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OCR for page 138
SThe Impact of AIDS Mortality on
Individual Fertility:
Evidence from Tanzania
Martha Ainsworth, Deon Filmer, and Innocent Semali
During the European demographic transitions, fertility decline was often but
not always preceded by an aggregate decline in mortality (Matthiessen and
McCann, 1978~. In sub-Saharan Africa, highlevels of child mortality are thought
to be an impediment to fertility decline. Caldwell et al. (1992), for example,
suggest that a decline in infant mortality to levels below 70 per 1,000 may be a
prerequisite for the onset of fertility decline, based on the experience of Botswana,
Kenya, and Zimbabwe.
Child mortality has declined and life expectancy increased in sub-Saharan
Africa in recent decades, but the spreading AIDS epidemic threatens this progress.
Nearly two-thirds of the 23 million people currently infected with human immu-
nodeficiency virus (HIV) worldwide live in sub-Saharan Africa (UNAIDS data,
cited in Ainsworth and Over, 1997~. AIDS is fatal and is striking two key
groups sexually active adults who become infected through sexual relations
and very young children who are infected from their mothers at birth or while
breastfeeding. The impact of AIDS on mortality is difficult to measure, as vital
registration systems in sub-Saharan Africa are subject to extensive underreporting
(Stover,1993~. However, the U.S. Bureau of the Census predicts that the decline
in African infant and child mortality will be stalled and reversed as a result of the
AIDS epidemic (Way and Stanecki, 1994~. Nicoll et al. (1994) predict that
mortality of children under the age of 5 in severely affected urban areas will
increase by one-third in eastern and central Africa and by as much as three-
quarters in southern Africa, sharply diminishing the existing differentials in child
mortality between urban and rural areas. Furthermore, levels of adult mortality in
the age group 15-50 can be expected to double, triple, or even quadruple in some
locales.
138
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
139
What will be the impact of heightened mortality from AIDS on fertility in
sub-Saharan Africa? There is remarkably little empirical evidence on this issue.
In fact, demographic modelers of the impact of the AIDS epidemic commonly
assume no fertility response to AIDS mortality. For example, The AIDS Epi-
demic and its Demographic Consequences (UN/WHO, 1991) presents seven
mathematical models for the demographic consequences of the spread of HIV,
none of which includes an individual fertility response. The World Bank's AIDS-
adjusted population projections assume no interaction between HIV prevalence
and fertility (Bos and Bulatao, 1992~.
In this chapter we review the channels through which we might expect both
positive and negative fertility responses to the heightened mortality of the AIDS
epidemic, summarize the evidence to date, and present new evidence of the
response of individual fertility behavior to heightened mortality based on three
data sets from Tanzania. In the next section we provide an overview of levels of
HIV infection in sub-Saharan Africa and the relation between HIV infection and
mortality. This is followed by a discussion of the channels through which height-
ened mortality from AIDS might induce changes in fertility. In the fourth section
we present results of multivariate analysis of individual fertility using three data
sets from Tanzania two national and one from the severely affected Kagera
region. The results suggest that, although there is evidence of a positive effect of
heightened child mortality on fertility, adult mortality at the household and com-
munity level tends to be associated with lower individual fertility. These results
are supported by an analysis of the effect of mortality on other indicators of
fertility intentions, such as the desire for additional children and patterns of
sexual behavior.
EXCESS MORTALITY FROM THE AFRICAN AIDS EPIDEMIC
Although sub-Saharan Africa has the highest number of current HIV infec-
tions of any region in the world, the prevalence of HIV varies considerably across
the continent and within countries. Figure 5-1 shows the adult seroprevalence
rate (the percentage of people aged 15-50 who are HIV-positive) for HIV-1
among "low-risk" urban populations, based on HIV/AIDS Surveillance Data Base
(Bureau of the Census, 1995~.1 These data are drawn from samples of pregnant
women attending antenatal clinics.2 In 12 countries, over 10 percent of pregnant
women in urban areas are infected with HIV. "High-risk" urban populations,
1 The discussion focuses on HIV-1 infection, which is the most prevalent variant of HIV in sub-
Saharan Africa (National Research Council, 1996).
2Note, however, that these data are not necessarily indicative of seroprevalence levels in a random
sample of the population; women attending antenatal clinics are often better educated and have
higher incomes than the general population.
