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From Death to Birth: Mortality Decline and Reproductive Change (1998)

Chapter: 10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India

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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Page 343
Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Page 344
Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Page 345
Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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Suggested Citation:"10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India." National Research Council. 1998. From Death to Birth: Mortality Decline and Reproductive Change. Washington, DC: The National Academies Press. doi: 10.17226/5842.
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10 Micro and Macro Effects of Child Mortality on Fertility: The Case of India P.N. Mari Bhat The assumption that a secular fall in mortality would eventually lead to a fertility reduction is central to the propositions of demographic transition theory. But when mortality began to decline dramatically in most of the developing world in the 1950s and the 1960s, the lack of a quick fertility response puzzled many pundits and policy makers. Financial and technical assistance flowed in unprecedented quantities to help deal with the rapid growth of population in the world's poorest regions. Now that many countries have experienced declines in fertility, it is possible to investigate the degree to which improvements in survival chances, especially those of children, are responsible for the current declines in fertility. In this chapter I attempt such an exercise for India, the second-most populous country in the world, which contributes one-fifth of the global popula- tion increase. Perhaps because of the increasing availability of survey data on individual couples, much of the recent analyses of the relationship between infant mortality and fertility has focused on the estimation of the replacement rate and on refining techniques to measure it. As the estimated replacement rates are generally sig- nificantly below unity, an increasing body of literature has concluded that de- clines in child mortality tend to accelerate population growth both in the short- and the long-run. But why would a large majority of couples choose a strategy that generally tends to undercompensate child loss in societies where children are valued for their economic contribution and for their support at old age? Because it is unlikely that the majority of couples would use a strategy that usually fails, the mean replacement rate of significantly below unity probably suggests infre- quent use of the strategy rather than its inefficiency. An alternative to replacement is hoarding, which is a response to perceived 339

340 MICRO AND MACRO EFFECTS: THE CASE OF INDIA mortality risk not necessarily learned from one's own experience. Consequently, true understanding of the influence of child mortality on fertility is impossible without a thorough analysis at both the micro and the macro levels (Preston, 1978~. In India I find that the macro relationship between child mortality and fertility is changing from a weak association to a strong bond. This shift appears to be occurring as a function of a growing preference for the replacement mecha- nism, increased access to family planning, and lags in the perception of mortality decline. As a consequence, it is contended that more than compensatory declines in fertility could result at certain phases of the mortality transition. In this chapter I focus on three aspects of the mortality fertility relationship with respect to India. First, I investigate the changing relationship between child mortality and fertility in the context of large regional variations in fertility and mortality levels observed in India (Bhat, 1996~. Second, I investigate the degree to which the fertility response is specific to the sex of the dead child. This has been a subject of several simulation studies in the past (May and Heer, 1968; Venkatacharya,1978~. Third, I investigate the implications for population policy of a family planning environment that emphasizes sterilization over reversible methods. The empirical results presented in this chapter are obtained using household and macro-level data, aggregated for various levels of administrative divisions. Period-specific indicators from census and registration systems are employed, as well as cohort measures from sample surveys. Table 10-1 gives a brief descrip- tion of the types of data employed, substantive themes addressed, and statistical methods employed at various levels of the analysis. THEORETICAL FRAMEWORK My conceptual framework rests on the useful distinction between hoarding and replacement effects of child mortality made by Ben-Porath (1978) and in- cludes some of the elements of the family-building model discussed by Lloyd and Ivanov (1988~. I assume hoarding, a family-building strategy based on the as- sumption that some children will not survive, is the typical form of behavior in high-mortality, high-fertility populations, whereas child replacement is the pre- dominant characteristic of family building in low-mortality, low-fertility settings. Such a switch in strategy is consistent with the notion of the demographic transi- tion as a process whereby individuals and households gain greater control over their vital events (see also Heer and Smith, 1968, and O'Hara, 1972~. Figure 10-1 portrays the expected relationship between total number of chil- dren ever born (B) and total child deaths (D) in cohorts that have completed their family-building process. Child deaths are represented on the horizontal axis and are assumed to reflect only the changes in child mortality (q) and not of live births. As child deaths fall, the number of births responds in a curvilinear fash- ion, as shown by the RH (replacement/hoarding) curve. The shape of the RH

341 ;^ o 4= ca ;^ so 4= ~ so .O ~ o ca ,4 · ~ 4.. 4= ~ v, 2 ca ca ca ~ sit ca ~ ¢ U. ·_4 Cq ¢ o 3 a' ·_4 o to ¢ EM ;^ o 4= ca · ~ ca ;^ ¢ o ca ca .= X ~X ~ .= . ~ ~ ° ~ U ~ ~ ~ ~ ~ ~ U ~ ~ ~ o Cd ~ Ct ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ V ~V V ;^ ;^ ~ o ~ o , ~ =) ~ =) cd ~ ca ~ ~ ~ ~ ~ ~ s~ E-° ~ ~- ° ~ ~V ~- ° ~ ~V ~V ~ ~ ~ ca ca ~ ~ ~, ;^ ~ O ~ O · ca · ~ ~ ~c,, ~ ~ R a e ~ e R ~ 2 R o o 0 ~3 ~= ~ ~ tC U u ~ ~ R e ~ ~e - ~R ~ R e C ~ ~ u ~ ~ ~ ca ~ ~ =4 ~ O ~ ~ ° {d V) V) ~ V) ~ ~ ca I ~ I R ~ tD ^ ~^ ~0 % o o ~ O ' ~0 0 O R ~ ~ . ~ ~ ~ O ~3 . ~ R ~ 3 ~ ~ ~ R e ~g ¢ ~ =0 ~ 9 2 ~ ;^ V, ;^ .g o . z V, z .^ ca ca ca .~ o V, o .^ C) s~ .^ ca ;^ V, o .~ .ca V, V, V, . . V, E~ o z

342 B b1 b2 be MICRO AND MACRO EFFECTS: THE CASE OF INDIA .* / l 1~ I / ~1 / Replacement Hoardinq / M ~ / ~ / / / / / / Bd H d3 d2 d1 D FIGURE 10-1 A macro model of the relationship between children ever born and child deaths in cohorts. curve is determined by the rate of substitution between the hoarding and the replacement strategies. At high levels of mortality, the RH curve is inelastic and the rate of substitu- tion low for several reasons. Because hoarding is associated with expected mortality rather than actual experience, the substitution rate is determined partly by perceived changes in mortality risks. Because there may be significant lags in the perception of mortality decline (see Montgomery, in this volume), large re- ductions in mortality may be necessary before they are perceived and acted upon. Furthermore, if mortality declines are not accompanied by an increase in the cost of children, there would not be a strong motive to avoid unwanted births. An extreme example of this is the decline in child mortality until point A in the graph which will not elicit any fertility response. Note that at extremely high mortality levels a price effect may be operating to suppress fertility levels (Schultz, 1976~. If few children survive, some may consider childbearing is not worth the effort.

P.N. MARI BHAT 343 Consequently, as mortality declines from this high level, some parents may revise upward their family size desires, and fertility levels may rise instead of falling. However, because the cost of contraception is typically high in these settings, it is doubtful that a significant price effect of mortality was actually present in preindustrial societies (see also Lloyd and Ivanov, 1988~. At low levels of mortality the RH curve is highly elastic. To see why this is so, Figure 10-1 includes a trend line for the desired number of births. This line (By) intersects the RH curve at points A and E. Beyond A and E, there is an unmet need for children, whereas unwanted fertility prevails between the region A and E. As mortality declines from point A in the RH curve, unwanted fertility (given by the vertical distance between the RH curve and the line B`3) begins to accumulate since desired family size falls, but substitution of replacement for hoarding does not occur at the desired speed. Unwanted fertility reaches its maximum at point M in the RH curve. But, as unwanted fertility rises, the cost of births also rises (implied by the fall in desired family size), and thus the total cost of inefficiency mounts in the hoarding regime. If now the cost of contraception also falls, more and more couples would consider switching to a replacement strategy. Consequently, unwanted fertility begins to decline and may reach point E where it totally disappears. This conceptual framework informs the empirical analysis to follow. In high-mortality settings, say above point M in the graph, I would expect a rela- tively minor fertility response to child mortality variations, even though couples in those populations may be employing an insurance strategy that generally over- compensates actual child loss. On the other hand, for populations in the region under M, or who fall between the points A and E, I would expect a relatively larger impact of child mortality on fertility even though the majority of couples may be practicing the replacement strategy, which may undercompensate child deaths. This anomaly is due to the fact that the slope of the RH curve that measures the fertility response to child mortality is influenced by the changing rate of substitution between the two strategies, indicating the need to pay careful attention to the functional form posited for the relationship between fertility and child mortality in the empirical analysis. TECHNICAL ISSUES IN ESTIMATION In the analysis below, period measures of fertility and mortality, taken from censuses and registration systems for large geographic regions, are employed, as well as cohort measures available from sample surveys for individuals and for larger aggregates. The object of the analysis is to quantify, as far as possible, the effect of a reduction in child deaths (D) on children ever born (B) using multiple regression techniques. A number of limitations of the regression approach have been raisedin the literature (see, for example, Brass and Barrett, 1978; Williams, 1977; Olsen, 1980~. However, if the objective is to quantify both replacement

344 MICRO AND MACRO EFFECTS: THE CASE OF INDIA and hoarding effects, the options available are quite limited. Therefore, I have pursued the regression approach, giving careful attention to the following ques- tions: What are the appropriate indicators of fertility and mortality? What is the appropriate functional form? What can be done about the problem of endogeneity of both births and deaths? And, what additional controls should be employed in the regression? For the cohort analysis, the information on the required variables (i.e., births and deaths) is directly available for cohorts at the end of childbearing. The problem is only one of defining an appropriate age cutoff. To have a sufficiently large sample, I use information on women aged 35 and older. For the analysis of period measures, the total fertility rate (TFR) is the appropriate choice for fertility because it is a surrogate measure of children ever born. For child mortality, the choice of an appropriate variable is less obvious because the relevant age interval changes as parents shift from a hoarding to a replacement strategy. Fortunately, because mortality levels at different intervals are strongly correlated, it should be sufficient to employ an age range that includes the majority of child deaths. I have used the under-5 mortality rate (q5), given that there is significant mortality beyond infancy in India. In the cohort analysis, the coefficient of child deaths in a linear regression of births and deaths (plus other appropriate controls) would give an estimate of the fertility response rate to a child death. To measure hoarding effects, one must add community-level measures of mortality as additional regressors. However, when cohort data refer to an aggregate, then the coefficient on the child death variable would capture a mixture of replacement and hoarding rates, and hereafter it is referred to as the RH rate, or simply as r. The RH rate may not be a constant, and is likely to increase as mortality declines. To model this relationship, I have regressed children ever born on the logarithm of child deaths. This functional form carries the implicit assumption that the effect of a child death on fertility is inversely proportional to total child deaths (8B = p8DID, where ~ is the regres- sion parameter). I refer to this functional form as the variable-rate form and the linear function as the constant-rate form. In the analysis of period measures, it is useful to employ a functional form that provides a direct estimate of the RH rate as a regression parameter. Because the regressor here is the mortality rate rather than the number of deaths, a regres- sion of logarithm of the TFR on under-5 mortality rate would give a direct estimate of the RH rate (8TFR/TFR = paq, or TAR = p8D). This is the constant- rate function. The variable-rate form in this case involves a regression of the logarithm of the TFR on the logarithm of the under-5 mortality rate. This func- tional form assumes that the effect of a reduction in child death on fertility is inversely proportional to child mortality rate (8TFR = pTFR8q/q = p8DIq). While regressing children ever born on child deaths, however, a serious problem of simultaneity arises because child deaths may be higher for a woman simply because she bore many children, even though her children's mortality rate

