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

Kearney, Melissa S. ; Levine, Phillip B.

ABSTRACT It is widely documented that places with higher levels of income inequality have lower rates of social mobility. But it is an open question whether and how higher levels of inequality actually lead to lower rates of mobility. We propose that one channel through which higher rates of income inequality might lead to lower rates of upward mobility is lower rates of human capital investment among low-income individuals. Specifically, we posit that greater levels of income inequality could lead low-income youth to perceive a lower rate of return on investment in their own human capital. Such an effect would offset any potential "aspirational" effect coming from higher educational wage premiums. The data are consistent with this prediction: Individuals from low socioeconomic backgrounds are more likely to drop out of school if they live in a place with a greater gap between the bottom and middle of the income distribution. This finding is robust in relation to a number of specification checks and tests for confounding factors. This analysis offers an explanation for how income inequality might lead to a perpetuation of economic disadvantage, and it has implications for the types of interventions and programs that would effectively promote upward mobility among youth of low socioeconomic status.

International comparisons show that the United States is a country that ranks high in its level of income inequality and low in its level of social mobility. Miles Corak (2006)--building on the theoretical contributions made by Gary Solon (2004)--was the first to show empirically that this relationship is part of a broader pattern that exists across countries. Countries with high levels of inequality also tend to exhibit lower rates of social mobility, as measured by greater intergenerational income persistence.

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Alan Krueger (2012) popularized this relationship as the "Great Gatsby Curve." Using data on the 50 states, we construct a Great Gatsby Curve for the United States. Figure 1 shows that states with greater levels of income inequality tend to have lower rates of social mobility. (1) This positive cross-sectional relationship between rates of income inequality and intergenerational income persistence often leads to claims about causality, implying that higher rates of income inequality lead to lower rates of mobility. (2) However, it is very much an open question as to whether income inequality actually causes lower rates of social mobility, and if so, through what channels.

In this paper we propose, and investigate, one important channel--curtailed investment in human capital--through which higher rates of income inequality might lead to lower rates of upward economic mobility for individuals from backgrounds of low socioeconomic status (SES). We hypothesize that income inequality can negatively affect the perceived returns on investment in education from the perspective of an economically disadvantaged adolescent, either through an effect on actual returns or through an additional effect on the perception of these returns. The notion we have in mind is that a greater gap between the bottom and the middle of the income distribution might lead to a heightened sense of economic marginalization, such that an adolescent at the bottom of the income distribution does not see much value in investing in his or her human capital. We call this "economic despair." This could be due to adverse neighborhood or school conditions driven by elevated rates of income inequality, but it need not be. This mechanism offers an explanation within the standard human capital framework of decisionmaking for why greater inequality--which might reflect in part a greater return on human capital investment--does not necessarily lead to greater rates of educational attainment for certain segments of the population.

To empirically explore this idea, we investigate whether places characterized by higher rates of income inequality have situations that lead to lower rates of high school graduation among individuals from low-SES families, controlling for individual and family demographics and broader contextual factors. Greater educational attainment is a key pathway along which an individual from a low-income background can move up in the income distribution and obtain a middle-class life, or potentially even higher. If children from low-income backgrounds are responding to large gaps between their economic reality and middle-class life by dropping out of school, that would perpetuate economic disadvantage and impede rates of upward mobility. It would be a mechanism whereby income inequality leads to less mobility, and might explain why certain places regularly seem to have high inequality and low mobility, or vice versa. Furthermore, it would have profound implications for society and the types of interventions needed to break the cycle.

Our discussion in section I of relevant background facts and ideas addresses a number of important issues. We describe key reasons why the Great Gatsby Curve might not reflect a causal negative relationship between income inequality and rates of social mobility. First, there is the well-known empirical complication that the level of income inequality in a place is correlated with many other factors that also might have an impact on rates of social mobility. Empirically identifying which factor is driving what is extremely difficult. Furthermore, some have argued that the relationship might be merely descriptive, and not actually consequential.

We also describe an empirical puzzle that others have pointed out, namely, that income inequality has been rising for many decades with no observable decrease in social mobility rates. We describe two features of our model and empirical results that might help resolve this puzzle. First, we argue that adolescents' perceptions and expectations about the society around them and their place in it are likely shaped by the more permanent features of the environment in which they grow up, including long-term measures of inequality. Transitory or very recent changes in inequality are less likely to have a profound effect on adolescents' perceptions and experiences. It might be the case that the effects of rising income inequality are not yet manifested in observed rates of social mobility. Second, we propose that lower-tail income inequality (as captured by the ratio of household income at the 50th and 10th percentiles of the distribution--the "50/10 ratio") is more relevant to thinking about upward mobility than is inequality at the top of the distribution. Lower-tail income inequality has been fairly flat during recent decades.

In section II, we present a stylized model of the decision to drop out of high school. This simple model generates the possible existence of both the "aspirational" and "despair" effects of greater levels of income inequality within an otherwise-standard human capital investment framework. In this section we also review related conceptual models.

In sections III and IV, we then turn to a detailed description of our empirical analysis and results. We use individual-level data pooled from five national surveys to investigate how income inequality affects the rate at which low-SES youth drop out of high school, controlling for individual background characteristics and aggregate-level contextual factors. The data provide robust evidence that higher levels of lower-tail income inequality lead boys from low-SES households to drop out of high school with greater frequency, controlling for a rich set of individual- and state-level characteristics. These data separately identify a negative effect of a higher high school wage premium on high school dropout rates and a positive effect of lower-tail income inequality on high school dropout rates. These two offsetting effects are consistent with our modified human capital investment model, in which inequality has competing aspirational and despair effects.