OCR for page 140
140
Percent Seropositive
Less than 0.1
0.1
0.2 to 1.0
1.1 to5.0
5.1 to10.0
Over 1 0.0
No Data
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
FIGURE 5-1 Percentage of the low-risk urban adult population infected with HIV-1,
circa 1995. SOURCE: Bureau of the Census (l995:Map 2~.
such as commercial sex workers and soldiers, have seroprevalence levels of 40
percent or higher in 12 countries (not shown in Figure 5-1~. Prevalence is gener-
ally lower in rural areas. However, because in most countries the overwhelming
share of the population is rural, even low rural rates of infection imply that the
majority of AIDS deaths occur in rural areas. The number of these deaths is
compounded by urban relatives who migrate to rural areas shortly before death,
the magnitude of which is not known.
Heterosexual transmission accounts for approximately 80-90 percent of all
adult HIV infections in sub-Saharan Africa (Mann et al., 1992; National Research
Council, 1996~. In many hard-hit countries, women are equally if not more likely
to be infected than men. A second important transmission route is from mother to
child. In Africa, roughly a quarter to a half of the children born to HIV-positive
OCR for page 141
MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
141
mothers themselves become infected, either through the birth process or through
breastfeeding (Lallemant et al., 1994~.
Thus, AIDS can be expected to increase mortality dramatically in Afnca
both among the very young and among adults in their prime childbearing and
economically active years. Way and Stanecki (1994) show a profile of age-
specific mortality rates in a population in which 20 percent of adults are infected
with HIV (Figure 5-2~. The baseline mortality in their comparison population
without HIV is clearly not from sub-Saharan Afnca, where infant mortality ranges
from 70-150 per 1,000 and where prevailing mortality among pnme-aged adults,
which ranges between 5 and 8 per 1,000, is roughly eight times higher than in a
developed country. Furthermore, their estimates of AIDS-related child mortality
likely do not include the deaths of HIV-negative children who are put at greater
risk because of the loss of their parents due to AIDS. Child mortality (ages 1-4)
may be more sensitive to AIDS than is infant mortality since many infected
children survive beyond 1 year of age (Valleroy et al., 1990; Way and Stanecki,
1994~. Nevertheless, Figure 5-2 illustrates the substantial impact that AIDS can
have on mortality early in life and in the prime age groups. Indeed, in many cities
160
140
120
100
o
O 80
113 60
40
20
without AIDS
with AIDS
A
0 10 20
A----- ~ -- I
9~) 40 50
Age
= ~1
60 70 80
FIGURE 5-2 Hypothetical impact of HIV on age-specific mortality, assuming 20 percent
of adults are infected. SOURCE: Way and Stanecki (1994:Fig. 11, p. 13).
OCR for page 142
42
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
in sub-Saharan Africa, seroprevalence rates among adults are even higher than
the 20 percent assumed in Figure 5-2.
The United Nations (1995) estimates that AIDS will increase the cumulative
mortality among children under the age of 5 by 7.8 percent in the 15 most
seriously affected African countries from 1980-2005. The effect increases with
age: Cumulative deaths among people aged 15-34 will be 25 percent higher and
among 35-49 cumulative deaths will be 61 percent higher. Because of the way in
which HIV is spread to children, households with AIDS-related child mortality
will also likely experience AIDS-related adult mortality. The clustering of deaths
of children and prime-aged adults in the same households distinguishes AIDS
from other causes of child mortality that do not threaten adults. Thus, when we
consider the effects of AIDS-related child mortality on fertility, we must at the
same time consider the effects of AIDS-related mortality among adults in their
prime years.
HOW AIDS-RELATED MORTALITY AFFECTS FERTILITY
Increased mortality due to the AIDS epidemic can induce changes in indi-
vidual fertility through many different channels, some biological and some be-
havioral. The posited effect of higher levels of child mortality is to raise fertility
and of higher adult mortality to lower fertility.
Child Mortality and Fertility
A couple's own child mortality can result in higher fertility through two
channels: (1) abrupt cessation of breastfeeding following the child's death, which
eliminates the protection afforded by breastfeeding's contraceptive effect and
raises the risk of another pregnancy (the "interval effect"; and (2) by an increase
in the number of births a couple must have to achieve a target number of surviv-
ing children (Preston, 1978~. This latter behavioral response to child mortality
may take two forms "replacement" of young children who die through addi-
tional births or simply bearing more children than needed to "insure" against
anticipated child mortality in the future.
