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80 has shown, for example, that the decision to contrast employers with employees is not as felicitous as expected. It would be preferable to contrast employers with farmers, since the difference in LF between these two categories is by far the largest for both Peru and Korea. It has also shown that AFB does not affect LF in the way expected in Peru and Korea. Since these are disparate countries, there may be a need to review our thinking about AFB, and to closely examine the data for an explanation for this apparent anomaly. We have also gained some insight into potential problems with the macro tests. m e tests we will present assume that the hypotheses about the nonsoc ioeconomic variables are valid. We now have evidence from two countries that this is not always the case for the LF equation. Therefore, our tests may not yield the expected results--not because our reasoning about socioeconomic effects is wrong, but because our reasoning about the adjustment and other variables needs to be revised. 2.6 MACRO ANALYSIS Our two fundamental hypotheses suggest a particular ordering of steps within the macro analysis. The first basic hypothesis is that the socioeconomic determinants of fertility affect the components of the reproductive process differently. m e second is that the components of the reproductive process are both additively and interactively affected by macro phenomena. Translating this second hypothesis into the language of structural equations and multi-level models, we hypothesize that the intercepts, and the effects of the socioeconomic determinants, of the components of the reproductive process vary across societies in meaning- ful and predictable ways. m e first hypothesis directs attention to within-country differences in the relationships between the micro socio- economic variables and each component of the fertility process. The second directs attention to between-country variability in these micro relationships. Before undertaking macro analysis of the second hypothesis, it is worth testing the first. If the socioeconomic determinants of the reproductive process do not differentially affect the components of the reproductive process, there is little point in testing the second hypothesis. Within-Country Differences To test the first major hypothesis, we summarize the contrasts, described earlier, to be used in the macro analysis. Using the criterion that the ratio of each coefficient to its estimated standard error must be at least as large as |1.96|, that is, using a p = 0.05 level of statistical significance (two-tailed test), we have tabulated the number of positive and negative significant effects for each socioeconomic variable present in the micro equations over the 15 WAS countries for age at first birth (AFB), early fertility (EF), and later fertility (LF). Table 2.9 presents these counts and shows that the significant effects of childhood

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81 TABLE 2.9 The Number of Instances in Which Each Socioecor.omic Explanatory Variable is Statistically Significant in the AFB, EF, and LF Strutural Equations, Summed over 15 WFS Countries Response Variable at the Micro Level Socioeconomic - Explanatory Variables AFT EF LF RESC . WED WBM HED + - + - + 2 2 0 O 0 1 10 0 0 0 2 2 O O 1 0 o _ 3 WSM + O _ 2 RES HOCC + - - o 6 o Note: The counts are based on a p = .05 level of statistical significance {two-tailed test}. The coefficients used to derive these counts are the contrasts, described in the text, which provide the response variables in the macro analysis. A blank indicates that the explanatory variable was not included in the particular micro specification.

