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

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

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

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

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

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

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).

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).

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

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

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

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

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

BARTHELEMY KUATE DEFO 265 new family and confers the status of a full family member for her in her husband's family. Thus, a number of rituals are associated with the birth of the first child. The new mother must fulfill these rituals to ensure her progeny. Pregnancy, for example, calls into play a series of rituals that are required to assure the continued fertility of the woman and protection of her children. Hence, the death of the firstborn (or second births) may have a large effect on both short- and long-term fertility responses, far exceeding the simple replacement effect. Hypothesis 3: The fertility response to a child loss (and the importance of mechanisms discussed above) varies by parity. Most previous studies of the effects of child mortality on fertility have as- sumed that those effects were the same across parities. Preston (1978:7) points out that in populations where conscious limitation of family size is negligibly impor- tant, completed family size can be viewed simply as the cumulative outcome of uncorrelated birth intervals spanning a woman's reproductive life. In such populations, it is legitimate to regard intervals and completed family size as simultaneously determined: hence interval effects translate immediately into fertility effects. This argument is consistent with observations from a number of studies on Af- rica. We allow the fertility response to infant and child mortality as well as the effects of all other measured and unmeasured variables to vary both by parity and duration of exposure. DATA SOURCES In the empirical analysis in this chapter, I use data from the 1978 Cameroon World Fertility Survey (CWFS) and the 1991 Cameroon Demographic and Health Survey (CDHS). The core questionnaires were very similar, making it easy to undertake comparative studies. Given the differences in behavior that may be expected between ever-married and never-married women, I restrict my data to fertility of ever-married women who did not have a premarital birth.) The CWFS was conducted from January to October 1978 under the auspices {Premarital births were dropped from the analyses because of the imprecision about the beginning of exposure and the duration of exposure to the risk of bearing a child and because it is not known the extent to which the survival status of the premarital birth may be related to fertility behavior of the women later in marriage. In general, premarital births are not identified as belonging to the girl in rural areas where there is a strong sense that a premarital birth is a shameful experience, bringing dishonor, disgrace, and embarrassment on the family of the woman, and parents will generally claim the birth as their own to avoid this. However, in trial analyses including women with premarital births, none of my inferences are altered and the conclusions from this study remain robust.

266 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON of the Cameroon Ministry of Planning and Regional Development in collabora- tion with the WFS. The CWFS is a large in-depth survey and the first that is nationally representative of Cameroon. A total of 8,219 women aged 15-54 years answered questions about their fertility, marriage histories, and other characteris- tics. Of these women, 1,253 were excluded from the analysis because they were aged 50-54, never married, or had had premarital births. The CDHS is a nationally representative sample of 3,871 women aged 15-49 years. Of these women, 835 were excluded because they were never married and 432 were excluded because they had premarital births. The final sample is comprised of 2,604 ever-married women with no premarital births. A preliminary inspection of the data revealed that the sample does not differ in terms of mortal- ity statistics from the original sample, and differences in fertility patterns be- tween the two samples are quite marginal. One drawback of the WFS- and DHS-type data sets is that the characteristics of parents are documented only at the time of the survey and not at the time that each child under study was exposed to the risk of mortality or each woman was exposed to the risk of a new conception. These characteristics may have changed during the reproductive life of the women and differed at the time of birth or death of their children. In most studies based on these data, the analysis is based on the assumption that those characteristics remain the same for a sufficiently long period into the past. Because I do not have such background variables that follow the sequence of exposure and occurrence, I make that assumption here as well. The selected variables are defined in Table 8-2. By construction, the estimated intervals measure the period from a birth to the conception of the next live birth. They are based on data for month and year of birth of children reported retrospectively in 1978 (for the CWFS) and 1991 (for the CDHS). In the CWFS, from the birth history data involving all births, both the year and month were reported for 41 percent of all births, the calendar year (but no month) was given for 48 percent, whereas for 11 percent of all births dates were reported in terms of "years ago" or age at event (Kuate Defo, 1996~. This implies that some dates of births (in months) were imputed. The imputation procedure in the WFS used other information reported by the respondent from which a logical period within which the birth probably occurred and then ran- domly assigned a date within that period. This situation can create problems in the analysis of birth intervals. For example, in the case of a following concep- tion, the problem may arise from the fact that the timing of the following concep- tion (or birth) is unspecified, and there may also be the possibility of reverse causation, misclassification of exposure, or selection bias. Strategies for dealing with these problems are considered in the Appendix. These data also provide the opportunity to relate the length of interbirth intervals to the survival status of previous children. Obviously, any variations between women in interbirth intervals that can be attributed to differences in child death experience give only a partial measure of the replacement effect

BARTHELEMY KUATE DEFO TABLE 8-2 Definition of Variables Used in the Multistate Hazards Analysis 267 Variable Definition Specification Duration (DUR) measures Exposure since first marriage (DUR1) Exposure since first birth (DUR2) Exposure since second birth (DUR3) Exposure since third birth (DUR4) Exposure since fourth birth (DUR5) Exposure since fifth birth (DUR6) Child mortality measures (CMM) The child who opens the birth-to-conception interval [i, i + 1) dies in his first year of life and at least 1 month before the conception of the child of parity i + 1 (i.e., the child closing the interval) (CMM1) The child who opens the birth-to-conception interval [i, i + 1) dies at least 1 month before the conception of the child who closes the future intervals [i + 2, i + 3) or higher (CMM2) The first (second) birth dies in the first year of life and at least 1 month before the conception of children of higher parities (CMM3) Number of months/100 spent in the current spell Length of the first conception interval, measured in months/100 Length of the second conception interval, measured in months/100 Length of the third conception interval, measured in months/100 Length of the fourth conception interval, measured in months/100 Length of the fifth conception interval, measured in months/100 Length of the sixth conception interval, measured  in months/100 Series of time-varying dummy variables capturing the sequencing of an infant death and couple's future reproductive behavior A dummy time-varying variable = 1 if a mother lost her child who opens the birth-to-conception interval [i, i + 1) in his first year of life and at least 1 month before the conception of the index child (i.e., the child of parity i + 1) (N.B.: this measure confounds the physiological and volitional replacement effects) A dummy time-varying variable = 1 if a mother lost her child who opens the birth-to-conception interval [i, i + 1) in his first year of life and at least 1 month before the conception of the child of rank i + 2, i + 3, i + 4, and so forth (N.B.: captures both infant and child mortality) A dummy time-varying variable = 1 if a mother lost her first (alternatively second) birth in his first year of life and at least 1 month before the conception of child of rank 2, 3, 4, 5, and 6 (alternatively rank 3, 4, 5, and 6) continued on next page

268 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-2 (continued Variable Definition Specification Mother has some education Low-fertility ethnic groups Muslim religion Employed before first marriage Sex composition of previous living children Changes in marital status Time trend A dummy time-invariant variable = 1 if a mother has attended primary level education or higher, and O otherwise A dummy time-invariant variable = 1 if a mother is affiliated with the ethnic groups of the Grand North and the East regions A dummy time-invariant variable = 1 if the mother is a Muslim, and O otherwise A dummy time-invariant variable = 1 if the woman was employed outside the home before her first marriage, and O otherwise A dummy time-varying variable = 1 if a mother has more previous living boys than girls, and O otherwise A dummy time-varying variable = 1 if a marriage or remarriage was dissolved (e.g., by divorce, separation, or death of the spouse), and O otherwise A dummy time-invariant variable = 1 if the conception occurred within the last 10 calendar years preceding the survey date because replacement of lost children can be accomplished not only through changes in birth intervals but also through prolonging the reproductive period. In addition, those aspects of the intentional replacement effect that influence timing will be mixed with the physiological effect, particularly in populations where family planning is practiced. FORMULATION AND ESTIMATION OF FERTILITY RESPONSE TO CHILD LOSS I formulate and implement a multistate duration hazard model as a frame- work for estimation of the effects of child mortality on fertility (for details, see the Appendix). My model assumes that experienced child mortality is exogenous to fertility behavior and that there is no other source of correlation between  mortality and fertility. This assumption excludes the possibility of hoarding behavior and ignores any other trade-off. This simplification is justified to some

BARTHELEMY KUATE DEFO 269 extent because there is apparently little evidence of either hoarding behavior or selectivity of child mortality in the fertility process in Cameroon, in part given the high incidence of sterility and strikingly low levels of contraceptive use in this setting. My empirical specification models fertility as a sequential decision- making process with a stochastic component whereby, at each moment in time, the couple decides on behaviors that affect the risk of conception. Life-cycle fertility is only one aspect of female life-cycle behavior. In this chapter, I focus on fertility histories, ignoring possible interrelationships between fertility and other life-cycle behavior such as labor supply, education, and marital decisions. My approach aims to estimate parameters of hazards for times to conceptions. Estimated parameters measure direct (given other decisions) and indirect (through other decisions) effects of infant mortality on fertility transitions. My unit of observation is a woman's entire fertility history, with a hazard equation for each birth-to-conception interval. The timing of a conception may depend on the duration since the wedding date (i.e., the age of the woman at first marriage), the duration since the last birth, the birth order, and the duration since a child died. I limit the analysis to fertility of ever-married women (thereafter referred to as marital fertility), that is, the woman first becomes at risk of a conception at the wedding date. Each subsequent conception interval starts at the date of termination of the previous pregnancy, which is the birth date of the previous child. I limit the analysis to conceptions ending in live births because, in most developing countries, reporting and dating of miscarriage, stillbirths, and induced abortions are known to be heavily flawed. Furthermore, much of this information was either not recorded in my data sets or the timing of events was unknown or the duration variables were heavily distorted. I account for these unmeasured characteristics in fertility outcomes by entering in the estimation equations woman-specific and parity-specific unobserved components. I do not account for a period of postpartum anovulation beyond the first month infertile period following a birth because the duration of this period can be influenced by the mother through the duration and intensity of breastfeeding. As such, breast- feeding is a form of contraception and endogenous to the fertility process. Larsen (1994) found that contraception has only a minor effect on estimates of sterility and fertility in countries such as Cameroon in which modern methods are cur- rently used by 6 percent or fewer of the female population of reproductive age. My analysis places fertility behavior within a life-cycle perspective. A com- mon way of characterizing the timing of births is in terms of the probability of a woman's first birth at different ages (or duration of exposure) and spacing be- tween subsequent birth parities (Hotz et al., in press). My modeling strategy of the effects of infant death on fertility starts with the premise that fertility is usually indicated by birth spacing, parity, and maternal age at maternity. I incor- porate these three dimensions of fertility by estimating dynamic models of the timing and spacing of births, while allowing those effects to vary by parity. I estimate the joint probability of first, second, third, fourth, fifth, and sixth con

2 70 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON captions, respectively, conditional on reaching the beginning of each subsequent interval without having had a conception of the next rank. Thus, I estimate dynamically the effects of infant mortality on fertility intervals. This approach is analogous to a piecewise hazard analysis of birth intervals (which would have involved as many separate likelihood functions as there are pieces of intervals) (e.g., Rodriguez et al., 1984; Mensch, 1985), except that it enriches this strategy by jointly estimating all birth intervals so that there is only one likelihood func- tion to be computed (Heckman and Walker, 1991; see also the Appendix). I model the duration of exposure to the risk of conceiving the JO child using a Weibull model (Lancaster, 1985; Heckman and Walker, 1991~.2 I model this by estimating the conditional fertility function: conditional on the number of chil- dren a woman has, what is the likelihood that she will bear another child given her mortality experience since a given prior time. Clearly, a young woman of high parity must of necessity have had closely spaced births, whereas an older woman of lower parity may well have had long intervals between her children. I allow for this time-varying covariate by estimating jointly the effects of covariates within distinct time-to-conception intervals (parities). Thus, the effects of each covariate are allowed to vary over a woman' s reproductive career through inter- actions with each period of exposure to the risk of conception. For example, the effects of mother's education are evaluated jointly for the following intervals: (1) from marriage date (or age at first marriage) to first conception, (2) between date of first birth and conception of second birth, (3) between date of second birth and conception of third birth, (4) between date of third birth and conception of fourth birth, (5) between date of fourth birth and conception of fifth birth, and (6) between date of fifth birth and conception of sixth birth. Thus, at a given parity, I have the cumulative reproductive history of the woman until that parity. Duration Dependencies Burst) In the absence of infant mortality, the baseline hazard function duration dependence Drift) consists of the duration of exposure to the risk of conception (i.e., the duration since the woman became at risk of conceiving the JO child). It includes, respectively, a general function of the age of the woman that corre- sponds to the wedding date (or maternal age at first union) for first conceptions and a general function of the duration since the last birth (or the birth date of the child initiating the birth-to-conception/censoring interval) for subsequent inter- vals. 2I also experimented with alternative specifications of the fertility response to changes in infant and child mortality by formulating hazards models assuming both the piecewise exponential (propor- tional hazard) and a Gompertz hazard model for the risk of a subsequent conception starting with the first birth, but none of my conclusions was altered with these alternative specifications.