The "interval" and "replacement" effects of child deaths that are due to
AIDS are unlikely to be strong because the parents of these children themselves
are infected. In fact, it is often due to the illness and death of a child that the
parents learn of their own infection. The parents may attempt to prevent future
births through abstinence, contraception, or abortion; abstinence to prevent re-
infection with HIV would also make a subsequent birth unlikely. The mother
may also succumb to AIDS before another pregnancy can come to term, making
it unlikely that one would observe her or her children's deaths in a sample of
women. Thus, elevated child mortality due to AIDS will probably exert a stron-
ger positive effect on fertility through the "insurance" channel by raising
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
143
uninfected couples' perceptions of their probable child mortality experience,
increasing their estimate of the number of excess births necessary to guarantee a
target number of surviving children.
Multivariate studies of the relation between a couple's own child mortality
and their fertility in African countries have generally confirmed a positive rela-
tionship (Akin and Shariff, 1993; Anker, 1985; Benefo and Schultz, 1996; Farooq,
1985; Okojie, 1989; Snyder, 1974~. However, most of these studies have treated
the couple's child mortality as exogenously determined. If one accepts the propo-
sition that child health and child mortality are the outcomes of household deci-
sions on health "inputs," such as consumption of food and health care, then the
exogeneity of child deaths is difficult to accept. Failure to take the endogeneity
of child deaths into account leads to biased estimates of the relationship with
fertility. Studies that examine the impact of a woman's own child mortality on
fertility are also problematic because they are confined to samples of women who
have had at least one live birth, which is in effect conditioning on an endogenous
variable (fertility). At least two studies have taken the endogeneity of child
mortality into account using African data. Okojie (1989) found in Bendel State,
Nigeria, a negative relation between a woman's predicted child survival and
fertility in rural areas and among women nearing the end of their reproductive
lives. Benefo and Schultz (1996) tested for and were unable to reject the exo-
geneity of child mortality in Cote d'Ivoire and Ghana. When child mortality was
treated as exogenous, they found a very weak replacement effect an increase in
fertility of one child in response to every 4-15 child deaths, depending on the
country and region. Preston (1978) points out that such weak relationships should
be expected in areas with a high demand for children; if couples want as many
children as possible, then a reduction in child mortality will not reduce fertility.
Although Ahn and Shariff (1993) did not account for the endogeneity of child
mortality, they also examined the impact of community infant and child mortality
rates, which can be considered exogenous to the household. They found high
infant mortality to be associated with a higher hazard of subsequent birth in Togo,
but high child mortality to be negatively associated with the hazard of subsequent
births in Uganda. These studies collectively suggest a positive, if sometimes
weak, relation between child deaths and fertility in sub-Saharan Africa.
Adult Mortality and Fertility
Heightened adult mortality due to AIDS may reduce desired family size and
the observed demand for children of individual women through the following
channels:
· AIDS mortality often occurs in young adulthood before the long-run ben-
efits of earlier child investments can be realized by the parents of those infected.
Heightened adult mortality rates due to AIDS will thus reduce the expected long
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44
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
run benefits of children, in turn lowering desired family size. High adult mortal-
ity may also prevent parents from investing in their children's schooling and
health care.
· Mortality of prime-aged adults in the household may reduce household
income (at least temporarily) and raise the demand for labor of the surviving
adults. This would raise the shadow cost of children and shrink the budget
constraint, both of which would tend to reduce the demand for children.
· High adult mortality will also leave many orphaned children to be ab-
sorbed by the households of relatives. These orphaned children make additional
claims on existing income and the time of adults and may reduce the demand for
additional children of their own.
Other Channels Through Which AIDS Morbidity and Mortality
May Affect Fertility
Any change in the demand for children or in biological factors affecting the
supply of children because of the AIDS epidemic will be reflected in correspond-
ing changes in the proximate determinants of fertility, such as contraceptive use,
breastfeeding, marriage, abortion, infecundity, and sterility (Bongaarts, 1978~.
Changes in the proximate determinants reflect, in most cases, individual choices
or their outcomes that are joint decisions with fertility. Gregson (1994) points out
many of the following effects of AIDS on the proximate determinants and, jointly,
with fertility:
· Fertility among infected women may decline because of illness, infertility
induced by other sexually transmitted diseases (STDs), increased use of contra-
ception, widowhood, and increased resort to abortion (Nicoll et al., 1994~.
