As mentioned earlier, we restrict our sample to first and second born children since these are the children subjected to the quasi-experimental design. Nonetheless, we also performed our analysis on the full sample of all children, although the results based on first and second born children only constitute our preferred estimates. We continue to restrict the sample to children residing in households with at least one sibling. The results are relegated to Appendix B.
In the interest of brevity, we simply highlight the main differences. First, the negative (local) average treatment effect estimated by TSLS is now statstically significant when using weight-for-age and Control Set A; all other TSLS estimates remain statistically insignificant (see Table B2).
Second, in Tables B4 (Unconditional Results) and B5 (Adjusted for Covariates), we now reject equality of the distributions in all cases when using height-for-age. Finally, in all cases in Tables B4 and B5, the distribution of weight-for-age in households with only two children is observed to second order dominate the corresponding distribution from larger households. Moreover, the rankings of the unconditional distributions (Table B4) are statistically meaningful.
In sum, while the majority of results – particularly those concerning the validity of our instru-ment – are unchaged when utilizing the full sample of children, we do find moderately stronger results pertaining to a quantity-quality trade-off for children between the 20th and 50th quantiles when using the more short-run measure of health (weight-for-age).
6 Conclusion
Although the theoretical trade-off between the quantity and quality of children is well-established, empirical evidence supporting such a causal relationship is limited. Moreover, most existing em-pirical studies focus on education as a measure of child quality and are limited to linear regression
analysis. While such results are easily interpretable, at best they provide evidence of the aver-age effect of the number of children on child-specific investments. In contrast, this study analyzes the impact of household size on the entire distribution of two measures of health using data from Indonesia, while accounting for the potential endogeneity of the quantity of children.
The analysis yields three main conclusions. First, distributions of weight-for-age are statistically different when we account for the endogeneity of the quantity of children. Second, despite the significant difference in the distributions across households with more than two or only two children, we fail to find statistically meaningful evidence of the quantity-quality trade-off over the whole distribution. In particular, using an identification strategy based on gender composition of the first two children, there is evidence that the quantity-quality trade-off applies to only some. Finally, while modest evidence of the trade-off is found when using a more short-run measure of health (based on weight), there is no statistically meaningful evidence of a trade-off on a long-run measure (based on height) once the endogeneity of fertility decisions is addressed.
While these findings are striking, future research is necessary to answer questions generated by this analysis. First, how robust are the results to alternative instruments that identify the trade-off from other subpopulations of compliers (e.g., twins, such as in Rosenzweig and Zhang (2006))? Second, utilizing other instruments for identification, are there larger gains from reducing the number of children from, say, six children in a family to five, or from two children to only one?
