vars n mean sd median trimmed mad min max range skew
ano* 1 74368 8.50 4.61 8.50 8.50 5.93 1.00 16.00 15.00 0.00
fem_share 2 74368 0.20 0.06 0.20 0.20 0.06 0.03 0.48 0.45 0.60
ch_bear 3 74368 0.22 0.07 0.21 0.21 0.06 0.00 0.51 0.51 0.34
x 4 74368 0.00 0.01 0.00 0.00 0.00 -0.19 0.85 1.03 10.28
kurtosis se
ano* -1.21 0.02
fem_share 0.57 0.00
ch_bear 0.54 0.00
x 426.49 0.00RD design
Introduction
Koppensteiner and Matheson (2021) found that an intervention on education infrastructure significantly affected childbearing. Their abstract:
“This article investigates the effect that increasing secondary education opportunities have on teenage fertility in Brazil. Using a novel dataset to exploit variation from a 57 percent increase in secondary schools across 4,884 Brazilian municipalities between 1997 and 2009, the analysis shows an important role of secondary school availability on underage fertility. An increase of one school per 100 females reduces a cohort’s teenage birthrate by between 0.250 and 0.563 births per 100, or a reduction of one birth for roughly every 50 to 100 students who enroll in secondary education. The results highlight the important role of access to education leading to spillovers in addition to improving educational attainment.”
Below some descriptive statistics for our variables of interest. ‘X’ is the school density at the municipality level centered at 1997 level. ‘fem_share’ is the female income share and ‘ch_bear’ is the childbearing dummy, both measured from 2010’s demographic survey data. We bind our analysis to the sample of women (couples) aged between 20 and 31 years old that are in couple.
Female income share: early vs late child-bearers
The share of couples whose female income share equals 0.5 was 0.0781427. These were dropped to implement McCrary’s (2008) test, thus suggesting the presence of the gender identity norm. The test rejects the null in both subpopulations, early and late child-bearers.
# McCrary's test (gender identity norm):
# Early child-bearers
summary(earlyd)
Manipulation testing using local polynomial density estimation.
Number of obs = 8226640
Model = unrestricted
Kernel = triangular
BW method = estimated
VCE method = jackknife
c = 0.5 Left of c Right of c
Number of obs 8068304 158336
Eff. Number of obs 5872 6160
Order est. (p) 2 2
Order bias (q) 3 3
BW est. (h) 0.01 0.012
Method T P > |T|
Robust 24.6585 0
P-values of binomial tests (H0: p=0.5).
Window Length / 2 <c >=c P>|T|
0.000 48 32 0.0929
0.001 128 128 1.0000
0.001 160 176 0.4132
0.002 240 224 0.4862
0.002 320 304 0.5482
0.002 432 336 0.0006
0.003 544 496 0.1450
0.003 608 544 0.0634
0.003 720 768 0.2231
0.004 880 880 1.0000# Late child-bearers
summary(lated)
Manipulation testing using local polynomial density estimation.
Number of obs = 8226640
Model = unrestricted
Kernel = triangular
BW method = estimated
VCE method = jackknife
c = 0.5 Left of c Right of c
Number of obs 7607648 618992
Eff. Number of obs 21648 24064
Order est. (p) 2 2
Order bias (q) 3 3
BW est. (h) 0.01 0.012
Method T P > |T|
Robust 16.0127 0
P-values of binomial tests (H0: p=0.5).
Window Length / 2 <c >=c P>|T|
0.000 32 32 1.0000
0.000 144 160 0.3897
0.001 448 368 0.0056
0.001 480 448 0.3089
0.001 656 640 0.6769
0.001 880 912 0.4640
0.001 928 912 0.7266
0.001 1088 1040 0.3083
0.002 1232 1104 0.0086
0.002 1408 1248 0.0020Estimates at the municipality level
Before evaluating the effect of childbearing on females’ income share we present two preliminary analysis. First the relationship between school infrastructure and childbearing, and then the relationship between infrastructure and females’ income share.
- The school density was obtained from the authors database (Koppensteiner and Matheson, 2021). It is available from 1996 to 2010, we added 1995 in order to have more infrastructure data prior the reform (in 1997)
- The female share of income and the childbearing dummy variable were contructed by us from the 2010 demographic census. This lead to almost 9 million observations that we aggregate at the municipality level.
- Our study focuses on a panel of (around 5k) municipalities, with the aim of assessing the impact of childbearing (rates) on the share of income received by females as of 2010.
