Trends in Family Effects on the Education of Black and ... · accounts for at least half the variance in educational attainment. Parental schooling, father's occupational status,

Trends in Family Effects on the Education of Black and White Brothers

Hsiang-Hui Daphne Kuo, Robert M. Hauser

Sociology of Education, Volume 68, Issue 2 (Apr., 1995), 136-160.

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Trends in Family Effects on the Education of Black and White Brothers

Hsiang-Hui Daphne Kuo Robert M. Hauser

University of Wisconsin-Madison

Among Black and White men born from 1907 to 1946, family background accounts for at least half the variance in educational attainment. Parental schooling, father's occupational status, size of sibship, intact family, farm background, and southern birth account for no more than half this common family effect. Family background has smaller effects on the attainments of younger than of older brothers. The effects of both measured and unmeasured family background characteristics on the educational attainments of Black and White men have declined. Among Blacks, there has been a similar decline in the effects of all measured family background characteristics, while among Whites, the decline is limited to farm background, intact family, and southern birth. The global, secular decline in inequality of educational attainments cuts across all sources of variation in schooling-measured and unmeasured common family characteristics and unmeasured individual characteristics.

D ifferences in educational attainment between Blacks and Whites are well documented. Census data

show that the gap in years of schooling has narrowed since 1940, when more than 70 percent of young Black adults, but less than 40 percent of young White adults had completed no more than an elementary education (Hauser 1993a: 276-77). The high school completion rate of Blacks aged 25-29 is now around 75 percent while that of young Whites is higher than 85 percent (Hauser 1993a: 284). About half of white college en- trants, but only one-third of Blacks, complete 16 or more years of school (Hauser 1991:8). Despite Blacks' persis- tently lower levels of completed schooling, there is mounting evidence that, among persons of similar social background, Blacks complete more years of schooling than do Whites (Hauser 1993b; Hauser and Phang 1993). Thus, it is important to measure Black-White differentials in schooling when social background is controlled and to consider whether effects of social background differ between Whites and Blacks. In

this article, we use structural equation models of sibling resemblance to estimate racial differentials in the effect of family background on educational attainment and to examine changes in the effect across cohorts of White and Black men born from 1907 to 1946.

The family is one of the important agents in the transmission of educational inequality. Usually, one specifies social background using a vector of measured social and economic variables, such as parental schooling, occupational status, or income, along with race, farn- ily size and structure, and geographic location. However, these measured variables need not and, in fact, do not exhaust the effect of family background, which includes all other family, school, or neighborhood characteristics-social, economic, psychological, or biological- that siblings may share. In this study we use data on the educational attainments of brothers to estimate the effects of family background in this broader sense, as well as to improve estimates of the effects of measured background characteristics.

Education of Black and White Brothers

Several studies have examined Black- White differentials in the effect of social and economic background on educational attainment (Gottfredson 1981; Hauser 1993b; Hauser and Featherman 1976; Hauser and Phang 1993; Hout and Morgan 1975; Kerckhoff and Campbell 1977; Porter 1974; Portes and Wilson 1976; Wolfle 1985). However, all but one of these studies addressed only the effects of measured variables on educational attainment and did not consider the broader concept of family background. Hauser and Featherman is the lone exception. It was based on the same data as the present analysis, but its methods are long-since outdated.1 Using structural models of sibling resemblance, it is possible to estimate the total effect of family background on educational attainment and to compare the contribution of measured and unmeasured family factors to Black-White differentials in schooling.

In this article, we not only examine Black-White differentials in the effects of family background and of measured background variables, but address other issues, such as the confounded effects of family structure and race and changes in the effects of background on schooling over time. We pose the following questions: Do effects of family background on educational attainments of Blacks differ from those of Whites? Do between- and within-family components of education differ for Blacks and Whites? Do the effects of family background decrease over time? Have the effects of measured background variables, such as parental education and occupation, declined? Are there Black-White differentials in the changing effects of measured and unmeasured family background?

RACE, BACKGROUND, AND SCHOOLING

The global effect of family background on educational attainment has been

' For example, because they did not estimate the absolute variance coniponents between and within families, their correlational approach missed some of the major trends identified in the present analysis.

widely discussed and analyzed. Blau and Duncan (1967:316-28) initiated research on family background using the concept of family climate, which they specified by the educational attainment of the brother of a 1962 respondent to the survey on Occupational Changes in a Generation (OCG). They also suggested that the brother's educational attainment might better be used as a second indicator of a common family factor, but they did not incorporate a latent family factor into a model that also included measured socioeconomic origins. Not long after Blau and Duncan's initial work, Jencks et al. (1972) and Duncan, Feather- man, and Duncan (1972) each made pioneering efforts-by combining information from several bodies of data-to construct models that included measured and unmeasured family background variables, but they did not carry out separate analyses for Blacks and Whites.

There have been few fully elaborated efforts to model the status attainment of Blacks, either alone or by contrasting it to that of Whites. For example, a handful of studies has examined differences in the process of educational attainment between Blacks and Whites, using a social psychological model of attainment (Gottfredson 1981; Kerckhoff and Campbell 1977; Porter 1974; Portes and Wilson 1976; Wolfle 1985).

Hauser and Featherman (1976) estimated correlations between educational attainments of brothers in the 1973 OCG to measure the total effect of family background, that is, shared background. They found that correlations between the educational attainments of men and their oldest brothers ranged from 0.53 to 0.59 across cohorts of men born from 1907 to 1951 and that measured family origins explained more than half this correlati~n.~ With plausible corrections

Later, more sophisticated analyses of sibling resemblance, for example, those of Olneck (1976) and of Hauser and Sewell (1986), also found that about 60 percent of the common variance in the educational attainments of brothers is explained by measured social and economic background variables.

Kuo and Hauser

for error in the measurement of schooling, they estimated that the observed correlation between brothers exceeded 0.65. Thus, common family factors may account for almost two-thirds of the variance in completed schooling among American men. Although Hauser and Featherman (see also Featherman and Hauser 1978) reported separate regression analyses of measured social background and schooling among Blacks and Whites, they did not conduct separate analyses of sibling resemblance.

Despite the advantages of sibling- based research designs in analyses of the effects of family background on educational attainment, race was not a focus of interest in earlier studies of siblings, mainly because of the small size of most sibling samples and the small share of minority populations in those samples. With the development of national data resources for the general population, it is now possible to use sibling studies to examine Black-White differences in schooling and economic success. Unfor- tunately, Hauser and Featherman's (1976) analysis failed to take advantage of this possibility in the 1973 OCG sample, and one purpose of this article is to make up for that omission. Hsueh (1992) used one of the few sibling data sets with a large sample of Blacks, the National Longitu- dinal Survey of Youth (NLSY), to study the effect of family structure on schooling. He treated race as one of many exogenous variables and found that be- ing Black has a positive effect on education and a negative effect on ability. However, his study did not examine Black-White differentials in the effects of family background on educational attainment.