BARTHELEMY KUATE DEFO Child Mortality Measures Z(t) and Replacement Effects 271 In this chapter, I am especially interested in the timing of replacement and the relationship between replacement strategy and family size. This is because little attention appears to have been paid in studies of the fertility response to child loss, to the possibility that such fertility behavior may be linked to achieved parity. Replacement behavior is detected by the inclusion of a series of measures of experienced child mortality. I explicitly account for the possibility that the effect of a child death on fertility may vary over time through the woman's reproductive life cycle. The replacement behavior is specified as a time-depen- dent variable. The death of a child is assumed to have both an instantaneous and lagged effect. I assume that the replacement effects may be parity dependent and may differ by such characteristics as religion, ethnicity, time period, and the sex composition of the surviving children. My formulation departs from previous procedures in the way I define the time-varying variables that capture the effects of the death of the child who opens the birth interval. I first estimate a series of models with infant mortality time- dependent covariates as dummy variables, each indicating whether the child who opens a given birth-to-conception interval has died: at least 1 month before the conception of the child who closes that interval; before the conception of the child who closes the immediately succeeding birth-to-conception interval; and so forth. For example, when assessing the effects of child mortality on the birth interval [i, i + 1), I examine whether the death of the child of rank i antedated the conception of child of rank i + 1. I also assume a normal conception period of 9 months plus an extra month of postpartum infertility following birth; I recognize that in the absence of good data on gestational length from most surveys- premature births are a particular case in which there may be confusion of cause and effect. A premature birth of rank i + 1 is associated with a shorter birth-to- conception interval [i, i + 1) because the duration of gestation is less than a full- term birth of 9 months. Also, prematurity increases the risk of stillbirth or infant death (Bakketeig et al., 1979; Hoffman and Bakketeig, 1984~. To purge for this potential bias, I assess both jointly and sequentially the effects of the death of child of rank, say i, on the birth-to-conception of live birth intervals [i, i + 1), [i + 1, i+2), [i+2, i+3), [i+3, i+4), end so forth. To assess the short-term effects of a child death, I measure the extent to which the death of a child of parity i (the child who opens the birth-to-conception interval [i, i + 1~) occurring in the first year of life and at least 1 month before the next conception of a child of parity i + 1 (the child who closes the birth-to- conception interval [i, i + 1~) significantly increases the risks of conceiving the child of parity i + 1. The fertility effects of an infant death in its first year of life and before the next conception is a mixture of the physiological effects (having to do with the curtailment of breastfeeding) and volitional replacement effects. The

2 72 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON mean duration of breastfeeding in Cameroon has changed little over time (19.3 months in the 1978 survey and 19.8 months in the 1991 survey). To assess the long-term effects of a child death, I use two measures of child mortality. The first captures the extent to which the death of a preceding child of parity i (i.e., the child who opens the birth-to-conception interval [i, i + 1~) at least 1 month before the conception of a child of parity i + 2, i + 3, i + 4, and so forth (i.e., the child who closes the birth-to-conception interval [i + 1, i + 2), [i + 2, i + 3), [i + 3, i + 4), and so forth, respectively), significantly increases the risk of conceiving a child of parity i + 2, i + 3, i + 4, and so on, respectively. In this case, the estimated causal effects of child loss on fertility will be termed "long-term" mortality effects since they operate in future subsequent intervals for which the child whose death is of interest is not the child who opens that birth-to-concep- tion interval. Furthermore, available evidence from Africa and elsewhere (for reviews, see Page and Lesthaeghe, 1981; Hull and Simpson, 1985; Winikoff et al.,1988; Popkin et al., 1993) has established that a major determinant of breast- feeding cessation is a new pregnancy, in that women stop breastfeeding once they realize they are pregnant. Thus, if I find, for example, that the death of child i significantly increases the risk of conception of child i + 2, i + 3, i + 4, and so on, I am then certain that such effects cannot be contaminated by prematurity or be ascribed to the physiological effect of lactation. Hence, the long-term mortality effects will be essentially attributable to behavioral (volitional) replacement ef- fects. The second measure examines the effect of the death of the first (or the second) child in its first year of life and at least one month before the conception of subsequent siblings, as the risk of conceiving a child of a higher birth order. Exogenous Time-Invariant Factors X and Time-Varying Regressors Y(t) The time-invariant exogenous variables include maternal education, ethnicity, religion, and employment before first marriage. These variables were selected for analyses because they have been shown to covary with child survival and reproductive behavior in Cameroon (Kuate Defo, 1996; Kuate Defo and Palloni, 1996; Larsen, 1994, 1995~. The time-varying exogenous variables in- clude the sex composition of the previous surviving siblings and marital dissolu- tion. I do not directly control for breastfeeding and contraception since these variables may be endogenous. Maternal Education Education, especially female education, has been seen theoretically as influ- encing fertility in several possible ways. Female education potentially raises the value of her time through the labor market, which means that the opportunity cost of her time forgone in child care is greater. This means that maternal education is likely to have effects on fertility independent of its economic implications

BARTHELEMY KUATE DEFO 273 (Rodriguez and Cleland, 1981), and some have argued that it is the cognitive shifts that education brings which are important in explaining its link to lower fertility and higher contraceptive use (Cleland and Wilson, 1987~. Following Ben-Porath (1978), I treat mother's schooling as reflecting the long-term desired family size, given the evidence on the fertility-education link in Africa (Acsadi et al., 1990~. Ethnicity In countries with considerable ethnic diversity, such as Cameroon, mortality and fertility levels have often been found to vary significantly with ethnicity, even when other factors correlated with ethnicity are held constant (United Na- tions, 1991; Kuate Defo, 1996~. I distinguish the lower than national average fertility ethnic groups (the Foulbe-Fulani and the Kaka-Baya from the northern and eastern provinces) from the other ethnic groups from the rest of the country. Each ethnic group has its set of customs, rituals, and practices associated with major life events (e.g., childbirth, marriages, deaths) that may influence the couple's fertility responses to their children's mortality. Such practices and rituals may include: (1) obstetric methods used by traditional birth attendants, especially in the eastern and northern provinces; and (2) traditions affecting the initiation, type, and duration of breastfeeding, particularly in the northern prov- ince where inappropriate weaning practices have been identified as the major cause of malnutrition (Kuate Defo, 1996~. Therefore, I expect ethnic affiliation to capture behavioral differences across population groups that are not ascribed to other unobservables. Religion The main religions in Cameroon are traditional, Muslim, Protestant, and Catholic. Religious differentials in demographic measures may reflect differ- ences in female education, contraceptive use, or beliefs about the length of the postpartum taboo. The Islamic canon prescribes a postpartum taboo only for as long as the bleeding lasts, which is considered to be 40 days. As a result, the 40- day rule appears frequently in the anthropological literature dealing with Islamic populations of the Sahel (Schoenmaeckers et al., 1981~. Many Muslim popula- tions, however, are quite clearly in transition from the traditional to the Islamic rule, whereas others seem to continue to adhere to the traditionally African pat- tern. Employment Before First Marriage In most developing countries, a woman's employment before marriage is a marker for higher socioeconomic status, higher level of education, and aspira

2 74 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON lions for modernity. To the extent that a woman' s exposure to the outside world gives her more choices and opportunities to make life-cycle decisions (e.g., tim- ing of marriage, timing and pace of childbearing), I would expect women who were employed before their first marriage to differ from others with respect to fertility and fertility responses to an eventual child death. Sex Composition of Living Children The sex of living children may influence the effects of infant mortality on fertility if the couple wants more boys or more girls. Because of the patriarchal nature of most lineages of the Cameroonian society, it is possible that the fertility response to an infant death may depend on the sex of surviving siblings. At least among the Muslims, the Arabic expression Abu-Elbanat (the father of daughters) is used widely as a derogatory description of fathers without sons, thus suggest- ing male preference among the Muslim populations of Cameroon. Moreover, in a number of studies, one of the latent forces in the stated desires of women who want additional children is the sex composition of their living children (e.g., Farah, 1982; Acsadi et al., 1990~. Finally, using data from urban Sahel, Trus sell et al. (1989) found that girls were less intensively breastfed than boys and that, as a result, the postpartum infertile period was shorter when the previous birth was a girl than a boy. Changes in Marital Status In Cameroon, marriage continues to offer women security and social sup- port. Thus, disruption of social ties and community contexts can be a highly stressful experience. In Africa, it is widely believed that it is a man's right to have offspring and that infertility is a woman's problem. Furthermore, it is considered legitimate for a man to abandon a childless or subfertile wife. There- fore, infertile women tend to experience greater marital instability and are more likely to have been married more than once. If such unobserved heterogeneity in fertility has a causal influence on marital status, then marital status cannot be strictly exogenous. However, since such unobserved variation will mostly affect early childbearing (the first or second births at best), I assume in this chapter that marital status is predetermined for most of the fertility process in Cameroon. Time Trend The time trend corresponds to the year in which the duration of exposure to the risk of conceiving a child begins. I explore the robustness of the estimated birth process models to the inclusion of this time trend variable. Traditional duration models abstract from life-cycle and period phenomena and focus on durations between events irrespective of their occurrence in either calendar time

BARTHELEMY KUATE DEFO 275 or in the life cycle of the individuals. I test for the importance of period effects by adding a dummy variable for conceptions occurring during the 10 years prior to each survey as a covariate to the baseline set of regressors. Restricting the analyses to the intervals, say beginning 2 and 10 years before the survey, may reduce recall error for intervals that began very long ago and reduce selection biases for very recent intervals, but this may lead to a downward bias in concep- tion rates (the key dependent variable here) since the inclusion, for example, of the closed birth intervals beginning as long as 10 years before the survey may overrepresent women with low fecundity (Guz and Hobcraft, 1991) and may not capture the significant reductions in the levels of sterility in Cameroon over the past two decades and the induced increase in fertility (Larsen and Menken, 1991; Larsen, 1995~. Accounting for Unobserved Heterogeneity In any given society at a given time, even though no conscious effort is made by individual families to limit fertility, actual fertility will fall short of reproduc- tive potential because of physiological conditions limiting fertility, such as mal- nutrition, or because of cultural circumstances such as breastfeeding practices or an intercourse taboo, which have the unintended effect of lowering fertility. This suggests that a number of unmeasured factors either specific to each woman (woman-specific unobserved heterogeneity) or specific to attained parity for a given woman (parity-specific unobserved heterogeneity) may have an influential role on her reproductive behavior and outcome. Perhaps the most important factors underlying the relationship between in- fant and child mortality and fertility in developing countries are the effects of nutrition and lactation. These factors are, however, unmeasured for the woman's entire reproductive career in most survey data, including the DHS or WFS data; although both surveys measured lactation for the last and penultimate children (WFS) or the children born within the preceding 5 years of the survey date (DHS), only the DHS has recently collected some anthropometric indicators for women at the time of the survey in selected countries, including Cameroon. Thus, the information on breastfeeding available in the WFS or DHS data does not allow us to tease out the role of lactation as a mediating mechanism in the relationship between child mortality and fertility over more than 5 years of the survey. Indeed, 5 years is a very short period for most demographic processes to capture changes in one phenomenon (e.g., fertility) in response to another (e.g., child mortality) in a way as to assess whether there are lagged effects. These unmeasured characteristics are particularly important for most African countries where an economic crisis has subjected the majority of families to a dramatic shift in purchasing power since the 1980s.

