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","Admin_Tax_Emp",
"edu_serv_lvl","edu_muni_school_area_per1000",
"PublS_CyclePath_per","pol_mun_road","Pillar2_pol",
"marr_civil","marr_rel","incomepc","income",
"expend_level","services_level","expenditure"
)
YEARS <- c(2010, 2020)df0 <- readr::read_csv(DATA_PATH, show_col_types = FALSE)
# key column (municipality id)
KEYCOL <- if ("istat" %in% names(df0)) "istat" else if ("ISTAT" %in% names(df0)) "ISTAT" else stop("No istat/ISTAT column found.")
# ensure expected columns exist
stopifnot(RUNNING %in% names(df0), REGION %in% names(df0))
# region as factor (fixed effects)
df0 <- df0 %>% mutate(.region_fe = factor(.data[[REGION]]))
# convenience alias to match older scripts
if (!("ireg" %in% names(df0))) df0 <- df0 %>% mutate(ireg = as.integer(.data[[REGION]]))
# -----------------------------
# Manual distance corrections
# -----------------------------
manual0 <- readxl::read_excel(MANUAL_DISTANCE_PATH)
# Expected columns in manual file:
# COD_REG, COMUNE, Treated, distance_updated
needed_manual <- c("COD_REG", "COMUNE", "Treated", "distance_updated")
stopifnot(all(needed_manual %in% names(manual0)))
manual <- manual0 %>%
mutate(
COD_REG = as.integer(COD_REG),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE))),
distance_updated = as.numeric(distance_updated)
) %>%
filter(!is.na(distance_updated)) %>%
select(COD_REG, Treated, COMUNE_clean, distance_updated)
df0 <- df0 %>%
mutate(
COD_REG = as.integer(.data[[REGION]]),
Treated = as.integer(Treated),
COMUNE_clean = stringr::str_squish(stringr::str_to_upper(as.character(COMUNE)))
) %>%
left_join(manual, by = c("COD_REG", "Treated", "COMUNE_clean")) %>%
mutate(
.running_original = .data[[RUNNING]],
# overwrite where manual distance exists
"{RUNNING}" := dplyr::if_else(!is.na(distance_updated), distance_updated, .data[[RUNNING]]),
.running_overwritten = !is.na(distance_updated)
)
cat("Manual distance overrides applied:\n")## Manual distance overrides applied:df0 %>%
summarise(
n_rows = n(),
n_overwritten_rows = sum(.running_overwritten, na.rm = TRUE),
n_overwritten_muni = n_distinct(.data[[KEYCOL]][.running_overwritten]),
n_regions = n_distinct(.region_fe),
years = if ("year" %in% names(df0)) paste(sort(unique(year)), collapse = ", ") else NA_character_
) %>%
print()## # A tibble: 1 × 5
## n_rows n_overwritten_rows n_overwritten_muni n_regions years
## <int> <int> <int> <int> <chr>
## 1 7080 68 34 8 2010, 2020# Optional: inspect which municipalities were overwritten
df0 %>%
filter(.running_overwritten) %>%
distinct(COD_REG, COMUNE, Treated, .running_original, !!sym(RUNNING)) %>%
arrange(COD_REG, COMUNE) %>%
head(25) %>%
print()## # A tibble: 25 × 5
## COD_REG COMUNE Treated .running_original distance_treated_positi…¹
## <int> <chr> <int> <dbl> <dbl>
## 1 3 Albiolo 1 -25.3 28.4
## 2 3 Albuzzano 1 -3.67 3.67
## 3 3 Belgioioso 1 -2.67 2.67
## 4 3 Bereguardo 1 -2.76 2.76
## 5 3 Borgo San Siro 0 5.23 -6.67
## 6 3 Campione d'Italia 1 -22.1 22.1
## 7 3 Ceranova 1 -1.91 10.9
## 8 3 Copiano 1 -2.07 8.31
## 9 3 Cura Carpignano 1 -2.55 6.3
## 10 3 Faloppio 1 -27.3 31.6
## # ℹ 15 more rows
## # ℹ abbreviated name: ¹distance_treated_positive_xcollapse_one_row_per_muni <- function(d, keycol, xcol, ycol, keep_year = FALSE) {
# Collapses to one row per municipality (mean across duplicates).
# Also carries Treated (or Treated_num) and COD_PROV when available.
gvars <- c(keycol)
if (keep_year && ("year" %in% names(d))) gvars <- c(gvars, "year")
d %>%
group_by(across(all_of(gvars))) %>%
summarise(
X = mean(.data[[xcol]], na.rm = TRUE),
Y = mean(.data[[ycol]], na.rm = TRUE),
Treated = dplyr::first(
if ("Treated" %in% names(d)) as.integer(.data[["Treated"]])
else if ("Treated_num" %in% names(d)) as.integer(.data[["Treated_num"]])
else NA_integer_
),
COD_PROV = dplyr::first(if ("COD_PROV" %in% names(d)) as.integer(.data[["COD_PROV"]]) else NA_integer_),
.region_fe = dplyr::first(if (".region_fe" %in% names(d)) .data[[".region_fe"]] else NA),
.groups = "drop"
)
}
make_sub <- function(d, h) {
# Filter to bandwidth window and drop missing (requires .region_fe).
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.region_fe),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_noFE <- function(d, h) {
# Filter to bandwidth window and drop missing (NO FE requirement).
sub <- d %>%
filter(!is.na(X), !is.na(Y),
dplyr::between(X, -h, h))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; with FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y), !is.na(.region_fe))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
make_sub_full_noFE <- function(d) {
# Drop missing but DO NOT bandwidth-trim (used for data-driven bandwidth selection; no FE requirement).
sub <- d %>% filter(!is.na(X), !is.na(Y))
if (nrow(sub) < 30) return(NULL)
if (stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0) < 10 || sum(sub$X >= 0) < 10) return(NULL)
sub
}
region_covs <- function(sub) {
# region dummies (no intercept) for rdrobust(covs=...)
stats::model.matrix(~ .region_fe - 1, data = sub)
}
residualize_region <- function(y, sub) {
# partial out region FE for plotting convenience
stats::residuals(stats::lm(y ~ .region_fe, data = sub))
}
extract_rdrobust <- function(rb, outcome, h, sample, year = NA_integer_, h_type = "MANUAL") {
tibble::tibble(
sample = sample,
outcome = outcome,
year = year,
h_type = h_type, # MANUAL vs AUTO
h_km = h, # manual h, NA for AUTO
p = P,
N = if (!is.null(rb$N)) sum(rb$N) else NA_integer_,
N_left = if (!is.null(rb$N)) rb$N[1] else NA_integer_,
N_right = if (!is.null(rb$N)) rb$N[2] else NA_integer_,
bw_left = if (!is.null(rb$bws)) rb$bws[1] else NA_real_,
bw_right = if (!is.null(rb$bws)) rb$bws[2] else NA_real_,
coef = list(rb$coef),
se = list(rb$se),
pv = list(rb$pv),
ci = list(rb$ci)
)
}
safe_rdrobust <- function(y, x, ..., label = "") {
# Wrapper to avoid hard stops from rdrobust numerical failures (e.g., non-PD matrices).
# Returns NULL on error and prints the error to the current output connection (sink-safe).
tryCatch(
rdrobust::rdrobust(y, x, ...),
error = function(e) {
cat("[Skip rdrobust ERROR] ", label, " : ", conditionMessage(e), "\n", sep = "")
return(NULL)
}
)
}
diff_means_test <- function(d, h, treated_col = "Treated") {
# Difference in means (treated - control) within |X| <= h, using Welch two-sample t-test.
sub <- d %>%
filter(!is.na(X), !is.na(Y), !is.na(.data[[treated_col]]),
dplyr::between(X, -h, h)) %>%
mutate(.tr = as.integer(.data[[treated_col]]))
if (!all(c(0L, 1L) %in% unique(sub$.tr))) return(NULL)
y1 <- sub$Y[sub$.tr == 1L]
y0 <- sub$Y[sub$.tr == 0L]
n1 <- sum(sub$.tr == 1L)
n0 <- sum(sub$.tr == 0L)
if (n1 < 5 || n0 < 5) return(NULL)
m1 <- mean(y1, na.rm = TRUE)
m0 <- mean(y0, na.rm = TRUE)
s1 <- stats::var(y1, na.rm = TRUE)
s0 <- stats::var(y0, na.rm = TRUE)
se <- sqrt(s1 / n1 + s0 / n0)
tt <- stats::t.test(Y ~ .tr, data = sub) # Welch by default
tibble::tibble(
h_km = h,
n_treated = n1,
n_control = n0,
mean_treated = m1,
mean_control = m0,
diff_treat_minus_control = m1 - m0,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}
