The effect of fertility decisions on excess female mortality in India

Abstract

In India, many parents follow son-preferring fertility-stopping rules. Stopping rules affect both the number of children and the sex composition of these children. Parents whose first child is male will stop having children sooner than parents whose first child is female. On average, parents of a first-born son will have fewer children and will have a higher proportion of sons compared to parents of a first-born daughter. An economic model in which sons bring economic benefits and daughters bring economic costs, shows the importance of sex composition on child outcomes: holding the number of siblings constant, boys are better off with sisters and girls are better off with brothers. Empirical evidence using the sex outcome of first births as a natural experiment shows that stopping rules can exacerbate discrimination, causing as much as a quarter of excess female child mortality. Another implication of the research is that the use of sex-selective abortion may lower female mortality, but raise male mortality.

Appendices

Appendix A: Proofs of Propositions 1, 2, and 3

Assuming parents have stopped their fertility at N children and taking Eq. 1 above and substituting in the budget constraints yields the following maximization problem.

$$ \begin{array}{rll} \displaystyle\max\limits_{k_B, k_G} U_T &=& U_1(Y_1 - \pi N k_B - (1-\pi) N k_G -NF) + U_2(Y_2 + \pi N D p(k_B) \\&&- (1-\pi) N D p(k_G)) + U_S(p(k_B)\pi N + p(k_G)(1-\pi N)) \end{array} $$

where k _B and k _G are health investments in boys and girls. 0 ≤ π ≤ 1 is the proportion of boys. There are N total children. D is the size of the cost or benefit of daughters and sons, respectively. Y ₁ and Y ₂ are parents’ income in periods 1 and 2. 0 ≤ p(k _i ) ≤ 1 is the number of surviving children of sex i, given health investment k _i . U _S is a concave function of number of surviving children. U _i and p are positive and strictly concave functions.

1.1 A.1 Proof of Proposition 1

Below are first-order conditions of the above utility function.

• First-order condition 1:

  $$ \frac{\frac{\partial U_T}{\partial k_B}}{\pi N} = -U'_1 + Dp'(k_B)U'_2 + U_S'p'(k_B) = 0 $$

• First-order condition 2:

  $$ \frac{\frac{\partial U_T}{\partial k_G}}{(1-\pi) N} = -U'_1 - Dp'(k_G)U'_2 + U_S'p'(k_G) = 0 $$

Below are the partial derivatives:

$$ \frac{\frac{\partial^2 U_T}{\partial k_B^2}}{(\pi N)^2} = U''_1 + D^2 p'(k_B)^2 U''_2 + \pi N D p''(k_B)U'_2 + U_S'p''(k_B)+U_S''p'(k_B)^2 < 0 $$

$$ \frac{\frac{\partial^2 U_T}{\partial k_G \partial k_B}}{\pi(1-\pi)N^2} = U''_1 - D^2 p'(k_G) p'(k_B) U''_2 + U_S''p'(k_B)p'(k_G) $$

is positive if D is large enough.

$$ \begin{array}{rll} \frac{\frac{\partial^2 U_T}{\partial k_G^2}}{(1-\pi)^2 N^2} &=& U''_1 + D^2 p'(k_G)^2 U''_2 - (1-\pi) N D p''(k_G)U'_2 \\&&+ U_S'p''(k_G)+U_S''p'(k_G)^2, \end{array} $$

which can be positive or negative depending on whether:

$$ D^2 p'(k_G)^2 U''_2 - (1-\pi) N D p''(k_G)U'_2 $$

is positive or negative. It is negative if D is large enough.

$$ \begin{array}{rll} \frac{\frac{\partial^2 U_T}{\partial k_B \partial \pi}}{N} &=& (k_B - k_G) U''_1 + D^2 p'(k_B) (p(k_B) +p(k_G)) U''_2 \\ &&+ U''_S p'(k_B)p'(k_G)(p(k_B)+p(k_G))< 0, \end{array} $$

since k _B  − k _G  > 0

$$ \begin{array}{rll} \frac{\frac{\partial^2 U_T}{\partial k_G \partial \pi}}{N} &=& N(k_B - k_G) U''_1 - N D^2 p'(k_G) (p(k_B) +p(k_G)) U''_2 \\ &&+ U''_S p'(k_G)p'(k_G)(p(k_B)+p(k_G))> 0 \end{array} $$

if D is large enough.