2 76 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON Woman-Specific Unobserved Heterogeneity Woman-specific unobserved characteristics include factors such as her pref- erences, fecundity, genetic effects on fecundity, individual adjustments in desired family size, perceived mortality risks from past and present experiences, and various social customs or events that inadvertently affect coital frequency, fecun- dity, or fetal mortality. Indeed, the long postpartum taboo has been a basic element in producing the child-spacing pattern in tropical Africa, although there are considerable differences with respect to its observance. Among unmeasured woman-specific factors that separately or jointly deter- mine child mortality and fertility are pathological factors. Their influence is particularly important in tropical Africa where they are usually either infections or malnutrition (Cantrelle et al., 1978~. I follow the demographic tradition (e.g., Bongaarts, 1981; Lesthaeghe,1989~. Conception is followed by gestation which is followed by a period of postpartum infecundity before a woman becomes at risk of the next conception. The time to first conception is a convolution of the time from menarche to marriage or cohabitation and the waiting time to preg- nancy given exposure. I estimate models with nonparametric woman-specific unobserved heterogeneity. Several unmeasured strategies can be employed to attempt replacement, such as resumption of sexual intercourse or interruption of contraceptive use, all of which leave an imprint in the length of a birth interval. Most of these characteristics are unmeasured in most survey data available to date. Thus, I control for such parity-specific unobserved characteristics in our models (see the Appendix). Parity-Specific Unobserved Heterogeneity Parity-specific unobserved heterogeneity captures the limiting behavior and the biological sterility at a given parity. The question of interest here hinges on how the limiting behavior is effected. Some women may not have another child even if they experience a child death; this may be the case if limiting behavior is due to medical reasons. Second, the social norm in most African societies is that when a woman's own daughter begins bearing children, her status of grand- mother may preclude her bearing children so that she can oversee the rearing of her grandchildren (Caldwell and Caldwell, 1981; Acsadi et al., 1990~. The extent to which such norms might be violated and the limiting behavior reversible if a child death should occur is unknown and deserves investigation. Evidence from the 1991 survey suggests that, in Cameroon, only 12.4 per- cent of women have a stated limiting behavior (no desire for additional children); this percentage increases with increases in the number of surviving children, from 0.2 percent among women with no surviving child to 35.5 percent among women with six or more surviving children (Balepa et al., 1992~. Thus, it is possible that some women may reverse their limiting behavior in the aftermath of

BARTHELEMY KUATE DEFO 277 a child death. These are unobserved factors that may affect the fertility behavior at a given parity and that I attempt to capture by specifying a parity-specific random component in my models (see the Appendix). The evidence regarding insurance strategy in Africa is scanty and at best conjectural, in part because of a lack of good data. On a world scale, most of the observed variations in natural fertility levels within marriage are probably due to variations in the length of the intervals between successive births, resulting mainly from variations in the length of the postpartum nonsusceptible period and from variations in fecundity. In some parts of Africa, high levels of sterility also play an important role in that a sizable number of women either remain childless (Larsen and Menken, 1991; Larsen, 1994, 1995) because of primary sterility or cease childbearing relatively early because of secondary sterility. Primary sterility normally results in no more than 5-6 percent of married women remaining permanently childless, although for several African populations, the figure ranges from 10 to 40 percent (Lesthaeghe et al., 1981~. In most previous studies of fertility, the assumption has been that all women eventually give birth; that is, there is no sterility or limiting behavior. This is an unrealistic assumption in the context of Cameroon, where infertility is quite high and well recognized. Clearly, in many societies, a certain fraction of couples cannot conceive any children because of reproductive deficiencies. Indeed, Larsen and Menken (1991) found that during the 1970s the prevalence of sterility was relatively high in Cameroon. Sterility is an important proximate determinant of fertility in Africa and in Cameroon. At the age of 34, the proportion of sterile women reached 40 percent in the CWFS of 1978 and 31 percent in the CDHS of 1991 (Larsen, 1994~. If efforts aimed at lowering sterility in Cameroon were to prove successful, an increase in fertility and population growth might follow. EMPIRICAL FINDINGS Table 8-3 assesses the effects of neonatal (first month of life) and postneona- tal (1-11 completed months) deaths of the first, second, third, and fourth parity children on the length of subsequent birth intervals, controlling for maternal parity. It shows the median birth intervals according to the survival status of the child initiating the interval at the time of the conception of the index child or at the time of censoring, as well as the reduction in the time elapsed to the time of the conception of the next birth that is associated with the death of the child who starts the interval. These median birth intervals were obtained by life table procedures to account for censoring of exposure to the risk of a following concep- tion. At the national level, the two data sets show a steady increase in median interval length with survivorship of the child, ranging from 22 months in the case of a death in the first month of life (in the CDHS) to 31 months in the case of a child who survives at least a year. The effect of infant mortality on birth spacing

2 78 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-3 Median Birth Intervals Between Parity i and Parity i + 1 Child Dies in the First Year of Life and before the Conception of the Index Child Child Survives the First Year of Life 0 Months 1-11 Months 0-11 Mon' Selected CWFS CDHS CWFS CDHS CWFS CDHS CWFS Variables (1) (2) (3) (4) (5) (6) (7) Overall length 30 31 24 22 26 25 25 Parity-specific pattern Parity 1 - 2 30 28 23 21 26 23 2- 3 29 29 24 21 24 27 3 - 4 30 29 23 28 26 26 4 - 5 30 30 24 22 27 25 Pattern by other selected characteristics Age at maternity <20 years 29 25 23 17 26 21 24 20+ 30 31 22 26 28 29 25 Education None 30 30 24 21 27 25 26 Some 30 31 24 23 24 25 23 Religion Catholic 29 31 24 21 25 26 24 Protestant 30 31 23 23 26 24 25 Muslim 29 29 26 23 28 26 27 may be appreciated more easily with the differences between intervals in which the child survived infancy and those intervals in which the infant died. In the top half of the table I examine the parity-specific pattern of variation in median birth interval associated with an infant death, whereas in the lower half of the table I examine the pattern of variation in median birth interval ascribed to an infant death by selected comparable characteristics in the two data sets. The overall pattern is that the reduction in median birth-to-conception inter- val for a child who dies in the first year of life compared with a child who survives through the first year of life is 5 months (or 17 percent reduction) and 7 months (or 22 percent reduction) in the CWFS and CDHS, respectively. When the analysis is fine-tuned by age, the reduction in median birth-to-conception interval for a child who dies compared with a child who survives is 6 months (or 20 percent reduction) and 9 months (or 29 percent reduction) in the neonatal period and 4 months (or 13 percent reduction) and 6 months (or 19 percent reduction) in the postneonatal period in the CWFS and CDHS, respectively.

BARTHELEMY KUATE DEFO 279 Life and dex Child Reductions in Median Birth Interval Associated with the Death of the Child Initiating the Birth Interval hs 0-11 Months CWFS CDHS CDHS CWFS CDHS (6) (7) (8) (1)-(3) (1)-(5) (1)-(7) (2)-(4) (2)-(6) (2)-(8) 25 25 24 6 4 5 9 6 7 23 25 23 7 4 5 7 5 5 27 24 24 5 5 5 8 2 5 26 25 26 7 4 5 4 3 3 25 25 24 6 3 5 8 5 6 24 19 6 3 5 7 4 6 25 28 8 2 5 5 2 2 26 24 6 3 4 9 5 6 23 24 6 6 7 8 6 7 24 24 5 4 5 9 4 7 25 24 7 4 5 8 7 7 27 25 3 1 2 6 3 6 These results consistently show that the reduction in median birth-to-conception interval associated with an infant death in the two data sets is larger in the neonatal period than in the postneonatal period, the difference being 3 months in the more recent data set (the CDHS data). These results support my hypothesis that the earlier a child death occurs the more quickly childbearing will be re- sumed. When the samples are stratified by selected characteristics such as parity, maternal age, female education, and religion, the emerging patterns show some strong similarities among certain subgroups of the population. For example, the results consistently show that in both data sets, the reduction in birth-to-concep- tion interval associated with an infant death occurring in the first year of life is again larger in the neonatal period than the postneonatal period. The largest difference in reduction (of 6 months, from 8 months to 2 months) between the neonatal and postneonatal is noted among older women. The pace of closure of

280 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON a birth-to-conception interval is quicker among teenagers than among older women, both in the neonatal and postneonatal period. In general, at the same parity, median birth intervals are shorter for women with child mortality experience, varying from around 30 months when the child survives the first year of life to 21 months when the child initiating the interval dies in the first month of life and before the conception of the second child (index child). For the first year as a whole, the average reduction in median birth interval between parities when the child who initiates the interval dies before the conception of the second (index child) is invariably 5 months in the two data sets, which suggests a robust finding. The pace of childbearing is much more rapid when the child dies in the neonatal period than in the postneonatal period. In particular, there is a shorter duration of the postpartum infertile period following a child death at first parity. These relationships between infant loss and pace of childbearing hold at all parities and are statistically significant in both data sets. Furthermore, in the two data sets, the difference in reduction between the neona- tal and the postneonatal period is about 3 months (or about 10 percent reduction), thus suggesting that the replacement of a lost child is approximately 3 months sooner when the child dies in the neonatal period than when it dies in the postneo- natal period. Multistate and Multivariate Hazard Estimates In this section, I examine the sign and magnitude of the effects of child loss on the timing and spacing of births with and without controlling for observed and unobserved covariates so as to test the hypotheses enunciated above. Such effects address questions of how fertility behavior responds to exogenous varia- tions in the child mortality experience and other observed and unobserved varia- tions in a woman's characteristics that affect her fertility decisions and prefer- ences. Knowledge of such measured and unmeasured effects may provide good approximations to the consequences of policy interventions (e.g., to reduce infant and child mortality) for fertility control and may provide important benchmarks against which to compare findings from other settings in Africa. The short-term mortality effects are termed "replacement behavior" effects and for them I distin- guish between the physiological and volitional replacement effects. The long- term mortality effects evoke mainly volitional replacement effects. Tables 8-4 through 8-10 present the parameter estimates of a six-equation joint hazard model of mortality effects on fertility. The analyses are restricted to the first six transitions, as discussed in the Appendix. These tables identify the birth-to-conception intervals during which there are statistically and demographi- cally significant effects of child mortality or other covariates on fertility behav- ior. The effect estimates for hazard models indicate the influence of a particular variable on the probability of a birth, net of the other variables. Where an effect estimate is positive, women in that category are more likely to give birth than

BARTHELEMY KUATE DEFO 281 women in the category with a negative effect estimate. The greater the difference in effects estimated between the highest and lowest values for categories of a particular covariate, the greater the impact of that covariate on the estimated risk of birth. Short-Term Mortality Effects on the Timing and Spacing of Births Tables 8-4 through 8-9 present the findings as they relate to short-term replacement effects of mortality on fertility. These tables show the results from a model with one measure of child mortality (abbreviated CMM1 in Table 8-2~. This measure captures the extent to which the death of the child who opens the birth-to-conception interval [i, i + 1) in its first year of life and at least 1 month before the conception of the (i + Ah child increases the risk of that following conception. Such a measure of the fertility response to a child death in its first year of life is a mixture of volitional replacement effects and physiological ef- fects having to do with the cessation of breastfeeding. Mortality effects attribut- able to volitional replacement effects alone are presented below. Table 8-4 shows the results from a six-equation joint hazard model with only the child mortality measure (CMM1) and the duration measures. As expected, the death of a child significantly increases the risk of the imme- diately following conception. For example, such risk is increased by 83 percent according to the CWFS data and 80 percent according to the CDHS data for the conception of the second child (when the first child dies in its first year of life and at least 1 month before the conception of the second child). Overall, the relative risks of a subsequent conception caused by the death of the child who starts the birth-to-conception interval vary between a low of 1.61 (for the transition to a third birth in the CWFS) to a high of 2.31 (for the transition to a sixth birth in the CDHS). Thus, the death of a child in the family leads to significantly lower probabilities of stopping childbearing, but there is no linear trend across parities. As hypothesized, the operation of the physiological re- placement mechanism (by breastfeeding cessation) links mortality in infancy with the length of birth intervals, and the stronger the mechanism, the shorter the length of birth-to-conception interval caused by a child death. This mechanism appears to be in operation here. Also, if the volitional replacement strategy is at work, an improvement in child mortality can never result in a fully compensatory reduction in births because fertility control is always imperfect; if couples replace births through a compression of birth-to-conception intervals, the fertility re- sponse to child loss will be fairly immediate, and the results here lend support to the operation of this mechanism (see also discussion on long-term replacement effects, below). The relatively large demographic impact of these physiological and volitional replacement effects is expected to occur in a country such as

282 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-4 Six-Equation Joint Hazard Model of Short-Term Mortality Effects on Fertility Without Controlling for Measured Covariates and Unobserved Heterogenity CWFS, 1978: Transition to Conception First Second Third Fourth Fifth Variable Birth Birth Birth Birth Birth Intercept 0.673** 0.945** -0.938** -0.909 -0.985 (0.023) (0.026) (0.031) (0.034) (0.041) in duration 0.262** 0.230** 0.188** 0.419** 0.418** (0.019) (0.008) (0~0135) (0.013) (0.017) Shift of the conception 0.604** 0.478** 0.541** 0.629** hazard upon infant death (0.045) (0.044) (0.053) (0.062) (CMMl)a Negative log-likelihood 24,555 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: ** 1 percent; *, 5 percent (two-tailed) Cameroon with high infant mortality, prolonged intense breastfeeding, and natu- ral fertility. Because women with a child death are likely to have had greater exposure to the risk of conception than those without, exposure must be controlled in the analysis as done here (for further detail, see the Appendix). In the absence of such control, the measured effects will exaggerate the replacement effect. The results show that the length of time to various conceptions is shorter in the CWFS than in the CDHS. For example, the relative risks of the logarithm of the duration of exposure to the risk of conceiving the first birth since first marriage is 1.30 in the CWFS and 1.90 in the CDHS. These results imply that the waiting times to conceptions is shorter in the CDHS (the 1991 data) than in the CWFS, thus suggesting a quicker pace of childbearing in the former than the latter data set. In Table 8-5, I assess the extent to which the short-term mortality effects on birth-to-conception intervals could be spurious owing to lack of controls for measured factors affecting mortality, fertility, or both. Thus, both fertility and mortality experience should be related to common factors such as education, socioeconomic status, and cultural factors. Holding the exogenous regressors constant, a child loss in infancy continues to accelerate significantly the times to the next conception and increases the fertility transition rates at all parities.

