Understanding the nature of the potential sample selection

NFHS collects information on the diseases experienced by a child before the survey interview. These data can be used to support the findings discussed above. Table 4 shows the estimates of the probability of a child younger than 12 months to have a diarrhea during two weeks prior the interview. The estimation controls for a wide range of characteristics of a child, its mother and the household it lives in and demonstrates that young children living in rural areas of India are more likely to experience diarrhea during the summer months or months around the start of the monsoon. We find no such effect for children living in urban areas of India whose families have better access to clean water and sanitation. These results provide some evidence to the hypothesis about the importance of the effect of postnatal disease environment and nutrition on children health outcomes later in life. We also use rainfall data to determine the effect of the postnatal environment on health. Table 4 shows the results of height-for-age regressions of Equation 2 where, in addition to the variables used in the estimations presented in Table 2, we added levels of rainfall during the month of a child’s birth at a district level. The coeffi- cients on the rainfall variables are significant only for girls residing in urban areas of India, which is different from finding by Manccini and Yong 2009. The inclusion of the rainfall attenuates the coefficients of the month of birth dummies for children in urban areas, especially for girls. Rainfall has little effect on the month-of-birth coefficients for rural areas. 12

A. Understanding the nature of the potential sample selection

Several types of sample selections on different stages of child’s life could potentially affect our results. The seasonal fertility patterns can be different for rich better- educated and poor less-educated families; selective survival can affect the com- position of children born in a particular month; and child outcomes may vary with the month of birth because of the differences in the parental effort. In this section we try to address these problems in turn. If, during certain seasons, more children are born in better-educated andor wealth- ier families, the correlation between children’s health outcomes and their months- of-birth can be attributed to the difference in resources available to the children for example, Bronson 1995. Buckles and Hungerman 2008 explain the effect of sea- son of birth on later health and professional outcomes by changes in the character- istics of women giving birth throughout the year in the United States. Dehejia and Lleras-Muney 2004 show that the changes in parental behavior and the differential fertility may result in difference in the health of children over the business cycle and also seasonally. In developing countries, women’s involvement in agricultural activities, food availability, the seasonality of marriages, and male migration are more important determinants of the seasonality of birth. Panter-Brick 1996 dem- 12. The district indicators are available only in the 1992 and 1998 rounds of NFHS. For that reason figures shown in Table 4 are based only on these two rounds of the data. In addition to the specification with the levels of rain falls at the month of birth, we also tried specifications with pre- and postnatal levels of rainfall. The prenatal rainfall has no significant effect on children health outcomes while the postnatal levels one and two months after birth of rainfall result in attenuation of the coefficients similar to the results shown in Table 4. These results are available from authors on request. Lokshin and Radyakin 191 Table 4 Left panel: Probability of a child younger than 12 months to have a diarrhea during two weeks prior to survey interview. Right panel: Does Child’s Height-for-Age Z-score Depends on the Level of Rainfall During the Month of Child’s Birth? Coefficients on the dummies for the interview months relative to the start of the monsoon. Pooled sample of 1992 and 1998 rounds of NFHS. Probability to have a Diarrhea HAZ with Rainfall Urban Rural Urban Rural Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Rainfall, mm1000 0.623 0.430 0.005 0.299 Rainfall, mm1000 2 ⳮ0.120 0.608 0.047 0.472 ⳮ5 0.005 0.102 ⳮ0.052 0.057 ⳮ0.045 0.107 ⳮ0.307 0.065 ⳮ4 0.175 0.106 ⳮ0.044 0.061 ⳮ0.007 0.111 ⳮ0.261 0.066 ⳮ3 ⳮ0.037 0.109 ⳮ0.029 0.057 ⳮ0.314 0.110 ⳮ0.204 0.065 ⳮ2 0.145 0.106 0.059 0.057 ⳮ0.136 0.108 ⳮ0.247 0.067 ⳮ1 0.144 0.102 0.097 0.055 ⳮ0.236 0.106 ⳮ0.167 0.065 Monsoon 0.232 0.102 0.168 0.054 ⳮ0.295 0.111 ⳮ0.248 0.068 Ⳮ1 0.110 0.099 0.126 0.053 ⳮ0.223 0.119 ⳮ0.156 0.075 Ⳮ2 0.103 0.103 0.128 0.053 ⳮ0.267 0.114 ⳮ0.057 0.072 Ⳮ3 0.006 0.104 0.057 0.054 ⳮ0.199 0.107 0.053 0.065 Ⳮ4 0.139 0.098 0.013 0.053 0.068 0.103 ⳮ0.079 0.061 Ⳮ5 0.030 0.103 ⳮ0.026 0.054 0.169 0.102 0.027 0.062 Ⳮ6 Reference month Number of observations 6,295 17,728 4,933 15,272 Note: is significant at 10 percent level; is significant at 5 percent level; is significant at 1 percent level. Standard errors are adjusted for clustering on a village level. onstrates that, in Nepal, seasonal rates of pregnancies are determined, among other things, by seasonality