Sibling Similarity in High School Graduation Outcomes: Causal Interdependency or Unobserved Heterogeneity?

Gerald S. Oettinger [*]

This paper uses data on age-adjacent sibling pairs from the National Longitudinal Survey of Youth to test for causal interdependencies between the high school graduation outcomes of older and younger siblings. Even after controlling for observable background characteristics, the graduation probability of an individual whose sibling graduated from high school exceeds the graduation probability of an individual whose sibling did not graduate by a large amount. However, this difference does not measure the causal effect of sibling graduation because of unobserved family factors and genuine simultaneity in the determination of all siblings' graduation outcomes. To measure the causal effect of sibling achievement on own achievement, I specify models in which sibling achievement is endogenous and estimate these models by two-stage methods using sibling-specific background characteristics as instruments. The evidence indicates that older sibling achievement has a positive causal effect on younger sibling achievement but that younger sibling achievement has no significant influence on older sibling achievement. These results are consistent with a model of intrafamily allocation in which parents learn about child endowments sequentially.

1. Introduction

There is widespread agreement among both social scientists and the public at large that the family plays a crucial role in influencing the development and eventual achievement of children. Less clear, however, is the relative importance of the many different contributions of parents and family to child outcomes. Although the effect of parental socioeconomic status on child outcomes probably has received the most study, research in several disciplines suggests that the size, composition, and behavior of the family unit are likely to be important determinants of child outcomes as well.

In the psychology literature, for example, an influential paper by Zajonc (1976) argues that siblings from the same household develop in predictably different ways because differences in birth order and age spacing imply that each sibling grows up in a distinct intellectual environment within the household. From a behavioral genetics perspective, Dunn and Plomin (1990) conclude that nonshared environment accounts for a large fraction of the sizable variation in personality and intelligence between siblings, and they argue that both parent-child interactions and sibling interactions have important child-specific effects that probably contribute heavily to nonshared environment. Finally, economic models of intrafamily allocation (Becker 1981; Behrman, Pollak, and Taubman 1982) show that parental investments in children's human capital, and therefore child outcomes, are likely to depend critically on family size, child endowments, and parental preferences regarding inequality among their children.

Previous research has examined how child achievement is influenced by family size (Blake 1989; Hanushek 1992), birth order (Behrman and Taubman 1986; Kessler 1991), and sex composition of the sibship (Butcher and Case 1994; Kaestner 1997; Hauser and Kuo 1998). However, there has been almost no analysis of whether the achievement of siblings influences a child's own achievement, despite the plausibility and potential policy relevance of such a relationship. Some evidence on this question is reported by Hanushek (1992), who finds that having higher achieving siblings raises a child's own achievement, but Hanushek treats sibling achievement as exogenous in his analysis.

The limited investigation of sibling achievement effects is perhaps somewhat surprising when one considers that several recent papers (Datcher 1982; Jencks and Mayer 1990; Case and Katz 1991; Corcoran, et. al. 1992; Evans, Oates, and Schwab 1992; Zax and Rees 1998) have examined how the average socioeconomic status of the individuals in a youth's neighborhood or school affects youth achievement. Robust evidence for neighborhood or school effects has been elusive, perhaps because average socioeconomic status in these broadly defined groups is a very noisy proxy for the socioeconomic status of the youth's actual peer group). [1] Given the potential biases inherent in using overly broad peer group measures, an analysis of the effect of siblings, who constitute a very narrow and intimate peer group, would seem to have some appeal. [2]

The present paper pursues this line of inquiry, analyzing whether sibling high school graduation outcomes have a causal effect on a youth's own probability of high school graduation. Such a causal linkage might exist for several reasons. For example, the achievement of siblings might have spillover effects if learning is to some extent a public good within the family unit. Second, the achievement of siblings might have a "role model effect," either by revealing information about a youth's own potential (and therefore affecting own effort) or through other mechanisms. Finally, the achievement of siblings might influence a youth's own outcome if parental investment in children's human capital tends either to offset or to reinforce ability or achievement differences across siblings. Of course, since the behavior of the family unit simultaneously influences the achievement of all of the children in the family and since many family factors are unobservable to the econometrician, a sibling's achievement should be treated as an endogenous explanatory variable in any econometric model of youth achievement.

Briefly summarizing the empirical results, I find that the raw probability of high school graduation is 42 percentage points higher for youths whose sibling in the sample graduated from high school than for youths with a nongraduating sibling in the sample and controlling for observable family-specific and individual-specific characteristics reduces this "effect" of sibling graduation by only about a third. However, estimates that recognize the endogeneity of the sibling graduation outcome are quite different. In particular, the estimated effect of older sibling graduation on the younger sibling's graduation probability is reduced but remains positive, substantial, and (marginally) significant. In contrast, the estimated effect of younger sibling graduation on the older sibling's graduation probability falls much further and is not significantly different from zero. Thus, the estimates suggest that older sibling achievement exerts a significant influence on, but is not substantially influenced by, younger si bling achievement. This asymmetric pattern of sibling achievement effects can be explained by several models of family behavior.

The remainder of the paper proceeds as follows. Section 2 describes the data used in the empirical analysis. Section 3 lays out the econometric model and describes strategies for estimating the causal effect of sibling achievement on own achievement. Section 4 presents the empirical results. Finally, section 5 contains a concluding discussion.

2. Data

The empirical analysis is performed using a sample of sibling pairs from the National Longitudinal Survey of Youth (NLSY). The NLSY began in 1979 as a survey of 12,686 American youths who were between the ages of 14 and 21 as of January 1, 1979. By design, the NLSY oversampled minority youths and youths from poorer socioeconomic backgrounds. Interviews have been performed annually since 1979. Extensive family background data were collected at the initial interview and detailed individual histories of educational attainment, labor market outcomes, and family formation have been compiled over time.

An important feature of the NLSY for the current analysis, which requires data on multiple siblings from each family, is that it includes all youths born between 1957 and 1964 in the original set of randomly selected households. This household-based sample design produced an initial sample containing 5863 siblings drawn from 2448 distinct households with multiple sibling respondents. Approximately 70% of these multiple-sibling respondent households contain exactly two sibling respondents; the remaining households contain three or more sibling respondents.

The sample that I use in the empirical work consists of a set of pairs of NLSY sibling respondents, with at most one pair per household. Because most of the NLSY households with multiple sibling respondents have only two sibling respondents, the choice of sibling pair is usually trivial. For households with three or more sibling respondents, however, I include only the oldest pair of respondent siblings. Although using data on every sibling respondent from each NLSY household would increase the sample size somewhat, it would require a substantial complication in the econometric model since one would have to allow for many more potential causal linkages between siblings. Consequently, I limit the sample to just the oldest pair of sibling respondents from each household. Note that the included sibling pairs are not necessarily the two oldest siblings in each family, but are rather the two oldest siblings who were surveyed by the NLSY. I further limit the sample to sibling pairs with complete data on high schoo l graduation outcomes and certain basic background characteristics (e.g., race, sex, birth order, sibship size, etc.), which reduces the sample to its final size of 2255 sibling pairs.