P.N. MARI BHAT 345 was the same as that of others. This problem can be remedied with a two-stage least-squares (TSLS) approach, using the proportion of children dead as an in- strument for child deaths (Olsen, 1980~. However, if fertility also influences the child mortality rate, this estimator can also be inconsistent. In the case of period measures, the problem of reverse or joint causation can also be addressed by the instrumental variable method, but appropriate instru- ments for child mortality are hard to find. As a partial remedy, I have used the child mortality variable lagged by several years. In this case, the lag structure was estimated using a distributed-lag model applied to annual time series data on fertility and mortality rates for the country as a whole. Because of my failure to fully address the problem of endogeneity of both births and deaths, my estimates of replacement and hoarding effects are subject to a potential upward bias. However, this bias is likely to be small because the effect of fertility on child survival is smaller than often claimed (Bongaarts, 1987~. Moreover, my regressions suggest that the existence of a strong correla- tion between the two is of recent origin, and there is no reason to expect the effect of fertility on child mortality to increase with time. Therefore, I am confident that the measured effects of child mortality on fertility are largely genuine. Because fertility levels are influenced by family size desires in addition to child mortality, it is essential to control for changes in the former so as to obtain an unbiased estimator of the effect of the latter on fertility. A question arises as to whether factors influencing unwanted fertility should also be used as covariates in the regression. An important insight on this can be obtained by examining the following identity for a cohort: B = D + C C4+ C- Cat =D+ Cat+ Cu. (1) where C is the number of surviving children, Ca! is the desired number of children, and Cu is the number of unwanted children. Essentially, the above equation states that children ever born is the sum of child deaths, surviving children desired, and surviving children unwanted. Note that the coefficient of all the terms on the right-hand side of the equation are equal to 1. Because of singularity, the model cannot be estimated from a regression analysis if all three variables are present. Suppose I drop unwanted fertility and impose the following model on the data: B=~+rD+pC~+u, (2) where u is the stochastic disturbance term, and or is a constant representing the

346 MICRO AND MACRO EFFECTS: THE CASE OF INDIA average unwanted births. By subtracting equation (1) from equation (2) and rearranging terms, I obtain Cu = or + (r- 1)D + (p - l)Ca! + u . (3) From equation (3) it is obvious that unwanted fertility is a direct conse- quence of r end p being different from 1. When the two parameters are less than 1, child deaths and desired family size are inversely related to unwanted fertility. When r is more than 1 (in the region below M in the RH curve in Figure 10-1), child deaths and unwanted children will be positively correlated. It is, however, difficult to visualize a situation in which p is larger than 1, which would imply that desired family size and unwanted fertility are positively related. Note that, as the nonstochastic variation in unwanted fertility is implicit in the parameters of child mortality and desired family size variables, unwanted fertility, or its prox- ies, should not be used as controls in the regression. Factors that influence desired family size such as female literacy could also be influencing unwanted fertility. Hence, the desired family size variable is used directly in the regressions wherever possible. This eliminates indirect effects of child mortality on fertility through changes in reported desired family size. Be- cause these effects are expected to have a net positive value, I could be underes- timating the total effect of child mortality on fertility. This should act to partly suppress the upward bias resulting from not fully accounting for the endogeneity of fertility and mortality. The above arguments are equally applicable to the analysis of period mea- sures. I would have preferred to use period measures of desired family size or wanted fertility in these regressions (see Bongaarts, 1990 and references therein). But data on these measures are hard to obtain, and I have been forced to use proxies such as female literacy to control for variations in desired family size. Consequently, I am unable to interpret unambiguously the child mortality coeffi- cients from these regressions as unconditional estimates of the RH rate. EMPIRICAL RESULTS National Trends Child mortality in India began to fall around 1921 and accelerated downward in the 1950s. The evidence for this, however, is largely indirect and based mainly on data from the decennial censuses (Bhat, 1989~. Fertility began its downward course in the 1960s, especially in certain pockets such as Kerala and Punjab (Bhat et al., 1984~. By the beginning of the 1970s, when the Sample Registration System (SRS) began to track annual trends in vital rates, the total fertility rate had fallen to fewer than six births per woman, and the infant and child (under-5) mortality rates were below 140 and 230 per 1,000 live births, respectively.

P.N. MARI BHAT Total FertiIity Rate Under-5 Mortality Rate 5.5 a) Cd .~ LL 5 a'45 cat 4 3.5 347 - 250 '\ 1 1 1970 1975 1 1 1980 1985 1990 Year a) - 200 ~ .~ - o ~1 - 150 _ - 100 FIGURE 10-2 Trends in the total fertility rate and the under-5 mortality rate, 3-year moving averages, all India, 1971-1991. Figure 10-2 shows the annual trends in fertility and child mortality (q5) since 1971 as recorded by the SRS, plotted as 3-year moving averages. The figure shows that, by the time the SRS began to keep records, fertility had already begun to fall rapidly. The TFR declined from 5.3 births per woman around 1971 to 4.4 in 1978, whereupon the decline came to a sudden halt and remained at that level until the downward trend resumed around 1983. Since then, the TFR has fallen continuously to reach 3.7 births per woman by 1991. Meanwhile, under-5 mor- tality fell slowly initially, but the pace picked up after 1976 to reach a level of 170 in 1982. After remaining at this level until 1985, it began to fall again rapidly to reach a level of 120 by 1991.i iThere is evidence to suggest that, because the SRS was just taking root in many areas at the beginning of 1970s, it was probably underestimating vital rates, especially fertility levels. After examining all available evidence, a Panel on India constituted by the Committee on Population and Demography of the U.S. National Academy of Sciences, put the TFR at 5.6 in 1971-1972 instead of 5.3 births per woman recorded by the SRS (Bhat et al., 1984). On the other hand, the panel con- cluded that SRS death rates, including child mortality, did not require any corrections at the national level. The logistical problems that cause greater underenumeration of births than deaths has, how

348 MICRO AND MACRO EFFECTS: THE CASE OF INDIA To what extent are these two trends related and what do they imply for the lag between changes in mortality and fertility? These issues are explored below by fitting a distributed-lag model to national-level data on fertility and child mortality using figures supplied by the SRS for the period 1970-1993. Table 10- 2 shows the results obtained when a geometric-lag function (also known as a Koyck lag) is employed. This infinite lag function assumes that the effect of child mortality on a given period of fertility decays geometrically with time, a reasonable approximation of the delayed fertility response to reductions in child mortality. The distributed-lag form of the variable-rate function can be written as t in TFR' = (x + ,B(1 - A) in q5,t + p(1 - it)/ in q5,t_1 + · + ut, (4) = oc+,B(l-~)>,/ 1nqst i +Ut, i=o where us is the random disturbance term. However, the model has been estimated in its simpler autoregressive form, wherein the fertility level of a given year is regressed against its level in the previous year and the level of child mortality in the same year.2 in AFRO = oc(1 - \) + ~ in TFR~_~ + p(1 - \) in q5 ~ + Vie, where vie = us- Mu_. (5) When the model is estimated in this form, the coefficient of lagged fertility provides an estimate of the parameter X, from which the implied mean lag of fertility response to child mortality can be computed as \/~1 - hi. The coefficient of the mortality rate gives information required for the computation of the RH rate. In the first specification, the under-5 mortality rate is employed as the only regressor apart from the lagged fertility variable. This specification suggests an RH rate of 2.8 births for the death of a child under-5 and a mean lag in the fertility response of 3.8 years (see Table 10-2~. This estimate of r may be high due to the ever, remained unclear. It could have arisen from the Indian custom of the mother returning to her natal home for delivery, if such births were not being properly recorded by the SRS enumerators in the early years of the SRS operation. The SRS performance appears to have improved markedly after the SRS sample units were replaced from those drawn using the 1961 census frame to those based on the 1981 census results. As such, fertility in India may have declined more rapidly than Figure 10-2 suggests (see Bhat, 1996). 2An attempt was also made to fit directly the distributed-lag form of the model through maximum likelihood procedures. However, it yielded less meaningful results, possibly because of autocorre- lation in residuals.

349 o EM a' 3 · _4 o .~ a' a' o a' o be ~ o o a' ~ ^ be ~ ·~ ~ o o Cq ~ a, Cq · ~ a' cq a' o ~ o sol ~ ¢ a' ~ .= Cq ~ a' VO Cq ~ ~ o O ~ a' . ~ ~ .~ ¢ ~ Em ~ o C) · ~ C) V, o C) · ~ C) V, o C) · ~ C) V, o .0 4= 1 4= · C) · ~ o v o .0 4= 1 4= · C) · ~ o v o .0 4= 1 4= · C) · ~ o v · ~ ;^ so o 4= x oo o ~ ~ cMoo ~ M cM o ~cM cM . . . . .. . ~ o ~ ~ ~ o ~ o o o o ~ . .. o o~ ~ ~ ~ o M . . . ~ o o ~ o . . . o o ~ ~ ~ ~ cM ~ cM ~ ocM ~ ~ ~ ~ cM ~ o o ~ cM . . . . . . . . . o o o 1 o c~ o ~ o 1 1 ~ ~oo ~ ~ I~ ~, ~ o . . . . . o oo ~ oo . . . . . . . . o o 1 1 o ~ o ~ o ~ ~ . . ca ;^ Cd ~ ~ 4.-, ~ ~ i~, o .e .e o E~ E~ V ~¢ ;^ ;^ X ;^ c,;, ~ o 4= ~ 4= ~ ~ · ~ '~ ~ o ~ ca s~ ;^