The use of condoms to prevent the spread of STDs, including AIDS, may
reduce unwanted births. At the same time, to the extent that condoms replace
more effective methods of birth control, fertility may rise.
One of the major strategies to slow the spread of AIDS is to offer treat-
ment for other "conventional" STDs, such as syphilis and gonorrhea, thought to
facilitate transmission of HIV. This intervention would have the beneficial side
effect of reducing levels of pathological sterility in many countries, which could
result in higher fertility.
· Other behavioral changes to prevent the spread of AIDS may include
delayed age at marriage, monogamy, and increased celibacy (Caldwell et al.,
1993~. These changes would be associated with lower fertility. However, HIV is
also spread through breast milk, and breastfeeding is a major determinant of the
period of postpartum infecundability. Any reduction in breastfeeding could re-
duce the period of postpartum infecundability and raise fertility unless compen-
sated for by higher contraceptive use or abstinence.
· In a review of the fertility effects of HIV counseling and testing programs,
.
.
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
145
Setel (1995) concludes that there is no evidence that women informed of their
HIV-positive status accelerate childbearing, while a few studies show that they
have somewhat lower subsequent fertility than women told they were HIV nega-
tive.
Finally, in the aggregate, AIDS mortality affects fertility through its impact
on the age structure of women of reproductive age. But there are other aspects of
the selective mortality of women of reproductive age that could affect aggregate
fertility. For example, if the women who are becoming infected are also those
who would have had fewer children in any event (for example, urban women),
then the women with lower fertility are selectively dying and overall fertility may
rise. Or, if these low-fertility women have already had the children they would
have had, aggregate fertility may remain unchanged. Many demographic model-
ers have assumed that women who die of AIDS will have already borne most of
the children they could expect in a lifetime and therefore would have very little
effect on aggregate fertility (Bos and Bulatao, 1992; Way and Stanecki, 1994~.
However, infection rates in Africa are on the increase among young females,
raising the possibility that many will die before having completed their lifetime
fertility.
A few medical researchers have found lower fertility among HIV-positive
women, although they have not been able to attribute the results to biological as
opposed to behavioral causes. Ryder et al. (1991) found somewhat lower fertility
and higher contraceptive use among HIV-positive women than among HIV-
negative women in a sample of women followed over 3 years following delivery
of a live-born child in Mama Yemo Hospital in Kinshasa, Zaire. Sewankambo et
al. (1995), in a recent study of 1,860 households in the rural Rakai district in
Uganda, found that the birth rate among HIV-positive women aged 15-49 was
169 per 1,000, whereas that for HIV-negative women was 213 per 1,000. Using
data from the same region of Uganda, Gray et al. (1995) found the prevalence of
pregnancy to be lower among HIV-infected women. In addition, there is some
evidence that HIV-positive mothers have a higher likelihood of spontaneous
abortion (Langston et al., 1995~.
To the best of our knowledge, there has been no empirical study of the
behavioral response of individual fertility to increased mortality due to AIDS.
Among the reasons for the lack of empirical work is the difficulty of identifying
AIDS mortality, the difficulty of observing a sufficient number of adult deaths to
measure their impact, the lack of longitudinal data, and the absence of observa-
tions on community-level measures of mortality. An added complication is that
the line of causation between child mortality and fertility runs in both direc-
tions high levels of fertility and closely spaced births are thought to raise the
risk of death to children and mothers. Indeed, as Nicoll et al. (1994) point out, the
impact of the epidemic on child mortality depends heavily on fertility. If all
infected women were to cease having children, then child mortality may increase
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146
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
very little. Thus, there is also the need for data with sufficient instruments to
separately identify the two relationships.
INDIVIDUAL FERTILITY RESPONSE IN TANZANIA
Tanzania, on the eastern coast of Africa, stretches to Lake Victoria in the
northwest, Lake Tanganyika in the west, and Lake Nyassa in the southwest. Per
capita gross national product (GNP) in the early 1990s was on the order of $100,
and about three-quarters of Tanzania's 24 million people live in rural areas (World
Bank, 1995~. The 1991/92 Demographic and Health Survey (DHS) estimated
Tanzania's total fertility rate at 6.3, infant mortality at 92 per 1,000 and under-5
mortality at 141 per 1,000 for the 5 years preceding the survey (Ngallaba et al.,
1993~. Results from the 1988 census indicate relatively higher levels of both
infant and under-5 mortality 15 and 191 per 1,000, respectively (Bureau of
Statistics, undated).