Then

$$ \begin{array}{rll} \frac{\partial k_B}{\partial \pi} = - \frac{Det \left |\begin{array}{cc} \dfrac{\partial^2 U_T}{\partial k_B \partial \pi} & \dfrac{\partial^2 U_T}{\partial k_B \partial k_G} \\ \dfrac{\partial^2 U_T}{\partial k_G \partial \pi} & \dfrac{\partial^2 U_T}{\partial k_G^2} \end{array} \right | }{Det \left |\begin{array}{cc} \dfrac{\partial^2 U_T}{\partial k_B^2} & \dfrac{\partial^2 U_T}{\partial k_B \partial k_G} \\ \dfrac{\partial^2 U_T}{\partial k_G \partial k_B} & \dfrac{\partial^2 U_T}{\partial k_G^2} \end{array} \right | } = - \frac{Det\left |\begin{array}{cc} - & + \\ + & - \end{array} \right | }{Det\left |\begin{array}{cc} - & + \\ + & - \end{array} \right | } \end{array} $$

Both of the determinants are positive if D is large enough and U′ _S  > DU′₂, that is, if the marginal utility of survival is larger than the marginal consumption utility in period 2, making $\frac{\partial k_B}{\partial \pi} < 0$. (That is $\frac{\partial^2 U_T}{\partial k_B \partial \pi} \frac{\partial^2 U_T}{\partial k_G^2} > \frac{\partial^2 U_T}{\partial k_B \partial k_G} \frac{\partial^2 U_T}{\partial k_G \partial \pi}$ and $\frac{\partial^2 U_T}{\partial k_B^2}\frac{\partial^2 U_T}{\partial k_G^2} > \frac{\partial^2 U_T}{\partial k_B \partial k_G} \frac{\partial^2 U_T}{\partial k_G \partial k_B}$). By First-order condition 2, this must be true: $\frac{U'_1}{p'(k_G)} = U'_S - DU'_2$, which is positive because $\frac{U'_1}{p'(k_G)}$ is positive. And, thus, we have proved Proposition 1.

1.2 A.2 Proof of Proposition 2

$$ \begin{array}{rll} \frac{\partial k_G}{\partial \pi} = - \frac{Det\left |\begin{array}{cc} \dfrac{\partial^2 U_T}{\partial k_B^2} & \dfrac{\partial^2 U_T}{\partial k_B \partial \pi}\\[3pt] \dfrac{\partial^2 U_T}{\partial k_G \partial k_B} & \dfrac{\partial^2 U_T}{\partial k_G \partial \pi} \end{array} \right | }{Det\left |\begin{array}{cc} \dfrac{\partial^2 U_T}{\partial k_B^2} & \dfrac{\partial^2 U_T}{\partial k_B \partial k_G} \\[3pt] \dfrac{\partial^2 U_T}{\partial k_G \partial k_B} & \dfrac{\partial^2 U_T}{\partial k_G^2} \end{array} \right | } = - \frac{Det\left |\begin{array}{cc} - & - \\ + & + \end{array} \right | }{Det\left |\begin{array}{cc} - & + \\ + & - \end{array} \right | } \end{array} $$

The determinant in the denominator will be positive as above. If D is large enough the determinant in the numerator is negative and $\frac{\partial k_G}{\partial \pi} > 0$. This proves Proposition 2.

1.3 A.3 Proof of Proposition 3

To understand what happens to incentives to continue having children, I change the model’s notation by letting πN = B and (1 − π) N = G.

$$ \begin{array}{rll} U_T(k_B, k_G) &=& U_1(Y_1 - B k_B - G k_G -(B+G)F) \\&&+ U_2(Y_2 + B D p(k_B) - G D p(k_G)) + U_S(p(k_B)B + p(k_G)G) \end{array} $$

So now there are explicitly B boys and G girls. Next we examine happens to parents’ expected utility from having marginally more children (assumed with 50 % probability to be a boy and 50 % probability of being a girl). That is, how does $0.5\frac{\partial U_T}{\partial B} + 0.5\frac{\partial U_T}{\partial G}$ change with an increase in π, holding N constant.

$$ \begin{array}{rll} \frac{\partial U_T}{\partial B} + \frac{\partial U_T}{\partial G} &=& (-k_B-k_G -F) U'_1+D(p(k_B)- p(k_G))U'2 \\&&+ U'_S(p(k_B)+p(k_G)) \end{array} $$

If we raise the proportion of boys, as B goes up and G goes down, k _B goes down and k _G goes up (from above). Although it is ambiguous what happens to period 1 and survival marginal utility (depending on how much k _B decreases and how much k _G increases), period 2 marginal utility of consumption must fall. As long as D is large enough, this effect will dominate, causing parents to gain less utility from an extra child. Thus, we have proved Proposition 3.

