Is There Really a Trade-Off? Family Size and Investment in Child Quality in India

Mehtabul Azam; Chan Hang Saing

doi:10.1515/bejeap-2017-0098

Published by De Gruyter January 23, 2018

Is There Really a Trade-Off? Family Size and Investment in Child Quality in India

Mehtabul Azam and Chan Hang Saing

From the journal The B.E. Journal of Economic Analysis & Policy

https://doi.org/10.1515/bejeap-2017-0098

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Abstract

We address the relationship between number of children and investment in child quality, known as quantity–quality (Q–Q) trade-off, for India. Using a number of investment and outcome measures, we find that the OLS estimates suggest the presence of Q–Q trade-offs in nine out of ten measures considered. Using the gender of the first-born child as an instrument, the trade-offs in all measures disappear. Given the concerns about the exogeneity of the instrument, we apply Oster (2016) bounds to assess the sensitivity of OLS estimates to omitted variables. We find robust trade-off estimates in three measures currently enrolled in school, years of schooling and height-for-age. The results are more robust when observing trade-offs in rural areas. Trade-offs appear in ever enrolled in school, private school attendance, expenditure on education and private coaching in addition to the trade-offs in the three measures for all India sample.

Keywords: quantity–quality trade-off; investment; educational outcomes; India

JEL Classification: O11; J13

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Appendix

Table 1:

Summary statistics of sample children aged 6–18.

	(1)	(2)	(3)
	Mean	SD	N
Outcome variables
Ever enrolled in school (1/0)	0.97	0.18	37,756
Currently enrolled in school (1/0)	0.89	0.31	37,756
Years of schooling	5.11	3.45	37,754
Attend private school (1/0)	0.29	0.45	37,764
Private coaching (1/0)	0.37	0.48	37,764
Log of education expenditure	6.30	2.99	37,764
Log of private coaching expenditure	1.69	3.12	37,764
Standardized reading score	−0.07	1.01	9,401
Standardized math score	−0.06	1.00	9,364
Height-for-age z score	−1.59	1.95	31,128
Explanatory variables
Child is girl (1/0)	0.48	0.50	37,764
Child-Age	11.75	3.61	37,764
Child-Age squared	151.16	86.35	37,764
Child’s birth order-2	0.31	0.46	37,764
Child’s birth order-3	0.19	0.39	37,764
Child’s birth order-4	0.10	0.30	37,764
Child’s birth rder-5 or more	0.08	0.27	37,764
Other backward castes	0.36	0.48	37,764
Scheduled castes	0.23	0.42	37,764
Scheduled tribes	0.08	0.27	37,764
Muslim	0.15	0.35	37,764
Log of per capita income	9.40	0.97	37,301
Joint-two mother observations from same household	0.03	0.16	37,764
Mother’s age	36.12	5.74	37,764
Mother’s age squared	1,337.25	419.72	37,764
Mother height in cm	151.19	8.23	36,966
Father’s age	41.12	6.52	37,764
Father’s age squared	1,732.99	550.94	37,764
Household main income source cultivation (1/0)	0.25	0.43	37,764
Household main income source salaried (1/0)	0.16	0.36	37,764
Household holds below poverty line card (1/0)	0.37	0.48	37,764
Household own TV (1/0)	0.59	0.49	37,764
Household own land (1/0)	0.48	0.50	37,764
Urban	0.31	0.46	37,764

Note: SD: Standard deviation. Survey weights are used.

Table 2:

Q–Q Trade-offs.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
				δ for β∗=0;	δ for	Oster’s bound,	Max
	No			Rmax=	β∗=0;	δ=1,	Rmax for
Dependent variable	controls	Controls	IV	1.3Ř	Rmax=1	Rmax=1.3Ř	β<0
							under
							δ=1
Ever enrolled in school (1/0)	−0.014***	−0.009***	0.026*	0.904	0.028	[−0.009, 0.003]	0.108
	(0.001)	(0.002)	(0.015)
R-squared	0.015	0.085	0.052
Currently enrolled (1/0)	−0.036***	−0.031***	0.005	1.146	0.093	[−0.031, −0.013]	0.259
	(0.002)	(0.003)	(0.024)
R-squared	0.034	0.192	0.180
Years of schooling completed	−0.187***	−0.230***	−0.000	2.370	2.211	[ −0.320, −0.230]	NA
	(0.018)	(0.021)	(0.161)
R-squared	0.007	0.757	0.753
Attend private school (1/0)	−0.047***	−0.031***	0.095**	0.938	0.124	[−0.031, 0.005]	0.381
	(0.003)	(0.003)	(0.038)
R-squared	0.027	0.297	0.230
Private coaching (1/0)	−0.006**	0.003	0.013	−0.424	−0.036	[0.003, 0.021]	NA
	(0.003)	(0.004)	(0.041)
R-squared	0.000	0.221	0.221
Log of education expenditure	−0.491***	−0.368***	0.366	0.934	0.113	[−0.368, 0.086]	0.333
	(0.020)	(0.025)	(0.232)
R-squared	0.068	0.261	0.214
Log of private coaching expenditure	−0.326***	−0.228***	0.284	0.982	0.132	[−0.228, 0.010]	0.388
	(0.018)	(0.025)	(0.246)
R-squared	0.028	0.300	0.277
Standardized reading score	−0.149***	−0.109***	0.165	0.786	0.103	[−0.109, 0.137]	0.353
	(0.012)	(0.016)	(0.171)
Observations	9,401	9,401	9,401
R-squared	0.054	0.287	0.248
Standardized math score	−0.168***	−0.105***	0.115	0.653	0.093	[−0.105, 0.200]	0.364
	(0.011)	(0.015)	(0.172)
Observations	9,364	9,364	9,364
R-squared	0.070	0.307	0.274
Height-for-age z score	−0.040***	−0.058***	−0.011	3.164	0.201	[−0.096, −0.058]	NA
	(0.012)	(0.016)	(1.188)
Observations	31,128	31,128	31,128
R-squared	0.001	0.173	0.172

Note: Standard errors in parentheses are calculated taking survey design into account and are clustered at the mother level. The coefficients refer to the coefficients of family size. The number of observations in each regression except for the last three dependent variables is 37,764. Control variables include district fixed effects, age and age squared of child, child’s gender, indicators for birth order of child (second, third, fourth and fifth), indicator if two mothers reside in same household, indicators for other backward castes, scheduled castes, scheduled tribes and Muslim, log of per capita income, age and age squared of mother, mother’s height, age and age squared of father, indicators for household main income source being cultivation or salary, indicator for household having below poverty line status and urban dummy. In column (3), sex of first-born child is used as an instrument for family size. Sample is restricted to children aged 6–18 for all outcomes, except for reading and math test, the sample of which is restricted in children aged 8–11 as tests were administered to only 8–11 age group children. ***p<0.01, ** p<0.05, *p<0.1.

Table 3:

Q–Q trade-off, rural sample.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
				δ for β∗=0;	δ for	Oster’s bound,	Max
	No			Rmax=	β∗=0;	δ=1,	Rmaxfor
Dependent variable	controls	Controls	IV	1.3Ř	Rmax=1	Rmax=1.3Ř	β<0
							under
							δ=1
Ever enrolled in school (1/0)	−0.013***	−0.010***	0.023	1.042	0.035	[−0.010; −0.000]	0.121
	(0.002)	(0.002)	(0.019)
R-squared	0.012	0.093	0.068
Currently enrolled (1/0)	−0.031***	−0.027***	0.004	1.330	0.108	[−0.027; −0.017]	0.279
	(0.003)	(0.004)	(0.030)
R-squared	0.023	0.198	0.190
Years of schooling completed	−0.174***	−0.201***	−0.152	2.320	1.918	[−0.251; −0.201]	NA
	(0.022)	(0.025)	(0.196)
R-squared	0.007	0.733	0.733
Attend private school (1/0)	−0.023***	−0.026***	0.088**	2.114	0.214	[−0.031; −0.026]	NA
	(0.004)	(0.004)	(0.044)
R-squared	0.008	0.245	0.172
Private coaching (1/0)	−0.001	0.001	0.020	1.309	−0.132	[0.001; 0.004]	NA
	(0.004)	(0.005)	(0.050)
R-squared	0.000	0.252	0.250
Log of education expenditure	−0.362***	−0.315***	0.297	1.245	0.127	[−0.314; −0.185]	0.318
	(0.024)	(0.029)	(0.276)
R-squared	0.040	0.230	0.190
Log of private coaching	−0.222***	−0.209***	0.308	1.581	0.239	[−0.208; −0.181]	0.480
expenditure	(0.022)	(0.029)	(0.283)
R-squared	0.016	0.324	0.293
Standardized reading score	−0.130***	−0.088***	0.293	0.778	0.980	[−0.088; 0.091]	0.350
	(0.015)	(0.019)	(0.235)
Observations	6,444	6,444	6,444
R-squared	0.041	0.285	0.187
Standardized math score	−0.137***	−0.094***	0.188	0.776	0.100	[−0.094; 0.104]	0.331
	(0.013)	(0.018)	(0.232)
Observations	6,419	6,419	6,419
R-squared	0.049	0.287	0.229
Height-for-age Z-score	−0.023	−0.063***	−0.099	74.690	5.125	[−0.132; −0.063]	NA
	(0.016)	(0.019)	(0.221)
Observations	21,165	21,165	21,165
R-squared	0.000	0.184	0.183

