Chapter 11 Regression Discontinuity Designs (RDD)
11.1 Libraries
library(dplyr) # data manipulation
library(tibble) # cuter dataframes
library(haven) # read dta files
library(rddensity) # density tests
library(rdrobust) # rdd estimation
library(ggplot2) # plot graphs
library(stargazer) # nice tables
library(stringr) # to combine strings11.2 What is the paper about?
Well, let’s look at the abstract:
“Does Islamic political control affect women’s empowerment? Several countries have recently experienced Islamic parties coming to power through democratic elections. Due to strong support among religious conservatives, constituencies with Islamic rule often tend to exhibit poor women’s rights. Whether this reflects a causal relationship or a spurious one has so far gone unexplored. I provide the first piece of evidence using a new and unique data set of Turkish municipalities. In 1994, an Islamic party won multiple municipal mayor seats across the country. Using a regression discontinuity (RD) design, I compare municipalities where this Islamic party barely won or lost elections. Despite negative raw correlations, the RD results reveal that, over a period of six years, Islamic rule increased female secular high school education. Corresponding effects for men are systematically smaller and less precise. In the longer run, the effect on female education remained persistent up to 17 years after, and also reduced adolescent marriages. An analysis of long-run political effects of Islamic rule shows increased female political participation and an overall decrease in Islamic political preferences. The results are consistent with an explanation that emphasizes the Islamic party’s effectiveness in overcoming barriers to female entry for the poor and pious.”
11.3 Let’s load the data.
empowerment = read_dta("data/meyersson/regdata0.dta")11.4 Select and rename variables
empowerment = empowerment %>%
select(vote_share_islam_1994 = vshr_islam1994,
islamic_mayor_1994 = i94,
log_pop_1994 = lpop1994,
no_of_parties_1994 = partycount,
share_women_hs_1520 = hischshr1520f,
share_men_hs_1520 = hischshr1520m,
pop_share_under_19 = ageshr19,
pop_share_over_60 = ageshr60,
sex_ratio_2000 = sexr,
win_margin_islam_1994 = iwm94,
household_size_2000 = shhs,
district_center = merkezi,
province_center = merkezp,
metro_center = buyuk,
sub_metro_center = subbuyuk,
pd_1:pd_67,
pcode = pcode)11.5 Create Sample
empowerment = empowerment %>%
filter(!is.na(share_women_hs_1520),
!is.na(vote_share_islam_1994),
!is.na(no_of_parties_1994),
!is.na(win_margin_islam_1994),
!is.na(islamic_mayor_1994),
!is.na(share_men_hs_1520),
!is.na(household_size_2000),
!is.na(log_pop_1994),
!is.na(pop_share_under_19),
!is.na(pop_share_over_60),
!is.na(sex_ratio_2000),
!is.na(district_center),
!is.na(province_center),
!is.na(metro_center),
!is.na(sub_metro_center))11.6 Create Vector of Control Variables
Z = empowerment %>%
select(vote_share_islam_1994,
no_of_parties_1994,
household_size_2000,
log_pop_1994,
pop_share_under_19,
pop_share_over_60,
sex_ratio_2000,
district_center,
province_center,
sub_metro_center,
metro_center)11.7 Summary Statistics
11.8 Histogram of Islamic Win Margin
We first need to create a dataframe for which our outcome and explanatory variables are available. This is at least what Meyersson does. It is not so clear whether this is the best way of doing it.
ggplot(empowerment) +
geom_histogram(aes(x = win_margin_islam_1994,
y = ..count../sum(..count..)*100),
binwidth = 0.02, color = "grey") +
labs(x = "Islamic Win Margin in 1994",
y = "Percent",
title = "Histogram of Islamic Win Margin") +
theme_bw()
out = rddensity(empowerment$win_margin_islam_1994)