diff_means_sign_test <- function(d) {
# Difference in means (X>=0 - X<0) using Welch two-sample t-test.
# Intended for within-square comparisons where "treated" is defined by the sign of the running variable.
sub <- d %>%
filter(!is.na(X), !is.na(Y)) %>%
mutate(.side = if_else(X >= 0, 1L, 0L))
if (!all(c(0L, 1L) %in% unique(sub$.side))) return(NULL)
y_pos <- sub$Y[sub$.side == 1L] # X >= 0
y_neg <- sub$Y[sub$.side == 0L] # X < 0
n_pos <- sum(sub$.side == 1L)
n_neg <- sum(sub$.side == 0L)
if (n_pos < 5 || n_neg < 5) return(NULL)
m_pos <- mean(y_pos, na.rm = TRUE)
m_neg <- mean(y_neg, na.rm = TRUE)
s_pos <- stats::var(y_pos, na.rm = TRUE)
s_neg <- stats::var(y_neg, na.rm = TRUE)
se <- sqrt(s_pos / n_pos + s_neg / n_neg)
tt <- stats::t.test(Y ~ .side, data = sub) # Welch by default
tibble::tibble(
n_pos = n_pos,
n_neg = n_neg,
mean_pos = m_pos,
mean_neg = m_neg,
diff_pos_minus_neg = m_pos - m_neg,
se_diff = se,
t_stat = unname(tt$statistic),
df = unname(tt$parameter),
p_value = tt$p.value
)
}# Output files (All Italy / Lombardia / Lombardia-square)
plots_pdf_all <- file.path(OUTDIR, "RD_plots_All_Italy_regFE_manualDistance.pdf")
plots_pdf_lomb <- file.path(OUTDIR, "RD_plots_Lombardia_noFE_manualDistance.pdf")
plots_pdf_square <- file.path(OUTDIR, sprintf("RD_plots_LombardiaSquare_area_x%0.2f_noFE_manualDistance.pdf", TARGET_AREA_SCALE))
plots_pdf_pavia <- file.path(OUTDIR, "RD_plots_Pavia_noFE_manualDistance.pdf")
results_csv <- file.path(OUTDIR, "rdrobust_results_All_Italy_Lombardia_Square_manualDistance.csv")
results_txt_all <- file.path(OUTDIR, "rdrobust_printout_All_Italy_regFE_manualDistance.txt")
results_txt_lomb <- file.path(OUTDIR, "rdrobust_printout_Lombardia_noFE_manualDistance.txt")
results_txt_sq <- file.path(OUTDIR, sprintf("rdrobust_printout_LombardiaSquare_area_x%0.2f_noFE_manualDistance.txt", TARGET_AREA_SCALE))
results_txt_pavia <- file.path(OUTDIR, "rdrobust_printout_Pavia_noFE_manualDistance.txt")
# Difference-in-means outputs (h = 40 km)
dm_csv_all40 <- file.path(OUTDIR, "diffmeans_FullItaly_h40.csv")
dm_csv_lomb40 <- file.path(OUTDIR, "diffmeans_Lombardia_h40.csv")
dm_csv_sq40 <- file.path(OUTDIR, "diffmeans_LombardiaSquare_h40.csv")
dm_csv_sqsign <- file.path(OUTDIR, "diffmeans_LombardiaSquare_sign.csv")
dm_csv_pavia <- file.path(OUTDIR, "diffmeans_Pavia_h20_30_40.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 (treated - control) within |X| <= 40 km (Full Italy)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
all_dm40[[length(all_dm40) + 1]] <- dm %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = yr)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar, " | year=", yr,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "
", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, " year=", yr, "
", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " Year=", yr, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = yr, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, " Year=", yr, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | Year=", yr, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = yr, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "esmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | Year=", yr, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}
next
}
# --- All other outcomes: collapse to 1 row per municipality ---
d1 <- collapse_one_row_per_muni(df0, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
# Difference in means (treated - control) within |X| <= 40 km (Full Italy)
dm <- diff_means_test(d1, h = H_DM)
if (!is.null(dm)) {
all_dm40[[length(all_dm40) + 1]] <- dm %>%
mutate(sample = "FULL_ITALY_regFE", outcome = yvar, year = NA_integer_)
cat("[Full Italy diff-means] h=", H_DM, " km | outcome=", yvar,
" | diff=", signif(dm$diff_treat_minus_control, 4),
" | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "
", sep = "")
} else {
cat("[Full Italy diff-means] Skip: insufficient treated/control data within ±", H_DM,
" km for outcome=", yvar, "
", sep = "")
}
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | FULL ITALY | p=", P, " | X in KM | REGION FE\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
# 1) RD plots (raw + region-adjusted) for MANUAL bandwidths
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip plot] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
rdplot(sub$Y, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | raw | h=", h, " km"))
Y_adj <- residualize_region(sub$Y, sub)
rdplot(Y_adj, sub$X, h = h, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | region FE residual | h=", h, " km"))
}
# 2) RD tables (MANUAL bandwidths; with region FE via covs)
for (h in BWS_KM) {
sub <- make_sub(d1, h)
if (is.null(sub)) {
cat("[Skip rdrobust] ", yvar, " h=", h, "km: too little usable data/variation\n", sep = "")
next
}
covs <- region_covs(sub)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | h=", h, " km | p=", P,
" | N used=", nrow(sub), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb <- rdrobust(sub$Y, sub$X, h = h, p = P, covs = covs)
print(summary(rb))
all_results[[length(all_results) + 1]] <- extract_rdrobust(rb, outcome = yvar, h = h, sample = "FULL_ITALY", year = NA_integer_, h_type = "MANUAL")
}
# 3) RD table (AUTO bandwidth; rdrobust selects bws)
sub_full <- make_sub_full(d1)
if (is.null(sub_full)) {
cat("[Skip AUTO rdrobust] ", yvar, ": too little usable data/variation\n", sep = "")
} else {
covs_full <- region_covs(sub_full)
cat("\n", strrep("-", 90), "\n", sep = "")
cat("RDROBUST — ", yvar, " | AUTO bandwidth (default) | p=", P,
" | N used=", nrow(sub_full), " | + REGION FE\n", sep = "")
cat(strrep("-", 90), "\n", sep = "")
rb_auto <- rdrobust(sub_full$Y, sub_full$X, p = P, covs = covs_full)
print(summary(rb_auto))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb_auto, outcome = yvar, h = NA_real_, sample = "FULL_ITALY", year = NA_integer_, h_type = "AUTO")
# Optional plots using h_plot = max(selected bws)
if (!is.null(rb_auto$bws) && all(is.finite(rb_auto$bws))) {
h_plot <- max(rb_auto$bws)
sub_plot <- make_sub(d1, h_plot)
if (!is.null(sub_plot)) {
rdplot(sub_plot$Y, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = yvar,
title = paste0(yvar, " | AUTO bw plot | h_plot=", round(h_plot, 2), " km"))
Y_adj <- residualize_region(sub_plot$Y, sub_plot)
rdplot(Y_adj, sub_plot$X, h = h_plot, p = P, binselect = "qsmv",
x.label = "Distance to Cutoff (km)",
y.label = paste0(yvar, " (adj. region FE)"),
title = paste0(yvar, " | AUTO bw plot (region FE resid) | h_plot=", round(h_plot, 2), " km"))
}
}
}
}## [Full Italy diff-means] h=40 km | outcome=gb_intensity | diff=0.004583 | p=5.036e-05 | N_t=734 N_c=637
##
## ==============================================================================================================
## Outcome: gb_intensity | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — gb_intensity | h=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 | 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 | 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=Admin_Tax_Emp | diff=0.1069 | p=0.1179 | N_t=232 N_c=217
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — Admin_Tax_Emp | h=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 | 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 | 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=PublS_CyclePath_per | diff=5.153 | p=9.42e-16 | N_t=694 N_c=602
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — PublS_CyclePath_per | h=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 | 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 | 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 | 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 | 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 | 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 | 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 | 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 | 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=services_level | diff=0.2873 | p=0.0668 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: services_level | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — services_level | h=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=expenditure | diff=314600 | p=0.527 | N_t=702 N_c=605
##
## ==============================================================================================================
## Outcome: expenditure | FULL ITALY | p=1 | X in KM | REGION FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=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) %>%
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=17
## # A tibble: 10 × 9
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 FULL_… gb_int… NA 40 734 637 0.00458 0.00113
## 2 FULL_… gb_reg… NA 40 734 637 -0.0390 0.0109
## 3 FULL_… evasio… NA 40 702 605 -2.86 0.437
## 4 FULL_… Admin_… NA 40 232 217 0.107 0.0681
## 5 FULL_… edu_se… NA 40 685 553 0.615 0.160
## 6 FULL_… edu_mu… NA 40 702 605 0.796 0.474
## 7 FULL_… PublS_… NA 40 694 602 5.15 0.633
## 8 FULL_… pol_mu… NA 40 702 605 -30.1 6.77
## 9 FULL_… Pillar… 2010 40 702 605 1.11 0.436
## 10 FULL_… Pillar… 2020 40 702 605 3.13 0.520
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()df_lombardia <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
sink(results_txt_lomb, split = TRUE)
cat("Using DF: Lombardia only (ireg==3) | rows=", nrow(df_lombardia),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_lombardia), "year", NA),
"\n", sep = "")## Using DF: Lombardia only (ireg==3) | rows=2814 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=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=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=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=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=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=17
## # A tibble: 10 × 9
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 694 133 -0.0120 0.00225
## 2 LOMBA… gb_reg… NA 40 694 133 0.0676 0.0115
## 3 LOMBA… evasio… NA 40 688 133 -2.77 0.741
## 4 LOMBA… Admin_… NA 40 226 49 0.143 0.0743
## 5 LOMBA… edu_se… NA 40 671 121 1.40 0.257
## 6 LOMBA… edu_mu… NA 40 688 133 3.24 0.816
## 7 LOMBA… PublS_… NA 40 680 133 6.74 0.764
## 8 LOMBA… pol_mu… NA 40 688 133 13.1 5.82
## 9 LOMBA… Pillar… 2010 40 688 133 2.07 0.703
## 10 LOMBA… Pillar… 2020 40 688 133 4.76 0.830
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 1 more variable: p_value <dbl>sink()# Columns (adjust only if your file differs)
COL_NAME <- "COMUNE"
COL_TREATED <- "Treated"
COL_BORDER <- "treated_border_municipality"
# Numerical tolerance to avoid boundary issues (meters)
EPS_M <- 1
guess_col <- function(df, candidates, label = "column") {
hit <- candidates[candidates %in% names(df)]
if (length(hit) == 0) stop("Could not find ", label, ". Tried: ", paste(candidates, collapse = ", "))
hit[[1]]
}
# Robust name normalization: lowercase, strip accents, drop punctuation, collapse whitespace
norm_name <- function(x) {
x <- as.character(x)
x <- str_trim(x)
fixed <- suppressWarnings(iconv(x, from = "latin1", to = "UTF-8"))
x[!is.na(fixed)] <- fixed[!is.na(fixed)]
x <- tolower(x)
x <- stringi::stri_trans_general(x, "NFD; [:Nonspacing Mark:] Remove; NFC")
x <- str_replace_all(x, "[’'`]", "")
x <- str_replace_all(x, "[^a-z0-9\\s]", " ")
x <- str_replace_all(x, "\\s+", " ")
str_trim(x)
}
inside_square <- function(points_sf, square_sfc) {
as.logical(sf::st_intersects(points_sf, square_sfc, sparse = FALSE)[, 1])
}
build_square_from_bbox_utm <- function(bbox_utm, area_scale = 1.25, eps = 1, utm_epsg = 32632) {
if (!is.finite(area_scale) || area_scale <= 0) stop("area_scale must be > 0.")
xmin <- bbox_utm[["xmin"]]; xmax <- bbox_utm[["xmax"]]
ymin <- bbox_utm[["ymin"]]; ymax <- bbox_utm[["ymax"]]
dx <- xmax - xmin
dy <- ymax - ymin
side_base <- max(dx, dy)
side_inflated <- side_base * sqrt(area_scale)
cx <- (xmin + xmax) / 2
cy <- (ymin + ymax) / 2
half <- (side_inflated / 2) + eps
sq <- sf::st_polygon(list(matrix(
c(cx - half, cy - half,
cx + half, cy - half,
cx + half, cy + half,
cx - half, cy + half,
cx - half, cy - half),
ncol = 2, byrow = TRUE
)))
list(
poly = sf::st_sfc(sq, crs = utm_epsg),
meta = list(
cx = cx, cy = cy,
side_base_m = side_base,
side_expanded_m = 2 * half,
side_multiplier = sqrt(area_scale),
area_scale = area_scale
)
)
}
# 1) Filter Lombardia from in-memory df0 (post distance overwrite)
lomb0 <- df0 %>%
filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
# 2) Determine coordinate column names
LATCOL_ALL <- guess_col(lomb0, c("lat", "LAT", "latitude", "Latitude"), "Lombardia latitude column")
LNGCOL_ALL <- guess_col(lomb0, c("lng", "LNG", "lon", "longitude", "Longitude"), "Lombardia longitude column")
# 3) Prep Lombardia points (WGS84)
lomb <- lomb0 %>%
mutate(
lat_num = suppressWarnings(as.numeric(.data[[LATCOL_ALL]])),
lng_num = suppressWarnings(as.numeric(.data[[LNGCOL_ALL]]))
) %>%
filter(!is.na(lat_num), !is.na(lng_num))
if (nrow(lomb) == 0) stop("Lombardia subset is empty after dropping missing coordinates.")