Table 1 presents (unweighted) sample means, standard deviations, and sibling correlations for the variables used in the empirical analysis. [3] Panel A summarizes the data for the outcome analyzed in this study--graduation from high school at or before age 19. The probability of graduation at or before age 19 is almost 0.75 for both older and younger siblings and graduation outcomes are strongly positively correlated between siblings. [4] Implicit in the means and correlation of sibling graduation outcomes is a contingency table describing the probability (empirical frequency) of graduation for each sibling conditional on the other sibling's graduation outcome. Specifically, the data imply that the younger sibling's graduation probability is 0.86 if the older sibling graduates from high school but is only 0.44 if the older sibling does not graduate. [5] Thus, in the raw data, the younger sibling's graduation probability rises by 42 percentage points if the immediately older sibling is a high school graduate.

Panel B presents sample moments for demographic and family background variables shared in common by siblings. This set of variables includes sibship size (i.e., the number of children in the family), number of females in the sibship, birth order of the older sibling, parents' educational attainment, average annual family income in the parental household over the calendar years 1978-1979 (reported by the head of the parental household), parents' immigrant status, and indicators for race. [6] To reduce measurement error in these variables, I compute the mean value reported by all of the respondent siblings in each NLSY household and then assign this within-family mean to both siblings in each pair in the sample. [7] Thus, panel B does not report sibling correlations since these correlations all equal one by construction.

Mean sibship size is naturally quite large, since the sample consists of individuals from families with at least two siblings in the NLSY, and the average sibship is approximately half female. Nearly half of the sibling pairs in the sample are the two first-born children in their families. Modal educational attainment is less than a high school degree for both mothers and fathers. Nevertheless, median family income in the sample of parental households ($24,014 in 1982-1984 dollars) is fairly close to median family income in the full U.S. population for the same years (approximately $26,300 in 1982-1984 dollars) because most of the parents of individuals in the sample were near the peak of their life cycle age--earnings profiles in 1978-1979. [8]

Last, panel C presents sample moments for various individual and environmental variables that can differ between siblings: sex, residence in an "intact" family during childhood, and labor market conditions at age 18. The sample is nearly half female and the sibling correlation in sex is weakly positive, implying that same-sex sibling pairs are slightly more common in the sample than are sister-brother pairs. The two family "intactness" indicators, one measured at age 14 and the other spanning ages 0-18, show that a substantial minority of youths spent part of their childhoods in households in which at least one biological parent was absent. As one would expect, this fraction is slightly larger among the younger siblings and the sibling correlation is large and positive for both intactness measures. [9]

The local labor market and national unemployment rates when respondents were 18 years old are included as measures of potential nonschool opportunities, which presumably influence enrollment decisions. Unfortunately, data on the local labor market unemployment rate at age 18 are only available for individuals who were 18 years old or younger when the survey began. As a result, I have data on the local labor market unemployment rate for only about one-third of the older sibling sample and three-fourths of the younger sibling sample. Average local and national unemployment rates at age 18 are both higher in the younger sibling sample, reflecting the fact that some individuals in this sample did not turn 18 until the recession years of the early 1980s. The sibling correlation in local unemployment rates at age 18 is strongly positive, reflecting either geographic variation in equilibrium unemployment rates or sluggish adjustment to local labor demand shocks. In contrast, the sibling correlation in the national unemployment rate is weakly negative.

3. Econometric Model

A general model for the achievement of pairs of siblings that allows each sibling's achievement to have a causal effect on the other sibling's achievement can be written as:

[[Y.sup.*].sub.1i] = [[delta].sub.1] [[Y.sup.*].sub.2i] + [X.sub.i][[beta].sub.1] + [Z.sub.li][[gamma].sub.1] + [[epsilon].sub.1i], (1)

[[Y.sup.*].sub.2i] = [[delta].sub.2] [[Y.sup.*].sub.1i] + [X.sub.i][[beta].sub.2] + [Z.sub.2i][[gamma].sub.2] + [[epsilon].sub.2I] (2)

For each sibling pair i, Equation 1 posits that some measure of the older sibling's achievement ([[Y.sup.*].sub.1i]) can be written as a linear function of the younger sibling's achievement ([[Y.sup.*].sub.1i]), shared family background characteristics ([X.sub.i]), background characteristics specific to the older sibling ([Z.sub.1i]), and a term representing unobserved individual and family factors ([[epsilon].sub.1i]). Symmetrically, Equation 2 posits that the younger sibling's achievement ([[Y.sup.*].sub.2i]) can be written as a linear function of the older sibling's achievement ([[Y.sup.*].sub.1i]), shared family background characteristics ([X.sub.i]), background characteristics specific to the younger sibling ([Z.sub.2i]), and a disturbance term capturing unobserved factors ([[epsilon].sub.2i]).

This empirical specification can be motivated by economic models of intrafamily allocation. In these models, parental investment in each child's human capital generally depends on how ability and other characteristics are distributed among all of the family's children. Depending on the parents' wealth and preferences, optimal investment in children's human capital could either amplify or mitigate initial ability differences between siblings. In either case, however, a child's own achievement would be related to sibling achievement through parents' allocation decisions. Alternatively, this specification also is consistent with the psychological research suggesting that a child's personality and intelligence might be influenced by interactions with and behavior of siblings.

The parameters of primary interest in the system given by Equations 1 and 2 are [[delta].sub.1] and [[delta].sub.2], which capture the causal effect of younger sibling achievement on older sibling achievement and the causal effect of older sibling achievement on younger sibling achievement, respectively. If parental investments in children's human capital tend to compensate inequalities in their children's initial endowments, or if for other reasons one child's achievement creates positive spillovers for siblings, then [[delta].sub.1] and [[delta].sub.2] should be positive. If instead, parents tend to reinforce initial ability differences or if achievement spillovers among siblings are negative, then [[delta].sub.1] and [[delta].sub.2] should be negative. Finally, the magnitudes of [[delta].sub.1] and [[delta].sub.2] will differ if sibling achievement effects are asymmetric within sibling pairs. For instance, if older sibling achievement has a larger effect on younger sibling achievement than the reverse, th en one should find /[[delta].sub.2]/ [greater than] /[[delta].sub.1]/.

Estimates of Equation 1 or 2 that treat sibling achievement as an exogenous explanatory variable will produce biased parameter estimates for two reasons. First, if there exists a common error component in [[epsilon].sub.1i] and [[epsilon].sub.2i], then the sibling's outcome will serve as a proxy for this unobserved family component and the estimates of [[delta].sub.1] and [[delta].sub.2] will be biased upward. In addition, even if there is no common component in the disturbances, [[delta].sub.1] and [[delta].sub.2] will be biased away from zero (assuming that both parameters have the same sign) because [[Y.sup.*].sub.1i] and [[Y.sup.*].sub.2i], are simultaneously determined. Thus, the estimation methodology must account for the endogeneity of sibling outcomes if consistent estimates of the effects of sibling achievement on own achievement are to be obtained. [10]

If the observed achievement measure were continuous, one could consistently estimate the parameters in Equations 1 or 2 by two-stage least squares (2SLS), given valid instruments. In the present study, however, only a dichotomous achievement measure--whether or not an individual graduates from high school by age 19--is observed. This introduces some complicating issues and suggests two potential estimation strategies. Under the first approach, one would posit that Equations 1 and 2 describe the structural system for a latent continuous measure of child achievement and that child j in family i graduates ([Y.sub.ji] = 1) if and only if her latent quality surpasses a threshold ([[Y.sup.*].sub.ji] [greater than] 0). In this case, one could solve Equations 1 and 2 for the latent variables' reduced form, and given a distributional assumption on the errors, one could obtain consistent estimates of the structural parameters by two-stage methods (Maddala 1983, pp. 246-7). For example, with normally distributed erro rs, one first would obtain probit estimates of each reduced-form achievement equation, then use these reduced-form estimates to predict each sibling's latent quality, and finally obtain probit estimates of each structural equation by replacing each sibling's unobserved latent quality with predicted latent quality.