By estimating sibling resemblance models in several cohorts, we can also investigate change over time in the effect of families on educational attainment. That is, since school completion is, in principle, cumulative and irreversible, intercohort changes in schooling may be observed in cross-sectional age comparisons.3 This design has been used exten-

This is perhaps a less satisfying assumption than it used to be. We now know that

sively in European studies of siblings. For example, the effects of family background on the educational attainments and occupational statuses of all siblings from 1,653 West German families declined across cohorts born in the 1930s, 1940s, and 1950s (De Graaf and Huinink 1992); within like-sex and cross-sex sibling pairs, the effect of father's occupational status grew weaker, but that of parental education was stable over the cohorts. In addition, Dronkers (1993) found that the resemblance of Dutch siblings declined across fraternal birth cohorts born before 1930, from 1930 to 1940, and after 1940. However, Hungar- ian data on siblings from five birth cohorts (before 1932,1932 to 1944,1945 to 1952, 1953 to 1959, and after 1959) failed to show the trend of decreasing sibling resemblance that had been found in Germany and the Netherlands (Toka and Dronkers 1993).

In the United States, a few studies examined changes in the effects of measured or unmeasured family background on educational attainment, and most of them used data from the 1962 or 1973 OCG survey^.^ In their regression analyses, Hauser and Featherman (1976) found that both the variability in schooling attributable to differences in social background and the variability independent of social background had declined. They reported similar increases in educational equality among Blacks and Whites. Their comparison of correlations between educational attainments of brothers also suggested that the resemblance in schooling attributable to the effect of measured family background was declining over cohorts.

After controlling for heterogeneity due to unmeasured family factors, Mare

survey respondents tend increasingly to ex- aggerate their levels of completed schooling as they age and that people continue to go to school at older ages than in the past.

Mare (1980) analyzed trends in discrete transitions from one level of schooling to the next in the 1973 OCG data, and Hout, Raftery, and Bell (1993) extended those analyses using cumulative files from the General Social Survey through 1989. Both analyses were restricted to White men.


(1993) found that the effect of father's schooling on siblings' schooling was essentially invariant over cohorts of men in the 1973 OCG data.5 Moreover, the total effect of family background also varied little, and the effect of father's schooling contributed only modestly to the overall effect of common family factors on school continuation. These findings reinforce the need for sibling- resemblance studies. However, like Hauser and Featherman (1976), Mare did not report separate analyses of the Black population. Furthermore, he used only father's and son's schooling as instrumental variables and thus ignored other measured variables as sources of sibling resemblance.

To study Black-White differentials in effects of family background on educational attainment, one has to take account of family structure, as well as the social and economic characteristics of parents. Single-parent families have socioeconomic consequences that are confounded with race. Since the 1960% the trends in marital status, fertility, marital stability, and child rearing have been similar among Blacks and Whites. How- ever, Black women have had a higher total fertility rate than have White women because of the higher proportion of births to unmarried mothers. Among Black women, marital fertility has been as low as that of White women since 1980. Thus, the number both of Black children living in female-headed families and of Black female-headed families have increased faster than among Whites (Garfinkel and McLanahan 1986; Jaynes and Williams 1989).

The effect of family structure on educational attainment has been studied extensively. Duncan and Duncan (1969), for example, found that occupational success was greater among men raised in two-parent families than among those

Mare's analysis was based on a latent class model of school transitions, in which the functional form is log-linear. For this reason, his findings about increasing or decreasing effects are not comparable to those of Hauser and Featherman (1976) or to those in our analysis, where educational attainment is treated as a quantitative variate.

raised in single-parent families and that the effect came from their higher educational attainment, Hauser and Feather- man (1976) noted that the elimination of single-parent families would have reduced the difference in educational attainments between Black and White men by 27.2 percent in the birth cohort of 1937-46 and by 39.4 percent in the birth cohort of 1947-51. In cohorts born in the late 1950s to early 1960s (from the NLSY), after family structure was controlled, Blacks had more education than Whites but lower ability (Hsueh 1992). In the High School and Beyond panel, large effects of single-parent and steppar- ent families on an array of educational outcomes, including high school dropout, were not explained by differences in parental involvement and behavior (As- tone and McLanahan 1991). Large effects of nonintact families on high school dropout persisted in the 1970s and 1980% even when a large set of measured household and family characteristics were controlled. The effects of nonintact families have been consistently larger among Whites than among Blacks (Hauser and Phang 1993).

Size of sibship and birth order are two other aspects of family structure that often appear in analyses of educational attainment. The negative effect of larger numbers of siblings on the educational attainment of both Blacks and Whites is well established (Blake 1989; Hauser and Featherman 1976), and it enters our analysis both as an exogenous variable and as a factor that influences the research design through the number of brothers of each OCG respondent.

Research on birth order has focused almost exclusively on differences in levels of ability or of completed schooling (Lindert 1977; Zajonc 1976; Zajonc and Markus 1975), but most studies have found little, if any, main effect of birth order on educational attainment (Hauser and Sewell 1985; Olneck and Bills 1979; Retherford and Sewell 1991; Steelman 1985, 1986). Because brothers' educational attainments are sometimes distin- guished by birth order in the 1973 OCG data, birth order enters our analysis as a factor that may moderate the influence of social and economic background; that

Kuo and Hauser

is, to a limited degree, we can examine whether effects of family background are greater or less among older or younger brothers. It is difficult to interpret such effects because they may reflect histori- cal change, as well as intrafamily pro- cesses. In full sibship data from the Wisconsin Longitudinal Study, no effects of relative birth order within gender on the educational attainment of brothers and sisters were found when the size and gender composition of sibships were controlled (Kuo and Hauser in press). However, Hauser and Wong (1989) found that the effects of family background were larger among older than among younger brothers in two Nebraska samples (Benin and Johnson 1984), in Olneck's (1976) Kalamazoo sample, and in Dronkers's (1988) sample of Dutch siblings.

DATA

The data used in this study are from the 1973 OCG, a supplement to the March Current Population Survey (CPS), which covered a national sample of men aged 20 to 65 (for details of the OCG, see Featherman and Hauser 1978). Although the OCG data are more than 20 years old, they are the only large American sample in which it is possible to compare the educational attainments of men and their brothers among Blacks and Whites and across time. Thus, these data remain a valuable resource of more than historic interest.

The OCG supplement ascertained the educational attainment of a man's oldest and youngest brothers who lived to age 25. The questions used to assess the educational attainment of the brother or brothers were as follows:

5c. How many brothers did you have? 5d. How many of these brothers were

older than you (born earlier)? 6a. Did any of your brothers live to age 25? 6b. Please indicate the highest grade of

school completed by the OLDEST of your brothers who lived to age 25.

6c. Please indicate the highest grade of school completed by the YOUNGEST of your brothers who lived to age 25.

The data also include information on educational attainments of respondents

and social and economic background, such as parental education and occupation, farm background, family size, and family structure. Unfortunately, the 1973 OCG did not include the measured ability of the respondent and his brothers, and it covered only male respondents and their brothers.

We determined the relative birth order of brothers from the information about the number of older brothers, but we do not know the actual ages of the brothers. After we eliminate the respondents younger than 25 and older than 64, there remain 9,184 respondents with two brothers reported and 5,527 respondents with one brother reported. In the current study, we divide the data into two subsamples: pairs and triads of broth- e r ~ . ~ Within the triads, we can address the issue of relative birth order by comparing outcomes between the "oldest" and "youngest" brothers, but even the relative birth order remains ambigu- ous within many of the pairs of brothers. Also, respondents in the triads typically, though not necessarily, come from larger families than do those with only one brother.

