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OCR for page 254
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
OCR for page 255
BARTHELEMY KUATE DEFO
255
high-fertility, high-mortality environment with very little modern contraceptive
use. The case of Cameroon thus raises questions about the response to mortality
in sub-Saharan Africa more generally where the levels of both mortality and
fertility remain high in most countries (Hill, 1993; Cohen, 1993~. In the virtual
absence of effective means of contraception other than breastfeeding, the short-
ening of birth interval induced by a reduction in infant and child survivorship
may signify a higher ultimate parity. Higher fertility may thus be largely a
biological response to higher mortality. It is more likely that the behavioral
response has a greater effect on the total number of children to whom a woman
gives birth, or alternatively, on the parity of her last live birth since women
entertain a rough idea of the number of surviving children they would like to
have, even if they do not have a predetermined target (van de Walle, 1992~. In
this chapter, I do not estimate a tightly structural model of fertility because the
main question does child mortality matter for fertility behavior? is still open.
A positive answer to this question has been assumed in the demographic transi-
tion theory literature, but without much factual basis from developing countries.
A central finding documented in this study is that current and past child mortality
experiences play a strong role in reproductive behavior in Cameroon, even after
correcting for measured and unmeasured heterogeneity.
EFFECTS OF INFANT AND CHILD MORTALITY ON
REPRODUCTIVE BEHAVIOR IN AFRICA: WHAT DO WE KNOW?
Empirical studies of the effects of infant and child mortality on fertility in
Africa fall into two broad categories: aggregate studies, which are based on
samples consisting of national or subnational averages usually using censuses,
cross-sectional surveys, or registration data; and individual-level studies, which
are based on sample survey observations drawn from the reproductive experience
of individual women. Table 8-1 presents an overview of published work that has
attempted to measure the fertility response to infant and child mortality, using
aggregate or individual data.
Aggregate Level
Studies based on aggregate data have one important advantage over indi-
vidual data: the potential for measuring the overall implications of improvements
in child survival for fertility and population growth. Because many of the hy-
pothesized effects of changes in mortality on fertility work through changes in
environmental conditions rather than through individual experience, studies based
on individual data alone can only measure accurately the physiological and voli-
tional replacement effects (United Nations, 1987~. These effects are not expected
to compensate fully for changes in mortality even if they operate jointly. Aggre-
gate studies of the effects of infant and child mortality on fertility in Africa are
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256 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON
TABLE 8-1 Synopsis of Published Studies of the Effects of Infant and Child
Mortality on Fertility in Afnca: Aggregate and Individual Data
Characteristics of the Study
Year/Period Measure
of Data
Source Collection Country/Strata Study Design Mortality Fertility
Barbieri, 1994 1985-1989 10 sub-Saharan DHS surveys Probability TFR for
African countriesa of dying women al
between 0-26 15-40
months
Bocquier, 1991 1986 Pikine, Senegal Retrospective Child death Probabilit
survey of 2,807 of a folio'
women aged 15-49 conceptio:
(and 7,632 births)
Brass, 1993 1969, 1978, Kenya 1969 census, 5Qlo TFR
1989 1977- 1978 WFS proportion
and 1989 DHS of children
surveys died per woman
Brass and Jolly, 1977-1978 Kenya and WFS and DHS 50lo TFR
1993 provinces surveys
and districts
Callum et al., 1980 Egypt Retrospective Child death Percent oi
1988 (WFS) survey with no a'
births; me
of childre
Cantrelle 1940-1972 12 sub-Saharan Retrospective loo, 2Q1 TFR, GF}
et al., 1978 African countriesb and prospective 2Qo
surveys
Cantrelle 1962-1968 Niakhar, rural Longitudinal Child death Mean birt
and Leridon, Senegal study of 8,456 interval