The two-stage probit estimation methodology assumes that the sibling's latent quality, rather than the sibling's graduation outcome, influences a child's own achievement. If instead the sibling graduation outcome has a causal effect, then the [[Y.sup.*].sub.ji] terms on the right-hand side of Equations land 2 should be replaced by the dichotomous graduation indicators, [Y.sub.ji]. However, Heckman (1978) shows that this modified model is logically inconsistent if the latent achievement variables (i.e., the [[Y.sup.*].sub.ji]) are continuously distributed. Logical consistency in the continuous latent variable formulation requires that either [[delta].sub.1] or [[delta].sub.2] equal zero, thereby ruling out the fully simultaneous specification in which each child both influences and is influenced by her sibling. [11] On the other hand, if the latent achievement variables are discrete random variables, the fully simultaneous model poses no logical inconsistency. Moreover, the results in Heckman and MaCurdy (198 5) imply that, in this case, consistent estimates of the structural parameters can be obtained via 2SLS estimation of a linear probability model in which a child's own graduation outcome is the dependent variable and the sibling's graduation outcome is an endogenous explanatory variable.

For brevity, only the 2SLS estimates of the linear probability models for sibling graduation outcomes are reported below. The least squares methodology has the advantage that simple diagnostic tests for the relevance of the first-stage instruments (Bound, Jaeger, and Baker 1995) and the validity of the model's overidentifying restrictions (Newey 1985) can be implemented easily. However, the unreported two-stage probit estimates were always qualitatively identical to the 2SLS linear probability model estimates.

Of course, in either specification, identifying the causal effect of sibling achievement on own achievement requires instruments that are correlated with sibling achievement but do not directly influence a youth's own achievement. The structure in Equations 1 and 2 implies that the background characteristics that are specific to the younger sibling ([Z.sub.2i]) can serve as instruments for younger sibling achievement ([Y.sub.2i]) in the equation for older sibling achievement. Similarly, the background characteristics that are specific to the older sibling ([Z.sub.1i]) can serve as instruments for older sibling achievement ([Y.sub.1i]) in the equation for younger sibling achievement.

Panel C of Table 1 lists the variables that comprise [Z.sub.ji] in the present analysis: the respondent's sex, the two alternative measures of family "intactness" during the respondent's childhood, and the local and national unemployment rates when the respondent was 18 years old. [12] If the sibling's values for these characteristics do not directly influence a child's own achievement, after controlling for shared family background characteristics and the child's own values for these characteristics, then the sibling's characteristics are valid instruments and the effect of sibling achievement on own achievement is identified. However, one might question whether these sibling characteristics really have no direct effect on a child's own outcome. For example, if parents who eventually split up provide a different home environment, even while married, than do parents who always remain together, then the sibling's intactness indicator might be correlated with unobserved determinants of own achievement and henc e not a valid instrument. Likewise, it is possible that the sex of the sibling closest in age directly influences a child's own achievement, even after controlling for the sex composition of the full sibship. I address these concerns in the empirical work by estimating several alternative specifications of the model, routinely testing overidentifying restrictions, and discussing potential alternative interpretations of the results.

4. Empirical Results

As a benchmark for comparison with the estimates that treat sibling achievement as endogenous, Table 2 presents results from single-equation ordinary least squares linear probability model estimates of the determinants of high school graduation. In these models, sibling achievement is taken to be an exogenous influence on a child's own achievement. Columns 1 and 2 report estimates of the determinants of high school graduation outcomes for older siblings, whereas columns 3 and 4 report analogous estimates for younger siblings. In all of the models, the exogenous explanatory variables consist of the variables listed in panels B and C of Table 1, plus some additional dummy variables that account for missing data. [13] The reported standard errors in this and all later tables are robust to the heteroscedasticity that least squares estimation induces because the dependent variable is binary.

The estimates in Table 2 are mostly similar for the older sibling and younger sibling samples. Whether an individual graduates from high school by age 19 is strongly positively correlated with the sibling's graduation outcome, even after controlling for observable shared and individual-specific background characteristics. In both the older and younger sibling samples, the probability of high school graduation by age 19 for individuals whose NLSY sibling graduated from high school by age 19 exceeds the graduation probability for those whose NLSY sibling did not graduate by age 19 by roughly 0.30, all else equal. Because the raw difference in graduation probabilities between individuals whose siblings graduated from high school and individuals whose siblings did not graduate is 0.42, differences in observable background characteristics account for only about 30% of the "effect" of sibling achievement on own achievement.

The measured effects of the other covariates on high school graduation are generally unsurprising, and most have been documented in previous research. [14] Other things equal, youths from families with higher incomes have higher graduation probabilities. Graduation probabilities are lower for youths with more siblings, especially in the younger sibling sample, but sibship sex composition seems to have little effect. Lower parental educational attainment also is associated with a lower graduation probability, with maternal education having a larger influence on older sibling graduation outcomes and paternal education having a more pronounced effect on the outcomes of younger siblings. There is marginal evidence that blacks are more likely to graduate and Hispanics are less likely to graduate than observationally equivalent whites.

Females have substantially higher graduation probabilities than males. This sex differential remains, although it is slightly smaller, if the analysis is limited to the population-representative subsample of the NLSY. Thus, the differential is not solely attributible to different graduation behavior among minorities and/or poor whites. Similarly, this sex differential exists, again with slightly reduced magnitude, if one analyzes the outcome "graduated by the 1991 NLSY interview" rather than "graduated by age 19." Thus, the differential does not result simply from delayed graduation among NLSY males. [15] Both measures of family "intactness" suggest that, other things equal, graduation probabilities are higher for youths who grow up in intact families. Finally, there is some evidence consistent with the idea that graduation probabilities rise when contemporaneous nonschool opportunities become less promising. In particular, a higher local labor market unemployment rate at age 18 is associated with a higher p robability of graduation, although the estimate is less precise in the older sibling sample since data on the local unemployment rate are unavailable for much of that sample. The positive measured effect of the national unemployment rate in the older sibling sample is probably partly explained by the missing local unemployment rate data given that local and national unemployment rates are positively correlated. [16]

To summarize, the evidence in Table 2 shows that sibling high school graduation outcomes are strongly positively correlated even after one controls for observable family and individual-specific determinants of graduation outcomes. However, these measured "effects" of sibling graduation outcomes on own graduation outcomes probably do not capture the causal effect of sibling achievement on own achievement, both because the sibling graduation outcome proxies for unobserved family factors and because sibling outcomes are simultaneously determined through family allocation decisions. Obtaining consistent estimates of the causal effect of sibling achievement on own achievement requires estimating a model that accounts for the endogeneity of sibling achievement.