Tanzania is among the countries most severely affected by the AIDS epi-
demic in Africa and in the world. The first case of AIDS was diagnosed in 1983
in the Kagera region, on the western shore of Lake Victoria and adjacent to
Uganda and Rwanda. HIV was probably in the region for a decade or more
before the first diagnosis. By 1992 there was a cumulative total of 38,416
reported AIDS cases from all regions of the country since the beginning of the
epidemic (Ministry of Health, cited in Mukyanuzi, 1994~. This was surely a
gross undercount, but by how much we cannot be sure. As of 1990 it was
estimated that between 400,000 and 800,000 people were infected, and it was
anticipated that AIDS would shortly become the major cause of death among
young children and prime-aged adults (World Bank, 1992~.
No one has undertaken a nationally representative seroprevalence survey in
Tanzania, so the true prevalence of HIV is unknown. Chin and Sonnenberg
(1991) compiled a map of the estimated HIV prevalence among sexually active
adults, by region, using the results of seroprevalence surveys of smaller, select
samples and the reported number of cases (Figure 5-3~. At that time, the highest
levels of infection were thought to be in Dar es Salaam and Kagera, followed by
Mwanza and Mbeya regions. Kagera, Mwanza, and Mbeya are all along major
transportation routes to adjacent countries, over which much cross-border trade
passes. A population-based seroprevalence survey of Kagera region in 1987
found an infection rate of 24.2 percent among adults aged 15-54 in the main town
of Bukoba (on the lake and about 100 km south of the Uganda border) (Killewo
et al., 1990a). Rural rates of infection were also high: 10 percent of adults in the
rural areas surrounding Bukoba and next to the lake,4.5 percent in the northwest-
ern part of the region bordering Rwanda and Uganda, but less than half a percent
in the southern part of the region. The infection rate among children 0-14 years
of age was 3.9 percent in Bukoba, with the highest levels among the youngest
children.
OCR for page 147
MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
Kigoma
Tabora
0 100 200 km
1 1 1
~ Singida
\
~Kilimaniaro
Ruvuma ~/
147
me'
Dar es Salaam
urban 4-7%
rural < 1 %
urban 7-1 0%
rural 1-3%
urban > 10%
rural > 3%
HIV Prevalence
urban < 4% I I
rural< 1% 1 l
FIGURE 5-3 Estimated HIV prevalence among sexually active adults, Tanzania, 1989.
SOURCE: Chin and Sonnenberg (1991), cited in World Bank (1992~.
In Western countries, the median time between infection with HIV and de-
velopment of AIDS and death is roughly 10 years (Moss and Bachetti, 1989;
Rutherford et al., 1990~. The incubation period is thought to be shorter in sub-
Saharan Africa because of higher underlying morbidity and lower nutritional
status (Killewo et al., l990b; National Research Council, 1996~. The extent to
which AIDS is contributing to overall mortality is not known. Results of the
1988 Tanzanian census reveal that the unadjusted death rates for adults aged 15-
49 ranged from 3.4 to 9.4 per 1,000 across the 20 regions of mainland Tanzania
(Ainsworth and Rwegarulira, 1992~. These adult death rates are based on raw
census data, without any adjustments for internal consistency or underreporting.
Although the levels may be underestimates, the differentials in mortality across
regions point to the areas with relatively higher mortality. The highest adult
mortality was recorded in Kagera region; Mbeya and Dar es Salaam, where HIV
infection is also widespread, had relatively high adult death rates as well (6.3 and
6.5 per 1,000, respectively). The results revealthat tinder-5 mortalityin 1985
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148
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
Under-5
Mortality Rate
Below 160
160- 189
190 - 219
220 and above
FIGURE 5-4 Under-5 mortality by district, Tanzania mainland, 1985. SOURCE: Data
from Bureau of Statistics (no date).
was higher around Lake Victoria and in the southern parts of Tanzania (Figure 5-
4~. These regional differentials in mortality reflect not only the effect of the
AIDS epidemic but the distribution of other underlying determinants of mortality
and nutritional status, such as household incomes, food prices, disease vectors
(such as mosquitos), and the availability of medical care.
The Model
Economic models of fertility in developing countries begin with a model of
a household that both produces and consumes (Becker, 1993; Schultz, 1981~.
