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8 Fertility Response to Infant and Child Mortality in Africa with Special Reference to Cameroon Barthe1!emy Kuate Defo INTRODUCTION Most demographic transition theorists would agree with the notion that cur- rent and future levels of infant mortality, combined with current stocks of chil- dren, are likely determinants of fertility, and many studies have shown a high correlation between infant and child mortality and fertility levels, both in their time trends and cross sectionally. Theoretical considerations, largely supported by empirical research findings, confirm the interdependence of child mortality and fertility. At a micro level, it has been found that the risk of a birth is significantly higher following the death of a child in the family (e.g., Ben-Porath, 1978; Olsen, 1980~. However, the prevalent direction of causation, its mecha- nisms, timing, and strength differ among populations. This study has two objectives: first, to provide an overview of the effects of infant and child mortality on fertility in African countries; and second, to assess the extent to which couples' reproductive behavior changes in response to child mortality using micro-data from Cameroon. These data contain information on the timing of all conceptions and infant mortality experiences of the respondents. They enable us to study the instantaneous and lagged effects of an infant death on the hazard of a conception and to derive replacement effects from hazard model estimates. These replacement effects provide insights into the contributions that declining infant and child mortality rates in Cameroon have had on the concur- rent fertility reduction. The estimated parameters integrate aspects of life- cycle fertility that have previously been studied in isolation of each other: completed fertility, childlessness, and interbirth intervals. In Cameroon the response to mortality involves volitional behavior in a 254

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BARTHELEMY KUATE DEFO 255 high-fertility, high-mortality environment with very little modern contraceptive use. The case of Cameroon thus raises questions about the response to mortality in sub-Saharan Africa more generally where the levels of both mortality and fertility remain high in most countries (Hill, 1993; Cohen, 1993~. In the virtual absence of effective means of contraception other than breastfeeding, the short- ening of birth interval induced by a reduction in infant and child survivorship may signify a higher ultimate parity. Higher fertility may thus be largely a biological response to higher mortality. It is more likely that the behavioral response has a greater effect on the total number of children to whom a woman gives birth, or alternatively, on the parity of her last live birth since women entertain a rough idea of the number of surviving children they would like to have, even if they do not have a predetermined target (van de Walle, 1992~. In this chapter, I do not estimate a tightly structural model of fertility because the main question does child mortality matter for fertility behavior? is still open. A positive answer to this question has been assumed in the demographic transi- tion theory literature, but without much factual basis from developing countries. A central finding documented in this study is that current and past child mortality experiences play a strong role in reproductive behavior in Cameroon, even after correcting for measured and unmeasured heterogeneity. EFFECTS OF INFANT AND CHILD MORTALITY ON REPRODUCTIVE BEHAVIOR IN AFRICA: WHAT DO WE KNOW? Empirical studies of the effects of infant and child mortality on fertility in Africa fall into two broad categories: aggregate studies, which are based on samples consisting of national or subnational averages usually using censuses, cross-sectional surveys, or registration data; and individual-level studies, which are based on sample survey observations drawn from the reproductive experience of individual women. Table 8-1 presents an overview of published work that has attempted to measure the fertility response to infant and child mortality, using aggregate or individual data. Aggregate Level Studies based on aggregate data have one important advantage over indi- vidual data: the potential for measuring the overall implications of improvements in child survival for fertility and population growth. Because many of the hy- pothesized effects of changes in mortality on fertility work through changes in environmental conditions rather than through individual experience, studies based on individual data alone can only measure accurately the physiological and voli- tional replacement effects (United Nations, 1987~. These effects are not expected to compensate fully for changes in mortality even if they operate jointly. Aggre- gate studies of the effects of infant and child mortality on fertility in Africa are

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256 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-1 Synopsis of Published Studies of the Effects of Infant and Child Mortality on Fertility in Afnca: Aggregate and Individual Data Characteristics of the Study Year/Period Measure of Data Source Collection Country/Strata Study Design Mortality Fertility Barbieri, 1994 1985-1989 10 sub-Saharan DHS surveys Probability TFR for African countriesa of dying women al between 0-26 15-40 months Bocquier, 1991 1986 Pikine, Senegal Retrospective Child death Probabilit survey of 2,807 of a folio' women aged 15-49 conceptio: (and 7,632 births) Brass, 1993 1969, 1978, Kenya 1969 census, 5Qlo TFR 1989 1977- 1978 WFS proportion and 1989 DHS of children surveys died per woman Brass and Jolly, 1977-1978 Kenya and WFS and DHS 50lo TFR 1993 provinces surveys and districts Callum et al., 1980 Egypt Retrospective Child death Percent oi 1988 (WFS) survey with no a' births; me of childre Cantrelle 1940-1972 12 sub-Saharan Retrospective loo, 2Q1 TFR, GF} et al., 1978 African countriesb and prospective 2Qo surveys Cantrelle 1962-1968 Niakhar, rural Longitudinal Child death Mean birt and Leridon, Senegal study of 8,456 interval 1971 live births Coale, 1966 1940-1962 13 sub-Saharan Retrospective loo, 2Q1 TFR African countriesC surveys Cochrane 1977-1978 Lesotho (1977) and Retrospective Child death Birth inte: and Zachariah, Kenya (1977- 1978) surveys 1984 (in [WFS] a study of 25 LDCs) Farah, 1982 1975 Greater Khartoum, Retrospective Child death CEB Sudan survey of 2,045 ever-married women aged 15-44