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82 residence (RESC) and wife's education (WED) on AFB are always positive. Thus, for example, over the 15 countries the effect of RESC is positive and significant in 2 and insignificant in the other 13. m e effect of WED on AFB is positive and significant in 10 of the countries, and insignificant in 5. Indeed, inspection of the individual contrasts in the AFE equation shows that even the insignificant contrasts are virtually always positive. Thus, the direction of the socioeconomic effects on AFB is a& hypothesized, given the evidence from the 15 WFS data sets. Considering next the socioeconomic effects on EF, Table 2.9 shows that the RESC effect is occasionally positive and never significantly negative, that the effect of WED is occasionally negative but never significantly positive, and that the effect of the respondent's working before marriage (WBM) is once negative but never significantly positive. Thus, the effect of RESC is as hypothesized, while those of WED and WBM are not. To this it should be added that out of 44 nonindependent replications (WBM is not available in the Fiji data set), in only 5 is a socioeconomic effect statistically s~gnif icant at the selected probability level (.05~. As can be seen from Table 2.9, EF is less often affected by prior socioeconomic status than either AFB or LF. This much, then, is consistent with expectations. On the other hand, the contrary results for WED and WBM that occur in three separate countries will require study before research can proceed beyond the results described in this chapter. This brings us to the socioeconomic determinants of LF, for which the significant effects are, with a single exception, negative as hypothe- sized. The exception is for husband's occupation (HOCC), and the country which yields this result has a sample of less than 250 women aged 40-44 in 1974. Of these respondents, no more than five had husbands who were employers. Thus, this exception does not suggest a substantive anomaly. For no single indicator of socioeconomic position are there omni- present effects on LF over the 15 countries. In fact, no socioeconomic indicator has a significant negative effect in even as many as half the countries. m is does not mean that the data disconfirm the hypothesis that LF should be most clearly determined by socioeconomic position, with AFB less so. A simple count of effects, ignoring HOCC, gives 14 signif i- cant socioeconomic effects for LF, as compared with 12 for AFB. Of course, there are more predictors in the LF equation, a fact which cuts two ways. On the one hand, it might be argued that any assessment such as this should adjust for the number of predictors. On the other hand, the larger the number of correlated predictors, the less the chance that any of them will be significant. All of this suggests what, on balance, should in any case be clear--that rigorous assessment of which fertility component is most, or least, determined by socioeconomic position can only be carried out within each data set for each country. This is a task that must be left for another occasion. Nevertheless, the simple tabulation presented in Table 2.g is highly suggestive. Again it should be recalled that these data refer only to the cohort aged 40-44 in 1974. This cohort would have spent a high proportion of its reproductive life, in many of these countries, in a period of rather slow socioeconomic development and in the absence of well-developed family planning programs.

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83 Differentials in targets and opportunities for fertility control would have been limited. An additional hypothesis, not pursued in this illus- trative presentation of one cohort, is that there will be intercohort differences in the strength of the socioeconom c effects.l5 To summarize, based on the counts in Table 2.9, it appears that socioeconomic position affects AFB positively, as expected, and LF inversely, again as expected. Socioeconomic position affects EF only weakly, and in both directions. Although this latter result is incon- sistent with expectations, the weakness of the impact is as hypothesized. m us, there is justification for further analysis of the data at the macro level. Between-Country Variability What is the appropriate strategy for exploratory macro analysis of the micro socioeconomic coefficients and intercepts of the AFB, EF, and LF structural equations? Although we touched on this question earlier in this chapter, the results summarized in Table 2.9 raise it again here. In particular, it could be asked whether we should be dichotomizing micro coefficients into statistically significant versus statistically insig- nificant groups, with the latter group then set equal to zero. We do not take this approach here because it dispenses with potentially useful information. There is, of course, no logical necessity for selecting p = 0.05, as we did to construct Table 2.9. If we incorporate knowledge, even imperfect knowledge, about the sampling errors of the coefficients, we can weight a coefficient more heavily the larger its ratio to its standard error. That is, the more "significant the coefficient, the more it should count in the analysis. Moreover, each of the contrasts focused on has been the subject of a concerted effort in hypothesis development. The generality of our hypotheses, permitting them to predict different signs in different settings, allows for variability in the magnitudes of the coefficients: a coefficient may be small and insignificant without thereby disproving our theory. Setting insignificant results to zero could thus mask impor- tant and interpretable patterns in the magnitudes of small and insignif icant coefficients in the micro equations. Simultaneous estimation of both the micro and macro effects by the method of maximum likelihood is almost possible. When the computer programs for this methodology become available, they will permit full use of all available information at both levels of analysis. In the present analysis, we carry out least squares regressions at the micro level, and separate weighted least squares regressions at the macro level. The implications of this strategy, which is reasonable as an exploratory procedure, are amply discussed by Mason (19807. In addition to these regressions, we also rely heavily on scatter diagrams that plot the micro intercepts and socioeconomic effects against the macro variables. As will be seen, this combination of data analysis tools proves sufficient for the task at hand. To describe the relationships of the intercepts and socioeconomic effects to the macro variables, Figures 2.1 to 2.23 present bivariate