It is not straightforward to specify a design for the analysis of the OCG data on brothers. Both birth order and family structure, each of which is of substantive interest, also affect the observation of exogenous and endogenous variables. A key problem in identifying relative birth order is that both an "oldest" and a "youngest" brother might be older than the respondent. Owing to the format of the questions about siblings, among the valid cases, we could determine the relative birth order only among 84.4 percent of the pairs of White brothers and 79.3 percent of the pairs of Black brothers, that is, pairs that included only an "oldest" or only a "youngest" brother.'

'Hereafter, we use "size of sibship" to refer to the number of brothers for whom we observed educational attainment, including the respondent. That is, we do not use it to refer to the actual number of brothers or sisters in a respondent's family of orienta- tion.

Valid cases include respondents who had siblings living up to 25, reported the educa-


Relative birth order was identifiable among all three members of 56.2 percent of the triads of White (non-Hispanic) brothers and 47.2 percent of the triads of Black brothers. Although the elimination of pairs or triads for which relative birth order could not be determined might not affect analyses of White brothers because the sample is large, the elimination of the indeterminate cases in the Black sample is more serious because the sample is much smaller. More important, the proportion of indeterminate birth orders is different among pairs and triads. Thus, we were con- cerned that an effort to focus the analysis on cases for which relative birth order is known could reduce statistical power and lead to bias in our findings.

Having rejected an effort to array the OCG data on brothers in terms of relative birth order, we identified educational outcomes in relation to the respondent, that is, following the references to the "oldest" and "youngest" brothers in the questions. The disadvantage of arranging the data this way is that we could not study the effect of birth order except in certain family configurations. When the relative birth order was clear, namely, in the distinction between the "oldest" and "youngest" brothers in triads, we at- tempted to determine whether birth order moderates the effect of family background on education. However, it should be kept in mind that these cases were selected in a complex way, namely, that they represent families with at least three male offspring who survived to age 25.

The questions about the education and occupation of the household head complicate the analyses of effects of family structure on education and, possibly, affect the definition of socioeconomic background. The questions asked were these:

Q8a. Were you living with both your parents most of the time up to age 16?

- - -

tion of at least one sibling, and reported all family background variables. A tabulation of the number of cases with identifiable birth order is available from the authors.

Q8b. If "No" above, who was the head of your family?

Ql l . Now we would like to find out what kind of work your father did when you were about 16 years old. If you were not living with your father, please answer for the person marked in question 8b.

Qlla. In what kind of business or indus- try did he work? . . .

412. What is the highest grade of school your father (or the person marked in 8b) completed? If you are not sure, please make a guess.

Q13. What is the highest grade of school your mother completed? If you are not sure, please make a guess.

In short, the report of the education and occupation of the head of the household might refer to a father, a mother, or someone else. Thus, for example, if the household head was the mother, we would have two reports of the mother's education, one as the household head (Question 12) and the other as the mother (Question 13).

Among nonintact families, mothers were the largest share of household heads, fathers were a smaller share, and the remainder were other relatives. "Other male relative," may have included grandfathers, stepfathers, or yet other relatives. We found that most respondents reported the same household head's education and mother's education, regardless of their family structure and the identity of the household head; however, some respondents from mother-headed, nonintact families reported the household head's and mother's education differently. It is thus difficult to figure out whose education and occupation the respondents from nonintact families reported.8 Therefore, we decided to use the term "household head," rather than "father," throughout our analysis, and hence the reports of the household head's education and occupation con- sist of the mother's, father's, male relative's, and female relative's educa-

We also suspect that some respondents probably reported their mothers' education by borrowing their fathers' education, since the question encouraged them to "make a guess."

Kuo and Hauser

tion and occupation-a practice that is comparable to the one used in most previous studies of the OCG data. However, the use of data for different individuals could influence the effect of socioeconomic background variables on the education of offspring in intact versus nonintact families.

If we had analyzed the data sepa- rately for each combination of family structure, number of brothers, race, and cohort, the design would have been excessively complicated and unwieldy and the number of cases in each of the cells of the design could have been quite small. Since the sample of respondents from nonintact families is small, considering our interest in disaggrega- tion by cohort (227 Blacks and 1,169 Whites), we sought to simplify the design by collapsing across family types. Thus, before turning to our analysis of intercohort change among Blacks and Whites, we first examine the effect of family structure on the process of educational attainment by comparing the effect of father's education and occupation in intact families with that of the household head's education and occupation in nonintact families. For this analysis, we use all the cases of sibling pairs (from respondents with one or two or more brothers) in which the relative birth order is identified. Thus, we also estimate the effect of relative birth order, although we do not pursue it later in the analysis.

METHODS

We use the multiple indicator, multiple cause (MIMIC) model as an ana- lytic framework for our analysis (Hauser and Goldberger 1971; Hauser and Wong 1989; Joreskog and Goldberger 1975). The MIMIC model specifies that exogenous social background characteristics affect the educational attainments of siblings through a single, unmeasured common family factor, which accounts for the resemblance in schooling among them. Although this model has only one type of outcome-educational attainment-it still provides insights about the total effect of family background on

educational attainment, the relationship of each observed variable with the measured family factor, and the relative importance of shared and nonshared sources of variation in attainment.

Figure 1 displays the path diagram of the MIMIC model used in earlier sibling resemblance models (Hauser and Wong 1989). The general model is

where q is the endogenous latent variable; 6 is a vector of exogenous latent variables with variance-covariance matrix @; { is a vector of disturbances, independent of q and I;, with variance covariance matrix 9; r is a parameter matrix of effects of 6 on q; and B is a parameter matrix of effects of q on q. In the model of Figure 1, there is only one q, which carries the effect of family background variables to the educational attainment of offspring; thus B is non- existent. However, in a later generaliza- tion of the model, we use B to express effects of family background that differ across cohorts. In general, the measurement models for the latent variables are

where X and Y are vectors of observ- able variables (indicators of 6 and q, respectively); Ax and Ay are parameter matrices giving the effects of I; and q on X and Y, respectively; and 0"nd 0' are the covariances of 8 and E,

respectively. In our specification, Equa- tion 2 is not shown in the diagram because we assume that each exogenous variable has only one indicator and that all elements in Ax are equal to one and 0"s equal to zero; that is, all I;s are perfectly measured by correspond- ing Xs. Equations 3 and 1 in matrix form for sibling pairs are

and


Intact Family

Xi = Father's Education Yl = Education 1 -&,

X2 = Mother's Education

X3 = Father's Occ Status

X4 = Fann Origin

XS = Number of Siblings

Xs = Southern Origin Y2 = Education 2 -E2

Non-Intact Family

x 1 = Head's Education

\ Yl = Education 1 -&,

Xz = Mother's Education

// X3 = Head's Occ Status

X4 = Fann Origin

X s = Number of Siblings y,,,

XB = Southern Origin Y2 = Education 2 -E2

Figure 1. MIMIC Model of Sibling Resemblance

where xkl, . . ., xks are the exogenous variables; ykl and yk2 are educational attainments of older and younger brothers; and the index k indicates groups, such as family type, race, or cohorts. In Equation 4, we specify Akll = 1 as a normalizing constraint, so Ah, becomes a proportional rescaling of the ykli to effects in the metric of y,.