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BARTHELEMY KUATE DEFO Child 257 Ire Mortality Effects Association Mortality lity Fertility Type of Analysis Replacement Insurance Fertility Utility TFR for Descriptive Unclear n.a. Yes ng women aged analysis and an 0-26 15-40 linear regression s analysis (aggregate data) death Probability Nonparametric Yes n.a. Yes of a following survival conception analysis (individual data) TFR Descriptive No n.a. No Lion analysis Wren (aggregate data) er woman TFR Descriptive No n.a. No analysis (aggregate data) death Percent of women Descriptive Yes Unclear Yes with no additional and multivariate births; mean number analyses of children born (individual data) Q1 TFR, GFR Correlation n.a. n.a. Unclear analysis (aggregate data) death Mean birth Descriptive Yes n.a. Yes interval analysis (aggregate data) Q1 TFR Correlation n.a. n.a. Unclear analysis (aggregate data) death Birth interval Multivariate Yes n.a. Yes analysis (individual data) death CEB Simple Yes n.a. Yes classification analysis (individual data) continued on next page

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258 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-1 (continue]) Characteristics of the Study Year/Period Measure of Data Source Collection Country/Strata Study Design Mortality Fertility Folta and Deck, No date Zimbabwe Participant Child death Fertility 1988 observation and following in-depth interviews a child de of 124 women Heer and Wu, 1966 Urban Morocco Area probability Number of the Number o 1978 sample of first three life births currently married children that subsequer women under age survived either to the 50 who had to age 10 or to third experienced 3 or the time of more live births interview Jensen, 1993 1988, 1990 Bungoma and Cross-sectional Number of CEB Kwale, Kenya interviews with children 132 women aged deceased 18-78 Jensen, 1996 1988-1989 Kenya, Zimbabwe, DHS surveys Infant & Hazard of Botswana child death following birth Livenais, 1984 1973, Rural Mossi, Cross-sectional loo TFR 1978 Burkina-Faso surveys Okojie, 1991 1985 Bendel state, Retrospective Proportion CEB Nigeria survey of 1,895 of surviving ever-married children women aged 15-50 Sembajwe, 1981 1973 Western Nigeria Retrospective Proportion of CEB survey children dead NOTES: TFR, total fertility rate; GFR, general fertility rate; loo, infant mortality rate; 2Q1 = sec- ond-year mortality rate; 2Qo, first two years mortality rate; Ado, first five years mortality rate; CEB, children ever born; n.a., not applicable;WFS, World Fertility Survey; DHS, Demographic and Health Survey; LDC, less-developed countries. aThe 10 sub-Saharan African countries are Botswana (1988), Burundi (1987), Ghana (1988), Kenya (1989), Liberia (1986), Mali (1987), Senegal (1986), Togo (1988), Uganda (1988-1989), and Zimbabwe (1988-1989).

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BARTHELEMY KUATE DEFO 259 Ire Mortality Effects Association Mortality lity Fertility Type of Analysis Replacement Insurance Fertility death Fertility Qualitative Yes ma. Yes following analysis a child death (individual data) er of the Number of Multiple Yes Unclear Yes tree life births classification n that subsequent analysis ed either to the (individual and 10 or to third aggregate data) he of few er of CEB Multiple Yes ma. Yes n classification Ed analysis (individual data) & Hazard of a Event history Yes ma. Yes leash following analysis birth (individual data) TFR Descriptive No ma. No analysis (aggregate data) Lion CEB Two-stage Yes ma. Yes viving ordinary least squares n (individual data) Lion of CEB Regression Yes ma. Yes n dead (individual analysis) bThe 12 countries are Benin (1961), Guinea (1954-1955), Burkina-Faso (1960-1961), Niger (1960), Angola (1940, 1950), Zaire (1955-1957), Cameroon (1960), Kenya (1962), Mozambique (1950), Rwanda (1952-1957), Tanzania (1957), and Uganda (1956). CThe 13 countries are Benin (1961), Guinea (1954-1955), Burkina-Faso (1960-1961), Niger (1960), Angola (1940, 1950), Zaire (1955-1957), Cameroon (1960), Kenya (1962), Mozambique (1950), Rwanda (1952-1957), Tanzania (1957), Uganda (1956), and Senegal (1963-1970, 1972).