Finally, are robust rankings possible if one examines bivariate distributions, such as health and education, or health and family income? Despite these open questions, answering these and other similar questions within a distributional framework is necessary for a deeper understanding of the nature of intrahousehold allocation as well as sound policymaking.
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Table 1: Summary Statistics
Variable More than Two Children Two Children
Mean SD Obs Mean SD Obs
Height-for-age (z-score) -1.843 1.119 810 -1.484 1.335 2103
Weight-for-age (z-score) -1.822 1.198 796 -1.545 1.344 2115
First two children are same sex (1 = yes) 0.514 0.5 1014 0.48 0.5 2594
First two children are daughter2 (1 = yes) 0.266 0.442 1014 0.229 0.421 2594
Age in months 93.677 27.061 966 62.929 37.128 2522
Gender (1=male) 0.499 0.5 1014 0.515 0.5 2594
First Child’s Gender (1 = male) 0.492 0.5 1014 0.494 0.5 2594
Second Child’s Gender (1 = male) 0.489 0.5 1014 0.527 0.499 2594
Father’s Education
Elementary School and below 0.427 0.495 1014 0.412 0.492 2594
Junior High School 0.17 0.375 1014 0.177 0.381 2594
Senior High School 0.259 0.439 1014 0.287 0.452 2594
University 0.144 0.351 1014 0.125 0.33 2594
Mother’s Education
Elementary School and below 0.527 0.5 1008 0.447 0.497 2574
Junior High School 0.157 0.364 1008 0.196 0.397 2574
Senior High School 0.229 0.421 1008 0.278 0.448 2574
University 0.087 0.282 1008 0.08 0.271 2574
Father’s Height 161.997 5.972 749 162.428 6.47 2011
Mother’s Height 150.968 5.36 849 151.01 5.363 2180
Father’s Weight 57.161 9.83 745 57.398 9.801 2005
Mother’s Weight 51.568 9.491 846 51.745 8.988 2172
Father’s Age 36.705 5.543 1014 34.878 6.48 2588
Mother’s Age 31.996 4.495 1008 30.085 5.318 2568
Father’s Religion (1 = Islam) 0.853 0.354 1014 0.891 0.312 2592
Mother’s Religion (1 = Islam) 0.854 0.353 1008 0.893 0.309 2572
Father’s Work Status (1 = Wrok) 0.988 0.108 1014 0.984 0.125 2594
Mother’s Work Status (1 = Wrok) 0.481 0.5 1008 0.486 0.5 2572
Region (1 = Urban) 0.485 0.5 1014 0.507 0.5 2594
Dweilling Type
Single Unit 0.777 0.416 1014 0.836 0.37 2594
Duplex 0.087 0.282 1014 0.079 0.269 2594
Multiple Unit 0.04 0.197 1014 0.035 0.185 2594
House on Stilts 0.096 0.294 1014 0.05 0.217 2594
Floor Type
Ceramic/Marble/Granite/Stone 0.162 0.369 1012 0.188 0.391 2594
Tiles/Terrazzo 0.186 0.389 1012 0.223 0.416 2594
Table 1 – (cont.) Summary Statistics
Variable More than Two Children Two Children
Mean SD Obs Mean SD Obs
Cement/Bricks 0.373 0.484 1012 0.354 0.478 2594
Lumber/Board/Bamboo 0.182 0.386 1012 0.122 0.328 2594
Dirt 0.098 0.297 1012 0.113 0.316 2594
Wall Type
Masonry (cement/brick) 0.609 0.488 1014 0.665 0.472 2594
Lumber/Board 0.271 0.445 1014 0.247 0.432 2594
Bamboo/Woven/Mat 0.119 0.324 1014 0.088 0.283 2594
Water Type
Pipe water 0.284 0.451 1006 0.266 0.442 2569
Well/Pump 0.262 0.44 1006 0.313 0.464 2569
Well water 0.308 0.462 1006 0.28 0.449 2569
Spring/Rain Water 0.056 0.229 1006 0.069 0.253 2569
River/Creek Water 0.051 0.219 1006 0.028 0.165 2569
Other 0.039 0.193 1006 0.044 0.204 2569
Decision on Children’s Health
Jointly made by husband and wife 0.025 0.155 889 0.032 0.175 2243
Only made by husband 0.126 0.332 889 0.117 0.322 2243
Only made by wife 0.094 0.293 889 0.088 0.283 2243
Otherwise 0.755 0.43 889 0.763 0.425 2243
House surrounded by
human/animal waste (1 = yes) 0.085 0.279 1014 0.068 0.252 2594
House surrounded by
piles of trash (1 = yes) 0.116 0.321 1014 0.119 0.324 2594
House surrounded by
stagnant water (1 = yes) 0.106 0.307 1014 0.097 0.296 2594
Stable under/next to
house (1 = yes) 0.217 0.412 1014 0.197 0.398 2594
Sufficient ventilation (1 = yes) 0.769 0.422 1012 0.801 0.399 2594
Yard is cleaned up (1 = yes) 0.681 0.466 1014 0.718 0.45 2594
House has a moderately
sized yard (1 = yes) 0.61 0.488 1014 0.616 0.486 2594