The effects of family background variables on the educational attainment of each brother in the constrained reduced form are the products of the correspond- ing ys and Ays. By testing hypotheses of equality between AYs within each cohort, family structure, or sibship, we compare the regressions of sibling's education on the family background variables. By testing hypotheses on the equality of A, or yk between (or among) groups (de-

fined by family structure, cohort, or race), we compare the effects of family background on education. When equality constraints hold among parameters, either within or between groups, the sampling variability of the parameter estimates is reduced, relative to those in unconstrained regressions.

As we stated before, one advantage of the sibling resemblance model is that we can study the variation of the unmeasured family component of educational attainment, which does not appear in an analysis of unrelated individuals. In Figure 1, 6 stands for the unmeasured but common family components or factors in the education of brothers, that is, the covariation of education between brothers that cannot be explained by the measured variables of family background. It can also be described as the unmeasured between-family (shared) variation. The ES stand for the variation of a brother's education that cannot be explained by the common family factor

Kuo and Hauser

(q); it is also known as the within-family (nonshared) variation.

FAMILY STRUCTURE AND BIRTH ORDER

We divide all sibling pairs in which relative birth order was identified into groups defined by family structure within each race, that is, White intact family, White nonintact family, Black intact family, and Black nonintact family. The endogenous variables are educational attainments of siblings, arrayed by their relative birth order; the exogenous variables are household head's education, household head's occupation, mother's education, farm background, number of siblings, and southern origin.

In the baseline model, we constrain all parameters except the variance-covariance matrix of the exogenous variables to be equal between groups (family types) for Whites and for Blackseg That is, the process of educational attainment, including the effects of family background on educational attainment of siblings, within-family variances, and between-family variances, do not vary by family structure within race. As Table 1 shows, the model with cross-group constraints fits fair1 well. For Blacks, the x 2 statistic is L' = 33.64 with 20 degrees of freedom (df); for Whites, L' = 112.49 with 20 df. The bic statistics are - 108.06 for Blacks and - 75.55 for Whites.10 Relative to the saturated model,

Also, none of the models estimated here or later in this article constrain the mean structure of the variables. That is, mean levels of social background and of educational attainment vary freely across groups.

lo In addition to X2 statistics, we use the bic statistic to evaluate goodness of fit. The bic statistic is based on Bayesian theory for a posteriori tests: bic = L2 - df x ln(N), where L2 is the likelihood-ratio x2 statistic, df is the degrees of freedom under the tested model or contrast, and N is the sample size. A satisfactory fit is indicated by a negative value of bic, and models with lower bic statistics are preferred (Raftery 1986, 1993, in press). We use bic as a secondary criterion of a model's fit when L2 is nominally statistically significant to avoid rejecting null in favor of trivial alternative hypotheses.

in which the bic statistic is 0 , the baseline model is acceptable.

Next, we test the overall hypothesis that the process of educational attainment in the intact family is different from that in the nonintact family. That is, we lift all across-group constraints on the parameters of r, AY, OE, and 9. The X2 statistics of this family-structure hypothesis are L2 = 28.38 with 1 0 df for Blacks and 57.52 with 1 0 df for Whites; the bic statistics are - 42.47 and - 52.21, respectively. That is, although these models are acceptable (using bic as the criterion), they are less attractive than the constrained models because bic is less negative. Thus, we choose not to reject the hypothesis that the process of educational attainment is invariant with respect to family structure." Consistent with these test statistics, the pooled coefficients in the baseline model are similar to those of intact families and of nonintact families in the second model. These findings lead us to combine the two family types in our analyses of intercohort change.

As was stated earlier, the lack of data on birth order in almost one-third of the sample unevenly reduces the sample size between racial groups and between sibship groups. Given that the observations of brothers' schooling were not arranged by relative birth order in the analysis of intercohort change, we use this subsample to test the interaction of relative birth order with family effects on schooling. The null hypothesis is that the effects of family background variables on older siblings do not differ from those on younger siblings. Literally, we impose the equality constraint, Akll = Akzl = 1. Under the constrained model, the X2 statistics increase by L~ = 49.42 with 1 df for Blacks and by L' = 292.70 with 1 df for Whites, for which the bic statistics are 42.33 and 283.30. Thus, we reject the hypothesis that family background affects older and younger brothers equally. The effect of family back-

'' Again, recall that our tests pertain to the effects of measured and unmeasured family background characteristics, not to mean differences in schooling between the children of intact and nonintact families.

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ground on the younger brother is only 69 percent of that on the older brother among Blacks and 77 percent among Whites.

FAMILY BACKGROUND AND INTERCOHORT CHANGES

In the remainder of the analysis, we arrange the samples of Blacks and Whites into eight groups each by the birth cohort of the respondent and the number of brothers for whom educational attainment was reported: size 3, age 25-34; size 3, age 3 5 4 4 ; size 3, age 45-54; size 3, age 55-64; size 2, age 25-34; size 2, age 35-44; size 2, age 45-54; and size 2, age 55-64.12 Figure 2 displays the data arrangement and the schematic framework of the model. The order of endogenous variables lists the respondent Cy,) first, followed by the oldest brother 01,) and the youngest brother Cy,). Note that the "oldest" may be either the oldest brother in the sibship or the brother born next after the respondent, and the "youngest" may be either the youngest brother in the sibship or the brother born just before the respondent. Thus, the relationship between the oldest and youngest brothers is always in the right relative birth order, but the relationship between the age of the respondent and either the oldest or the youngest brother is unclear.

Some Notes on Method

We used methods for the estimation of structural equation models with missing data that were introduced in Allison (1987) and Allison and Hauser (1991) to combine data for pairs and triads of brothers. By combining equality constraints across subsamples with the in- troduction of null parameters for missing variables, we could estimate multiple group models simultaneously for groups defined by the presence or absence of certain 0bservations.~3 That is, we intro-

l 2 Descriptive statistics and variance- covariance matrices for the subsamples are available from the authors.

13 This treatment of missing moments is required within LISREL; other computer

duced pseudo-values for the moments of missing variables and specified innocu- ous fixed values for their factor loadings and variances.

To elaborate, Equation 4 for pairs of brother is reparameterized as

Ykl hkll is] = [&I 1 q 4 +[S 1 (6)

where k indicates the groups (sibship size and cohort) and fork = 5, . . ., 8 (the groups of brother pairs), ~ $ 3 1 = 0 and 8'*k31 = 1. The values of 8\, and hi3 are arbitrary because the endogenous variable Cy,,) has not been observed and the fixed values do not affect the fit of the model or other parameter estimates. We also added a second latent variable (q) to the model of Figure 1 to specify intercohort change in the global effect of family background on education. The structural model is

where, unlike Equation 5, there is no disturbance for qkl in Equation 7. In Equation 8, when r and AY are invariant across cohorts, the specification that P121 = 1 and Pk2 , # 1 for k = 2, . . ., 8 permits global intercohort changes in the effect of family background; otherwise, P I , , = Pk21 = 1 for all k. It is actually a matter of indifference whether we permit the disturbance to appear in Equation 7 or in Equation 8, but only one such common variance term is identified.

Because the sample was selected from the general population, the age of the respondents' siblings ranged widely. That is, the cohorts were based on the OCG respondents, but their brothers may have belonged to other cohorts. The age spread could produce larger variations in education among brothers in triads than in pairs. We found that the social and economic characteristics of pairs

programs, for example, EQS, do not require this kind of model specification to estimate a model with missing variables.