Table 3 presents the 2SLS linear probability model estimates of Equations 1 and 2. Columns 1-4 report various estimates of the determinants of older sibling high school graduation, and the analogous estimates for younger siblings are shown in columns 5-8. For each of these subsamples, I report the results from several different specifications. The estimates in columns 1, 2, 5, and 6 use the indicator for whether the respondent lived with both biological parents at age 14 as the "family intactness" measure, whereas the estimates in the other columns use the indicator for whether the respondent lived with both biological parents in all years from birth to age 18.

In addition, the variables used as instruments differ across the alternative specifications in Table 3. Recall that identifying the effect of sibling graduation on a child's own graduation probability requires sibling-specific variables that directly influence the sibling's graduation outcome but not the child's own graduation probability. In the current data set, the available sibling-specific background characteristics are an indicator for whether the sibling is female, an indicator for whether the sibling grew up in an intact family, and the local labor market and national unemployment rates when the sibling was age 18. [17] The estimates in columns 1, 3, 5, and 7 use this full set of variables as instruments for the sibling graduation outcome, thus assuming that each of these sibling-specific variables has no direct influence on a child's own graduation probability. Columns 2, 4, 6, and 8 relax this assumption somewhat by allowing a child's own graduation probability to depend on whether her sibling live d in a nonintact family, even after controlling for own residence in a nonintact family. This direct dependence could arise if the duration or timing of the spell of residence in a nonintact family influences

achievement. Specifications that make even weaker identifying assumptions are not reported in the table, but are summarized below.

The first stage (reduced form) estimates of the 2SLS estimates in Table 3 are shown in Appendix A. Although I do not discuss these first-stage estimates in any detail, the signs and magnitudes of these reduced-form coefficient estimates all seem plausible and, in fact, are quite similar to the coefficient estimates on the corresponding variables in Tables 2 and 3. Moreover, the second-stage instruments (i.e., the exogenous variables that are excluded from the second-stage regression) are always highly significant in the first-stage regression, with p-values less than 0.001 in all of the model specifications in Table 3. Thus, the diagnostic suggested by Bound, Jaeger, and Baker (1995) indicates that the sibling-specific variables used as instruments for the sibling graduation outcome are indeed strongly correlated with sibling graduation.

Turning to the results in Table 3, the estimate of the older sibling equation (columns 1-4) generally suggest that younger sibling achievement has a small effect on older sibling achievement. In particular, the point estimates imply that younger sibling graduation raises the probability of older sibling graduation by only four to eight percentage points, and the hypothesis that younger sibling graduation has no effect on older sibling graduation is never rejected. It is worth noting, however, that the confidence intervals for the effect of younger sibling graduation are rather wide. Nevertheless, the point estimates stand in sharp contrast to the large estimated effect of younger sibling graduation in the single-equation estimates.

The estimates of the younger sibling equation (columns 5-8), on the other hand, suggest that older sibling achievement has a substantial positive causal effect on younger sibling achievement. Specifically, the point estimates suggest that older sibling graduation raises the probability of younger sibling graduation by 19 to 24 percentage points. The magnitudes of these estimated effects of older sibling graduation on younger sibling graduation are three to five times as large as the estimated effects of younger sibling graduation on older sibling graduation. And, while the estimate of the effect of older sibling graduation is also rather imprecise, the hypothesis that older sibling graduation has no effect on younger sibling graduation is rejected at least marginally at conventional significance levels (p = 0.122, 0.100, 0.140, and 0.097 in columns 5-8, respectively).

The coefficient estimates on the other control variables are, for the most part, similar to those obtained in Table 2. Other things equal, a 10% increase in family income raises the probability of graduation by slightly less than one percentage point. An additional male child in the household reduces the probability of graduation by around 1.5 percentage points. In addition, graduation probabilities are 5 to 15 percentage points lower for an individual whose mother or father did not graduate from high school than for an otherwise similar individual whose parents both graduated from high school. Graduation probabilities are several percentage points higher for females and individuals from intact families, and are perhaps somewhat higher (lower) for blacks (Hispanics) than for observationally equivalent whites. Finally, graduation probabilities appear to rise somewhat with increases in the local unemployment rate (i.e., as nonschool opportunities worsen).

Although the standard errors are large, the asymmetry between the apparently large effect of older sibling achievement on younger sibling achievement and the apparently minor effect of younger sibling achievement on older sibling achievement is noteworthy. This asymmetry can be explained by an intrafamily allocation model in which parents prefer to compensate for differences in their children's initial endowments but only learn about their children's endowments sequentially. In this setting, parents shift investment toward a younger child if they discover that an older child is unusually gifted, and therefore high older sibling achievement causes higher younger sibling achievement. Parents also would like to shift investment toward the older child if they discover that the younger child is very able but, if child endowments are revealed sequentially, this information may arrive too late to allow much effective reallocation of investment. Consequently, younger sibling achievement has a smaller effect on older sibling achievement. Alternatively, the evidence also is consistent with the simple idea that older siblings are more influential teachers and role models for younger siblings than the reverse.

Although these causal explanations for the asymmetric sibling achievement effects seem plausible, it is also possible that these estimated effects are biased because of correlation between the instruments and error terms. Fortunately, the models in Table 3 are overidentified, thereby allowing the validity of the overidentifying restrictions to be tested. Given the least squares estimation framework, the overidentification test proposed by Newey (1985) can be applied easily. [18] The results of these overidentification tests are presented at the bottom of Table 3. In none of the specifications are the overidentifying restrictions even close to rejected at conventional significance levels. Thus, these tests give no suggestion that the 2SLS estimates are biased because the instruments and disturbances are correlated.

Of course, the overidentifying restrictions might not be rejected simply because the test has low power. Consequently, I also estimated 2SLS specifications that made even weaker identifying assumptions than the models in Table 3. For example, I estimated a specification in which whether the sibling lived in a nonintact family and the unemployment rates when the sibling was 18 years old were allowed to directly affect a child's own graduation outcome. Thus, in this specification, the indicator for whether the sibling is female is the only instrument for the sibling's graduation outcome and the model is exactly identified. The results from this model are similar to those in Table 3. [19] I also estimated a specification in which the indicators for whether the sibling is female and whether the sibling lived in a nonintact family were allowed to directly influence a child's graduation outcome. In this model, the only instruments for the sibling graduation outcome were the unemployment rates when the sibling was 18 years old. Unfortunately, the standard errors on the estimated effects of the sibling graduation outcomes become very large in these specifications, and no meaningful inferences can be drawn.

The discussion in the previous paragraph makes clear that the key identifying restriction driving the empirical findings is the assumption that the sex of the age-adjacent sibling does not directly influence a child's own graduation outcome; given this restriction, additional restrictions do not change the results qualitatively. Although this assumption can be questioned, it should be noted that it is not assumed that sibship sex composition has no effect on a child's educational attainment. Indeed, by including the number of females in the sibship as a family-specific determinant of educational attainment, I allow precisely for possible effects of overall sibship sex composition. [20] Rather, the crucial assumption for the consistency of the 2SLS estimates is that, after controlling for overall sibship sex composition, the sex of an age-adjacent sibling has no additional direct effect on a child's own achievement (through parental allocation decisions or otherwise).

