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7 increase fertility in a number of ways. In populations where breastfeed- ing is common, an infant death shortens birth intervals by reducing the length of postpartum amenorrhea (Chowdhury et al., 1976~. Parents may deliberately replace a lost child (Preston, 1977) or hoard children in anticipation of additional deaths in the future (Taylor et al., 19761. In the other direction, an increase in family size can increase mortality risks, since resources must be spread over more family members (Watson et al., 19797. Our model isolates an effect of early child mortality on later fertility and an effect of early fertility on later child mortality. This reduces the need for concern about simultaneity between child mor- tality and fertility. It also provides leverage on the simultaneity between child mortality and contraceptive use. Thus, the temporal disag- gregation contained in the model resolves simultaneities that arise when process is ignored and fertility is perceived simply as children ever born. Our three-component decomposition does not remove all potential simultaneities from the model. We considered each remaining potential simultaneity, and in each instance concluded that there is insufficient theoretical or conceptual justification for identifying the relevant parameters, given the variables in the WFS. For this reason, the m~cro- level structural equations model is block-recursive. We felt that the encroachments of simultaneity bias were more than offset by the benefits of partitioning children ever born into early and later fertility. Finally, there is a derived advantage resulting from modeling process rather than a count. Cochrane (1979) and Hermalin and Mason (1980), among others, envision a curvilinear relationship between education and children ever born at the micro level. Since children ever born is the sum of early and later fertility, it follows that our micro model contains an implied relationship between education and children ever born. Any endogenous variable or linear combination of endogenous variables in a structural equations model can be expressed as a function of nothing more than the exogenous variables. Because children ever born is a linear combination of early and later fertility, it can be expressed as a func- tion of respondent education and childhood residence. Our structural equations model contains curvilinear relationships and interaction terms. The implied reduced-form expression of children ever born as a function of respondent education and childhood residence also involves a curvilinearity in the education-children ever born relationship. The rationale for this curvilinearity is more extensive than and has a somewhat different basis from that for the direct modeling of children ever born. 1. 2 OVERA7Ih'W OF THE MODEL As a basis for further discussion of the model, Figure 1.2 depicts its causal structure and component variables. Abbreviations used in Figure 1.2 and hereafter are defined in the Glossary (page 1211. The model contains four blocks of variables indicated by Roman numerals across the top of Figure 1.2. Block I contains the exogenous variables, while Blocks II-IV correspond to the three components of the

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8 BLOCK BLOCK BLOCK UNLOCK RESC i WED \ \\_ is/ LF FEC At\ DUR FIGURE 1.2 Causal Diagram of Proposed Mode 1 RES WSM HED HOCC EF*WED ~ / // EF *HOCC // SCB*WED ~ / SCB*HOCC

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9 fertility process as defined above: onset, operationalized as age at first birth {AFB), appears in Block II; early fertility (EF) in Block IIT; and later fertility (LF) in Block IV. This causal model follows usual path diagrammatic conventions (Duncan, 1975) , except for the deliberate omission of arrows indicating stochastic error terms. Inter- actions are indicated by the frequently seen .*n notation, which has its origin in the Fortran programing language. Variables that are constitu- ents of interactions are always assumed to be present additively as well. Thus the model is hierarchical. AS an introduction to the model, the present discussion cuts across blocks to highlight points of similarity and difference with other models and with well-known theoretical discussions. The detailed exposition in Section 1.3 explains the model on a block-by-block basis. The remainder of this section considers intermediate variables, child mortality, sex composition, socioeconomic variables, and interactions. Throughout, we assume that the model will be applied to five-year birth cohorts of WFS respondents stratified, where possible, by ethnicity. Intermediate Fertility Variables A hallmark of sociological analyses of fertility is attention to .. . . what might be called the production side of fertility" (Easterlin, 1978:59) , specifically the intermediate fertility variables. Davis and Blake (1956 ~ distinguish three classes of these variables, which translate socioeconomic variability into differential fertility: those affecting exposure to intercourse; those influencing the chances of conception; and those related to gestation and successful parturition. Although the present model includes many of these variables, the causal assumptions underlying the Davis and Blake framework must be modified because of the constraints of cross-sectional survey data. In particular, the model does not force the fertility effects of socioeconomic factors to flow solely through the intermediate variables, nor does it assume that all of these variables are predetermined with respect to fertility. Among the first class of the Davis and Blake intermediate variables, being in a union is the most critical precondition for exposure to inter- course. Number of unions (NMAR) and time spent in unions (DURJ, appearing in Block III of Figure I.2, are adjustment variables in the determination of later fertility outcomes. Because the time between birth of the first child and age 30 places limits on exposure to early fertility, AB may be interpreted as an Exposure variable" in its relation to EF. We do not explicitly model age at marriage because, as an indicator of initial exposure to intercourse, it poses problems of noncomparability across, and even within, societies. Consiensual unions are common in many Latin American and Caribbean societies. Cohabitation often precedes formal marriage, and the social characteristics of partners help determine whether such an informal union will be formalized (Caldwell et al., 1980~. In some Asian countries, on the other hand, the formal marriage ceremony can precede cohabitation by one or more years (Goode, 1963:2331. Even in the absence of cross-national comparability problems, inclusion of age at marriage would be redundant. Although marriage and first birth