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84 scatter plots with associated regression lines.16 mese lines are derived from bivariate weighted regressions, using the estimated vari- ances of the micro intercepts and coeffici-~.~ts as reciprocal weights. Except for the parameters involved in the LF Hero equations, bivariate analysis is all that is required to test our hypotheses. For the LF intercept and socioeconomic effects, our hypotheses are multivariate. To test them, we will also report the results of multiple weighted regres- sions at the macro level. For those scatter diagrams shown here in which a measure of socio- economic development is the macro predictor, the indicator is social setting in the Mauldin et al. (1978) index. Use of this variable enables the reader to dichotomize on the social setting dimension, since the left-most six points are always those for countries in the low category of the index. Similarly, for the diagrams that use family planning program strength as the macro predictor, the left-most five are always those countries in the low category of the Mauldin et al. (1978) family planning program strength index. Only two of these countries are in the low category on both dimensions. Certain of the results differ depending on whether social setting rank or gross domestic product per capita is the macro socioeconomic development variable. Although we discuss this at the appropriate point, we do not present additional scatter plots for GDP per capita. For the 15 countries at hand, the correlation between the two variables is .86, so that the scatter diagrams would be quite similar. In addition, where GDP per capita seems to make the greatest difference, our hypotheses are multivariate, and the bivariate plots would not be informative. In testing the macro hypotheses, we first discuss the results for the socioeconomic position coefficients, and then turn to consideration of the results for the micro equation intercepts. AFB and EF Slopes Figures 2.1 and 2.2 display the bivariate scatter and regression lines for the coefficients obtained in the AFB micro regressions. In each instance, the y-axis refers to realized values of regression coefficients, and the x-axis to social setting rank. We hypothesized that these relationships would be positive. Instead, they are both negative, with a poor fit. The dispersion of these scatters suggests that no nonlinear function would improve the fits meaningfully (although it would take pictorial representation of the regression weights to confirm this). These findings are based on the use of the social setting ranks. Use of GDP per capita yields a positive effect on the SES coefficients, though again the weighted bivariate regression fits the data poorly. This discrepancy in results suggests that the data do not support the hypoth- esis (although neither do they disconfirm it). Next, we hypothesized that there would be no relationship between the magnitudes of the SES effects in the EF equations and level of socioeconomic development (see Table 2.2~. Figures 2.3 to 2.~ display regression lines with consistently negative slopes. The fits associated with these lines, however, are in all cases very poor. Furthermore, the

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85 1. t200 ~ 4. .69667 .27333 ·. 15000 4, — - .57333 ~ 4. - . 99667 - 1.4200 4. - 1.8433 -2 .2667 .F -2.6900 ~ . . — Am_ I_ . 1 . 0000 2.5556 4.1111 5 .6667 7.2222 ~ — ~ — — — — ~ — — — — 4 — — — — ~ — — — — 4 _ _ ~ _ _ ~ _ _ _ ~ _ _ _ ~ 10.333 13 144 SSR 8. 777 a t 1.889 15 Coo FIGURE 2.1 Plot of Childhood Residence (RESC) Coefficients from Al?B Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y = .11 - .019 (SSR)

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86 8.0700 7.1644 $;.2589 - ·1 S.3533 .4478 3.5422 2 .6367 1.7311 + .82556 - . 8 OOC)0 - 1 . . . . . · 2.5556 5.6667 8.7778 FIGURE 2 .2 Plot of Wife ' s Education (WED) Coeff icients from AFB Micro Equations Against Social Setting Ranks (SSR) with Bivariate (weighted) Regression Line: Y = 3.77 - .0085 (SSR)

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87 . ssooo ~ 4. .251t1 4~. - .87778 - 1 + 4~ - .42667 .76556 - 1 . 1044 ~ - 1.4433 4. - 1.7822 4. -2. 121 t - 2 . 4600 - - 5.6667 7. 222~ - ~ — — 4 — — — — ~ _ — — _ ~ _ _ _ _ ~ _ _ ~ 10.333 8.7778 . 1 t .889 . , _ ~ _ ~ ~ 13.444 SSQ 15.000 FIGURE 2.3 Plot of Childhood Residence (RESC) Coefficients from EF Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y = .23 - .034(SSR)