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260 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON either cross-sectional studies based on national aggregates using data drawn from several African countries (e.g., Coale, 1966; Cantrelle et al., 1978; Barbieri, 1994) or from a specific country, subregion, or province within a country (e.g., Heer and Wu, 1978; Livenais, 1984; Brass, 1993; Brass and Jolly, 1993~. The general finding from these aggregate-level studies is that in Africa mor- tality decline has had either no effects or unclear effects on fertility. Thus, the evidence from these studies is inconclusive. The absence of a demonstrable link between childhood mortality and fertility at the aggregate level apparently may stem from the fact that intermediate variables, which act more directly on these rates, are obscuring the strong positive relationship at work at the individual level (Cantrelle et al., 1978~. In Kenya, for example, Brass (Brass, 1993; Brass and Jolly, 1993), analyzing previous child mortality declines, and their effect on recent fertility declines, argues that "the observations supply no evidence of any consistent relation between the falls in fertility and the preceding (and continu- ing) child mortality trends" (Brass, 1993:78~. Coale (1966) and Cantrelle et al. (1978) found that the zero-order correlations for the 47 subregions of countries for which data were available between aggregate fertility and mortality rates were -0.38 and -0.37, respectively, thus failing to support the widely observed posi- tive association between childhood mortality and fertility. Individual Level In recent years, most of the published research on the mortality-fertility relationships has been based on survey data, such as the World Fertility Surveys (WFS) and the Demographic and Health Surveys (DHS). The individual-level studies reviewed in Table 8-1 consistently show that the death of an infant leads to a shorter interval between that birth and the next, and therefore provides a clear indication that, at the individual level, there is a significant fertility response to child loss. For example, a detailed study of the Sine region of Senegal (Cantrelle and Leridon, 1971) shows that the death of an infant (which is equivalent to weaning) affects fertility. Cochrane and Zachariah (1984) use data from the WFS of Kenya and Lesotho (among other countries studied) to measure the influence of neonatal (0-1 month) and postneonatal (2-11 months) deaths of first, third, and fifth children on the length of subsequent birth interval. They find that birth intervals are reduced following the death of a child. They also show that breastfeeding is an important factor affecting differences in birth intervals. Fur- thermore, they found that the reduction in birth intervals is significantly greater for neonatal deaths than postneonatal deaths for the interval between the first and second birth but not for the other parities. This finding suggests that the mortal- ity-induced reduction in birth interval may vary across parity. Analyzing the possible effects of mortality on fertility among the Yoruba in Nigeria, Sembajwe (1981) observes that the proportion of children dead increases as the number of children ever born alive increases. In this society, however, the answer "up to

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BARTHELEMY KUATE DEFO 261 God" to the question about the family size does not seem to be influenced by the experience of child loss. The study by Callum et al. (1988) uses individual- and community-level data from the Egypt WFS to attempt to assess both replacement and insurance effects of child mortality through an examination of actual fertility outcomes according to the number of children who have died for women of equal parity and family size. Their fertility outcomes during the 5 years preceding the survey were related to the number of children ever born and living and the number of children who had died during the 5 years prior to the date of interview. As regards the replacement effects, they found that (1) an infant death is associated with a reduction of about 6 months (roughly 15-20 percent) in the interval to the next live birth; (2) there is a significantly lower likelihood of contraceptive use in the event of an infant death, which persists after controlling for parity and socioeco- nomic status; and (3) most of the reduction in interval length among nonusers of contraception is accounted for by the biological effect of the reduction in the anovulatory period. Regarding the insurance effect, there was some evidence of an individual insurance response to the experience of child loss, especially in Cairo, Alexandria, and urban lower Egypt. The authors speculate that, in the context of relatively high mortality, common in Africa, an insurance strategy is more likely to be adopted in response to generally perceived rather than individu- ally experienced mortality risks, and that, therefore, measurement at the indi- vidual level fails to capture the full effect of the insurance response. The fertility response to child loss in Kenya deserves special attention for two reasons. First, it is the only African country for which there have been several studies of the mortality effects on fertility both at the aggregate and individual levels. Second, there are sharp discrepancies between findings at the aggregate level and at the individual level: All aggregate-level studies find either no effects or unclear effects of child mortality on fertility (Coale, 1966; Cantrelle et al., 1978; Brass, 1993; Brass and Jolly, 1993; Barbieri, 1994), whereas all individual-level studies (Cochrane and Zachariah, 1984; Jensen, 1993, 1996) find strong evidence of fertility response to child loss. This raises important popula- tion policy and substantive questions regarding the weight to give to the evidence of mortality effects on fertility at the aggregate level versus individual level in Africa more generally. Contraceptive use seems to have played a role in the strength of the relationship between mortality and fertility in Kenya. Indeed, child mortality was one of the main factors used to explain the high fertility rate in Kenya during the late 1970s, and child survival programs were estimated to be more cost effective than family planning programs in terms of lowering fertility (Cochrane and Zachariah,1984~. Looking at the linkage between child mortality and contraceptive use, Njogu (1992) identified in the late 1970s a strong and negative effect on contraceptive use among women who had experienced child loss. Ten years later the overall level of child mortality had declined and the effect of contraceptive use had lessened. Kelley and Nobbe (1990) point to the