We also report the results from a number of alternative specifications. First, we investigate whether the observed relationship between income inequality and dropout rates is being driven by a number of potential confounding factors, such as other features of the income distribution (including upper-tail income inequality), aggregate poverty rates, and incarceration rates. Second, we devote considerable attention to the potential mechanisms that drive the observed empirical relationship between lower-tail income inequality and the decision of low-SES youth to drop out of school. The data do not offer support for a number of potential explanations for the link--including, most notably, residential segregation or eroded public school funding. Although we are ultimately unable to empirically establish a precise mechanism, the empirical relationship that we document is consequential, implying that greater levels of income inequality can perpetuate lower rates of social mobility, in part by leading low-income youth to engage in more dropout behavior. We conclude with a discussion of policy implications.

I. Background

The cross-sectional correlation between income inequality and intergenerational income persistence (which indicates a lack of social mobility) is not necessarily a causal relationship. In this section, we first elaborate on these points. Second, we discuss what measures of income inequality are likely most relevant to rates of upward mobility for low-income adolescents. Third, we explain how these observations might be relevant to the Ending that social mobility rates do not appear to have fallen during recent decades. Fourth, we describe the cross-sectional relationship between income inequality and high school dropout rates. These discussions set the stage for us to then move on to a discussion of our proposed model characterizing the educational investment decisions of adolescents.

I.A. Interpreting the Cross-Sectional Correlation between Inequality and Mobility

One of the fundamental tenets of empirical economics is that correlation is not causation. As basic as this point is, it is one of which we often have to remind ourselves. For instance, in pathbreaking work on the measurement of mobility in the United States, Raj Chetty and others (2014a) report that the strongest correlates of high mobility areas are (i) less residential segregation, (ii) less income inequality, (iii) better primary schools, (iv) greater social capital, and (v) greater family stability. As an empirical statement of correlation, these are interesting findings. However, as the authors themselves emphasize, they are not indicative of causal relationships. They provide some insight into areas where further exploration should start--although not end--into understanding how the characteristics of a place might determine individual-level outcomes.

Unfortunately, in measuring outcomes that reflect economic disadvantage, many things are correlated, making it nearly impossible to determine what is actually driving these relationships. These correlations raise many questions and suggest a number of possible explanations. In May 2015, the Brookings Institution, as part of its Social Mobility Memos blog series, featured a series of seven blogs about the Great Gatsby Curve in which various authors offered other correlational observations as potential explanations for what is really causing low rates of upward mobility, including single-parent households, the failure to adequately invest in early childhood education, the breakdown of civic institutions, cultural norms, and the like. (3) The bottom line is that the evidence available to date has provided documentation of a negative correlation between inequality and mobility along with a host of other things, all of which are interesting, but none of which pushes the bar in terms of what can be presumed to be causal. To inform public policy, however, we really need to know about causal pathways.

Furthermore, the negative correlation between inequality and mobility may simply reflect something about the composition of the population, as noted by Corak (2013). It may not be that one causes the other, but rather that both high inequality and low mobility reflect underlying population characteristics. Gregory Mankiw (2013a) observes that low social mobility could occur even if there were equality of opportunity because of the inheritability of talent, intellect, and interpersonal skills. (4) If the entire population had equal inherited skills, inequality would be low and mobility would be great because realizing higher or lower economic outcomes would be largely the result of chance. If, however, a population comprises individuals with a large degree of variation in talents and abilities, then we might expect both high inequality in income and high persistence in income between parents and children, even in a full meritocracy. (5) This interpretation of the relationship has drastically different policy implications than if it reflects causation.

I.B. The Relevant Measure of Income Inequality for Upward Mobility Consequences

This paper is motivated to a large degree by the question of seemingly fixed differences across places. Why do some places consistently have high inequality with low mobility, and other places consistently have low inequality with high mobility? Taking an international perspective, year after year, the United States and the United Kingdom--generally considered low-mobility countries--have among the highest rates of income inequality for high-income countries, while Finland and Norway--generally considered high-mobility countries--tend to have low rates of income inequality. In the United States, we do not have annual measures of mobility, but certain places consistently have high rates of income inequality--for example, New York and Washington--while other places do not. (6)

This way of describing the situation makes it clear that we should be focused on long-standing differences in inequality, not year-to-year changes. In our conceptual framework and our empirical analysis, we focus on the permanent or semipermanent economic and cultural landscape in the place where an adolescent lives, as opposed to short-term fluctuations. If a state experiences a temporary decrease in income inequality, it is unlikely, for example, that neighborhoods will change sufficiently quickly and visibly that either economic opportunities or perceptions thereof will be altered. We thus explicitly refer to income inequality as a "fixed" characteristic of a place, and our empirical analysis reflects this.

Furthermore, as an empirical fact, there is much more cross-sectional variation in lower-tail income inequality across states, as compared with the situation within a state over time. In the income data we describe below--which represent the 1980, 1990, and 2000 censuses--we find that the average standard deviation in the 50/10 ratio across states (averaged over time) is 0.43. Using the same data, we find that the average standard deviation in the 50/10 ratio over time within a state (averaged across states) is much lower, at 0.16.

Beyond the issue of permanent-versus-transitory characteristics, there is an important question about what is the most relevant inequality metric for economic mobility. We argue that the gap between the bottom and the middle of the income distribution is more relevant for the decisions of low-SES youth than the gap between the bottom and the top of the income distribution. We are explicitly interested in the upward economic mobility of low-SES children; and for children born into poverty or low-income families, we expect that their point of reference is more likely to be the middle of the distribution rather than the top. If the Great Gatsby Curve captures behavioral effects associated with growing inequality and the likelihood of moving up the economic ladder for those near the bottom, we propose that the 50/10 ratio is the more relevant measure of income inequality. As our results below show, the data support this supposition.