BARTHELEMY KUATE DEFO y Effects ved 283 CDHS, 1991: Transition to Conception fourth Fifth Sixth First Second Third Fourth Fifth Sixth lirth Birth Birth Birth Birth Birth Birth Birth Birth -0.909 0.034) -0.985** (0.041) 0.959** (0.044) -0.429** (0.031) -0.735** (0.031) -0.804** (0.043) -0.885** (0.050) -0.797 (0.052) -1.048** (0.061) l.419** 0.418** 0.428** 0.646** 0.934** 0.938** 1.086** 1.101** 1.128** 0.013) (0.017) (0.016) (0.029) (0.0253) (0.029) (0.031) (0.039) (0.045) l.541** 0.629** 0.496** 0.589** 0.694** 0.767 0.631** 0.838** 0.053) (0.062) (0.070) (0.054) (0.057) (0.063) (0.068) (0.081) 10,772 aDeath of the immediately preceding child in the first year of life and 1 month before the concep- tion of the index child. The relative risks of a subsequent conception caused by a child death appear to change rather trivially for all transitions, with a small reduction of 6 percent in the relative risk of conceiving the second birth (from 1.83 to 1.77 in the CWFS, and from 1.80 to 1.74 in the CDHS) reflecting the highest impact of controlling for measured covariates that, not surprisingly, affect fertility independently of the mortality effects. Although female education has been shown elsewhere to influence fertility behavior, the two data sets from Cameroon fail to show significant effects of education. This finding is not surprising, because the pronatalist ethic in Cameroon until recently means that most women tend to aspire to high fertility. There are significant ethnic differences in fertility. The low-fertility ethnic groups are less likely to bear a conception at each transition compared with the high- fertility ethnic groups. This is especially the case for the transition from first marriage to the conception of the first birth and the transition from the first birth to the conception of the second birth. Women who are employed before their first marriage have lower conception risks and are likely to postpone their first three conceptions. The data fail to detect any significant differences at higher parities. In fact, after correcting for unobserved heterogeneity (see Tables 8-6 and 8-7 below), these women tend to have higher conception hazards for parity five (for woman-specific unobserved heterogeneity) and for parity four (for par

284 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-5 Six-Equation Joint Hazard Model of Short-Term Mortality Effects on Fertility Controlling for Measured Covariates CWFS, 1978: Transition to Conception First Second Third Fourth Fifth Variable Birth Birth Birth Birth Birth Intercept -0.486* * -0.466* * -0.472* * -0.442* * -0.467 (0.030) (0.044) (0.048) (0.057) (0.062) in duration 0.313** 0.357** 0.349** 0.589** 0.570** (0.018) (0.010) (0.011) (0.014) (0.018) Shift of the conception 0.574** 0.475** 0.539** 0.626** hazard upon infant death (0.047) (0.050) (0.055) (0.065) (CMMl)a Mother is educated 0.013 -0.076 0.009 -0.037 -0.009 (0.059) (0.061) (0.077) (0.073) (0.076) Low-fertility -0.322** -0.195** -0.056 -0.152** -0.128* ethnic groups (0.059) (0.061) (0.077) (0.073) (0.052) Muslim religion 0.076* -0.043 0.001 -0.019 -0.128* (0.033) (0.041) (0.044) (0.050) (0.052) Shift of the conception -0.247 * * -0.333 * * -0.245 * * -0.392* * -0.442 hazard upon marital (0.043) (0.063) (0.063) (0.065) (0.081) dissolutions Employed before -0.259** -0.065 -0.142* 0.033 0.089 first marriage Mother has more previous -0.637** -0.765** -0.699** -0.697 living boys than girls (0.043) (0.049) (0.056) (0.065) Time trends -0.765** -1.174** -0.799** -0.982** -0.914 (0.101) (0.133) (0.134) (0.115) (0.181) Negative log-likelihood 23,657 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed).

BARTHELEMY KUATE DEFO y Effects 285 CDHS, 1991: Transition to Conception Birth Fifth Sixth First Second Third Fourth Fifth Sixth irth Birth Birth Birth Birth Birth Birth Birth Birth ).442** -0.467** -0.607** -0.423** -0.254** -0.311 ** -0.437** -0.269** -0.433 i.057) (0.062) (0.075) (0.033) (0.057) (0.067) (0.080) (0.090) (0.110) 589** 0.570** 0.528** 0.670** 1.148** 1.226** 1.254** 1.335** 1.324** i.014) (0.018) (0.018) (0.023) (0.026) (0.029) (0.032) (0.038) (0.041) 539** 0.626** 0.475** 0.556** 0.694** 0.756** 0.637** 0.818** i.055) (0.065) (0.072) (0.055) (0.059) (0.066) (0.070) (0.085) ).037 -0.009 -0.071 0.015 -0.004 0.042 -0.073 -0.085 -0.011 i.073) (0.076) (0.088) (0.039) (0.037) (0.043) (0.045) (0.064) (0.063) ).152** -0.128* -0.079 i.073) (0.052) (0.068) ).019 -0.128* 0.126* 0.076* -0.046 0.125* -0.094* 0.047 -0.121* i.050) (0.052) (0.066) (0.037) (0.038) (0.050) (0.046) (0.064) (0.068) ).392** -0.442** -0.020 i.065) (0.081) (0.115) 033 0.089 -0.009 ).699** -0.697** 0.600** -0.787** -0.900** -0.694** -0.859** -0.789 i.056) (0~065) (0.075) (0.063) (0.068) (0.078) (0.086) (0.112) ).982** -0.914** -1.180** -0.463** -0.470** -0.286** 0.121** 0.304* -0.249 i.115) (0.181) (0.280) (0.063) (0.062) (0.096) (0.130) (0.129) (0.158) 10,371 aDeath of the immediately preceding child in the first year of life and 1 month before the concep- tion of the index child. bMonth before the conception of the index child. CTen-year period preceding survey.

286 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON ity-specific unobserved heterogeneity) than other women, perhaps indicating a catching-up behavior. There are also significant religious differences in the transition to the con- ception of the first birth and to higher (five or more) conceptions. In both the CWFS and CDHS, the hazard of first conception is significantly higher among Muslim women than among others. At higher parities, there is no consistent pattern of shift of the conception hazard by religious affiliation. The CWFS for which the information is available suggests negative (and significant at least for the first birth) effects of maternal employment outside the home and fertility; this finding is consistent with earlier studies that have found a negative association between female labor force participation and fertility. As regards changes in marital status, marital dissolution shifts downward the conception hazard at all transitions, although no significant effect of marital dissolution is found for the sixth transition after controlling for parity-specific unobserved heterogeneity (Tables 8-6 and 8-7~. In essence, married women are more likely to have children than are unmarried women. The sex composition of previous surviving children shows significant differ- ences in subsequent fertility behavior. When the couple has more surviving boys than girls, there are significant decreases in the conception hazard at all parities and in both data sets. This result is robust to controls for both woman-specific unobserved heterogeneity and parity-specific unobserved heterogeneity (Tables 8-6 through 8-8~. Basically, the relative risks of a subsequent conception associ- ated with the sex of previous children favoring boys range between 0.45 and 0.55 in both data sets, which corresponds to a reduction in the risks of conception varying between 45 and 65 percent. Thus, the sex of the previous children appears to affect subsequent fertility behavior, but this has no bearing on the mortality effects of the child who opens the index birth-to-conception interval (i.e., the birth-to-conception interval under study). Indeed, I also investigate the interaction between the sex of the previous children and the death of the child who starts the index birth-to-conception interval, but both data sets fail to show any significant interaction effects (results not shown). In my analysis, I explore the robustness of the estimated birth process model to the inclusion of a time trend variable. I test for the importance of period effects by adding a dummy variable for conceptions occurring during the 10 years before each of the surveys as a covariate to the baseline set of regressors. In all of the specifications and in both data sets, I find a consistent and negative effect of the calendar period (fertility behavior of the last 10 years preceding the survey date) on all transition rates, suggesting a decline in fertility levels in Cameroon. More recent births are less likely to be followed by another conception than births that occurred further in the past. These results suggest that the intervals between successive parities have lengthened over time (for more recent parity cohorts). Consistent with the negative relationship between time trend and hazard of the following conception, the hazard rates for all parities and both data sets have

BARTHELEMY KUATE DEFO 287 declined at all parities over time. Indeed, the decline reaches 26 percent for the conditional probability of first, second, and third births and 24 percent for the hazard of a fourth birth (see Table 8-8 below). Controlling for period effects has little influence on the estimates of other regressors, although the negative time trend estimates are statistically significant. In particular, corrections for woman-specific unobserved heterogeneity and par- ity-specific unobserved characteristics do not weaken this effect (Tables 8-6 through 8-8~. During the 1980s, infertility declined significantly among women less than 40 years old, and women's expected numbers of infertile years between the ages of 20 and 39 fell from 7.3 to 6.0 years between the 1978 WFS and the DHS of 1991 (Larsen, 1995~. But I find no evidence that declining sterility (captured in the unobserved components introduced in my models) could explain the observed trend in declining conception hazards in recent periods. It is pos- sible that the economic crisis that Cameroon, just as most African countries, has undergone since the mid-1980s may have affected the fertility behavior of couples in recent years. Table 8-6 displays the short-term replacement effects after correcting for woman-specific unobserved heterogeneity (while holding exogenous covariates constant). The nonparametric maximum likelihood estimator for the mixing distribution involves a two point-of-support distribution for the unobserved het- erogeneity (no additional points could be estimated because of convergence prob- lems).3 In Table 8-6 I consider the possibility that woman-specific unobserved char- acteristics may influence the robustness of the replacement effects. Although there are significant unobserved characteristics of the woman affecting her con- ception risks, these unobservables are empirically unimportant in explaining the fertility responses to child loss in both the CWFS and the CDHS. In particular, a comparison of the estimated relative risks of a following conception caused by the death of the child who starts the index birth-to-conception interval in the gross effects model (i.e., Table 8-4) and in Table 8-6 shows that those risks change little after correcting for woman-specific unobserved factors. For ex- ample, the relative risk of conceiving the second child is 1.83 and 1.78 before and after such correction in the CWFS and hardly changes for the subsequent inter- vals; similarly, whereas the relative risks of conceiving the second child decrease by nearly 25 percent after such correction in the CDHS, there is no change after such correction worthy of notice for the other transitions in the CDHS. 3However, it has been shown that the result for a two point-of-support model are quite similar to those for a three point-of-support distribution for the unobserved heterogeneity (Popkin et al., labs). Note that for all estimated models using the CDHS, my models could not converge beyond the fourth parity once I introduce unobserved components in the estimation equations. Thus, the results with the CDHS are restricted only to the first four transitions in all models with woman-specific or parity- specific unobserved heterogeneities.