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262 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON high correlation between infant mortality and family planning use at the regional level, the highest use of contraceptives being found in areas with low infant mortality. Jensen's study (1996) uses data from two areas in Kenya (the Muslim Kwale in Coast Province and the Christian Bungoma in Western Province) and finds a strong influence of child mortality on fertility and contraceptive use, suggestive of hoarding behavior. In both areas child mortality is associated with high fertility and constitutes the strongest barrier toward using modern contra- ceptives. There are virtually no good ethnographic studies of relevance to the fertility response to child loss in Africa. The only published work to our knowledge is the study by Folta and Deck (1988) in Zimbabwe. This study uses participant obser- vation and in-depth interviews of 124 Shona women in Zimbabwe to show that social pressure to replace a dead child can lead to immediate pregnancy with poor nutrition, poor infant health, and thus a recurring cycle of infant death. In this setting, the death of a child (especially the first child) potentially undermines the stability of the family, its social relationships, women's health and status, eco- nomic security, and marital longevity. HYPOTHESES Fertility is inextricably bound up with many aspects of economic and social behavior. At both the micro and the macro level, it is useful to think of fertility as mediated by a set of variables defining exposure to intercourse, the probability of conception, and the probability of successful gestation and parturition. These intermediate variables constitute components of a conceptual framework of the determinants of fertility, which, by definition, must stand between fertility and any type of social or economic explanation. All elements of choice or social behavior work through the intermediate variables to influence fertility. The relationships between infant mortality and fertility are exceedingly com- plex, and many of the factors involved are poorly understood. A joint decline of infant mortality and fertility rates in recent years as observed in Cameroon is typical for a number of African countries (for reviews, see Locoh and Hertrich, 1994; Hill, 1993; Cohen, 1993) and non-African countries (United Nations, 1987) over the past decade. The sources of this correlation may be categorized accord- ing to the direction of the effect. First, infant mortality and fertility may be positively correlated if both in- vestments in child health and demand for children are functions of the same prevailing influential variables (Preston, 1978; Panis and Lillard, 1993~. Second, a rapid pace of childbearing may cause high mortality. The over- whelming evidence is that short birth intervals have strong effects on infant and child mortality; such a result has been reported in Cameroon (Kuate Defo and Palloni, 1996) and elsewhere (for a review, see Hobcraft, 1994~. This effect of fertility on mortality can occur because of (1) increased sibling competition for