House has kitchen
outside (1 = yes) 0.271 0.445 1012 0.266 0.442 2594
No. of Rooms 5.386 2.639 1014 5.463 2.612 2594
House Size 75.536 67.265 1014 82.532 182.343 2594
Boil Water (1 = yes) 0.921 0.27 983 0.95 0.218 2499
Own Farm (1 = yes) 0.331 0.471 1006 0.299 0.458 2569
Table 1 – (cont.) Summary Statistics
Variable More than Two Children Two Children
Mean SD Obs Mean SD Obs
Female Household Head (1 = yes) 0.033 0.178 1014 0.028 0.165 2594
Number of Health Facilities
Hospitals 2.655 1.432 1014 2.797 1.59 2594
Integrated Health Post 8.888 5.588 1014 9.502 5.54 2594
Private Practice 27.86 9.191 1014 28.751 9.719 2594
Commnuity Health Centers 7.855 2.89 1014 8.209 3.543 2594
Traditional Practices 5.514 3.384 1014 5.381 3.054 2594
Minimum distance of Health Facilities
Hospitals 17.012 22.689 1014 15.882 21.751 2594
Integrated Health Post 5.643 62.677 1014 3.986 48.03 2594
Private Practice 0.416 0.512 1014 0.438 0.602 2594
Commnuity Health Centers 1.137 1.385 1014 1.045 1.05 2594
Traditional Practices 0.775 1.821 1014 0.796 2.103 2594
Table 2: Regression Results
Height-for-age Weight-for-age
Model 1 Model 2 Model 3 Model 1 Model 2 Model 3
(1) (2) (3) (4) (5) (6)
Control Set A B C A B C
Panel A: OLS Results
Morethan 2 -0.207*** -0.123** -0.114* -0.190*** -0.117* -0.110*
[0.058] [0.059] [0.059] [0.064] [0.064] [0.065]
Panel B: IV Results
Morethan 2 -0.294 0.170 0.312 -1.426 -0.474 -0.378
[0.916] [1.143] [1.033] [1.029] [1.131] [1.012]
Panel C: Weak-IV Robust Inference
Anderson-Rubin F 0.102 0.022 0.090 2.192 0.173 0.136
p-value 0.749 0.883 0.764 0.139 0.677 0.713
Stock-Wright S stat 0.102 0.022 0.093 2.192 0.178 0.140
p-value 0.749 0.882 0.760 0.139 0.673 0.708
Panel D: Reduced Form
Samesex2 -0.016 0.007 0.015 -0.078 -0.022 -0.019
[0.050] [0.049] [0.049] [0.053] [0.052] [0.052]
Number of Obs 2863 2399 2399 2861 2399 2399
1Note – Robust standard errors in brackets. *** p < 0.01, ** p < 0.05, * p < 0.1.
2Columns (1)-(3) report results for Height-for-age using Control set A, B, and C, respectively;
Columns (4)-(6) report results for Weight-for-age using Control set A, B, and C, respectively. See text for detail of the variables in each control set.
3Panel D reports reduced form estimates where morethan2 is excluded from these regressions.
Table3:TheEffectsofIVonMoreThan2(FirstStage) Height-for-ageWeight-for-age Model1Model2Model3Model1Model2Model3 (1)(2)(3)(4)(5)(6) ControlSetABCABC SameSex20.055***0.043**0.048***0.055***0.045***0.051*** [0.017][0.018][0.018][0.017][0.018][0.018] F-test10.8725.9287.31810.8806.7278.310 p-value0.0010.0150.0070.0010.0100.004 Kleibergen-PaaprkWaldStat10.8916.0807.55110.8996.8998.574 p-value0.0010.0140.0060.0010.0090.003 NumberofObs286323992399286123992399 1Note–Robuststandarderrorsinbrackets.***p<0.01,**p<0.05,*p<0.1 2Columns(1)-(3)reportresultsforHeight-for-ageusingControlsetA,B,andC,respectively;Columns(4)- (6)reportresultsforWeight-for-ageusingControlsetA,B,andC,respectively.Seetextfordetailofthe variablesineachcontrolset.
Table 4: The Effects of Alternative IVs on Fertility (First Stage)
Height-for-age Weight-for-age
Model No. of obs Model No. of obs
(1) (2) (3) (4)
Panel A Endog Var: Morethan 1 -0.014 3762 -0.014 3785
IV: Daughter 1 [0.010] [0.010]
Panel B Endog Var: Morethan 2 -0.027 2399 -0.028 2399
IV: Daughter 1 [0.019] [0.019]
Panel C Endog Var: Morethan 2 0.03 2399 0.032 2399
IV: Daughter 2 [0.025] [0.025]
1Note – Robust standard errors in brackets. *** p < 0.01, ** p < 0.05, * p < 0.1
2Columns (1)-(3) report results for Height-for-age using Control set A, B, and C, respec-tively; Columns (4)-(6) report results for Weight-for-age using Control set A, B, and C, respectively. See text for detail of the variables in each control set.
