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114 GDP instead of positively, and that EF, for which we had no strong hypotheses, is slightly positively associated with SSR and GDP. AS for LF, it has a very minute inverse relationship with SSR and GDP. Although the direction of association was expected, the goodness of fit was not. Indeed, all of these fits involving the means are weak and not statistically significant at conventional levels. However, this is unsurprising given the degree of scatter observed repeatedly in the course of this analysis. Moreover, these results are telling in another way: mean AFB, EF, and LF are summary measurements based on univariate d istributions . Rather high correlations at the country level are usual when measures of this kind are employed. mat we have not found such correlations in this analysis suggests that the composition of the 15-country sample being used may be working against an effective test of the theory Future research, based on a larger sample of countries, may overcome this problem. 2 . 7 SUMMARY AND DISCUSSION The material presented in this chapter divides naturally into three distinct foci linked by the need to begin assessing the empirical adequacy of the theory developed in Chapter 1. We began the main work of this chapter by extending and operationalizing the macro-level aspects of the theory. AS part of this effort, we presented a rationale for using measures of socioeconomic development and family planning program effort as indicators of what we mean to convey by the traditional/transitional vocabulary employed in Chapter 1. We then translated Chapter 1 hypotheses about coefficient sign variation (or the lack thereof) across social settings into hypotheses about the effects of macro variables on micro coefficients when the latter are collected over countries to form a dependent variable at the macro level. This translation process was carried out with great explicitness, partly because of the complexity of the ideas, but also to demonstrate that the operationalized macro hypotheses rest on a serious reasoning effort. In developing these hypotheses, we attempted to show the power of the multi-level framewor k (Hermalin and Mason, 1980; Mason, 1980) for developing contextual theory and, by example, showed how to work back and forth between dual charac- terizations in order to derive hypotheses. This was essentially the key to deriving hypotheses about the macro determinants of intercept vari- ability. On the one hand, these determinants are driving a particular kind of coefficient at the micro level; on the other hand, the macro equation for the intercepts collected across countr ies provides the "main ef fects ~ of the macro var tables on the micro level response var table. In sum, our multi-level approach, as well as the methodology we have used to derive hypotheses, is rarely seen in population research, and we have therefore spelled it out. The second major effort in this chapter consisted of an analysis and comparison of the estimated AFB, EF, and LF structural equations for Peru and Korea. Although a discussion of the results for one or two countries seems essential if the macro analysis is to be well understood, presenta- tion of the estimated equations for Peru and Korea has value in its own

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115 right. It is only in examining the data for these two countries that we could present all of the coefficients in the equations. This exercise showed, for example, that the effects of age at first birth on later fertility were quite different from those hypothesized. Moreover, by explaining which quantities were to be used in the subsequent macro analysis, we could identify those quantities which were not to be used later. In general, the operationalizat~on employed at the micro level uses the discrete treatment for the socioeconomic variables. Our purpose in following this approach was to make our initial inspection of the micro data as informative as possible, so that we could revise the specification using appropriate scat es for those variables for which scaling is plaus- ible. We did not originally intend to conduct macro comparative analysis using the socioeconomic variables in discrete form. That we did so reflects the dialectic of research. Having arrayed the micro results, it became clear that the macro analysis was but a step away from the self-contained inspection of the micro results. Why not see whether the data even roughly support our hypotheses? Hard thinking about the extent to which they do not should lead to attempts at improving the micro specification. This leads to the third and final major contribution of this chapter. If we make no distinction among the micro socioeconomic variables, Table 2.2 contains entries indicating 10 hypotheses at the macro level. We have tested these hypotheses in a highly preliminary fashion using data from 15 countries. Given so few macro data, it is hardly surprising that our results are weak and mixed. In brief, the clearest support for our theory is found in the macro results for the socioeconomic effects in the later fertility equation. Although the fits are poor, and the macro effects accordingly fragile, it is nonetheless striking that we found consistent support in the signs of the macro coeff icients of the inter- active specification involving S. FP, and S.FP. The results for the LF intercept and for the parameters involved in the AFB and EF micro equations are more equivocal. Since the work presented here is no more than preliminary, the question posed by these results is not whether they show the theory to be wrong or to survive a test, but rather their implications for the next round of research. Because of the f indings for the socioeconomic coefficients in the LF equation, we find the results essentially rewarding, and approach f urther work with some optimism Not having obtained these results might have been ~ cause for pessimism about the soundness of our approach. Tn f urther research, we will consider the following points, not listed in order of importance ~ i . e ., numer ically coded instead of polytomi zed ~ . 1. All micro predictors should be scaled where possible. This has been our goal from the start, but the macro analysis reinforces it. In particular, the standard errors of slopes are constructed directly from all observations, whereas those of contrasts from polytomies are affected by the number of observations in the categories involved in the contrast. In other words, the contrast between the extremes of the education categories, for example, dispenses with the information about the

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116 intervening categories, and is equivalent to constructing the education slope from the lowest and highest categories. This introduces error, and could have played a role in weakening the results for the effects of education on later fertility. Hermalin and Mason (1980) obtained clearer results in macro regressions in which education slopes formed the dependent variable. 2. We should try to purge the micro specification of variables that appear to be making no contribution. The work before marriage (WBM) variable in the later fertility equation may be a case in point. Its failure to attain ~significance,. as indicated in Table 2.9, is suggestive, but just that. 3. We need to examine closely the performance of the adjustment variables. Are they working in the ways expected, and are they linked to the socioeconomic variables in the ways hypothesized or assumed? 4. More generally, we need to estimate the full structural model and the nature of the macro variability of all the parameters ascertained, whether they are held to be invariant with respect to the traditional/ transitional continuum, or specified to vary meaningfully across it. 5. To the extent possible, we need to extend our sampling of countries. However they turn out, the results will be more reliable the larger the number of countries on which they are based. 6. We need to develop and implement efficient methods for esti- mating all of the parameters in the multi-level model. m is is in process, and it should be possible to obtain improved parameter estimates in the near future. 7. We need to consider whether our macro-level specification should be extended to include additional variables. m e justification for our analysis at the macro level depends ultimately on the assumption of exchangeability of the macro disturbances. m is amounts to considering whether the theory is in fact testable with the particular collection of countries being used. Perhaps regional or cultural specificity dominates the kinds of socioeconomic effects with which we are most concerned. If so, what options are available for dealing with this problem? We have already noted that the bivariate relationships between AFB, EF, and LF with SSR and GDP are exceptionally weak--essentially nil. It is reasonable to expect that AFB and LF in particular would be clearly associated with SSR and GPD. That they are not suggests that there may be something unusual about the data which pervades our entire macro analysis. 8. Finally, `t may be that the cohort we have sampled--women aged 40-44 in 1974--is not optimal for exemplifying the kinds of effects we think exist. AS part of our ongoing research, we are also studying a more recent cohort using the specif ication seen here. In sum, we have made a start with a comprehensive theory. The results obtained thus far are sufficiently encouraging to warrant further development of the empirical tests. AS the above discussion indicates, we will try to take account of diverse possibilities in this further effort, and have numerous ideas about the direction of our ongoing research.