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.61000 4. .43889 4 .26778 4. .96667 - 1+ - . 74444 - 1 + 4. - .24556 -.41667 4P - .58778 ~ 4. - .75889 - .93000 1 . 0000 . 2.5556 88 . 4 . 1 1 1 1 5 .6667 7. 2222 , 8.7778 . - - - - - ~ _ _ _ ~ _ _ _ ~ _ ~ _ _ ~ 10.333 13 444 S5Q 1 1 . 8 8 ° 1 5 . 00 FIGURE 2.4 Plot of Wife's Education tWED) Coefficients from EF Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y ~ .046 - .026 (SSR)

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89 . 70000 ~ 4. .S311 1 .36222 . 19333 4. . _ _ - . 24444 _ ~ 4444 - .31333 - .48222 -.6511 1 - .82000 . . . 4. _ _ _ _ 4. _ _ _ _ ~ _ _ _ _ 4. _ _ _ _ ~ _ _ _ _ + _ _ _ _ ~ _ _ _ _ ~ _ _ — — ~ — — — — 4. — — — — 4. — — — — ~ — — — — ~ — — — — ~ — — — — 4 — — — — · — — — — ~ — — — — + — — — — 4 1.0000 4.1111 7.2222 10.333 13 444 SSQ 2.5556 5.6667 8.t778 1 1 889 15.000 FIGURE 2.5 Plot of Work Before Marriage (WBM) Coefficients from EF Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y ~ .16 - .0098(SSR)

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so parallel results based on GDP per capita are consistent with those seen for social setting rank. Nevertheless, the results here are ambiguous. If we focus on fit, we can conclude that the data are consistent with our hypothesis. On the other hand, if we feel that the negative slopes cannot be ignored, then we have a puzzle. Our hypothesis of no relationship indicates that we have no a priori basis for predicting a positive or a negative relationship, not that there can be no systematic relationship. Should we treat the three replications of a negative association between the EF socioeconomic coefficients and level of socioeconomic development as meaningful, or should we treat these replications as artifacts of a highly unusual accidental sample of countries? m e answer to this question must await later analysis. Thus far, we have examined the micro results for the socioeconomic effects in the AFB and EF micro equations. We have found that the macro equations relating the micro coefficients to social setting rank have very poor fits, as can be seen from the scatter diagrams; moreover, the slopes over countries for the AFB socioeconomic determinants are slight, and either positive or negative, depending on the macro indicator used. For the socioeconomic effects in the EF micro equations, the between- country slopes are barely negative, the fits poor. These results certainly do not strongly support our hypotheses. There should be positive slopes for the coefficients in the AFB equation, and no slopes for the coefficients of the EF equation. We could decide to emphasize the lack of fit in these macro bivariate relationships, or we could conclude that the unexpected negative slopes merit study in future work with these data. It would be premature to reach a decision at this point, since the results for the socioeconomic determinants of LF also need to be taken into account. LF Slopes Our hypotheses about macro variability in the micro socioeconomic determinants of LF are multivariate. In particular, we have theorized that the level of socioeconomic development should have a negative effect on the coefficients; that the level of family planning program effort should interact with socioeconomic development; and that the ~main" effect of family planning programs should be negative, with the interactive effect positive. In considering the realities of macro-level data analysis based on 15 observations, it is clear that the interaction we have hypothesized may not be detectable. If so, it is essential that we develop a hypothesis for a simpler model. Given the need to retain both the developmental and family planning dimensions, this simpler model should be multivariate, include socioeconomic development and family planning program effort as predictors, and be additive. With this simplification, we can hypothesize that the effect of family planning program effort should become positive. Our reasoning is that most of the 15 countries fall into the high category of the Mauldin et al. (1978) social setting index, and that the coefficients in the LF equation that are statistically significant by the criterion used in the construction of Table 2.9 are negative. Thus, the data are weighted toward the high

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104 ~ . 74~ + 4.1522 ~ 4- 3.5644 ~ 4- 2 . 9767 + 4. 2.3889 1 .801 1 1 .2 133 .62556 4. 4~ .37778 - 1+ + -.55000 4. - — _ . · _ + _ ~ _ _ _ _ ~ _ _ _ _ ~ _ _ _ 4~ — _ 1.0000 ~ . 1 1 1 1 7.2222 10.333 13. 444 SSP 2.5556 5.6667 8 . 7778 1 1 889 15 . O'J~ _ FIGURE 2.18 Plot of Kusband~s Occupation (HOCC) Derived Effects from LF Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y a .19 - .036(SSR)