As expected, the centered school density (running variable) shows a break in the continuity of its distribution when evaluated at school density in 1997:
Manipulation testing using local polynomial density estimation.
Number of obs = 74368
Model = unrestricted
Kernel = triangular
BW method = estimated
VCE method = jackknife
c = 0 Left of c Right of c
Number of obs 27514 46854
Eff. Number of obs 10638 20123
Order est. (p) 2 2
Order bias (q) 3 3
BW est. (h) 0.001 0.002
Method T P > |T|
Robust -4.6296 0
P-values of binomial tests (H0: p=0.5).
Window Length / 2 <c >=c P>|T|
0.000 20 10098 0.0000
0.000 84 10152 0.0000
0.000 187 10241 0.0000
0.000 277 10372 0.0000
0.000 424 10520 0.0000
0.000 565 10664 0.0000
0.000 710 10817 0.0000
0.000 836 10954 0.0000
0.000 987 11110 0.0000
0.000 1150 11281 0.0000
First
The following illustrates the relationship between school infrastructure i.e. the number of schools per 100 females (in schooling age) and the child bearing rate. Both are calculated at the municipality level.
The running variable in the horizontal axis (school density) is centered at the level at the beginning of the school infrastructure intervention in 1997. The first plot provides a full overview of the sample, whereas the next one provides a zoom near the cutoff (school density in 1997).
[1] "Mass points detected in the running variable."
[1] "Mass points detected in the running variable."
A preliminary sharp RD that measures the LATE of the intervention shows a reduction in the childbearing probability of about 0.3 percent:
Sharp RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 20495 31737
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 0.006 0.006
BW bias (b) 0.015 0.015
rho (h/b) 0.408 0.408
Unique Obs. 14162 21781
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.003 0.002 -1.884 0.060 [-0.007 , 0.000]
Robust - - -1.916 0.055 [-0.007 , 0.000]
=============================================================================In other words an increase in one school per 100 female students reduces the teenager births in 0.3 births per 100 females. Very close to the reference paper magnitude, which is included by the confidence interval.
Second
Now we verify the relationship between infrastructure intervention and the female income share (expected positive).
[1] "Mass points detected in the running variable."
[1] "Mass points detected in the running variable."
A sharp RD on this relationship verifies that the intervention increased the females’ income share in about 0.76` percent:
Sharp RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 19105 29531
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 0.005 0.005
BW bias (b) 0.013 0.013
rho (h/b) 0.395 0.395
Unique Obs. 14162 21781
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional 0.007 0.002 4.404 0.000 [0.004 , 0.011]
Robust - - 4.445 0.000 [0.004 , 0.011]
=============================================================================Manual Fuzzy RD
From the previous results we can infer the effect of childbearing on the female income share. The first and second result represented the first and second stage of a manually implemented Fuzzy RD. The LATE of childbearing on females’ income share is obtained as the ratio of both effects. An increase of one percent in the childbearing probability leads to a 2.22 percent decrease in females’ income share.
Automatic Fuzzy RD
The one-step estimator delivers a similar result:
Fuzzy RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 18707 28908
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 0.005 0.005
BW bias (b) 0.013 0.013
rho (h/b) 0.362 0.362
Unique Obs. 14162 21781
First-stage estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.004 0.002 -2.180 0.029 [-0.007 , -0.000]
Robust - - -2.244 0.025 [-0.008 , -0.001]
=============================================================================
Treatment effect estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -1.906 0.926 -2.058 0.040 [-3.721 , -0.091]
Robust - - -1.964 0.050 [-3.726 , -0.004]
=============================================================================| Coeff | P>|z| | |
|---|---|---|
| Conventional | -1.905672 | 0.0396133 |
| Bias-Corrected | -1.865202 | 0.0440033 |
| Robust | -1.865202 | 0.0495184 |
where the S.E. are clustered at the municipality level. An increase of one percent in the childbearing probability leads to a 1.8652023 percent decrease in females’ income share.