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10 signal quite different role transitions (Casterline and Trussell, 1980), the ages at which they occur are highly correlated at the micro level (Hirschman and Rindfuss, 1980~. The second category of Davis-Blake intermediate fertility variables governs the chances of conception. Contraceptive usage is the most widely studied of these variables because of its major role in family planning programs. Of course, women who use a birth control method substantially lower their risk of future births. It is difficult to document this by correlating, as is often done, current use of contraception with children ever born. This is because in transitional societies, women with larger families have greater motivation than those with smaller families to contracept, and are therefore more likely to be current contraceptors. For this and other reasons, we treat contraceptive use pattern (LCU)--not merely whether the respondent is a current contraceptor--as one of the ultimate endogenous variables in Block IV of the model, where it appears contemporaneously with later fertility (LF). In transitional settings, socioeconomic and demographic factors should affect LF and LOU in opposite ways (e.g., a positive relationship between education and LOU and a negative one between education and LF). These relationships should be minor, if present at all, in traditional societies. Fecundity is another conception variable appearing in the model. Analyses based on cross-sectional survey data typically rely on self- reported fecundity (FEC) for a direct measure of respondent ability to bear children. This self-report appears in Block III of Figure 1.2. Women who believe they are subfecund should be less likely than others to use contraception and to have large numbers of children after age 30. Age at first birth (AFsB) also provides an indirect measure of fecundity. Other things being equal, subfecund women should have a later age at first birth than fecund women. The model does not include an indicator of breastfeeding patterns. Lactation prolongs postpartum amenorrhea, lengthens the interval between births, and depresses aggregate fertility levels. Unfortunately, the WFS lacks the information necessary to model the micro-level effects of breastfeeding patterns. The surveys focus on behavior associated with respondents' most recent births, many of which occurred after respondents reached age 30. Consequently, recent breastfeeding patterns are not causally prior to one of the model's main response variables--later fertility (LF). Moreover, the quality of the WFS data on breastfeeding that do exist is questionable (Jain and Bongaarts, 1980~. Although we lack desirable micro-level measures of breastfeeding, it is possible to devise macro-level breastfeeding indicators based on aggregated WFS data to explain parameter variability across settings at the micro level. The work of Bongaarts (1980) suggests that breastfeeding should be quite important in this connection. m e third class of intermediate fertility variables pertains to stillbirth, miscarriage, and abortion. Induced abortion is the most important variable from a policy standpoint, having played an important part in the fertility transition of some countries (Omran, 1971~. Survey data on abortion tend to be unreliable, however (Srikantan, 19821. More- over, not all surveys sponsored by the WFS include a question about abortion. Our treatment of this variable is thus similar to that of breastfeeding. 8