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105 . 74= + 4 . 1 522 4. 3.5644 ~ 4~ 2 .9767 4. 2.3889 4. 1.8011 1.2 133 4 .62556 · 37778 -1+ . 55000 - 2 .6667 . 8 . 0000 . — ~ — — — — ~ — — — — ~ — — — _ 4. _ _ _ _ 4, _ _ _ ~ _ _ _ _ . _ ~ 10 657 16. 000 t ~ . 33 3 18.667 _ _ ~ _ _ _ _ ~ _ _ _ _ ~ 2 1 . 3 3 3 F P S 21 .00O FIGURE 2.19 Plot of Husband''; Occupation (HOCC) Derived Effects from LF Micro Equations Against Family Planning Program Scores {FPS), with Bivariate "weighted} Regression Line: Y - .21 - .019 (PPS)

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106 In sum, only in a highly specific way can the bivariate information in the scatter diagrams be used to test the multivariate macro hypotheses about between-country variability in the effects of the socioeconomic determinants of LF. To test the multivariate macro hypotheses about the micro socio- economic determinants of LF (shown in Table 2.2), we use the alternative measures of socioeconomic development and family planning program effort described in the third section of this chapter. These alternatives are labeled as follows: SSD is the dummy variable for social setting, SSR is the rank variable for social setting, GDP is gross domestic product per capita, FPD is the dummy variable for family planning program effort, and FPS is the family planning effort score. Since our hypotheses are the same for each micro socioeconomic variable, we begin by pooling all of the micro coefficients in the LF equation and specifying (2.8) Yj = 40 + 41Sj + 42(FP~j ~ 43(S.FPJj + Yk + ad where j (j = 1,...,15) subscripts countries, 40 is the intercept, S is a measure of socioeconomic development, FP is a measure of family planning program effort, S FP is the interaction of S with FP, and Yk (k = 1,...,K) is an additive nuisance parameter that distinguishes the net mean value over the 15 countries of the kth micro socioeconomic effect from similar means for other socioeconomic effects. The nuisance parameters allow for consistently different magnitudes of micro effects. They are included additively since to include them interactively would amount to separate specifications for each micro socioeconomic effect. However, because we do not have separate hypotheses, our analysis begins by pooling all of the coefficients in the fashion described. We estimate equation {2.8) in three different ways, using (1) SSD, FPD, and SSD.FPD; (2) SSR, FPE, and SSR.FPE; and (3) GDP, FPE, and GDP.FPE. Table 2.10 presents the results. The signs of the regression coefficients presented in Table 2.10 are strikingly consistent with our hypotheses about the effects of the macro variables on the micro coefficients. In particular, when socioeconomic development and family planning program effort are dichotomized, the two ~main. effects are negative, and the "interactive" effect is positive. This pattern is also present in the estimates based on GDP and FPS. It is not apparent, however, in the results based on SSR and FPS. For that operationalization, only the effect of socioeconomic development is as hypothesized. Even so, the results presented in Table 2.10 are remark- able, given the complexities of the theory we are testing, and the nature of the sample we are working with. To determine whether the findings based on pooling over coefficients are based on particular micro socioeconomic variables (e.g., those of RESC), we have also examined the data in disaggregated form. Table 2.11 presents the results of this inquiry in nonnumeric form. For each type of micro coefficient, we have fit the three alternative representations of the macro variables, trying both the interactive and the additive specifications. Table 2.11 indicates whether the signs of the macro effects (but not magnitude or statistical significance--which are not readily ascertained by the methodology we have used) are as hypothesized.