Thus, if parents have a general tendency to favor sons or daughters, this should be accounted for by the sibship sex composition variable, and therefore, the sex of the age-adjacent sibling is not required in a child's own graduation equation. However, if parents tend to favor both sons and later borns at the expense of early-born daughters, then the large positive effect of older sibling achievement on younger sibling achievement in the 2SLS estimates might partly reflect this direct benefit of having an older sister. Similarly, if older sisters enhance the development of younger siblings more than older brothers do, then the measured effect of older sibling achievement on younger sibling achievement again might partly reflect this direct contribution of older sisters.

To summarize, estimation methods that recognize the endogeneity of sibling achievement reveal an asymmetry between the effect of younger sibling achievement on older sibling achievement and the effect of older sibling achievement on younger sibling achievement. Although younger sibling graduation has an insignificant effect on older sibling graduation, older sibling graduation seems to raise the graduation probability of younger siblings. Moreover, the point estimates suggest that the "older sibling achievement effect" might be quite substantial, but considerably smaller effects are also plausible given the relatively large standard errors. These asymmetic effects of sibling achievement are consistent with a model of intrafamily allocation, in which child endowments are revealed gradually, or a model of sibling interactions, in which older sibling behavior exerts greater influence on younger sibling behavior than the reverse. It remains possible, however, that part of the measured gain to younger siblings of having a high-achieving older sibling actually represents direct benefits of having an older sister.

5. Conclusion

Although theoretical models of family behavior in both economics and other social sciences suggest that sibling achievement is likely to have a causal effect on a child's own achievement, little empirical research has explored this question and even less has addressed the fact that sibling outcomes are simultaneously determined. The present paper has tried to fill this gap by analyzing data from the NLSY to see whether the high school graduation outcomes of age-adjacent siblings are causally interdependent. The (rather imprecise) point estimates from models that treat sibling achievement outcomes as endogenous suggest that younger sibling graduation has little effect on older sibling graduation but that older sibling graduation raises the probability of younger sibling graduation by perhaps 20 percentage points.

Although not the only possible explanation, these findings can be accounted for by economic models of intrafamily allocation. In particular, the finding that increases in older sibling achievement raise younger sibling achievement is, like the evidence in Hanushek (1992), consistent with parents pursuing compensatory investment strategies in allocating human capital investment among their children. At the same time, the absence of a significant effect of younger sibling achievement on older sibling achievement suggests that parental learning about child endowments may be largely sequential, making it difficult to condition investment in older children on the endowments of their younger siblings.

The finding that "sibling influence" tends to run from older siblings to younger siblings, but not in the reverse direction, has potential implications for policy. For example, this result suggests that, holding sibship size and other family characteristics constant, a given amount of public spending on low-birth-order children might have a higher social return than equal spending on children of higher birth order.

Although tests of overidentifying restrictions give no hint that the instruments used in the analysis are invalid, a possible alternative explanation for the asymmetry between the effect of younger sibling achievement on older sibling achievement and the effect of older sibling achievement on younger sibling achievement is that having an immediately older sister directly benefits own development, given sibship size. This possibility suggests that further investigation of the effects of sibship sex composition on development and how these effects are mediated by other family and sibship characteristics would be a worthwhile endeavor. Moreover, even if the effects of sibling achievement on own achievement measured here are causal, the present study has not pinned down the magnitudes of these effects with much precision. Obtaining precise estimates will require better data on background characteristics that differ between siblings and, hence, are potential instruments for sibling achievement. Such variables cou ld be constructed given detailed knowledge of the time profiles of family income, parental employment activity, parental marital status, child care arrangements, and neighborhood of residence over the entire childhood of each child in the family. Clearly, these data requirements are substantial and such an analysis must be left for future work.

(*.) Department of Economics, University of Texas, Austin, TX 78712, USA; E-mail [e-mail].

I thank Stephen Bronars, Daniel Hamermesh, and seminar participants from Texas, Texas A&M, and the U.S. Bureau of Labor Statistics for comments. Two anonymous referees provided especially helpful comments. All errors are my own.

Received August 1997; accepted April 1999.

(1.) Geronimus, Bound, and Neidert (1996) analyze the potential biases from using an aggregate explanatory variable to proxy for an unmeasured microexplanatory variable.

(2.) Of course, because actual peer groups extend beyond siblings, any measured sibling effects need not capture the effects of other, nonsibling peer influences.

(3.) Using the NLSY sample weights to compute population-representative summary statistics yields somewhat higher mean values for the high school graduation probability and the family socioeconomic status variables and a somewhat smaller mean sibship size compared to the unweighted means in Table 1. These differences occur because of the oversampling of minorities and poor whites in the NLSY. However, the sibling correlations are basically the same whether or not one uses the sample weights. Similar results are obtained if one computes unweighted means and standard deviations for the full civilian NLSY sample (instead of just for the sample of sibling pairs).

(4.) The probability of graduation by age 19 is about 0.82 if the data are weighted to be representative of the youth population.

(5.) Symmetrically, the older sibling's conditional graduation probability is 0.84 if the younger sibling graduates from high school but is only 0.41 if the younger sibling does not graduate.

(6.) Because the sample consists of pairs of consecutively born siblings, the younger sibling's birth order equals the older sibling's birth order plus 1, and thus there is no need to define a separate variable for the younger sibling's birth order.

(7.) In practice, this procedure probably only reduces measurement error slightly because the reported data on the shared family background variables are very highly correlated across siblings. However, forming within-family averages for the common family background variables also preserves sample observations because data on common family background are recorded as missing only if none of the siblings in the family report the relevant information.

(8.) Median family income in the U.S. population is taken from the Economic Report of the President (1993).

(9.) Although large, the measured sibling correlations in the family intactness indicators understate the true sibling correlations if the individual reports are subject to random misclassification error.

(10.) I assume that [[Y.sup.*].sub.1i] and [[Y.sup.*].sub.2i] are the only endogenous variables in the system. Thus, all of the background variables in [X.sub.i] and [Z.sub.ji] are treated as exogenous. Although number of children is clearly an object of parental choice, I follow previous empirical studies (e.g., Hanushek 1992) in treating the number of children as exogenous.

(11.) If the [[Y.sup.*].sub.ji] continuous random variables and both [[delta].sub.1] [not equal to] 0 and [[delta].sub.2] [not equal to] 0, then the individual event probabilities cannot sum to one.

(12.) I also tried including in [Z.sub.ji] an indicator for residence in an urban area at age 14 and an indicator for whether the adult female in the household worked in the labor market when the respondent was 14 years old. Neither of these variables ever had a significant effect. Augmenting [Z.sub.ji] with either of these variables does not change qualitatively any of the estimated sibling achievement effects reported below.

(13.) Full details of the empirical specification are provided in the footnote of Table 2.

(14.) The estimated coefficients on the birth order dummies and the parents' immigrant status dummies, which are not reported in Table 2 or the later tables, are always small and insignificant.

(15.) Tabulations of Current Population Survey data for the same birth cohort as in the NLSY also reveal higher high school graduation probabilities for females, but the difference between males and females is smaller than in the NLSY.

