Income inequality, social mobility, and the decision to drop out of high school.

Kearney, Melissa S. ; Levine, Phillip B.

V.D. Remaining Potential Confounding Factors

In the last set of horserace specifications, table 7 presents the results of including one additional set of interactions with other state-specific factors that could simply represent confounding factors. These include the percentage of the state's population that is minority, the state's poverty rate, the state's incarceration rate, and the fraction of employment in the manufacturing sector. (25) The goal here is to determine whether one of these state-specific factors is a contextual factor that is related to state-level income inequality and is driving the differential high school dropout rates. The results reported in table 7 do not indicate that this is the case. Interactions between each of these factors and SES are universally insignificant, and their inclusion in the regression model has no substantive impact on the estimated effect of the interactions between lower-tail inequality and individual SES. (26)

V.E. The Role of Underlying Differences in Ability

As described above, a potential alternative explanation for the link between high inequality and low mobility is that in locations with greater demographic diversity, a mechanical correlation will link the two. The more similar the underlying populations, the lower the inequality (by definition) and the greater the mobility because chance will play a greater role in determining who succeeds in any given period. In essence, this is an argument about the underlying distribution of ability.

We explore this alternative within the context of educational outcomes, using test scores as a proxy for underlying ability. Specifically, we use data from scores on the Armed Forces Qualifying Test (AFQT), which was administered to participants in the NLSY79 and NLSY97 surveys. The AFQT is used by the military to determine eligibility and placement, and the score is reported as a standardized percentile ranking. These data have been used by empirical researchers in the past for similar purposes (Hermstein and Murray 1994; Neal and Johnson 1996; Belley and Lochner 2007). We hasten to note that the AFQT is not a direct measure of innate ability; on this point, Elizabeth Cascio and Ethan Lewis (2006) show that exogenous increases in educational attainment lead to increases in AFQT scores, especially for minorities. It is most appropriately considered a cumulative measure of ability, reflecting innate endowments, environmental influences, and the result of formal and informal human capital investment. Still, these test scores provide information about cognitive ability at the time the examination was taken.

The purpose of the empirical analysis reported in table 8 is to determine whether these differences in the AFQT measure of cognitive ability can explain any share of the higher relative rate of dropout behavior among low-SES boys in high-inequality places. As in the tables above, the first column is included for the purpose of comparison; it reports the results from a model analogous to our main specification taken from table 1 for boys, with the estimated point estimate on the interaction of primary interest being 0.042 (with a standard error of 0.016). (27) Because the AFQT is only available in NLSY79 and NLSY97, the second column presents the same regression for just these two data sets. The results indicate a somewhat larger point estimate of 0.067 for the effect of inequality on dropping out, but the smaller sample size leads to greater imprecision as well (with a standard error of 0.029). The third column of this table examines what happens if we control for AFQT as an explanatory variable in a specification that is otherwise identical to that in column 2. We find that doing so does reduce the point estimate by about one-third, from 0.067 to 0.045. This is not statistically different from the estimated effect in column 1, but the standard error is now 0.028 (owing to the smaller sample size coming from having to restrict the analysis to just two data sets), and so this estimate is no longer statistically significant from zero.

In column 4, we treat AFQT as the dependent variable and estimate a model that is otherwise equivalent to those estimated above. The point estimates indicate that low-SES youth in high-inequality areas have lower AFQT scores; this relationship is marginally statistically significant (p value = 8.3 percent). This result helps explain why the estimated impact of inequality for low-SES boys fell when we added AFQT: It appears that low-SES boys who live in high-inequality locations have AFQT scores that are even lower than those for low-SES boys overall. (28)

There are two possible interpretations of these results. For readers inclined to interpret the AFQT as measuring innate ability, one could conclude that the exclusion of the AFQT variable in previous analyses leads to an upwardly biased estimate of the relationship between income inequality and dropout rates; still, two-thirds of the effect remains. An alternative interpretation is that part of the effect of income inequality is captured by decreased educational investment before the actual dropout event. This corresponds to a leading view of dropout behavior as a process rather than a discrete event: A student begins to demonstrate irregular attendance, then multiple failed courses, and eventually the obstacles to graduation feel overwhelming and the student drops out (Rumberger 2011). In other words, discouraged students stop applying themselves early. This could show up as a lower AFQT score, consistent with the finding of Cascio and Lewis (2006) that an exogenous increase in education leads to higher AFQT scores. Their finding would imply that decreased effort in school, and in learning more broadly, would result in a lower AFQT score. Regardless of interpretation, the impact of greater inequality on dropout behavior is substantial, albeit somewhat smaller if one accepts the interpretation that the AFQT measures innate ability.

VI. Self Reported Reasons for Dropping Out of School

In an attempt to explore students" own stated reasons for why they dropped out of school--and to see if they are consistent with our proposed model--we take advantage of data from the High School and Beyond survey. In 1980, high school sophomores were initially surveyed, and then they were resurveyed in 1982. We focus on those in the 1982 survey who left school after their sophomore-year interview in 1980. The sample for this "dropout survey" includes 2,421 individuals, or roughly 8 percent of the initial 1980 cohort. These individuals were asked why they dropped out and were given a set of 16 possible reasons; they were allowed to mark as many as applied. Though we acknowledge that students' self-reported reasons for dropping out of school might not accurately reflect their underlying motivations, there is potentially something to be learned from whether the stated reasons were academic in nature.

A focus on perceptions, as discussed above, implies that the high school dropout decision is less likely to be driven by academic difficulties. In other words, if a student perceives a lower benefit to remaining in school, then he or she will choose to drop out at a lower threshold of academic difficulty. We look to the data to see if there is any support for such a notion. The most direct measure of academic difficulty is the response "had poor grades / not doing well." Other reasons that might reasonably be considered academic include expelled or suspended; did not get into desired program; school grounds too dangerous; and moved too far from school. The remaining 11 options include stated reasons that are less directly academic: had to support family; offered job and chose to work; school wasn't for me / didn't like it; wanted to travel; wanted to enter military; friends were dropping out; married or marriage plans; pregnant; illness/disability; couldn't get along with teachers; and couldn't get along with students. Looking at the share of students who report each particular reason, and how these compare across states by inequality level, we see that 51 percent of dropouts in the least-unequal states reported that they dropped out because of poor academic performance, as compared with only 21 percent of students who dropped out in the most-unequal states. This is the only particular reason (of the 16) that shows a difference in shares across states by inequality level that is statistically significant.

Regression-adjusted results are similar. Controlling for the same set of individual- and state-level controls as described in equation 6 above, and controlling for a state fixed effect, the data indicate that low-SES students in the highest and middle-range inequality states are 25 to 29 percentage points less likely to cite poor grades as a reason for dropping out. This represents a nearly 50 percent reduction in citing poor grades. This reason has by far the largest difference between low-SES students in high- and low-inequality states. Although not conclusive, these survey data are broadly consistent with the notion that low-SES boys in more unequal states are more likely to drop out, not because they are struggling academically but potentially because they perceive a lower return from staying in school. In other words, for the same level of academic performance, low-SES students in more unequal places are more likely to drop out of school.

VII. Discussion

In this paper, we have proposed a mechanism whereby greater levels of income inequality might lead to lower rates of upward mobility, namely, lower levels of high school completion among individuals from low-income backgrounds. We empirically test the proposition, and also test for the role of confounding factors and potential mechanisms. Our analysis offers compelling evidence that low-SES youth, boys in particular, are more likely to drop out of high school if they live in a place where the gap between the bottom and middle of the income distribution is wider.

The fact that boys appear to respond to greater levels of income inequality by dropping out of school more often is consistent with a growing body of evidence suggesting that boys suffer greater educational and labor market consequences from family and economic disadvantage (Bertrand and Pan 2013; Autor and others 2015; Chetty and others 2016). However, these patterns do not necessarily mean that low-SES girls are not affected by the economic disadvantage or conditions around them. They might simply respond on different margins. For instance, in Kearney and Levine (2014) we use empirical methods analogous to those we have used in this paper and find that low-SES girls in more unequal places are significantly more likely to become young, unmarried mothers. (29)

We interpret the findings as being consistent with--albeit not a conclusive demonstration of--a model of decisionmaking where a persistently wide gap between the bottom and middle of the income distribution has a negative effect on the perceived likelihood of economic success through human capital investments. This could occur either through impeded opportunity in actuality or through an effect on perceptions, shaped by a variety of factors experienced throughout one's childhood. The finding that higher levels of lower-tail income inequality lead to greater rates of dropout is robust to including the high school graduate wage premium in the regression model. In fact, the data indicate that the wage premium itself reduces the dropout rate, but household income inequality has an offsetting positive effect. In an additional set of models that examine potential mediating factors--including residential segregation and school financing--the data reject the hypotheses that any of the identified contextual factors are responsible for the relationship. Because the data do not offer support for any of these direct mechanisms, we are left with a residual explanation about perceptions. Future work is needed, ideally drawing on the insights from multiple disciplines--including, for example, social psychology--to attempt to more directly investigate this line of explanation.