I.C. The Mismatch between Time Series and the Cross-Sectional Patterns of the Inequality-Mobility Relationship

The descriptive evidence on the relationship between income inequality and mobility presents something of a paradox. As we have described, there is a relationship in the cross section, but there does not seem to be a similar relationship across time. The overall rate of income inequality in the United States has generally been rising since the 1970s. If inequality causally led to a decrease in mobility, one would expect to see the increase in income inequality begin to appear in mobility trends at some point. In terms of our earlier discussion, one might expect continuing increases in income inequality over many years to eventually change the economic and cultural landscape in a way that would lead to an erosion of social mobility. However, recent evidence from Chul-In Lee and Solon (2009), using the Panel Study of Income Dynamics, and from Chetty and others (2014b), using linked parent/child tax records, shows no reduction in social mobility in recent decades. Though this evidence is not the final word on the matter, and critics have pointed out limitations, the finding that economic mobility does not appear to have fallen raises the question of whether inequality and mobility are causally finked after all.

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These facts are documented in figure 2, which reports trend data on social mobility from Chetty and others (2014b) and Lee and Solon (2009), along with the trend in two measures of income inequality in the United States: the 90/50 ratio and the 50/10 ratio (which reflect ratios of different percentiles of the income distribution). For the 90/50 and 50/10 ratios, the horizontal axis in figure 2 reflects the year in which income is measured. For the mobility measure taken from Chetty and others (2014b), year reflects birth cohort; for the mobility measure taken from Lee and Solon (2009), year reflects the year in which the son's income was recorded. Neither of the two mobility measures shows any obvious trend in economic mobility in recent decades. In terms of income inequality, the top of the distribution has been pulling away from the middle. As shown in the figure, the 90/50 ratio has risen almost continuously for the past several decades. However, lower-tail inequality, as captured by the 50/10 ratio, has been roughly flat in recent decades. If our supposition is correct that lower-tail inequality is more relevant to mobility than upper-tail inequality, this could help reconcile the apparent puzzle of rising income inequality and flat economic mobility. The fact that the 50/10 ratio is flat aligns with the flat mobility profile.

I.D. Income Inequality's Relation to High School Dropout Rates

Though there is a vast economics literature examining potential explanations for the rise of income inequality during the past four decades, there remains an important need for more research on its social consequences. This is precisely what we are interested in exploring. In this paper, we are focused on whether there might be negative effects on educational outcomes for children born into low-income homes, which would then have implications for upward mobility. We start by looking at the aggregate relationship, just to see what that the correlational relationship looks like.

Aggregate data show that places with higher levels of income inequality have lower high school completion rates. Figure 3 displays this relationship across states. For the reasons given above, we focus on a long-term average measure of income inequality. We construct the 50/10 ratio for each state in each of the 1980, 1990, and 2000 censuses, and we use the average across census years. We then compare this state-level measure with the state-level "dropout rate," which is 1 minus the four-year graduation rate. The correlation in these data is strong: Places with higher levels of income inequality tend to have higher dropout rates. One-quarter or more of those who start high school in Louisiana, Mississippi, Georgia, or the District of Columbia fail to graduate in a four-year period, as compared with fewer than 10 percent in Vermont, Wisconsin, North Dakota, and Nebraska. Lower-tail inequality is much greater in the former group of states.

Of course, many other things might be driving this relationship, including differences in the underlying characteristics of individuals living in these locations, so this is only meant to raise the possibility of a causal relationship; the plotted relationship can only be interpreted as correlational at this point. Our empirical analysis relies on individual-level data, so we are able to empirically control for individual-level demographic characteristics as well as aggregate-level differences across places. This allows us to pursue an empirical investigation of whether there is a causal link between aggregate-level income inequality and individual-level educational attainment.

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II. Motivating Framework: Modeling the Decision to Stay in School

Before turning to our empirical investigation, we present a simple theoretical model that is intended to spur asking the question of why higher levels of income inequality might increase the likelihood of dropping out of high school for those at the bottom of the income distribution.

II.A. A Stylized Model of the Decision to Drop Out of School

Here we offer an extremely stylized model of the decision to remain in school. This model is a straightforward adaptation of the model we laid out in Kearney and Levine (2014) to describe the decision of young, unmarried women to delay childbearing. An individual chooses to drop out of school in the current period if the following condition is met:

(1) [u.sup.d] + E([V.sup.d]) > [u.sup.e] + E([V.sup.e]),

where [u.sup.d] is current-period utility if the student drops out, and [u.sup.e] is current-period utility if he or she remains enrolled. V is the present discounted sum of future period utility; we assume that E([V.sup.e]) > E([V.sup.d]).

If [u.sup.d] < [u.sup.e], it is never optimal to drop out. But if [u.sup.d] > [u.sup.e], which would be the case if the student experiences substantial utility costs from remaining in school (for example, psychic costs), then that current-period utility boost needs to be compared with the potential option value lost. Dropping out of school negatively affects expected future utility by leading to lower levels of consumption in the future. For simplicity, we characterize utility in future periods as taking high and low values, [U.sup.high] and [U.sup.low], respectively. We assume that dropping out reduces the likelihood of achieving [U.sup.high]. We define [U.sup.low] to be the level achieved by a student who does drop out. The present discounted value of the future utility stream is thus deterministic and is captured by [V.sup.low]. If the adolescent remains enrolled, there is some positive probability p that he or she will achieve the high utility position, [U.sup.high], in future periods.

We can therefore write the condition to drop out of school as

(2) [u.sup.d] + [V.sup.low] > [u.sup.e] + [pV.sup.high] + (1 - p) [V.sup.low].