# Ensure border column exists (for compatibility with attached script)
if (!COL_BORDER %in% names(lomb)) lomb[[COL_BORDER]] <- 0L
# Optional hard-coding (ported from the attached script; affects only Treated_num and border flag)
APPLY_HARDCODING <- TRUE
if (isTRUE(APPLY_HARDCODING) && (COL_NAME %in% names(lomb)) && (COL_TREATED %in% names(lomb))) {
force_treated_raw <- c(
"Ceranoval", "Ceranova", "Lardirago", "Roncaro",
"Sant'Aleesio con Vialone", "Sant'Alessio con Vialone",
"Vistarino", "Cura Carpignano", "Albuzzano", "Copiano",
"Filighera", "Trivolzio", "Marcignago",
"Nosate", "Turbigo", "Vizzola Ticino", "Campione d'Italia",
"Ranco", "Sangiano", "Monvalle", "Faloppio", "Leggiuno", "Albiolo"
)
force_control_raw <- c(
"Vivegano", "Vigevano",
"Gambolò", "Gambolò",
"Borgo San Siro"
)
force_treated_border_raw <- c(
"Bereguardo", "Torre d'Isola", "Pavia", "Valle Salimbene", "Linarolo",
"Belgioioso", "Belgioso", "Belgioiso",
"Tosce de' Negri", "Torre de' Negri",
"Spessa",
"San Zenone al Po", "San Zenone Al Po",
"Zerbo"
)
force_border1_raw <- c("Vivegano", "Vigevano", "Borgo San Siro")
lomb <- lomb %>% mutate(
name_norm = norm_name(.data[[COL_NAME]]),
Treated_num = suppressWarnings(as.integer(.data[[COL_TREATED]]))
)
force_treated <- unique(norm_name(force_treated_raw))
force_control <- unique(norm_name(force_control_raw))
force_treated_border <- unique(norm_name(force_treated_border_raw))
force_border1 <- unique(norm_name(force_border1_raw))
lomb <- lomb %>%
mutate(
Treated_num = if_else(name_norm %in% force_treated, 1L, Treated_num),
Treated_num = if_else(name_norm %in% force_control, 0L, Treated_num),
Treated_num = if_else(name_norm %in% force_treated_border, 1L, Treated_num),
!!COL_BORDER := if_else(name_norm %in% force_treated_border, 1L, .data[[COL_BORDER]]),
!!COL_BORDER := if_else(name_norm %in% force_border1, 1L, .data[[COL_BORDER]])
) %>%
select(-name_norm)
}
# 4) Read the baseline square dataset to infer the footprint bbox
base0 <- readr::read_csv(BASE_SQUARE_PATH, show_col_types = FALSE)
# If baseline has the region column, enforce Lombardia-only footprint; else use all rows.
if (REGION %in% names(base0)) {
base0 <- base0 %>% filter(as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA)
}
LATCOL_BASE <- guess_col(base0, c("lat", "LAT", "latitude", "Latitude"), "baseline square latitude column")
LNGCOL_BASE <- guess_col(base0, c("lng", "LNG", "lon", "longitude", "Longitude"), "baseline square longitude column")
base <- base0 %>%
mutate(
lat_num = suppressWarnings(as.numeric(.data[[LATCOL_BASE]])),
lng_num = suppressWarnings(as.numeric(.data[[LNGCOL_BASE]]))
) %>%
filter(!is.na(lat_num), !is.na(lng_num))
if (nrow(base) == 0) stop("Baseline square dataset has no valid coordinates after filtering.")
# 5) Build SF points and infer baseline square footprint in UTM
lomb_sf_wgs <- st_as_sf(lomb, coords = c("lng_num", "lat_num"), crs = 4326, remove = FALSE)
lomb_sf_utm <- st_transform(lomb_sf_wgs, UTM_EPSG)
base_sf_wgs <- st_as_sf(base, coords = c("lng_num", "lat_num"), crs = 4326, remove = FALSE)
base_sf_utm <- st_transform(base_sf_wgs, UTM_EPSG)
bbox_base <- st_bbox(base_sf_utm)
sq <- build_square_from_bbox_utm(bbox_base, area_scale = TARGET_AREA_SCALE, eps = EPS_M, utm_epsg = UTM_EPSG)
in_sq <- inside_square(lomb_sf_utm, sq$poly)
df_lomb_square <- lomb_sf_utm %>%
mutate(in_expanded_square = in_sq) %>%
filter(in_expanded_square) %>%
st_drop_geometry()
# 6) Write square dataset + metadata
square_out_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f.csv", TARGET_AREA_SCALE))
square_meta_file <- file.path(OUTDIR, sprintf("lombardia_square_area_x%0.2f_metadata.csv", TARGET_AREA_SCALE))
readr::write_csv(df_lomb_square, square_out_file)
meta <- tibble::tibble(
baseline_n = nrow(base),
expanded_n = nrow(df_lomb_square),
target_area_scale = TARGET_AREA_SCALE,
side_multiplier = sq$meta$side_multiplier,
side_base_m = sq$meta$side_base_m,
side_expanded_m = sq$meta$side_expanded_m
)
readr::write_csv(meta, square_meta_file)
cat("\n=== Lombardia square constructed ===\n")##
## === Lombardia square constructed ===cat("Square dataset: ", square_out_file, "\n", sep = "")## Square dataset: output/lombardia_square_area_x1.25.csvcat("Square metadata: ", square_meta_file, "\n", sep = "")## Square metadata: output/lombardia_square_area_x1.25_metadata.csvprint(meta)## # A tibble: 1 × 6
## baseline_n expanded_n target_area_scale side_multiplier side_base_m
## <int> <int> <dbl> <dbl> <dbl>
## 1 546 658 1.25 1.12 83583.
## # ℹ 1 more variable: side_expanded_m <dbl>sink(results_txt_sq, split = TRUE)
cat("Using DF: Lombardia square subsample | rows=", nrow(df_lomb_square),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_lomb_square), "year", NA),
"\n", sep = "")## Using DF: Lombardia square subsample | rows=658 | key=istat | yearcol=yearcat("Running var: ", RUNNING, " (KM) | manual bandwidths=", paste(BWS_KM, collapse = ", "),
" | p=", P, " | NO regional FE\n\n", sep = "")## Running var: distance_treated_positive_x (KM) | manual bandwidths=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: 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: 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: 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: expenditure | LOMBARDIA SQUARE | p=1 | X in KM | NO region FE
## ==============================================================================================================##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=30 km | p=1 | N used=317 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 317
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 186
## Eff. Number of Obs. 131 186
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 131 186
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1826407.3501613902.328 -1.132 0.258[-4989597.788 , 1336783.087]
## Robust - - -1.615 0.106[-1730029.922 , 166742.297]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=40 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-1085395.0961049889.006 -1.034 0.301[-3143139.735 , 972349.544]
## Robust - - -1.378 0.168[-6451852.084 , 1124291.563]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | h=50 km | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 132 197
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 50.000 50.000
## BW bias (b) 50.000 50.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 197
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-762565.683801757.625 -0.951 0.342[-2333981.753 , 808850.387]
## Robust - - -1.304 0.192[-7631610.569 , 1534500.775]
## =============================================================================
## NULL
##
## ------------------------------------------------------------------------------------------
## RDROBUST — expenditure | AUTO bandwidth (default) | p=1 | N used=329 | NO region FE
## ------------------------------------------------------------------------------------------
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 329
## BW type mserd
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 197
## Eff. Number of Obs. 10 43
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 3.574 3.574
## BW bias (b) 8.478 8.478
## rho (h/b) 0.422 0.422
## Unique Obs. 129 189
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional415457.424446302.935 0.931 0.352[-459280.254 , 1290195.103]
## Robust - - 1.641 0.101[-230817.238 , 2607050.435]
## =============================================================================
## NULLdev.off()## quartz_off_screen
## 2sink()
# Export square-sample difference-in-means results at 40 km
dm_sq40 <- dplyr::bind_rows(sq_dm40)
if (nrow(dm_sq40) > 0) {
readr::write_csv(dm_sq40, dm_csv_sq40)
cat("\n[Square diff-means] Wrote: ", dm_csv_sq40, " | rows=", nrow(dm_sq40), "\n", sep = "")
print(
dm_sq40 %>%
dplyr::select(sample, outcome, year, h_km, n_treated, n_control,
diff_treat_minus_control, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means] No usable data within ±40 km for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means] Wrote: output/diffmeans_LombardiaSquare_h40.csv | rows=17
## # A tibble: 10 × 11
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 LOMBA… gb_int… NA 40 197 132 -0.0148 2.49e-3
## 2 LOMBA… gb_reg… NA 40 197 132 0.135 1.66e-2
## 3 LOMBA… evasio… NA 40 197 132 -0.845 8.22e-1
## 4 LOMBA… Admin_… NA 40 70 48 0.0854 3.92e-2
## 5 LOMBA… edu_se… NA 40 195 120 3.08 2.97e-1
## 6 LOMBA… edu_mu… NA 40 197 132 3.89 9.31e-1
## 7 LOMBA… PublS_… NA 40 196 132 10.9 1.29e+0
## 8 LOMBA… pol_mu… NA 40 197 132 18.5 1.32e+1
## 9 LOMBA… Pillar… 2010 40 197 132 1.67 8.35e-1
## 10 LOMBA… Pillar… 2020 40 197 132 4.63 9.56e-1
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 3 more variables: t_stat <dbl>, df <dbl>, p_value <dbl># Export square-sample sign-based difference-in-means results (X>=0 vs X<0; no bandwidth trim)
dm_sqsign <- dplyr::bind_rows(sq_sign_dm)
if (nrow(dm_sqsign) > 0) {
readr::write_csv(dm_sqsign, dm_csv_sqsign)
cat("\n[Square diff-means SIGN] Wrote: ", dm_csv_sqsign, " | rows=", nrow(dm_sqsign), "\n", sep = "")
print(
dm_sqsign %>%
dplyr::select(sample, outcome, year, n_pos, n_neg,
diff_pos_minus_neg, se_diff, t_stat, df, p_value) %>%
head(10)
)
} else {
cat("\n[Square diff-means SIGN] No usable data in square for any outcome; skipping export.\n", sep = "")
