows=“, nrow(dm_sqsign),”“, sep =”“) print( dm_sqsign %>% dplyr::select(sample, outcome, year, n_pos, n_neg, diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>% head(10) ) } else { cat(”No usable data in square for any outcome; skipping export.“, sep =”“) }
{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)
# 1) Bandwidth-based diff-in-means (|X| <= 40 km): treated vs control by Treated indicator
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).\n")
}
cat("\n")
# 2) Within-square sign-based diff-in-means (X >= 0 vs X < 0): no bandwidth trimming
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).\n")
}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