Table5:DistributionalTestsofUnconditionalChildren’sHealth. DistributionsObservedTestofFirstOrderDominanceSecondOrderDominance RankingEqualityPrd∗≤0Prs∗≤0 XYd1,MAXd2,MAXd(SimpleBoot)s1,MAXs2,MAXs(SimpleBoot) NoIV A.Height-for-Age TwoChildrenMorethanTwoNonep=0.0000.0383.0480.0380.0560.137222.1950.1370.134 B.Weight-for-Age TwoChildrenMorethanTwoNonep=0.0140.0182.2160.0180.2860.018200.4750.0180.448 WithIV A.Height-for-Age TwoChildrenMorethanTwoNonep=0.2201.0181.3531.0180.0021.36059.6071.3600.030 B.Weight-for-Age TwoChildrenMorethanTwoNonep=0.0260.1311.8910.1310.0020.177107.3940.1770.184 1Note–Robuststandarderrorsinbrackets.***p<0.01,**p<0.05,*p<0.1 2P-valuesobtainedusing500bootstraprepetitions.
Table6:DistributionalTestsofChildren’sHealthAdjustedforCovariates DistributionsControlSetObservedTestofFirstOrderDominanceSecondOrderDominance RankingEqualityPrd∗≤0Prd∗≤0 XYd1,MAXd2,MAXd(SimpleBoot)s1,MAXs2,MAXs(SimpleBoot) NoIV A.Height-for-Age TwoChildrenMorethanTwoANonep=0.0000.0482.7190.0480.0220.194165.8070.1940.092 TwoChildrenMorethanTwoBNonep=0.0000.0543.7290.0540.0100.274257.7750.2740.074 TwoChildrenMorethanTwoCNonep=0.0000.0523.0760.0520.0120.257201.3500.2570.072 B.Weight-for-Age TwoChildrenMorethanTwoANonep=0.0040.0202.3350.0200.2520.020195.7290.0200.448 TwoChildrenMorethanTwoBXSSDYp=0.0121.2191.9481.2190.0760.000112.8830.0000.564 TwoChildrenMorethanTwoCXSSDYp=0.0081.0131.9801.0130.0620.000116.9330.0000.594 WithIV A.Height-for-Age TwoChildrenMorethanTwoANonep=0.1480.9011.4700.9010.0001.47368.9561.4730.024 TwoChildrenMorethanTwoBNonep=0.1240.9511.4180.9510.0002.41149.8792.4110.026 TwoChildrenMorethanTwoCNonep=0.0680.9711.5390.9710.0002.33949.6182.3390.028 B.Weight-for-Age TwoChildrenMorethanTwoANonep=0.0120.1142.0280.1140.0040.170120.1900.1700.204 TwoChildrenMorethanTwoBNonep=0.0460.3831.7160.3830.0001.36964.4541.3690.084 TwoChildrenMorethanTwoCNonep=0.0520.4961.7540.4960.0001.37463.6891.3740.102 1Note–Robuststandarderrorsinbrackets.***p<0.01,**p<0.05,*p<0.1 2P-valuesobtainedusing500bootstraprepetitions.
−10−50510beta
0 .05 .1 .15 .2
delta
Lower Limit, UCI Upper Limit, UCI Note: Solid green line is TSLS Estimate
(a) Height-for-age
−10−50510beta
0 .05 .1 .15 .2
delta
Lower Limit, UCI Upper Limit, UCI Note: Solid green line is TSLS Estimate
(b) Weight-for-age
Figure 1: Sensitivity Analysis of Instrument Variable
Note: Control set C is utilized.
−2.5−2−1.5−1−.50
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(a) Height-for-age
−2−1.5−1−.50
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(c) Height-for-age
−1−.50.51
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(d) Weight-for-age
Instrument: SameSex2
Figure 2: Unconditional Quantile Treatment Effects
−2−1.5−1−.50.5
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(a) No Instrument
−.50.511.52
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(c) No Instrument
−.50.511.52
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(e) No Instrument
−.50.511.52
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(f) Instrument
Control Set C
Figure 3: Quantile Treatment Effects Adjusted for Covariates: Height-for-age z-scores
−2−1.5−1−.50
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(a) No Instrument
−1−.50.5
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(c) No Instrument
−.50.511.5
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(e) No Instrument
−.50.511.52
0 10 20 30 40 50 60 70 80 90 100
Quantile
Lower Limit, 90% CI Upper Limit, 90% CI QTE
(More Than Two Kids − Two Kids)
Quantile Treatment Effect
(f) Instrument
Control Set C
Figure 4: Quantile Treatment Effects Adjusted for Covariates: Weight-for-age z-scores