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BARTHELEMY KUATE DEFO 263 resources (including child care, family assets, and income); (2) increased oppor- tunities for transmission of infectious diseases as a result of overcrowding, which has been shown to be an important determinant of infant and child mortality in Cameroon; or (3) the maternal depletion syndrome, in which a rapid pace of fertility may imply that the mother has not had sufficient time to regain her health or nutritional status to adequately host a fetus and facilitate its normal growth. Finally, high child mortality may induce high fertility (Preston, 1978~. This may happen as a result of several mechanisms. The death of the child initiating the birth interval may trigger the rapid closure of the interval either through a physiological replacement mechanism whereby the death of the child leads to cessation of breastfeeding and the consequent shortening of postpartum amenor- rhea; through a volitional replacement mechanism (that is, the responsiveness of pregnancy decisions to the occurrence of the death of infants who either never breastfed or stopped breastfeeding before death); or through a generalized sur- vival uncertainty (that is, as the probability of survival falls, there is also a tendency to have children earlier and thus closely spaced). In assessing the effects of infant mortality on fertility, I depart from previous studies on Africa (and reviewed above) and other parts of the world that have shown that, over the course of the family life cycle, couples learn about child- bearing and child mortality (e.g., Preston, 1978; Ben-Porath, 1978; Mensch, 1985; United Nations, 1987~. These experiences may well lead them to revise and adjust their desired number of children and possibly diminish or increase their propensity to replace deceased children. Because we do not explicitly model breastfeeding and contraceptive behavior (since these variables may be endog- enous to the fertility decision), we cannot empirically distinguish these two causal mechanisms directly for the short-term replacement effects. (That is, we cannot separate the physiological from the volitional replacement effects of the death of child of parity i who opens the interval [i, i + 1) and dies within the first year and before the conception of the child of parity i + 1.) In this case we group these two physiological and volitional replacement mechanisms of increased risks follow- ing conception under the term "replacement behavior." Moreover, it has been shown that, in many parts of sub-Saharan Africa where prolonged breastfeeding is prescribed and sexual intercourse during lactation is forbidden, the physiologi- cal effect is culturally built into behavior patterns (Ware, 1977~. For the long- term replacement effects in the subsequent intervals, significant effects of the death of a child of parity i on the hazards of conceiving children of parity i + 2, i + 3, i + 4, and so forth cannot be ascribed to a biological/physiological mecha- nism but only to a volitional (behavioral) mechanism, as discussed below. Fur- thermore, because the level of contraceptive use is low in Cameroon (the level of use of efficient contraceptive methods was 2 percent in 1978 and only 16 percent in 1991 of which one-fourth was accounted for by modern methods) and there has been no marked increase in contraceptive use between the two surveys (DSCN, 1983; Balepa et al., 1992), the probability of using contraception in a particular

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264 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON period would change marginally. This is tantamount to confining our analysis to women who did not use any form of contraception during the waiting time to succeeding conception. Thus, the very nature of the data (mostly noncon- tracepting women) allows us to isolate to a greater extent the mediating effect of breastfeeding alone on conception rates in response to mortality. This is a "natu- ral" sample and there is no bias since women who do not use contraception are not self-selected for lower fertility. There is as yet little evidence of conscious limitation of family size in most sub-Saharan African societies (Caldwell and Caldwell, 1981; van de Walle, 1992~. Evidence indicates that, in most sub- Saharan African societies, postpartum abstinence is practiced specifically to en- sure that the supply and quality of breast milk are adequate and to enhance child survival (Page and Lesthaeghe,1981~. Knowledge and use of indigenous contra- ceptive practices usually seem to be aimed at preventing conception at certain times (thus affecting the waiting time to the next conception and birth) or from certain unions that are undesirable, rather than at limiting the ultimate size of the family. Hence, the potential effect of a child death on birth spacing is at its maximum in this setting. In this chapter, I test three hypotheses regarding the fertility responses to child death: Hypothesis 1: A child death has both instantaneous (short-term) and lagged (long-term) effects on conception risks (or birth-to-conception intervals). The instantaneous effect is likely to be more important in a setting where there is little conscious decision to space births or to limit fertility, and couples practice little or no contraception, as in Cameroon until the late 1980s (Balepa et al., 1992~. Hypothesis 2: The fertility response to child loss is stronger for the death of first-parity births (and eventually second-parity births) than for the death of higher-parity births. Many African societies attach special cultural values to the first offspring. This may affect the way the survival of the first born is perceived by the couple and the community, and a loss of a first child by death is often interpreted as the failure of the mother to fulfill her proper role in society. In most African societ- ies, women are expected to become pregnant shortly after marriage, and the pressure on these women is often high to produce living children so as to secure their status with the husband's family. For example, Folta and Deck (1988) note that among the Shona in Zimbabwe, it is after the birth of the first child that women are provided with their own dwellings, and it is critical that certain rituals be followed properly to prevent illness and death of this child. The eagerness with which African unions are stabilized is reflected in the quantum and tempo for the first birth: First-birth intervals are typically shorter than other intervals. For the new mother, the firstborn is a sign of belonging to a