Appendix B: Savings and credit

To illustrate as simply as possible how allowing parents to borrow against future dowry payments may reverse Proposition 1, I simplify the model by focusing solely on boys, so that the maximization problem becomes:

$$ \begin{array}{rll} \displaystyle\max\limits_{k_B, S} U_T(k_B, S) &=& U_1(Y_1 - B k_B - S) + U_2(Y_2 + B D p(k_B) + RS) \\&&+ U_S(Bp(k_B)) \end{array} $$

where R is the rate of interest + 1. Let πN = B and (1 − π) N = G.

The first-order conditions are:

$$ \begin{array}{rll} \begin{array}{l} \dfrac{\partial U_T}{\partial k_B} = -BU'_1 + DBp'(k_B)U'_2 + U'_SBp'(k_B) = 0\\[6pt] \dfrac{\partial U_T}{\partial S} = -U'_1 + RU'_2 = 0 \end{array} \end{array} $$

Parents will always set S to satisfy

$$ R = \frac{U'_1}{U'_2} = D p'(k_B) + \frac{U'_Sp'(k_B)}{U'_2}. $$

Parents invest in their sons until the return from investing in sons is equal to the return from saving. If U _S (Bp(k _B )) = 0, i.e., parents only care about the economic benefits of sons, then for however many sons they have, they will invest in their sons up until D p′(k _B ) = R. Thus, regardless of the number of sons, parents will not change their investment and child mortality will not change. If U′ _S  > 0, this is no longer an equilibrium. To see why, note that if B increases, ceteris paribus, U′₁ goes up and U′₂ goes down. If S is set such that again $R = \frac{U'_1}{U'_2}$, via borrowing against future child benefits, then $D p'(k_B) + \frac{U'_Sp'(k_B)}{U'_2} > R$, since U′₂ is smaller than before. Thus, in equilibrium, k _B must rise somewhat, giving the exact opposite result as in Proposition 1. Of course, if R is sufficiently large, parents will never borrow against future child benefits, and Proposition 1 will again hold. Since Proposition 2 stems from the overall wealth increase of extra sons, and not from the inter-period resource re-allocation as for sons, the introduction of savings and credit should not change Proposition 2.

Appendix C: Heterogeneity in sex ratios at birth across states

India has large differences in sex ratios across states. For example, Punjab State has the worst child (age 0–6) sex ratio in India and the 1991 Indian census estimated this ratio at 1.14, rising to 1.26 in 2001. Thus, it is important to calculate the sex ratio at birth by state to make sure that some states with low sex ratios (e.g., Kerala) are not masking the sex ratios of states like Punjab. Table 7 presents sex ratios for the larger states of India for births within 10 years of being surveyed for the RCH II. The small states are not shown because their low sample size and correspondingly large confidence intervals make them uninformative. About half of the states have a sex ratio of first-borns above 1.07 (although 1.07 is within most of the states’ confidence intervals). In order to ensure that the estimates in the paper are robust to the possibility that sex-selective abortion is occurring amongst first-borns in the states with first-born sex ratios above 1.07, the regressions in Eq. 2 are estimated with just the states with sex ratios below 1.07 in Table 7, and the results are similar to those reported in Table 3. The results are shown in Table 8.

Table 7 M/F ratio by large Indian state, age 0–10 at time of survey

Table 8 OLS: effect of a first-born boy on child mortality in states with a male/female sex ratio of first-borns < 1.07

Appendix D: Estimation that includes deaths in the first month of life

The results in Table 3 are robust to the inclusion of the deaths of children between 0 and 1 month. These deaths are included in Table 9 below. The results are similar to those above: a first-born boy predicts about a 0.4 percentage point increase in the probability of a higher order boy dying and about a 0.3 percentage point decrease in the probability of a higher order girl dying. A logit analysis analogous to the one performed as a robustness check for the OLS analysis yields similar estimates when deaths in the first month of life are included (estimations not shown).

Table 9 OLS: effect of a first-born boy on child mortality, including first month of life