}##
## [Square diff-means SIGN] Wrote: output/diffmeans_LombardiaSquare_sign.csv | rows=17
## # A tibble: 10 × 10
## sample outcome year n_pos n_neg diff_pos_minus_neg se_diff t_stat df
## <chr> <chr> <dbl> <int> <int> <dbl> <dbl> <dbl> <dbl>
## 1 LOMBARDIA_… gb_int… NA 197 132 -0.0148 2.49e-3 5.95 236.
## 2 LOMBARDIA_… gb_reg… NA 197 132 0.135 1.66e-2 -8.14 302.
## 3 LOMBARDIA_… evasio… NA 197 132 -0.845 8.22e-1 1.03 224.
## 4 LOMBARDIA_… Admin_… NA 70 48 0.0854 3.92e-2 -2.18 93.1
## 5 LOMBARDIA_… edu_se… NA 195 120 3.08 2.97e-1 -10.3 252.
## 6 LOMBARDIA_… edu_mu… NA 197 132 3.89 9.31e-1 -4.18 245.
## 7 LOMBARDIA_… PublS_… NA 196 132 10.9 1.29e+0 -8.42 286.
## 8 LOMBARDIA_… pol_mu… NA 197 132 18.5 1.32e+1 -1.40 239.
## 9 LOMBARDIA_… Pillar… 2010 197 132 1.67 8.35e-1 -2.00 283.
## 10 LOMBARDIA_… Pillar… 2020 197 132 4.63 9.56e-1 -4.85 263.
## # ℹ 1 more variable: p_value <dbl>if (!("COD_PROV" %in% names(df0))) {
warning("COD_PROV not found in df0; skipping Pavia-province estimates (COD_PROV=18).")
} else {
# Province of Pavia within Lombardia: COD_REG == 3 & COD_PROV == 18
df_pavia <- df0 %>%
filter(
as.integer(.data[[REGION]]) == REGION_CODE_LOMBARDIA,
as.integer(.data[["COD_PROV"]]) == 18
)
# Requested Pavia-only bandwidths (km)
BWS_PAVIA <- c(20, 30, 40)
# ---- logging (sink-safe) ----
sink(results_txt_pavia, split = TRUE)
on.exit({ while (sink.number() > 0) sink() }, add = TRUE)
cat("Using DF: Pavia province only (COD_REG==3 & COD_PROV==18) | rows=", nrow(df_pavia),
" | key=", KEYCOL,
" | yearcol=", ifelse("year" %in% names(df_pavia), "year", NA),
"\n", sep = "")
cat("Running var: ", RUNNING, " (KM) | bandwidths=", paste(BWS_PAVIA, collapse = ", "),
" km | p=", P, " | NO regional FE\n\n", sep = "")
# ---- treated/control counts (unique municipalities) ----
tcol_raw <- if ("Treated" %in% names(df_pavia)) "Treated" else if ("Treated_num" %in% names(df_pavia)) "Treated_num" else NA_character_
if (is.na(tcol_raw)) {
cat("[WARN] Neither Treated nor Treated_num found in df_pavia; cannot tabulate treated/control counts from the raw DF.\n")
} else {
tc_pavia <- df_pavia %>%
distinct(.data[[KEYCOL]], Treated = as.integer(.data[[tcol_raw]])) %>%
count(Treated, name = "n_muni") %>%
arrange(Treated)
cat("Treated/control counts (unique municipalities) in Pavia province:\n")
print(tc_pavia)
if (nrow(tc_pavia) < 2) {
cat("[WARN] Only one Treated status present in Pavia province after filtering.\n")
}
}
# ---- local helper: subsetting to h and basic checks ----
make_sub_pavia_h <- function(d, h) {
sub <- d %>%
filter(!is.na(X), !is.na(Y),
dplyr::between(X, -h, h))
if (nrow(sub) < 20) return(NULL)
if (!is.finite(stats::sd(sub$X, na.rm = TRUE)) || stats::sd(sub$X, na.rm = TRUE) == 0) return(NULL)
if (sum(sub$X < 0, na.rm = TRUE) < 5 || sum(sub$X >= 0, na.rm = TRUE) < 5) return(NULL)
sub
}
# ---- Pavia: diff-in-means + rdrobust for h in {20,30,40} ----
pavia_dm <- list()
for (yvar in OUTCOMES) {
if (!(yvar %in% names(df_pavia))) {
cat("\n[Skip] Missing outcome: ", yvar, "\n", sep = "")
next
}
# --- Pillar2_pol: run separately by year (2010/2020) ---
if (yvar == "Pillar2_pol" && ("year" %in% names(df_pavia))) {
for (yr in YEARS) {
dY <- df_pavia %>% filter(year == yr)
d1 <- collapse_one_row_per_muni(dY, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | Year=", yr, " | PAVIA PROVINCE | p=", P, " | NO region FE\n", sep = "")
cat("Bandwidths: ", paste(BWS_PAVIA, collapse = ", "), " km\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
for (h in BWS_PAVIA) {
# Difference-in-means within |X|<=h km (treated - control)
dm <- diff_means_test(d1, h = h, treated_col = "Treated")
if (!is.null(dm)) {
pavia_dm[[length(pavia_dm) + 1]] <- dm %>%
mutate(sample = "PAVIA_noFE", outcome = yvar, year = yr)
cat("[Pavia diff-means] h=", h, " km | diff=",
signif(dm$diff_treat_minus_control, 4), " | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Pavia diff-means] Skip: insufficient treated/control data within ±", h, " km.\n", sep = "")
}
# RDROBUST at bandwidth h (if it fails, continue)
sub <- make_sub_pavia_h(d1, h)
if (is.null(sub)) {
cat("[Pavia rdrobust] Skip: too little usable data/variation within ±", h, " km.\n", sep = "")
next
}
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P,
label = paste0("PAVIA|", yvar, "|Year=", yr, "|h=", h))
if (is.null(rb)) next
print(summary(rb))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "PAVIA_noFE", year = yr, h_type = "MANUAL")
}
}
next
}
# --- All other outcomes ---
d1 <- collapse_one_row_per_muni(df_pavia, keycol = KEYCOL, xcol = RUNNING, ycol = yvar, keep_year = FALSE)
cat("\n", strrep("=", 110), "\n", sep = "")
cat("Outcome: ", yvar, " | PAVIA PROVINCE | p=", P, " | NO region FE\n", sep = "")
cat("Bandwidths: ", paste(BWS_PAVIA, collapse = ", "), " km\n", sep = "")
cat(strrep("=", 110), "\n", sep = "")
for (h in BWS_PAVIA) {
# Difference-in-means within |X|<=h km (treated - control)
dm <- diff_means_test(d1, h = h, treated_col = "Treated")
if (!is.null(dm)) {
pavia_dm[[length(pavia_dm) + 1]] <- dm %>%
mutate(sample = "PAVIA_noFE", outcome = yvar, year = NA_integer_)
cat("[Pavia diff-means] h=", h, " km | diff=",
signif(dm$diff_treat_minus_control, 4), " | p=", signif(dm$p_value, 4),
" | N_t=", dm$n_treated, " N_c=", dm$n_control, "\n", sep = "")
} else {
cat("[Pavia diff-means] Skip: insufficient treated/control data within ±", h, " km.\n", sep = "")
}
# RDROBUST at bandwidth h (if it fails, continue)
sub <- make_sub_pavia_h(d1, h)
if (is.null(sub)) {
cat("[Pavia rdrobust] Skip: too little usable data/variation within ±", h, " km.\n", sep = "")
next
}
rb <- safe_rdrobust(sub$Y, sub$X, h = h, p = P,
label = paste0("PAVIA|", yvar, "|h=", h))
if (is.null(rb)) next
print(summary(rb))
all_results[[length(all_results) + 1]] <-
extract_rdrobust(rb, outcome = yvar, h = h, sample = "PAVIA_noFE", year = NA_integer_, h_type = "MANUAL")
}
}
# Export Pavia diff-means results (all requested bandwidths)
dm_pavia <- dplyr::bind_rows(pavia_dm)
if (nrow(dm_pavia) > 0) {
readr::write_csv(dm_pavia, dm_csv_pavia)
cat("\n[Pavia diff-means] Wrote: ", dm_csv_pavia, " | rows=", nrow(dm_pavia), "\n", sep = "")
print(dm_pavia %>%
dplyr::select(sample, outcome, year, h_km,
n_treated, n_control,
diff_treat_minus_control, se_diff, t_stat, df, p_value) %>%
head(12))
} else {
cat("\n[Pavia diff-means] No usable outcomes for diff-means export.\n", sep = "")
}
# close sink explicitly (also covered by on.exit)
sink()
}## Using DF: Pavia province only (COD_REG==3 & COD_PROV==18) | rows=364 | key=istat | yearcol=year
## Running var: distance_treated_positive_x (KM) | bandwidths=20, 30, 40 km | p=1 | NO regional FE
##
## Treated/control counts (unique municipalities) in Pavia province:
## # A tibble: 2 × 2
## Treated n_muni
## <int> <int>
## 1 0 132
## 2 1 50
##
## ==============================================================================================================
## Outcome: gb_intensity | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=0.005213 | p=0.1308 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.014 0.007 2.053 0.040 [0.001 , 0.026]
## Robust - - 1.713 0.087 [-0.003 , 0.046]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=0.007225 | p=0.02946 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.009 0.006 1.436 0.151 [-0.003 , 0.021]
## Robust - - 1.681 0.093 [-0.003 , 0.042]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=0.007483 | p=0.02422 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.007 0.006 1.139 0.255 [-0.005 , 0.018]
## Robust - - 1.562 0.118 [-0.004 , 0.039]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: gb_reg_rate | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=-0.04788 | p=0.000407 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.028 0.028 -1.004 0.315 [-0.082 , 0.026]
## Robust - - 0.189 0.850 [-0.116 , 0.141]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=-0.04693 | p=0.0002668 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.041 0.026 -1.593 0.111 [-0.092 , 0.009]
## Robust - - -0.011 0.992 [-0.117 , 0.116]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=-0.04613 | p=0.0003289 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.048 0.025 -1.896 0.058 [-0.097 , 0.002]
## Robust - - -0.038 0.970 [-0.117 , 0.113]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: evasione | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=1.649 | p=0.1815 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 4.179 2.417 1.729 0.084 [-0.558 , 8.915]
## Robust - - 3.368 0.001 [6.795 , 25.718]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=1.453 | p=0.2315 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.705 2.317 1.599 0.110 [-0.835 , 8.246]
## Robust - - 3.100 0.002 [4.852 , 21.537]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=1.413 | p=0.2435 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.860 2.294 1.683 0.092 [-0.636 , 8.356]
## Robust - - 2.903 0.004 [3.923 , 20.234]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Admin_Tax_Emp | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=0.1186 | p=0.2401 | N_t=8 N_c=42
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 50
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 42 8
## Eff. Number of Obs. 42 8
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 42 8
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.015 0.149 -0.098 0.922 [-0.308 , 0.278]
## Robust - - -1.411 0.158 [-1.064 , 0.173]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=0.09142 | p=0.3671 | N_t=8 N_c=48
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 56
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 8
## Eff. Number of Obs. 48 8
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 30.000 30.000
## BW bias (b) 30.000 30.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 8
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.026 0.149 0.171 0.864 [-0.267 , 0.318]
## Robust - - -1.522 0.128 [-1.117 , 0.140]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=0.09142 | p=0.3671 | N_t=8 N_c=48
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 56
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 48 8
## Eff. Number of Obs. 48 8
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 48 8
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.049 0.153 0.319 0.750 [-0.251 , 0.348]
## Robust - - -1.515 0.130 [-1.129 , 0.145]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: edu_serv_lvl | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=1.278 | p=0.01075 | N_t=49 N_c=102
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 151