Note: Standard errors in parentheses are calculated taking survey design into account and are clustered at the mother level. The coefficients refer to the coefficients of family size. The number of observations in each regression except for the last three dependent variables is 25,568. Control variables include district fixed effects, age and age squared of child, child’s gender, indicators for birth order of child (second, third, fourth and fifth), indicator if two mothers reside in same household, indicators for other backward castes, scheduled castes, scheduled tribes and Muslim, log of per capita income, age and age squared of mother, mother’s height, age and age squared of father, indicators for household main income source being cultivation or salary and indicator for household having below poverty line status. In column (3), sex of first-born child is used as an instrument for family size. Sample is restricted to children aged 6-18 for all outcomes, except for reading and math test, the sample of which is restricted children aged 8-11 as tests were administered to only for 8-11 age group children. ***p<0.01, **p<0.05, *p<0.1.

Table 4:

Correlation between first-born girl and household characteristics (mother-level).

Dependent variable: First born is girl
Other backward castes	−0.005
	(0.011)
Scheduled castes	−0.017
	(0.011)
Scheduled tribes	−0.004
	(0.019)
Muslim	−0.010
	(0.016)
Log of per capita income	−0.029***
	(0.005)
Joint-two mother observations from same household	−0.014
	(0.022)
Mother’s age	−0.018**
	(0.009)
Mother’s age squared	0.000***
	(0.000)
Mother’s height in cm	0.001
	(0.000)
Father’s age	0.004
	(0.007)
Father’s age squared	−0.000
	(0.000)
Household main income source cultivation (1/0)	0.004
	(0.012)
Household main income source salaried (1/0)	0.001
	(0.012)
Household holds below poverty line card (1/0)	−0.031***
	(0.009)
Household own TV (1/0)	−0.019**
	(0.009)
Household own land (1/0)	0.007
	(0.011)
Urban	0.017
	(0.013)
Constant	0.893***
	(0.157)
Observations	18,935
R-squared	0.025

Note: Each observation represents a mother. Standard errors in parentheses are calculated taking survey design into account and clustered at the district level. The model also includes district-fixed effects. ***p<0.01, **p<0.05, *p<0.1.

Table 5:

Q–Q trade-offs. IV method.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
Dependent variables	Ever	Currently	Years of	Attend	Private	Log of	log of	Standardized	Standardized	Height-
	attended	enrolled	schooling	private	coaching	education	private	reading	math score	for-age
	school	in school	(1/0)	school	(1/0)	expenditure	coaching	score		Z-score
	(1/0)	(1/0)					expenditure
First stage
First-born girl	0.195***	0.195***	0.195***	0.195***	0.195***	0.195***	0.195***	0.166***	0.166***	0.206***
	(0.021)	(0.021)	(0.021)	(0.021)	(0.021)	(0.021)	(0.021)	(0.027)	(0.027)	(0.022)
Weak identification test
Cragg–Donald Wald F statistic	364.57	364.57	364.43	365.00	365.00	365.00	365.00	76.90	75.71	333.13
Kleibergen–Paap Wald rk F statistic	88.08	88.08	88.04	88.17	88.17	88.17	88.17	37.57	36.91	85.17
2 SLS results
Family size	0.026	0.005	-0.001	0.095**	0.013	0.338	0.285	37.570	0.116	−0.013
	(0.015)	(0.024)	(0.161)	(0.038)	(0.042)	(0.232)	(0.246)	(0.172)	(0.173)	(0.188)
Observations	37756	37756	37754	37764	36,960	37764	37764	9401	9364	31128
R-squared	0.053	0.181	0.753	0.231	0.222	0.214	0.277	0.249	0.274	0.173

Note: Standard errors in parentheses are calculated taking survey design into account and are clustered at the mother level. Control variables include district-fixed effects, age and age squared of child, child’s gender, indicators for birth order of child (second, third, fourth and fifth), indicator if two mothers reside in the same household, indicators for other backward castes, scheduled castes, scheduled tribes and Muslim, log of per capita income, age and age squared of mother, mother’s height, age and age squared of father, indicators for household main income source being cultivation or salary, indicator for household having below poverty line status and urban dummy. Sample is restricted to children aged 6-18 for all outcomes, except for reading and math test. Reading and math test score sample consists of children aged 8-11, as tests were administered to only 8-11 age group children. ***p<0.01, **p<0.05, *p<0.1.

Published Online: 2018-1-23

Is There Really a Trade-Off? Family Size and Investment in Child Quality in India

Abstract

References

Appendix

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