Robustness checks
Our main estimate at the municipality level assumes that a local linear regression fits well the data. We now implement additional non-linear polinomial regressions of order 2 and 3 to test for the robustness of our results. The results verify the robustness to alternative non-linear specifications:
Fuzzy RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 22695 35335
Order est. (p) 2 2
Order bias (q) 3 3
BW est. (h) 0.008 0.008
BW bias (b) 0.021 0.021
rho (h/b) 0.402 0.402
Unique Obs. 14162 21781
First-stage estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.004 0.002 -2.332 0.020 [-0.008 , -0.001]
Robust - - -2.392 0.017 [-0.008 , -0.001]
=============================================================================
Treatment effect estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -1.756 0.811 -2.165 0.030 [-3.345 , -0.167]
Robust - - -2.089 0.037 [-3.321 , -0.106]
=============================================================================Fuzzy RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 25070 40336
Order est. (p) 3 3
Order bias (q) 4 4
BW est. (h) 0.014 0.014
BW bias (b) 0.031 0.031
rho (h/b) 0.437 0.437
Unique Obs. 14162 21781
First-stage estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.005 0.002 -2.572 0.010 [-0.009 , -0.001]
Robust - - -2.610 0.009 [-0.009 , -0.001]
=============================================================================
Treatment effect estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -1.538 0.662 -2.322 0.020 [-2.836 , -0.240]
Robust - - -2.275 0.023 [-2.821 , -0.210]
=============================================================================| Coeff | P>|z| | |
|---|---|---|
| Conventional | -1.756014 | 0.0303588 |
| Bias-Corrected | -1.713131 | 0.0346438 |
| Robust | -1.713131 | 0.0367305 |
| Coeff | P>|z| | |
|---|---|---|
| Conventional | -1.537845 | 0.0202463 |
| Bias-Corrected | -1.515500 | 0.0221366 |
| Robust | -1.515500 | 0.0229294 |
Transmission channel
The childbearing effect on women’s income share may be channeled through their educational achievement. We test for this transmission channel by identifying the LATE of childbearing on three binary human capital indicators of literacy, high school and undergraduate studies achievements.
Effects on high school completion:
Fuzzy RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 20110 31070
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 0.006 0.006
BW bias (b) 0.013 0.013
rho (h/b) 0.439 0.439
Unique Obs. 14162 21781
First-stage estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.003 0.002 -1.941 0.052 [-0.007 , 0.000]
Robust - - -2.043 0.041 [-0.007 , -0.000]
=============================================================================
Treatment effect estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -2.691 1.422 -1.893 0.058 [-5.478 , 0.095]
Robust - - -1.589 0.112 [-5.220 , 0.546]
============================================================================= Coeff P>|z|
Conventional -2.691156 0.05836568
Bias-Corrected -2.336942 0.10021961
Robust -2.336942 0.11216762Effects on undergraduate studies completion:
Fuzzy RD estimates using local polynomial regression.
Number of Obs. 74368
BW type mserd
Kernel Triangular
VCE method NN
Number of Obs. 27514 46854
Eff. Number of Obs. 19790 30615
Order est. (p) 1 1
Order bias (q) 2 2
BW est. (h) 0.005 0.005
BW bias (b) 0.015 0.015
rho (h/b) 0.356 0.356
Unique Obs. 14162 21781
First-stage estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -0.003 0.002 -1.985 0.047 [-0.007 , -0.000]
Robust - - -1.992 0.046 [-0.007 , -0.000]
=============================================================================
Treatment effect estimates.
=============================================================================
Method Coef. Std. Err. z P>|z| [ 95% C.I. ]
=============================================================================
Conventional -1.262 0.646 -1.953 0.051 [-2.529 , 0.004]
Robust - - -1.913 0.056 [-2.566 , 0.031]
============================================================================= Coeff P>|z|
Conventional -1.262312 0.05076932
Bias-Corrected -1.267318 0.04985907
Robust -1.267318 0.05580338Pseudo panel analysis
We observe couples across different age cohorts in our data. Childbearing prevalence is heterogeneous across cohorts but seems to stabilize at 26 years of age :
It can be argued that older women should cumulate greater effects on their income share, so we perform the Fuzzy RD on every age-cohort (from 20 to 30) at the municipality level i.e. each RD estimate is performed over a cross-section of muncipalities at a given age-cohort.
| AgeGroup | LATE | SE | p_value | |
|---|---|---|---|---|
| 2 | 23 | -0.2846346 | 0.1622724 | 0.0794212 |
| 7 | 26 | -1.2435483 | 0.5554635 | 0.0251717 |
| 10 | 30 | -1.9651224 | 0.7680608 | 0.0105109 |
We find that not every age-cohort identifies statistically significant effects. Focusing on those age-cohorts that are significant at a 10% level (23, 26 and 30 years of age) clearly suggest that the childbearing effects do increase with women’s age