288 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-6 Six-Equation Joint Hazard Model of Short-Term Mortality Effects on Fertility Controlling for Measured Covariates and Woman-Specific Unobserved Heterogeneity CWFS, 1978: Transition to Conception First Second Third Fourth Fifth Variable Birth Birth Birth Birth Birth Intercept -7.481 ** 0.016** -0.362** -1.073** -5.086 (0.204) (0.136) (0.145) (0.119) (0.408) in duration 2.324** 0.363** 0.349** 0.612** 0.982** (0.070) (0.009) (0.011) (0.020) (0.031) Shift of the conception 0.575** 0.475** 0.547** 0.610** hazard upon infant death (0.047) (0.049) (0.055) (0.054) (CMMl)a Mother is educated 0.014 -0.075 0.009 -0.037 -0.008 (0.059) (0.060) (0.077) (0.073) (0.076) Low-fertility -0.096* * -0.196* * 0.057 -0.153 * * -0.051 ethnic groups (0.028) (0.044) (0.049) (0.052) (0.056) Muslim religion 0.005 -0.043 0.002 -0.019 -0.118* (0.025) (0.041) (0.044) (0.049) (0.048) Employed before -0.448** -0.070 -0.144* 0.054 0.192** first marriage (0.036) (0.060) (0.059) (0.058) (0.068) Mother has more previous -0.693** -0.768** -0.707** -0.878 living boys than girls (0.043) (0.049) (0.056) (0.055) Shift of the conception 0.006 -0.339** -0.244** -0.376** -0.349 hazard upon marital (0.037) (0.064) (0.063) (0.063) (0.077) dissolutions Time trendsC -0.502** -1.182** -0.800** -1.011 ** -1.103 (0.106) (0.133) (0.135) (0.120) (0.147) Woman-specific 7.766** -0.485** -0.111 0.635** 4.706** unobserved (0.185) (0.130) (0.138) (0.095) (0.405) heterogeneity Negative log-likelihood 21,759 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed).

BARTHELEMY KUATE DEFO y Effects 289 CDHS, 1991: Transition to Conception fourth Fifth Sixth First Second Third Fourth lirth Birth Birth Birth Birth Birth Birth -1.073** -5.086** 4.779 -4.917** -4.212** -3.472** -5.209** 0.119) (0~408) (0.795) (0.156) (0.158) (0.213) (0.665) l.612** 0.020) l.547** 0.055) 0.982** (0.031) 0.610** (0.054) 0.682** (0.029) 0.483** (0.070) 2.122** (0.084) 2.069** (0.074) 0.295** (o.o39) 1.711** (0.047) 0.656** (0.050) 1.738** (0.052) 0.706** (0.056) -0.037 -0.008 -0.071 0.014 -0.004 -0.042 -0.075 0.073) (0.076) (0.087) (0.039) (0.037) (0.045) (0.045) -0.153** -0.051 0.083 0.052) (0.056) (0.058) -0.019 -0.118* 0.083 0.195** -0.041 0.047 -0.074 0.049) (0.048) (0.058) (0.039) (0.044) (0.047) (0.050) 1.054 0.192** -0.017 0.058) (0.068) (0.087) -0.707** -0.878** -0.688** -0.913** -1.083** -0.855** 0.056) (0.055) (0.073) (0.042) (0.057) (0.064) -0.376** -0.349** -0.048 0.063) (0-077) (0.103) -1.011 * * -1.103 * * -1.245* * -0.312* * -0.079 -0.359* * -0.033 0.120) (0.147) (0.256) (0.085) (0.094) (0.105) (0.097)  l.635** 4.706** 4.222** 5.055** 4.271** 3.362** 4.926** 0 095) (0.405) (0.791) (0.144) (0.152) (0.209) (0.662) 7,293 aDeath of the immediately preceding child in the first year of life and 1 month before the concep- tion of the index child. bone month before the conception of the index child. CTen-year period preceding the survey.

290 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON The effects of woman-specific unobserved factors appear to be most impor- tant for the transition from first marriage to first birth in both data sets and to fluctuate somewhat for subsequent transitions. The strikingly high relative risks of conceiving the first child associated with woman-specific unobserved charac- teristics may be capturing the woman's inherent fecundity following intensive exposure to the risk of conception after first marriage, since motherhood is the normal expectation for a new bride in most African societies. Note that in the CWFS, the coefficients for the woman-specific unobserved heterogeneity are negative for the transition to the conception of the second and third births (and negative and statistically significant for the transition from first birth to the con- ception of the second birth). By contrast, results from the more recent CDHS survey consistently show all the coefficients for woman-specific unobserved het- erogeneity to be positive and statistically significant, thus suggesting a positive relationship between those unmeasured characteristics and the probabilities of a following conception. Recall that the CWFS was fielded in 1978 and that until the late 1970s, there was little sign of reduction in the incidence of primary and secondary sterility in Cameroon (David and Voaz, 1981; Larsen and Menken, 1991; World Health Organization, 1991; Larsen, 1994, 1995~. These results seem to capture the incidence of secondary sterility among women in Cameroon until the late 1970s and the changing trends in the incidence of sterility over time in Cameroon, which seem to have increased women' s fertility desires and to have reduced their waiting time to conceptions. Table 8-7 presents the short-term replacement effects after correcting for parity-specific unobserved heterogeneity (while holding constant the measured factors). In both data sets, correcting for parity-specific unobserved factors slightly lowers the relative risks of a subsequent conception in the aftermath of a child death. The reduction in relative risks ranges between 10 percent (for the transi- tion to the conception of the third birth) to around 16 percent (for all other transitions) in the CWFS and between 10 percent (for the transition to the concep- tion of the third birth) and 23 percent (for the transition from first marriage to the conception of the first birth) in the CDHS. However, the explanatory power of the mortality effects remains unchanged after such correction. The estimated replacement effects remain statistically significant for all transitions and for both data sets. Net of the measured covariates, the implied stopping probabilities associated with parity-specific unobserved heterogeneity show no consistent pattern and essentially fluctuate from one parity to the next, but the magnitude of the differ- ential diminishes at higher birth orders in both data sets. It is possible, for example, that in families with many children there is a greater likelihood that some of the children were not wanted or were expected to die. In such a case the death of a child would not call for replacement, and this will affect the pattern of effects of parity-specific unobserved factors.

BARTHELEMY KUATE DEFO 291 In Table 8-8, I jointly account for woman-specific and parity-specific unob- served heterogeneities in the hazards of conception and the associated mortality effects. Again, it is found that for all parities, the fertility responses to child mortality are indeed robust to controls for unobservables. There are significant fertility differences by parity-specific unobserved het- erogeneity: The higher fertility of women is reflected in their lower stopping probability at any birth order, although there is a tendency to increase when woman-specific heterogeneity is accounted for. The relative risks of a subse- quent conception of the second and third births are 1.78 and for the fourth birth are 1.93, which are quite similar to the relative risks obtained from the previous models for the same transitions (see Tables 8-6 and 8-7~. Overall, the short-term replacement behavior is indeed robust. Long-Term Mortality Effects on the Timing and Spacing of Births Tables 8-9 and 8-10 examine the long-term mortality effects on fertility. Two measures of mortality are used. The first measure captures the long-term mortality effects of a child who opens the birth-to-conception interval [i, i + 1) and dies at least 1 month before the conception of children of parities i + 2, i + 3, i + 4, and so forth (abbreviated CMM2 in Table 8-2~. The second measure focuses on the mortality of the first (and the second) birth and explores the effects of the death of the first child (or the second child) in its first year of life and at least 1 month before the conception of the second, third, fourth, fifth, and sixth births (or the third, fourth, fifth, and sixth births in the case where the death of the second birth is of interest) (abbreviated CMM3 in Table 8-2~. Table 8-9 presents the results for the survival status of the preceding siblings prior to the conception of the index child, whether or not the mortality experienced was within the first year of life. In Table 8-9 I evaluate the net effects of the mortality of the first, second, third, fourth, and fifth birth on future fertility behavior while controlling for the survival of other children. I find that the mortality of the first children (in the CWFS) and the first and second children (in the CDHS) have significant positive effects on the probabilities of conceiving children of higher birth orders. I pursue the extent to which the death of the first and second child significantly increases the risks of conceiving children of higher birth orders in Table 8-10, restricted to the CDHS data for which such effects emerge strongly and consis- tently. Much of the replacement effect may not show up in terms of differences in birth interval length but rather in additional subsequent births. To capture fully the volitional replacement effect, child deaths before some specific parity must be related to subsequent fertility. This also avoids the confounding effects of fertility on mortality. A common approach in previous studies has been to compare the additional children born subsequent to a specific parity between women who have experi- enced a child death up until that point and those who had not. In Tables 8-9 and

292 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-7 Six-Equation Joint Hazard Model of Short-Term Mortality Effects on Fertility Controlling for Measured Covariates and Parity-Specific Unobserved Heterogeneity CWFS, 1978: Transition to Conception First Second Third Fourth Fifth Variable Birth Birth Birth Birth Birth Intercept 0.132** -0.186** -0.182** -0.192** -0.247 (0~024) (0.037) (0.045) (0.053) (0.057) in duration 1.298** 1.046** 1.025** 1.160** 1.363** (0.014) (0.011) (0.014) (0.023) (0.030) Shift of the conception 0.426** 0.375** 0.370** 0.453** hazard upon infant death (0.032) (0.041) (0.043) (0.043) (CMMl)a Mother is educated 0.016 -0.065 0.008 -0.037 -0.008 (0.059) (0.060) (0.077) (0.073) (0.076) Low-fertility -0.052 -0.130* * 0.068 -0.201 * * 0.040 ethnic groups (0.028) (0.039) (0.051) (0.059) (0.057) Muslim religion 0.167** -0.035 -0.041 0.005 -0.126* (0.028) (0.035) (0.044) (0.049) (0.048) Employed before -0.293** -0.075 -0.348** 0.252** 0.098 first marriage (0.026) (0~052) (0.057) (0.056) (0.070) Mother has more previous -0.809** -0.455** -0.750** -0.762 living boys than girls (0.034) (0.046) (0.052) (0.052) Shift of the conception -0.099** -0.225** -0.279** -0.592** -0.231* hazard upon marital (0~027) (0.053) (0.061) (0.069) (0.082) dissolutions Time trendsC -0.594** -1.401** -1.095** -0.640** -0.857 (0.102) (0.117) (0.155) (0.157) (0.164) Parity-specific stopping Parity 0 Parity 1 Parity 2 Parity 3 Parity 4 unobserved heterogeneity Estimates -1.710** -2.639** -1.806** -2.621 ** -2.488 (0.043) (0.083) (0.063) (0.116) (0.126) Implied probabilities 0.153 0.067 0.141 0.068 0.077 Negative log-likelihood 21,213 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed).

BARTHELEMY KUATE DEFO y Effects 293 CDHS, 1991: Transition to Conception fourth Fifth Sixth First Second Third Fourth lirth Birth Birth Birth Birth Birth Birth -0.192** -0.247** -0.401** -0.014 0.030 0.016 0.139* 0.053) (0.057) (0.071) (0~027) (0.043) (0.047) (0.057) .160** 1.363** 1.074** 1.929** 2.192** 2.363** 2.335** 0.023) (0.030) (0.040) (0.024) (0.045) (0.056) (0.101) l.370** 0.453** 0.344** 0.328** 0.588** 0.605** 0.043) (0.043) (0.057) (0.039) (0.041) (0.050) -0.037 -0.008 -0.071 0.014 -0.004 0.042 -0.074 0.073) (0.076) (0.087) (0.039) (0.037) (0.045) (0.045) -0.201 ** 0.040 0.059) (0.057) (0.064) 1.005 -0.126* 0.075 0.203** -0.085* -0.004 -0.151* 0.049) (0.048) (0.059) (0.027) (0.039) (0.045) (0.052) l.252** 0.098 0.044 0.056) (0.070) (0.083) -0.750** -0.762** -0.712** -0.712** -0.783** -0.598** 0.052) (0.052) (0.067) (0.047) (0.049) (0.056) -0.592** -0.231 * 0.003 0.069) (0.082) (0.098) -0.640** -0.857** -1.534** -0.246** 0.002 -0.385** -0.210* 0.157) (0.164) (0.223) (0.056) (0.092) (0.106) (0.110) 'arity 3 Parity 4 Parity 5 Parity O Parity 1 Parity 2 Parity 3 -2.621 ** -2.488** -2.853** -1.997** -2.459** -2.093** -2.170** 0.116) (0.126) (0.191) (0.068) (0.121) (0.113) (0.141) 1.068 0.077 0.054 0.119 0.079 0.110 0.102 6,787 aDeath of the immediately preceding child in the first year of life and 1 month before the concep- tion of the index child. bone month before the conception of the index child. CTen-year period preceding the survey.