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 102 49
## Eff. Number of Obs. 102 49
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 102 49
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.482 1.101 1.346 0.178 [-0.676 , 3.640]
## Robust - - 0.219 0.826 [-4.619 , 5.783]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=1.25 | p=0.0107 | N_t=49 N_c=119
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 168
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 119 49
## Eff. Number of Obs. 119 49
## 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 49
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.513 1.037 1.460 0.144 [-0.519 , 3.545]
## Robust - - -0.166 0.868 [-5.248 , 4.430]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=1.265 | p=0.009716 | N_t=49 N_c=120
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 169
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 120 49
## Eff. Number of Obs. 120 49
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 120 49
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.591 1.017 1.564 0.118 [-0.403 , 3.585]
## Robust - - -0.227 0.820 [-5.291 , 4.191]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: edu_muni_school_area_per1000 | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=-0.6247 | p=0.6357 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.897 2.926 -0.307 0.759 [-6.632 , 4.838]
## Robust - - -1.151 0.250 [-22.872 , 5.948]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=-0.9281 | p=0.4715 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.427 2.597 -0.164 0.870 [-5.517 , 4.664]
## Robust - - -0.877 0.381 [-18.837 , 7.194]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=-0.8592 | p=0.5044 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.421 2.500 -0.169 0.866 [-5.321 , 4.478]
## Robust - - -0.762 0.446 [-17.608 , 7.751]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: PublS_CyclePath_per | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=8.665 | p=0.0004919 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 1.580 4.592 0.344 0.731 [-7.419 , 10.580]
## Robust - - -0.407 0.684 [-31.733 , 20.824]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=8.537 | p=0.0005453 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 2.776 4.059 0.684 0.494 [-5.179 , 10.732]
## Robust - - -0.382 0.702 [-31.200 , 21.022]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=8.554 | p=0.0005305 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3.289 3.887 0.846 0.397 [-4.329 , 10.906]
## Robust - - -0.330 0.742 [-30.497 , 21.711]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: pol_mun_road | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=-7.029 | p=0.3626 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -33.351 17.075 -1.953 0.051 [-66.819 , 0.116]
## Robust - - -2.003 0.045 [-192.274 , -2.099]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=-10.37 | p=0.1797 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -20.876 13.656 -1.529 0.126 [-47.641 , 5.889]
## Robust - - -2.113 0.035 [-182.146 , -6.849]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=-10.79 | p=0.1625 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -15.809 12.469 -1.268 0.205 [-40.247 , 8.629]
## Robust - - -2.075 0.038 [-175.602 , -5.002]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2010 | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=-0.3503 | p=0.7724 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.282 2.440 -0.935 0.350 [-7.065 , 2.501]
## Robust - - -0.953 0.341 [-14.995 , 5.185]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=-0.4202 | p=0.7202 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.735 2.285 -0.759 0.448 [-6.213 , 2.743]
## Robust - - -0.915 0.360 [-13.265 , 4.823]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=-0.4465 | p=0.703 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.497 2.224 -0.673 0.501 [-5.856 , 2.862]
## Robust - - -0.861 0.389 [-12.741 , 4.966]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: Pillar2_pol | Year=2020 | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=1.969 | p=0.1532 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.092 2.778 -0.753 0.452 [-7.537 , 3.354]
## Robust - - -0.366 0.715 [-13.695 , 9.389]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=1.944 | p=0.1552 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.307 2.657 -0.868 0.385 [-7.514 , 2.901]
## Robust - - -0.778 0.437 [-14.599 , 6.304]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=1.87 | p=0.171 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -2.013 2.624 -0.767 0.443 [-7.156 , 3.131]
## Robust - - -0.954 0.340 [-15.279 , 5.274]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: marr_civil | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=3.585 | p=0.2653 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -3.037 5.571 -0.545 0.586 [-13.955 , 7.882]
## Robust - - -1.013 0.311 [-58.831 , 18.740]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=3.391 | p=0.2877 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.268 4.641 -0.058 0.954 [-9.364 , 8.828]
## Robust - - -0.922 0.357 [-55.539 , 20.006]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=3.415 | p=0.2839 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.503 4.318 0.117 0.907 [-7.960 , 8.966]
## Robust - - -0.835 0.404 [-53.503 , 21.538]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: marr_rel | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=0.9202 | p=0.5786 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -3.233 2.880 -1.123 0.262 [-8.878 , 2.411]
## Robust - - -1.341 0.180 [-33.952 , 6.365]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=0.7424 | p=0.6485 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.713 2.232 -0.767 0.443 [-6.088 , 2.663]
## Robust - - -1.195 0.232 [-31.188 , 7.558]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=0.7479 | p=0.6457 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -1.279 2.002 -0.639 0.523 [-5.203 , 2.645]
## Robust - - -1.095 0.274 [-29.922 , 8.478]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: incomepc | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=2553 | p=3.063e-06 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3540.959 1467.150 2.413 0.016 [665.397 , 6416.520]
## Robust - - 1.295 0.195 [-3542.408 , 17325.467]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=2435 | p=6.515e-06 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3688.972 1343.065 2.747 0.006 [1056.613 , 6321.330]
## Robust - - 1.321 0.187 [-3145.847 , 16151.315]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=2461 | p=5.378e-06 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 3682.804 1297.291 2.839 0.005 [1140.161 , 6225.447]
## Robust - - 1.402 0.161 [-2659.923 , 16043.871]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: income | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=31610000 | p=0.2945 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-60615438.90840909516.738 -1.482 0.138[-140796618.339 , 19565740.523]
## Robust - - -1.383 0.167[-604216676.815 , 104217675.170]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=28800000 | p=0.3393 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-35039621.80232084832.898 -1.092 0.275[-97924738.731 , 27845495.128]
## Robust - - -1.386 0.166[-599703951.106 , 102929496.844]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=29040000 | p=0.335 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-26450456.91928950626.151 -0.914 0.361[-83192641.505 , 30291727.667]
## Robust - - -1.318 0.187[-586973410.969 , 114898572.764]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: expend_level | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=-0.6265 | p=0.1318 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.336 0.900 -0.373 0.709 [-2.100 , 1.429]
## Robust - - 0.529 0.597 [-2.956 , 5.140]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=-0.5313 | p=0.1879 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.570 0.839 -0.680 0.497 [-2.215 , 1.074]
## Robust - - 0.369 0.712 [-2.937 , 4.298]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=-0.5242 | p=0.1928 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional -0.649 0.822 -0.790 0.429 [-2.259 , 0.961]
## Robust - - 0.266 0.790 [-3.034 , 3.987]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: services_level | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=0.5927 | p=0.2412 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.165 1.134 0.145 0.885 [-2.059 , 2.388]
## Robust - - 0.170 0.865 [-4.848 , 5.767]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=0.8035 | p=0.102 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.247 1.039 0.238 0.812 [-1.790 , 2.284]
## Robust - - 0.198 0.843 [-4.313 , 5.282]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=0.8236 | p=0.09342 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.283 1.010 0.280 0.780 [-1.696 , 2.261]
## Robust - - 0.228 0.820 [-4.153 , 5.244]
## =============================================================================
## NULL
##
## ==============================================================================================================
## Outcome: expenditure | PAVIA PROVINCE | p=1 | NO region FE
## Bandwidths: 20, 30, 40 km
## ==============================================================================================================
## [Pavia diff-means] h=20 km | diff=252800 | p=0.3682 | N_t=50 N_c=113
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 163
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 113 50
## Eff. Number of Obs. 113 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 20.000 20.000
## BW bias (b) 20.000 20.000
## rho (h/b) 1.000 1.000
## Unique Obs. 113 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-556222.157356667.928 -1.559 0.119[-1255278.452 , 142834.137]
## Robust - - -1.374 0.169[-5587560.976 , 982134.904]
## =============================================================================
## NULL
## [Pavia diff-means] h=30 km | diff=246200 | p=0.3785 | N_t=50 N_c=131
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 181
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 131 50
## Eff. Number of Obs. 131 50
## 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 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-367996.542274074.374 -1.343 0.179[-905172.444 , 169179.359]
