Accessible Requires Authentication 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

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.

JEL Classification: O11; J13

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Appendix

A
Table 1:

Summary statistics of sample children aged 6–18.

(1)(2)(3)
MeanSDN
Outcome variables
Ever enrolled in school (1/0)0.970.1837,756
Currently enrolled in school (1/0)0.890.3137,756
Years of schooling5.113.4537,754
Attend private school (1/0)0.290.4537,764
Private coaching (1/0)0.370.4837,764
Log of education expenditure6.302.9937,764
Log of private coaching expenditure1.693.1237,764
Standardized reading score0.071.019,401
Standardized math score0.061.009,364
Height-for-age z score1.591.9531,128
Explanatory variables
Child is girl (1/0)0.480.5037,764
Child-Age11.753.6137,764
Child-Age squared151.1686.3537,764
Child’s birth order-20.310.4637,764
Child’s birth order-30.190.3937,764
Child’s birth order-40.100.3037,764
Child’s birth rder-5 or more0.080.2737,764
Other backward castes0.360.4837,764
Scheduled castes0.230.4237,764
Scheduled tribes0.080.2737,764
Muslim0.150.3537,764
Log of per capita income9.400.9737,301
Joint-two mother observations from same household0.030.1637,764
Mother’s age36.125.7437,764
Mother’s age squared1,337.25419.7237,764
Mother height in cm151.198.2336,966
Father’s age41.126.5237,764
Father’s age squared1,732.99550.9437,764
Household main income source cultivation (1/0)0.250.4337,764
Household main income source salaried (1/0)0.160.3637,764
Household holds below poverty line card (1/0)0.370.4837,764
Household own TV (1/0)0.590.4937,764
Household own land (1/0)0.480.5037,764
Urban0.310.4637,764

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

B
Table 2:

Q–Q Trade-offs.

(1)(2)(3)(4)(5)(6)(7)
δ for β=0;δ forOster’s bound,Max
NoRmax=β=0;δ=1,Rmax for
Dependent variablecontrolsControlsIV1.3ŘRmax=1Rmax=1.3Řβ<0
under
δ=1
Ever enrolled in school (1/0)0.014***0.009***0.026*0.9040.028[0.009, 0.003]0.108
(0.001)(0.002)(0.015)
R-squared0.0150.0850.052
Currently enrolled (1/0)0.036***0.031***0.0051.1460.093[0.031, 0.013]0.259
(0.002)(0.003)(0.024)
R-squared0.0340.1920.180
Years of schooling completed0.187***0.230***0.0002.3702.211[ 0.320, 0.230]NA
(0.018)(0.021)(0.161)
R-squared0.0070.7570.753
Attend private school (1/0)0.047***0.031***0.095**0.9380.124[0.031, 0.005]0.381
(0.003)(0.003)(0.038)
R-squared0.0270.2970.230
Private coaching (1/0)0.006**0.0030.0130.4240.036[0.003, 0.021]NA
(0.003)(0.004)(0.041)
R-squared0.0000.2210.221
Log of education expenditure0.491***0.368***0.3660.9340.113[0.368, 0.086]0.333
(0.020)(0.025)(0.232)
R-squared0.0680.2610.214
Log of private coaching expenditure0.326***0.228***0.2840.9820.132[0.228, 0.010]0.388
(0.018)(0.025)(0.246)
R-squared0.0280.3000.277
Standardized reading score0.149***0.109***0.1650.7860.103[0.109, 0.137]0.353
(0.012)(0.016)(0.171)
Observations9,4019,4019,401
R-squared0.0540.2870.248
Standardized math score0.168***0.105***0.1150.6530.093[0.105, 0.200]0.364
(0.011)(0.015)(0.172)
Observations9,3649,3649,364
R-squared0.0700.3070.274
Height-for-age z score0.040***0.058***0.0113.1640.201[0.096, 0.058]NA
(0.012)(0.016)(1.188)
Observations31,12831,12831,128
R-squared0.0010.1730.172

  1. 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.