350 MICRO AND MACRO EFFECTS: THE CASE OF INDIA omission of some relevant variables that may change along with child mortality. When time is used as an additional regressor, the estimated RH rate falls to 1.4 and the estimated mean mortality lag is 2.7 years. In the final specification in Table 10-2, I examine the effect of the stagnation in fertility between 1978-1984 on parameter estimates. A time variable was interacted with a dummy variable for this period and used as an additional regres- sor. Note that a linear time variable would not capture this effect if the stagnation were caused by extraneous factors such as changes in family planning effort during and following the Emergency Period (1975-1976) or from a change of sampling units in the SRS. The interaction dummy is very statistically significant and the implied level of RH rate falls to 0.35, with a mean lag of 3.4 years. Thus, the estimates of the mean lag of fertility with respect to a change in mortality derived from the national data are fairly stable at around 3 years, even though the lag coefficient is not statistically significant in any of the above specifications. On the other hand, estimates of the RH rate vary considerably under different model specifications from 2.8 to 0.4. Clearly not much confi- dence can be placed in the estimates of the RH rate from this analysis. However, the estimated mean lag of 3 years seems quite reasonable and, more importantly, is the only estimator I have. As such, it is accepted without further scrutiny. Its statistical insignificance has not been given undue importance because the analy- sis was based on only 23 observations. State-Level Analysis Two types of data are available at the state level, both of which help to clarify the changing nature of the mortality-fertility relationship. Annual esti- mates of the total fertility rate and of child mortality are available for 15 major states of India from the SRS from 1970 onward. Furthermore, cohort data are available from two national surveys conducted in 1970 and 1992-1993. Analysis of Period Measures Although the SRS began to provide state-level information in 1970, its per- formance initially was not very satisfactory in some states. Only after its sam- pling units were overhauled in the 1980s did the SRS reach near completeness in its reporting of vital events (Bhat, 1996~. However, by using census and survey data, it is possible to construct an adjusted set of demographic estimates for 13 major Indian states at the beginning of the 1970s. These are used here in conjunc- tion with the SRS estimates for later years. Partly because of the changing quality of the SRS data, and partly because information on other indicators such as literacy are unavailable on an annual basis, I examine the state-level data at three discrete points in time: 1970-1972, 1980-1981, and 1990-1992. In Figure 10-3, I have plotted the estimates of the TFR (in log scales) against

P.N. MARI BHAT 7 4~ ~5 4J ,, . ~ I, - A - 4 ~4 - LL ~3 4~ o 2 ~- 351 ~ 1971 0 1991 + lgS1 + ~ ~+ ~ ooo a +0 o + o °0 ^0 + ++ + 0 + + a 0 +0 + + + 1 1 it 1 ' ''- ~ ~1-- 1' 0 50 100 150 200250 300 Lagged Under-5 Mortality Rate FIGURE 10-3 Relationship between the total fertility rate and lagged under-5 mortality rate for major states of India, 1971, 1981, and 1991. the under-5 mortality rate, the latter lagged by 3 years, as suggested by the analysis of national data. A clear positive association between the two is visible, but it does not appear to be as strong as the one observed in the case of time series data for all of India. A striking feature of the graph is that the estimates for the early 1970s stand apart from others, suggesting that the relationship might have undergone a structural modification in the 1970s. Table 10-3 presents the results of ordinary least-squares (OLS) regressions for each of the three time periods. In all these regressions, the child mortality variable was lagged 3 years as suggested by the analysis of national-level data. When child mortality was used as the sole regressor, its coefficient increased from 1.9 in 1970-1972 to 3.3 in 1980-1982, and further to 5.4 in 1990-1992. As estimates of the RH rate, these are almost certainly biased upward because of the omission of certain variables that influence the desire for children. When female literacy (measured as the proportion of females aged 7 and older who are literate) is included as an additional regressor, the implied RH rate falls substantially. The new estimates of r are 0.1 around 1971, 1.9 around 1981, and 2.7 around 1991. Interestingly, the coefficient of female literacy shows no clear pattern of change over time (see Table 10-3~.

352 _' o ,, o a' ~ ~ o ·s a' o Em ~ o ° be o 1 - C') o {3N Cq ~ o ° Cq {3~\ a' ~ be Ct a' ~ Cq ~ ~ o ~ a' 1 ~ C ~ so a' O ~ ·~ o O ~ o b1) ~ . ~ C a' C) 1 a' ° . ~ a' ¢ ~ EM ~ 4= ca Ed v 4= C) so V, Cal X V, V, Cal C) .~ so ;^ 4= 4= o v ~ o w o w ~ o o .- ~·0 cM w cM ~w ~ w c) w ~ ~ oo ~ s~ ~ w c) w ~ ~ o ~ s~ ~ o ~ ~ ~ ~ cM ~ ~ o cM . . .. . . o o oo o o ~ o ~ ~ ~ cM ~ ~ ~ oo . . .. . . o o oo o o ~ ~ o . . . ~ ~ o ~ oo ~ ~ ~ oo . . . Ol Ol Ol ~ ~ ~o ~ oo . . .. . . ~ ~ ~o ~ ~ ~ ~ o oo ~ ~ . . . . . . o ~ ~ ~ o o~ ~ ~ ~ oo ~ ~ ~ . . .. . . oo ~ ~ ~ ~ ~ ~ o~ ~ ~ ~ oo ~oo ~ ~ . . .. . . ~ o o~ ~ ~ ~ oo ~ oo ~ ~ l l l ~ o o oo o o \ o ~ ~ ~ o ~ ~ ~ o w w o ca w w w 0^ - ~ o ~ w ~ o ~ 4= w ca ~ ~ w o c) v, l v) ~o . ca _I ·~ ~o S~ ca E-4 ca 4= c~ ~ w ·c) ~ w o c) ~ 4= =' 4= x ~ w c) ~ x ca w w ~ ~ m · ca ~ W W Z .. ~ E~ m O z

P.N. MARI BHAT 353 A likelihood ratio test is used to check for the possibility of structural change. It rejects the hypothesis of no structural change between 1971 and 1981 but fails to confirm a change over the subsequent decade. Because the quality of my data for the period 1970-1972 is relatively poor, the statistical inference of structural change during the 1970s may be attributable to data problems. However, the continuity of a rising trend in the mortality rate coefficient over the 1980s (though this is statistically insignificant) and the absence of a clear trend in the coefficient on female literacy, argue strongly in favor of a structural change in the mortality- fertility relationship. If one accepts the hypothesis of structural change, however, the suggested level of the RH rate in the 1980s appears to be too high. Unfortunately, multi- colinearity problems prevented me from including additional regressors in the analysis apart from female literacy. However, to make optimal use of the avail- able information, I combine the state-level data from all three periods and subject them to a pooled cross-sectional time series analysis. The standard errors of the estimates presented in Table 10-3 show that there is no reason to suspect that the error variance has changed significantly over time, and hence there appears to be no serious violation of the usual regression assumptions if the analysis is per- formed on the pooled data. There are two principal methods of pooling. The first approach, known as the fixed-effects model, assumes that the intercept terms represent time-invariant effects on the dependent variable and differ for each cross-sectional unit. This model is estimated through OLS using dummy variables for each of the cross- sectional units. A second approach, known as the random-effects model, as- sumes that the residuals of the same cross-sectional units are correlated because of the random nature of the intercept term (possibly because of omission of relevant variables that are uncorrelated with those included in the model). This model is estimated using two-step generalized least squares. The random-effects model has the advantage of making greater use of the total variation in fertility, which results in savings in the degrees of freedom because only one intercept term must be estimated. On the other hand, it is more vulnerable to biases arising from omission of relevant variables. Results of the two methods of pooling are shown in Table 10-4. In the case of constant-rate function, it can be seen that the time-child mortality interaction dummies are significant under both the fixed-effects and the random-effects mod- els, which confirms the hypothesis of structural change. In particular, note that the interaction dummy for 1990-1991 is significant, showing that the change was not simply confined to the 1970s but carried forward to the subsequent decade. On the other hand, with one exception, when the variable-rate function is used, the interaction dummies are all insignificant. The implication is that the logarith- mic function adequately captures the transformation that occurs in the fertility response to child mortality declines during the transition. The functional fit, however, is not perfect. The interaction dummy is negative for the period 1970

354 o Cq a' VO o I' a' a' o EM o be o o Cq ho Cq a' be a' o a' VO Cq Cq s°- cq cot .= VO a, ·0 ~ Em o ~ oo o, Cq Do Cq ~ ~ Car o o ~ . ¢ Em ~o ca 4= C) o V, o ca x V, o o C) · ~ C) V, o .0 4= 1 s~ o 4= o ·~ ·C) ~ V, o C) · ~ C) V, o s~ o 4= o ·4~= ·c) ~ v, ~ · - ~ ;^ s~ o 4= x ~ ~ ~ ~ o ~ ~ ~ ~ ~ o o~ ~ ~ ~oo ~ ~o ~ oo . .. .. . . . .. .. . . cM ~ ~cM ~ oo ~ cMo ocM ~ cM ~ ~ ~ ~ ~oo ~ ~oo ~ ~ o o~ ~oo ~ ~ooo ~o ooo ~ ~ ~ oo~ ~ ~ ~oo~ ~ ~ o ooo . .. .. . ... .. .. . .. Ol O Ol I ~ ~ ~ o 0 Ol Ol O Ol O ~ ~ o 1 ~ oo o cM O I~) C') -I ~ ~O ~O. ~ o c~ ~ c ~11 ~ ~oo ~11 c~ oo ~o oo ~o oo ~ cM ~ M ~ ~ ~ oo M o o oo ~ ~cM ~oo ~ . . . . . . . . . . . . . Ol O O1 1 1 ~ ~ o 0 Ol O O1 1 1 ~ ~ o oo ~o ~ oocM ~ cM cM ~cM . . . . . .. . . . . . ~ ~ cM cM cM ~ ~o ~ ~ ~ o ~ ~ ~cM o ~ ~cM ~ ~ ~ ~c~ oo oo ~ oo ~ ~ ~oo c~ ~ c ~ ~ c~ c ~O ~ O . . . . . . .. . . . . . . .. Ol O Ol ~ ~ ~ ~ o 0 1 Ol O Ol O ~ ~ o 1 c~ oo oo ~O . . . . oo c~ c ~ O oo ~ 0 . ~ oo '~ c~) O ~1 1 Cd ~1 00 1 1 ~ - o o 1 ~ c~c~ ~ . . . . O O . oo ~ 0 1 1 Cd o o 1 1 ~ ~ o O O c' ~ c ~c' ~ ~ c~ =~, t~ ~ ' ° ° 1~3 ~ ~ ~ ~ ~ .,, e e °- ~ ~ 0 0 0 ~. ~ ~ V ~ ca S~ C~ ca 4= ca . ~ ca ca ca C~ .~ O V, 0 ca S~ t004 O ca C) X ca C) .0 O ·e C) s~ ~ s~ .^ ~= 4= ca O ~ ~ oo V) O E~ O Z