This condition indicates that the change in lifetime utility from staying in school comes from two opposite-signed sources: (i) the loss of currentperiod enjoyment for staying in school and having restricted time for leisure and other activities, and (ii) a positive probability of achieving the high-utility state in the future. Rearranging terms, we see that a student will choose to remain enrolled if and only if

(3) [[pV.sup.high], + (1 - p)[V.sup.low]] - [V.sup.low] > [u.sup.d] - [u.sup.e].

Of course, the student does not perfectly observe p (Manski 1993). Instead, the student bases the decision on his or her perception of p, in particular, on his or her perception of his or her individual-specific p. Let us call this subjective probability of one's individual likelihood of success conditional on investment q. We would expect--though it need not be the case--q to vary positively with actual returns, as captured by p. So, for example, increases in the actual return on investment in schooling would lead to a greater perception of returns. However, there are external factors--call them x--that affect an individual's perceptions of his or her own likely returns from staying in school. These external factors could reflect influences throughout childhood or at any stage in a child's life.

For example, students who know few others who went to college may incorrectly assume that they would not benefit from college--"It's not for people like me." In other words, for a given level of p, students of different socioeconomic backgrounds may differ in their individual value of q. In essence, we can think of q as a function of p and x; q = q(p,x). It is not our intention to empirically distinguish between the separate roles played by p and x. Rather, we want to raise this conceptual possibility and note that income inequality might have an effect on perceived returns q, either through an effect on p or x.

Incorporating this discussion, we can rewrite the condition for deciding not to drop out as

(4) [[qV.sup.high] + (1 - q)[V.sup.low]] > [V.sup.low] + ([u.sup.d] - [u.sup.e]).

If an adolescent perceives that he or she has a sizable chance of achieving economic success--and thereby capturing [V.sup.high]--by investing in education, the comparison is more likely to favor the choice to stay enrolled. Conversely, if the student perceives that even if he or she stays enrolled, his or her person-specific chances of economic success are sufficiently unlikely--in other words, if q is very low--then the comparison is more likely to favor dropping out in the current period.

Rearranging expression 4, we can define a reservation subjective probability, [q.sup.r], such that an individual wifi stay enrolled in school if and only if

(5) q [greater than or equal to] [q.sup.r] = ([u.sup.d] - [u.sup.e]/[V.sup.high] - [V.sup.low]).

We propose that one's perception of the likelihood of economic success, q, increases in socioeconomic status, SES, such that dq/d(SES) > 0. Sakiko Ikoma and Markus Broer (2015) provide suggestive evidence that is consistent with this proposition based on tabulations of the nationally representative High School Longitudinal Survey. They report that the overwhelming majority of 9th graders aspire to go to college, but by 11th grade, low-SES students are substantially less likely to expect they will enroll in college, even among those students with high test scores. Their drop-off in aspirations and expectations is substantially greater than among comparable high-SES students with similar test scores.

We additionally propose that one's perceived probability of success, q, is a function of the interaction between being of low SES and inequality, ineq, such that if the individual is of low SES, [dq/d(ineq)] < 0. This last proposition says that for an adolescent near the bottom of the income distribution, a greater gap between one's position and the middle of the distribution might have a negative effect on one's subjective q. If the experience of the middle class is sufficiently far from one's own experience, then the student's perceived returns from staying in school are low. Our main goal with the empirical analyses of this paper is to determine whether there does appear to be an effect of income inequality on dropout rates, conditional on rates of disadvantage and other relevant features of the aggregate environment. A secondary goal is to explore potential mechanisms that would be consistent with this line of inquiry, but we do not purport to exhaustively test for potential channels.

This framework has important implications for how to conduct our empirical analysis in terms of the appropriate level of geography. The way we are thinking about the possible effects of income inequality implies that the appropriate unit is a fairly broad area, such as a state or a metropolitan statistical area (MSA). These would allow for the effects of any type of residential or institutional segregation that might occur as a result of widened income inequality and would affect perceptions of success. If we were motivated by relative deprivation theories based on more localized comparisons, we would instead want to define income inequality much more locally.

II.B. Income Inequality, Socioeconomic Status, and Lifetime Income

The discussion above raises the question of whether low-SES youth from more unequal places actually do have a lower chance of earning higher levels of income later in life. Note that our framework does not require this to be the case, because an adolescent's decision is determined by q(p,x), not just p, but it is still an interesting and relevant question to pursue. We offer two pieces of supporting evidence suggesting that this is indeed the case.

First, in Kearney and Levine (2014) we examine data from the restricted-use 1979 National Longitudinal Survey of Youth (NLSY79) geocoded data. (7) We find that children who grow up in low-SES households and who live in a state with high lower-tail income inequality are estimated to have permanent incomes that are more than 30 percent lower than similar children in low lower-tail inequality states (high- and low-inequality states are distinguished by a 1-point increase in the 50/10 ratio). If perceptions of economic success are gauged on actual outcomes, then these findings are consistent with our proposition.

Second, here we estimate rates of return on education to see whether the return is lower for low-SES youth in more unequal places. We are using the term "return" loosely here, as this analysis is not designed to isolate a causal effect. This is meant to be a suggestive exercise, not a definitive analysis of rates of return on education. Again using data from the NLSY79, we track each respondent's average hourly wage from his or her primary job between 1998 and 2012 (all in 2015 dollars), which corresponds to the years when respondents would have been between ages 34 and 55. We estimate regression models of the natural log of hourly wages on educational attainment (as measured in years) and demographic characteristics (race or ethnicity, gender, and age) separately by SES (as captured by the mother's educational attainment category) and state-level income inequality (low, medium, and high).