1971 live births
Coale, 1966 1940-1962 13 sub-Saharan Retrospective loo, 2Q1 TFR
African countriesC surveys
Cochrane 1977-1978 Lesotho (1977) and Retrospective Child death Birth inte:
and Zachariah, Kenya (1977- 1978) surveys
1984 (in [WFS] a study
of 25 LDCs)
Farah, 1982 1975 Greater Khartoum, Retrospective Child death CEB
Sudan survey of 2,045
ever-married
women aged 15-44
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BARTHELEMY KUATE DEFO
Child
257
Ire Mortality Effects Association
Mortality
lity Fertility Type of Analysis Replacement Insurance Fertility
Utility TFR for Descriptive Unclear n.a. Yes
ng women aged analysis and
an 0-26 15-40 linear regression
s analysis
(aggregate data)
death Probability Nonparametric Yes n.a. Yes
of a following survival
conception analysis
(individual data)
TFR Descriptive No n.a. No
Lion analysis
Wren (aggregate data)
er woman
TFR
Descriptive No n.a. No
analysis
(aggregate data)
death Percent of women Descriptive Yes Unclear Yes
with no additional and multivariate
births; mean number analyses
of children born (individual data)
Q1 TFR, GFR Correlation n.a. n.a. Unclear
analysis
(aggregate data)
death Mean birth Descriptive Yes n.a. Yes
interval analysis
(aggregate data)
Q1 TFR Correlation n.a. n.a. Unclear
analysis
(aggregate data)
death Birth interval Multivariate Yes n.a. Yes
analysis
(individual data)
death CEB Simple Yes n.a. Yes
classification
analysis
(individual data)
continued on next page
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258 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON
TABLE 8-1 (continue])
Characteristics of the Study
Year/Period Measure
of Data
Source Collection Country/Strata Study Design Mortality Fertility
Folta and Deck, No date Zimbabwe Participant Child death Fertility
1988 observation and following
in-depth interviews a child de
of 124 women
Heer and Wu, 1966 Urban Morocco Area probability Number of the Number o
1978 sample of first three life births
currently married children that subsequer
women under age survived either to the
50 who had to age 10 or to third
experienced 3 or the time of
more live births interview
Jensen, 1993 1988, 1990 Bungoma and Cross-sectional Number of CEB
Kwale, Kenya interviews with children
132 women aged deceased
18-78
Jensen, 1996 1988-1989 Kenya, Zimbabwe, DHS surveys Infant & Hazard of
Botswana child death following
birth
Livenais, 1984 1973, Rural Mossi, Cross-sectional loo TFR
1978 Burkina-Faso surveys
Okojie, 1991 1985 Bendel state, Retrospective Proportion CEB
Nigeria survey of 1,895 of surviving
ever-married children
women aged 15-50
Sembajwe, 1981 1973 Western Nigeria Retrospective Proportion of CEB
survey children dead
NOTES: TFR, total fertility rate; GFR, general fertility rate; loo, infant mortality rate; 2Q1 = sec-
ond-year mortality rate; 2Qo, first two years mortality rate; Ado, first five years mortality rate; CEB,
children ever born; n.a., not applicable;WFS, World Fertility Survey; DHS, Demographic and Health
Survey; LDC, less-developed countries.
aThe 10 sub-Saharan African countries are Botswana (1988), Burundi (1987), Ghana (1988),
Kenya (1989), Liberia (1986), Mali (1987), Senegal (1986), Togo (1988), Uganda (1988-1989), and
Zimbabwe (1988-1989).
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BARTHELEMY KUATE DEFO
259
Ire Mortality Effects Association
Mortality
lity Fertility Type of Analysis Replacement Insurance Fertility
death Fertility Qualitative Yes ma. Yes
following analysis
a child death (individual data)
er of the Number of Multiple Yes Unclear Yes
tree life births classification
n that subsequent analysis
ed either to the (individual and
10 or to third aggregate data)
he of
few
er of CEB Multiple Yes ma. Yes
n classification
Ed analysis
(individual data)
& Hazard of a Event history Yes ma. Yes
leash following analysis
birth (individual data)
TFR Descriptive No ma. No
analysis
(aggregate data)
Lion CEB Two-stage Yes ma. Yes
viving ordinary least squares
n (individual data)
Lion of CEB Regression Yes ma. Yes
n dead (individual analysis)
bThe 12 countries are Benin (1961), Guinea (1954-1955), Burkina-Faso (1960-1961), Niger
(1960), Angola (1940, 1950), Zaire (1955-1957), Cameroon (1960), Kenya (1962), Mozambique
(1950), Rwanda (1952-1957), Tanzania (1957), and Uganda (1956).
