From Death to Birth Mortality Decline and Reproductive Change (1998) / Chapter Skim
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3 The Impact of Infant and Child Mortality Risk on Fertility
3 The Impact of Infant and Child Mortality Risk on Fertility
Pages 74-111
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From page 74... ...
(2) The "demographic transition," the change from a high fertilityhigh infant and child mortality environment to a low fertility-low mortality environment, which has occurred in all developed countries, has been conjectured to result from the fertility response to the improved survival chances of offspring.
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From page 75... ...
Specifically, I demonstrate how replacement and hoarding "strategies," which are prominent hypotheses about reproductive behavior in this setting, fit explicitly into the dynamic model and how these concepts are related to the question posed above. I review a number of empirical methods for estimating the quantitative effect of infant and child mortality risk on fertility, connecting them explicitly to the theoretical framework.
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From page 76... ...
.5 This result can arise because births per se are costly. At the higher mortality rate, although the number of surviving children is lower for the same number of births, increasing the number of surviving children by having additional births is costly.
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From page 77... ...
Because utility is actually lower when there are two surviving children as opposed to one, if the survival rate were unity (zero mortality risk) only one child would be optimal.
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From page 78... ...
Sequential Decision Making In formulating the theoretical linkages between infant and child mortality and fertility, the early contributors to this area of research clearly had in mind sequential decision-making models under uncertainty. No biological or econom~c constraints would force couples to commit to a particular level of fertility that is invariant to actual mortality experience.
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From page 79... ...
andp2 (the child mortality rate, conditional on first-period survival)
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From page 80... ...
THE IMPACT OF INFANT AND CHILD MORTALITY RISK ONFERTIL[lY No (surYiYir~g) children One sunriv~ng young cold Formally, let nj = 1 indicate a birth at the beginning of period j = 1, 2 of the family's life cycle and zero otherwise.
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From page 81... ...
No saving children ~ U(03 FIGURE 3-2 Decision tree: Periods 2 and 3. consumption, Y- con, utility in period 2 is that period's consumption, Y- cn2, and period 3 utility is consumption in that period plus the utility from the number of surviving children in that period, Y + U(N3)
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From page 82... ...
It is this gain that represents the motivation for "replacement" behavior. To isolate the effect of the infant mortality risk on second-period fertility, suppose that the child mortality probability P2 is zero.
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From page 83... ...
Further increases in the infant mortality rate would eventually lead to optimally having zero births (at some level of P1 (1 pl)
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From page 84... ...
Both replacement and hoarding behavior depend on the curvature of the utility function. The analysis of the second-period decision, taking the first-period birth decision as given, does not provide a complete picture of the effect of infant and child mortality risk on the family's fertility profile.
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From page 85... ...
If we assume that infant mortality risk (when child mortality risk is zero) is such that case (2)
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From page 87... ...
, while in the last segment the family has no births (between P2 = 0.552 and 1.0~. As seen in the table, expected births first increase and then decrease as the child mortality rate increases.
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From page 88... ...
In this regard, it is useful to divide the discussion of estimation issues into two cases corresponding to whether the population is homogeneous or heterogeneous with respect to mortality risk. Population-Invariant Mortality Risk Consider a sample of families for whom we observe fertility and infant and child mortality histories.
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From page 89... ...
, (7) where E1 is the expectations operator given the information set at period 1 and is taken over the distribution of infant and child mortality and birth costs, and the value functions in the integral of equation <7' are given by equation (4~.
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From page 90... ...
. Otherwise, in the dynamic model, one would have to allow for a distribution over future infant and child mortality risk (conditional on current information)
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From page 91... ...
7Thus, replacement rates are not restricted to infant deaths. 18It is also possible for the replacement rate to be larger than one if children die at older ages.
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From page 92... ...
Analogous replacement rates would measure the excess births that would arise from the death of a child of any age given any birth and death history. The value in estimating replacement effects for policy analysis rests on an assumption about the extent to which effective programs alter families' perceptions about mortality risk.
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From page 93... ...