There are important policy implications of this work regarding the types of programs needed to improve the economic trajectory of children from low-SES backgrounds. Successful interventions would focus on ways for low-SES youth to increase the likelihood of achieving economic success. These interventions could focus on improving the actual rate of return on investing in human capital for them, as we often discuss. But they also could focus on improving perceptions. College scholarship programs for low-SES high school graduates, for instance, may make college a better investment for low-income youth and increase the return associated with graduation from high school. But they could also alter the student's perception that going to college is the sort of activity that he or she can achieve. Other such interventions might take the form of mentoring programs that connect youth with successful adult mentors, or school and community programs that focus on establishing high expectations and providing pathways to graduation. They could also take the form of early childhood parenting programs that work with parents to create more nurturing home environments to build self-esteem and engender positive behaviors.

One might view the results described above regarding AFQT scores as suggesting that earlier interventions in a child's life are preferable because they can alter children's academic circumstances well before the point where they are deciding whether or not to stay in school. This evidence, along with evidence from other research, supports the notion that early intervention can have large payoffs. Nonetheless, it is worth noting that there is great social value in identifying interventions that can help improve the trajectory of economically disadvantaged children growing up in high-inequality areas who have already fallen behind.

We believe these implications are consistent with the new set of results coming out of the Moving to Opportunity for Fair Housing (MTO) experiment. MTO was a randomized controlled trial that offered housing vouchers and mobility counseling to inner-city, low-income families living in public housing. The results from the first generation of MTO movers provided little evidence that moving to a low-poverty neighborhood led to noticeable improvements in adult economic outcomes or teenagers' educational attainment (Kling, Liebman, and Katz 2007). However, more recent evidence from Chetty, Nathaniel Hendren, and Katz (2016) that children who moved when they were very young had higher college attendance rates and ultimately received higher wages. The authors' interpretation of these findings is that the greater resources in the low-poverty area had more time to take effect on the younger children. Although we do not dispute this interpretation, our model would additionally suggest that an important reason why the program was successful for younger children is because it changed their perceptions of what would be possible for them. Those children who moved at younger ages not only had the advantage of greater resources for a longer period of time, but they also spent less time with a highly disadvantaged peer group, which might have altered their perceptions of what was possible for them.

This interpretation also builds nicely on the contributions of Flavio Cunha and others (2006), and Cunha and James Heckman (2007), among others, arguing that "skills beget skills." The theory is that investments in skill at an early age compound and have a larger eventual effect on economic well-being than investments in skill at an older age. Our conceptualization might be complementary to this view, insofar as "perceptions beget perceptions." This is not to say that interventions later in life do not have the ability to improve one's perceptions, but it may be more difficult to overcome this hurdle.

Our analysis has demonstrated that a greater, persistent gap between the bottom of the income distribution and the middle leads to lower rates of high school completion among economically disadvantaged youth, boys in particular. These findings have implications for the potential of disadvantaged youth to achieve upward mobility and for the types of policies that are likely to be successful. Furthermore, they reflect a plausible channel through which higher rates of income inequality might causally lead to lower rates of social mobility. To improve rates of upward mobility, economically disadvantaged youth need reasons to believe that they can achieve economic success.

ACKNOWLEDGMENTS We are indebted to our discussants, Robert Moffitt and Miles Corak, and to our editors, Janice Eberly and James Stock, for detailed comments that have greatly improved this paper. We also thank Susan Dynarski, Nora Gordon. Judith Hellerstein, Caroline Hoxby, Robin McKnight, and Lesley Turner for helpful conversations and comments on an early draft. We acknowledge helpful comments from seminar participants at the American University School of Public Affairs, the University of Notre Dame, Stanford University, the University of New Hampshire, the University of Texas at Austin, the Federal Research Bank of Cleveland's Income Distribution Workshop, and the National Bureau of Economic Research Universities' Research Conference on Poverty, Inequality, and Social Policy. We thank Riley Wilson for research assistance. We are grateful to the Smith Richardson Foundation for providing financial support for this project. Any views expressed are those of the authors alone.

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Comments and Discussion

COMMENT BY

MILES CORAK Like all nicely crafted papers, this one by Melissa Kearney and Phillip Levine helps answer some important questions, while at the same time raising other equally important and interesting questions. My comments revolve around the answers they offer to three questions that help inform public policy directed to social mobility: (i) Inequality of what? (ii) Social mobility for whom? and (iii) Whither the dropout rate?

INEQUALITY OF WHAT? The authors focus our attention on the degree of inequality in the lower half of the income distribution. This is an important lesson for researchers examining intergenerational mobility. The theoretical starting points in this literature are the seminal papers by Gary Becker and Nigel Tomes (1979, 1986), and by Gary Solon (2004, 2015), who refines the Becker-Tomes theoretical framework for the study of differences in mobility over time and across space. In particular, Solon (2004) alerts us to the importance of the return to human capital as a determinant of the degree of relative intergenerational mobility, with a higher return offering more incentive for parents to invest in the human capital of their children. This leaves open the issue of which families have the greatest opportunity to make these investments, the presumption being the most educated will ramp up to a much greater degree, giving their children a longer stride in the march up the income ladder. This is what drives an inverse causal relationship between inequality and intergenerational mobility. But this is a presumption, and Kearney and Levine helpfully point out that we may need to pay attention to the heterogeneity of returns across socioeconomic groups. Higher returns to schooling will be a force leading all children to get more schooling, and though there may be all sorts of reasons why the rich will move forward with more zeal, it is important to appreciate that the incentives will be dulled for the less advantaged if greater inequality induces, in their words, "relative disenchantment." Inequality of what? It is inequality in the lower half of the income distribution that bites, and matters for this causal channel.

This opens up a public policy concern about behavior, and by implication policy should be directed to the perceptions, information, and actions of youth raised by low-status families in high-inequality areas. But another dimension of this paper also needs to be noted. Kearney and Levine base their analysis on a particular definition of income: total income, which includes all market sources of income, and also all income from government transfers. Inequality of what? The returns to education should be assessed in terms of not just market incomes but also total income returns. If income transfers are in play, then this would seem to raise other policy concerns, particularly if we buy their story that inequality is causal. If this is the case, then the implication would be that policymakers should also direct their attention to shrinking the gap between middle and bottom incomes. The paper seems to leave us with questions about whether to directly raise the prospective incomes of high school graduates. But if income transfers influence the type of inequality that matters, why not address inequality directly and let the behavior take care of itself?

SOCIAL MOBILITY FOR WHOM? This question of whether to address inequality directly is particularly relevant, given the answer the paper offers to a second question: Social mobility for whom? The findings focus our attention on the influence of relative incomes on upward mobility from the bottom in an absolute indicator: Lower-tail inequality has a negative impact on the prospect of graduating from high school. But this is true only for boys; there are no substantive results for girls. With respect to public policy, it makes one wonder about the logic of a narrow and focused design for income support policies like the Earned Income Tax Credit, and in particular about the rationale for excluding the male population from one of the most important innovations in the delivery of income support.

But Kearney and Levine's answers to "Social mobility for whom?" cut even deeper. In the series of "horserace" regressions they use to assess the robustness of their main findings, the only thing that seems to bite is a measure of ability, as described in their table 8 and the associated discussion. Imperfect as the Armed Forces Qualifying Test (AFQT) is as a measure of ability, the authors' analysis does raise, as they correctly mention, a link between their findings and the well-developed literature on the importance of investments during the early years--the view that child development moves recursively through a series of interrelated stages. Social mobility for whom? For boys, but most likely for boys who seem to have reached the first years of high school with lower AFQT scores. It is interesting to note that Bruce Bradbury and others (2015), among others, have found that there are certainly significant gaps in mathematics and reading test scores between children from different socioeconomic groups at the age when they are about to begin high school (my figure 1 is adapted from their figure 2.5). But they also find that the distributions in test scores when these same children were of kindergarten age are almost exactly the same. We pretty well know the distribution of test scores in mathematics and reading at age 14 from the distribution of test scores at age 4 and 5. So if you continue to believe that policy should be directed to behavior, then you also need to ask yourself whether it should be focused on children during the high school years, or on the early years. It is beyond the scope of this paper to offer an answer to this question, but it needs to be addressed before any specific lessons are drawn.