CThe 13 countries are Benin (1961), Guinea (1954-1955), Burkina-Faso (1960-1961), Niger
(1960), Angola (1940, 1950), Zaire (1955-1957), Cameroon (1960), Kenya (1962), Mozambique
(1950), Rwanda (1952-1957), Tanzania (1957), Uganda (1956), and Senegal (1963-1970, 1972).
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260 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON
either cross-sectional studies based on national aggregates using data drawn from
several African countries (e.g., Coale, 1966; Cantrelle et al., 1978; Barbieri,
1994) or from a specific country, subregion, or province within a country (e.g.,
Heer and Wu, 1978; Livenais, 1984; Brass, 1993; Brass and Jolly, 1993~.
The general finding from these aggregate-level studies is that in Africa mor-
tality decline has had either no effects or unclear effects on fertility. Thus, the
evidence from these studies is inconclusive. The absence of a demonstrable link
between childhood mortality and fertility at the aggregate level apparently may
stem from the fact that intermediate variables, which act more directly on these
rates, are obscuring the strong positive relationship at work at the individual level
(Cantrelle et al., 1978~. In Kenya, for example, Brass (Brass, 1993; Brass and
Jolly, 1993), analyzing previous child mortality declines, and their effect on
recent fertility declines, argues that "the observations supply no evidence of any
consistent relation between the falls in fertility and the preceding (and continu-
ing) child mortality trends" (Brass, 1993:78~. Coale (1966) and Cantrelle et al.
(1978) found that the zero-order correlations for the 47 subregions of countries
for which data were available between aggregate fertility and mortality rates were
-0.38 and -0.37, respectively, thus failing to support the widely observed posi-
tive association between childhood mortality and fertility.
Individual Level
In recent years, most of the published research on the mortality-fertility
relationships has been based on survey data, such as the World Fertility Surveys
(WFS) and the Demographic and Health Surveys (DHS). The individual-level
studies reviewed in Table 8-1 consistently show that the death of an infant leads
to a shorter interval between that birth and the next, and therefore provides a clear
indication that, at the individual level, there is a significant fertility response to
child loss. For example, a detailed study of the Sine region of Senegal (Cantrelle
and Leridon, 1971) shows that the death of an infant (which is equivalent to
weaning) affects fertility. Cochrane and Zachariah (1984) use data from the WFS
of Kenya and Lesotho (among other countries studied) to measure the influence
of neonatal (0-1 month) and postneonatal (2-11 months) deaths of first, third, and
fifth children on the length of subsequent birth interval. They find that birth
intervals are reduced following the death of a child. They also show that
breastfeeding is an important factor affecting differences in birth intervals. Fur-
thermore, they found that the reduction in birth intervals is significantly greater
for neonatal deaths than postneonatal deaths for the interval between the first and
second birth but not for the other parities. This finding suggests that the mortal-
ity-induced reduction in birth interval may vary across parity. Analyzing the
possible effects of mortality on fertility among the Yoruba in Nigeria, Sembajwe
(1981) observes that the proportion of children dead increases as the number of
children ever born alive increases. In this society, however, the answer "up to
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BARTHELEMY KUATE DEFO
261
God" to the question about the family size does not seem to be influenced by the
experience of child loss.
The study by Callum et al. (1988) uses individual- and community-level data
from the Egypt WFS to attempt to assess both replacement and insurance effects
of child mortality through an examination of actual fertility outcomes according
to the number of children who have died for women of equal parity and family
size. Their fertility outcomes during the 5 years preceding the survey were
related to the number of children ever born and living and the number of children
who had died during the 5 years prior to the date of interview. As regards the
replacement effects, they found that (1) an infant death is associated with a
reduction of about 6 months (roughly 15-20 percent) in the interval to the next
live birth; (2) there is a significantly lower likelihood of contraceptive use in the
event of an infant death, which persists after controlling for parity and socioeco-
nomic status; and (3) most of the reduction in interval length among nonusers of
contraception is accounted for by the biological effect of the reduction in the
anovulatory period. Regarding the insurance effect, there was some evidence of
an individual insurance response to the experience of child loss, especially in
Cairo, Alexandria, and urban lower Egypt. The authors speculate that, in the
context of relatively high mortality, common in Africa, an insurance strategy is
more likely to be adopted in response to generally perceived rather than individu-
ally experienced mortality risks, and that, therefore, measurement at the indi-
vidual level fails to capture the full effect of the insurance response.