(16.) The sample correlation between local and national unemployment rates is 0.47 in the sample of observations with local unemployment rate data.

(17.) In addition, the set of potential instruments includes an indicator for missing sibling data on family intactness and an indicator for missing sibling data on the local labor market unemployment rate.

(18.) Newey's (1985) overidentification test statistic can be computed as the sample size multiplied by the uncentered [R.sup.2] from a regression of the 2SLS residuals on all of the exogenous (under the null hypothesis) variables in the system. Although Newey develops this test Statistic in the context of models with continuous dependent variables, Evans and Schwab (1995, p. 967) claim that "this class of tests is the best available diagnostic" for models with binary dependent variables, and they apply this test statistic in their analysis of the effects of Catholic school attendance on high school graduation and college entry.

(19.) In particular the point estimate on the younger sibling graduation outcome in the older sibling equation is around -0.05 with a standard error of about 0.20, whereas the point estimate on the older sibling graduation outcome in the younger sibling equation is about 0.27 with a standard error of about 0.15.

(20.) Butcher and Case (1994) provide evidence that sibship sex composition influences the educational attainment of females, but Kaestner (1997) and Hauser and Kuo (1998) question the robustness of this finding.

References

Becker, Gary S. 1981. A treatise on the family. Cambridge, MA: Harvard University Press.

Behrman, Jere R., and Paul Taubman. 1986. Birth order, schooling, and earnings. Journal of labor Economics 4:S121-45.

Behrman, Jere R., Robert E. Pollak, and Paul Taubman. 1982. Parental preferences and provision for progeny. Journal of Political Economy 90:52-73.

Blake, Judith. 1989. Family size and achievement. Berkeley, CA: University of California Press.

Bound, John, David A. Jaeger, and Regina M. Baker. 1995. Problems with instrumental variables estimation when the correlation between the instruments and the endogenous explanatory variable is weak. Journal of the American Statistical Association 90:443-50.

Butcher, Kristin F., and Anne Case. 1994. The effect of sibling sex composition on women's education and earnings. Quarterly Journal of Economics 109:531-63.

Case, Anne C., and Lawrence F. Katz. 1991. The company you keep: The effects of family and neighborhood on disadvantaged youths. NBER Working Paper No. 3705.

Center for Human Resource Research. 1995. NLS Handbook. Ohio State University.

Corcoran, Mary, Roger Gordon, Deborah Laren, and Gary Solon. 1992. The association between men's economic status and their family and community origins. Journal of Human Resources 27:575-601.

Datcher, Linda P. 1982. Effects of community and family background on achievement. Review of Economics and Statistics 64:32-41.

Dunn, Judy, and Robert Plomin. 1990. Separate lives: Why siblings are so different. New York: Basic Books. Economic Report of the President. 1993. Washington, DC: U.S. Government Printing Office.

Evans, William N., and Robert M. Schwab. 1995. Finishing high school and starting college: Do Catholic schools make a difference? Quarterly Journal of Economics 110:941-74.

Evans, William N., Wallace E. Oates, and Robert M. Schwab. 1992. Measuring peer group effects: A study of teenage behavior. Journal of Political Economy 100:966-91.

Geronimus, Arline T., John Bound, and Lisa J. Neidert. 1996. On the validity of using census geocode characteristics to proxy individual socioeconomic characteristics. Journal of the American Statistical Association 91:529-37.

Hanushek, Eric A. 1992. The trade-off between child quantity and quality. Journal of Political Economy 100:84-117.

Hauser, Robert, and Hsiang-Hui Daphne Kuo. 1998. Does the gender composition of sibships affect women's educational attainment? Journal of Human Resources 33:644-57.

Heckman, James J. 1978. Dummy endogenous variables in a simultaneous equation system. Econometrica 46:931-59.

Heckman, James J., and Thomas E. MaCurdy. 1985. A simultaneous equations linear probability model. Canadian Journal of Economics 18:28-37,

Jencks, Christopher, and Susan E. Mayer. 1990. The social consequences of growing up in a poor neighborhood: A review. In Inner city poverty in the United States, edited by Laurence E. Lynn, Jr., and Michael G. H. McGeary. Washington, DC: National Academy Press, pp. 111-87.

Kaestner, Robert, 1997. Are brothers really better? Sibling sex composition and educational achievement revisited. Journal of Human Resources 32:250-84.

Kessler, Daniel. 1991. Birth order, family size, and achievement: Family structure and wage determination. Journal of Labor Economics 9:413-26.

Maddala, G. S. 1983. Limited-dependent and qualitative variables in econometrics. Cambridge, UK: Cambridge University Press.

Newey, Whitney K. 1985. Generalized method of moments specification testing. Journal of Econometrics 29:229-56.

Zajonc, R. B. 1976. Family configuration and intelligence. Science 192:227-36.

Zax, Jeffrey S., and Daniel I. Rees. 1998. Environment, ability, effort, and earnings. Unpublished paper, University of Colorado at Boulder.

          Descriptive Statistics for Sample of NLSY Sibling Pairs
                                                            Standard
Variable                                           Mean     Deviation
A. High School Graduation Outcome
   Older sib graduated by age 19                      0.729      0.445
   Younger sib graduated by age 19                    0.743      0.437
B. Family Characteristics (Same for Both
   Siblings)
   Sibship size (number of children in family)        5.06       2.53
   Number of females in sibship                       2.41       1.65
   Older sib is first-born child in family            0.435      0.496
   Older sib is second-born child in family           0.208      0.406
   Older sib is third-born child in family            0.141      0.349
   Older sib is fourth-born child in family           0.091      0.288
   Mother's education [less than] 12 years            0.451      0.498
   Mother's education [greater than] 12 years         0.174      0.377
   Father's education [less than] 12 years            0.441      0.497
   Father's education [greater than] 12 years         0.226      0.418
   1978-1979 average annual income of parental
   household (in 1982-1984 dollars)              28,468     19,747
   Immigrant mother                                   0.111      0.315
   Immigrant father                                   0.107      0.310
   Black                                              0.269      0.444
   Hispanic                                           0.162      0.368
C. Individual Characteristics (May Vary Between
   Siblings)
   Older sib is female                                0.466      0.499
   Younger sib is female                              0.480      0.500
   Older sib lived in nonintact family at age 14      0.274      0.441
   Younger sib lived in nonintact family at age
   14                                                 0.287      0.453
   Older sib lived with both biological parents
   through age 18                                     0.679      0.467
   Younger sib lived with both biological
   parents through age 18                             0.655      0.475
   Local unemployment rate when older sib was 18
   years old                                          6.85       2.39
   Local unemployment rate when younger sib was
   18 years old                                       7.99       3.04
   National unemployment rate when older sib was
   18 years old                                       7.00       0.91
   National unemployment rate when younger sib
   was 18 years old                                   7.33       1.30
                                                   Sibling
Variable                                         Correlation
A. High School Graduation Outcome
   Older sib graduated by age 19
   Younger sib graduated by age 19                  0.426
B. Family Characteristics (Same for Both
   Siblings)
   Sibship size (number of children in family)       --
   Number of females in sibship                      --
   Older sib is first-born child in family           --
   Older sib is third-born child in family           --
   Older sib is third-born child in family           --
   Older sib is fourth-born child in family          --
   Mother's education [less than] 12 years           --
   Mother's education [greater than] 12 years        --
   Father's education [less than] 12 years           --
   Father's education [greater than] 12 years        --
   1978-1979 average annual income of parental
   household (in 1982-1984 dollars)                  --
   Immigrant mother                                  --
   Immigrant father                                  --
   Black                                             --
   Hispanic                                          --
C. Individual Characteristics (May Vary Between
   Siblings)
   Older sib is female
   Younger sib is female                            0.066
   Older sib lived in nonintact family at age 14
   Younger sib lived in nonintact family at age
   14                                               0.827
   Older sib lived with both biological parents
   through age 18
   Younger sib lived with both biological
   parents through age 18                           0.698
   Local unemployment rate when older sib was 18
   years old
   Local unemployment rate when younger sib was
   18 years old                                     0.788
   National unemployment rate when older sib was
   18 years old
   National unemployment rate when younger sib
   was 18 years old                                -0.139