[FIGURE 1 OMITTED]

This paper does not have an explicit identification strategy to uncover causal effects. The authors are well aware of this reality, and their analysis is geared toward assessing how robust the conditional expectations they uncover are to a host of additional factors that could also plausibly be playing a role. In the standard way, one can never "prove" a hypothesis, only hope to disprove it. That they have succeeded in failing to disprove their hypothesis will certainly leave some readers unconvinced. But the ideas they put forward merit consideration as the literature on the determinants of schooling moves ahead. Kearney and Levine's thesis might prove fruitful in considering a third question: Whither the high school dropout rate?

WHITHER THE HIGH SCHOOL DROPOUT RATE? There has been much discussion about whether or not trends in inequality and social mobility are informative. Why do we not see falling social mobility in an era of higher inequality? The answer given in the opening pages of Kearney and Levine's paper is that we are focusing on the wrong type of inequality. Inequality has been on the rise because of higher top income shares, but the mobility process is driven by middle-level inequality, according to Raj Chetty and others (2014), or by lower-tail inequality, according to Kearney and Levine. Measured in these ways, inequality has not risen, and we should not be surprised by the fact that social mobility has been flat. Fair enough. But there are also reasons to think that trends in inequality and intergenerational mobility are not informative because of the long lags involved in the processes linking the two, and because the adjustment dynamics may well be nonmonotonic, as described by Martin Nybom and Jan Stuhler (2013).

But all this makes more sense when the focus is on intergenerational income mobility, a comparison of the adult incomes of children with the incomes of their parents. For many important outcomes in the process of child development, such as high school graduation, we do not need to wait as long to get accurate measurements of the degree of mobility. Richard Murnane (2013) offers a careful survey of what we know about the high school dropout rate, and he describes an important puzzle: High school graduation rates have been on the rise since about 2000, yet there has been essentially no trend in the wage rate of dropouts relative to graduates. Now it may be that the more important wage is that relative to college graduates, or it may be that something else is going on. Could it be that in some way parents and youth are getting the message that schooling matters, and it matters more now than for past generations? As research in this area continues, it will certainly be important to examine whether and in what way the disenchantment hypothesis, and possible changes in disenchantment, that Kearney and Levine eloquently put forward is part of the answer to this puzzle.

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Murnane, Richard J. 2013. "U.S. High School Graduation Rates: Patterns and Explanations." Journal of Economic Literature 51, no. 2: 370-42.

Nybom, Martin, and Jan Stuhler. 2013. "Interpreting Trends in Intergenerational Income Mobility." Discussion Paper no. 7514. Bonn: Institute for the Study of Labor (IZA).

Solon, Gary. 2004. "A Model of Intergenerational Mobility Variation over Time and Place." In Generational Income Mobility in North America and Europe, edited by Miles Corak. Cambridge University Press.

--. 2015. "What Do We Know So Far about Multigenerational Mobility?" Working Paper no. 21053. Cambridge, Mass.: National Bureau of Economic Research.

COMMENT BY

ROBERT A. MOFFITT This interesting paper by Melissa Kearney and Phillip Levine is another contribution to the literature on the pernicious effects of growing income inequality. However, unlike most of the studies of this issue to date, Kearney and Levine make a serious attempt to estimate the causal spillover effects of income changes in one part of the distribution on the behavior of groups in a different part of the distribution. In their specific case, they are interested in what happens to the educational attainment of children who come from disadvantaged families if the 50th percentile of income--an income level far above their own--rises, holding constant their own income. (1) At least for boys, they find that such a rise increases the rate of their high school dropout (relative to that of higher-income families), which, if correct, would be a disturbing result.

Kearney and Levine rightly point out that most of the literature on this question does not attempt to make causal statements about the effects of inequality on individual outcomes. Their discussion of the literature largely focuses on examinations of the correlation between intergenerational income rank mobility and the level of income inequality across time or across areas, which is not quite what they are examining, because the educational attainment of low-income groups (their outcome variable) is not the same as rank mobility, even of educational attainment. Rank mobility is measured as the relative intergenerational income--or education--mobility of children coming from different income or educational strata. The object of interest in the rank mobility literature is the probability that children from low-income families, for example, have a chance of improving their incomes sufficiently to actually pass up children growing up in middle-income families. Kearney and Levine do not examine this directly; they only look at the relative probabilities of dropping out of high school for children from low-income versus higher-income families, and whether a change in these relative probabilities could generate a change in the later adult earnings gap between such children without a change in rank. My own view is that Kearney and Levine's outcome is more important than rank mobility, but I also think that much of the motivating discussion in their paper, which examines rank mobility, is not directly germane to their analysis.

An implication of their result, to which they refer only briefly, is that a natural extrapolation of their findings would suggest that a rise in the 50th percentile level of income, which lowers the educational attainment of those in the lower quantiles, should increase inequality even further by lowering incomes at the bottom. This would raise the ratio of the 50th percentile level of income relative to the bottom even further, and would hence raise inequality even more, which could lead to further reductions in educational attainment at the bottom. This would constitute a negative feedback loop.

In any case, Kearney and Levine do not attempt to address causality with the conventional methods of correcting for endogeneity with instrumental variables or by a search for natural experiments where an arguably exogenous shock to inequality is used to obtain a superior estimate of its effect on individual family outcomes. Instead, theirs is an examination of whether the cross-sectional correlation between inequality and those outcomes is reduced when one controls, in a regression setting, for a variety of influences that might reasonably be thought to be generating the raw, unconditional correlation. In the language of the causal effects literature, this is the method of "selection on observables," to be contrasted with "selection on unobservables." That they do not attempt to examine the latter is probably the chief concern that many will have about their analysis. In the end, after controlling for many observables that they can measure with their data, they are left with a significantly positive correlation between the level of inequality and the low educational attainment of low-income boys. As they readily admit themselves, what they have done is to identify a "residual" correlation whose source is still not known but that they are willing to interpret as reflecting a true causal effect.

Kearney and Levine make an argument that, alternatively, using a cross-area, differences-in-differences strategy by examining the relationship between changes in inequality and changes in educational attainment across different areas is unlikely to work because short-term changes in inequality are likely to be transitory and are therefore not likely to have much of an effect on something like educational decisions. I find this convincing for changes at the annual frequency, but I am not clear on why longer-run differential changes in inequality across areas could not be used for such an exercise. Inequality has no doubt grown at different rates in different areas over the longer run, not least because of differences in their industrial structures, and the correlation of these rates with changes in educational attainment over a similar time frame would more likely pick up the effect of quasi-permanent changes in inequality on outcomes, not transitory ones.