The results, reported in figure 4, indicate that among individuals living in low-inequality states, the estimated rate of return from an additional year of schooling is roughly constant across SES categories, averaging roughly 10.5 percent. The estimated rate of return is lower, on average, for youth from all SES categories in high-inequality states. However, that reduction in the rate of return is especially pronounced among low-SES children (those whose mothers dropped out of high school). Individuals born to low-SES mothers in high-inequality states see a roughly 8 percent rate of return to education, as compared with 10.6 percent for low-SES youth in less-unequal states. To the extent that adolescents are basing their perceived likelihood of achieving economic success on actual rates, these data are consistent with a diminished perception of success among lowSES youth in more-unequal places.

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II.C. Related Conceptual Models

Our model is related to a set of models that emphasize the role of one's relative position in society in determining individuals' attitudes and behaviors. An influential theory in social science posits a role for relative deprivation--as distinct from absolute deprivation--in leading to acts of social unrest. In the economics literature, Erzo Luttmer (2005) conducts an empirical investigation of this idea and documents that people are less happy when they live around other people who are richer than themselves. In the field of psychology, Mesmin Destin and others (2012) provide evidence that students who perceive themselves to be of lower social status (within a high school setting) suffer worse emotional distress, which has negative consequences for their academic performance. The authors conclude that "students' perception of their location on a relevant social hierarchy is related to their emotional state, academic behaviors, and academic achievement in such a way that it could reinforce the stability of their current location on the hierarchy" (Destin and others 2012, p. 1578). Along these lines, the relative position of individuals could lead to feelings of alienation from society that in turn lead them to want to engage in rebellious types of behaviors, perhaps including dropping out of school.

Garance Genicot and Debraj Ray (2014) propose a theoretical model that leads to the same prediction as our "economic despair" model. Their model proposes that society-wide economic outcomes affect individual aspirations. Aspirations that are slightly above one's position lead to increased human capital investment; but if aspirations get too far from one's current position, that could lead to frustration and lower levels of human capital investment.

Tara Watson and Sara McLanahan (2011) present evidence that relative income matters for the marriage decision of low-income men. They interpret their model within the framework of an identity construct, based largely on the identity model developed by George Akerlof and Rachel Kranton (2000). Specifically, Watson and McLanahan (2011) hypothesize that individuals perceive a threshold income required for marriage, and that this threshold is influenced by an individual's local reference group. One could imagine an extension of this theory that applies to educational attainment. Perhaps individuals perceive a threshold type of person who completes higher levels of education; youth at the bottom of the income distribution in more unequal places may be more likely to view themselves as the low achievers in their reference group.

All these perspectives describe a potential mechanism linking high inequality to lower rates of high school completion. They are useful because they offer a conceptual framework for thinking about the issue, and a useful framework to guide the empirical analysis and interpretation of results. We are ultimately unable to perform a rigorous econometric examination of this hypothesis, however, because reliable measures of perceptions and attitudes with detailed demographic and geographic information are not available to us.

III. The Empirical Strategy

The preceding discussion provides insight regarding a potential mechanism between income inequality and educational outcomes for economically disadvantaged youth. In this section we present the methods and data we use to examine this relationship.

III.A. Our Empirical Approach

The goal of our econometric analysis is to determine whether individuals from disadvantaged backgrounds who live in areas with high rates of income inequality experience greater high school dropout rates. We estimate individual-level regressions that model an individual's educational outcome as a function of individual-level characteristics (including SES), state and year fixed effects, and, crucially, the interaction of SES and the level of inequality in the place where this individual lives. It is this interaction term that gives us the main coefficient of interest and indicates whether low-SES youth in high-inequality locations are relatively more likely to drop out of high school.

The formal econometric model takes the following form:

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where the outcome is some measure of educational attainment (mainly having dropped out of high school, but also GED attainment or high school graduation in some specifications), I is our measure of income inequality, and LS and MS are indicators of low and middle SES, respectively. The subscripts i, s, and c index individuals, states, and birth cohorts, respectively; and [[gamma].sub.s] and [[gamma].sub.c] represent state and cohort fixed effects. Cohort variation comes from the different data sets. The vector X consists of additional personal demographic characteristics--gender, race or ethnicity, and an indicator for living with a single parent at age 14. The vector E captures environmental factors, including relevant public policies and labor market conditions in the state and year in which the respondent was age 16. (8) We have specified this model focusing on state-level variation, but we also consider variation at the MSA level.

It is important to note that our measure of income inequality is a long-run average (not subscripted by c), so we are estimating the impact of persistent differences in inequality, not transitory differences. This contrasts with a more typical panel data approach exploiting transitory variation in the explanatory variable of interest. For example, Susan Mayer (2001) uses the 1993 data from the Panel Study of Income Dynamics to exploit variation over time in state-level income inequality, as measured by the Gini coefficient, to investigate whether levels of income inequality by state and year affect individual-level educational outcomes. In her regression models, which include both state and year fixed effects, there is no evidence of a statistically significant relationship. We do not find this to be surprising, given that it would be quite remarkable for year-to-year fluctuations in income inequality to translate into changes in institutions, norms, or attitudes such that educational outcomes responded at such a fine interval of time.

The main shortcoming of this empirical strategy is that any omitted, state-specific factor that is fixed over time and correlated with long-term measures of income inequality may generate biased results if it has disproportionate effects on the educational attainment of low-SES youth. To determine whether potential confounders are playing this role, we estimate a series of "horserace" regressions of the following form:

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

In essence, our approach involves including potential alternative state factors ([A.sub.s]) that could plausibly affect the relative educational attainment of low-SES youth and examining whether the results change when we include them in the same manner in which we have included the inequality*SES interactions. If the coefficients on the interaction terms of primary interest change when we add the additional interactions between SES and these alternatives, then it would suggest that the results generated by equation 6 are biased estimates of the causal effect of inequality. It is impossible to rule out this form of bias unless we try including every possible alternative, but if what we believe to be important alternatives have no impact, then we can be more confident in a causal interpretation of our findings.