The sample consists of the 2255 NLSY sibling pairs. Data are missing on particular variables as follows: mother's education is missing for 30 sibling pairs, father's education is missing for 118 sibling pairs, parental family income is missing for 132 sibling pairs, whether the respondent lived continuously with both biological parents from birth through age 18 is missing for 191 older sibs and 164 younger sibs, and the local labor market unemployment rate when the respondent was 18 years old is missing for 1515 older sibs and 554 younger sibs.

                 Ordinary Least Squares Linear Probability
                   Estimates of the Determinants of High
                     School (HS) Graduation by Age 19
                                     Older Siblings         Younger Siblings
                                          (1)         (2)         (3)
Sib Graduated from HS by Age 19          0.299       0.296       0.297
                                        (0.024)     (0.024)     (0.024)
Log of Family Income                     0.071       0.068       0.067
                                        (0.016)     (0.016)     (0.016)
Sibship Size                            -0.006      -0.006      -0.016
                                        (0.006)     (0.006)     (0.006)
Number of Females in Sibship             0.003       0.002       0.001
                                        (0.008)     (0.008)     (0.008)
Mother's Education [less than] 12       -0.116      -0.119      -0.067
                                        (0.023)     (0.023)     (0.023)
Mother's Education [greater than] 12     0.021       0.024      -0.003
                                        (0.020)     (0.020)     (0.020)
Father's Education [less than] 12       -0.032      -0.035      -0.091
                                        (0.023)     (0.023)     (0.023)
Father's Education [greater than] 12     0.018       0.016       0.025
                                        (0.021)     (0.021)     (0.021)
Black                                    0.018       0.020       0.045
                                        (0.023)     (0.023)     (0.023)
Hispanic                                -0.058)     -0.054      -0.023
                                        (0.030)     (0.030)     (0.030)
Female                                   0.109       0.111       0.102
                                        (0.018)     (0.018)     (0.018)
Lived in Nonintact Family at Age 14     -0.057        --        -0.034
                                        (0.022)                 (0.021)
Lived in Intact Family at Ages 0-18       --         0.092        --
                                                    (0.020)
Local Unemployment Rate at Age 18        0.008       0.009       0.006
                                        (0.006)     (0.006)     (0.003)
National Unemployment Rate at Age 18     0.019       0.019      -0.003
                                        (0.010)     (0.010)     (0.007)
[R.sup.2]                                0.284       0.290       0.270
                                       (4)
Sib Graduated from HS by Age 19       0.295
                                     (0.024)
Log of Family Income                  0.065
                                     (0.016)
Sibship Size                         -0.016
                                     (0.006)
Number of Females in Sibship          0.001
                                     (0.008)
Mother's Education [less than] 12    -0.069
                                     (0.023)
Mother's Education [greater than] 12 -0.003
                                     (0.020)
Father's Education [less than] 12    -0.092
                                     (0.023)
Father's Education [greater than] 12  0.024
                                     (0.021)
Black                                 0.045
                                     (0.023)
Hispanic                             -0.024
                                     (0.030)
Female                                0.102
                                     (0.018)
Lived in Nonintact Family at Age 14    --
Lived in Intact Family at Ages 0-18   0.056
                                     (0.020)
Local Unemployment Rate at Age 18     0.006
                                     (0.003)
National Unemployment Rate at Age 18 -0.003
                                     (0.007)
[R.sup.2]                             0.272

Heteroscedasticity-robust standard errors are in parentheses. All specifications also include controls for child's birth order, mother's immigrant status, father's immigrant status, top-coded family income data, and dummy variables for missing data for each of the variables in the model for which data are missing on some observations. See the footnote of Table 1 for a list of the variables with missing data on some observations.

              2SLS Linear Probability Model Estimates of the
                Determinants of High School (HS) Graduation
                                 by Age 19
                                     Older Siblings
                                          (1)         (2)     (3)     (4)
Sibling Graduated From HS by age 19      0.043       0.059   0.074   0.082
                                        (0.164)     (0.166) (0.151) (0.163)
Log of Family Income                     0.096       0.096   0.089   0.089
                                        (0.023)     (0.023) (0.022) (0.022)
Sibship Size                            -0.013      -0.012  -0.012  -0.012
                                        (0.008)     (0.008) (0.008) (0.008)
Number of Females in Sibship             0.009       0.009   0.007   0.007
                                        (0.009)     (0.009) (0.009) (0.009)
Mother's Education [less than] 12       -0.144      -0.142  -0.143  -0.142
                                        (0.029)     (0.029) (0.028) (0.029)
Mother's Education [greater than] 12     0.022       0.022   0.025   0.025
                                        (0.021)     (0.021) (0.021) (0.021)
Father's Education [less than] 12       -0.060      -0.058  -0.059  -0.058
                                        (0.029)     (0.030) (0.028) (0.029)
Father's Education [greater than] 12     0.027       0.027   0.025   0.025
                                        (0.023)     (0.023) (0.022) (0.023)
Black                                    0.029       0.028   0.029   0.029
                                        (0.025)     (0.025) (0.025) (0.025)
Hispanic                                -0.071      -0.071  -0.065  -0.064
                                        (0.032)     (0.032) (0.031) (0.032)
Female                                   0.114       0.114   0.116   0.116
                                        (0.019)     (0.019) (0.019) (0.019)
Lived in Nonintact                      -0.066      -0.077    --      --
  Family at Age 14                      (0.024)     (0.039)
Sibling Lived in Nonintact                 --        0.014    --      --
  Family at Age 14                                  (0.039)
                                     Younger Siblings
                                           (5)          (6)     (7)     (8)
Sibling Graduated From HS by age 19       0.218        0.244   0.188   0.240
                                         (0.141)      (0.148) (0.127) (0.145)
Log of Family Income                      0.075        0.073   0.075   0.071
                                         (0.021)      (0.022) (0.020) (0.021)
Sibship Size                             -0.017       -0.017  -0.018  -0.017
                                         (0.007)      (0.007) (0.007) (0.007)
Number of Females in Sibship              0.003        0.002   0.004   0.003
                                         (0.009)      (0.009) (0.009) (0.009)
Mother's Education [less than] 12        -0.080       -0.076  -0.086  -0.077
                                         (0.032)      (0.032) (0.030) (0.032)
Mother's Education [greater than] 12     -0.001       -0.002  -0.001  -0.002
                                         (0.020)      (0.020) (0.020) (0.020)
Father's Education [less than] 12        -0.096       -0.095  -0.099  -0.095
                                         (0.025)      (0.025) (0.024) (0.025)
Father's Education [greater than] 12      0.027        0.027   0.028   0.026
                                         (0.021)      (0.021) (0.021) (0.021)
Black                                     0.048        0.046   0.048   0.046
                                         (0.023)      (0.023) (0.023) (0.023)
Hispanic                                 -0.029       -0.027  -0.032  -0.030
                                         (0.031)      (0.032) (0.031) (0.031)
Female                                    0.100        0.101   0.100   0.100
                                         (0.018)      (0.018) (0.018) (0.018)
Lived in Nonintact                       -0.037       -0.051    --      --
  Family at Age 14                       (0.023)      (0.037)
Sibling Lived in Nonintact                  --         0.019    --      --
  Family at Age 14                                    (0.038)
Lived in Intact           --      --     0.103   0.105    --      --
  Family at Ages 0-18                   (0.022) (0.027)
Sibling Lived in Intact   --      --      --    -0.003    --      --
  Family a Ages 0-18                            (0.029)
Local Unemployment       0.009   0.009   0.010   0.010   0.006   0.006
  Rate at Age 18        (0.006) (0.006) (0.006) (0.006) (0.003) (0.003)
National Unemployment    0.020   0.020   0.019   0.019  -0.002  -0.002
  Rate at Age 18        (0.010) (0.010) (0.010) (0.010) (0.007) (0.007)
Overidentification Test
  P-value                0.695   0.554   0.858   0.586   0.424   0.311
  Degrees of Freedom       4       3       5       3       4       3
Lived in Intact          0.062   0.068
  Family at Ages 0-18   (0.022) (0.026)
Sibling Lived in Intact   --    -0.015
  Family a Ages 0-18            (0.030)
Local Unemployment       0.006   0.006
  Rate at Age 18        (0.003) (0.003)
National Unemployment   -0.002  -0.002
  Rate at Age 18        (0.007) (0.007)
Overidentification Test
  P-value                0.431   0.282
  Degrees of Freedom       5       3