The fertility response to child loss in Kenya deserves special attention for
two reasons. First, it is the only African country for which there have been
several studies of the mortality effects on fertility both at the aggregate and
individual levels. Second, there are sharp discrepancies between findings at the
aggregate level and at the individual level: All aggregate-level studies find either
no effects or unclear effects of child mortality on fertility (Coale, 1966; Cantrelle
et al., 1978; Brass, 1993; Brass and Jolly, 1993; Barbieri, 1994), whereas all
individual-level studies (Cochrane and Zachariah, 1984; Jensen, 1993, 1996) find
strong evidence of fertility response to child loss. This raises important popula-
tion policy and substantive questions regarding the weight to give to the evidence
of mortality effects on fertility at the aggregate level versus individual level in
Africa more generally. Contraceptive use seems to have played a role in the
strength of the relationship between mortality and fertility in Kenya. Indeed,
child mortality was one of the main factors used to explain the high fertility rate
in Kenya during the late 1970s, and child survival programs were estimated to be
more cost effective than family planning programs in terms of lowering fertility
(Cochrane and Zachariah,1984~. Looking at the linkage between child mortality
and contraceptive use, Njogu (1992) identified in the late 1970s a strong and
negative effect on contraceptive use among women who had experienced child
loss. Ten years later the overall level of child mortality had declined and the
effect of contraceptive use had lessened. Kelley and Nobbe (1990) point to the
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262 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON
high correlation between infant mortality and family planning use at the regional
level, the highest use of contraceptives being found in areas with low infant
mortality. Jensen's study (1996) uses data from two areas in Kenya (the Muslim
Kwale in Coast Province and the Christian Bungoma in Western Province) and
finds a strong influence of child mortality on fertility and contraceptive use,
suggestive of hoarding behavior. In both areas child mortality is associated with
high fertility and constitutes the strongest barrier toward using modern contra-
ceptives.
There are virtually no good ethnographic studies of relevance to the fertility
response to child loss in Africa. The only published work to our knowledge is the
study by Folta and Deck (1988) in Zimbabwe. This study uses participant obser-
vation and in-depth interviews of 124 Shona women in Zimbabwe to show that
social pressure to replace a dead child can lead to immediate pregnancy with poor
nutrition, poor infant health, and thus a recurring cycle of infant death. In this
setting, the death of a child (especially the first child) potentially undermines the
stability of the family, its social relationships, women's health and status, eco-
nomic security, and marital longevity.
HYPOTHESES
Fertility is inextricably bound up with many aspects of economic and social
behavior. At both the micro and the macro level, it is useful to think of fertility as
mediated by a set of variables defining exposure to intercourse, the probability of
conception, and the probability of successful gestation and parturition. These
intermediate variables constitute components of a conceptual framework of the
determinants of fertility, which, by definition, must stand between fertility and
any type of social or economic explanation. All elements of choice or social
behavior work through the intermediate variables to influence fertility.
The relationships between infant mortality and fertility are exceedingly com-
plex, and many of the factors involved are poorly understood. A joint decline of
infant mortality and fertility rates in recent years as observed in Cameroon is
typical for a number of African countries (for reviews, see Locoh and Hertrich,
1994; Hill, 1993; Cohen, 1993) and non-African countries (United Nations, 1987)
over the past decade. The sources of this correlation may be categorized accord-
ing to the direction of the effect.
First, infant mortality and fertility may be positively correlated if both in-
vestments in child health and demand for children are functions of the same
prevailing influential variables (Preston, 1978; Panis and Lillard, 1993~.