We consider four categories of these other state factors. The first set of factors addresses the measurement of income inequality. As noted above, we use the 50/10 ratio as our primary measure of inequality. In our past work on early, nonmarital childbearing, we found that the 50/10 ratio was the most empirically relevant measure for determining rates of early, nonmarital childbearing. However, we recognize that there are reasons why upper-tail inequality might be particularly important for educational outcomes. We empirically explore the impact of including the 90/50 ratio, as well as the 10th and 50th percentiles of the income distribution on their own. (9)

The second set of alternative factors we consider are measures of the wage returns on investment in education. This is important because it enables us to identify the incentive effect of higher returns (as in a standard Becker model) separately from any offsetting discouragement effect of the type we propose. Third, we consider a set of alternatives that could be considered mediating factors to determine the mechanism whereby increased inequality alters educational attainment. Fourth, we include a set of potential confounding factors that might lead to omitted variable bias if not explicitly interacted with SES and included in the model. A final set of regressions is estimated to determine the extent to which differences in distributions of underlying ability would alter the interpretation of our findings.

III.B. The Data

To estimate these models, we use five sources of individual-level data. Three of these sources are obtained from the National Center for Education Statistics--the National Educational Longitudinal Survey (NELS), High School and Beyond (HSB), and the Educational Longitudinal Survey (ELS)--and the other two are the 1979 and 1997 cohorts of the National Longitudinal Survey of Youth (NLSY79 and NLSY97). (10) Each of these data sets has the distinct advantage of including detailed measures of educational attainment, including the ability to separately identify those who receive a degree by passing a GED test and those who receive a traditional high school degree. Their combination also generates a sample of tens of thousands of teenagers who are moving through (or just recently completed) their high school years. NLSY79 originally surveyed 12,686 respondents born between 1957 and 1964 (ages 14-22 in 1979). HSB originally surveyed more than 30,000 high school sophomores in 1980, of whom about 15,000 were invited to participate and 13,682 did so in the second follow-up four years later. (11) We measure high school completion in that year. NELS surveyed 14,915 8th graders in 1988 who were also surveyed in 1994, when we can determine whether they completed high school. NLSY97 surveyed 8,984 respondents born between 1980 and 1984 (ages 12-18 in 1997). ELS surveyed 15,300 10th graders in the spring of 2002; and these same students were also surveyed in 2006, when high school completion could be measured. In combination, a maximum of 65,567 respondents are available. In reality, mainly because of missing state identifiers, missing information regarding SES (defined below as level of maternal education), and sample attrition, we have available 53,150 teens for our analysis. (12) Limited time variability is available when we combine these data sets, but our analysis relies on long-term geographic variability, as we described above.

A critical feature of these data, as captured in our econometric models, is a measure of the youths' SES. The measure that is available in each of these data sets is the mother's level of education. We distinguish students according to whether their mother dropped out of high school, graduated from high school, or attended college (regardless of her graduation status). Although maternal education does not perfectly predict economic status, we take advantage of the fact that it is strongly correlated with SES.

Although the availability of all five of these data sets provides a unique opportunity to generate a large sample of high school students and to follow them through the completion (or not) of their degree, their combination also presents challenges. In particular, identifying a consistently selected sample and outcome measure is somewhat complicated. Sample selection is an issue because individuals entered the samples at different ages and grades. For instance, the NELS initially surveyed 8th graders and the ELS and HSB initially surveyed 10th graders. Survival in high school until 10th grade represents a degree of success that changes the composition of the sample because more poorly performing students may drop out before they make it to 10th grade. We discuss issues like these in the online data appendix. (13) We account for this in our econometric specification by including data set dummy variables, which we have labeled in the model as cohort fixed effects, given that data sets identify cohorts. We focus on three consistent measures of educational attainment across data sets. In each of these data sets, we are able to determine (i) whether a student completed high school and received a traditional diploma, (ii) whether a student received a GED, or (iii) whether a student never obtained a high school degree via either route.

Our measures of income inequality are defined over pretax, posttransfer household income using micro data from the 1980, 1990, and 2000 censuses. These data sets are available from the Integrated Public Use Microdata Series database (known as IPUMS-USA; Ruggles and others 2015); they capture details of the income distribution over a comparable period as our micro-level data sets. We take one observation per household, adjust the data for inflation to denominate dollars in a common year, calculate relevant percentiles of the income distribution (unweighted), and then define state- and year-level income inequality ratios (50/10 and 90/50) based on these data. (14) We exclude those residing in group quarters, but we impose no other sample restrictions.

We then take the long-term average over all years for a state. As we described above, we take this approach because we are trying to capture something about the permanent or semipermanent economic and cultural landscape in the place where an adolescent lives, as opposed to short-term fluctuations. Simple correlations across states in state-level income ratios between the three censuses are high, supporting this approach. For instance, the correlation across states in the 50/10 ratio between 1980 and 1990 and between 1980 and 2000 are .81 and .74, respectively. Correlations in the 90/50 ratio are even higher. Moreover, the 50/10 ratio has been largely stable over time, as simple transformations from published Census Bureau data indicate. (15)

IV. The Empirical Results

The preceding discussion established the tools we use to examine the relationship between income inequality and educational attainment. This section provides the initial results from this analysis.