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11 Child Mortality Micro-level fertility models typically allow for a link between infant/ child mortality and fertility. However, specification of this relation- ship varies, some authors viewing mortality as exogenous (Boulder and Mankiw, 1981) and others treating it as simultaneous with fertility (Olsen, 19801. In our model, both fertility and child mortality are endogenous. However, as noted above, by using a similar decomposition for child deaths and the fertility process' the model allows early child mortality (ECM) to influence subsequent fertility and early fertility to influence later child mortality (LCM). ECM appears in Block III of Figure 1.2, and LCM in Block IV. Because we cannot identify within-block simultaneities, we specify contemporaneous disturbance correlations, or the generalized linear model equivalent thereof, between ECM and EF, and between LCM and LF. As suggested earlier, there are several reasons for expecting infant/child mortality to affect fertility. One involves the inverse relationship between infant mortality and the length of birth intervals. Women stop breastfeeding when their infants die, and thus lose the protection from conception afforded by breastfeeding. The younger the infant at death, the shorter the interval between the birth and the resumption of menses and ovulation. In the model, most of this physio- logical effect is incorporated in the ECM-EF and LCM-LF disturbance correlations. This effect is expected to hold for both traditional and transition=] settings, although its relative importance will depend on breastfeeding patterns. The physiological component of the ECM-LF relationship should be confined to just a single birth interval--the one bracketing the mother's 30th birthday. m is relationship is largely driven by behavioral factors. Of these, the major ones are predicated on the existence of family-size targets and fertility control, and therefore pertain to transitional settings only. One such factor is the replacement effect (Preston, 1977) and the hoarding effect (Taylor et al., 19761. Women who experience a child death may have one or more children to replace the one lost and to insure against future losses. Such reactions account for the behavioral component of the ECM-LF relationship. m e EF-ECM contemporaneous disturbance correlation will also reflect replacement effects and micro-level hoarding effects. m e LF-LCM contemporaneous disturbance correlation should be less sensitive to these effects because older mothers are less able than younger ones to react in this way to child mortal Fertility may respond to mortality conditions in yet another way. Micro-economic models frequently assume that parental decisions about family size are made prior to the onset of fertility. Guesses about future child deaths represent one input into these decisions (Easterlin, 1978~. While mortality conditions are exogenous in this approach, they no longer refer to individual-level variables (Boulder and Mankiw, 1981~. Since parents have not themselves experienced an infant or child death, they must necessarily base their guesses about future mortality risks on the experience of others. Thus mortality conditions may fruitfully be included at the macro level. We will in fact examine contextual mortality

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12 effects in future macro-level analyses of variability in the coefficients of the micro model. The expectation that fertility affects child mortality also derives from both physiological and behavioral hypotheses. Infants born to mothers who are early or late in their reproductive years, whose previous birth was recent, and who are at high parity are apparently at greater risk of prematurity, low birth weight, and congenital malformation (Watson et al., 1979~. Both the EF-LCM relationship and the LF-LCM contemporane- ous disturbance correlation should reflect these physiological effects. High parity and close spacing may also increase the competition between children for family resources, thereby raising mortality risks for all but especially younger children. Again, this influence should be most pronounced in the EF-LCM relationship and the LF-LCM contemporaneous disturbance correlation. Sex Composition Our model assumes that later fertility is more responsive than early fertility to explicit family-size targets and deliberate decision making. If stock-taking takes place, it may be midway through the reproductive years. At that time, decisions about future births--if in fact such decisions are made--are based on the number of surviving children and some guesses about the future. Parents may also be concerned about sex composition, especially minimum numbers of boys and girls (Arnold et al., 1975; Bulatao, 1979~. Son preference is present to some degree in most cultures (William- son, 1976), apparently often encouraging high levels of fertility (Khan and Sirageldin, 1977), although most parents still want at least one daughter (Arnold et al., 1975~. Strong son preference is probably based on sharp sex differences in the social, economic, and cultural roles fulfilled by children. The roles of daughters may not be so highly valued as those of sons, although daughters tend nevertheless to be of some benefit to their parents (especially since sharp sex differences imply that sons cannot carry out the obligations of daughters). In addressing the effect of sex composition on later fertility outcomes, we therefore specify separate boy sufficiency (SCB) and girl sufficiency (SCG) variables (Block III of Figure 1.2~. A sufficiency of sons and daughters should encourage fertility regulation and lower later fertility in transitional settings, although the effects need not be identical for the two sexes. These expectations do not apply to traditional settings because family-size targets and associated decision making are presumed absent. Sex composition is also relevant to child mortality. Chen et al. (1981) show that son preference in Bangladesh results in greater female than male mortality because of a sex bias in the distribution of food and health care services. Thus families with a predominance of boys among their early births should experience fewer child deaths ceteris Minibus. Although the model does not include a variable for sex composition per se, its hypothesized effect should be captured indirectly through potential SCB-LCM and SCG-LCM links. The importance of these links