Nevertheless, Kearney and Levine's main finding is that there is still a residual, positive, cross-sectional correlation between income inequality in a state and the likelihood that a boy from a disadvantaged family will fail to complete high school, even after controlling for a number of observable differences in both family and state characteristics. They suggest that this residual correlation is a result of "despair," meaning that a child at the bottom of the income distribution "does not see much value in investing in his or her human capital." Kearney and Levine's simple economic model posits that an increase in inequality (for example, an increase in the level of the 50th percentile of income) changes the child's perception of the utility value of investing in education. I think it would be helpful to parse this presumed effect into two different effects. One is that an increase in inequality changes the child's perception of the monetary return to investing in education, while the second is that it changes the utility value of attaining a higher level of education and income, even if there is no change in the monetary return. I can more easily imagine the term "despair" being associated with the latter mechanism than with the former. Though the latter mechanism could be interpreted, for example, by supposing that if a low-income child thinks he is increasingly unlikely to catch up, much less pass up (in the sense of rank mobility) a middle-class child in future income, the child might attach less utility value to attempting to increase his or her income through education. But for the former mechanism to work, if I am a low-income child and I see that middle-class children are making more money than they used to if they graduate from high school, somehow this leads me to think that I will make less money by graduating from high school than I did before, and I curtail my educational investments accordingly. (2)

The difference is important because the former explanation is related to the idea of incomplete or inaccurate information, which has been the subject of discussion in the literature for many years. The classic hypothesis by William Julius Wilson (1987), discussed in Kearney and Levine's paper, is really about the perceptions of the monetary rate of return, arguing that the departure of middle-class families from neighborhoods where low-income families live means that disadvantaged families no longer see success stories around them, leading them to conclude that success is unlikely. (Kearney and Levine test for this by controlling for income segregation and find it not to matter, but they admit that their state-level segregation variable may not capture what is a much more geographically local phenomenon.) In addition, recent work by Caroline Hoxby and Sarah Turner (2013) has discovered that many high-achieving high school students from low-income families do not apply to good colleges that they could surely get into. Further, they find that if they provide information on college grad uation rates, instructional resources, and application procedures to such students, coupled with waivers of college application fees, they are led to apply to better colleges. This supports an information story. At much earlier ages than Kearney and Levine are studying, Flavio Cunha, Irma Elo, and Jennifer Culhane (2013) have studied whether the failure of low-income parents to invest in their preschool children's human capital by reading books and devoting time and resources to their children is because they do not perceive the return to those investments to be high. All these information stories lead directly to policy interventions that improve information, and Kearney and Levine discuss some somewhat related possible interventions in their final section. (3) But for these stories to provide an explanation for Kearney and Levine's findings, it has to be the case that information is reduced when median income rises, which is more difficult to imagine.

The mechanism behind the perceptions effect hypothesized by Kearney and Levine also could bear more thought. The mechanism is an extremely local one, suggesting that children in low-income families perceive changes in the income of middle-class families in their geographic areas. But in my home city of Baltimore, children from the sprawling, low-income West Baltimore part of the city almost never venture outside their neighborhoods, and even a trip downtown is a major one, usually fraught with uncertainty and tension. These children have no doubt always perceived that the city's middle-class neighborhoods are different from theirs, but I am not sure how they are able to figure out that the gap between them and the middle-class children has grown. The mechanism needs to be local, because perceptions of inequality garnered through television or through social media are more likely to be national in scope and would not be based on local increases in income inequality.

The failure of low-income children to improve their educational outcomes in light of increasing monetary returns to education has been identified as a long-standing puzzle in the literature. Claudia Goldin and Lawrence Katz (2008, figure 1.5 and table 2.7) show that completed years of education for boys stopped rising for children born around 1950, who came of age just when rates of return to education started to strongly rise, and that this has occurred in the face of rising economic returns to high school completion. James Heckman and Paul LaFontaine (2010) and Richard Murnane (2013) show specifically that high school graduation rates drifted downward between 1970 and 2000. Goldin and Katz (2008, pp. 347-50) suggest that this has occurred because primary and secondary schools are failing to provide students with the skills necessary for college, because high school dropouts are especially unprepared, and because financial access to higher education has declined given rising tuitions and other college costs. (4) Alan Krueger ((2003)) likewise believes that credit constraints have hindered educational attainment and that school quality measures, such as class size, have an important impact, while Pedro Cameiro and Heckman (2003) identify deficiencies in preschool investment in both cognitive and noncognitive traits as well as a lack of school choice and school incentives as the primary problems. Murnane (2013) suggests that the decline in the high school graduation rate has been caused by poor skills preparation for students entering high school, coupled with rising high school graduation requirements, and with the rise of the GED, which provides weak training, as an alternative.

But what is missing when this literature is considered is why these barriers to investment in education would be correlated with the level of median income in a state, especially if the culprit is not a lower rate of return to high school completion in high-inequality states, as Kearney and Levine find. (5) They test for differences in school quality using per-student expenditures and pupil/teacher ratios and find that this does not change the result, although these quality measures are admittedly rough. For any of the other above-noted explanations to work, one would need to find that college tuition, credit constraints, GED credentials, or preschool investments differ across states with different levels of income inequality.

In the end, I find Kearney and Levine's paper to be more important for its negative results than for its positive ones. Showing that controlling for a list of the usual suspects as to why so many low-income children fail to complete high school does not significantly reduce the correlation between local income inequality and high school dropout rates is a discouraging but useful finding. The remaining task is to further explore the residual and its sources, and I look forward to reading more research by Kearney and Levine and others on this important topic for public policy.

REFERENCES FOR THE MOFFITT COMMENT

Cameiro, Pedro, and James J. Heckman. 2003. "Human Capital Policy." In Inequality in America: What Role for Human Capital Policies? by James J. Heckman and Alan B. Krueger, edited by Benjamin M. Friedman. MIT Press.

Cunha, Flavio, Irma Elo, and Jennifer Culhane. 2013. "Eliciting Maternal Expectations about the Technology of Cognitive Skill Formation." Working Paper no. 19144. Cambridge, Mass.: National Bureau of Economic Research.

Goldin, Claudia, and Lawrence F. Katz. 2008. The Race between Education and Technology. Belknap Press.

Heckman, James J., and Paul A. LaFontaine. 2010. "The American High School Graduation Rate: Trends and Levels." Review of Economics and Statistics 92, no. 2: 244-62.

Hoxby, Caroline, and Sarah Turner. 2013. "Expanding College Opportunities for High-Achieving, Low Income Students." Discussion Paper no. 12-014. Stanford: Stanford University, Stanford Institute for Economic Policy Research.

Krueger, Alan B. 2003. "Inequality, Too Much of a Good Thing." In Inequality in America: What Role for Human Capital Policies? by James J. Heckman and Alan B. Krueger, edited by Benjamin M. Friedman. MIT Press.

Luttmer, Erzo F. P. 2005. "Neighbors as Negatives: Relative Earnings and Well-Being." Quarterly Journal of Economics 120, no. 3: 963-1002.

Manski, Charles F. 2004. "Measuring Expectations." Econometrica 72, no. 5: 1329-76.

Mumane, Richard J. 2013. "U.S. High School Graduation Rates: Patterns and Explanations." Journal of Economic Literature 51, no. 2: 370-422.

Wilson, William Julius. 1987. The Truly Disadvantaged: The Inner City, the Underclass, and Public Policy. University of Chicago Press.

(1.) Kearney and Levine do not hold family income fixed, but rather the family's education level, race, and family structure. In addition, in most of their analyses they only examine the effects of changes in the 50/10 ratio, not the effects of changes in the 50th percentile, holding constant the 10th percentile. However, their table 3 shows that the same result is obtained for a specification that estimates the effect of the 50/10 ratio, holding constant the 10th percentile. This implies that the way I have stated their central finding is consistent with their results, especially if the 10th percentile is interpreted as a proxy for the income of disadvantaged families, which I believe is one possible interpretation.

(2.) The Luttmer (2005) paper cited by Kearney and Levine shows that lower-income families are unhappier when they live close to higher-income families, but this does not directly relate to perceptions of rates of return.

(3.) Probably the most recent ambitious attempt to gather data on children's and parents' perceptions of the rate of return to education is that of Manski (2004), who has devised survey questions intended to elicit the full distribution of perceived potential earnings outcomes under different levels of education.

(4.) College costs could affect high school dropout rates if teenagers see high school completion as a stepping-stone to college.

(5.) Kearney and Levine show that the actual monetary return to high school completion is lower in high-inequality states than in low-inequality states, but it is lower for children from families at all income levels, not just low-income children.

GENERAL DISCUSSION Benjamin Friedman noted that while it is true that especially today much of the discussion of inequality and mobility does focus on rank mobility, there is certainly a long tradition of focusing on the relationship between inequality and level mobility. There is some discussion along these lines in the economics literature, he noted, but there is even more in the political science literature. One should not think that the relevant trade-off is only inequality versus a relationship to rank mobility; level mobility matters too.

Friedman also suggested that rising college tuitions might well be a relevant factor in a student's decision to drop out of high school. He argued that it is not true that the only rationale for graduating from high school, rather than dropping out, is that the graduate then, with probability equal to 1, takes the kind of job that is available to high school graduates. Graduating from high school in effect presents a fork in the decision tree, with some probability of going directly to work but also some probability of going on to college, and all that then follows. Of course, if one does not graduate from high school, those probabilities are, for all practical purposes, also equal to 0. The rise in college tuitions, at state institutions in particular, he believed, might therefore be relevant to the discussion.