IV.A. Descriptive Analysis

To highlight the identification strategy that we use, we initially present the results of a descriptive analysis of educational outcomes for teenagers by their SES and the level of income inequality that exists in their state. Figure 5 presents the results of this descriptive analysis. Foreshadowing the results from our subsequent formal econometric analysis, we present these results just for boys. We classify states into those in the top, bottom, and middle two quartiles of inequality as measured by the 50/10 ratio. (16) The bars represent the percentage of boys who dropped out of high school. Boys are separated into categories according to their mother's educational attainment to proxy for SES, along with the level of inequality that exists in their state.

Figure 5 groups SES categories so that the pattern in educational outcomes by inequality status within SES category is readily apparent. We see that about 5 percent of boys from higher-SES families drop out of high school regardless of the level of income inequality in their state. No obvious pattern is evident among the middle-SES boys in different inequality categories either. Among low-SES boys, however, higher inequality is clearly associated with higher rates of dropping out of high school. The magnitude of the difference is sizable. Low-SES boys in high-inequality states are almost 6 percentage points more likely to drop out of high school than low-SES boys in low-inequality states.

[FIGURE 5 OMITTED]

IV.B. State-Level Analysis

These findings from our descriptive analysis are confirmed when we estimate the regression models described in equation 6. In essence, these regressions are analogous to the data reported in figure 5, with the exception that the 50/10 ratio is treated continuously rather than in categories and additional explanatory variables are included. Table 1 presents these results for all students in the sample and then separately for boys and girls. (17) Each column isolates a different measure of educational outcomes: high school dropout, GED attainment, and high school graduation. The percentage of students in each category is displayed just above the regression results to aid in interpretation. When we focus on dropping out of high school for all students (top panel), we see that a 1-point increase in the 50/10 ratio increases the likelihood of dropping out by 2.3 percentage points for students from low-SES families. This estimate is not quite statistically significant, with a p value of 12.3 percent. When we explore differences in estimates by gender, however, we see that boys in particular are more likely to drop out of high school when they grow up in a low-SES household in an area marked by high inequality. Moving from a relatively low-inequality to high-inequality state represents a 1-point increase in the 50/10 ratio. This means that making such a move for a boy from a low-SES family increases the likelihood of dropping out of high school by age 20 by 4.1 percentage points. The analogous estimate for girls is considerably smaller, statistically insignificant, and marginally significantly different than the estimate for boys (p value = 8.6 percent). Estimates for the other two outcomes (receiving a GED or graduating from high school) are too imprecise to determine whether the increase in dropping out for boys came mainly from either of them.

IV. C. MSA-Level Analysis

In the next set of regressions, we examine what happens if we run the main analysis at the level of an MSA, instead of state. For some large states, such as California and Texas, the MSA may be the more relevant level of geographic boundaries for defining economic conditions and institutions.

Table 2 focuses on the outcome of dropping out of high school, and it repeats the analysis of the impact of inequality and mobility by MSA rather than state. The models reported here are analogous to those in table 1 except that these regressions exclude policy variables set at the state level. Omitting these variables from the state-level models has virtually no impact on the results. We are also forced to omit the NELS and HSB data from our analysis because we are not able to identify geography below the state level in the base year in these data sets. MSA-level results are similar to state-level results. Lower-SES teens, and particularly boys, who grow up in MSAs with greater lower-tail income inequality are considerably more likely to drop out of high school. The p value for the gender difference in effects on dropping out of high school is 0.0004. The general pattern in the data, which shows that boys' dropout rates are more likely to be affected by inequality than girls' rates, leads us to focus the remainder of the analysis on boys. We also focus the remainder of our reported results solely on the outcome of dropping out of high school.

V. An Examination of Potential Explanations

In the next set of tables, we estimate models of the form of equation 7 that are designed to examine the extent to which other state-specific factors may matter, and we revise our interpretation of a causal impact of income inequality. In each of these tables, to facilitate comparison, we also include the results of our base specification from table 1 in the first column.

V.A. Alternative Measures of the Income Distribution

Table 3 reports the results of estimating the main equation of interest using various measures of the income distribution. The alternatives we consider are the 90/50 ratio; the 10th and 50th percentiles of the income distribution, separately; and the share of income going to the top 1 percent of households. Data on the share of income going to the top 1 percent of households were obtained from an online appendix to Chetty and others (2014a). Those data are available at the level of commuting zones, and we aggregated them to the state level. Each of the alternative measures of the income distribution captures different attributes. The 90/50 ratio represents income inequality at the top of the income distribution. This is the part of the distribution that has grown over time. We have argued that the 50/10 ratio is a better measure of inequality for the low-SES population because it may more realistically indicate what would be available to them if they were able to move up the ladder; but this is an empirical question. We also include the 10th and 50th percentiles of the income distribution separately to enable us to understand whether our findings based on their ratio are actually attributable to one of the two components separately. The income share going to the top 1 percent addresses the impact of very-high-end inequality.

As described above, we include the interaction of the 50/10 ratio and SES, along with interactions between SES and these other measures. The estimates reported in table 3 provide support for the notion that the 50/10 ratio is the relevant measure of income inequality for the outcomes of low-SES boys. Interactions with the other measures are generally statistically insignificant and have no impact on the estimated effect of the interaction between the 50/10 ratio and low SES. If anything, including the 90/50 ratio strengthens the relationship between the 50/10 ratio among low-SES boys and dropping out of high school.

V.B. The Role of Wage Inequality

Recall from our earlier discussion that if greater inequality reflects a greater return on investment in human capital, the Becker framework predicts that all else remaining equal, students should invest more when income inequality is greater. Solon (2004) formalizes this concept in a model where parents make human capital investments in their children. (18) Building on the theoretical foundation of Gary Becker and Nigel Tomes (1979), he shows that parental investment in a child's human capital increases when the payoff from that return is higher--that is, when there is more wage inequality. In our framework, this would entail a reduction in the likelihood of dropping out of high school. (19)

The specifications reported in table 4 address this possibility directly by considering a distinct offsetting role from the incentive effect of wage differentials. In column 2, we estimate a regression model that includes separate interaction terms for low SES with lower-tail inequality, and low SES with the wage premium for high school graduates relative to high school dropouts. The high school graduate wage premium is calculated from the same census data that we used to estimate measures of inequality, except that the sample is restricted to those between ages 21 and 64.

