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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.

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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

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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).

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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.

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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

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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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174 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. REFERENCES Ahn, N., and A. Shariff 1993 A Comparative Study of Fertility Determinants in Togo and Uganda: A Hazards Model Analysis. Paper prepared for the XIInd General Population Conference of the IUSSP, Montreal, Canada, August 24-September 1. Ainsworth, M. 1996 Economic Aspects of Child Fostering in Cote d'Ivoire. Pp. 25-62 in T. Paul Schultz, ea., Research in Population Economics volume 8. Greenwich, Conn.: JAI Press. Ainsworth, M., and A.A. Rwegarulira 1992 Coping with the Impact of the AIDS Epidemic in Tanzania: Survivor Assistance. AFTPN Working Paper no. 6. The World Bank, Washington, D.C. Ainsworth, M., G. Koda, G. Lwihula, P. Mujinja, M. Over, and I. Semali 1992 Measuring the Impact of Fatal Adult Illness in Sub-Saharan Africa: An Annotated House- hold Questionnaire. Living Standards Measurement Study Working Paper no. 90. The World Bank, Washington, D.C. Ainsworth, M., S. Ghosh, and I. Semali 1995 The Impact of Adult Deaths on Household Composition in Kagera Region, Tanzania. Paper presented at the Annual Meetings of the Population Association of America, San Francisco, Calif., April 6. Ainsworth, M., and M. Over 1997 Confronting AIDS: Public Priorities in a Global Epidemic. New York: Oxford Univer- sity Press.

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