In general, the number of deaths must rise with the number of births for a constant mortality rate, and the resulting positive correlation between births and deaths is built into the estimated replacement effect. 22Notice that in the three-period model, knowledge of al, the proportion of families not having a child in period 1, and of g2, the proportion of families who have both a birth in the first period and for whom the infant dies, is sufficient to solve equation (11)
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From page 94... ...
(14) The ordinary least-squares regression estimator overstates the true replacement rate because deaths and births are positively correlated independently of the existence of replacement; families with more births experience more deaths simply because their "sample" size is larger.
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From page 95... ...
Such "average" replacement rates could be quite different for samples that differ, for example, only in the age distribution of the families (women) , but with the same underlying infant mortality risk, preferences, and birth costs.
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From page 96... ...
or (9~) could be obtained for each geographic area, recalling that replacement rates depend on the level of infant mortality risk.
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From page 97... ...
Thus, the estimates of mortality risk would be influenced not only by observed mortality rates, but also by the fertility response to mortality risk. Approximate decision rules (equation (17~)
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From page 98... ...
It is important to stress that the problem with this procedure exists even if there is no child mortality risk; it has nothing to do with hoarding behavior. However, if there was significant child mortality and the risk varied in the population, child mortality rates would also not be a valid instrument for estimating replacement effects because they affect fertility independently (through the direct effect and the hoarding effect)
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From page 99... ...
Learning Families may not know their own infant and child mortality risk. Deaths may provide useful information about that risk.
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From page 100... ...
or (9~. The other prominent measure of replacement behavior, based on birth and death histories, found in the literature is the differenced mean closed interval (DMCI)
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From page 101... ...
But PPRs do not uniformly rise with additional deaths; indeed, the likelihood of a women moving from a third to a fourth birth declines with the number of infant deaths. One possible explanation of this phenomenon would be that women with more deaths learn that they have a higher infant mortality rate, which reduces subsequent fertility (the direct effect)
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From page 102... ...
. Table 3-3, for all levels of completed family size and regardless of the birth order of the infant death, retrospectively obtained mean closed intervals are about one year less when an infant death is experienced.
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From page 103... ...
The corrected estimate that assumes a homogeneous mortality rate in the population is negative, implying that there are actually fewer births when there is an infant or child death. This result is consistent with the negative "direct" effect of higher infant mortality.
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From page 104... ...
104 o a' Cam o .
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From page 105... ...
Controlling for innate infant frailty, however, would provide an estimate of the replacement rate that is uncontaminated by unobserved mortality risk. Olsen estimates a replacement rate of 0.17 using this method.
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From page 106... ...
in the estimation of replacement effects. Mroz and Weir report that simulations conducted prior to estimation, omitting controls for unobserved heterogeneity in the fecund hazard rate and recognizing that they accounted for the cessation of lactation due to an infant death, resulted in the probability of a birth increasing in the number of surviving children (conditional on parity, age, duration, and age at marriage)
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From page 107... ...
Given this framework, the household chooses in each period whether or not to have a child.27 For the purpose of estimation, Wolpin assumes that the time-varying preference parameter is drawn independently over both time and across households from a normal distribution. The mortality rate faced by the household is assumed known to the researcher, measured by the state-level mortality rate in each period, and the researcher is assumed to forecast future mortality rates exactly as the household is assumed to do, namely based on the extrapolated trend in the mortality rate at the state level.
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From page 108... ...
Given the finding there that the marginal utility of surviving children is essentially constant, which led to the negligible estimated replacement rates, the potential hoarding response, if child mortality were significant in that environment, would also be negligible since hoarding also depends on concavity as shown in equation (3)
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From page 109... ...
Given that in their sample the infant mortality rate is less than 3 percent, this experiment may be within sample variation. At the sample average of 2.5 births per woman, an additional 0.25 deaths per woman leads to 0.17 more births and therefore to 0.08 fewer surviving children.
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From page 110... ...
1976 Fertility response to child mortality: Micro data from Israel. Journal of Political Economy 84(2)
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From page 111... ...
1984 An estimable dynamic stochastic model of fertility and child mortality. Journal of Political Economy 92(5)
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