Household members derive utility from their children and from other consump-
tion goods. However, children also have a potentially important contribution to
household production activities and their future earnings may be an important
OCR for page 171
MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
(c) TKAP Sample of Women Aged 15-49 and Sample of Men Aged 15-59
171
Women Aged 15-49
(n = 3,950)
Men Aged 15-59
(n= 1,948)
Standard Standard
Variable Mean Deviation MeanDeviation
Individual-level variables
Birth in past year (0/1) 0.194 0.396
Want another child (0/1) 0.616 0.486 0.8760.329
Ever had sexual intercourse,
ages 15-19 (0/1) 0.528 0.500 0.6350.482
Frequency of sexual
intercourse in
past 4 weeks 4.314 5.943 4.8337.159
Age 28.001 8.980 31.01411.641
Age squared 864.68 546.19 1097.31806.03
Years of schooling 4.485 3.926 5.7104.368
Years of schooling
squared 35.526 208.791 51.677305.408
Household-level variables
Water from closed
source (0/1) 0.361 0.480 0.4230.494
Flush or pit toilet
facility 0.906 0.292 0.9210.269
Floor of parquet, finished
wood, or cement (0/1) 0.228 0.419 0.2680.443
Household member owns
a bicycle (0/1) 0.339 0.473 0.3550.479
Household member owns
a car (0/1) 0.019 0.136 0.0170.128
Community-level variables
Rural HH (0/1) 0.732 0.443 0.6920.462
North highland zone (o/l)a 0.109 0.312 0.0950.293
Central zone (o/l)a 0.087 0.281 0.0930.290
South highland zone (o/l)a 0.148 0.355 0.1840.388
Southern zone (o/l)a 0.079 0.271 0.0820.275
Lake zone (o/l)a 0.368 0.482 0.2780.448
Road is seasonal or
is a path (o/l)a 0.238 0.426 0.2160.411
Distance to primary
school (km)b 0.660 1.907 0.7242.007
Village has one or more
health workers (o/l)b 0.375 0.484 0.3650.481
Distance to nearest health
facilityb 4.372 7.071 4.5437.490
Nearest health facility
is a pharmacy (o/l)b 0.063 0.244 0.0800.271
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72
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
(c) TKAP Sample of Women Aged 15-49 and Sample of Men Aged 15-59
(con tin uedf)
Women Aged 15-49
(n = 3,950)
Men Aged 15-59
(n= 1,948)
Standard Standard
Variable Mean Deviation Mean Deviation
Nearest health facility
is a hospital (o/l)b 0.128 0.335 0.115 0.320
Nearest health facility
is a health center (o/l)b 0.170 0.375 0.192 0.394
Number of family planning
methods available at
nearest facilityb 2.209 1.486 2.204 1.534
Pill available at nearest
facility (o/l)b 0.751 0.443 0.710 0.454
Injections available at
nearest facility (o/l)b 0.298 0.457 0.327 0.469
Condoms available at
nearest facility (o/l)b 0.799 0.401 0.809 0.393
IUD available at
nearest facility (o/l)b 0.218 0.413 0.245 0.430
aCoastal zone (Tanya, Morogoro, Coast, and Dar es Salaam regions), north highland zone (Arusha
and Kilimanjaro regions), central zone (Dodoma and Singida regions), south highland zone (Iringa,
Mbeye, and Rukwa regions), southern zone (Lindi, Mtwara, and Ruvumba regions), lake zone
(Tabora, Kigoma, Shinyanga, Kagera, Mwanza, and Mara regions).
bCommunity and facility data from 1991/92 Tanzania Demographic Health Survey (see Beegle,
1995, for details).
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
APPENDIX 5-B:
ESTIMATION OF THE DETERMINANTS OF FERTILITY
Specification and Estimation
173
The probit model assumes an underlying linear index function (Bi*) for
woman i of the following form:
Bi* = Taxi + Vi'
(1)
where Xi is a set of explanatory variables and vi is an error term that is distributed
normally with mean 0 and with variance ceil (which is normalized to 1 in the
estimation). Actual (observed) birth in the last 12 months (Bi) is given by
Bi = 1 if Bi* 2 0, Bi = 0 otherwise.
(2)
The probit model is a convenient (and commonly used) method to estimate a
model with a dichotomous outcome. However, it is sensitive to misspecification.
A non-normal distribution of vi or omitted variables can cause the parameter
estimates to be biased. In this chapter we check the robustness of our results to
certain types of violations of the underlying assumptions (see below). However,
we leave more formal tests for future work.