## Robust - - -1.339 0.181[-5506441.398 , 1036074.988]
## =============================================================================
## NULL
## [Pavia diff-means] h=40 km | diff=247800 | p=0.3754 | N_t=50 N_c=132
## Sharp RD estimates using local polynomial regression.
##
## Number of Obs. 182
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 132 50
## Eff. Number of Obs. 132 50
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 40.000 40.000
## BW bias (b) 40.000 40.000
## rho (h/b) 1.000 1.000
## Unique Obs. 132 50
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional-303951.854244380.481 -1.244 0.214[-782928.794 , 175025.087]
## Robust - - -1.288 0.198[-5427355.180 , 1122000.182]
## =============================================================================
## NULL
##
## [Pavia diff-means] Wrote: output/diffmeans_Pavia_h20_30_40.csv | rows=51
## # A tibble: 12 × 11
## sample outcome year h_km n_treated n_control diff_treat_minus_con…¹ se_diff
## <chr> <chr> <dbl> <dbl> <int> <int> <dbl> <dbl>
## 1 PAVIA… gb_int… NA 20 50 113 0.00521 0.00343
## 2 PAVIA… gb_int… NA 30 50 131 0.00722 0.00328
## 3 PAVIA… gb_int… NA 40 50 132 0.00748 0.00328
## 4 PAVIA… gb_reg… NA 20 50 113 -0.0479 0.0132
## 5 PAVIA… gb_reg… NA 30 50 131 -0.0469 0.0125
## 6 PAVIA… gb_reg… NA 40 50 132 -0.0461 0.0125
## 7 PAVIA… evasio… NA 20 50 113 1.65 1.23
## 8 PAVIA… evasio… NA 30 50 131 1.45 1.21
## 9 PAVIA… evasio… NA 40 50 132 1.41 1.20
## 10 PAVIA… Admin_… NA 20 8 42 0.119 0.0932
## 11 PAVIA… Admin_… NA 30 8 48 0.0914 0.0961
## 12 PAVIA… Admin_… NA 40 8 48 0.0914 0.0961
## # ℹ abbreviated name: ¹diff_treat_minus_control
## # ℹ 3 more variables: t_stat <dbl>, df <dbl>, p_value <dbl>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_pavia_tbl <- read_if_exists(dm_csv_pavia)
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, dm_pavia_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")
}| sample | outcome | year | h_km | n_treated | n_control | mean_treated | mean_control | diff_treat_minus_control | se_diff | t_stat | df | p_value |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| FULL_ITALY_regFE | Admin_Tax_Emp | NA | 40 | 232 | 217 | 2.116000e-01 | 1.047000e-01 | 1.069000e-01 | 6.810000e-02 | -1.5689 | 263.9063 | 0.1179 |
| FULL_ITALY_regFE | Pillar2_pol | 2010 | 40 | 702 | 605 | 1.030911e+02 | 1.019818e+02 | 1.109300e+00 | 4.363000e-01 | -2.5422 | 1264.0717 | 0.0111 |
| FULL_ITALY_regFE | Pillar2_pol | 2020 | 40 | 702 | 605 | 1.082077e+02 | 1.050731e+02 | 3.134600e+00 | 5.196000e-01 | -6.0322 | 1213.0992 | 0.0000 |
| FULL_ITALY_regFE | PublS_CyclePath_per | NA | 40 | 694 | 602 | 8.948700e+00 | 3.795300e+00 | 5.153400e+00 | 6.333000e-01 | -8.1370 | 1293.9643 | 0.0000 |
| FULL_ITALY_regFE | edu_muni_school_area_per1000 | NA | 40 | 702 | 605 | 1.230680e+01 | 1.151080e+01 | 7.960000e-01 | 4.737000e-01 | -1.6803 | 1142.0987 | 0.0932 |
| FULL_ITALY_regFE | edu_serv_lvl | NA | 40 | 685 | 553 | 6.213100e+00 | 5.598600e+00 | 6.146000e-01 | 1.604000e-01 | -3.8325 | 1197.1503 | 0.0001 |
| FULL_ITALY_regFE | evasione | NA | 40 | 702 | 605 | 2.366820e+01 | 2.652410e+01 | -2.855900e+00 | 4.370000e-01 | 6.5353 | 1080.5819 | 0.0000 |
| FULL_ITALY_regFE | expend_level | NA | 40 | 702 | 605 | 4.682300e+00 | 4.317400e+00 | 3.650000e-01 | 1.315000e-01 | -2.7750 | 1263.7726 | 0.0056 |
| FULL_ITALY_regFE | expenditure | NA | 40 | 702 | 605 | 1.303206e+06 | 9.885862e+05 | 3.146199e+05 | 4.971639e+05 | -0.6328 | 1109.3779 | 0.5270 |
| FULL_ITALY_regFE | gb_intensity | NA | 40 | 734 | 637 | 2.630000e-02 | 2.170000e-02 | 4.600000e-03 | 1.100000e-03 | -4.0669 | 1367.6470 | 0.0001 |
| FULL_ITALY_regFE | gb_reg_rate | NA | 40 | 734 | 637 | 2.323000e-01 | 2.713000e-01 | -3.900000e-02 | 1.090000e-02 | 3.5739 | 1353.7433 | 0.0004 |
| FULL_ITALY_regFE | income | NA | 40 | 702 | 605 | 1.573040e+08 | 1.010564e+08 | 5.624754e+07 | 5.035691e+07 | -1.1170 | 877.9505 | 0.2643 |
| FULL_ITALY_regFE | incomepc | NA | 40 | 702 | 605 | 2.172215e+04 | 2.052724e+04 | 1.194910e+03 | 1.727427e+02 | -6.9173 | 1296.8672 | 0.0000 |
| FULL_ITALY_regFE | marr_civil | NA | 40 | 702 | 605 | 1.482760e+01 | 1.148600e+01 | 3.341700e+00 | 3.693300e+00 | -0.9048 | 1022.6959 | 0.3658 |
| FULL_ITALY_regFE | marr_rel | NA | 40 | 702 | 605 | 7.500000e+00 | 5.528900e+00 | 1.971100e+00 | 1.199600e+00 | -1.6431 | 1077.4800 | 0.1007 |
| FULL_ITALY_regFE | pol_mun_road | NA | 40 | 702 | 605 | 5.742370e+01 | 8.755950e+01 | -3.013580e+01 | 6.775000e+00 | 4.4481 | 1168.0684 | 0.0000 |
| FULL_ITALY_regFE | services_level | NA | 40 | 702 | 605 | 6.166700e+00 | 5.879300e+00 | 2.873000e-01 | 1.566000e-01 | -1.8347 | 1179.4232 | 0.0668 |
| LOMBARDIA_SQUARE_noFE | Admin_Tax_Emp | NA | 40 | 70 | 48 | 1.561000e-01 | 7.070000e-02 | 8.540000e-02 | 3.920000e-02 | -2.1768 | 93.1033 | 0.0320 |
| LOMBARDIA_SQUARE_noFE | Pillar2_pol | 2010 | 40 | 197 | 132 | 1.026539e+02 | 1.009875e+02 | 1.666400e+00 | 8.349000e-01 | -1.9958 | 283.1122 | 0.0469 |
| LOMBARDIA_SQUARE_noFE | Pillar2_pol | 2020 | 40 | 197 | 132 | 1.080096e+02 | 1.033749e+02 | 4.634700e+00 | 9.562000e-01 | -4.8472 | 262.8148 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | PublS_CyclePath_per | NA | 40 | 196 | 132 | 1.314510e+01 | 2.249100e+00 | 1.089600e+01 | 1.294100e+00 | -8.4195 | 285.8390 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | edu_muni_school_area_per1000 | NA | 40 | 197 | 132 | 1.291310e+01 | 9.023400e+00 | 3.889700e+00 | 9.314000e-01 | -4.1762 | 244.8945 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | edu_serv_lvl | NA | 40 | 195 | 120 | 7.892300e+00 | 4.816700e+00 | 3.075600e+00 | 2.972000e-01 | -10.3494 | 252.2341 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | evasione | NA | 40 | 197 | 132 | 2.560490e+01 | 2.644980e+01 | -8.449000e-01 | 8.218000e-01 | 1.0281 | 223.8484 | 0.3050 |
| LOMBARDIA_SQUARE_noFE | expend_level | NA | 40 | 197 | 132 | 4.939100e+00 | 3.924200e+00 | 1.014800e+00 | 2.847000e-01 | -3.5652 | 271.6508 | 0.0004 |
| LOMBARDIA_SQUARE_noFE | expenditure | NA | 40 | 197 | 132 | 2.593024e+06 | 2.018421e+05 | 2.391182e+06 | 1.512973e+06 | -1.5805 | 196.8032 | 0.1156 |
| LOMBARDIA_SQUARE_noFE | gb_intensity | NA | 40 | 197 | 132 | 2.340000e-02 | 3.830000e-02 | -1.480000e-02 | 2.500000e-03 | 5.9488 | 235.5566 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | gb_reg_rate | NA | 40 | 197 | 132 | 3.019000e-01 | 1.666000e-01 | 1.354000e-01 | 1.660000e-02 | -8.1419 | 301.9977 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | income | NA | 40 | 197 | 132 | 3.101343e+08 | 3.913533e+07 | 2.709990e+08 | 1.674416e+08 | -1.6185 | 197.1256 | 0.1072 |
| LOMBARDIA_SQUARE_noFE | incomepc | NA | 40 | 197 | 132 | 2.328246e+04 | 1.967258e+04 | 3.609885e+03 | 3.132317e+02 | -11.5246 | 324.8732 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | marr_civil | NA | 40 | 197 | 132 | 2.537560e+01 | 5.204500e+00 | 2.017110e+01 | 1.158300e+01 | -1.7414 | 199.1994 | 0.0831 |