Heteroscedasticity-robust standard errors are in parentheses. Additional explanatory variables are listed in the footnote of Table 2. All specifications use an indicator for whether the sibling is female, the local unemployment rate when the sibling was 18 years old (plus a dummy for missing data on the local unemployment rate), and the national unemployment rate when the sibling was 18 years old as instruments fur the sibling's graduation outcome. Columns 1 and 5 use an indicator for whether the sibling lived in a nonintact family at age 14 as an additional instrument. Columns 3 and 7 use an indicator for whether the sibling lived in an intact family at ages 0-18 (plus a dummy for missing data on sibling residence at ages 0- 18) as an additional instrument.

                                 Appendix
                Reduced-Form Estimates of the Determinants
                of High School Graduation by Age 19 (First
              Stage of the 2SLS Linear Probability Estimates)
                                            Older Siblings
                                                 (1)         (2)
Log of Family Income                            0.102       0.097
                                               (0.017)     (0.017)
Sibship Size                                   -0.014      -0.014
                                               (0.007)     (0.007)
Number of Females in Sibship                    0.011       0.009
                                               (0.009)     (0.009)
Mother's Education [less than] 12              -0.149      -0.151
                                               (0.024)     (0.024)
Mother's Education [greater than] 12            0.023       0.026
                                               (0.021)     (0.021)
Father's Education [less than] 12              -0.065      -0.068
                                               (0.024)     (0.024)
Father's Education [greater than] 12            0.030       0.028
                                               (0.022)     (0.022)
Black                                           0.034       0.036
                                               (0.025)     (0.024)
Hispanic                                       -0.072      -0.067
                                               (0.031)     (0.031)
Female                                          0.114       0.117
                                               (0.019)     (0.019)
Lived in Nonintact Family at Age 14            -0.077        --
                                               (0.040)
Lived in Intact Family at Ages 0-18               --        0.105
                                                           (0.028)
Local Unemployment Rate at Age 18               0.003       0.004
                                               (0.008)     (0.008)
National Unemployment Rate at Age 18            0.021       0.021
                                               (0.012)     (0.012)
Sibling is Female                              -0.006      -0.003
                                               (0.019)     (0.019)
Sibling Lived in Nonintact Family at Age 14     0.011        --
                                               (0.039)
Sibling Lived in Intact Family at Ages 0-18       --        0.004
                                                           (0.028)
Local Unemployment Rate When Sibling            0.005       0.005
  Was Age 18                                   (0.004)     (0.004)
National Unemployment Rate When Sibling         0.002       0.003
  Was Age 18                                   (0.009)     (0.009)
[R.sup.2]                                       0.199       0.203
                                            Younger Siblings
                                                  (3)          (4)
Log of Family Income                             0.097        0.093
                                                (0.017)      (0.017)
Sibship Size                                    -0.020       -0.020
                                                (0.006)      (0.006)
Number of Females in Sibship                     0.004        0.004
                                                (0.009)      (0.009)
Mother's Education [less than] 12               -0.112       -0.113
                                                (0.024)      (0.024)
Mother's Education [greater than] 12             0.005        0.005
                                                (0.021)      (0.021)
Father's Education [less than] 12               -0.111       -0.112
                                                (0.023)      (0.023)
Father's Education [greater than] 12             0.035        0.034
                                                (0.021)      (0.021)
Black                                            0.056        0.056
                                                (0.024)      (0.024)
Hispanic                                        -0.043       -0.044
                                                (0.031)      (0.031)
Female                                           0.100        0.100
                                                (0.019)      (0.019)
Lived in Nonintact Family at Age 14             -0.047         --
                                                (0.039)
Lived in Intact Family at Ages 0-18                --         0.069
                                                             (0.028)
Local Unemployment Rate at Age 18                0.011        0.011
                                                (0.004)      (0.004)
National Unemployment Rate at Age 18             0.000        0.000
                                                (0.009)      (0.009)
Sibling is Female                                0.032        0.033
                                                (0.019)      (0.019)
Sibling Lived in Nonintact Family at Age 14      0.000         --
                                                (0.039)
Sibling Lived in Intact Family at Ages 0-18        --         0.009
                                                             (0.028)
Local Unemployment Rate When Sibling            -0.010       -0.011
  Was Age 18                                    (0.008)      (0.008)
National Unemployment Rate When Sibling          0.009        0.009
  Was Age 18                                    (0.012)      (0.012)
[R.sup.2]                                        0.215        0.222

Heteroscedasticity-robust standard errors are in parentheses. All specifications also include the variables listed in the footnote of Table 2 as controls. Column 1 reports first-stage estimates for the 2SLS estimates in columns 5 and 6 of Table 3. Column 2 reports first-stage estimates for the 2SLS estimates in columns 7 and 8 of Table 3. Column 3 reports first-stage estimates for the 2SLS estimates in columns 1 and 2 of Table 3. Column 4 reports first-stage estimates for the 2SLS estimates in columns 3 and 4 of Table 3.