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The effect of fertility decisions on excess female mortality in India


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.

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  2. See Keyfitz (1968) pp. 379–384 for a brief exposition on the mathematics of stopping rules.

  3. This assumption does not have an effect on the comparative statics of the model.

  4. See Eswaran (2002) for a model of fertility and mortality that includes intra-household bargaining.

  5. I follow along the lines of Rosenzweig and Schultz (1982). I avoid the complexity of probability distributions that are in Cigno (1998) and discrete children with binomial survival distributions as in Sah (1991). Note that the analytic results could change if expected utility and probability distributions of child survival are used, depending upon the choice of utility function, distribution, and risk aversion parameters.

  6. By “intrinsic” preferences for child survival, I mean anything outside of parents’ costs and benefits included in the D variable, which could include any economic costs and benefits of children. If parents do care intrinsically more about boys than girls (for cultural or social reasons), this strengthens the predictions of the model. The reason for the model’s simplification is that economic incentives are sufficient to explain discrimination even if there are non-economic incentives for discrimination as well. One could go further and argue that the unfair economic incentives only exist because of social incentives, and the author concedes that this may be the case. Yet, a number of parents who find these social incentives unjust and do in fact care equally about their sons and daughters in a non-economic sense, may discriminate because of the economic incentives propagated by the social preferences of others.

  7. As shown in Appendix B, if there are perfect credit markets, I predict the opposite of Proposition 1. However, given empirical evidence in India, it is likely that many households are, in fact, credit-constrained.

  8. In the case of a discrete, rather than continuous, change in N, the expected future cost of an additional daughter depends on two competing factors. The first is the sex composition effect, which increases the mortality rate of all daughters if an extra daughter is added to the household. This effect is stronger in HH2 compared to HH1, and, thus, HH2 has a lower expected future cost (in terms of income) from an extra daughter. However, parents with a high proportion of daughters (HH2) are relatively poor compared to parents with the same number of children, but a lower proportion of daughters (HH1). Thus, if parents are sufficiently risk-averse, then the expected future income loss for HH2, although smaller than the expected future income loss for HH1, creates a larger loss in expected future utility for HH2 compared to HH1. That parents in India, in fact, follow fertility-stopping rules indicates that parents in general are not so risk-averse that they are unwilling to risk having an additional daughter.

  9. Twins as a first pregnancy is another exogenous outcome that affects the number of children born and the sex composition of these children. Yet, it cannot reliably be used as an extra instrument because twins are different from non-twins, in particular having lower birth weight on average. This means that, for example, a pair of boy twins are biologically weaker than two sons born separately (Rosenzweig and Zhang 2009). To simplify the empirical analysis, I exclude all households with first-born twins which make up approximately 0.5 % of all observations.

  10. Dahl and Moretti (2008) use a similar estimation technique in the USA and find that first-born girls are disadvantaged compared to first-born boys. For example, first-born girls’ parents are more likely to be divorced. Interestingly, a first-born girl in the USA predicts higher fertility, although by only one-fiftieth as much as in India.

  11. Illiterate individuals are coded as having no years of education, which is not necessarily true. The estimates are robust to simply including dummy variables for literate/illiterate instead of years of education.

  12. See, for example, Simmons et al. (1978, 1982), and Smucker et al. (1980).

  13. Only 12 % of women in the RCH II have a child at age 35 or older, and more than 70 % of women aged 35 years and older have been sterilized.

  14. See Chahnazarian (1988) for a review of literature on the biologically normal sex ratio at birth and Parazzini et al. (1998) on global trends in the sex ratio at birth.

  15. Using back-of-the-envelope calculations, I find that 1.7 percentage points of first-born daughter households are missing from the survey due to recall and survival bias.

  16. A similar pattern of rising sex ratios for births more distantly in the past has been reported in Bangladesh (Majumder et al. 1997).

  17. The NFHS surveys were implemented by IIPS with the support of the Indian Government’s Ministry of Health and Family Welfare. The 1992/1993 round consists of 89,777 ever-married women, the 1998/1999 round consists of 89,199 ever-married women, and the 2005/2006 round consists of 124,385 women (married or not). All of the rounds restrict the age of respondents to 15–49. The relatively fewer number of births in the NFHS compared the RCH II cause wider fluctuations and larger confidence intervals.

  18. We may expect a similar bias if infanticide was responsible for the above-normal sex ratios of first-births in older women since we would expect only the families with the worst socioeconomic situation to resort to such measures. Note that a first-born boy predicts approximately an extra 3 weeks between the first and second birth. There is evidence that shorter birth intervals cause low birth weight and, hence, higher mortality rates (Gribble 1993). This would bias the results in the opposite direction and result in higher mortality rates amongst first-born girl households.

  19. This is the mortality rate of individual children as opposed to the mean of average child mortality within households reported in Table 2.

  20. The author does not, therefore, advocate that parents should selectively abort female first pregnancies. Rather, the graph points out that girls of birth order two and higher have lower mortality rates (and boys have higher mortality rates) if they have a first-born brother compared to a first-born sister. A sensible policy would be to implement programs that raise the relative value of daughters. Such a policy would both directly incentivize parents to invest more in the health of their daughters and indirectly allow an increase in girls’ resources by lowering desired fertility.

  21. About 20 children were included even though they were born before the cutoff dates.

  22. Similar discrimination against girls in vaccinations is reported in Borooah (2004).

  23. SKDRDP in Dharmasthala, India, for example, has held several free mass weddings which they have made attractive by using the strong religious influence of the Dharmasthala temple.


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I thank Christopher Udry, Dean Karlan, Mark Rosenzweig, and Paul Schultz for guidance. I thank Alessandro Cigno, Greg Fischer, Prabhat Jha, Stephan Klasen, and two anonymous referees for their valuable comments and suggestions. This paper also benefited from seminar participants at Yale University, Williams College, and the Centre for Global Health Research and participants at the 2009 Courant Research Centre Inaugural Conference, the 2009 Northeastern Universities Development Conference, the 2010 Canadian Health Economics Study Group Annual Meeting, and the 2010 Canadian Economics Association Annual Meeting.

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Correspondence to Daniel Rosenblum.

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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.

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.


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

Both of the determinants are positive if D is large enough and U S  > DU2, 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.

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.

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, U1 goes up and U2 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 U2 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

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Rosenblum, D. The effect of fertility decisions on excess female mortality in India. J Popul Econ 26, 147–180 (2013).

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  • Child mortality
  • Fertility
  • India
  • Sex composition

JEL Classification

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  • O12