summary(out)##
## Manipulation testing using local polynomial density estimation.
##
## Number of obs = 2629
## Model = unrestricted
## Kernel = triangular
## BW method = estimated
## VCE method = jackknife
##
## c = 0 Left of c Right of c
## Number of obs 2314 315
## Eff. Number of obs 965 301
## Order est. (p) 2 2
## Order bias (q) 3 3
## BW est. (h) 0.305 0.283
##
## Method T P > |T|
## Robust -1.3937 0.1634
##
##
## P-values of binomial tests (H0: p=0.5).
##
## Window Length / 2 <c >=c P>|T|
## 0.004 11 9 0.8238
## 0.009 18 26 0.2912
## 0.013 32 34 0.9022
## 0.017 42 48 0.5984
## 0.021 52 57 0.7018
## 0.026 68 62 0.6612
## 0.030 74 71 0.8682
## 0.034 94 79 0.2871
## 0.038 113 86 0.0650
## 0.043 131 90 0.007011.9 Doing RDD by Hand
empower_left = empowerment %>%
filter(win_margin_islam_1994 < 0,
win_margin_islam_1994 >= -.24)
empower_right = empowerment %>%
filter(win_margin_islam_1994 > 0,
win_margin_islam_1994 <= .24)
lm_left = lm(share_women_hs_1520 ~ win_margin_islam_1994, empower_left)
lm_right = lm(share_women_hs_1520 ~ win_margin_islam_1994, empower_right)
intercept_left = lm_left$coefficients[1]
intercept_right = lm_right$coefficients[1]
difference = intercept_right - intercept_left
print(str_c("The RD estimator is ", difference, "."))## [1] "The RD estimator is 0.0317363445877732."11.10 rdrobust Package
11.10.1 RDD with and without controls
# rdd with and without controls: women
summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.240, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 728 293
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.240 0.240
## BW bias (b) 0.240 0.240
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.030 0.015 1.979 0.048 [0.000 , 0.059]
## Robust - - 1.411 0.158 [-0.011 , 0.066]
## =============================================================================summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.240, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 728 293
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.240 0.240
## BW bias (b) 0.240 0.240
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.025 0.009 2.894 0.004 [0.008 , 0.043]
## Robust - - 2.607 0.009 [0.008 , 0.053]
## =============================================================================# rdd with and without controls: men
summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.323, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 1038 304
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.323 0.323
## BW bias (b) 0.323 0.323
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.012 0.010 1.159 0.247 [-0.008 , 0.031]
## Robust - - 1.607 0.108 [-0.004 , 0.045]
## =============================================================================summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.323, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 1038 304
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.323 0.323
## BW bias (b) 0.323 0.323
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.009 0.009 1.026 0.305 [-0.008 , 0.026]
## Robust - - 1.621 0.105 [-0.004 , 0.042]
## =============================================================================11.10.2 Different bandwidths
# different bandwiths: women
summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.120, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 369 220
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.120 0.120
## BW bias (b) 0.120 0.120
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.030 0.011 2.757 0.006 [0.009 , 0.052]
## Robust - - 2.262 0.024 [0.005 , 0.064]
## =============================================================================summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.480, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 1742 310
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.480 0.480
## BW bias (b) 0.480 0.480
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.022 0.008 2.883 0.004 [0.007 , 0.036]
## Robust - - 2.677 0.007 [0.007 , 0.045]
## =============================================================================# different bandwidths: men
summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.161, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 493 254
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.161 0.161
## BW bias (b) 0.161 0.161
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.018 0.011 1.686 0.092 [-0.003 , 0.040]
## Robust - - 1.238 0.216 [-0.011 , 0.048]
## =============================================================================summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.646, covs = Z, cluster = empowerment$pcode))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 2270 314
## Order est. (p) 1 1
## Order bias (q) 2 2
## BW est. (h) 0.646 0.646
## BW bias (b) 0.646 0.646
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.008 0.008 1.061 0.289 [-0.007 , 0.024]
## Robust - - 1.011 0.312 [-0.009 , 0.029]
## =============================================================================11.10.3 Different control functions
# different control functions: women
summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.240, covs = Z, cluster = empowerment$pcode, p = 2))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 728 293
## Order est. (p) 2 2
## Order bias (q) 3 3
## BW est. (h) 0.240 0.240
## BW bias (b) 0.240 0.240
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.030 0.012 2.608 0.009 [0.008 , 0.053]
## Robust - - 2.569 0.010 [0.009 , 0.064]
## =============================================================================summary(rdrobust(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994, h = 0.240, covs = Z, cluster = empowerment$pcode, p = 3))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 728 293
## Order est. (p) 3 3
## Order bias (q) 4 4
## BW est. (h) 0.240 0.240
## BW bias (b) 0.240 0.240
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.037 0.014 2.570 0.010 [0.009 , 0.065]
## Robust - - 1.889 0.059 [-0.001 , 0.070]
## =============================================================================# different control functions: men
summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.323, covs = Z, cluster = empowerment$pcode, p = 2))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 1038 304
## Order est. (p) 2 2
## Order bias (q) 3 3
## BW est. (h) 0.323 0.323
## BW bias (b) 0.323 0.323
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.019 0.012 1.626 0.104 [-0.004 , 0.042]
## Robust - - 1.557 0.120 [-0.006 , 0.052]
## =============================================================================summary(rdrobust(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994, h = 0.323, covs = Z, cluster = empowerment$pcode, p = 3))## Call: rdrobust
##
## Number of Obs. 2629
## BW type Manual
## Kernel Triangular
## VCE method NN
##
## Number of Obs. 2314 315
## Eff. Number of Obs. 1038 304
## Order est. (p) 3 3
## Order bias (q) 4 4
## BW est. (h) 0.323 0.323
## BW bias (b) 0.323 0.323
## rho (h/b) 1.000 1.000
## Unique Obs. 2312 315
##
## =============================================================================
## Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
## =============================================================================
## Conventional 0.023 0.015 1.557 0.120 [-0.006 , 0.052]
## Robust - - 1.268 0.205 [-0.012 , 0.055]
## =============================================================================11.11 RDD Plots
11.11.1 Main Outcomes: Women
rdplot(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Women in Highschool (15-20)",
y.lim = c(0, .5))
rdplot(empowerment$share_women_hs_1520, empowerment$win_margin_islam_1994,
h = 0.240,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Women in Highschool (15-20)",
y.lim = c(0, .5))
empower_plot = empowerment %>%
filter(win_margin_islam_1994 >= -0.240,
win_margin_islam_1994 <= 0.240)
rdplot(empower_plot$share_women_hs_1520, empower_plot$win_margin_islam_1994,
h = 0.240,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Women in Highschool (15-20)",
y.lim = c(0, .25))
11.11.2 Main Outcomes: Men
rdplot(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Men in Highschool (15-20)",
y.lim = c(0, .5))
rdplot(empowerment$share_men_hs_1520, empowerment$win_margin_islam_1994,
h = 0.240,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Men in Highschool (15-20)",
y.lim = c(0, .5))
rdplot(empower_plot$share_men_hs_1520, empower_plot$win_margin_islam_1994,
h = 0.240,
x.label = "Running Variable: Islamic Vote Share",
y.label = "Share of Men in Highschool (15-20)",
y.lim = c(0, .25))