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13 should depend not on whether the setting is transitional or traditional, but on the presence and strength of ethnic or cultural son preference. This can be taken into account by stratif Location on ethnicity and with specif ic ethnographic knowledge. Finally, sufficiency of children of each sex when mothers reach age 30 depends on early fertility {EF) and early child mortality (ECH). A desire for, say, two sons and one daughter requires that a minimum of three children be born and survive. We therefore model SCB and SCG as f unctions of these early outcomes. Socioeconomic Variables Our ultimate aim in developing a comprehensive fertility model is to tap empirically the many ways in which socioeconomic status (SES) affects fertility behavior. We distinguish two types of socioeconomic variables: exogenous and endogenous character istics of respondents and their husbands or partners. The exogenous variables, appearing in Block I of Figure 1.2, include respondent's education (WED) and childhood residence (RESC). The endogenous variables consist of respondent's premarital work experience (WBM) in Block II, and postmarital work experience (WSM), current residence (RES), husband's education (HED), and husband's occupation (HOCC) in Block III. mese variables incorporate al' of the socioeco- nomic information in the WAS standard recode tapes. Our hypotheses on the effects of these variables depend on societal context. In traditions 1 settings, there should be a positive but weak relationship between socio- economic status and fertility. In transitional settings, there should be an inverse relationship, due largely to low levels of later fertility associated with high socioeconomic status. Although other approaches (Davis and Blake, 1956; Easterlin, 1978) allow for indirect socioeconomic effects on fertility behavior, our approach is apparently unique in delineating such effects through other socioeconomic variables. We hypothesize, for example, that respondent's education (WED) influences premarital work experience (WBM), and that this in turn affects postmarital work experience tWSM), with implications for later fertility. Another indirect socioeconomic path of interest is the link between respondent' s education and late fertility through husband's education (HED). Schultz (1974) and others have compared the fertility impact of wife's and husband's education. In our model, current husband's education depends on wife's education. Thus the direct effect of husband's education on later reproductive behavior and ~ ater child mortality is actually a component of the reduced-form effect of wife's education, making comparisons of the kind carried out by Schultz (1974) inappropriate. Interactions We have defined traditional and transitional contexts as the ideal-typic extremes of a continuum of settings that might be found in Third World countries. As societies move away from the equilibrium of a traditional