Education of Black and White Brothers 147

differed from those of triads, among both Blacks and Whites. In general, brothers appearing in pairs had more favorable social background and completed more schooling than did brothers appearing in triads. That is, brothers in pairs had parents with more schooling and household heads with higher-status occupa- tions; were less likely to be of farm origin; and, of course, came from smaller sibships. The one interesting exception to this pattern is that there was almost no difference between the pairs and triads in the chance of having been raised in a nonintact family (1 = intact, 2 = nonintact), presumably because the effect of family dissolution on the number of births offset that of social depriva- tion on family dissolution.

To comprehend the variations among brothers and to ensure the consistency of analyses of intercohort change between the pairs and triads, we first examine hypotheses related to the number of brothers that were observed. Figure 2 presents the comparison of parameters in the groups shown at the left-hand side of the page (pairs) with those in the groups shown at the right-hand side of

the page (triads), assuming for the mo- ment that there is no variation in parameters across cohorts. Our objective is to select a model with satisfactory specifications within cohorts as a baseline model for the analysis of intercohort changes. Table 2 shows the goodness of fit and the sequence of model selection for Whites and Blacks. Hypotheses about restrictions within cohorts are reported in the first panel. Hypotheses about intercohort change in parameters are reported in the second panel. The selection of our preferred final model is reported in the third panel. Tables 3 and 4 report estimates of parameters of the preferred model. Finally, we decomposed the components of variance for each brother into measured between- family variance, unmeasured between- family variance, and within-family variance, and these estimates are illustrated for the several cohorts of respondents in Table 5.

Within-cohort Restrictions

The baseline model permits no intercohort variation in parameters, but places

Cohort 1

YI = REd +&I

x, = lntact x, = NSib x7 =South Y3 +E3 x7=South 6 2 y3 = S2Ed +&3

Cohort 2

Cohort 3

x1 = HHed

x, = Med x3 = Med X4 = Farm x, = lntact

x, = NSib x7 =South Y3 +&3 X7=South

Figure 2. OCG Sibling Model: Pairs and Triads of Brothers in Four Cohorts

Table 2. Model Selection, OCG Respondents and Their Brothers

White (n = 20,609) Black (n = 1,997)

Model or Hypothesis Lz df bic Lz df bic

Specific Hypotheses about Brother Pairs vs. Triads 0. Baseline model 1163.65 158 -405.84 430.68 158 - 770.03 1. 0 + equality constraints on AYkl, 1165.18 159 -414.24 430.70 159 - 777.60 2. 1 + equality constraints on 6;,, 1220.81 160 - 369.80 431.27 160 - 784.63 3. 1 + equality constraints on +,,, 1168.19 160 -421.17 - - -

2 + equality constraints on +,,, - - - 432.52 161 - 790.98 4. 3 + equality constraints on AYk,, 1203.62 161 - 395.67 440.65 162 - 790.45 5. 3 + equality constraints on 6'k,2 1171.09 161 -428.20 432.62 162 - 798.48

Specific Hypotheses about Cohort Effects A. 5 -equality constraints on hYk,, in triads 1150.56 158 -418.93 424.48 159 - 783.82 B. 5 -equality constraints on Ayk2, in pairs 1144.35 158 -425.14 421.02 159 - 787.28 C. 5 -equality constraints on AYk3, in triads 1150.53 158 -418.96 419.50 159 - 788.80 D. 5 -equality constraints on 6',,, - - - 354.12 159 - 854.18

5 -equality constraints on Wkll in triads 1112.83 158 -456.66 - - - E. 5 -equality constraints on -aSkll in pairs 1110.84 158 -458.65 - - - F. 5 -equality constraints on 6',,, 1138.50 158 -430.99 389.87 159 - 818.43 G. 5 -equality constraints on 1108.40 158 -461.09 392.34 159 -815.96 H. 5 -equality constraints on gk,, 968.80 158 - 600.69 391.33 159 - 816.97 I. 5 -equality constraints on $,, 1134.24 158 -435.25 389.11 159 -819.19 J. 5 -equality constraints on r 955.23 140 - 435.46 374.10 141 - 697.42

Final Model Selection Al. D+F+G+H - - - 280.44 150 - 859.47

D+E+F+G+H 829.85 146 - 620.44 - - - A2. A l + I 794.51 143 -625.98 229.34 147 -887.77 A3. A l+J 595.42 125 -646.27 213.45 129 -766.87 A4. A1 -constraints on effects of farm background, E:

intact family, and southern origin 656.99 137 - 703.90 261.00 141 -810.52 O A5. A4+I 646.88 134 220.90 138 -827.82 - 684.21

a

F E 8

Kuo and Hauser

--- m c o m 0 ) b O *"I '9 --- NOCO WaNhl ?=!N b * b --- o ID m I n m b 4 m " I --- * * a * m N '-!'-!4 m * I n --- (0 Q, hl a c o r n NNC? --- In CO PI aa CO aa '-! m * m m m

5 A 0

+

--- b a a * m * m 9 9 9 --- Q, + m ~ a a m 5 2 2

- - --- 2 o c o + m + b O h l '-! - - - - - - - - '9 '9 '9"

* - * - --- (0 - - " " ' - - -

Q, O N * Q , " b O b Q ,

'9 + cl " " I N In I D I n b

Education of Black and White Brothers 151

Table 5. Components of Variance in Preferred Models: White and Black OCG Respondents, bv Number of Brothers and Birth Cohort

Percentage

Population and Between-Family within- Within- Birth Cohort Measured Unmeasured Familv Total Measured Unmeasured Familv

White Men Three-brother sibship 193746 2.643 2.084 5.201 9.928 26.62 20.99 52.39 1927-36 2.937 3.049 5.844 11.830 24.83 25.77 49.40 1917-26 3.252 3.299 6.382 12.933 25.14 25.51 49.35 1907-16 3.203 3.844 6.924 13.971 22.93 27.51 49.56

Two-brother sibship 1937-46 2.356 2.084 4.273 8.713 27.04 23.92 49.04 1927-36 2.943 3.049 4.971 10.963 26.84 27.81 45.34 1917-26 3.400 3.299 5.378 12.077 28.15 27.32 44.53 1907-16 3.377 3.844 5.669 12.890 26.20 29.82 43.98

Black Men Three-brother sibship 193746 1.290 2.951 3.185 7.426 17.37 39.74 42.89 1927-36 3.239 3.852 5.144 12.235 26.47 31.48 42.04 1917-26 4.707 4.363 7.182 16.252 28.96 26.85 44.19 1907-16 4.257 5.179 6.706 16.142 26.37 32.08 41.54

Two-brother sibship 1937-46 1.612 2.951 3.185 7.748 20.81 38.09 41.11 1927-36 4.677 3.852 5.144 13.673 34.21 28.17 37.62 1917-26 6.623 4.363 7.182 18.168 36.45 24.01 39.53 1907-16 3.309 5.179 6.706 15.194 21.78 34.09 44.14

only two sets of equality constraints on parameters of pairs and triads within the same cohort. Specifically, within pairs and within triads, all parameters are the same in each cohort, but the effects of exogenous variables on the common family factor (r) and the global effect of the common family factor on education (P,, = 1) are constrained to be equal, regardless of the number of brothers and of cohort. Furthermore, the loadings (Ay,,,) of the respondents' education on the common family factor in triads (but not in pairs) are normalized to unity. Thus, in this specification, a significant departure of AYHz from unity among the brother pairs would suggest that there is an overall difference in the effect of measured social background on the educational attainment of respondents who appeared in pairs versus those who appeared in triads. The likelihood-ratio test statistics are L' = 1163.65 for Whites and L2 = 430.68 for Blacks, each with 158 df; the bic statistics are - 405.84 and -770.03, respectively. Thus, although we would nominally reject this baseline model, the bic statistics suggest that the fit is not bad, given the size of the samples. The question remains

whether a significantly better fit can be achieved without compromising the objective of parsimonious intercohort comparison.