| LOMBARDIA_SQUARE_noFE | marr_rel | NA | 40 | 197 | 132 | 1.041120e+01 | 2.712100e+00 | 7.699000e+00 | 3.596700e+00 | -2.1406 | 207.6600 | 0.0335 |
| LOMBARDIA_SQUARE_noFE | pol_mun_road | NA | 40 | 197 | 132 | 5.996450e+01 | 4.145630e+01 | 1.850820e+01 | 1.318970e+01 | -1.4032 | 239.3458 | 0.1618 |
| LOMBARDIA_SQUARE_noFE | services_level | NA | 40 | 197 | 132 | 6.020300e+00 | 3.636400e+00 | 2.383900e+00 | 3.132000e-01 | -7.6125 | 250.0019 | 0.0000 |
| LOMBARDIA_noFE | Admin_Tax_Emp | NA | 40 | 226 | 49 | 2.123000e-01 | 6.930000e-02 | 1.430000e-01 | 7.430000e-02 | -1.9253 | 272.9930 | 0.0552 |
| LOMBARDIA_noFE | Pillar2_pol | 2010 | 40 | 688 | 133 | 1.030420e+02 | 1.009721e+02 | 2.069900e+00 | 7.033000e-01 | -2.9434 | 192.4854 | 0.0036 |
| LOMBARDIA_noFE | Pillar2_pol | 2020 | 40 | 688 | 133 | 1.081309e+02 | 1.033710e+02 | 4.760000e+00 | 8.303000e-01 | -5.7329 | 185.9243 | 0.0000 |
| LOMBARDIA_noFE | PublS_CyclePath_per | NA | 40 | 680 | 133 | 8.969900e+00 | 2.232200e+00 | 6.737600e+00 | 7.639000e-01 | -8.8198 | 322.6428 | 0.0000 |
| LOMBARDIA_noFE | edu_muni_school_area_per1000 | NA | 40 | 688 | 133 | 1.223630e+01 | 8.995800e+00 | 3.240500e+00 | 8.160000e-01 | -3.9710 | 170.1296 | 0.0001 |
| LOMBARDIA_noFE | edu_serv_lvl | NA | 40 | 671 | 121 | 6.217600e+00 | 4.818200e+00 | 1.399400e+00 | 2.570000e-01 | -5.4454 | 179.6788 | 0.0000 |
| LOMBARDIA_noFE | evasione | NA | 40 | 688 | 133 | 2.370840e+01 | 2.648280e+01 | -2.774400e+00 | 7.415000e-01 | 3.7419 | 166.4346 | 0.0003 |
| LOMBARDIA_noFE | expend_level | NA | 40 | 688 | 133 | 4.668600e+00 | 3.969900e+00 | 6.987000e-01 | 2.442000e-01 | -2.8617 | 174.6090 | 0.0047 |
| LOMBARDIA_noFE | expenditure | NA | 40 | 688 | 133 | 1.274137e+06 | 2.003569e+05 | 1.073780e+06 | 4.424388e+05 | -2.4270 | 718.3957 | 0.0155 |
| LOMBARDIA_noFE | gb_intensity | NA | 40 | 694 | 133 | 2.620000e-02 | 3.820000e-02 | -1.200000e-02 | 2.200000e-03 | 5.3325 | 178.2202 | 0.0000 |
| LOMBARDIA_noFE | gb_reg_rate | NA | 40 | 694 | 133 | 2.333000e-01 | 1.657000e-01 | 6.760000e-02 | 1.150000e-02 | -5.8679 | 399.3290 | 0.0000 |
| LOMBARDIA_noFE | income | NA | 40 | 688 | 133 | 1.553849e+08 | 3.885463e+07 | 1.165303e+08 | 4.908374e+07 | -2.3741 | 730.1087 | 0.0178 |
| LOMBARDIA_noFE | incomepc | NA | 40 | 688 | 133 | 2.172953e+04 | 1.964564e+04 | 2.083897e+03 | 2.312401e+02 | -9.0118 | 283.9242 | 0.0000 |
| LOMBARDIA_noFE | marr_civil | NA | 40 | 688 | 133 | 1.459160e+01 | 5.165400e+00 | 9.426200e+00 | 3.516900e+00 | -2.6803 | 786.8116 | 0.0075 |
| LOMBARDIA_noFE | marr_rel | NA | 40 | 688 | 133 | 7.457800e+00 | 2.691700e+00 | 4.766100e+00 | 1.229400e+00 | -3.8767 | 777.7312 | 0.0001 |
| LOMBARDIA_noFE | pol_mun_road | NA | 40 | 688 | 133 | 5.437120e+01 | 4.122350e+01 | 1.314770e+01 | 5.817800e+00 | -2.2599 | 409.9536 | 0.0244 |
| LOMBARDIA_noFE | services_level | NA | 40 | 688 | 133 | 6.127900e+00 | 3.646600e+00 | 2.481300e+00 | 2.728000e-01 | -9.0954 | 171.9903 | 0.0000 |
| PAVIA_noFE | Admin_Tax_Emp | NA | 20 | 8 | 42 | 1.621000e-01 | 4.350000e-02 | 1.186000e-01 | 9.320000e-02 | -1.2720 | 7.7814 | 0.2401 |
| PAVIA_noFE | Admin_Tax_Emp | NA | 30 | 8 | 48 | 1.621000e-01 | 7.070000e-02 | 9.140000e-02 | 9.610000e-02 | -0.9510 | 8.7795 | 0.3671 |
| PAVIA_noFE | Admin_Tax_Emp | NA | 40 | 8 | 48 | 1.621000e-01 | 7.070000e-02 | 9.140000e-02 | 9.610000e-02 | -0.9510 | 8.7795 | 0.3671 |
| PAVIA_noFE | Pillar2_pol | 2010 | 20 | 50 | 113 | 1.005410e+02 | 1.008913e+02 | -3.503000e-01 | 1.207600e+00 | 0.2901 | 102.7554 | 0.7724 |
| PAVIA_noFE | Pillar2_pol | 2010 | 30 | 50 | 131 | 1.005410e+02 | 1.009612e+02 | -4.202000e-01 | 1.169800e+00 | 0.3592 | 94.8980 | 0.7202 |
| PAVIA_noFE | Pillar2_pol | 2010 | 40 | 50 | 132 | 1.005410e+02 | 1.009875e+02 | -4.465000e-01 | 1.167400e+00 | 0.3825 | 94.3359 | 0.7030 |
| PAVIA_noFE | Pillar2_pol | 2020 | 20 | 50 | 113 | 1.052453e+02 | 1.032758e+02 | 1.969400e+00 | 1.368300e+00 | -1.4394 | 99.0409 | 0.1532 |
| PAVIA_noFE | Pillar2_pol | 2020 | 30 | 50 | 131 | 1.052453e+02 | 1.033012e+02 | 1.944100e+00 | 1.357300e+00 | -1.4323 | 97.9993 | 0.1552 |
| PAVIA_noFE | Pillar2_pol | 2020 | 40 | 50 | 132 | 1.052453e+02 | 1.033749e+02 | 1.870400e+00 | 1.356000e+00 | -1.3793 | 97.7724 | 0.1710 |
| PAVIA_noFE | PublS_CyclePath_per | NA | 20 | 50 | 113 | 1.080320e+01 | 2.138700e+00 | 8.664500e+00 | 2.346200e+00 | -3.6930 | 58.0284 | 0.0005 |
| PAVIA_noFE | PublS_CyclePath_per | NA | 30 | 50 | 131 | 1.080320e+01 | 2.266300e+00 | 8.536900e+00 | 2.328100e+00 | -3.6669 | 56.3410 | 0.0005 |
| PAVIA_noFE | PublS_CyclePath_per | NA | 40 | 50 | 132 | 1.080320e+01 | 2.249100e+00 | 8.554100e+00 | 2.326900e+00 | -3.6761 | 56.2346 | 0.0005 |
| PAVIA_noFE | edu_muni_school_area_per1000 | NA | 20 | 50 | 113 | 8.164200e+00 | 8.788900e+00 | -6.247000e-01 | 1.315200e+00 | 0.4750 | 112.1944 | 0.6357 |
| PAVIA_noFE | edu_muni_school_area_per1000 | NA | 30 | 50 | 131 | 8.164200e+00 | 9.092200e+00 | -9.281000e-01 | 1.284300e+00 | 0.7226 | 107.4793 | 0.4715 |
| PAVIA_noFE | edu_muni_school_area_per1000 | NA | 40 | 50 | 132 | 8.164200e+00 | 9.023400e+00 | -8.592000e-01 | 1.282600e+00 | 0.6699 | 107.1727 | 0.5044 |
| PAVIA_noFE | edu_serv_lvl | NA | 20 | 49 | 102 | 6.081600e+00 | 4.803900e+00 | 1.277700e+00 | 4.900000e-01 | -2.6075 | 86.0476 | 0.0108 |
| PAVIA_noFE | edu_serv_lvl | NA | 30 | 49 | 119 | 6.081600e+00 | 4.831900e+00 | 1.249700e+00 | 4.782000e-01 | -2.6135 | 80.1984 | 0.0107 |
| PAVIA_noFE | edu_serv_lvl | NA | 40 | 49 | 120 | 6.081600e+00 | 4.816700e+00 | 1.265000e+00 | 4.774000e-01 | -2.6495 | 79.8206 | 0.0097 |
| PAVIA_noFE | evasione | NA | 20 | 50 | 113 | 2.786280e+01 | 2.621350e+01 | 1.649300e+00 | 1.226200e+00 | -1.3451 | 106.0312 | 0.1815 |
| PAVIA_noFE | evasione | NA | 30 | 50 | 131 | 2.786280e+01 | 2.641020e+01 | 1.452600e+00 | 1.207000e+00 | -1.2035 | 103.1799 | 0.2315 |
| PAVIA_noFE | evasione | NA | 40 | 50 | 132 | 2.786280e+01 | 2.644980e+01 | 1.413000e+00 | 1.204500e+00 | -1.1730 | 102.6311 | 0.2435 |
| PAVIA_noFE | expend_level | NA | 20 | 50 | 113 | 3.400000e+00 | 4.026500e+00 | -6.265000e-01 | 4.125000e-01 | 1.5190 | 104.4495 | 0.1318 |
| PAVIA_noFE | expend_level | NA | 30 | 50 | 131 | 3.400000e+00 | 3.931300e+00 | -5.313000e-01 | 4.006000e-01 | 1.3262 | 97.4651 | 0.1879 |
| PAVIA_noFE | expend_level | NA | 40 | 50 | 132 | 3.400000e+00 | 3.924200e+00 | -5.242000e-01 | 3.997000e-01 | 1.3115 | 96.8490 | 0.1928 |
| PAVIA_noFE | expenditure | NA | 20 | 50 | 113 | 4.495993e+05 | 1.967903e+05 | 2.528090e+05 | 2.787176e+05 | -0.9070 | 56.6008 | 0.3682 |
| PAVIA_noFE | expenditure | NA | 30 | 50 | 131 | 4.495993e+05 | 2.033595e+05 | 2.462398e+05 | 2.773824e+05 | -0.8877 | 55.5740 | 0.3785 |
| PAVIA_noFE | expenditure | NA | 40 | 50 | 132 | 4.495993e+05 | 2.018421e+05 | 2.477572e+05 | 2.772567e+05 | -0.8936 | 55.4766 | 0.3754 |