Second, a rapid pace of childbearing may cause high mortality. The over-
whelming evidence is that short birth intervals have strong effects on infant and
child mortality; such a result has been reported in Cameroon (Kuate Defo and
Palloni, 1996) and elsewhere (for a review, see Hobcraft, 1994~. This effect of
fertility on mortality can occur because of (1) increased sibling competition for
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BARTHELEMY KUATE DEFO
263
resources (including child care, family assets, and income); (2) increased oppor-
tunities for transmission of infectious diseases as a result of overcrowding, which
has been shown to be an important determinant of infant and child mortality in
Cameroon; or (3) the maternal depletion syndrome, in which a rapid pace of
fertility may imply that the mother has not had sufficient time to regain her health
or nutritional status to adequately host a fetus and facilitate its normal growth.
Finally, high child mortality may induce high fertility (Preston, 1978~. This
may happen as a result of several mechanisms. The death of the child initiating
the birth interval may trigger the rapid closure of the interval either through a
physiological replacement mechanism whereby the death of the child leads to
cessation of breastfeeding and the consequent shortening of postpartum amenor-
rhea; through a volitional replacement mechanism (that is, the responsiveness of
pregnancy decisions to the occurrence of the death of infants who either never
breastfed or stopped breastfeeding before death); or through a generalized sur-
vival uncertainty (that is, as the probability of survival falls, there is also a
tendency to have children earlier and thus closely spaced).
In assessing the effects of infant mortality on fertility, I depart from previous
studies on Africa (and reviewed above) and other parts of the world that have
shown that, over the course of the family life cycle, couples learn about child-
bearing and child mortality (e.g., Preston, 1978; Ben-Porath, 1978; Mensch, 1985;
United Nations, 1987~. These experiences may well lead them to revise and
adjust their desired number of children and possibly diminish or increase their
propensity to replace deceased children. Because we do not explicitly model
breastfeeding and contraceptive behavior (since these variables may be endog-
enous to the fertility decision), we cannot empirically distinguish these two causal
mechanisms directly for the short-term replacement effects. (That is, we cannot
separate the physiological from the volitional replacement effects of the death of
child of parity i who opens the interval [i, i + 1) and dies within the first year and
before the conception of the child of parity i + 1.) In this case we group these two
physiological and volitional replacement mechanisms of increased risks follow-
ing conception under the term "replacement behavior." Moreover, it has been
shown that, in many parts of sub-Saharan Africa where prolonged breastfeeding
is prescribed and sexual intercourse during lactation is forbidden, the physiologi-
cal effect is culturally built into behavior patterns (Ware, 1977~. For the long-
term replacement effects in the subsequent intervals, significant effects of the
death of a child of parity i on the hazards of conceiving children of parity i + 2, i
+ 3, i + 4, and so forth cannot be ascribed to a biological/physiological mecha-
nism but only to a volitional (behavioral) mechanism, as discussed below. Fur-
thermore, because the level of contraceptive use is low in Cameroon (the level of
use of efficient contraceptive methods was 2 percent in 1978 and only 16 percent
in 1991 of which one-fourth was accounted for by modern methods) and there has
been no marked increase in contraceptive use between the two surveys (DSCN,
1983; Balepa et al., 1992), the probability of using contraception in a particular
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264 FERTILITY RESPONSE IN AFRICA WITH SPECIAL REFERENCE TO CAMEROON
period would change marginally. This is tantamount to confining our analysis to
women who did not use any form of contraception during the waiting time to
succeeding conception. Thus, the very nature of the data (mostly noncon-
tracepting women) allows us to isolate to a greater extent the mediating effect of
breastfeeding alone on conception rates in response to mortality. This is a "natu-
ral" sample and there is no bias since women who do not use contraception are
not self-selected for lower fertility. There is as yet little evidence of conscious
limitation of family size in most sub-Saharan African societies (Caldwell and
Caldwell, 1981; van de Walle, 1992~. Evidence indicates that, in most sub-
Saharan African societies, postpartum abstinence is practiced specifically to en-
sure that the supply and quality of breast milk are adequate and to enhance child
survival (Page and Lesthaeghe,1981~. Knowledge and use of indigenous contra-
ceptive practices usually seem to be aimed at preventing conception at certain
times (thus affecting the waiting time to the next conception and birth) or from
certain unions that are undesirable, rather than at limiting the ultimate size of the
family. Hence, the potential effect of a child death on birth spacing is at its
maximum in this setting.