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107 TABLE 2.10 Weighted Regression of Socioeconomic Coefficients from the LF Micro Equation on Alternative Macro Indicators of S and FP Alternative Measures of S and FP Explanatory Variables and SSD SSR GDP Other Regression Information FPD FPS FPS Coefficient typea ~ .2761 r .276 ~ ~ .2763 S -. 22 -. 0009 -. 002 FP -.16 . 0009 -. 02 S FP .003 -.0015 -.00004 Intercept .19 -.01 .4S R2 .353 .354 .400 MPR2b .107 .107 .171 N 101 101 101 aNuisance parameters not presented; [.276] is multipl e R2 due to inclus ion of dummy var. tables for coef f icient type . bMPR2 is the multiple partial correlation squared, due to adding in S. FP, and S FP into a specif ication already including the dummy var tables for coef f ic lent type . In each instance, the analysis beg ins with the interactive specif ication. If the signs are not all as hypothesized, we try the additive specif i- cation. me entries in Table 2~11 indicate whether the interactive specification yields the hypothesized Signer and if note whether the additive specification does. Lack of an entry means that neither specification xesu:~~ Are all coefficients smith signs as hypothesized. In every case. ant least ane no the m;—an ~ff-~1~ w:~= ; n the TV; ~^A direction ~ ~ ~ _ _ ~ · - __ As,! 41~_ sac ~ —~ _ m e pattern in Table 2.11 indicated that for every single micro socioeconomic determinant of LF, there is at least one alternative among the measurement choices made for which the interactive specification yields all three macro coefficients with signs as hypothesized. In general, the data provide a certain amount of support for our hypotheses about the macro variability of the socioeconomic effects in the LF equation across settings. Given the complexity of the hypotheses, the paucity of macro data, and the discrepancies found between data and

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108 TABLE 2.11 Model Corresponding to Predicted Sign Pattern of Macro Effects, Separately for Each Socioeconomic Coefficient of the LF Micro Equation Alternative Measures of S and FP Model Based on Micro SSD SSR GDP Coefficient For: FPD FPS FPS RESC WBM HED WSM RES WED HOCC Additive Additive Interactive Interactive Additive Interactive -- Additive -- Interactive Interactive Interactive -- Interactive Interactive Interactive Interactive Note: See text for description of criteria underlying choice of model. hypotheses in other parts of this analysis, we do not wish to state too strongly this congruence between results and hypotheses. If we could establish statistical significance for the macro coefficients, it Is quite possible that none of the effects would be significant at conventional levels. On the other hand, the consistency across coefficient type is not to be dismissed, not even on the grounds that coefficients from each micro data set are bound to be correlated. Although we do not have seven independent replications (there are seven micro socioeconomic effects in the LF equation), there is certainly greater statistical leverage than could be gained with just a single coefficient type. In sum, then, we are cautiously optimistic about the findings for the LF equation. Intercepts As the last step in the macro analysis, we test the hypotheses about the intercepts of the AFB, EF, and OF micro equation. Our hypotheses about the AFB and EF intercepts are bivariate; for them, the scatter diagrams and bivariate weighted regressions reported in Figures 2.20 and 2.21 are

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109 appropriate. There should be a positive relationship between socio- economic level and the intercepts for AFB and EF. For the AFB intercepts, the relationship with social setting rank is essentially nil. Although the regression coefficient is negative, as is the parallel regression employing GDP, the coefficient for social setting dichotomized is positive. Regardless of the measurement used, the fit is weak, although that for GDP is distinctly the best. For the EF inter- cepts, the relationship with socioeconomic development is positive, regardless of which among the three measures defined earlier is used. Moreover, the fits of the alternative bivariate regressions are stronger than those for the AFB intercepts, though still comparatively very weak. Thus for the AFB and EF intercepts, the evidence for our hypotheses is mixed. For the AFB intercepts, there seems to be virtually no systems atic variability that can be captured with the measures of socioeconomic development. For the EF intercepts, the sign of the socioeconomic development effect is positive as hypothesized, but again the variability across countries is not highly systematic. Finally, for the LF intercepts, Figures 2.22 and 2.23 present bivariate scatters and regressions for social setting ranks (SSR) and family planning program scores (FPS), respectively. In general, all of the discussion preparatory to the multivariate analysis of the micro socioeconomic determinants of the LF micro equation is applicable here. Recall, however, that our hypothesis about the S.FP interaction is that the coeff icient for the product term should be negative. Moreover, to allow for the possibility that the data will not support estimation of the interactive specification, we must consider the signs of the additive effects of S and FP on the intercepts. Inspection of the additive specification makes it clear that these signs must both remain negative. We have computed the same family of specifications for the LF inter- cepts that we used in studying the LF socioeconomic coefficients, looking at both interactive and additive specifications, and trying the different measures of socioeconomic development and family planning program effort. The results of these regressions do not at all support our hypotheses, regardless of the measures selected. This is unsurprising, given the tentativeness with which our hypotheses about the LF intercept were advanced. Failure to obtain strong confirming results concerning the intercepts does not necessarily demonstrate a problem with our theory. The hypotheses about the macro determination of the intercepts are easily the most tentative, least compelling, and most complex of the entire theory. and depend on the validity of hypotheses about numerous parameters, including some that do not appear explicitly in the operationalization of the model. For example' we have had to make assumptions or develop hypotheses about the nature of the macro association between the means of certain micro variables and the macro indicators. In future research efforts, we will focus on the constituents of the i ntercepts, trying to pin down the reasons for the lack of suppor t for our hypotheses about them, and revising these hypotheses if necessary. A starting point in these efforts might well be to examine the between- country variability in the means of AFB, EF, and LF. For the 15 countries at hand, we find for example, that AFB varies independently of SSR and