P.N. MARI BHAT 355 1972 and positive for the period 1990-1992, suggesting that the rise in the fertility response rate is sharper than is implicit in the logarithmic functional form. In the case of the constant-rate function, the estimates on the interaction dummies imply that the RH rate increased from a value close to zero in the period 1970-1972 to 1.3 in the period 1980-1981, and further to 2.7 in the period 1990- 1992. There is no significant difference in the estimates of the RH rate from the fixed- and random-effects models, and the results are similar to those presented in Table 10-3 for the regressions that included female literacy as a covariate. In the variable-rate function, the implied mean level of the RH rate can be computed from the estimated coefficient of child mortality from the regression that ex- cluded the interaction dummies by dividing it by the sample mean of the under-5 mortality rate. The estimates so derived are 2.4 and 2.5 under the fixed-effects and the random-effects models, respectively. These certainly are very large effects and could suggest rapid substitution of replacement for hoarding. Alter- nately, the estimated effects could be high due to insufficient controls for changes in desired family size or because of simultaneity problems. It is necessary to examine estimates from alternate sources before commenting on their reliability. Analysis of Cohort Measures Cohort data have two distinct advantages over period measures. First, with cohort data, there is no need to worry about lags in the mortality-fertility relation- ship because the cohort measures reflect the cumulative fertility response to child mortality experience by the end of the reproductive period. Second, a cohort analysis allows us to control explicitly for variation in desired family size, cir- cumventing the need to use proxies such as female literacy, which may also partly capture some portion of unwanted fertility. Below I analyze state-level information on children ever born, children dead. and desired family size for married women aged 35-44 from two national surveys conducted in 1970 and 1992-1993. The 1970 survey was carried out by the Operations Research Group (1970) and covered the entire country, but the rel- evant data are available only for 10 major states (Srinivasan et al., 1984~. The 1992-1993 information comes from the National Family Health Survey and is available for all 23 states (International Institute for Population Sciences, 1995), but I have confined the analysis to 15 major states for which the sample sizes are relatively large. Further details on the data used in the analysis are available in an unabridged version of this chapter (see Bhat, 1997~. As discussed above, the analysis involves the regression of number of chil- dren ever born (B) with number of child deaths (D) and desired family size (Cay. Because the number of child deaths would depend partly on the number of children ever born, the OLS estimate of the RH rate is biased upward. Hence I also estimate the model using two-stage least squares with the proportion of

356 MICRO AND MACRO EFFECTS: THE CASE OF INDIA children who have died and desired family size as instruments for the number of child deaths. Results are presented in Table 10-5. When child deaths are used as the sole regressor, the 1970 survey data suggest an RH rate of 0.18 when the model is estimated through OLS and 0.07 when it is estimated through TSLS. These rates are slightly higher when desired family size is added as an additional regressor (0.40 for OLS and 0.22 for TSLS). The effect of desired family size on children ever born in 1970 is estimated to be negative and negligible under both procedures. Because these estimates are based on only ten observations, none of the coefficients are large enough to be statistically significant. On the other hand, the data for 1992-1993 show substan- tially larger effects of both child deaths and desired family size on children ever born. A parsimonious specification of child deaths on children ever born sug- gests an RH rate of 2.3 under OLS and 2.0 under TSLS procedures. When desired family size is introduced as an additional regressor, these estimates fall to 1.8 and 1.5, respectively. On the other hand, a reduction in desired family size by one child is estimated to reduce ever-born children by 0.4 of a child under the OLS procedure and by 0.5 of a child under the TSLS procedure. These estimated effects are statistically significant. Furthermore, the difference in the estimated effects of child mortality and desired family size between 1970 and 1992-1993 conforms with my notion of structural change. To throw further light on these changes, information from the two surveys can be compared over time for the same state. The data show that, in India as a whole (more specifically in the 10 states used in this analysis), completed family size declined from 5.7 children in 1970 to 4.3 children in 1992-1993, or by 1.4 children during a period of about 22 years. At the same time, child deaths declined by 0.6 children and desired family size declined by 1.2 children. Thus, the total demand for children declined by 1.8 children, whereas the actual decline in total fertility was only 1.4 children. My conceptual diagram shows that this typically happens when a country is above point M on the RH curve (see Figure 10-1~. The implied increase in unwanted children from 0.3 in 1970 to 0.7 in 1992-1993 would seem surprising at first sight as it coincided with the rapid expansion of family planning services in India. However, this increase could be the result of excessive reliance on sterization as a method of fertility control, the low cost of unwanted fertility, and unanticipated declines in child mortality while pursuing an insurance strategy. From the data presented in Table 10-6, a quick estimate of the RH rate can be made by assuming that changes in child deaths and desired family size elicit identical fertility responses. This is an unsatisfactory assumption, but it provides a minimum bound on the RH rate in the population. Using this assumption, the fertility response rate can be computed by dividing the change in children ever born by the sum of the changes in child death and desired family size. For all of India, this estimate equals 0.78. However, it would be incorrect to equate a change in the number of child deaths with a change in the desired family size,

357 a' a' VO ·_4 Cq a' ·_4 VO .~ a' ·_4 Cq a' Cq a' o s~ o Cq o ~ b1) ¢ bC ~ o o ~ . ¢ ~ E~ o ca o .0 ca ca s~ V, V, E~ o .0 ca ca s~ V, o o 4= C) · ~ C) V, o 4= C) · ~ C) V, o · C) o v o 4= ~o ~ ~ ·C) ·C) ~ ~ o V, V o · C) o v o 4= ~o ~ ~ ·C) ·C) ~ ~ o V, V · ~ ;^ s~ o 4= x o o . . . o o o o oo . . . ~ ~ ~ ~ ~o ~ ~ ~ ~ cM ~ ~ o ~ cM ~ ~ ~ cM ~ ~ ~ ~ ~ oo oo cM . . . . .. . . . . o o ~ o o o~ o ~ o o ~ 1 1 M ~oo ~ . . .. o 1 ~1 ~ 1 ~1 1 ~1 M ~ ~ oo ~oo oo oo oo o ~ o ~o ~ cM . . .. . .. . o 1 ~o0 0 ~1 ~o 1 1 ~1 ~ ~ oo . . . ~ o oo ~ ~ o ~ ~ ~ ~ ~ ~ oo M cM o ~ . . . . . o o ~ o o o 1 cM .. . . o1 ~1 ~ 1 ~1 1 ~1 o o o . . . o ~ ~ ~ ~ oo ~ ~ oo ~ . . . . . ~ o ~ o o ~ ~ ~ oooo~ ~ ~ Moo ~ cM . . ... . . 1 ~ O O O ~1 ~ O O 1 1 ~1 ~= ~ ~ ,^~ a ~a~ ~ a ~ O V) ~ ~ ~ 3, ~ :^ ~ · - ~ ~ ~ ~ 0o Z~ ca S~ ca 4= ca O 4= V, V, E~ .^ ca ca ca 5- O V, O . . V, E~ o z

358 _' a' ·_4 VO L A c-) · Cot a' ~ _ _' to a' ~ ~ q ~ Ir, be o .~ o JO of Em ·_4 o sat · _4 o a' a' be a' ¢ ·_4 a' ~ be ~ o ~ a, 3 E¢- sit 4= 4= cat 1 ·_4 o V, sit 4= 4= cat 1 ·_4 sit o a 4= 4= to · _4 V o v o v o o · - ~ . . . . .. . ~ ~ o ~ oo ~ 1 1 1 1 oo ~ ~ ~ ~ . . . . . M o M o ~ . . . . . ~ ~ ~ ~ o ~ o ~ ~ ~ ~ . . . . .. . Ol Ol Ol I ~O O . . . . . ~ ~ o ~ o . . . . . O M . . . . . . . I Ol Ol I O O O . . . . . ~ ~ o ~ o . . . . . ~ ~ ~ ~ o . . ~ 1 ~ ~ ~ o c) ca ca ca o ;^ ·~ 4= · - ~ c) · - ~ .N ;^ - ~ ca ca ca o ~ . ~ ~ . ca ~ o ~ ) 4~) ~ o ~ ~ ~ . 4= ca ~ ~ . o ~ ~ ~ o ~ ~ .= ca ~ 4= ca , ·n E~ .. ca V ~ ~ ~ ~ ~3 C) x o 4= ;^ 5 ·_4 ca d] ca .= ca - o E~ ;^ V, ;^ .~ o .~ z o

P.N. MARI BHAT 359 since this ignores any biological response. Given prolonged breastfeeding in India, one can expect a biological replacement of about 30 percent of child deaths to occur virtually automatically (Preston, 1978~. If I assume that a child death would elicit a response rate of 0.3 over and above the response to changes in desired family size, the above data imply an RH rate of 0.97. Actually, the true level of the RH rate implied by the data is even higher because I have not yet allowed for the effects of a switch in strategy. The data on regional variations presented in Table 10-6 show that over the intersurvey period, the demand conditions changed about equally in north and south India. Desired family size fell by 1.1 children in the north and by 1.3 children in the south. By contrast, children ever born declined by 0.5 births in the north and by 1.9 births in the south. The reason for the anomaly can be found in the trends in the number of unwanted children in the two areas. In north India there has been a sharp increase in the number of unwanted children, where a situation of unmet need for children had existed previously. Thus, north India has moved from a point beyond A on the RH curve to a region between points A and M (see Figure 10-1~. In south India, where a significant amount of unwanted childbearing was already present in 1970, the situation had remained more or less stable during the intersurvey period. However, it is quite possible that south India has traversed to a distance below M on the RH curve from an equidistant point above M. Consequently, unwanted fertility has remained more or less the same in south India, and the level of unwanted children in 1992-1993 is about the same in the two regions. Again using the assumption that child loss and desired family size have the same effect on fertility, the implied RH rates are 0.34 in north India and 0.97 in south India. If I allow for a biological response, the implied levels are 0.54 in north India and 1.17 in south India. The higher response rate in the case of south India is in keeping with its position on the RH curve. These estimates of RH rate are derived without explicitly taking into account the possibility of structural change and are computed by imposing restrictions on the effects of child loss and desired family size. It is possible to derive alternate estimates, allowing for structural change and without imposing the restrictions on the model parameters by conducting a pooled cross-sectional time series analysis, as I did in the case of period measures (see Table 10-7~. However, in this case, I have data to pool for only two periods and ten cross-sectional units. The fixed- effects model is estimated using both OLS and TSLS procedures. In the latter, the instrumental regression for child deaths included the proportion of dead chil- dren and other exogenous variables in the model. The results of the constant-rate form suggest an RH rate for 1992-1993 of 1.9 under the OLS fixed-effects model, 1.6 under the TSLS fixed-effects model, and 1.7 under the random-effects model. On the other hand, the effect of a change in desired family size on children ever born during the same period is estimated to be 0.7 under OLS and TSLS fixed-effects models, and 0.5 under the random