We next test hypotheses about the relationship between the family factor and the respondents' education. Al- though the baseline model states that the number of brothers observed affects the dependence of schooling on the family factor, assuming that the effects of specific variables on the common family factor do not vary, the next hypothesis, line 1 in Table 2, states that the effects of family background on the schooling of respondents do not vary. This model fits negligibly worse than the baseline model; with an increase of 1 df, the contrast in L' is equal only to 1.53 for Whites and 0.02 for Blacks.

Next, conditioning on Model 1, we add constraints of equality in the within- family variances of respondents' schooling, O',,, = O',,,, where p and t pertain to pairs and triads. Model 2 says that, with equal effects of the family factor on the education of respondents between pairs and triads of brothers, the within- family variances of respondents are also invariant between the pairs and triads.

Kuo and Hauser

The aim of both Models 1 and 2 is to test the homogeneity of the respondents' education between pairs and triads of brothers. Model 2 fits worse for Whites than does Model 1: L2 = 1220.81 with 160 df and bic = -369.80. However, Model 2 fits better for Blacks: L2 = 431.27 with 160 df and bic = -784.63. Thus, the within-family variances of respondents differ between pairs and triads among Whites, but not among Blacks.

Model 3 specifies that the unmeasured between-family variances do not vary between pairs and triads of brothers. The constraint fits the data well; with an increase of 1 df, L' increases only by 3.01 for Whites and by 1.25 for Blacks. The hypothesis cannot be rejected. Up to now, we can claim that the data are fairly homogeneous between pairs and triads of brothers with the exception of the within-family variances of White respondents. Next, Models 4 and 5 test hypotheses about the education of oldest brothers. Conditioning on Model 3, Model 4 constrains the loadings of educational attainment of oldest brothers to be the same in pairs and triads, that is, Ayp,, = Ay,,,. Similarly, Model 5 conditions on Model 3, but adds the constraint that within-family variances of oldest brothers are equal in pairs and triads, that is, 0',,, = 0',,,. Briefly, we reject Model 4 but accept Model 5. That is, the loadings of the family factor for the oldest brothers are significantly different between pairs and triads of brothers for both Blacks and Whites, while the within- family variances are similar. It is under- standable that the effects on education of the oldest brother would differ between pairs and triads. The oldest in a triad is more likely to be older than the respondent than the oldest in a pair, given that the former come from larger families, and the spacing between the respondents and the oldest is probably larger in triads than in pairs.

Thus, Model 5 is our preferred model at this stage of the analysis. We find that the data from pairs and triads of brothers are homogeneous, except that the within- family variances of White respondents differ and the family background effects on the oldest brothers are significantly

different among both Blacks and Whites. In the next stage of the analysis, we use Model 5 as the baseline model to analyze intercohort changes.

Intercohort Changes

We first test hypotheses about the loadings of the education of each brother on the common family factor across cohorts. Then, we test hypotheses about the within-family variances of each brother; about the between-family variances; about the global effect of family background on education; and, finally, about the effects of specific family background variables. Throughout these tests, we maintain the specifications of Model 5 within cohorts. For example, when the intercohort constraints on the unmeasured between-family variances (JI,,) are released, the equality constraints on the variances between the brother pairs and triads of the same cohort are maintained because, in the previous stage of the analysis, we accepted the model with that equality constraint. Unlike the previous stage of the analysis, we do not nest the tests of these hypotheses. In each test, we relax one of the restrictions on intercohort change that is imposed by Model 5. We want to select a better model than Model 5 as the new baseline to answer questions related to intercohort change, and these tests help us choose among hypotheses of substantive interest.

Models A through C in the second panel of Table 2 test for intercohort change of the common family factor on the education of each brother (A"). Mod- els without those intercohort equality constraints fit negligibly better than Model 5: With 3 df less, L2 only decreases by 7.14, 11.60, and 13.12 for Blacks and by 20.53, 26.74, and 20.56 for Whites. Thus, bic increases to - 783.82, -787.28, and -788.80 among Blacks and to -418.93, -425.14, and -418.96 among Whites. That is, although the relative effects of family background on the education of each sibling relative to those among respondents differ between pairs and triads of brothers, they do not change across cohorts.

Models D through G test hypotheses


about change in within-family variances across cohorts for respondents and their brothers. Models without intercohort equality constraints on the within- family variances yield an improved fit: With 3 df less, L' decreases by 78.50, 42.75, and 40.28 among Blacks and by 58.26, 60.25, 32.59, and 62.69 among Whites. The bic statistics improve to - 854.18, - 818.43, and - 815.96 among Blacks and to -456.66, -458.65, - 430.99, and - 461.09 among Whites.14 The improved fit of Model F for Whites is marginal (compared to Model 5), but since we rejected the hypothesis of constant within-family variances in all other cases, we decided to do so here as well.

Substantively, Models H, I, and J are more interesting. They test hypotheses directly related to family background or the common family factor. The hypothesis in Model H is that the variance in the unmeasured common family factor (JI ,, = J l n z ) changes across cohorts. ~ o d e f H improves the fit: The contrast of L2 to Model 5 is 41.29 for Blacks and 202.29 for Whites, each with 3 df. The bic statistics are - 816.97 and - 600.69. Model I tests the hypothesis that the global effect of the common factor on educational attainment changes across cohorts, with unmeasured between- family and within-family variances un- changed. That is, we permit P ,, = P,, to vary across cohorts. Model ffits better than Model 5 among Blacks, when bic is used as a criterion. L2 = 389.11 with 159 df and bic = - 819.19. However, it does not improve the fit decisively for Whites relative to Model 5: L' = 1134.24 with 158 dfand bic = -435.25. That is, there is evidence of a global change in the effect of measured family background among Blacks, but not among Whites. Finally, Model J says that the specific -effect of each family background variable changes over cohorts. It does not improve the fit substantially among

l4 We estimated one more model for Whites than for Blacks because the within-family variances for White respondents were significantly different between pairs and triads of brothers, while those for Black respondents were not significantly different.

Blacks or among Whites: L2 = 374.10 for Blacks with 141 df, and L' = 955.23 for Whites with 140 d j the bic statistics are - 697.42 and - 435.46. Thus, although a single parameter for change in the effect of family background variables has some merit (among Blacks, at least), intercohort changes are not large enough to appear significant when all the coefficients of background variables are per- mitted to vary freely.