Two main issues arise in the estimation of this model. First, when including
income in the analysis of fertility, it must be treated as (potentially) endogenous.
Second, in the Kagera sample, the fact that there are as many as three observa-
tions per woman in the sample may affect our results. We address below how
these problems were dealt with.
The Potential Endogeneity of Household Consumption
In the estimation of the determinants of having had a birth in the past 12
months for two of the data sets (KHDS and THRDS), we estimate models that
include the effect of household permanent income. Consistent with what is done
in this literature we use the log of total household consumption expenditures per
adult as a proxy for income. Household expenditures cannot necessarily be
assumed as exogenous to fertility decisions. For example, if children themselves
contribute to household income then the causal relationship runs in both direc-
tions.~°
Including an endogenous right-hand side regressor will lead to inconsistent
crobit parameter estimates. Smith and Blundell (1986) and Rivers and Vuong
{OFor recent discussions of these and other explanations of the endogeneity of income in African
contexts see Benefo and Schultz (1996), as well as Montogomery et al. (1995).
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THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
(1988) propose an erogeneity test for a model with a dichotomous dependent
variable and a potentially endogenous continuous explanatory variable. In the
present case, we rewrite equation (1) to include the log of household expenditures
per adult:
Bi* = Taxi + YEi + Vi
where Bi = 1 if Bi* 2 0, Bi = 0 otherwise.
Ei = 8iXi + 82Zi + Hi'
where Bi is the event of having a birth, Xi is a set of exogenous variables, Ei is the
log of household expenditure per adult, and 0, it, hi, and 82 are parameters to be
estimated. The set of variables Zi are the identifying instruments, that is they
affect fertility only through their effect on Ei.
Smith and Blundell show that an exogeneity test for E is a t-test of the
significance of the parameter or in the following probit regression:
Bi* = ~Xi+7Ei+ ~Ui+Vi,
(5)
where ui are the residuals estimated from equation (4~. If the estimate of or is
significantly different from zero then we must treat Ei as endogenous.
The set of instrumental variables we use differs somewhat for the two
samples. They are in general, however, characteristics of the head of the house-
hold and the value and/or characteristics of household assets. In both analyses the
set includes the sex, age squared, education, and education squared of the head of
the household. For the KHDS it includes in addition to the head's characteristics
the value of farm equipment, the value of farm buildings, the value of livestock,
the value of business assets, a dummy for whether or not a household member
owns the dwelling, and if so the value of the dwelling, and the area of banana
crops harvested. For the THRDS it includes in addition to the head's character-
istics the total number of cows, bulls, and oxen currently owned, a dummy for
whether or not a household member owns the dwelling, and if so the value of the
dwelling and a series of dummies equal to one if the dwelling has walls made of
mud or wood, has a floor made of earth or wood, has a roof made of grass or mud,
and has windows or screens.
The validity of these variables as instruments for income is dependent on the
assumption that they affect the probability of a birth in the past year only through
their impact on income (or its proxy, expenditures). The head of the household
may or may not be the husband of the woman in question, and therefore his or her
characteristics (conditional on the women's characteristics) are unlikely to affect
the probability of a birth in the past 12 months directly. Characteristics and the
value of the dwelling and productive assets are potentially good measures of
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
175
"exogenous" wealth if there is a low turnover in the ownership of these assets,
that is that they capture that part of income that is not endogenously related to the
probability of birth in the past year. But, if only the characteristics of the head are
used as instruments, none of the results of this chapter are substantially changed.
The first-stage regressions perform well in the sense that they explain a good
part of the variance of the dependent variable. The adjusted it-squared in the
KHDS sample is 0.32 and in the THRDS is 0.39. The instruments perform well
in the sense that they explain a reasonable part of this variance. The incremental
R square of adding the set of instruments in the first-stage regression is about 0.05
in the KHDS sample and about 0.08 in the THRDS sample. In addition, both sets
of instruments are jointly significantly different from zero at the 99 percent level.
When the residual from the first-stage estimation is included in the second-
stage probit regression for birth in the past year (equation 5), the l-tests reject
exogeneity in both samples (and in both model specifications in the KHDS analy-
sis). l l
Therefore, to control for the endogeneity of expenditure, we estimate equa-
tion (2) in a first step and then use the predicted value of Ei (that is Ei) to estimate
Bi* = DXi + Hi + Vi
(6)
In the THRDS results, the asymptotic covariance matrix derived from this probit
is then adjusted for the fact that Ei is a variable predicted from an auxiliary
regression. This is done using the formula given in Maddala (1983:245~.