294 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-8 Six-Equation Joint Hazard Model of Short-Term Mortality Effects on Fertility Controlling for Measured Covariates and Woman-Specific and Parity-Specific Unobserved Heterogeneities CDHS, 1991: Transition to Conception First Second Third Fourth Variable Birth Birth Birth Birth Intercept -11.242** 1.089** 0.872** 0.222* (0.210) (0.066) (0.073) (0.090) in duration 9.643** 2.637** 2.664** 2.449** (0.144) (0~041) (0.055) (0.105) Shift of the conception hazard 0.582* * 0.581 * * 0.656* * upon infant death (CMMl)a (0.038) (0~042) (0.05 Mother is educated 0.016 -0.005 0.043 -0.076 (0.039) (0.037) (0.046) (0.044) Muslim religion 0.181 ** -0.177** 0.085 -0.049 (0.028) (0.037) (0.047) (0.056) Mother has more previous -0.747** -0.909** -0.854** living boys than girls (0.047) (0.057) (0.065) Time trendb -0.298** -0.312** -0.305* -0.267* (0.056) (0.092) (0.107) (0.120) Woman-specific 16.126** -1.414* -1.197* -0.546** unobserved (0.398) (0.056) (0~056) (0.074 heterogeneity Parity-specific Parity 0 Parity 1 Parity 2 Parity 3 stopping unobserved heterogeneity Estimates -1.953** -2.248** -1.879** -1.744** (0.106) (0.108) (0.107) (0.138) Implied probabilities 0.124 0.095 0.132 0.149 Negative log-likelihood 125 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed). aDeath of the immediately preceding child in the first year of life and 1 month before the concep- tion of the index child. bTen-year period preceding the survey.

BARTHELEMY KUATE DEFO 295 8-10, I find that there are indeed strong volitional replacement effects, at least as regards the death of the first child in both data sets and the second child in the CDHS. In either case, the death of the first (or second) child is shown to signifi- cantly increase the hazard of conceiving children of parity 2, 3, 4, 5, and 6 (for the death of the first child) and children of parity 3, 4, 5, and 6 (for the death of the second child). Table 8-9 presents the mortality effects using the first measure (CMM2) of the long-term effects. I find that in both data sets, the death of the first child is significantly associated with increased relative risks of conceiving the second, third, fourth, fifth, and sixth children. These relative risks are at least 20 percent higher than the baseline risks (the risks of conception following a surviving child) in both data sets and range from 1.18 to 1.39. As regards the death of the second child, the CWFS data are consistent only with the short-term mortality effects, but fail to show significant long-term effects. The CDHS data, on the other hand, show consistently that the death of the second child has both short-term and long- term mortality effects on birth spacing. Indeed, the relative risks of the concep- tion of the third, fourth, fifth, and sixth children associated with the death of the second at least 1 month before the conception of each of these children range from 1.33 (for the transition to the conception of the third birth) to 2.07 (for the transition to the conception of the sixth birth), although the increase in such risks is not monotonic. The CWFS data further suggest that the death of the third child increases significantly the relative risks of conceiving the fifth child, but not the fourth or the sixth, whereas the death of the fourth child tends to significantly reduce the risks of conceiving the fifth child once previous mortality experience within the family is taken into account. Similarly, the CDHS data suggest that the death of the third child significantly reduces the risks of conceiving the fifth birth. Because the more widely spaced pattern is the pattern of childbearing that most couples choose in most African societies because of postpartum taboos and prac- tices and longer breastfeeding durations, it will be easier to replace a child death with an additional birth through a compression of interbirth intervals. On the other hand, if couples plan closely spaced births, they will have to replace any child deaths later in a woman's reproductive span when fecundity may have declined. This may explain some of the insignificance of the higher-parity effects of the mortality of previous children. These results are somewhat consistent with Ben-Porath's (1978) study in which most of the coefficients of previous death of a child were not statistically significant: They tended to be positive and smaller in absolute size than the generally negative coefficients of the older siblings who died. These findings would indicate that, when a death occurs and the next birth occurs earlier, subsequent births may not be shifted back by full change in birth intervals, which is another way of saying that replacement is partial as many previous studies have shown (e.g., Preston, 1978~.

296 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-9 Six-Equation Joint Hazard Model of Long-Term Mortality Effects on Fertility: The Child Who Opens the Birth-to-Conception Interval [i, i + 1) Dies at Least 1 Month Before the Conception of Children of Higher Parities (CMM2) CWFS, 1978: Transition to Conception First Second Third Fourth Fifth Variable Birth Birth Birth Birth Birth Intercept -0.672** -0.724** -0.788** -0.747** -0.763 (0.022) (0.022) (0.026) (0.030) (0.03 ) in duration 0.261** 0.169** 0.142** 0.360** 0.347** (0.018) (0.009) (0.014) (0.012) (0.019) Shift of the conception hazard upon death First child 0.201** 0.327** 0.292** 0.253 (0.048) (0.060) (0.066) (0.060) Second child 0.204* * 0.157 -0.193 (0.069) (0.110) (0.167) Third child 0.101 0.381 * (0.085) (0.145) Fourth child -0.104* (0.051) Fifth child Negative log-likelihood 24,873 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed).

BARTHELEMY KUATE DEFO Effects , i + 1) . . Sties 297 CDHS, 1991: Transition to Conception Fifth Sixth First Second Third Fourth Fifth Sixth Birth Birth Birth Birth Birth Birth Birth Birth 747** -0.763 -0.758** -0.429** -0.501 ** -0.556** -0.570** -0.558** -0.858 i30) (0.035) (0.040) (0.031) (0.031) (0.034) (0.038) (0.043) (0.049) 50** 0.347** 0.389** 0.646** 0.831** 0.859** 0.943** 0.990** 10.014 }12) (0.019) (0.028) (0.022) (0.022) (0.0262) (0.0275) (0.042) (0.046) )2** 0.253 0.162* 0.330** 0.332** 0.278** 0.240* 0.319* i66) (0.060) (0.079) (0.058) (0.061) (0.073) (0.097) (0.125) 57 -0.193 -0.269 0.284* 0.605** 0.304* 0.726 10) (0.167) (0.139) (0.124) (0.195) (0.149) (0.216) 31 0.381* 0.094 -0.020 -0.055 -0.363 i85) (0.145) (0.117) (0.090) (0.098) (0.113) -0.104* -0.018 -0.016 -0.080 (0.051) (0.068) (0.066) (0.081) -0.045 (0.072) -0.005 (0.053) 11,062

298 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON TABLE 8-10 Six-Equation Joint Hazard Model of Long-Term Mortality Effects on Fertility: The First (or Second) Child Who Opens the Birth-to Conception Interval [i, i + 1) Dies in Its First Year of Life and at Least 1 Month before the Conception of Children of Higher Parities (CMM3) CDHS, 1991: Transition to Conception Variable First Second Third Fourth Fifth Sixth Birth Birth Birth Birth Birth Birth Intercept in duration Shift of the conception hazard upon death in the first year of life -0.429** -0.969** -1.402** -1.713** -1.012** -1.668** (0.030) (0.082) (0.459) (0.392) (0.240) (0.207) 0.645** 0.844** 0.868** 0.937** 0.981** 0.982** (0.023) (0.022) (0.025) (0.026) (0.037) (0.042) First child 0.517** 0.947** 1.258** 0.559* 1.100** (0.080) (0.459) (0.393) (0.243) (0.216) Second child 0.494 1.030* 0.431 0.995** (0.463) (0.395) (0.232) (0.210) Negative log-likelihood 11,020 NOTES: Standard errors are in parentheses below the estimated coefficients. Significance level: **, 1 percent; *, 5 percent (two-tailed). Effects of the First Child's Death on Long-Term Fertility Behavior Tables 8-9 and 8-10 show the effects of the survival status of preceding siblings on the hazards of conception of the subsequent births. Table 8-10 fine- tunes the indicator of the mortality experience of preceding siblings by focusing on the survival of the first two siblings in the first year of life at the time of the conception of the index child who is the third, fourth, fifth, and sixth child (when assessing the effects of the first child's death), while controlling for the survival status of the second birth. These indicators are designed to test my second hypothesis regarding the distinctive role played by the survival status of the first (and to some extent the second birth) on the fertility decision process of couples as they go through their life-cycle fertility. Before having children, couples have little knowledge on which to base expectations of the future health and survival of their offspring. As they begin to

BARTHELEMY KUATE DEFO 299 have children and develop or revise family-building strategies, it is plausible that their perceptions of their "luck" with children the probability of survival and their inherent frailty are, in large part, based on their experience with the first born. Moreover, as discussed above, in most African cultures in general and in Cameroon in particular, the first child has special meaning in a social context where specific rituals and values are attached to the first born, and on which the prestige, social integration, and family recognition of the new mother is founded. As in Table 8-9, in Table 8-10 I assess the distribution of the effects of the death of the first and second births on subsequent birth intervals. Such estimates clearly separate the physiological mechanism from the purely behavioral mecha- nism of child replacement. Indeed, since breastfeeding does not extend beyond a given birth interval for the child initiating the interval, the effects of the death of child of parity j on the probability of conceiving child of rank say j + 3 is independent of the breastfeeding status of child j. Table 8-10 shows the matrix of transition to higher parities given the survival status of the first and second births. In all transitions, the death of the first child significantly shifts upward the hazard of conceptions of higher-order births. This result is robust across the two data sets. I find that, even when the first child survival status is considered only in the first year of life at the time of the conception of the subsequent births, there are still robust fertility responses to that mortality experience. In contrast, deaths of higher-order children are less associated with increased hazards of subsequent conception. These results sug- gest that the death of the first child may be more crucial for life-cycle fertility behavior than the death of higher-parity siblings. The long-term response sug- gests that volitional replacement or insurance behavior is occurring. It is, how- ever, surprising that the survival experience of subsequent children is so much less important. Mensch (1985) suggests that if the timing of the volitional re- sponse depends on the level of fertility, then it can be expected that, in a setting where fertility and desired family size are high, a conscious response to mortality will appear only at later parities. My results suggest that this conjecture is not confirmed by the Cameroon data. As discussed, the social context of reproduction in most African societies is likely to make the couple have a complete lack of "security" as regards their chances to have progeny following the first child's death. Hence, the death of the first born (or second births) may have a large effect on both short- and long-term fertility responses, far exceeding the simple replacement effect. Therefore, the fertility behavior of a woman may be more influenced over time by the sense of "insurance" derived from the survival status of her first birth rather than a set target family size. Thus, the empirical implication of the long-term replacement strategy caused by the death of a first birth may be evidence of hoarding behav- ior. Indeed, Ben-Porath (1978) notes that hoarding and replacement behavior are substitutes in that families may learn to expect high mortality and respond to it by hoarding. This argument is especially pertinent in the African context because

300 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON many African women find it difficult to understand that the number of their offspring is, to a large extent, within human control (van de Walle, 1992~. Child- lessness and infertility are often ascribed to supernatural forces rather than to the outcome of impaired reproductive health (Larsen, 1995~. Parity-Specific Effects of the Fertility Response to Child Loss As noted above, most previous studies of the effects of child mortality on fertility have assumed that those effects were the same across parities. Essen- tially, such studies preclude the reproductive life-cycle perspective in assessing the effects of child death on the hazards of closing the birth interval. That is, the effects of all variables are constrained to be equal across parities. This assump- tion may have undesirable effects on the life-cycle perspective to reproductive behavior since it assumes, among other things, that the process is homogeneous across parities when, in fact, the effects of many variables, including mortality, are parity specific. In fact, countless demographic, epidemiologic, and medical studies have consistently shown that firstborns had higher mortality risks than subsequent births and that above parity 4 or so, the mortality risks increase with parity. Previous analyses of the effects of child mortality on birth intervals raise a number of problems. Couples with many children are more likely than couples with few children to have shorter intervals on the one hand and more experience of child deaths on the other. This may create a spurious negative correlation between child mortality and closed birth intervals and exaggerate the effect of prior mortality on the birth intervals. My specification of the time sequence of child mortality and subsequent conception eliminates such bias. The two data sets show that the magnitude of the relative risks of a subsequent conception due to a child death vary across parity, as expected. Furthermore, the effects of a number of measured covariates, as well as unobserved factors (particularly woman-specific unobserved heterogeneity), tend to vary greatly by parity. I also attempted a number of interaction effects between mortality measures and selected covariates. But none of them was statistically significant in the final models. In particular, I test the hypothesis that the death of a child of the preferable sex may result in a different pattern of fertility response than the death of a less preferable one by interacting the preceding child mortality experience with sex of the deceased child. SUMMARY AND DISCUSSION In this chapter I formulate and estimate a system of hazard models as a reduced-form approach to dynamic models of fertility response to child loss. In both data sets used and for all estimated transitions, child deaths reduce the length of birth intervals and increase the probability of conceiving a subsequent child.