Michael Klein spoke next, suggesting that a high school in an inner city might not be the same as a high school in a suburb. The returns to a high school education might mean something very different, depending on the location. In places with higher inequality, there could be a perception that the school is worse or the school could in fact be worse, and the cost of dropping out might be perceived to be much lower. The concept of a "high school dropout," he explained, might really be a heterogeneous thing in terms of expected income if the student attended a really good or really bad high school.

Janice Eberly was interested in the authors' findings on gender differences, specifically the finding that there is no effect of low socioeconomic status and inequality on girls, but a significant effect on boys. She was also interested in this finding's relationship to a finding from another paper by the authors: that girls of low socioeconomic status in more unequal places are significantly more likely to become young, unmarried mothers. (1) These two results seemed puzzling when put together because the authors were essentially finding that girls of lower socioeconomic status tend to have higher rates of teen pregnancy but that they nonetheless tend to stay in school. Eberly wondered if the explanation for this finding was that the gender effect on education was just so strong that it swamped the potential pregnancy effect, or if policy interventions for teenage mothers in schools were truly effective at keeping them in school, and whether there was something to learn from that fact.

Scott Winship had two comments. First was a general comment about the Great Gatsby Curve, which plots the positive relationship observed between inequality and intergenerational social immobility. He noted that some measurement issues actually weaken the significance of the curve, and highlighted some other research that fails to show a relationship between rank mobility and inequality. Second, Winship wondered why the authors had omitted a finding from an earlier version of their paper, which indicated that when a state's level of intergenerational mobility was entered into the model, it was so collinear with cross-sectional inequality that the authors could not distinguish separately between the effect of inequality and that of mobility. There was no mention of this result in the conference draft, which gave Winship the impression that no covariates the authors examined reduced the effect of inequality.

Valerie Ramey and discussant Miles Corak were of the opinion that most of what affects students' discount rates for the future happens before age 5, so if one were to look at policy prescriptions, they should ideally be targeted to that age group. Ramey pointed to evidence suggesting that these discount rates are probably not inborn, and can be affected by many characteristics of a child's environment, such as whether the parents use cigarettes or other drugs. This would support the notion that targeting policies to children under the age of 5 may help them to favorably revise their future discount rates at an early age, which down the road could make them less likely to drop out of high school.

Martin Baily suggested that it might be beneficial to implement interventions aimed at informing students about what it is like to be a high school dropout versus not being one. If students are simply given information about the options available to them, or what it is like to be in a dropout job versus a graduate job, they might be affected. He cited a paper in which the authors find that simply giving young women information about what it was like to be pregnant and unmarried made them less likely to end up in that situation. (2) Perhaps similar interventions could be applied to students considering dropping out of high school.

Robert Gordon noted that it matters a lot for the 50/10 ratio--the ratio of the 50th and 10th percentiles of the earnings distribution--whether inequality is due to the 50th percentile being too high or the 10th percentile being too low. If the cause is that the 10th percentile is too low, then there may just be a population of single mother-headed households living in poverty in which the mothers happen to drop out of high school; in this case, nothing can be concluded about inequality, as what has been found is simply that these types of families have a higher propensity to drop out of high school.

Gordon also observed that there had not been much discussion about race, which could potentially be important, given that boys and girls were found to have experienced different outcomes. Given that there is a sizable fraction of African American teenage boys in prison who cannot complete high school, he wondered what would happen to the inequality and high school dropout data if African Americans were removed from the sample.

Brad Hershbein wondered if the authors could push the data on high school characteristics a little bit further, particularly for rural versus urban schools. The exercise could perhaps shed some light on the issue of whether there is an information problem or a perception problem, points raised earlier by Baily and Klein, respectively. Either the students know that they don't know (perception problem), or don't know that they don't know (information problem), what Hershbein called a "Rumsfeldian uncertainty," a nod to former U.S. secretary of defense Donald Rumsfeld, who stated, "There are known knowns ... there are known unknowns" during a U.S. Department of Defense news briefing on February 12, 2002.

Abigail Wozniak agreed with Friedman that looking at college tuition costs might be an important component of a student's decision to drop out of high school. Related to Gordon's point about incarceration and crime, Wozniak encouraged the authors to look at some of the work that had been done on the crack epidemic and how it changed expected returns for young men during that period, and subsequently how it has since reversed itself, potentially playing a role in the rising high school completion rates seen in recent years. She cautioned that the authors might be putting too much weight on the explanatory power of their horserace-style regression models, and referred them to the research of Emily Oster, who has done some nice work on the subject.

Justin Wolfers complimented Corak for his handling of the Great Gatsby Curve, which Wolfers admitted he long thought was one of the most interesting stylized facts in all of social science. He believed the paper's framing around whether the Great Gatsby Curve is a causal relationship was an ill-posed question. He explained that rising inequality caused by a rise in the price of inheritable skill would cause the highly skilled to be rich, therefore causing their kids to be well off. On the other hand, rising inequality due to a rise in the price of noninheritable skill would not, meaning that there are just different forms of variation. It might also be the case that "kid quality" is a normal good, meaning that it increases with income, creating a direct link from parents' wealth to child's success.

Wolfers also thought that it was important to be clear about whose behavior the authors were describing. In the despair-based model, the authors are describing the student's decision not to go on to college. Resource constraints, on the other hand, might mean that it is the parents' decision whether the student does not go on to college. Wolfers was also worried that a large proportion of young men whose mothers dropped out of high school might be incarcerated, and therefore not in the data set.

Finally, on the policy implications, Wolfers suggested that, in resource-poor environments, human capital education might not actually be the right investment for some students to make. The authors' policy conclusions seemed to follow only if the rate of return to investing in high school was high for all students.

Melissa Kearney began by addressing some of the policy implications. In his presentation, Corak had suggested focusing on lowering the 50/10 ratio by bringing up the 10th percentile. Kearney fully agreed. There are many reason why improving the material well-being of people at the bottom is important. But somewhat to their surprise, the authors also found that, while being poor is bad, the gap between the poor and the well-off is also bad.

Responding to comments about how early to invest in students, the authors agreed that it was important to invest in kids at an early age. They believed this to be very consistent with their results from the recent Moving to Opportunity for Fair Housing program, which suggested that it was in fact the kids who moved early who got the benefits, and if they moved when they were teens, they essentially missed out on the benefit. However, Kearney believed that it was still important not to give up on struggling teens, and felt uncomfortable with the policy discussion thus far that seemed to be suggesting that the only thing that matters is early childhood education; it cannot be that we just have to give up on kids who are 10 years old and in a bad position, she explained. She was encouraged by some new results coming out of the Chicago Urban Lab's evaluation of the Match Education program, which have shown that intensive tutoring programs with a mentoring component are really improving the graduation rates of some of the most academically disadvantaged kids. Similarly, evaluations of the Pathways to Education program in Toronto have shown that investing resources in high school kids from very disadvantaged areas does tend to increase their high school graduation rates. (3) So yes, Kearney agreed that investing in students early on is great, but argued there are also things that can be done to help teenagers finish high school.

Kearney made it clear that the authors did not use rank mobility, and that they were not interested in "churning for the sake of churning." Conversations among the general public sometimes focus on social mobility from the perspective of rank mobility, and the authors were more interested in kids at the bottom having potential to move up in the income distribution. Part of what the authors wanted to accomplish with their paper was to pivot to focusing on not just upper-level income inequality but also on lower-level income inequality, and not just churning social mobility for the sake of churning, but upward mobility for poor kids.

Some questions were raised about the authors' use of cross-sectional variation. Kearney noted that there is no shortage of papers finding that places with high levels of income inequality have bad outcomes. She argued that the authors were moving beyond that by using individual-level data, by comparing kids from disadvantaged homes in more and less unequal places. It is true, however, that the authors had not randomly assigned income inequality, and they did not have a great instrument for long-term inequality in some places. What they wanted to confirm was that income inequality was having a negative effect on kids at the bottom. They work really hard in the paper to say that it is actually the gap in the distribution that matters, and not something else going on in the state. The authors had run many regressions to show that, empirically, there is something about the 50/10 ratio that is related to the dropout rate of disadvantaged kids, and that it is a more important predictor than, say, the incarceration rate or the share of manufacturing workers.