We report the final stage of model selection in the third panel of Table 2. The new baseline is Model 5 with constraints relaxed as in Models D, E (for Blacks only), F, G, and H; that is, we maintain intercohort equality constraints on the loadings of the education of each brother on the common family factor (Xy) and on the effects of measured family background (r and B), and we release the intercohort constraints on all variances (q and 0'). The new baseline model states that the effects of the common family factor on the education of the respondents and their brothers and the effects of measured social background on schooling are constant across cohorts, while the unmeasured variance components, within- or between-families, vary across cohorts. Model A1 fits very well in comparison with Model 5: L2 = 280.44 with 150 df for Blacks and L2 = 829.85 with 146 df for Whites. The bic statistics are -859.47 and -620.44. Conditional on this new baseline model, we test Hypotheses I and J again. As before, Hypothesis I improves the fit for Blacks only, and Hypothesis J cannot be accepted either for Blacks or Whites. That is, the global effects of family background change over cohorts only for Blacks. However, for Whites, the fit of Hypothesis J relative to Model A1 is better than relative to Model 5. It is possible that the effects of some, but not all exogenous variables change over time among Whites.

In the left panel of Table 3, we report the parameter estimates of Model A3 for White brothers. While the effects of the household head's and mother's education do not change over cohorts, the effects of the household head's occupation are smaller in the first two cohorts than in the last two cohorts. The nega-

Kuo and Hauser

tive effects of the total number of siblings increase slightly over cohorts. How- ever, the negative effects of farm background, nonintact family, and southern origin decline regularly across cohorts. In Model A4, we test the hypothesis of intercohort variation in the effects of just these three family background variables: farm background, nonintact family, and southern origin. When con- trasted with Model Al, Model A4 does not improve the fit significantly for Black brothers, but it does improve the fit significantly for White brothers. That is, the effects of family background do not change globally over cohorts for Whites, but there is a significant intercohort change in the effects of farm background, nonintact family, and southern origin.

Model A4 is the preferred final model for Whites, and Model A2 is the preferred final model for Blacks. For both Blacks and Whites, the variances of unmeasured factors, within families and between families, change over cohorts. Among Whites, the effects of the common family factor on the education of each brother vary within each sibship. While the effects of socioeconomic background, such as the household head's occupation and education and the mother's education, do not vary over cohorts, the effects of farm background, southern origin, and family structure do. Among Blacks, the effect of each measured family background variable on the education of brothers changes consistently across cohorts.

Estimates of Parameters

The parameter estimates of our preferred final model are reported in the right-hand panels of Tables 3 and 4. They show that for White men and their brothers, the negative effects of farm, nonintact family, and southern origin declined over the cohorts. Thus, the disadvantage of growing up on a farm, living in a nonintact family, or growing up in the South was greater for White men in the first two cohorts than for those born later, and growing up on a farm had almost no effect on the most recent cohort of Whites. For Black men

and their brothers, with the declining importance of measured family background variables, the contrast appears primarily to lie between the most recent cohort-born after the middle of the Great Depression-and the other three cohorts.

We cannot compare the coefficients of the socioeconomic background of Blacks directly with those of Whites, because the global effect of family background is constant for Whites, but varies among Blacks. However, in inspecting the coefficients reported for Model A3, we do not see large differences between them. Of the other family background variables, first, the disadvantage of growing up on a farm or in the South is larger for Black men than for White men. The differences between Black and White men increased over time even though the global effect of family background on education for Black men was declining. Second, living in a nonintact family was more disadvantageous for White men than for Black men in every cohort; thus, although nonintact families are an obsta- cle to school completion, the findings appear to offer partial support for claims of resilience among Black nonintact families (see also Hauser and Phang 1993). Finally, the negative effect of the number of siblings is significantly larger among White men than among Black men.

Comparing our findings to those of Hauser and Featherman (1976, Table 11), we see that the coefficients of Model A3 are slightly different. Generally, our estimates of effects on the education of respondents are lower than theirs, except those of the household head's occupation and farm background. A distinct difference between our analyses and theirs occurs in the effect of southern origin among Black men. In Hauser and Featherman's study, the effects of southern origin on education declined rapidly for Black men, from -1.783 to - .163; in this study, they declined only from - .878 to - .443 in Model A3 and from - ,585 to - ,362 in the preferred final model. Our samples, as well as our models, differ from those of Hauser and Featherman. Our model adds mother's education, excludes cases in which moth-


er's education is missing, and does not include respondents who were only brothers.

Variance Components

Declining family effects can also be seen in the between-family and within- family variances. Table 5 reports estimates of selected variance components. We decomposed the total variances for each brother into three components: measured between-family variance (that explained by the exogenous variables), unmeasured between-family variance, and within-family variance. We are primarily interested in comparisons of variances and percentages across the cohorts of White men and Black men.

The variance components declined regularly across time, both among the respondents and their brothers. That is, with a few exceptions, mainly involving the two oldest cohorts, the components of educational inequality, within and between families, declined among Black and White men born in the first half of this century. Among the White respondents, the share of common family variance due to measured causes did not vary much above or below 25 percent. However, the share of unmeasured between-family variance declined over time, and that of within-family variance increased over time. The same pattern also occurred among White brothers.15

Among Black men, as among White men, the main story is the declining educational inequality in the three cohorts born after World War I. The variance in schooling declined abso- lutely, both between and within families. The relative importance of common measured variance declined, but the shares both of unmeasured between- family and within-family variance increased. These trends in variances and percentages are more or less determined by the change in the global effect of the family factor, but that by no means mihimizes the importance of the trend. Thus, for these cohorts, the process of

" Estimates of the variance components for brothers are available from the authors.

educational attainment did not contrib- ute to increasing socioeconomic differ- entiation within the Black population.

The apparent increase in the share of within-family variance in schooling should be interpreted with great caution, for it may be an artifact of measurement error. In none of our analyses did we attempt to correct for random measurement error, either in social background or attainment, yet there is good evidence that there were such errors in the OCG data (Bielby, Hauser, and Featherman 1977). We had initially hoped to correct all our estimates for response error, but we discovered that there were inconsistencies between our estimates of error variance in social background characteristics and the observed variances in the Black population. These inconsistencies occurred because the small samples used to estimate measurement models (N = 578 non-Blacks and N = 348 Blacks) covered all age cohorts, while we were attempting to estimate cohort- specific models.

In the case of social background variables, unreliability is probably not a major problem because we used several measured background variables; however, we may have slightly understated the contribution of measured background characteristics to the explanation of between-family variance. The problem of unreliability is more serious in the educational attainments of respondents and their brothers because the model puts all the measurement error variance into the unexplained, within- family variance components. It does so because the between-family variance is actually estimated by the covariance between the schooling of brothers, which is unaffected by random response error in educational attainment. Consequently, the estimates in Table 5 tend to overes- timate both the absolute magnitude of within-family variance in schooling and its share in the total variance.