BARTHELEMY KUATE DEFO 301 Basically, a child death in the family leads to significantly lower probabilities of stopping at a given parity, particularly at lower parities. Thus, replacement behavior is a significant phenomenon, occurs fairly quickly, and has long-term effects (particularly following the death of the first child). In both data sets, an infant death is shown to be associated with a reduction of the median birth interval of 5 months. Several studies summarized by Preston (1978) suggest a maximum of 13 months, whereas the evidence from Cameroon (where there is still full adherence to the practice of breastfeeding) points to values between 4 and 9 months at the national level. Estimates obtained by Grummer-Strawn et al. (in this volume) are approximately 6 months for the African countries studied, 4 months for Asia, and 3 months for Latin America. I also find that the reduction in birth intervals is greater for neonatal deaths than postneonatal deaths. Basi- cally, the earlier a child death, the more quickly childbearing would resume and the shorter the subsequent interbirth interval. The average interval between births increased steadily from 14.8 months following a stillbirth to 15.9 months if the first baby of two died within 1 month, to 35.1 months if the firstborn survived at least 2 years. This is almost certainly true for other African societies, particu- larly those where long periods of postnatal abstinence are traditionally practiced. Controlling for a series of measured covariates has negligible influence on these results. Furthermore, there is little evidence that unobservables correlated across observations (women) or across parities for the same woman, which have received much attention in the demographic literature, are empirically important in explaining fertility responses to a child death once woman-specific and parity- specific stopping behavior has been accounted for. The estimated effects of other variables in the regressions are found to be very similar both in the presence and absence of controls for unobserved heterogeneity, suggesting that these con- trols although significantly associated with the hazards of conception are not critical for studying the effects of infant and child mortality on fertility. The effects of the death of the first birth on fertility in the future (transitions from the third birth to the conception of the fourth birth, from the fourth birth to the conception of the fifth birth, and from the fifth birth to the conception of the sixth birth) are indicative of strong lagged fertility responses to child death, in addition to robust instantaneous fertility responses to the first child loss (transi- tion from the first birth to the conception of the second birth). The most likely situation may be one in which couples' replacement strategy and reaction to the first child's death is swift and their attempts to accelerate a conception will follow shortly after the death of a wanted child. Furthermore, response with longer lags is also possible and appears to significantly matter. Ben-Porath (1978) notes that there might be a learning process in a sequential framework when experienced mortality affects expected mortality. This learning process seems consistent with my findings that the death of the first two children (and especially the firstborn) shift upward the conception hazards for the subsequent births, thereby reducing the average birth intervals among women who have lost

302 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON their first children compared with those who have not (even after controlling for the mortality of higher-order births). My finding that an infant death has both short-term and long-term effects on fertility behavior is consistent with the evidence generated elsewhere in Africa (e.g., Bocquier, 1991~. I had hypothesized that the behavioral replacement effect could be accomplished by compressing interbirth intervals, as my results across parities show. Furthermore, I note as expected that the empirical implication of the behavioral replacement mechanism is a lagged fertility response to changes in mortality, as shown by the robust findings regarding the mortality effects of the first and second births on future reproductive behavior. In comparing the increases in conception risks in the short-term upon infant death (when the child who opens the birth-to-conception interval dies in the first year of life and at least 1 month before the conception of the index child) (e.g., Table 8-8) and the increases in conception risks in the long-term upon death of infants of successive parities (when a child who opens the birth-to-conception interval [i, i + 1) dies in the first year of life and at least 1 month before the conception of the child of parity i + 2, i + 3, i + 4, and so forth) (Table 8-10), my results demonstrate that the volitional replacement mechanism is generally less powerful than the physiological replacement effect working through breast- feeding, since all the estimated risks in the model confounding the physiological and volitional replacement effects are higher than those of the models of voli- tional replacement effects alone. Despite an ever-growing body of data on African demography and a range of theories of demographic change, much is still unclear about the relationships between mortality and fertility in this region, especially the insurance strategy of fertility response to child loss. Furthermore, much more empirical research has been devoted to the replacement-type fertility response to infant and child mortal- ity and to the physiological effect than to the extent to which surrounding mortal- ity conditions affect individual fertility, as in the case involving the insurance effect. Any empirical studies of the insurance effect require some measure of couples' perceptions of child death risks (see Montgomery, in this volume). The ideal data for such analysis would be from prospective surveys that provide direct before and after comparisons of stated intentions as well as actual behavior. There is a need to combine quantitative and qualitative research methodologies to address these links, because the knowledge and understanding of the sociocul- tural context of the fertility and mortality processes in Africa is still limited. Aggregate data reviewed here indicate a fairly sluggish response of fertility to infant mortality in the studies in African countries, in contrast to a few studies carried out elsewhere using aggregate time series data that have looked at the effects of infant and child mortality on fertility over time (Yamada, 1984; Schultz, 1985) and have found significant effects. The lack of significant effects in Africa may be due at least in part to left-out variables (possibly operating simulta- neously on fertility and mortality) that may operate in one context and not in the

BARTHELEMY KUATE DEFO 303 other, or to the nature of the data and its quality, or to measurements and estima- tion problems, or a combination of the above. It is likely that the way in which fertility responds to improvements in child survival in Africa will depend not only on the age pattern of declines but also on changes in the distribution of causes of death. In this respect, an emerging issue in the link between child mortality and fertility is the impact of the HIV epidemic on fertility (Cohen and Trussell, 1996~. In areas where AIDS deaths are concen- trated, it is possible that there is a desire to increase fertility to replace lost adults (Ainsworth et al., in this volume). At the same time, Gregson (1994) suggests that the prevalence of HIV and AIDS may reduce fertility, principally through an increased and more effective use of condoms. At the present, however, evidence is not sufficient to cast further light on the potential relationships (Cohen and Trussell, 1996~. APPENDIX: HAZARD MODELS AS A REDUCED-FORM APPROACH TO DYNAMIC (LIFE-CYCLE) MODELS OF FERTILITY RESPONSE TO CHILD MORTALITY This appendix presents my implementation of a system of hazard models for the estimation of the effects of mortality on times to conception. The framework is derived from a general framework for estimation of flexibly parameterized competing risks and multistate duration models (Lancaster, 1985; Heckman and Singer, 1985~. Leung (1988) critically evaluates standard assessment methods and favors the use of hazard models in which right-censored conception intervals and time-varying covariates can be handled. My model follows that specification and also controls not only for woman-specific unobserved heterogeneity as sev- eral previous studies have done (e.g., Newman and McCulloch, 1984; Leung, 1988; Panis and Lillard, 1993), but also for parity-specific stopping unobserved heterogeneity (as in Heckman and Walker, 1990, 1991~. This system consists of a six-equation joint equation model in which each equation represents the hazard of making a particular transition to a birth of parity j, caused by the death of a child of lower parity. My measures of mortality (described in the text) are designed to establish the time sequence between the timing of a child death and the timing of subsequent conceptions, a necessary exposure-occurrence condition to make causal inferences between the occurrence of a child death and the shift in risks of a following conception. I describe the essential features of this six-equation joint equation hazard models as a reduced-form approach to the life-cycle models of fertility that have been developed in the literature, and I apply this system of hazard models to fertility response to infant and child mortality. Such a system of hazard models within a life-cycle perspective is important for several reasons. First, introducing a decision-making process within a life-cycle framework (i.e., couples essentially

304 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON update their decisions regarding childbearing over their reproductive career) makes explicit the existence of other life-cycle options among which couples may choose to substitute their fertility at different ages over the life cycle. As such, changes in mortality experience over the life cycle may result in changes in the timing of fertility demand (thus implying parity-specific decision making), even if they do not cause lifetime fertility to change. Second, the life-cycle context is also the appropriate setting within which to consider the consequences of the stochastic nature of human reproduction and reproductive behavior. Third, the dynamic setting provides a more appropriate context within which to examine the relationships between infant and child mortality and fertility. Finally, model- ing human reproduction as a stochastic process has a long tradition in population biology and mathematical demography (Sheps and Menken, 1973~. My empirical specification follows the econometric approaches to life-cycle models of fertility. I pay attention to the timing of first birth and the spacing between births, and I argue that the spacing of births is influenced by the past and recent infant mortality experience of couples. Thus, since biological constraints would prevent most couples from having all desired births at once, it is of interest to ask, once the first birth occurs, what mechanisms lead to longer or shorter birth intervals? Two considerations suggest examining explicitly dynamic fertility models. The first is the inherently multiperiod nature of the data. The second is that, from both theoretical and policy perspectives, the age at first birth, the spacing between births, and the joint timing of fertility with other life-cycle choices have important ramifications, in part because the fertility decision is inherently discrete and there is considerable heterogeneity in completed family size. Thus, any single equation approach inherently runs into the problem of how to treat the women who never experienced the event (e.g., a woman who never had a birth in regressions on age at first birth) or women who never (up to the interview date) had a subsequent birth in regressions on birth spacing. One approach to this problem is standard hazard modeling (Lancaster, 1990~. In that approach, instead of directly modeling the timing of the event, one models the probability of the occurrence of the event in each period (Newman and McCulloch, 1984~. That is, the probability of the JO birth in period (or by exposure) i, conditional on it not having occurred through period i - 1. This hazard approach provides a natural way to model incomplete histories, nonoccurrence of the event (a subsequent birth), and a set of covariates. Such an approach has been attempted in a few previous studies (e.g., Mensch, 1985~. In her study, Mensch examines the timing of replacement hypothesis by carrying out separately the analysis for specific birth intervals (or parities). It, however, does not solve several other problems (for a review, see Hotz et al., in press). First, it provides little insight into how to summarize the information in past and future covariates. Second, it does not solve the dynamic selection problem. To be in the sample of individuals on which one estimates the time between the first and second birth, one must have had a first birth. This is a selected sample. This

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

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<t' + ~kZ(t)~- (7) Parity dependence is incorporated by allowing coefficients to vary with par- ity. One important feature of this system of hazard model formulation is that it provides a natural way to allow time-varying covariates to affect the timing of the

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

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

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

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.