360 o o a' a' o o o · C a' ~ C o ~ o a' ~ VO bC 1 ~ Cq ·0 Cq Cq s°- ~ o a' .= a' VO a' · E~ ~ a' o o o Cq ~ Cq ¢ ~ o o ~ ¢ E~ ~o ca ~ o == c ~ o ~ V ca 4= C) x · ~ V, V, E~ ca 4= C) x V, o o 4= · ~ v o C) o v · ~ s~ oo ~ CM o o ~ oo CM . . . . . . CM ~ CM o ~ ~ CM ~ o ~ o ~ CM ~ ~ ~ ~oo ~ ~ ~ ~ ~ oo ~ . . . . . . .. ~ o ~ ~ o ~ o o ~ 1 1 cM ~ ~ ~ cM ~ ~ ~ ~ cM . . . . . o ~ ~ ~ ~cM M ~ ~ ~ ~ ~o . . . . . .. . ~ o ~ ~ o ~ o o ~ 1 1 · ~ ~ oo oo ~ oo ~ ~ ~ ~ . . . . . oo cM ~ ~ oo o ~oo ~ oo ~ ~ ~ ~ . . . . . . . . O ~ I Ol ~ O - 0 ~ x x R R R O R R R R c-4 ~ ca ca O V, V, E~ ca ca 4= ca ;^ .~ O V, O ca =~ s~ t004 O ca R · ~ ~ ~ ~ ~ 00 R . .^ ~ ~ ~ ~ ~ ~ O .O .O -, ~ R ~ 9 ^ V) s~ .. ^~ V, ca ~ s~ ~ ~ ~ ~0 Z ca

P.N. MARI BHAT 361 effects model. The implied difference in the effects of child death and desired family size is substantially larger than 0.3, indicating that additional forces must be inflating the size of the fertility response. Statistically, however, the differ- ence between the two coefficients is significant only in the random-effects model, perhaps due to the fact that the results are based on only 20 observations. The significance of the interaction dummy of child mortality in all three models supports the hypothesis of structural change with respect to child mortal- ity. The implied level of the RH rate for 1970 is close to zero in all three models. In the case of desired family size, there is also an indication of a structural shift, but its interaction dummy, though negative, is not statistically significant. The results of the variable-rate form (not shown) reveal the following (see Bhat, 1997, for further details): · The logarithmic form for the changing effects of child mortality is an adequate but imperfect representation of reality. · The mean RH rate implied by the analysis was 1.4 under the OLS fixed- effects model, 1.2 under the TSLS fixed-effects model, and 1.0 under the ran- dom-effects model. These estimates are significantly lower than the ones ob- tained from the analysis of period measures using the variable-rate form. In summary, the state-level analysis strongly suggests the possibility of a structural shift in the relationship between child mortality and fertility. An indi- cation to this effect comes from the pooled cross-sectional time series analyses of both period and cohort measures of fertility and child mortality, controlling for changes in desired family size. The fertility response rate appears to rise sharply but is adequately captured by expressing child mortality in proportionate terms. The cohort analysis suggests a mean response rate of about one birth for a decline of one child death. The period analysis suggests an even higher response rate, which is consistent with the evidence that the response rate is rising as child mortality declines. However, the response rate for changes in family size desires is also rising, perhaps reflecting a general increase in couples' ability to exercise their reproductive choices. District-Level Analysis Thanks to some special questions in the 1981 census, for the first time it became possible to estimate reliably fertility and child mortality at the district level. Although similar data were collected in the 1991 census, much of them are yet to be published. However, using the data on children enumerated in the age interval 0-6 years, I have derived elsewhere estimates of the birth rate and total fertility rate from the 1991 census at the district level (Bhat, 1996), which should serve as fairly good approximations to the levels of fertility that prevailed during the period 1984-1990. Where data for some explanatory variables are unavail

362 MICRO AND MACRO EFFECTS: THE CASE OF INDIA able for 1991, and if intercensal changes are expected to be small, the data from the 1981 census have been used to supply the missing information. Table 10-8 presents the results of OLS regressions on district-level estimates of the TFR derived from the 1991 census. Briefly, four categories of variables were considered for the analysis: structural elements of the economy that bear on fertility behavior; social, religious, and gender differentials that affect fertility; factors that govern ideational change and individual modernity; and, indicators of child health and family planning program effort. Conceptually, I view the first two categories of variables as representing the superstructure that, although slow to change, can facilitate or regulate the impact of the more direct forces of change represented by the third and fourth categories of variables. A brief description of the variables employed in the regression, along with sample means, standard deviations, and the expected sign of the coefficients in the multivariate context are available in the Appendix table. In the first specification of the model, I include all relevant variables. This regression is found to explain 90 percent of the variation in the log of the TFR. All variables, except for a few proxies for economic development and family planning effort, are statistically significant and show the expected relationship to fertility. Because the economic variables are highly correlated, their separate influences cannot be estimated from the data. The same is true for the family planning variables, which are available only at the state level and are strongly correlated with the media exposure variables. When the powerful media vari- ables are dropped, family planning variables, especially the unmet need for con- traception, show strong statistical significance (see Bhat, 1996~. As can be seen from Table 10-8, the under-5 mortality rate is highly significant, and implies an RH rate of 0.63. In the second specification of the model, the family planning variables- unmet need for contraception and sterilization target achievement are dropped on the grounds that they could be capturing part of unwanted fertility. Female and child labor force participation rates and age at marriage are also dropped because their inclusion could be objected to on the grounds of endogeneity. In addition, the child mortality rate is employed in logarithmic form. As can be seen from Table 10-8, these changes have little influence on the estimated effects of either child mortality or other covariates. The implied mean RH rate, computed by dividing its coefficient by the sample mean of under-5 mortality rate, is 0.65 instead of 0.63 suggested earlier. On the whole, the district-level data suggest an RH rate in the neighborhood of 0.65 under different model specifications. However, the use of a 10-year lag in mortality may have biased the estimates of the RH rate downward. If the true lag is only 3 years, then my estimate of the RH rate would be about 0.8, which is still substantially lower than the state-level analyses suggest. At the same time, it is not at all clear how much of the variation in desired family size the covariates used in the district regressions captured and how much unwanted fertility they

P.N. MARI BHAT TABLE 10-8 Results of Ordinary Least-Squares Regressions with District- Level Estimates of the Total Fertility Rate, 1984-1990 363 Specification 1 Specification 2 Explanatory Variable Parameter l-Ratio Parameter l-Ratio Economic Structure Male workers in -0.1024 1.15 -0.0995 1.15 agriculture Agricultural laborers 0.1255 2.41 0.1211 2.40 Female work -0.1150 1.13 participation Child laborers 0.5586 1.95 Banks per populationa -0.0662 2.79 -0.0617 2.58 Social Structure Joint family 1.4521 8.39 1.6017 11.02 Female age at marriagea -0.3649 2.77 Population sex ratioa 0.2735 1.75 0.2445 1.81 Muslims 0.6009 7.76 0.6135 8.32 Scheduled tribes 0.1469 2.73 0.1400 3.17 Ideational Factors Female literacy -0.4633 5.07 -0.5508 6.90 Media exposureb -0.6874 4.16 -0.6938 5.46 Cinema exposureb -0.2814 2.13 -0.2568 2.14 Transportation and communication workersa -0.0081 0.43 -0.0086 0.46 Population densitya -0.0347 3.17 -0.0383 4.16 Health and Family Planning Under-5 mortalityC 0.6309 4.50 0.1339 5.34 Target achievements 0.0666 0.80 Unmet need for contraceptionb 0.0888 0.42 Constant 0.8302 0.71 0.4648 0.49 Adjusted R2 0.895 0.892 N 326 326 aUsed in logarithmic form. bInformation was available only at the state level. CLagged by 10 years; used in logarithmic form in Specification 2.

364 MICRO AND MACRO EFFECTS: THE CASE OF INDIA omitted. Unfortunately data on desired family size are not available at the district level. Individual-Level Analysis In macro-level analyses, hoarding and replacement effects become con- founded, but micro-level data provide an opportunity to separate these two ef- fects. Micro-level data can be used in several different ways to investigate the effect of child mortality on fertility, for example, through the analyses of parity progression ratios or birth intervals. However, to be consistent with the macro analysis presented above, I have employed a multiple regression approach. The data come from the National Family Health Survey of 1992-1993 for two states, Karnataka in the south and Uttar Pradesh in the north. Uttar Pradesh serves as a case study of a population at an early stage of demographic transition (TFR = 5.2, infant mortality rate = 94), while Karnataka presents the case of an area at a fairly advanced stage of the transition (TFR = 2.9, infant mortality rate = 67~. The data have been analyzed for cohorts at the end of their reproductive lives, as well as for all women of reproductive age. The cohort analysis employed data on chil- dren ever born, children dead, and desired family size, whereas the analysis of all married women examined data on contraceptive practice with child loss as one of the key determinants. In addition, in both analyses an indicator of community- level mortality was included to check for the presence of hoarding behavior. Cohort Analysis The data examined here refer to married women aged 35-49 at the time of the survey who have had at least one live birth. The data were analyzed using the Olsen technique (Olsen, 1980; Trus sell and Olsen, 1993~. This technique incor- porates two estimators of the replacement rate, one based on the OLS regression of children ever born on child deaths and the other derived from the TSLS regression using proportion of dead children as an instrument for child deaths. Although the former estimate is always biased, Olsen and Trussell note that the latter can be consistent in some cases but needs adjustment under certain circum- stances. Trussell and Olsen have suggested ways to correct both estimates using various diagnostic tools. The main diagnostic criterion is the implied within- parity variance of the child mortality rate, which indicates whether the probabil- ity of a child death is constant for all women or correlated with their fertility. The results of this procedure are reported in Table 10-9. The unadjusted estimate of the replacement rate from the OLS procedure is 1.19 for Karnataka and 0.94 for Uttar Pradesh. The TSLS procedure implies significantly lower estimates, 0.75 and 0.59, respectively, for the two states. When the diagnostic criteria suggested by Trussell and Olsen are examined for Karnataka, the implied within-parity variation in mortality is negative (which is

365 o a' o a O ~ Is ~ 1 a' .= O C) Cal ED ~ a' O ,= O ~ VO ¢ ~ O a' Cal ~ can · ~ O ~ ~ ·= ¢ EN of 11 1 ca ¢ ca At 4= 4= on 11 ca ¢ at ca O~ OO ~ ~ O O~ ~ ~ ~ ~ ... .. . . . ~OOO OO O CM CM ca V, ~ ~O OOO ca o 1 1 1 1 1 1 1 ca w O ~O o .0 4= ~ s~ ca ca .0 ¢ ~ ¢m ¢m ¢m¢m ;^ 4= 4= 9e a =,, ,, O ,, ,a, a~ c ~C ~ ~ ¢ ~4 ~c=; ,~, ~ w S~ : - o. o .= .S ~W o o ~W S ~ ~o ~ ~ O ·s O ca 4= W ;~ ca ·0 ca . d] m ~ ~ ~ 0 ·= ca O ~ w ~ ~ S~ ~ W ~ ~ ~ ~ ~ ~ ,~ ca O .~ ~ 60 > 0 ~ ,~ ~ ~ o~ ~ ~ = ~ ~ ~ o 4= w ·~ ~ ~ w ~ ~ ~ ~ w w ~ . o ~ ~ o o ~ ~ c ..¢ ~ ~ ~ ^ o o E~ ¢ V V o ~ ~ ~ z