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110 22 . 520 22.''7 2 1 . 7 1 3 2 1.3 10 + 20.907 + 20 1CO 9 697 ~ 9. 2~3 4. _ + 18.830 4. + — — — — ~ — — — — ~ — — — — ~ — — — — 4. — — — — ~ — — — — ~ — — — — ~ — — — — ~ — — — — ~ — — — — ~ — — — — ~ — — — — ~ — — — — 4 — — - — 4 — — — - ~ — — — — ~ — — — — ~ — - — — ~ 1 .0000 4. t 1 1 1 7.2222 10.333 13. 44.1 SS~ 2.5556 5.6667 8 7778 1 1 . S89 15 . 00O FIGURE 2.20 Plot of Intercepts from AFB Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line: Y = 20.63 - .027(SSR)

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111 14.230 4. 1 3. 6 1 2 1 2 . 994 12.377 . ~ 1.759 ~ 1t. 1-31 ~ J 10.523 9.9056 9.2878 4- S.67~0 +. ~ — ~ — — — — 4~ — 4 — — — — 4 — — — — ~ — — — — 4- — — — — ~ — — — — ~ — — — — ~ _ _ — _ ~ _ _ _ _ ~ _ _ _ _ ~ _ _ _ _ ~ _ _ _ _ ~ _ . ~ 4 ~ ~ ~ ~ 7. .222 10. 3~3 2 .5556 5.6667 8. 7778 1 t .889 8.7778 1 ~ `] ~ ~ S - FIGURE 2.21 Plot of Intercepts from EF Micro Equations Against Social Setting Ranks (SSR), with Bivariate "weighted) Regression Line: Y = 10.55 + .024 (SSR)

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112 .69000 - . 80567 4. . . -2.3013 ~ 4. - 3 . 7970 -5 .2927 .h -6.7883 4. 4. -a. 2840 ~ -9.7797 - 1 1 .275 . . . . . . . . . -12 .77 1 +. 4. _ _ _ _ ~ _ _ _ _ + _ _ _ _ ~ _ _ _ _ ~ _ _ _ _ ~ _ _ _ _ + _ _ _ _ ~ _ _ ~ _ _ _ ~ _ _ _ _ 4- _ _ _ _ 4. _ _ _ _ · _ — _ _ ~ — — — — ~ — — — — ~ — — — — ~ — — — — + — — — — ~ 1.0000 4.1111 7.2222 10.333 13.444 SSR 2.5556 5.6667 8.7778 1 1 .889 15.000 FIGURE 2.22 Plot of Intercepts from LF Micro Equations Against Social Setting Ranks (SSR), with Bivariate (weighted) Regression Line : Y = -4 .65 + .085 (SSR) .

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113 .69000 - .80567 . . . -2 .3013 4. ~ ~ 4. -3.7970 -5 .2927 4. -6.7883 4. 4~ -8.2840 -9.7797 - 1 1 .275 - t2 .77 ~ 4 4. O. . . - FIGURE 2.23 Plot of Intercepts from LF Micro Equations Against Family Planning Program Scores (EMS), with Bivariate (weighted) Regression Line: Y = -5.90 + .12 (FPS)

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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