The results of this specification indicate that, even with this additional interaction term in the model, the point estimate on the interaction term between low-SES and lower-tail inequality is virtually unchanged from the initial specification. The data indicate a positive effect of income inequality on the likelihood that a disadvantaged youth drops out of school, conditional on the high school wage premium. The high-school-graduate to high-school-dropout wage premium itself is estimated to reduce the likelihood of dropping out for low-SES boys, although it is insufficiently precise to be statistically significant.

V.C. Residential Segregation and Other Potential Mediating Factors

There are a number of pathways along which income inequality could hinder the educational attainment of disadvantaged students. In the introductory chapter of the edited volume Whither Opportunity, Greg Duncan and Richard Murnane (2011) discuss the possibility that income inequality has an effect on neighborhoods, families, labor markets, and the educational system in ways that affect educational outcomes. (20) In this section, we empirically examine factors along these lines. We begin with measures of residential segregation. To the extent that higher income inequality is associated with increased residential segregation--as empirically demonstrated by Watson (2009)--this could be a pathway along which income inequality affects the educational attainment of disadvantaged youth. Greater residential segregation can affect social and labor market networks, the presence of high-achieving role models, and the establishment of peer groups and norms.

The influential work of William Julius Wilson (1987) emphasizes the role of "social isolation" in driving rates of urban joblessness and non-marital childbearing. He hypothesizes that the lack of exposure to mainstream, middle-class role models plays an important role. Anne Case and Lawrence Katz (1991) provide an early example of nonexperimental empirical research, suggesting significant neighborhood peer effects for criminal behavior as well as the likelihood that youth are out of school and out of work. The widely studied Moving to Opportunity for Fair Housing demonstration program--run by the U.S. Department of Housing and Urban Development--was predicated on the notion that helping low-income families move out of high-poverty neighborhoods would yield measurable economic self-sufficiency benefits. (21)

To investigate neighborhood segregation as a mediating channel, we incorporate into our empirical model indexes of racial segregation, income segregation, and poverty segregation. To the extent that any of these factors, when interacted with SES, have a statistically significant effect or alter the estimated impact of the inequality*SES interactions, one could conclude that they are important mediating factors. We obtain the three segregation measures from the online data appendixes to Chetty and others (2014a, 2014b). The racial segregation measure is a multigroup Theil index calculated at the census-tract level for four groups: white alone, black alone, Hispanic, and other. The income segregation measure is calculated as a rank-order index by census tract using the definition laid out by Sean Reardon (2011). (22) The poverty segregation index captures the extent to which individuals in the bottom quartile are segregated from those in the top three quartiles. We have averaged these commuting zone measures up to the state level (population-weighted) for our state-level analysis. Thus, for example, a state like Texas (with highly segregated commuting zones) will be classified as highly income segregated, and Utah will not.

The results reported in table 5 provide no evidence of this sort of effect. None of the coefficients of the interactions with these factors in columns 2 through 4 are statistically significant, and their inclusion has a negligible impact on the inequality*SES interactions. The lack of support in the data for these factors is noteworthy, but we hasten to add that it should not be interpreted as definitive evidence against an important role for residential segregation in affecting the educational outcomes of poor youth. Rather, these regression results imply that the average level of segregation in the state is not driving the empirical relationship we find between state-level income inequality and individual-level education outcomes.

Another potential mechanism whereby income inequality might affect the dropout rates of low-SES youth is a reduced public provision of educational inputs. Political economy considerations of whether higher levels of income inequality would lead to lower levels of public goods provision (including public school expenditures) are actually ambiguous. More money in the hands of the rich could reduce transfers of resources to the poor. Alternatively, if the rich were to become more fearful about the poor agitating for social change, that could increase transfers. Furthermore, under the median voter model, with greater inequality, the median declines relative to the mean, and the preferences of the median voter for more distribution from the rich prevail. Recent empirical evidence on the relationship between income inequality and public revenue for school spending shows that public school spending increases as the level of local income inequality rises (Boustan and others 2013; Corcoran and Evans 2010; Gordon 2013). Nonetheless, we run the relevant regression to investigate public school expenditures as a mediating pathway.

Table 6 reports the results from a regression that includes the interaction of state-level 50/10 inequality and educational inputs. Educational inputs are measured by per-pupil educational expenditures and pupil/teacher ratios. (23) In our data, we see that per-pupil educational expenditures and pupil/teacher ratios are only weakly correlated with state-level lower-tail income inequality (.14 and -.23, respectively), making it unlikely that these are omitted variables driving the observed link between income inequality and dropout behavior. The regression results confirm that this is not the case. The data do not indicate a direct effect of these measures on the rate at which low-SES individuals drop out of high school. Nor does the inclusion of these measures alter the conclusion that greater lower-tail income inequality leads to higher rates of high school dropout behavior among low-SES individuals.

Table 6 also considers aggregate levels of social capital and family structure as potential mediating factors. Social capital is a measure introduced by Robert Putnam (2000) that combines voter turnout rates, the fraction of people who return their census forms, and measures of participation in community organizations. (24) Family structure is measured by the fraction of children living in single-parent households. Although social capital and the fraction of children living with single parents are more strongly correlated with our measure of income inequality, including these variables in the model similarly has little impact. Ultimately, the data fail to provide evidence that any of these potential factors is the mediating mechanism driving the empirical relationship we document.