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BARTHELEMY KUATE DEFO 305 simple hazard model provides no insight into the effects of that selection. Fi- nally, this model has the unfortunate characteristic of mixing the parameters for the speed with which the event occurs with the parameters for whether or not the event occurs. No such restriction follows from economic theory. A dynamic econometric strategy that addresses these problems has been formulated by Heckman (Heckman and Singer, 1985; Heckman and Walker, l991~. Heckman's formulation is in continuous time and consists of applying systems of hazard models (Heckman and Walker, 1991~. Life-cycle fertility is naturally analyzed using the standard birth process of the stochastic processes literature (Hoer et al., 1987; Sheps and Menken, 1973) where completed fertility is viewed as the result of separate processes governing the transition to each parity. In its most general form, the model posits that current period fertility is a function of age, time since last birth, the woman' s time-invariant (observed and unobserved) characteristics, and all the time-varying covariates (both observed and unobserved). Thus, one has a system of hazard models (one for each parity) linked by woman-specific common observed and unobserved covariates. Newman and McCulloch (1984) and Heckman and Singer (1985) developed a refinement (in continuous time) of this system of hazards approach, and their model suggests some natural simplifi- cations of this general (inestimable) specification. In Heckman's feasible estima- tion in continuous time (and applied in this study), the current period hazard is modeled as a linear index function that includes a general function of the age of the woman and a general function of the duration since the last birth. A woman's birth history is assumed to evolve in the following way. The woman becomes at risk of conceiving the first birth at calendar time ~ = 0 (here assumed to be the date of first marriage). I define a finite-state continuous-time birth process Bath, ~ > 0, B(~) Q. where the set of possible attained birth states (parities) is finite ED = (0,1,2,...,N), N < Ad. Q defines the number of children born. B(~) is parity attained at time I. Transition occurs on or after ~ = 0. I assume that all durations Ti,...,TN conditional on the appropriate history H have absolutely continuous distributions. In my specification, and following Heckman's formulation in continuous-time of the system of hazards approach to fertility behavior (Heckman and Singer, 1985; Heckman and Walker, 1991), I implement a continuous-time approach to the system of hazard models of fertility response to infant and child mortality. Within the framework of this system of hazards, if a woman becomes at risk for the conception of the JO birth at time ~0 - 1), the conditional hazard at duration tj is j~tj | Harm- 1) + tj]) = poll {tj | Harm- 1) + tj]) expL\~.Dur~t) + AX + 1ljY(t) + djZ(t)], (1) where t is the waiting time to conception (that is, the birth-to-conception interval t) for a given woman. Z(t) captures the mortality effects, X represents a vector of time-invariant covariates, Y(t) represents a vector of time-varying covariates, and

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306 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON Dur(t) is a vector of duration dependencies. If no child dies, Z(t) is set to zero. These variables are described in greater detail in the text. The baseline hazard ,Uoj {tj | Hand - 1) + tj] ~ is a risk shared by all women. Under the assumption that all durations Ti,...,TN are absolutely continuous given H. equation (1) can be integrated to obtain the survivor function: S{tj ~ H[~0 - l ~ + tj] ~ = expel- k Thou I Hang - l) + u] ~ dull, (2) I = O. 1, ..., tj. Under this function of survivorship, the birth process evolves as follows. A woman at risk for a first birth at ~ = 0 continues childless a random length of time ti governed by the survivor function S{ti | HE~0) + ti] ~ = expL- ~ (Lou | HE~0) + u] ~ dull, I = 0, ..., tit (3) At calendar time To = ~1), the woman conceives and moves to the state B(~) = 1. In the general case where Balk = k - 1 for Ark - 1) < T < take, and To = Arks - tick - 1) is governed by the conditional survivor function: S{tk | H[~(k - 1) + tk]~ = expL- ~ (pk{U | Hawk - 1) + ups dull, (4) I=0, 1,...,tk. Thus, the conditional density function of duration Tk = tk is (pk~tk I H[~(k-1) + tki) )(S{tk I H[~(k-1) + tki) ). (5) If Hincludes all relevant conditioning information of the entire birth process, the conditional hazard function of ATE, A, TN) given HE~0) + Iitii, (i = 1, ..., N) is therefore Anti ,- ., tN I HE~0) + Citify = Elk ~k~tk I H[~(k-1) + tkil, (6) where k = 1, ..., N and i = 1, ..., N. To simplify the notation, denoting Mu the conditional hazard function of the birth process in equation (6), I obtain from equation (1~: AT Elk look {tk I H[~(k-1) + tk] ~ exp[\kDur~t) + p~ + ~kY OCR for page 254
BARTHELEMY KUATE DEFO 307 transition to each parity separately from how they affect completed family size (for a review, see Hotz et al., in press). Estimation of the joint hazard function defined in equation (7) proceeds under the assumption that the baseline hazard function can be efficiently repre- sented by a Weibull hazard model defined as AT ilk eXP[7k + 0/ + ~kY(t) + ~kZ(t)it~k ~ (8) where Ok and ilk are the intercept and the slope of the Weibull hazard for the risk of the conception of the kid birth at time Ark- 1), respectively. Note that rook {tk ~ Hawk 1) + tki) = eXp[7k + ark logy = exp(7k~t~k (9) specifies the Weibull hazard rate. The Weibull hazard model is used because previous studies from various settings within the framework of dynamic models of fertility behavior (e.g., Lancaster, 1985; Heckman and Walker, 1987, 1990, 1991; Popkin et al., 1993) have shown that the duration structure of life-cycle fertility is well represented by a Weibull. Furthermore, the Weibull distribution is an important generalization of the exponential distribution and allows for a power dependence of the hazard on time. Finally, the Weibull model is, to some extent, preferable to other models because of the larger maximized log likelihood (Kalbfleisch and Prentice, 1980~. In the models specified so far, I have assumed that all covariates that might confound the association between child mortality and fertility are measured. This is unlikely to be the case if unobserved population heterogeneity is present. Indeed, Heckman et al. (1985) have shown the empirical importance of account- ing for unobservables in the analysis of timing and spacing of births, both on policy and interpretive grounds. Accounting for them is often necessary so as to produce estimates that isolate genuine behavioral effects of covariates (such as child mortality) on fertility, and the existence of unobservables provides a moti- vation and interpretation for the presence of statistically significant lagged birth intervals in fitted survival rates for birth parities beyond the first parity (Heckman and Walker, 1991~. Hence, although the methods for dealing with unobserved heterogeneity in demographic research are still undeveloped (Trussell and Rodriguez, 1990), it is possible to assess the sensitivity of my estimates to unob- served heterogeneity. Almost always, whenever unobserved heterogeneity has been introduced in waiting-time models, a random-effects structure has been assumed; I follow that tradition. At the individual level, fertility regressions are generally subject to the standard unobserved individual characteristics concern of the labor supply literature (for a review, see Hotz et al., in press). In my specifi- cation, I distinguish two forms of heterogeneity in life-cycle fertility: woman- specific unobserved characteristics that are known to the woman and affect her