Multiple Observations on a Single Woman in the KHDS
Random-Effects Probit
The KHDS data were collected over four interviews, separated by approxi-
mately 6 months each. In our current analysis we have pooled the data across
waves 2, 3, and 4, and therefore a woman can appear up to three times in the
sample. To be able to include deaths up to 30 months of age, we exclude wave 1
observations from this analysis. Estimating this model as a probit regression on
pooled data produces consistent but inefficient estimates (Maddala, 1987~. To
improve the efficiency of the estimates, we estimate a random-effects probit
model (reviewed in Maddala, 1987~.
The random-effects probit model derives from a decomposition of the error
iiIn the KHDS model with deaths of household members, the ~ statistic has a value of 2.711 (t
statistics derived from a pooled probit estimation with huber standard errors). In the THRDS it has a
value of 2.903. We note that the derivation of this test was done under the assumption of cross-
sectional data.
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176
THE IMPACT OF AIDS MORTALITY: EVIDENCE FROM TANZANIA
term given in equation (1). Including subscripts for time periods, equation (1) for
woman i in time period t becomes
Bit* = Exit + Wi + V it ~
(7)
where Bit= 1 if Bit* 2 0, Bit = 0 otherwise, where wi is a woman-specific time-
invariant unobserved variable that is distributed normally with mean zero and
variance ceil. This model is estimated using a method proposed by Butler and
Moffitt (1982).
In general these results are very similar to the pooled sample with simple
probit estimation. The estimate of the share of the variance that is woman
specific (p) is equal to approximately 0.34 and is significantly different from
zero. However, the point estimates, as well as the statistical significance of these,
are not very different.
One Observation per Woman
A woman can appear either one, two, or three times in the sample. If the
number of times a woman is present in the sample is related to the issues under
study, this could potentially bias our results. To investigate the sensitivity of our
estimates to this, we estimate the models using only one observation, selected at
random over the three waves, per woman.
The biggest difference between these estimates and those in the random-
effects model is that the community mortality variables are no longer significant,
although the signs remain. In general the household-level mortality variables
exhibit the same patterns, although the effect of a female death in the past 18-24
months is no longer significant, and the effect of the death of a husband in the
past 30 months is larger.
Transforming the Results from A Probit or Tobit Regression
In Tables 5-1 through 5-6, the probit parameter estimates have all been
transformed to correspond to the marginal effect of a change in one of the inde-
pendent variables on the expected value of the dependent variable (i.e., the prob-
ability that it equals one). If the underlying model for the observed variable B is
Bi * = pXi + Vi,
(8)
where Bi = 1 if Bi * 2 0, Bi = 0 otherwise, then the change in the probability that
B equals 1 due to a change in one of the X's, bE(B)I6X~, is equal to pif(z), where
pi is the probit parameter estimate on A, f() is the standard normal probability
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MARTHA AINSWORTH, DEON FILMER, AND INNOCENT SEMALI
177
density function, and z is equal to ~X. In the reported results, OX is evaluated at
the means of the X' s.
The Tobit parameter estimates have been transformed to correspond to the
marginal effect of a change in the independent variables on the expected value of
the dependent vanable. If the underlying model for the observed variable T is
Ti* = DXi + Pi,
~ ~. ~ ~
(9)
where If= ~,~~ it ~,~~ > (), ~ ~ = () otherwise, then the change in the expected value
of T due to a change in one of the X's, bE(l~l6X~, is equal to piF(z), where pi is
the Tobit parameter estimate on X, F() is the standard normal cumulative distn-
bution function, and z is equal to Xp/c,, where c, is the standard deviation of £.
McDonald and Moffitt (1980) recommend evaluating this at the mean of the X's.
ACKNOWLEDGMENTS
We thank Ed Bos, Barney Cohen, Will Dow, Tom Mernck, Mark Montgom-
ery, and participants in World Bank and Committee on Population seminars for
comments on earlier drafts. The opinions expressed in this chapter are those of
the authors and do not necessarily reflect the policy of The World Bank or its
member governments. This research was financed by The World Bank Research
Committee, RPO#680-46.
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Representative terms from entire chapter:
aids epidemic