Kearney noted that where this research needed to go next was to figure out how its findings show up "on the ground." Do the neighborhoods where these kids live have worse schools? Do they have thinner job networks? The authors would like to look at tax data to get at more local geography, and to have ethnographers and social psychologists interview the kids with the authors' hypotheses in mind. The authors felt equipped to handle some of the questions raised in the room, while they felt other questions needed to be addressed by other social scientists. Phillip Levine added that there appears to be interesting empirical regularity that seems like it is suggesting something consistent with the model the authors were describing, but noted that they certainly would need to go a lot further before actually drawing specific conclusions about the mechanisms.

(1.) Melissa S. Kearney and Phillip B. Levine, "Income Inequality and Early Nonmarital Childbearing," Journal of Human Resources 49, no. 1 (2014): 1-31.

(2.) Melissa S. Kearney and Phillip B. Levine, "Media Influences on Social Outcomes: The Impact of MTV's 16 and Pregnant on Teen Childbearing," American Economic Review 105, no. 12(2015): 3597-632.

(3.) See for example, Philip Oreopoulos, Robert S. Brown, and Adam M. Lavecchia, "Pathways to Education: An Integrated Approach to Helping At-Risk High School Students," Working Paper no. 20430 (Cambridge, Mass.: National Bureau of Economic Research, 2014).

MELISSA S. KEARNEY

University of Maryland

PHILLIP B. LEVINE

Wellesley College

(1.) Social mobility is a concept that includes the likelihood of moving up or down in the income distribution, which is specifically labeled as economic mobility, but may also include changes in position in other distributions as well, like educational attainment, occupational status, and health. We restrict our attention to economic mobility in this paper, but adopt the common approach of using the terms "social mobility" and "economic mobility" interchangeably. The specific mobility measure used here is taken from Chetty and others (2014a), and reflects the correlation in the income rank of parents and their adult child. It is worth noting that if we replaced the Gini coefficient with alternative measures of income inequality, we see the same relationship. In particular, the figure looks the same using the 50/10 ratio of income, which is our primary measure of income inequality in this paper, as described below.

(2.) For example, in a conversation at The Atlantic's 2004 Economy Summit, Jason Furman (2014) stated, "I think we think all else being equal, more inequality will lead to less relative mobility." Sawhill (2014) asserts that when the rungs of the ladder are farther apart, it gets harder to climb them.

(3.) The blog posts can be found at www.brookings.edu/blog/social-mobility-memos.

(4.) Becker and Posner (2012, 2013) make the same point.

(5.) Mankiw (2013b) makes this point clearly by offering as an example the skill of chess players. If we have one group of chess players who are all of roughly comparable ability, then who wins and loses the matches will be closer to a random draw, and mobility through the rankings will be high. If another group of chess players has some with greater ability and others who are weaker, then inequality in wins and losses will be higher, and mobility will be lower.

(6.) For instance, using data from the Integrated Public Use Microdata Series, we found that the correlation in the 50/10 ratio between the 1980 and 2000 census years averaged .74 across states (Kearney and Levine 2014).

(7.) We distinguish youth respondents by their parents' educational attainment and define "permanent income" to be the average of all inflation-adjusted values of family income observed 15 or more years after the original 1979 survey, when youth respondents are in their late 20s or older. The sample used in that exercise includes all 8,226 respondents who lived with at least one of their parents at age 14 and who provided any income values in the 1994 survey or beyond. We assign the level of inequality to each respondent based on the respondents' 1979 state of residence.

(8.) These variables include the state unemployment rate at age 16, the state minimum wage, state education policies (compulsory schooling age and indicators for high school exit exam requirements), state welfare policies (family cap and maximum benefit from Aid to Families with Dependent Children or Temporary Assistance for Needy Families for a family of three), state abortion policies (Medicaid funding, parental notification/consent, and mandatory delay laws), and an indicator variable for State Children's Health Insurance Program implementation and Medicaid family planning waiver implementation. Information on exit exam requirements by state and year is taken from Dee and Jacob (2007) and Dietz (2010). Information on compulsory school laws by state and year is obtained from the National Center for Education Statistics' "Digest of Education Statistics" (various years; https://nces. ed.gov/programs/digest). Detailed source information and notes about the construction of the other variables in this list are provided in Kearney and Levine (2012). We have also experimented with interacting all the policy variables with SES indicators and found that the results were unaltered by doing so. In addition, we include dummy variables indicating the data set that the observation came from.

(9.) A possible concern is that inequality ratios are driven by persistent high school graduation rates in a place, which would induce an endogeneity problem with this specification. To address that possibility, we reran our regression analyses with 50/10 ratios constructed just among high school graduates. This analysis yielded similar findings to those reported below.

(10.) For all data sets other than High School and Beyond, geographic identifiers are only available for those with restricted-use data agreements. This means that we are not able to share our data with other researchers, although we are happy to provide our programs so that those who are able to obtain their own agreement can follow our steps. Formal state identifiers are not available at all for High School and Beyond, but researchers, such as Grogger (1996), have identified ways to provide educated guesses of state of residence for survey respondents. We are grateful to Jeff Grogger for providing us with his data indicating state identifiers for these data.

(11.) This survey also included more than 28,000 high school seniors in 1980, but we do not use them because many high school dropouts never make it to be seniors in high school; using these data would introduce substantial selection bias.

(12.) Sample attrition reduces the sample size to 61,067. Missing educational attainment reduces it further to 59,286. Missing maternal education brings the final sample size down to 53,150.

(13.) The online appendixes for this and all other papers in this volume may be found at the Brookings Papers web page, www.brookings.edu/bpea under "Past Editions."

(14.) Total household income in the census is defined as the sum of eight categories: (i) wages, salary, commissions, bonuses, or tips from all jobs; (ii) self-employment net income; (iii) interest, dividends, net rental income, royalty income, or income from estates and trusts; (iv) Social Security or Railroad Retirement Board benefits; (v) Supplemental Security Income; (vi) any public assistance or welfare payments from the state or local welfare office; (vii) retirement, survivor, or disability pensions other than Social Security; and (viii) any other sources of income received regularly, such as Veterans Affairs payments, unemployment compensation, child support, or alimony.

(15.) For the relevant percentiles necessary to construct the income ratios, see U.S. Census Bureau, table IE-1, "Selected Measures of Household Income Dispersion" (https:// www.census.gov/hhes/www/income/data/historical/inequality).

(16.) States fall into the following categories, with the 50/10 ratio in parentheses. Low inequality: UT (3.40), NV (3.49), VT (3.54), ID (3.59), NH (3.61), NE (3.71), IA (3.72), WI (3.72), AK (3.75), OR (3.77), WY (3.78), ME (3.80), IN (3.80). Middle inequality: CO (3.81), AZ (3.81), ND (3.82), HI (3.82), SD (3.84), FL (3.85), MT (3.86), DE (3.87), KS (3.88), MN (3.90), WA (3.92), MD (3.98), VA (4.03), PA (4.03), CT (4.06), MO (4.07), OH (4.08), CA (4.15), OK (4.19), NC (4.19), NM (4.21), NJ (4.22), MI (4.22), WV (4.25), AR (4.28). High inequality: IL (4.29), RI (4.38), TX (4.40), TN (4.44), SC (4.45), MA (4.52), KY (4.54), MS (4.59), GA (4.66), NY (4.77), AL (4.85), LA (5.03), DC (5.66).

(17.) We have also estimated these models separately by race and ethnicity, but the data were not sufficiently powerful to yield statistically significant differences across groups.

(18.) We are agnostic as to whether this decision ultimately rests with the adolescent, his parent, or some combination thereof.

(19.) Although our analysis focuses on cross-sectional variation, our framework also yields some potential insights regarding trends in educational attainment over time. Despite the growing rate of return on education that has been taking place over time, the high school dropout rate has been roughly constant, until, perhaps, recently (Goldin and Katz 2010). According to our theoretical framework, increased educational incentives associated with higher educational wage premiums may be counteracted with a greater "desperation effect" associated with growing income inequality, generating an ambiguous prediction regarding educational attainment. As noted above, though, the 50/10 ratio has been relatively flat during the past few decades, which is consistent with generally unchanged rates of dropping out of high school in our framework.