366 MICRO AND MACRO EFFECTS: THE CASE OF INDIA theoretically impossible), and the mortality rate is random (diagnostic D). Trussell and Olsen advise that under these circumstances the confidence attached to the estimates should not be very high; however, the OLS estimates can be corrected using their formula and compared with the uncorrected TSLS esti- mates. The closer the two estimates, the higher the degree of confidence that they capture the true replacement rate. The corrected OLS estimate for Karnataka was 0.66, which was reasonably close to the uncorrected TSLS estimate of 0.75. However, the observed variance on child death was substantially higher than that computed using Olsen's formula, which implies that both estimates may be over- stating the true replacement effect (see Trus sell and Olsen, 1983~. When the diagnostic tests are applied to Uttar Pradesh, the results suggest that the child mortality rate cannot be assumed to be constant across women, nor can it be assumed to be uncorrelated with fertility (diagnostic C). The estimated correlation between the mortality rate and the fertility rate under two different distributional assumptions is in the range of 0.64-0.70. Adjusted estimates of the replacement rate are close to zero, which is implausibly low in the presence of lengthy breastfeeding. Hence, Olsen's technique appears to overcorrect for the correlation between fertility and mortality. In his original paper, Olsen suggested a way to estimate the hoarding rate under the assumption that the entire correla- tion between mortality rate and fertility is due to hoarding (Olsen, 1980~. This will, of course, provide an upper-bound estimate of the hoarding effect. Under this assumption, the hoarding rate is about 2.4 births per child death in Uttar Pradesh. For Karnataka, a similar estimate could not be derived because the computed within-parity variance of the child mortality rate was negative. When desired family size is directly controlled in the regression, as in the state-level analysis, a problem arises. As many as 20 percent of women gave nonnumeric responses to the question on desired family size. Because these women could belong to a nonrandom group, their exclusion could bias the re- sults. To circumvent this problem, I create a dummy variable for these women (GOD), which takes the value of 1 if they failed to report a desired family size and zero otherwise. And on the desired family size variable they were assigned a value of zero. To use the individual-level data to check for hoarding, I added the commu- nity-level mortality rate, measured as the proportion of dead children among children ever born to women aged 35-49 by district of residence as an additional regressor. Because the National Family Health Survey was a sample survey, it was not possible to use geographic subdivisions smaller than the district level. Thus, the variable is measured with a large error (though of random nature) that could result in a downward bias in my estimated coefficient. In the regression analysis I test two functional forms. In the first specification I assume that fertility responds linearly to the changes in community-level mortality; in the second I use a logarithmic form on the assumption that the hoarding response to child mortality is inelastic at high levels.

P.N. MARI BHAT 367 Tables 10-10 and 10-11 show the results of this analysis for Karnataka and Uttar Pradesh, respectively. For the sake of brevity, only the results of the TSLS regressions are presented. When child deaths is the sole regressor, the results are fundamentally the same as those reported in connection with the Olsen technique. The inclusion of desired family size variable, along with the dummy for nonnumeric responses, reduces the implied replacement rate from 0.75-0.62 in the case of Karnataka, and from 0.59-0.52 in the case of Uttar Pradesh. Interest- ingly, the coefficient of desired family size (0.62 for Karnataka and 0.60 for Uttar Pradesh) is about the same as the coefficient on the child death variable. Even more significant is the fact that the coefficient on the desired family size variable is not substantially different from the estimate I obtained using macro-level co- hort data, whereas there is a large difference in the estimated effects of child mortality from the two data sets. This is consistent with my belief that the macro- level effects of a reduction in child mortality are larger because it is influenced by the substitution of replacement for hoarding over the course of the transition. It can also be noted that the dummy variable for nonnumeric response is also strongly significant in my micro-level regressions. The estimated coefficient on this variable suggests that women who gave nonnumeric responses to the ques- tion on desired family size have an average desired family size of 4.6 in Karnataka and 4.9 in Uttar Pradesh. This was computed by dividing the coefficient on the dummy variable GOD by the coefficient on the desired family size variable. Those women who provided a numeric response reported an average desired family size of 2.7 in Karnataka and 3.7 in Uttar Pradesh, suggesting that women who failed to provide a numeric answer to the question on family size desires were indeed different. When the district-level mortality variable is introduced into the regression in linear form, it is significant in Karnataka but not in Uttar Pradesh. The coeffi- cient of the variable is substantially different in the two states (4.9 in Karnataka and 0.7 in Uttar Pradesh). However, when the variable is employed in logarith- mic form, it is significant in Uttar Pradesh as well, and the difference in the coefficients is substantially smaller (0.7 in Karnataka and 0.3 in Uttar Pradesh). Again, these results conform to my a priori expectations that lags in the percep- tion of mortality decline tend to weaken fertility response to community-wide changes in child mortality at higher levels. From these results it is also possible to obtain a rough idea of the relative size of replacement and hoarding effects. At the sample mean, the estimated coeffi- cients of district-level mortality imply a hoarding response of 0.9 and 0.2 births per child death in Karnataka and Uttar Pradesh, respectively. It is important to recognize that these rates do not reflect the absolute level of hoarding; they show the change in hoarding response in response to declines in community-level mortality. One could expect this response to be relatively weak in a high-mortal- ity state such as Uttar Pradesh. As noted above, for the two states, the estimates of replacement rate are 0.6 and 0.5, respectively. Thus, the total effect of a

368 MICRO AND MACRO EFFECTS: THE CASE OF INDIA TABLE 10-10 Two-Stage Least-Squares Regression Results of Children Ever Born with Child Deaths and Desired Family Size Using Individual-Level Data on Married Women Aged 35-49, National Family Health Survey, Karnataka, 1992-1993 Specification 1 Specification 2 Specifica Variable Parameter l-Ratio Parameter l-Ratio Parameter Any child deaths Male child deaths Female child deaths Desired family size District child mortality District child mortality (in logarithmic scale) Dummy variablesa GOD SEX DFS x SEX Constant Adjusted R2 N 0.752 13.5 4.077 58.4 0.306 1,209 0.623 11.6 0.626 12.7 2.865 14.5 2.268 15.7 0.393 1,207 0.567 0.623 4.875 2.832 1.548 0.390 1,207 aGOD is a dummy variable for women who gave a nonnumeric response to the question on desired family size. For these women, the desired variable has been set at zero. SEX is a dummy variable for sex preference. Women who had the desired sex combination of children when their change in child loss experience works out to be 1.5 in Karnataka and 0.7 in Uttar Pradesh. As levels of fertility and mortality in Karnataka are fairly close to the all-India average, and those of Uttar Pradesh significantly higher, these estimates appear to be consistent with the RH rates derived from the cohort analysis of state-level data. Two additional model specifications examine the extent to which sex prefer- ence affects the mortality-fertility relationship. First, I test the possibility that boys who die are replaced more frequently than girls. This appears to be the case, although the difference is not statistically significant in either state. The esti- mated replacement rates are 0.60 and 0.51, respectively, for male and female children in Karnataka and 0.50 and 0.47 in Uttar Pradesh. As expected, the sex difference is larger in Karnataka where volitional replacement is greater. In a final specification I examine the effect of sex-specific reproductive goals by introducing a dummy variable for the sex composition of children (SEX) and interacting it with the desired family size variable. This dummy variable equals 1 for all women fortunate enough to have their desired sex composition of chil

P.N. MARI BHAT en Ever el Data ataka, 369 Specification 3 Specification 4 Specification 5 Specification 6 tio Parameter l-Ratio Parameter l-Ratio Parameter l-Ratio Parameter l-Ratio 0.567 10.0 0.574 10.2 - 0.599 6.7 0.610 6.8 - 0.513 5.7 0.509 5.6 0.623 12.6 0.627 12.7 0.565 11.0 0.301 3.5 4.875 4.2 0.671 3.8 0.639 3.5 0.574 3.2 2.832 14.3 2.849 14.4 2.722 13.3 1.655 5.0 -1.420 4.0 0.367 3.4 1.548 7.0 3.570 9.6 3.995 10.4 4.939 11.1 0.390 0.390 0.384 0.394 1,207 1,207 1,013 1,013 first n births were equal to the total desired family size were coded as 1. All others were assigned a value of 0. DFS, desired family size. dren when they attain their desired family size and 0 otherwise. Only about 60 percent of the women in Karnataka and 50 percent of women in Uttar Pradesh had attained their desired sex composition when they reached their desired family size. The results of my analysis (Tables 10-10 and 10-11) show that failure to attain the preferred sex composition reduces the effect of desired family size on fertility by about 15 percent in Karnataka and 17 percent in Uttar Pradesh. But even in a situation where sex-specific targets are attained, my results imply that only about two-thirds of the change in desired family size is reflected in children ever born in both the states (see Bhat, 1997, for details). In sum, the cohort analysis of individual-level data has shown that the re- placement rate is much below 1. My estimates may be slightly high because I have only partially taken into account the problem of simultaneity. The replace- ment rate is marginally higher for male deaths than for female deaths. Also evident is a hoarding effect, measured in terms of a fertility response to variations in district-level mortality. In an environment of high mortality risk, hoarding behavior is insensitive to small changes in mortality. The estimated coefficients

370 MICRO AND MACRO EFFECTS: THE CASE OF INDIA TABLE 10-11 Two-Stage Least-Squares Regression Results of Children Ever Born with Child Deaths and Desired Family Size Using Individual-Level Data on Married Women Aged 35-49, National Family Health Survey, Uttar Pradesh, 1992-1993 Specification 1 Specification 2 Specifica Variable Parameter l-Ratio Parameter l-Ratio Parameter Any child deaths Male child deaths Female child deaths Desired family size District child mortality District child mortality (in logarithmic scale) Dummy variables a GOD SEX DFS x SEX Constant Adjusted R2 N 0.586 26.5 5.048 108.1 0.337 3,504 0.524 23.2 0.602 24.4 2.955 24.1 2.761 28.6 0.431 3,498 0.51 0.58' 0.68! 2.93~ 2.62' 0.42' 3,498 aSee footnote to Table 10-10. Of district-level mortality suggest that a decrease in child mortality of one child death reduces hoarding by 0.9 births in Karnataka and 0.2 births in Uttar Pradesh. Thus, the total effect of a decrease in one child death is estimated to be around 1.5 in Karnataka and 0.7 in Uttar Pradesh. These estimated total effects compare favorably with those derived from the analysis of state-level data but are higher than those derived from district-level data. Interestingly, my estimates suggest that the experience of own-child mortality and desired family size have fertility effects of roughly the same order of magnitude, even though there is an additional biological component to the former. The effect of the latter could be overstated by a rationalization in the reports of family size desires, but this is partly offset by the desire to have children of a particular sex. Determinants of Contraceptive Use From the individual-level analysis of data on children ever born, children dead, and desired family size I distinguished between hoarding and replacement effects, but I could not separate volitional from physiological components of the