In this chapter, I test three hypotheses regarding the fertility responses to
child death:
Hypothesis 1: A child death has both instantaneous (short-term) and lagged
(long-term) effects on conception risks (or birth-to-conception intervals).
The instantaneous effect is likely to be more important in a setting where
there is little conscious decision to space births or to limit fertility, and couples
practice little or no contraception, as in Cameroon until the late 1980s (Balepa et
al., 1992~.
Hypothesis 2: The fertility response to child loss is stronger for the death of
first-parity births (and eventually second-parity births) than for the death of
higher-parity births.
Many African societies attach special cultural values to the first offspring.
This may affect the way the survival of the first born is perceived by the couple
and the community, and a loss of a first child by death is often interpreted as the
failure of the mother to fulfill her proper role in society. In most African societ-
ies, women are expected to become pregnant shortly after marriage, and the
pressure on these women is often high to produce living children so as to secure
their status with the husband's family. For example, Folta and Deck (1988) note
that among the Shona in Zimbabwe, it is after the birth of the first child that
women are provided with their own dwellings, and it is critical that certain rituals
be followed properly to prevent illness and death of this child.
The eagerness with which African unions are stabilized is reflected in the
quantum and tempo for the first birth: First-birth intervals are typically shorter
than other intervals. For the new mother, the firstborn is a sign of belonging to a
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BARTHELEMY KUATE DEFO
305
simple hazard model provides no insight into the effects of that selection. Fi-
nally, this model has the unfortunate characteristic of mixing the parameters for
the speed with which the event occurs with the parameters for whether or not the
event occurs. No such restriction follows from economic theory. A dynamic
econometric strategy that addresses these problems has been formulated by
Heckman (Heckman and Singer, 1985; Heckman and Walker, l991~. Heckman's
formulation is in continuous time and consists of applying systems of hazard
models (Heckman and Walker, 1991~. Life-cycle fertility is naturally analyzed
using the standard birth process of the stochastic processes literature (Hoer et al.,
1987; Sheps and Menken, 1973) where completed fertility is viewed as the result
of separate processes governing the transition to each parity. In its most general
form, the model posits that current period fertility is a function of age, time since
last birth, the woman' s time-invariant (observed and unobserved) characteristics,
and all the time-varying covariates (both observed and unobserved). Thus, one
has a system of hazard models (one for each parity) linked by woman-specific
common observed and unobserved covariates. Newman and McCulloch (1984)
and Heckman and Singer (1985) developed a refinement (in continuous time) of
this system of hazards approach, and their model suggests some natural simplifi-
cations of this general (inestimable) specification. In Heckman's feasible estima-
tion in continuous time (and applied in this study), the current period hazard is
modeled as a linear index function that includes a general function of the age of
the woman and a general function of the duration since the last birth.
A woman's birth history is assumed to evolve in the following way. The
woman becomes at risk of conceiving the first birth at calendar time ~ = 0 (here
assumed to be the date of first marriage). I define a finite-state continuous-time
birth process Bath, ~ > 0, B(~) £ Q. where the set of possible attained birth states
(parities) is finite ED = (0,1,2,...,N), N < Ad. Q defines the number of children
born. B(~) is parity attained at time I. Transition occurs on or after ~ = 0. I
assume that all durations Ti,...,TN conditional on the appropriate history H have
absolutely continuous distributions. In my specification, and following
Heckman's formulation in continuous-time of the system of hazards approach to
fertility behavior (Heckman and Singer, 1985; Heckman and Walker, 1991), I
implement a continuous-time approach to the system of hazard models of fertility
response to infant and child mortality. Within the framework of this system of
hazards, if a woman becomes at risk for the conception of the JO birth at time ~0
- 1), the conditional hazard at duration tj is
j~tj | Harm- 1) + tj]) = poll {tj | Harm- 1) + tj]) expL\~.Dur~t)
+ AX + 1ljY(t) + djZ(t)],
(1)
where t is the waiting time to conception (that is, the birth-to-conception interval
t) for a given woman. Z(t) captures the mortality effects, X represents a vector of
time-invariant covariates, Y(t) represents a vector of time-varying covariates, and
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Representative terms from entire chapter:
fertility response
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
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
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