of marriage which, in turn, is determined by agricultural cycles, and marital disruptions related to out-migration of males and agricultural activities; the peaks of conception are observed in the beginning of the monsoon season of June-July and rice harvesting in December. Rajagopalan, Kymal, and Pei 1981 documented the strong effect of agricultural cycles on births in Tamil Nadu in India, emphasizing large differences in the seasonality of birth between urban and rural areas. Agricultural cycles are shown to influence timing of birth and infant mortality in Sub-Saharan Africa; in rural families fewer children are born during the months of high demand for female labor even though children born in these months have higher chances of survival Atradi 2005. To evaluate the differences in the fertility patterns across socioeconomic groups, we estimate the relationships between the month of birth, household wealth, and maternal education, controlling for the characteristics of a household and a mother. This relationship can be expressed as: ¯ ProbM ⳱1⳱f ␤ I Ⳮ␥ E Ⳮ␲ X Ⳮε , k⳱1, . . . ,12, 5 ik k i k i k i ik where ProbM ik ⳱1 is the probability of child i to be born in month k. Given an unordered structure of the month-of-birth variable and assuming that ’s are in- ε ik dependent and identically Gumbel distributed, we applied the multinomial logit spec- ification for this estimation. 13 A significance of the coefficients and would ␤ ␥ k k indicate that household wealth and education of the mother affect the probability of a child to be born in a certain month of the year. Table 5 shows the multinomial logit estimates of the coefficients on the wealth index and maternal education for 11 month-of-birth relative to the start of the mon- soon categories for boys and girls using the pooled sample of three waves of NFHS. For children residing in urban areas wealth and maternal education have no signifi- cant impact on the seasonality of their births. The effects of wealth and mothers’ education on the month of birth are significant for rural children born during summer months. But the pattern of this significance differs from the patterns we would expect to observe based on Figure 4. For example, better-off rural households are more likely to have their children born in the summer months. But months close to the beginning of monsoon are the “bad” months to be born in, in terms of health out- comes. We find no effect of wealth and maternal education on timing of birth of urban children. The results of likelihood ratio tests of the significance of household wealth index and maternal education in determining a child’s month of birth are shown in the bottom part of Table 5. These tests confirm that both wealth index and maternal education contribute little to determining the month of year in which a child will be born and thus our empirical results should not be affected by this type of selection bias. 13. The Independence of Irrelevant Alternatives assumption of the Multinomial Logit is clearly violated in the case of modeling the month of birth. A multinomial probit model MNP would be more appropriate for estimating Equation 5. However, estimation of MNP with 12 categories appears to be computationally infeasible. Lokshin and Radyakin 193 Table 5 Does the Month of Birth depend on Household Wealth, Education of the Mother, or whether the Child Was Wanted. Multinomial Logit and SML Coefficients on household wealth, maternal education, and child’s “desirability” dummy. Household wealth indexMLogit Education of the motherMLogit “Desirability” of a childMLogit and SFIML Urban Rural Urban Rural Urban Rural Urban Rural Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error Coefficient Standard Error ⳮ5 ⳮ0.003 0.058 ⳮ0.004 0.046 ⳮ0.008 0.009 ⳮ0.005 0.007 ⳮ0.021 0.085 0.025 0.059 Winter ⽤ ⳮ4 0.000 0.061 ⳮ0.030 0.047 ⳮ0.002 0.009 ⳮ0.011 0.007 0.064 0.089 0.122 0.061 ⳮ0.126 0.728 ⳮ0.095 1.046 ⳮ3 ⳮ0.025 0.059 ⳮ0.003 0.046 ⳮ0.006 0.009 ⳮ0.002 0.007 0.145 0.089 0.024 0.059 ⳮ2 0.038 0.060 ⳮ0.006 0.047 ⳮ0.011 0.009 ⳮ0.010 0.007 ⳮ0.008 0.087 0.034 0.060 ⳮ1 0.033 0.058 0.041 0.046 ⳮ0.018 0.009 ⳮ0.009 0.007 0.111 0.087 0.015 0.059 Spring Monsoon ⳮ0.007 0.058 0.062 0.045 0.001 0.008 ⳮ0.003 0.007 0.114 0.085 0.103 0.059 0.254 0.540 ⳮ2.078 1.091 Ⳮ1 0.004 0.056 0.079 0.044 ⳮ0.014 0.008 ⳮ0.010 0.006 0.016 0.081 0.054 0.057 Ⳮ2 0.007 0.056 ⳮ0.016 0.044 ⳮ0.007 0.008 ⳮ0.003 0.006 0.107 0.082 0.056 0.057 Summer Ⳮ3 0.073 0.056 0.016 0.044 ⳮ0.008 0.008 0.002 0.006 0.046 0.081 0.012 0.056 0.442 0.622 ⳮ2.075 0.950 Ⳮ4 0.055 0.056 0.054 0.043 ⳮ0.014 0.008 ⳮ0.001 0.006 0.096 0.081 0.001 0.055 Ⳮ5 ⳮ0.017 0.056 ⳮ0.036 0.045 ⳮ0.007 0.008 ⳮ0.005 0.006 0.175 0.083 0.031 0.057 Fall Ⳮ6 Reference MonthSeason LR test 6.004 15.660 9.851 8.840 11.892 13.033 9.522 10.113 Note: is significant at 10 percent level; is significant at 5 percent level; is significant at 1 percent level. Standard errors are adjusted for clustering on a village level. ⽤ Winter indicates that a child is born six to four months prior to the start of the monsoon; Spring indicates three to zero months prior to the monsoon; Summer— zero to three months after the start of the monsoon; Fall—four to six months after the start of the monsoon.

B. The “unplanned pregnancy” selection