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308 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON reproductive behavior and parity-specific unobserved characteristics that are not known to the woman but that may produce their own dynamics if the woman learns about her unobservables over the life cycle, as discussed in the text. My concern for parity-specific unobserved characteristics in fertility analysis follows a long-standing demographic tradition that postulates changing female fecundity across parities as an important determinant of fertility (Gin), 1924; Sheps, 1965; Sheps and Menken, 1973~. Fecundity differences among women undoubtedly contribute to declining parity-specific hazards that are a universal feature of fertility data, but it is difficult to obtain good measures of fecundity (Bongaarts, 1981; Acsadi et al., 1990~. Heckman and Walker (1991:11-15) show that, under most conditions, if there is persistent heterogeneity across parities, estimates of the parameters of the hazards obtained by estimating the model separately will be biased. Cameroon is a quasi-non-contracepting (natural fertility) society through the late 1980s. In such a setting, my dynamic formulation of the fertility behavior models implies that woman-specific (approximately) time-invariant population heterogeneity in the unobserved component of preferences (including coital fre- quency assumed to be time-invariant within each period or interval) and response to child mortality experience will not always have similar effects on interbirth timing as it has on first-birth timing. Such differences in effects is implicit in my dynamic formulation that treats timing of first birth separately from birth spacing. The assumption that the unobserved component of the model is time invariant underlies the classical demographic model of fecundity of Gini (1924), Sheps (1965), and Sheps and Menken (1973~. These unobserved characteristics are assumed independent of the initial state of the birth process. Thus, consistent with Heckman's general formulation (Heckman and Singer, 1985; Heckman and Walker, 1987, 1990, 1991), my specification of the heterogeneity detaches the interval until the first birth from subsequent interbirth intervals. Such an ap- proach is more appealing in developing countries in general than in developed countries, because the modal family size (around five children per woman in Cameroon) in the former is considerably higher than in the latter (it stands at about two children per woman). This implies that in developed countries, there will be generally one interbirth interval (as in the Heckman and Walker's (1990) study in Sweden where third births are not common and fourth births are rare), making estimation of the correlation in unobservables between interbirth inter- vals impossible; this is in contrast to the situation in sub-Saharan African coun- tries (and in Cameroon in particular) where the average family size is five or higher. Strongly peaked preferences for a given number of children will be fitted through nondefective hazards for parities below the desired fertility size and essentially zero hazards thereafter. This was the case, for example, in Heckman and Walker (1987,1990,1991), who use this characteristic of the model to focus on the decision to have a third child in Sweden, and in the present study where I use this feature of the model to focus on the decision to have a sixth child in Cameroon. I account for woman-specific and parity-specific unobserved hetero