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14 society, socioeconomic differences in fertility behavior should be created or modified as new ideas and structures evolve. People at different socioeconomic levels will not respond simultaneously or equally to such changes. It is known that norms supporting small family size and contra- ceptive use are often accepted first by those of the highest socioeconomic status, diffusing gradually to those of lower status. mis accounts in part for the widening of socioeconomic differentials that accompanies fertility decline. In our model, this variable participation and diffusion translate into interactions involving socioeconomic status. We specify two sets of interaction terms, the first involving early fertility (EF), and the second boy suff iciency (SCB). Parental decisions regarding later fer- tility (LF) and contraceptive use patterns {LCU)--if in fact such decisions are made--should be based on early fertility experience (both numbers and presence of sons). For those of lower socioeconomic status, the effects of early fertility and boy sufficiency on LF may be non- existent or even positive, reflecting level of fecundity. For those of higher socioeconomic status, the effects should be inverse--for example, the more children early on, the fewer children later on. Figure 1.3 schematically represents this reversal of effects. The same logic applies to LCU, mutatis mutandis. Among the variables in the WFS data sets, wife's education (WED) and husband's occupation (HOCC) are most likely to interact with early fertility behavior in the determination of late fertility behavior. These interactions are symbolized by EF*WED, EF*HOCC, SCB*WED, and SCB*HOCC in Block III of Figure 1.2. As noted earlier, we will stratify the data by ethnicity (sample size permitting) in our empirical analyses, so that ethnicity will also interact with early fertility outcomes (and every other explanatory variable in the model, for that matter). Trickle-down processes and the differential impact of social change on socioeconomic groups need not be the only factors affecting inter- actions in the micro model. For example, family planning programs making cheap and effective contraceptive methods universally available, and mass media campaigns designed to provide broad exposure to alternative fer- tility norms may reduce socioeconomic differentials in fertility related behavior. Our analyses will allow for a range of possibilities, through a specification that includes interactions involving socioeconomic status at the micro level, and by treating the degree of interaction as a function of family planning program strength and other variables measured at the macro level. Variables Omitted From the Model Our model excludes two variables prominent in other models--desired family size and the costs of fertility regulation--for reasons given below. WFS standard recode tapes include an indicator of desired family size, used in some analyses (Westoff, 1980~. However, it is unclear whether desired family size has meaning for all WFS respondents, especially in settings where fertility regulation is not practiced.

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15 J - CC UJ J Low SES / / / / - High SES Medium SES - - - EAR LY FE RTI LITY FIGURE 1.3 The Nature of the Interaction Hypothesized Between Early Fertility and Socioeconomic Status, in the Determination of Later Fertility, for Transitional Settings Moreover, placing desired family size in the causal structure is problematic. Micro-economic models typically envision a single family- size decision made prior to the birth of the first child. Our partition of early and later fertility implies at least one decision, midway through the reproductive years. Both approaches assume that family-size goals are predetermined with respect to the ultimate endogenous variables in the model. However, since responses to desired family size questions are quite sensitive to post hoc rationalization, this variable as usually

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~6 measured is in fact endogenous. In addition to these problems of com- parability and causal placement, the WFS measure of desired family size has questionable reliability (Westoff, 1980:2) and an unknown correspon- dence to underlying preferences (Szykman, 1982~. Our model also omits the costs of fertility control. Easterlin (1978) defines three types of cost: fixed costs, which might be tapped by knowledge of contraception; variable costs, which refer to the recurring expense of purchasing contraceptive supplies; and psychic costs, which involve attitudes toward and norms governing contraceptive use. m e higher these costs, the less likely contraceptive use will be. Although the WFS standard recode tapes include indicators of contracep- tive knowledge, they lack information about variable and psychic costs. It is doubtful that adding either desired family size or cost factors would much improve the predictive power of the model. If appropriate and reliable indicators were available, we would place these variables in the causal structure so that they mediated the influence of socioeconomic variables on later fertility and contraceptive use. Weir effects are, in our model, implicit in those of the socioeconomic variables. The model could easily be modified to accommodate these variables should better information become available. Finally, given that the WFS countries are located along the traditional/transitional continuum, it is plausible to view desired family size and fertility regulation costs as relatively invariant either within countries or for well-defined social groups within countries. If so, it would be conceptually appropriate to account for these two vari- ables at the macro level. As noted earlier, we plan to construct aggre- gated or global macro variables that can be used to analyze varability across settings in the micro-level coefficients of the model. 1.3 THE STRUCTURAL EQUATIONS This section explains the sixteen structural equations of the processual model, as well as our expectations about the nature and direction of the relationships involved. Because these expectations depend on societal context, we continue to invoke the ideal-typic traditional/transitional distinction described above. Table 1.2 summarizes these cross-setting expectations about the signs of all coefficients in the structural equations. The following discussion also provides relatively precise definitions of the variables comprising the model, all of which depend on data available from WFS standard recode tapes. For simplicity, each structural equation is treated as if it were estimable as a multiple regression. Although actual estimation might be considerably more complex, allowance here for details specific to discrete and ordinal response variables would detract from explication of the substantive hypotheses underlying the model.3 Onset Taken by themselves, Blocks I and II of Figure 1.2 depict a model of fertility onset, defined as age at first birth (AFB). His provides an