We think it is reasonable to suspect that the error variance in reports of schooling-unlike the true within-family and between-family variances-is relatively constant across cohorts. That is, we doubt that the trend, if any, in absolute reporting errors about the re-

Kuo and Hauser

spondents' schooling could be as large as that in the actual distribution of schooling. On the assumption that reporting errors did not change across time, we used published estimates of the error variance of schooling in the March CPS to correct the within-family error variance components for respondents (Bielby et al. 1977: 1258,1262) and found that it had little effect on the variance components for White men. For example, among White respondents from triads of brothers in the birth cohorts of 1937 to 1946, the estimated share of within- family variance declined from 52.4 percent to 47.4 percent when the adjust- ment for response error was introduced. However, the error variance was substantially larger among Blacks (2.25 rather than 0.94), and the effect of the correction was much larger. In the adjusted series for Black respondents from triads of brothers, the measured between- family variance was relatively constant across cohorts, ranging from 25 to 34 percent. The share of unmeasured between-family variance increased sharply, from a range of 31 to 39 percent in the three oldest cohorts to 57 percent in the youngest cohort. Obversely, the share of within-family variance declined from 32 and 35 percent in the two oldest cohorts to just 18 percent in the youngest cohort. Again, there is no evidence to suggest an absolute increase in social differentia- tion within the Black population. One could argue relatively, that the share of family effects on educational inequality increased, but this argument would apply only to family characteristics other than measured social background and family structure.

DISCUSSION

The schooling of American men and their brothers is affected strongly by measured social background characteristics: paternal and maternal schooling, occupational status, number of siblings, intact family, farm origin, and southern birth.16 These effects have not been

16 Even though we worked with a subsample of the cases analyzed by Hauser and

markedly different among Blacks and Whites, but nonintact families and larger sibships appear to have handicapped Whites more than Blacks. Among White men and Black men, the effects of measured social background on the educational attainments of brothers can be specified as working through a single, common family factor. However, those effects differ by relative birth order; they are larger for older than for younger brothers. This may be another instance in which a global social trend-the declining influence of families on schooling-holds even within families (Hauser and Sewell 1985). Family type-intact versus nonintact-is not associated with substantial differences in the effects of measured background variables on men's educational attainments.

Effects of social background on schooling have declined among Blacks and Whites, but the pattern of change appears different in the two groups. Among Blacks, the data are consistent with a sharp, global decline in the effect of all background characteristics between cohorts born from 1937 to 1946 and all earlier cohorts, but among Whites, there appears to have been a gradual decline in the effects of just three specific background characteristics: farm background, southern origin, and family structure. The sharp disjuncture in family effects between Black men who grew up during and after World War I1 and those who grew up in earlier decades is suggestive of the massive impact of th2 migration of the Black population to urban areas and to the North. Unfortu- nately, because the OCG time series ended with men born just after the end of World War 11, the analysis does not

Featherman (1976), our estimated standard errors are much smaller, partly because of our failure to use a correction for the CPS sample design effect that Hauser and Feather- man applied. More important, by constrain- ing estimates of the effects of social background variables across multiple observations of schooling, that is, those of respondents and their brothers, we substantially reduced the sampling variability of the elements of T, relative to the regression coefficients estimated by Hauser and Featherman.


add to our understanding of the changing effects of race, social class, and family in recent years.

It would be difficult to attribute the declining effects of family background to a single source in either the White or the Black population. European analysts have described similar changes with references to increasing individuation and the decline of ascription. Such a conjec- ture may apply to the global decline in the effect of family variables among Black men. However, among White men, declining effects of background are limited to just three variables: intact family, southern birth, and farm origin. These trends are suggestive of rather specific changes in social conditions that affect educational chances- the diffusion of urban, industrial ways of life to rural areas and throughout the American South and, possibly, the shift from widowhood to divorce as the major source of family dissolution and the increasing preva- lence of divorce. In any event, there was no global source of change in the effects of families on the schooling of White American men.

As Hauser and Featherman (1976) anticipated, we found that a modest vector of measured social background characteristics accounts for about one- quarter of the variance in men's schooling, but for about one-half the common family variance. Roughly one-half the variance in White men's schooling occurs within families, that is, it is not explained either by measured or unmeasured common family characteristics. Similar observations hold for Black men, except that the within-family variance is smaller and may have declined as a share of the total.

Despite the stable effects of measured socioeconomic background among White men, inequality of educational attainment among American men declined through the first half of the 20th century. The variance in measured effects of social and family background declined, along with that of unmeasured common family influences and that of differences within families. Thus, the equalization of schooling among American men born in the first half of the century appears to have been effected by reduced inequal-

ity from every source. This need not have been the case. One might imagine, for example, that the effects of measured background characteristics could have remained constant, thus increasing the share of educational inequality created by family inequality. Even though the effects of some measured family characteristics declined, one could imagine that family resources and practices, other than the purely socioeconomic, need not have become more equal.17 Neither need it have been the case that inequality of educational outcomes declined within families. Thus, the data point to a remarkable pattern of reduced inequality in the distribution of schooling.

We believe that our research has answered some important questions about trends and differentials in educational stratification, but it also leaves many questions unanswered. How have the effects of family origins changed among Blacks and Whites in cohorts born after the end of World War II? How does the history of family influences on the schooling of American women compare with that among American men? What role has academic ability played in the changing influence of families? We hope that it may soon be possible to enrich and extend this statistical history of change in educational stratification.

REFERENCES

Allison, Paul D. 1987. "Estimation of Linea Models with Incomplete Data." Pp. 71-101 in Sociological Methodology 1987, edited by Clifford C. Clogg. Washington, DC: American Sociological Association.

Allison, Paul D. and Robert M. Hauser. 1991. "Reducing Bias in Estimates of Linear Models by Remeasurement of a Random

17 In fact, these components of variance might have become larger over time, rather than smaller. In the Wisconsin Longitudinal Study, the measured and unmeasured between-family variance in schooling is greater in small than in large families (Kuo and Hauser 1994). Thus, the secular decline in fertility might have increased the variance in schooling between families. It would be possible to examine this hypothesis directly within the OCG data.

Kuo and Hauser

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Hsiang-Hui Daphne Kuo, MS in sociology, is a doctoral candidate, Department of Sociology, University of Wisconsin-Madison. Her main fields of interest are social stratification, social demography, research methods, and statistics. She is currently working on a doctoral thesis on family structure and sibling resemblance.

160 Kuo and Hauser

Robert M. Hauser, Ph.D., is Vilas Research Professor, Department of Sociology, University of Wisconsin-Madison. His main fields of interest are social stratification, aging, research methods, and social indicators. He is currently conducting studies of the life course in a sample of Wisconsin high school graduates and of sibling resemblance based on the 1994 General Social Survey and is developing new indicators of educational trends.

Earlier versions of this article were presented at the May 1994 meeting of the Population Association of America and at the June 1994 meeting of the Working Group on the Low Income Population, Institute for Research on Poverty, University of Wisconsin-Madison. This research was supported by the Vilas Trust Estate; the Office of the Assistant Secretary for Planning and Evaluation, U.S. Department of Health and Human Services; and the Spencer Foundation and by a core grant from the National Institute of Child Health and Human development (HD-05876) for support of the Center for Demography and Ecology at the Uni- versity of Wisconsin-Madison. Computation was performed using SPSS-X and LISREL 7.20 on a VAX (VMS). All the data used in this article are in the public domain and are available from the Data and Program Library Service, University of Wisconsin-Madison or from the Inter- University Consortium for Political and Social Research, University of Michigan, Ann Arbor. The opinions expressed herein are those of the authors. Address all correspondence to Robert M. Hauser, Department of Sociology, University of Wisconsin-Madison, 1180 Observatory Drive, Madison, Wisconsin 53706; e-mail: [email protected].

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