| PAVIA_noFE | gb_intensity | NA | 20 | 50 | 113 | 4.570000e-02 | 4.050000e-02 | 5.200000e-03 | 3.400000e-03 | -1.5207 | 127.1993 | 0.1308 |
| PAVIA_noFE | gb_intensity | NA | 30 | 50 | 131 | 4.570000e-02 | 3.850000e-02 | 7.200000e-03 | 3.300000e-03 | -2.2040 | 118.5500 | 0.0295 |
| PAVIA_noFE | gb_intensity | NA | 40 | 50 | 132 | 4.570000e-02 | 3.830000e-02 | 7.500000e-03 | 3.300000e-03 | -2.2828 | 118.6946 | 0.0242 |
| PAVIA_noFE | gb_reg_rate | NA | 20 | 50 | 113 | 1.204000e-01 | 1.683000e-01 | -4.790000e-02 | 1.320000e-02 | 3.6229 | 139.5169 | 0.0004 |
| PAVIA_noFE | gb_reg_rate | NA | 30 | 50 | 131 | 1.204000e-01 | 1.674000e-01 | -4.690000e-02 | 1.250000e-02 | 3.7467 | 132.0328 | 0.0003 |
| PAVIA_noFE | gb_reg_rate | NA | 40 | 50 | 132 | 1.204000e-01 | 1.666000e-01 | -4.610000e-02 | 1.250000e-02 | 3.6884 | 131.8364 | 0.0003 |
| PAVIA_noFE | income | NA | 20 | 50 | 113 | 6.817765e+07 | 3.657029e+07 | 3.160735e+07 | 2.988213e+07 | -1.0577 | 58.9553 | 0.2945 |
| PAVIA_noFE | income | NA | 30 | 50 | 131 | 6.817765e+07 | 3.937519e+07 | 2.880246e+07 | 2.989694e+07 | -0.9634 | 59.1025 | 0.3393 |
| PAVIA_noFE | income | NA | 40 | 50 | 132 | 6.817765e+07 | 3.913533e+07 | 2.904232e+07 | 2.987724e+07 | -0.9721 | 58.9550 | 0.3350 |
| PAVIA_noFE | incomepc | NA | 20 | 50 | 113 | 2.213388e+04 | 1.958081e+04 | 2.553070e+03 | 5.020864e+02 | -5.0849 | 68.3963 | 0.0000 |
| PAVIA_noFE | incomepc | NA | 30 | 50 | 131 | 2.213388e+04 | 1.969852e+04 | 2.435362e+03 | 4.969607e+02 | -4.9005 | 66.0009 | 0.0000 |
| PAVIA_noFE | incomepc | NA | 40 | 50 | 132 | 2.213388e+04 | 1.967258e+04 | 2.461305e+03 | 4.971001e+02 | -4.9513 | 66.0748 | 0.0000 |
| PAVIA_noFE | marr_civil | NA | 20 | 50 | 113 | 8.620000e+00 | 5.035400e+00 | 3.584600e+00 | 3.189300e+00 | -1.1240 | 63.5476 | 0.2653 |
| PAVIA_noFE | marr_civil | NA | 30 | 50 | 131 | 8.620000e+00 | 5.229000e+00 | 3.391000e+00 | 3.161600e+00 | -1.0725 | 61.5728 | 0.2877 |
| PAVIA_noFE | marr_civil | NA | 40 | 50 | 132 | 8.620000e+00 | 5.204500e+00 | 3.415500e+00 | 3.159100e+00 | -1.0812 | 61.3871 | 0.2839 |
| PAVIA_noFE | marr_rel | NA | 20 | 50 | 113 | 3.460000e+00 | 2.539800e+00 | 9.202000e-01 | 1.649100e+00 | -0.5580 | 70.4743 | 0.5786 |
| PAVIA_noFE | marr_rel | NA | 30 | 50 | 131 | 3.460000e+00 | 2.717600e+00 | 7.424000e-01 | 1.621300e+00 | -0.4579 | 66.3931 | 0.6485 |
| PAVIA_noFE | marr_rel | NA | 40 | 50 | 132 | 3.460000e+00 | 2.712100e+00 | 7.479000e-01 | 1.619500e+00 | -0.4618 | 66.1287 | 0.6457 |
| PAVIA_noFE | pol_mun_road | NA | 20 | 50 | 113 | 3.066960e+01 | 3.769880e+01 | -7.029200e+00 | 7.683700e+00 | 0.9148 | 94.9937 | 0.3626 |
| PAVIA_noFE | pol_mun_road | NA | 30 | 50 | 131 | 3.066960e+01 | 4.103520e+01 | -1.036560e+01 | 7.669200e+00 | 1.3516 | 95.5334 | 0.1797 |
| PAVIA_noFE | pol_mun_road | NA | 40 | 50 | 132 | 3.066960e+01 | 4.145630e+01 | -1.078670e+01 | 7.662800e+00 | 1.4077 | 95.3368 | 0.1625 |
| PAVIA_noFE | services_level | NA | 20 | 50 | 113 | 4.460000e+00 | 3.867300e+00 | 5.927000e-01 | 5.027000e-01 | -1.1791 | 98.1365 | 0.2412 |
| PAVIA_noFE | services_level | NA | 30 | 50 | 131 | 4.460000e+00 | 3.656500e+00 | 8.035000e-01 | 4.863000e-01 | -1.6522 | 89.7072 | 0.1020 |
| PAVIA_noFE | services_level | NA | 40 | 50 | 132 | 4.460000e+00 | 3.636400e+00 | 8.236000e-01 | 4.857000e-01 | -1.6957 | 89.3748 | 0.0934 |
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")
}| sample | outcome | year | n_pos | n_neg | mean_pos | mean_neg | diff_pos_minus_neg | se_diff | t_stat | df | p_value |
|---|---|---|---|---|---|---|---|---|---|---|---|
| LOMBARDIA_SQUARE_noFE | Admin_Tax_Emp | NA | 70 | 48 | 1.561000e-01 | 7.070000e-02 | 8.540000e-02 | 3.920000e-02 | -2.1768 | 93.1033 | 0.0320 |
| LOMBARDIA_SQUARE_noFE | Pillar2_pol | 2010 | 197 | 132 | 1.026539e+02 | 1.009875e+02 | 1.666400e+00 | 8.349000e-01 | -1.9958 | 283.1122 | 0.0469 |
| LOMBARDIA_SQUARE_noFE | Pillar2_pol | 2020 | 197 | 132 | 1.080096e+02 | 1.033749e+02 | 4.634700e+00 | 9.562000e-01 | -4.8472 | 262.8148 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | PublS_CyclePath_per | NA | 196 | 132 | 1.314510e+01 | 2.249100e+00 | 1.089600e+01 | 1.294100e+00 | -8.4195 | 285.8390 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | edu_muni_school_area_per1000 | NA | 197 | 132 | 1.291310e+01 | 9.023400e+00 | 3.889700e+00 | 9.314000e-01 | -4.1762 | 244.8945 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | edu_serv_lvl | NA | 195 | 120 | 7.892300e+00 | 4.816700e+00 | 3.075600e+00 | 2.972000e-01 | -10.3494 | 252.2341 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | evasione | NA | 197 | 132 | 2.560490e+01 | 2.644980e+01 | -8.449000e-01 | 8.218000e-01 | 1.0281 | 223.8484 | 0.3050 |
| LOMBARDIA_SQUARE_noFE | expend_level | NA | 197 | 132 | 4.939100e+00 | 3.924200e+00 | 1.014800e+00 | 2.847000e-01 | -3.5652 | 271.6508 | 0.0004 |
| LOMBARDIA_SQUARE_noFE | expenditure | NA | 197 | 132 | 2.593024e+06 | 2.018421e+05 | 2.391182e+06 | 1.512973e+06 | -1.5805 | 196.8032 | 0.1156 |
| LOMBARDIA_SQUARE_noFE | gb_intensity | NA | 197 | 132 | 2.340000e-02 | 3.830000e-02 | -1.480000e-02 | 2.500000e-03 | 5.9488 | 235.5566 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | gb_reg_rate | NA | 197 | 132 | 3.019000e-01 | 1.666000e-01 | 1.354000e-01 | 1.660000e-02 | -8.1419 | 301.9977 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | income | NA | 197 | 132 | 3.101343e+08 | 3.913533e+07 | 2.709990e+08 | 1.674416e+08 | -1.6185 | 197.1256 | 0.1072 |
| LOMBARDIA_SQUARE_noFE | incomepc | NA | 197 | 132 | 2.328246e+04 | 1.967258e+04 | 3.609885e+03 | 3.132317e+02 | -11.5246 | 324.8732 | 0.0000 |
| LOMBARDIA_SQUARE_noFE | marr_civil | NA | 197 | 132 | 2.537560e+01 | 5.204500e+00 | 2.017110e+01 | 1.158300e+01 | -1.7414 | 199.1994 | 0.0831 |
| LOMBARDIA_SQUARE_noFE | marr_rel | NA | 197 | 132 | 1.041120e+01 | 2.712100e+00 | 7.699000e+00 | 3.596700e+00 | -2.1406 | 207.6600 | 0.0335 |
| LOMBARDIA_SQUARE_noFE | pol_mun_road | NA | 197 | 132 | 5.996450e+01 | 4.145630e+01 | 1.850820e+01 | 1.318970e+01 | -1.4032 | 239.3458 | 0.1618 |
| LOMBARDIA_SQUARE_noFE | services_level | NA | 197 | 132 | 6.020300e+00 | 3.636400e+00 | 2.383900e+00 | 3.132000e-01 | -7.6125 | 250.0019 | 0.0000 |
This Rmd writes the following files to output/:
RD_plots_All_Italy_regFE_manualDistance.pdfRD_plots_Lombardia_noFE_manualDistance.pdfRD_plots_LombardiaSquare_area_x<scale>_noFE_manualDistance.pdflombardia_square_area_x<scale>.csvlombardia_square_area_x<scale>_metadata.csvrdrobust_results_All_Italy_Lombardia_Square_manualDistance.csvrdrobust_printout_All_Italy_regFE_manualDistance.txtrdrobust_printout_Lombardia_noFE_manualDistance.txtrdrobust_printout_LombardiaSquare_area_x<scale>_noFE_manualDistance.txtRD_plots_Pavia_noFE_manualDistance.pdfrdrobust_printout_Pavia_noFE_manualDistance.txtdiffmeans_FullItaly_h40.csvdiffmeans_Lombardia_h40.csvdiffmeans_LombardiaSquare_h40.csvdiffmeans_Pavia_h40.csv