BARTHELEMY KUATE DEFO 311 REFERENCES Acsadi, G., G. Johnson-Acsadi, and R. Bulatao 1 Go Population Growth and Reproduction in Sub-Saharan Africa: Technical Analyses of Fer- tility and Its Consequences. Washington, D.C.: The World Bank. Bakketeig, L., H. Hoffman, and E. Harley 1979 The tendency to repeat gestational age and birth weight in successive births. American Journal of Obstetrics and Gynecology 195:1086-1103. Balepa, M., M. Fotso, and B. Barrere 1992 Enque^te De'mographique et de Sante' Cameroun 1991. Yaounde: Direction Nationale du Deuxieme Recensement General de la Population. Barbieri, M. 1994 Is the current decline in infant and child mortality in sub-Saharan Africa a sign of future fertility changes? Pp. 21-42 in T. Locoh and V. Hertich, eds., The Onset of Fertility Transition in Sub-Saharan Africa. Liege, Belgium: Ordina Editions. Ben-Porath, Y. 1978 Fertility response to child mortality: Microdata from Israel. Pp. 161-180 in S. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Bocquier, P. 1991 Les relations entre mortalite des enfants et espacement des naissances dans la Banlieue de Dakar (Senegal). Population 46:813-831. Bongaarts, J. 1981 The impact on fertility of traditional and changing child-spacing practices. Pp. 111-129 in H. Page and R. Lesthaeghe, eds., Child-Spacing in Tropical Africa: Traditions and Change. New York: Academic Press. Brass, W. 1993 Child mortality improvement and the initiation of fertility falls in Kenya. International Population Conference 1:73-80. Brass, W., and C. Jolly, eds. 1993 Population Dynamics of Kenya. Committee on Population, National Research Council. Washington, D.C.: National Academy Press. Caldwell, J., and P. Caldwell 1981 The function of child-spacing in traditional societies and the direction of change. Pp. 73- 92 in H. Page and R. Lesthaeghe, eds., Child Spacing in Tropical Africa: Traditions and Change. New York: Academic Press. Callum, C., S. Farid, and M. Moussa 1988 Child loss and its impact on fertility. Pp. 239-278 in A. Hallouda, S. Farid, and S. Cochrane, eds., Egypt: Demographic Responses to Modernization. Cairo: Central Agency for Public Mobilization and Statistics. Cantrelle, P., and H. Leridon 1971 Breast-feeding, mortality in childhood and fertility in a rural zone of Senegal. Population Studies 25:505-533. Cantrelle, P., B. Ferry, and J. Mondot 1978 Relationships between fertility and mortality in Tropical Africa. Pp. 181-205 in S. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Cleland, J., and C. Wilson 1987 Demand theories of the fertility transition: An iconoclastic view. Population Studies 41 :5-30. Coale, A. 1966 Estimates of fertility and mortality in Tropical Africa. Population Index 32.

312 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON Cochrane, S., and K. Zachariah 1984 Infant and Child Mortality as a Determinant of Fertility: The Policy Implications. World Bank Staff Papers no. 556. Washington, D.C.: The World Bank. Cohen, B. 1993 Fertility levels, differentials and trends. Pp. 8-67 in K. Foote, K. Hill, and L. Martin, eds., Demographic Change in Sub-Saharan Africa. Committee on Population, National Re- search Council. Washington, D.C.: National Academy Press. Cohen, B., and J. Trussell, eds. 1996 Preventing and Mitigating AIDS in Sub-Saharan Africa. Committee on Population, Na- tional Research Council. Washington, D.C.: National Academy Press. David, N., and D. Voaz 1981 Societal causes of infertility and population decline among the settled Fulani of North Cameroon. Man 16:644-664. DSCN (Direction de la Statistique et de la Comptabilite Nationale) 1983 Enque^te Nationale sur la Fe'condite' du Cameroun 1978, Rapport Principal. Yaounde: Ministere de l'Economie et du Plan. Farah, A. 1982 The influence of child mortality on fertility related attitudes and behavior in Greater Khartoum. Cairo Demographic Centre Research Monograph Series 10:227-261. Folta, J., and E. Deck 1988 The impact of children's death on Shona mothers and families. Journal of Comparative Family Studies 19:433-451. Gini, C. 1924 Premieres recherches sur la fecondabilite de la femme. Proceedings of International Mathematics Congress 2:889-892. Gregson, S. 1994 Will HIV become a major determinant of fertility in sub-Saharan Africa? Journal of Development Studies 30(3):650-679. Guz, D., and J. Hobcraft 1991 Breast-feeding and fertility: A comparative analysis. Population Studies 45:91-108. Heckman, J., and B. Singer 1984 A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica 52:271-320. 1985 Social science duration analysis. In J. Heckman and B. Singer, eds., Longitudinal Analy- sis of Labor Market Data. Cambridge, England: Cambridge University Press. Heckman, J., and J. Walker 1987 Using goodness of fit and other criteria to choose among competing duration models: A case study of the Hutterite data. In C. Clogg, ea., Sociological Methodology. Washing- ton, D.C.: American Sociological Association. 1990 The relationships between wages and income and the timing and spacing of births: Evi- dence from Swedish longitudinal data. Econometrica 58:1411-1441. 1991 Economic models of fertility dynamics: A study of Swedish fertility. Research in Popu- lation Economics 7:3-91. Heckman, J., J. Hotz, and J. Walker 1985 New evidence on the timing and spacing of births. American Economic Review 75:179- 184. Heer, D., and J. Wu 1978 Effects in rural Taiwan and urban Morocco: Combining individual and aggregate data. Pp. 135-159 in S.H. Preston, ea., The Effects of Infant and Child Mortality on Fertility. New York: Academic Press.

BARTHELEMY KUATE DEFO 313 Hill, A. 1993 Trends in childhood mortality. Pp. 153-217 in K.A. Foote, K. Hill, and L. Martin, eds., Demographic Change in Sub-Saharan Africa. Washington, D.C.: National Academy Press. Hobcraft, J. 1994 The Health Rationale for Family Planning: Timing of Births and Child Survival. New York: United Nations. Hoel, P., S. Port, and C. Stone 1987 Introduction to Stochastic Processes. Prospect Heights, Ill.: Waveland Press. Hoffman, H., and L. Bakketeig 1984 Heterogeneity of intrauterine growth retardation and recurrence risks. Seminars in Perinatology 8:15-24. Hotz, J., J. Klerman, and R. Willis in The economics of fertility in developed countries: A survey. In M. Rosenzweig and O. Stark, eds., Handbook of Population and Family Economics. Amsterdam, Holland: North-Holland. Hull, V., and M. Simpson 1985 Breast-feeding, Child Health and Child Spacing: Cross-Cultural Perspectives. London: press Croom Helm. Jensen, A. 1993 Child Survival and Fertility in Kenya. Paper presented at the XXIIIrd IUSSP Interna- tional Population Conference, Montreal, Canada, August. 1996 The Impact of Child Mortality on Fertility in Kenya, Zimbabwe and Botswana: Re- examining the Links. Unpublished manuscript, Norwegian Institute for Urban and Re- gional Research, Oslo, Norway. Kalbfleisch, J.D., and R.L. Prentice 1980 The Statistical Analysis of Failure Time Data. New York: John Wiley & Sons. Kelley, A., and C. Nobbe 1990 Kenya at the Demographic Turning Point? Hypotheses and a Proposed Research Agenda. World Bank Discussion Papers no. 107. Washington, D.C.: The World Bank. Kuate Defo, B. 1996 Areal and socioeconomic differentials in infant and child mortality in Cameroon. Social Science and Medicine 42:399-420. Kuate Defo, B., and A. Palloni 1996 Determinants of mortality among Cameroonian children: Are the effects of breast-feed- ing and pace of childbearing artifacts? Genus LI:69-96. Lancaster, T. 1985 Generalized residuals and heterogeneous duration models with applications to the Weibull models. Journal of Econometrics 28:54. 1990 Larsen, U. 1994 Sterility in sub-Saharan Africa. Population Studies 48(3):459-474. 1995 Differentials in infertility in Cameroon and Nigeria. Population Studies 49:329-346. Larsen, U., and J. Menken 1991 Individual level sterility. A new method of estimation with application to sub-Saharan Africa. Demography 28:229-249. Lesthaeghe, R. 1989 Reproduction and Social Organisation in Sub-Saharan Africa. Berkeley: University of California Press. The Econometric Analysis of Transition Data. New York: Cambridge University Press.

314 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON Lesthaeghe, R., P. Ohadike, J. Kocker, and H. Page 1981 Child-spacing and fertility in sub-Saharan Africa: An overview of issues. Pp. 3-23 in H. Page and R. Lesthaeghe, eds., Child Spacing in Tropical Africa: Traditions and Change. New York: Academic Press. Leung, S. 1988 A test for sex preferences. Journal of Population Economics 1:95-114. Livenais, P. 1984 Declin de la mortalite dans ltenfance et stabilite de la recondite dans une zone rurale Mossi (Haute-Volta). Cahiers ORSTOM XX(2):273-282. Locoh, T., and V. Hertrich, eds. 1994 The Onset of Fertility Transition in Sub-Saharan Africa. Liege, Belgium: Ordina Edi- tions. Mensch, B. 1985 The effect of child mortality on contraceptive use and fertility in Colombia, Costa Rica, and Korea. Population Studies 39(2):309-327. Newman, J., and C. McCulloch 1984 A hazard rate approach to the timing of births. Econometrica 52:939-961. Njogu, W. 1992 Trends and determinants of contraceptive use in Kenya. Demography 28:83-99. Okojie, C. 1991 Fertility response to child survival in Nigeria: An analysis of microdata from Bendel State. Research in Population Economics 7:93-112. Olsen, R. 1980 Estimating the effect of child mortality on the number of births. Demography 17:429 443. Olsen, R., and K. Wolpin 1983 The impact of exogenous child mortality on fertility: A waiting time regression with dynamic regressors. Econometrica 51:731-749. Page, H., and R. Lesthaeghe, eds. 1981 Child Spacing in Tropical Africa: Traditions and Change. New York: Academic Press. Panis, C., and L. Lillard 1993 Timing of Child Replacement Effects on Fertility in Malaysia. Labor and Population Program Working Paper Series 93-13. Santa Monica, Calif.: RAND. Popkin, B., D. Guilkey, J. Akin, L. Adair, and R. Udry 1993 Nutrition, lactation and birth spacing in Filipino women. Demography 30:333-352. Preston, S.H., ed. 1978 The Effects of Infant and Child Mortality on Fertility. New York: Academic Press. Rodriguez, G., and J. Cleland 1981 Socio-economic determinants of marital fertility in twenty countries: A multivariate analysis. In World Fertility Survey Conference 1980: Voorburg, Netherlands: International Statistical Institute. Record of Proceedings 2. Rodriguez, G., J. Hobcraft, J. Menken, and J. Trussell 1984 A comparative analysis of the determinants of birth intervals. WFS Comparative Studies 30: 1-30. Schoenmaeckers, R., I. Shah, R. Lesthaeghe, and O. Tambashe 1981 The child-spacing tradition and the postpartum taboo in tropical Africa: Anthropological evidence. Pp. 25-71 in H. Page and R. Lesthaeghe, eds., Child Spacing in Tropical Africa: Traditions and Change. New York: Academic Press. Schultz, T.P. 1985 Changing world prices, women's wages, and the fertility transition: Sweden, 1860-1910. Journal of Political Economy 93(6): 1126- 1154.

BARTHELEMY KUATE DEFO 315 Sembajwe, I. 1981 Fertility and Infant Mortality Amongst the Yoruba in Western Nigeria. Changing Family Project Series Monograph no. 6. Canberra, Australia: Department of Demography. Sheps, M. 1965 An analysis of reproductive patterns in an American isolate. Population Studies 19:65- 80. Sheps, M., and J. Menken 1973 Mathematical Models of Conception and Birth. Chicago, Ill.: University of Chicago Press. Trussell, J., and G. Rodriguez 1990 Heterogeneity in demographic research. Pp. 111-132 in J. Adams, D. Lam, A. Hermalin, and P. Smouse, eds., Convergent Issues in Genetics and Demography. Oxford, England: Oxford University Press. Trussell, J., E. van de Walle, and F. van de Walle 1989 Norms and behavior in Burkinabe fertility. Population Studies 43(3):429-454. United Nations 1987 Family Building by Fate or Design. New York: United Nations. 1991 Child Mortality in Developing Countries: Socio-Economic Differentials, Trends and Implications. New York: United Nations. van de Walle, E. 1992 Ware, H. 1977 The relationship between infant mortality and fertility: Replacement and insurance ef- fects. Pp. 205-222 in International Population Conference, Vol. I. Mexico. Liege, Bel Fertility, conscious choice and numeracy. Demography 29:487-502. glum: IUSSP. Winikoff, B., M. Castle, and V.H. Laukaran 1988 Feeding Infants in Four Societies: Causes and Consequences of Mothers' Choices. New York: Greenwood Press. Wolpin, K. 1984 An estimable dynamic stochastic model of fertility and child mortality. Journal of Politi- cal Economy 92(5):852-874. World Health Organization 1991 Infertility. Geneva: World Health Organization. Yamada, T. 1984 Causal Relationships between Infant Mortality and Fertility in Developed and Less De- veloped Countries. National Bureau of Economic Research (NBER) Working Paper no. 1528. NBER, Cambridge, Mass. Yi, K., J. Walker, and B. Honore 1987 CTM: A User's Guide. Unpublished manuscript, National Opinion Research Center, University of Chicago.