(20.) Chetty and Hendren (2015) show that low-income children who move to a better neighborhood, as measured by the outcomes of those children already living there, experience improved outcomes themselves, with those moving at a younger age experiencing greater gains. They use methods including sibling differences and family fixed effects to provide statistical identification and they show that these childhood moves generate greater gains when their new community is characterized by less concentrated poverty, less income inequality, better schools, a larger share of two-parent families, and lower crime rates. This part of the analysis, however, does not attempt to determine which, if any, of these place-based characteristics have a causal relationship with child outcomes later in life. Nor does it attempt to figure out whether income inequality, per se, has a negative effect on the outcomes of low-income children, and if so, through what mechanisms.

(21.) We describe the findings of that experiment, and how they relate to our findings, in our discussion section below.

(22.) The income segregation measure captures the extent to which households of different income percentiles are evenly distributed among residential locations. For example, if 10 percent of a census tract is below the 10th percentile, that indicates no segregation at that level. The overall statistic essentially calculates this for all 100 percentiles and then aggregates up, putting more weight near the middle of the distribution where there should be more equality. The segregation index is maximized if and only if there is no variation in income within any neighborhood. The segregation index is minimized if and only if within each neighborhood, the income distribution is identical to that in the population. This Reardon (2011) measure has the desirable property that it is insensitive to rank-preserving changes in the income distribution.

(23.) We thank Elizabeth Cascio for generously sharing the historical data she compiled on per-pupil expenditures and pupil/teacher ratios.

(24.) We obtained these data and the fraction of children with a single parent from the online appendix to Chetty and others (2014a).

(25.) Incarceration data are compiled by the U.S. Department of Justice, Office of Justice Programs, and were downloaded from http://www.ojp.usdoj.gov. Poverty rate data come from the U.S. Census Bureau's "Historical Poverty Tables" at http://www.census.gov/hhes/ www/poverty/data/historical/people.html. Manufacturing data were obtained from the online appendix to Chetty and others (2014a).

(26.) We have also estimated many of the horserace specifications at the MSA level and confirmed that defining the geographic area at this level does not alter the qualitative results. Not all alternative characteristics considered in the main state-level regressions are available at the MSA level. Appendix table 1 reports results from including the interaction of SES with alternative measures of the income distribution. Appendix table 2 reports results from including the interaction of SES with segregation measures. Appendix table 3 reports results from including the interaction of SES with the fraction of children living with single parents and the fraction of employment in the manufacturing sector. The results correspond to the results from the state-level regressions: The estimated coefficient on the 50/10 interaction is not qualitatively changed from the addition of the new interaction. Furthermore, in all regressions but one, the estimated coefficient on the added interaction term is not statistically different from zero. The one exception is for the interaction of low SES with racial segregation measured at the MSA level. In this regression, MSA-level racial segregation appears to be positively related to dropout rates. Future work should pursue an investigation of mechanisms and look at different levels of geography. For the purposes of the present paper, the finding is upheld that there is an empirical relationship between lower-tail inequality and the likelihood that a low-SES boy drops out of school, and that does not appear to be driven by confounding factors at the aggregate level.

(27.) The only minor difference between this specification and that in table 1 is that we omit ail policy variables since we will subsequently be restricting the sample to just two data sets, leaving us with very limited variation across states over time. As the results indicate, dropping those variables has virtually no impact on the findings.

(28.) Multiplying the point estimate of -4.38 from the low-SES interaction term in column 4 with the point estimate of -0.005 on the AFQT variable from column 3 yields 0.022, suggesting that the lower AFQT scores of boys in high-inequality states would lead to a 0.022 percentage point relative increase in dropout rates, which is exactly the difference we see between columns 2 and 3. This is another way to see that differences in AFQT capture about one-third of the estimated effect of inequality on the dropout rates of low-SES boys.

(29.) One might think that a higher level of early, nonmarital childbearing would lead to increased dropout rates among girls. However, existing evidence suggests that higher high school dropout rates among teen mothers is more likely to reflect selection issues than a causal effect of teen motherhood. Given our reading of that evidence and literature, which we summarize in Kearney and Levine (2012), we do not view it as inconsistent or surprising that in our earlier paper we found that low-SES girls in more unequal states are more likely to become young mothers, but in this paper we do not find that they are more likely to drop out of school.

Table 1. The Impact of Long-Term Inequality, by State, on
Educational Attainment by Age 20, by Socioeconomic Status
and Gender (a)

                             (1)          (2)           (3)
                         High school      GED       High school
                         dropout (b)   attainment    graduate

                                          All

Percent in category         10.1          4.8          85.1
50/10 ratio * mom is        0.023       -0.006        -0.017
  high school dropout      (0.015)      (0.010)       (0.016)
50/10 ratio * mom is        0.018        0.010        -0.028
  high school graduate     (0.014)      (0.008)       (0.013)

                                          Boys

Percent in category         11.2          5.5          83.3
50/10 ratio * mom is        0.041       -0.018        -0.022
  high school dropout      (0.015)      (0.015)       (0.018)
50/10 ratio * mom is        0.025        0.013        -0.037
  high school graduate     (0.017)      (0.009)       (0.016)

                                         Girls

Percent in category          9.1          4.1          86.8
50/10 ratio * mom is        0.007        0.005        -0.012
  high school dropout      (0.019)      (0.010)       (0.022)
50/10 ratio * mom is        0.009        0.006        -0.015
  high school graduate     (0.014)      (0.011)       (0.016)

Sources: National Educational Longitudinal Survey; High School and
Beyond; Educational Longitudinal Survey; National Longitudinal
Survey of Youth, 1979 and 1997.

(a.) Additional explanatory variables in each regression include
maternal educational attainment, gender, race or ethnicity, an
indicator variable for living with a single parent at age 14, the
state unemployment rate at age 16, the state minimum wage, state
education policies, state welfare policies, state abortion
policies, indicator variables for State Children's Health Insurance
Program implementation and Medicaid family planning waiver, and
state and cohort fixed effects. See the text for specific state
education, welfare, and abortion policies. Standard errors in
parentheses are clustered by state. The total sample size is
53,150, with 25,816 boys and 27,334 girls.

(b.) The p value of a test comparing the equality of coefficients
in column 1 by gender in response to a change in the interaction
between the 50/10 ratio and mom is high school dropout is 0.086.

Table 2. The Impact of Long-Term Inequality, by Metropolitan
Statistical Area, on the Likelihood of Dropping Out of High
School, by Socioeconomic Status and Gender (a)

                            (1)       (2)       (3)
                            All      Boys      Girls

Percent in category (b)    12.3      14.1      10.6
50/10 ratio * mom is       0.036     0.073     0.002
  high school dropout     (0.013)   (0.018)   (0.016)
50/10 ratio * mom is       0.020     0.028     0.009
  high school graduate    (0.011)   (0.016)   (0.012)

Sources: Educational Longitudinal Survey; National Longitudinal
Survey of Youth, 1979 and 1997.

(a.) Additional explanatory variables in each regression include
maternal educational attainment, race or ethnicity, an indicator
variable for living with a single parent at age 14, and MSA and
cohort fixed effects. The p value of a test comparing the equality
of coefficients by gender for high school dropout mothers is
0.0004. Standard errors in parentheses are clustered by MSA. The
total sample size is 22,304, with 11,042 boys and 11,262 girls.

(b.) High school dropouts as a percent of the total sample.

Table 3. The impact of Alternative Income Distribution Measures
on Boys' Likelihood of Dropping Out of High School, by
Socioeconomic Status (a)

                                                       (3)
                               (1)       (2)     10th percentile
                              50/10     90/50       of income
                              ratio     ratio    distribution (b)

Correlation between 50/10               0.67          -0.63
  ratio and characteristic
50/10 ratio * mom is          0.041     0.058         0.041
  high school dropout        (0.015)   (0.025)       (0.024)
50/10 ratio * mom is          0.025     0.023         0.024
  high school graduate       (0.017)   (0.019)       (0.021)
State characteristic * mom     --       0.069         0.0002
  is high school dropout               (0.072)       (0.005)
State characteristic * mom     --       0.004         -0.001
  is high school graduate              (0.050)       (0.003)

                                                      (5)
                                   (4)            Income share
                             50th percentile       of the top
                                of income         1 percent of
                             distribution (b)   the distribution

Correlation between 50/10         -0.20               0.38
  ratio and characteristic
50/10 ratio * mom is              0.041              0.042
  high school dropout            (0.016)            (0.018)
50/10 ratio * mom is              0.024              0.029
  high school graduate           (0.017)            (0.017)
State characteristic * mom       -0.0001             -0.001
  is high school dropout         (0.001)            (0.003)
State characteristic * mom       -0.0003             -0.001
  is high school graduate        (0.001)            (0.002)

Sources: National Educational Longitudinal Survey; High School
and Beyond; Educational Longitudinal Survey; National
Longitudinal Survey of Youth, 1979 and 1997.