P.N. MARI BHAT en Ever el Data Pradesh, 371 Specification 3 Specification 4 Specification 5 Specification 6 tio Parameter l-Ratio Parameter l-Ratio Parameter l-Ratio Parameter l-Ratio 0.518 22.2 0.512 22.0 0.502 11.9 0.470 11.1 0.589 24.0 0.594 23.9 0.492 19.8 0.688 1.1 0.527 12.4 0.446 10.3 0.299 8.1 0.319 2.3 0.309 2.2 0.317 2.3 2.932 23.6 2.909 23.4 2.468 19.8 1.522 8.8 -1.567 7.7 0.328 6.7 2.624 16.8 3.281 13.2 3.933 15.6 4.892 17.5 0.429 0.428 0.406 0.417 3,498 3,498 3,140 3,140 replacement effect. Such a distinction is possible from an analysis of deliberate fertility regulation. From the timing and methods used to regulate fertility, it is also possible to throw light on hoarding behavior. The data analyzed here pertain to 3,585 married women of Karnataka aged 13-49 in 1992-1993 with at least one living child. The National Family Health Survey, from which these data are derived, did not collect information on com- plete contraceptive history and cannot be subjected to an event-history analysis. Instead, logit models were used to analyze the determinants of contraceptive status of women at the time of the survey. A multinomial logit analysis model was used to predict whether women are nonusers of contraception, users of reversible methods, or users of nonreversible methods (i.e., sterilization). The parameter estimates of the model were normalized on the nonusers. Covariates included in the analysis were of three types: demographic characteristics of women and their children, socioeconomic variables, and community characteris- tics. The key variables of interest are the number of dead sons, the number of dead daughters, the age of the first surviving child, and the contextual child

372 MICRO AND MACRO EFFECTS: THE CASE OF INDIA mortality level, measured at the district level. Results of the analysis are pre- sented in Table 10-12. Loss of a boy is inversely related to the acceptance of sterilization, after controlling for the number of boys ever born. However, loss of a girl makes little difference to sterilization acceptance. A Wald test showed that the sex difference in the response to a child death experience is statistically significant at the 1 percent level. Interestingly, the experience of a child loss of either sex is not a statistically significant predictor of the use of a reversible method of contracep- tion. Perhaps I obtain confounding results in this case because of the presence of two opposing forces: users of reversible methods tend to be self-selected for their higher child mortality experience (as the positive sign of the coefficients seem to suggest), but continuity of use is affected adversely by subsequent child mortality because of the replacement motive. The regression based on the current status measure cannot capture this dynamic aspect, but indicates the underlying hetero- geneity through a large standard error of the estimate. Nevertheless, from the estimated net effect of near zero, it would not be wrong to conclude that greater access to reversible methods would help lower fertility levels in relatively high child mortality settings. Wolpin (in this volume) has proposed a measure of the replacement rate based on a comparison of birth probabilities of women during a fixed time period who start out with the same number of live births but differ in their past child mortality experience. My logit analysis achieves much the same objective indi- rectly, except that it is based on the comparison of contraceptive behavior and therefore reflects only the volition component of the replacement. The similarity can be made clearer by directly controlling for the number of live births by running separate logistic regressions on different groups of women classified according to their number of children ever born. The results of this analysis are also presented in Table 10-12 for women who have borne 1, 2, 3, 4, and 5+ children. Because of sample size limitations, here I have used only the binary logit model that considered two groups: users and nonusers of any method of contraception at the time of the survey. The results of this analysis show that the effect of child loss experience is quite large and negative at parities below 5. The coefficient on male child death is strongly significant at parities 3 and 4 whereas that of female child loss is significant only at parity 3. The coefficients of child loss experience are also quite large and negative at parities 1 and 2 but are not statistically significant. It is interesting to note that, unlike the analysis on all women, parity-specific analy- sis indicates that the death of a girl also tends to reduce the rate of contraceptive adoption, though not to the same extent as the death of a boy. The marginal effect of a child death on the contraceptive prevalence rate can be evaluated at each parity by multiplying the respective coefficient by the cross product of proportion of users and proportion of nonusers at that parity. My estimates imply that, by elimination of a child death, the contraceptive prevalence

P.N. MARI BHAT 373 rate would rise by 16, 20, and 9 percent at parities 2, 3, and 4, respectively. However, the combined result of these changes is expected to cause an increase of only 4 percent in the level of contraceptive practice of all married women (5 percent from the elimination of a male child death and 3 percent from a female child). This is because a large percentage of child deaths in the population is accounted for by women with five or more births who respond only weakly to their own child mortality experience, possibly because they are self-selected for higher family size desires or for greater reliance on an insurance strategy. A rough estimate of the mean replacement rate can be derived by multiplying the expected increase in the contraceptive practice by the total fertility rate and dividing by the proportion of nonusers of contraception. As the TFR was about 3.0 and about 50 percent of the married women (including childless women) were not using contraception in Karnataka, the average increase of 4 percent in the contraceptive prevalence rate implies a volitional replacement rate of 0.24 births per child death (0.30 for boys and 0.16 for girls). In addition, if a biological component of 0.3 is associated with prolonged breastfeeding, the implied total replacement rate would be 0.54, almost identical to the estimate derived from the cohort analysis using desired family size as a control (0.56~. However, the cohort analysis indicates a smaller sex differential in the response rate than suggested here. Because an overwhelming majority of women (87 percent in my sample) who use contraceptives use sterilization, a nonreversible method, children's sur- vival after acceptance of contraception could be a real concern. To test for its possible effects, age of the first surviving child at the time of the survey was used as an additional covariate. The results obtained in the case of all women show that the age of the first child and its square are strongly significant in the steriliza- tion equation and marginally significant in the case of reversible methods (see Table 10-12~. The older the child is, the more likely that his or her parents would accept sterilization. As one would expect, the effect of child's age is nonlinear; the estimated age function implies that prevalence of sterilization peaks when the first surviving child is 24 years old. Because the mean interval between steriliza- tion acceptance and the survey was about 8 years, the result suggests that accep- tance of contraception rises until the child is 16 years old. Thus, parents appeared to be concerned about child survival to ages much beyond infancy, and it is in such conditions that hoarding behavior flourishes. Although the coefficient of age of the first child is marginally significant in the case of women who use a reversible method, a Wald test reveals that the estimated effect is substantially smaller than that on sterilization acceptance (sig- nificant at the 0.001 level). Thus, my empirical results support the contention that sterilization tends to promote hoarding behavior. By demonstrating the importance of age of the child on contraceptive accep- tance I can demonstrate the existence of an insurance motive, but it is difficult to quantify a hoarding rate. The use of contextual child mortality as an additional

374 ·_4 o a' o o = a' o o a' Cq o Cq a' o o Cq Cq ¢ ·bC o o Cq o ~ C~ ~ 1 o ~ o ~ a' ¢ ~ E~ ~. o m v o S~ z ;^ o ;^ o ca o · ~ ¢ S~ O 4.;, ~o V, · ~ S~ ;^ 4= x * * * * * * * * * * 0 ~00 ~00CM 00 0 ~0 ~CM 000 ~CM00 ~0 CM 0 ~00 ~0 ~00 ~0CM . . . ... .. ..... ... . O Ol O Ol 11 ° o 0 Ol Ol Ol OlO O O OlO Ol * * * * * * * * cM ~ ~ oo ~ c~ ~ c ~ ~ ~ ~ ~ c~ ~ oo o ~ c ~ ~ ~ o cM cM ~ o o o~ o c c~ o ~ o ~ cM ~ o o ~ c~o o o oo ~ . . . . . . . . . . .. . . .. . O Ol O O1 11 ° Ol O Ol I Ol OO Ol O OlO O ~ * * * * * * * * * * * * * * * * * * * * * M oo ~ ~ ~ ~ ooo ~ ~ o ~ ~ ~ oo ~ ~ c~c~ o ~ o~ ~c cM . . . . . . . . . . .. . . .. . O Ol ~ O1 1 11 Ol O Ol Ol Ol O O O O Ol Ol O ~ * * * * * * * * * * * * oo ~ ~ o oo ~ oo ~ ~ cM cM ~ ~ ~ cM ~ ~ ~ o o oo c~ ~ ~ o ~ ~ ~oo o ~ o ~ oo c~ o oo o oo ~ ~ o oo ~ ~o o o o o ~ . . . . . . . . . . . . . . . . . O Ol O O1 1 1 Ol Ol O Ol Ol Ol Ol O Ol O O O O * * * * ~ oo ~ ~ oo o ~o cM ~ o o ~ ~ . . . . . O Ol O1 1 1 1 1 ~1 1 * * * * M ~ ~ ~ c~ o ~ o ~ ~ ~ c~ o o o o o ~ o o o ~ o . . . . . . . . . Ol Ol Ol Ol O O O O Ol ~ ~ ~ ~ o ~ ~ c~ oc~ o oo o oo ~ ~o o o o . . .. . . . Ol Ol OlO O O O * M cM ~ c~ ~ ~ c~ o ~ o o ~ ~ o o o . . .. . . . O Ol OlO O O Ol * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ** M ~ o cM ~ ~ ~ ~ c~ cM o c~ ~ ~c~ o ~ o cM o c~ cM c~ o c~ o c~ o o cM oo o o o . . . . . . . . . . . . .. . . . o o ~ o o o o o o o ~ o oo o o o 1 1 ' 1 1 1 1 1 1 1 ~ ~c . . Ol O * oo ~ . . Ol Ol ° 0° R ~ o o ~ = ~ ~ ·~ 0 0 C) C) ,~ ~ ~ ~.; ~ ~ ~ ~ ~ ~ ~ ~ ~ ~S ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ R ~ o<, c,) c,) cd cd c,) cd ~ t.4 ~ C) C) 4= ^~D ^~D ,r~ ,r ~ ~ O O 2 2 ~ ~ 2 ~ ~ ~o ~ 2