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BARTHELEMY KUATE DEFO 309 geneities by augmenting the conditional hazard in equation (8) to obtain the following form: But,..., to I HE~0) + Iiti]; O. d,) = Elk exp [7k + p~ + ~kY(t) + ~kZ(t) + (k~ + Skeet k (10) where (I) represents the unobserved characteristics of the woman, and d) captures the parity-specific stopping unobserved characteristics. In my empirical imple- mentation of the system of hazards described here, I estimate the distribution of unobservables by the nonparametric maximum likelihood estimator (NPMLE) procedure described in Heckman and Singer (1984~. This procedure approxi- mates any distribution function of unmeasured covariates with a finite mixture distribution. The approximation is designed to maximize sample likelihood. Each of the parameters (including the factor loading on the random effect) is allowed to vary with parity. Because equation (10) produces estimators obtained from exponential models based on a maximum likelihood approach, those esti- mators are generally more efficient than those obtained from nonexponential waiting-time distribution models (Olsen and Wolpin, 1983; Wolpin, 1984~. A useful feature of the Heckman and Singer (1984) NPMLE used here is that it allows for the possibility of point mass d) = -no, a value that sets hazard (10) to zero to allow a distinction between limiting behavior and the biological sterility discussed in the text. The only model in the literature similar to the Heckman' s formulation is that of Newman and McCulloch (1984) who estimate a birth process with duration dependence modeled as a three-point spline and assume a parametric distribution of the unobserved heterogeneity, which excludes parity- specific unobserved heterogeneity. Basically, they take the random effect to be person-specific and time invariant. In my empirical implementation of the speci- fication of the woman-specific time-invariant random effect, I use Heckman and Singer's (1984) NPMLE for the mixing distribution of the heterogeneity compo- nent, since, when parametric models are used, the results are sensitive to the distribution imposed on the unmeasured covariates. Following Heckman and Walker (1987, 1991), I generalize this system of hazard models to include previous durations; that is, for the transition to second birth, I have as covariates the duration between first marriage and first birth, in addition to the time of exposure to the risk of conceiving a second birth since the birth of the first birth; for the transition to the third birth, I have as covariates the duration between first marriage and first birth, between first and second births, in addition to the time of exposure to the risk of conceiving a third birth since the birth of the second birth, and so on. Clearly, women who experience a first birth learn something about their d>, and this information might enter their information set and affect fertility decisions (e.g., coital frequency, contraceptive decisions) for the second birth. In particular, I model the probability of no birth within interval t of the jth birth (the survivor function) as

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310 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON Sj~tj ~ Harm- 1) + tji, O) =P(i-~)+ r1 -P(i-~)3 Em [1 -hiked, (11) k = 1, 2, ..., N. where hake is the probability of the JO birth in interval t, conditional on the jib birth not having occurred through interval t- 1. In other words, this survivor function is the probability of parity-specific stopping behavior after the ~ - Ah birth, plus the probability that there is not parity-specific stopping behavior, but that the birth has not occurred yet. Because the fertility process only runs for a finite time (in the WFS and DHS surveys and in the CWFS and CDHS in particular, the fertility process is truncated at age 49), some of the (1 - P) women who do not exhibit parity-specific stopping behavior will nevertheless never have the jib birth, eventually under some time path of covariates according to the specification of the model. Uncorrected heterogeneity leads to biased estimates of duration variables. Unobserved variables are permitted to be functions of time since marriage (for the transition to the first conception) and since the last birth (for the transition to subsequent a conception). For example, the fertility level and schedule of women who experience a child death at a given point in time is a biased estimate of the fertility level and schedule that women with similar observed characteristics would have had had they not experienced a child death. Thus, the fertility responses to a child death may not be only a function of other measured charac- teristics of the woman, but may also be related to unmeasured characteristics associated with each woman and each parity of a particular woman. This system of hazards formulation in continuous time suggests natural re- strictions on how the covariates enter the model. As in the static models, my models are implemented including only current period (interval) covariates in the current period (interval) hazard. The model thus summarizes the values of past and current covariates through its dependence on parity, time since first marriage, time since last birth, and the dynamic selection of the time-invariant random effect (or unobserved heterogeneity). A general multistate computer program, CTM, is used to estimate the model (Yi et al., 1987~. ACKNOWLEDGMENTS This research was supported by a grant from the Subvention Generale du Conseil de Recherche en Sciences Humanes of Canada to the University of Montreal. Thanks are due to Joel Tokindang for his research assistance, and to Mark Montgomery, Tom LeGrand, Julie DaVanzo, Alberto Palloni, Barney Cohen, and two anonymous referees for their insightful comments on an earlier draft of this manuscript.

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