(a.) See the notes to table 1. Interacted state characteristics
are listed in the column headings.

(b.) Incomes are measured in ten-thousands of dollars.

Table 4. The Impact of Educational Wage Premiums on Boys'
Likelihood of Dropping Out of High School, by Socioeconomic
Status (a)

                                              (2)            (3)
                                          High school      College
                                          graduate to    graduate to
                                  (1)     high school    high school
                                 50/10    dropout wage     graduate
                                 ratio      premium      wage premium

Correlation between 50/10
  ratio and characteristic                    0.27           0.35
50/10 ratio * mom is high        0.041       0.046          0.037
  school dropout                (0.015)     (0.015)        (0.017)
50/10 ratio * mom is high        0.025       0.023          0.022
  school graduate               (0.017)     (0.018)        (0.019)
State characteristic * mom is     --         -0.117         0.039
  high school dropout                       (0.076)        (0.043)
State characteristic * mom is     --         0.029          0.024
  high school graduate                      (0.062)        (0.043)

Sources: National Educational Longitudinal Survey; High School
and Beyond; Educational Longitudinal Survey; National
Longitudinal Survey of Youth, 1979 and 1997.

(a.) See the notes to table 1. Interacted state characteristics
are listed in the column headings.

Table 5. The Impact of Measures of Segregation on Boys'
Likelihood of Dropping Out of High School, by Socioeconomic
Status (a)

                                                 (2)
                                     (1)       Racial
                                    50/10    segregation
                                    ratio       index
Correlation between 50/10 ratio
  and characteristic                            0.05
50/10 ratio * mom is high school    0.041       0.040
  dropout                          (0.015)     (0.017)
50/10 ratio * mom is high school    0.025       0.025
  graduate                         (0.017)     (0.015)
State characteristic * mom is        --        0.0008
  high school dropout                         (0.0008)
State characteristic * mom is        --        -0.0008
  high school graduate                        (0.0004)

                                       (3)           (4)
                                     Income        Poverty
                                   segregation   segregation
                                      index         index
Correlation between 50/10 ratio
  and characteristic                  0.47          0.26
50/10 ratio * mom is high school      0.040         0.037
  dropout                            (0.016)       (0.017)
50/10 ratio * mom is high school      0.025         0.024
  graduate                           (0.017)       (0.017)
State characteristic * mom is         0.050         0.281
  high school dropout                (0.396)       (0.496)
State characteristic * mom is        0.0001         0.050
  high school graduate               (0.204)       (0.260)

Sources: Chetty and others (2014a, 2014b); National Educational
Longitudinal Survey; High School and Beyond; Educational
Longitudinal Survey; National Longitudinal Survey of Youth,
1979 and 1997.

(a.) See the text and the notes to table 1. Interacted state
characteristics are listed in the column headings.

Table 6. The Impact of Potential Mediating Factors on Boys' Likelihood
of Dropping Out of High School, by Socioeconomic Status (a)

                                             (2)
                               (1)        Per-pupil           (3)
                              50/10      educational     Pupil/teacher
                              ratio    expenditure (b)     ratio (c)

Correlation between 50/10                   0.17             -0.24
  ratio and characteristic
50/10 ratio * mom is          0.041         0.036            0.029
  high school dropout        (0.015)       (0.015)          (0.015)
50/10 ratio * mom is          0.025         0.016            0.020
  high school graduate       (0.017)       (0.012)          (0.015)
State characteristic * mom     --          -0.001           -0.003
  is high school dropout                   (0.003)          (0.002)
State characteristic * mom     --          -0.005            0.004
  is high school graduate                  (0.002)          (0.002)

                                                  (5)
                                  (4)         Fraction of
                                Social       children with
                             capital index   single parents

Correlation between 50/10        -0.44            0.64
  ratio and characteristic
50/10 ratio * mom is             0.045           0.036
  high school dropout           (0.019)         (0.019)
50/10 ratio * mom is             0.016           0.015
  high school graduate          (0.019)         (0.022)
State characteristic * mom       0.008           0.092
  is high school dropout        (0.008)         (0.247)
State characteristic * mom      -0.007           0.192
  is high school graduate       (0.005)         (0.221)

Sources: Chetty and others (2014a); National Educational
Longitudinal Survey; High School and Beyond; Educational
Longitudinal Survey; National Longitudinal Survey of Youth, 1979
and 1997, Per-pupil expenditures and pupil/teacher ratios were
obtained from historical data compiled by Elizabeth Cascio.

(a.) See the notes to table 1. Interacted state characteristics are
listed in the column headings.

(b.) The per-pupil expenditure is measured in thousands of dollars.

(c.) Pupil/teacher ratios are divided by 10.

Table 7. The Impact of Potentially Confounding State
Characteristics on Boys' Likelihood of Dropping Out
of High School, by Socioeconomic Status (a)

                               (1)
                              50/10          (2)              (3)
                              ratio    Percent minority   Poverty rate

Correlation between 50/10                    0.41             0.63
  ratio and characteristic
50/10 ratio * mom is high     0.041         0.053            0.056
  school dropout             (0.017)       (0.018)          (0.026)
50/10 ratio * mom is high     0.024         0.021            0.021
  school graduate            (0.012)       (0.017)          (0.021)
State characteristic * mom     --          -0.0007           -0.003
  is high school dropout                   (0.0004)         (0.004)
State characteristic * mom     --           0.0001           0.001
  is high school graduate                  (0.0003)         (0.002)

                                                     (5)
                                   (4)           Fraction of
                              Incarceration     employment in
                             per 1,000 people   manufacturing

Correlation between 50/10          0.44             -0.10
  ratio and characteristic
50/10 ratio * mom is high         0.043             0.043
  school dropout                 (0.021)           (0.015)
50/10 ratio * mom is high         0.008             0.024
  school graduate                (0.014)           (0.017)
State characteristic * mom        -0.047            0.221
  is high school dropout         (0.092)           (0.148)
State characteristic * mom        0.066             0.012
  is high school graduate        (0.045)           (0.105)

Sources: U.S. Department of Justice; U.S. Census Bureau; Chetty
and others (2014a); National Educational Longitudinal Survey;
High School and Beyond; Educational Longitudinal Survey; National
Longitudinal Survey of Youth, 1979 and 1997.

(a.) See the notes to table 1. Interacted state characteristics
are listed in the column headings.

Table 8. The Relationship between Socioeconomic Status,
Inequality, and Armed Forces Qualifying Test Scores for Boys (a)

                               (1)            (2)
                            All five       NLSY79 and
Sample                    data sets (b)    NLSY97 (c)

                           High school    High school
Dependent variable        dropout rate    dropout rate

Mean                          0.112          0.177
50/10 ratio * mom is          0.042          0.067
  high school dropout        (0.016)        (0.029)
50/10 ratio * mom is          0.024          0.077
  high school graduate       (0.018)        (0.025)
Armed Forces Qualifying        --              --
  Test

                              (3)             (4)
                           NLSY79 and      NLSY79 and
Sample                       NLSY97          NLSY97
                                          Armed Forces
                          High school      Qualifying
Dependent variable        dropout rate   Test score (d)

Mean                         0.177            50.7
50/10 ratio * mom is         0.045           -4.48
  high school dropout       (0.028)          (2.49)
50/10 ratio * mom is         0.057           -4.10
  high school graduate      (0.023)          (2.27)
Armed Forces Qualifying      -0.005            --
  Test                      (0.0002)

Sources: National Educational Longitudinal Survey; High School and
Beyond; Educational Longitudinal Survey; National Longitudinal
Survey of Youth, 1979 and 1997.

(a.) Standard errors, in parentheses, are clustered by state.

(b.) The five data sets used are listed in the sources line. The
estimates in column 1 differ slightly from previous estimates
because no state-level policy variables are included.

(c.) The sample used in column 2 is restricted to those
observations with available Armed Forces Qualifying Test scores to
compare to column 3. The sample size for columns 2 through 4 is
7,955.

(d.) Armed Forces Qualifying Test scores are reported as
standardized percentile rankings.