C
Table 3:

Q–Q trade-off, rural sample.

(1)(2)(3)(4)(5)(6)(7)
δ for β=0;δ forOster’s bound,Max
NoRmax=β=0;δ=1,Rmaxfor
Dependent variablecontrolsControlsIV1.3ŘRmax=1Rmax=1.3Řβ<0
under
δ=1
Ever enrolled in school (1/0)0.013***0.010***0.0231.0420.035[0.010; 0.000]0.121
(0.002)(0.002)(0.019)
R-squared0.0120.0930.068
Currently enrolled (1/0)0.031***0.027***0.0041.3300.108[0.027; 0.017]0.279
(0.003)(0.004)(0.030)
R-squared0.0230.1980.190
Years of schooling completed0.174***0.201***0.1522.3201.918[0.251; 0.201]NA
(0.022)(0.025)(0.196)
R-squared0.0070.7330.733
Attend private school (1/0)0.023***0.026***0.088**2.1140.214[0.031; 0.026]NA
(0.004)(0.004)(0.044)
R-squared0.0080.2450.172
Private coaching (1/0)0.0010.0010.0201.3090.132[0.001; 0.004]NA
(0.004)(0.005)(0.050)
R-squared0.0000.2520.250
Log of education expenditure0.362***0.315***0.2971.2450.127[0.314; 0.185]0.318
(0.024)(0.029)(0.276)
R-squared0.0400.2300.190
Log of private coaching0.222***0.209***0.3081.5810.239[0.208; 0.181]0.480
expenditure(0.022)(0.029)(0.283)
R-squared0.0160.3240.293
Standardized reading score0.130***0.088***0.2930.7780.980[0.088; 0.091]0.350
(0.015)(0.019)(0.235)
Observations6,4446,4446,444
R-squared0.0410.2850.187
Standardized math score0.137***0.094***0.1880.7760.100[0.094; 0.104]0.331
(0.013)(0.018)(0.232)
Observations6,4196,4196,419
R-squared0.0490.2870.229
Height-for-age Z-score0.0230.063***0.09974.6905.125[0.132; 0.063]NA
(0.016)(0.019)(0.221)
Observations21,16521,16521,165
R-squared0.0000.1840.183

  1. 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.

D
Table 4:

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

Dependent variable: First born is girl
Other backward castes0.005
(0.011)
Scheduled castes0.017
(0.011)
Scheduled tribes0.004
(0.019)
Muslim0.010
(0.016)
Log of per capita income0.029***
(0.005)
Joint-two mother observations from same household0.014
(0.022)
Mother’s age0.018**
(0.009)
Mother’s age squared0.000***
(0.000)
Mother’s height in cm0.001
(0.000)
Father’s age0.004
(0.007)
Father’s age squared0.000
(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)
Urban0.017
(0.013)
Constant0.893***
(0.157)
Observations18,935
R-squared0.025

  1. 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.

E
Table 5:

Q–Q trade-offs. IV method.

(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
Dependent variablesEverCurrentlyYears ofAttendPrivateLog oflog ofStandardizedStandardizedHeight-
attendedenrolledschoolingprivatecoachingeducationprivatereadingmath scorefor-age
schoolin school(1/0)school(1/0)expenditurecoachingscoreZ-score
(1/0)(1/0)expenditure
First stage
First-born girl0.195***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 statistic364.57364.57364.43365.00365.00365.00365.0076.9075.71333.13
Kleibergen–Paap Wald rk F statistic88.0888.0888.0488.1788.1788.1788.1737.5736.9185.17
2 SLS results
Family size0.0260.005-0.0010.095**0.0130.3380.28537.5700.1160.013
(0.015)(0.024)(0.161)(0.038)(0.042)(0.232)(0.246)(0.172)(0.173)(0.188)
Observations3775637756377543776436,96037764377649401936431128
R-squared0.0530.1810.7530.2310.2220.2140.2770.2490.2740.173

  1. 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

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