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376 MICRO AND MACRO EFFECTS: THE CASE OF INDIA regressor provides a means by which one can not only detect hoarding behavior but can also quantify the fertility response. As in the case of cohort analysis presented above, the level of contextual mortality was measured at the district level. As seen in Table 10-12, this variable was strongly significant in both sterilization and reversible method equations. Interestingly, the effect is larger in the case of reversible method use; the Wald test confirmed this at a 5 percent level. The greater sensitivity of reversible method use to variations in contextual mortality is in line with my expectation that mortality decline induces a switch from a predominantly hoarding to a predominantly replacement regime. Clearly, as more couples adopt a replacement strategy, use of reversible methods should increase. I also find an increase in the use of sterilization associated with declines in community-level mortality because it reduces the number of children required for insurance. The results of parity-specific analysis also conform to my a priori expecta- tions. The district-level child mortality variable is significant at most parities, but its effect is nearly three times larger at parity four than at any other parity (see Table 10-12~. Because the average desired family size in Karnataka is about three children, many have a fourth child primarily for insurance. Thus, contex- tual mortality has greater bearing on contraceptive acceptance at this parity. By multiplying by the contraceptive prevalence rate and dividing by the mean child mortality rate, the coefficient of contextual mortality can be con- verted to an estimate of the hoarding response to a change in community-level mortality. The weighted average of method-specific effects implies a hoarding response of 2.1 births per child death, whereas the weighted average of parity- specific coefficients implies a response rate of 2.0 births. If I add to this the replacement effect of 0.54, estimated earlier, I obtain a total RH rate of 2.6 children per child death, which is significantly higher than the estimate of 1.5 derived from the cohort analysis of women aged 35-49. The difference in the estimates obtained from period and cohort analyses suggests a rising trend in the RH rate, an indication consistent with the hypothesis of a structural shift. The almost exclusive reliance on sterilization in the Indian family planning program tends to promote hoarding behavior. This point becomes even clearer when the timing of sterilization is examined. Due to certain social as well as technical reasons, most women find it advantageous to accept sterilization imme- diately after delivery. The data for Karnataka imply that the interval between the last live birth and the acceptance of sterilization is less than a month in 58 percent of cases and 1 month in another 14 percent of the cases (Table 10-13~. This obviously raises questions as to the parents' concern about the survival of the last child. The question becomes even more intriguing when one observes that the sex ratio of the last live birth is highly skewed with 144 male births for 100 female births among sterilized couples. Thus, there is a clear indication that couples waited to have a son before accepting a nonreversible method. Most likely, couples do not accept sterilization as soon as the desired family size is

P.N. MARI BHAT 377 TABLE 10-13 Percentage Distribution of Sterilized Couples by Interval Between Birth of Last Child and Date of Sterilization and According to Sex of Last Child, Karnataka, 1992-1993 Sex of Last Child Interval in Months Male Female Either Sex 0 59.0 56.6 58.0 1 14.6 14.1 14.4 2-3 7.0 7.6 7.2 4-6 2.6 3.1 2.8 7-11 1.6 2.8 2.1 12+ 9.8 9.9 9.8 Inconsistent/not reported 5.4 5.9 5.6 Sterilized couples 1,020 710 1,730 SOURCE: National Family Health Survey, Karnataka. reached but they wait until after the next birth to decide whether to discontinue childbearing. If the next child is a boy, the survival safeguard is considered complete and couples accept sterilization immediately after the child is born. Perhaps parents would have accepted contraception after the preceding birth if reversible methods were easily accessible. The strong influence of the sex com- bination of children on sterilization acceptance seen in Table 10-12 partly reflects this sex-specific hoarding behavior. In short, the analysis of contraceptive acceptance patterns shows that the prevalence rates for sterilization, a method used by a overwhelming majority of couples in India to control their fertility, is lower because of their experience of child loss and their concerns about the survival of their living children. The estimated reduction in sterilization prevalence because of child loss implies a volitional response of about 0.25 for a child death in Karnataka. The strong presence of hoarding is indicated both by the significance of first child's age to contraceptive acceptance and by the timing of sterilization, which suggests that the last child born is a hoarded child and in many cases is insurance against the death of a son. The analysis unambiguously shows that the almost exclusive reliance on sterilization, and its provision mainly as a postpartum service, has accentuated the hoarding response, increased inefficiency (in the form of un- wanted fertility), and enhanced the effect of son preference on fertility. CONCLUDING REMARKS The analysis presented in this chapter is based on the premise that as indi- viduals gain increasing control over their fertility and mortality risks, they switch

378 MICRO AND MACRO EFFECTS: THE CASE OF INDIA from a hoarding to a replacement strategy to cope with the uncertainties of child survival. The shift occurs because over the transition mortality risks beyond infancy reduce substantially, the amount and cost of unwanted fertility increase, and improved access to family planning methods make it more feasible to use a replacement strategy. However, at initial stages of the transition, the substitution Of replacement for hoarding occurs at a sluggish pace because of lags in indi- vidual perception of community-wide mortality declines, the low cost of un- wanted fertility, and the lack of access to family planning services. Conse- quently, the relationship between fertility and child mortality is generally weak at this stage. As conditions change, couples increasingly switch to a replacement strategy. Because replacement can be less than fully compensatory, and hoarding often results in excess fertility, the switch tends to accelerate the fertility decline. Even though replacement is incomplete at the family level, at the macro level, the mortality-fertility relationship is characterized by increasing returns to scale. My data for India show that the replacement rate is substantially below 1, about 0.5-0.6, of which about one-half is a volitional component. I interpret the low rates of volitional replacement as evidence that the majority of Indian women have still not adopted a replacement strategy. This is supported by the signifi- cance of variations in community-level mortality as demonstrated in the multi- variate analysis of household-level data and the analysis of macro-level data that suggest that declines in child mortality currently bring more than compensatory changes in fertility. This is a different situation than two decades ago when the magnitude of the fertility response indicated deceasing returns to scale. Thus, the strategy shift appears to have begun. The implication of this result to health policy is fairly obvious. Whatever the fertility response in the past, structural changes have occurred, and current investments in child survival programs would trigger more than compensatory effects on fertility and thus contribute signifi- cantly in reducing global population growth. To maximize this effect, it is essential to strengthen fertility control programs, focusing mainly on reversible methods. As my analysis of Indian data shows, almost exclusive reliance on sterilization has favored the insurance strategy and delayed the adoption of a pure replacement mechanism.

P.N. MARI BHAT APPENDIX Appendix tables begin on following page. 379

380 a' a' Cq Cq a' .~ o x o Cq ·_4 VO a' a' ~ a' · _4 ·0 o ~ ·~ ·0 ~ ~ o ~ o ~ a' VO ~ ^ a c., .= ·= ~4 o Cq ·Cq ¢ ¢ X C Cq a' bC a' ¢ ~ · ~ o X ~ + -- 1 + 1 +1 + + -- 1 o oo o o ~CM ~C . ~ C~ o ~o~ o ~ .0 o o o o CM o~ ~ o o o V, o ~oo o C ~ oo o oo o~ C ~C ~C CM o ~CM~ o o ~o o o o ~o~ o o o o ~ ~ oo ~o ca 8 c ~ ~ ~ A ~ ~ - ~t . ~o ~ o ~ o ~ o ~ ~o ~ ~ ~ ~ o o ~ o ~ ~ .~= ~ ~ =0 ~ aO s =0 ~ ~o ,~, ~ ~ e ~ ° .~.<,` e 0= e ~ m ~>~m ~m 0 4= ~·C) ~·~ C) Ct ~ C ~ ~ ~ ' ~' ~ ~ 5

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382 MICRO AND MACRO EFFECTS: THE CASE OF INDIA REFERENCES Ben-Porath, Y. 1978 Fertility response to child mortality: Microdata from Israel. Pp. 161-180 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Bhat, M. 1989 Mortality and fertility in India, 1881-1961: A reassessment. In T. Dyson, ea., India's Historical Demography: Studies in Famine, Disease and Society. London: Curzon Press. 1996 Contours of fertility decline in India: A district-level study based on the 1991 census. Pp. 96-177 in K. Srinivasan, ea., Population Policy and Reproductive Health. New Delhi: Hindustan. 1997 Micro and Macro Effects of Child Mortality on Fertility: The Case of India. Population Research Center Report no. 94. Dharawad, India: JSS Institute of Economic Research. Bhat, M., S.H. Preston, and T. Dyson 1984 Vital Rates in India. Report no. 24, Committee on Population and Demography. Wash- ington, D.C.: National Academy Press. Bongaarts, J. 1987 Does family planning reduce infant mortality rates? Population and Development Re- view 13(2):323-334. 1990 The measurement of wanted fertility. Population and Development Review 16(3):487- 506. Brass, W., and J.C. Barrett 1978 Measurement problems in the analysis of linkages between fertility and child mortality. Pp. 209-233 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Heer, D.M., and D.O. Smith 1968 Mortality level, desired family size and population increase. Demography 5(1):104-121. International Institute for Population Sciences (IIPS) 1995 National Family Health Survey, India, 1992-93. Bombay: IIPS. Lloyd, C.B., and S. Ivanov 1988 The effects of improved child survival on family planning practice and fertility. Studies in Family Planning 19(3): 141-161. May, D.A., and D.M. Heer 1968 Son survivorship motivation and family size in India: A computer simulation. Population Studies 22(2):199-210. O'Hara, D.J. 1972 Mortality risks, sequential decisions on births, and population growth. Demography 9(3):485-498. Olsen, R. 1980 Estimating the effect of child mortality on the number of births. Demography 17(4):429 443. Operations Research Group 1970 Family Planning Practices in India. Baroda, India: Operations Research Group. Preston, S.H. 1978 Introduction. Pp. 1-18 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Schultz, T.P. 1976 Interrelationship between mortality and fertility. Pp. 239-289 in R.G. Ridker, ea., Popu- lation and Development: The Search for Selective Interventions. Baltimore, Md.: Johns Hopkins University Press.

P.N. MARI BHAT 383 Srinivasan, K., S.J. Jeejeebhoy, R.A. Easterlin, and E.M. Crimmins 1984 Factors affecting fertility control in India: A cross-sectional study. Population and Development Review 10(2):273-296. Trussell, J., and R. Olsen 1983 Evaluation of the Olsen technique for estimating the fertility response to child mortality. Demography 20(3):391-405. Venkatacharya, K. 1978 Influence of variations in child mortality on fertility: A simulation model study. Pp. 235- 257 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Williams, A.D. 1977 Measuring the impact of child mortality on fertility: A methodological note. Demogra- phy 14(4):581-590.

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The last 35 years or so have witnessed a dramatic shift in the demography of many developing countries. Before 1960, there were substantial improvements in life expectancy, but fertility declines were very rare. Few people used modern contraceptives, and couples had large families. Since 1960, however, fertility rates have fallen in virtually every major geographic region of the world, for almost all political, social, and economic groups. What factors are responsible for the sharp decline in fertility? What role do child survival programs or family programs play in fertility declines? Casual observation suggests that a decline in infant and child mortality is the most important cause, but there is surprisingly little hard evidence for this conclusion. The papers in this volume explore the theoretical, methodological, and empirical dimensions of the fertility-mortality relationship. It includes several detailed case studies based on contemporary data from developing countries and on historical data from Europe and the United States.

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