Can Socioeconomic Status Substitute for Race in Affirmative Action College Admissions Policies? Evidence From a Simulation Model

This paper simulates a system of socioeconomic status (SES)−based affirmative action in college admissions and examines the extent to which it can produce racial diversity in selective colleges. Using simulation models, we investigate the potential relative effects of raceand/or SES-based affirmative action policies, alongside targeted, race-based recruitment, on the racial and socioeconomic distribution of students in colleges. These simulations suggest three important patterns: (1) neither SES-based affirmative action nor race recruiting policies on their own can reproduce levels of racial diversity achieved by race-based affirmative action; however, SES-based affirmative action in combination with targeted recruitment, although likely expensive, shows the potential to yield racial diversity levels comparable to race-based affirmative action; (b) the use of affirmative action policies by some colleges reduces the diversity of similar-quality colleges that do not have such policies; (c) overall, the combination of SES-based affirmative action and race recruiting results in slightly fewer Black and Hispanic students that are academically overmatched than under race-based affirmative action, but the schools that use the combination policy also see an overall reduction in the academic achievement of the students they enroll. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 2 Can Socioeconomic Status Substitute for Race in Affirmative Action College Admissions Policies? Evidence from a Simulation Model In its 2013 Fisher v. University of Texas at Austin (Fisher I) decision, the Supreme Court upheld the concept of race-conscious affirmative action but issued a challenge to university administrators and scholars: In order to use race-based affirmative action, they must show “that no workable race-neutral alternatives would produce the educational benefits of diversity” (Fisher v. University of Texas at Austin, 2013, p. 11). After the Fisher case returned in 2015, the Court again emphasized the need for “regular evaluation of data” to ensure “that race plays no greater role than is necessary” (Fisher v. University of Texas at Austin (Fisher II), 2016, p. 11). Both decisions acknowledged that racial diversity is a legitimate goal of public university admissions policies, but the Court expressed skepticism about whether racebased affirmative action policies would continue to be necessary to achieve that goal. To that end, it is crucial that scholarship continues to evaluate the relative effectiveness of different types of admissions policies to increase racial diversity in selective colleges. Two potential workable race-neutral alternative admissions policies that might yield racial diversity at selective universities are affirmative action based on socioeconomic status (SES) rather than race, and recruitment efforts that target underrepresented racial minority students. Such policies would avoid the constitutional challenge of relying on race to determine admission, but can they produce sufficient racial diversity to satisfy universities’ legitimate educational interests? This paper addresses that question. This question is, of course, hypothetical; few colleges, for example, currently use affirmative action based on SES in any substantial way. As a result, standard methods for evaluating existing policies cannot tell us how well they work. Moreover, college admissions and enrollment decisions at different universities are interdependent: Because students can apply to many colleges but enroll in only one, CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 3 changes in admissions policies at one school may affect enrollment patterns at other schools. Thus, even if we knew the impacts of SES-based affirmative action in one university, those findings might not indicate what would happen if such policies were implemented in many universities. Given the hypothetical nature of SES-based affirmative action and the interdependent nature of the university admissions and enrollment processes, one useful approach to understanding the potential impacts of different admissions policies is to use simulation models informed by the best available data. Well-designed simulations can allow rapid experimentation with a variety of policies and can provide insight into the probable effects of these policies on both individual universities and on the higher education system as a whole. Although simulations are not definitive about what would actually happen under a given policy, they can describe patterns of likely outcomes under assumptions derived from other research and can provide guidance regarding the probable effectiveness of different types of policies. With these aims in mind, this paper uses a simulation model to investigate the dynamic effects of various types of affirmative action college admission policies on campuses’ racial diversity, as well as resulting changes in the average academic achievement of students, both at schools that use these policies and those that do not. We also examine a common claim made by opponents of affirmative action: that students admitted under such plans are academically out-matched by their peers. CURRENT PATTERNS OF RACIAL DIVERSITY AT SELECTIVE COLLEGES AND UNIVERSITIES Any race-neutral affirmative action approach faces a serious challenge. Even with the legality of race-conscious affirmative action policies, Black and Hispanic students remain underrepresented in higher education, particularly at selective institutions. Very selective colleges (those colleges with Barron’s selectivity ratings of 1, 2, or 31) have many more White, and many fewer Black and Hispanic, students 1 Barron’s Profiles of American Colleges (www.barronspac.com) provides selectivity rankings for most 4-year colleges in the United States. Colleges are ranked on a scale from 1 (most selective) to 6 (least selective). These CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 4 than the U.S. population of 18-year-olds overall. This distribution is evident in Figure 1, which shows the postsecondary enrollment status of members of the high school class of 2004 by race and type of college or university. Appendix A includes a comparable figure describing the income composition of postsecondary institutions where we see lower-income students are likewise underrepresented at more selective colleges (see also Chetty, Friedman, Saez, Turner, & Yagan, 2017). [Figure 1 here] In general, Black and Hispanic enrollment is lower in selective colleges and universities. The most selective colleges, however, are slightly more racially diverse than those just below them in the selectivity rankings. This difference may be partially the result of race-based affirmative action policies used by some of these most selective colleges. It may also result from the additional sources of financial aid available that more selective colleges can use to support a more diverse class of students (Hoxby & Avery, 2012). Although we do not know what the racial composition of these most selective colleges would be in the absence of any race-based affirmative action, their enrollments would likely consist of fewer than 10 percent Black or Hispanic students, much lower than the 30 percent Black and Hispanic individuals comprise in the overall population of 18-year-olds. Existing research on the effects of affirmative action support these hypotheses. Evidence of affirmative action is most visible at selective, state-flagship universities (Backes, 2012; Brown & Hirschman, 2006; Hinrichs, 2012; Long, 2007). The elimination of affirmative action policies in some states has resulted in drops in the enrollment of Black and Hispanic students at these schools (Backes, 2012; Brown & Hirschman, 2006; Dickson, 2006; Hinrichs, 2012; Long, 2007). Some of this enrollment drop may be attributable to a decline in applications, perhaps because underrepresented minority (URM) rankings are based on the high school GPAs, high school class rank, and SAT/ACT scores of enrolled students, as well as the proportion of applicants admitted. Colleges ranked in the top two categories (1 and 2) in 2004 had median SAT® scores of at least 575, admitted fewer than 50 percent of applicants, and enrolled students with median GPAs of about 3.5 and in the top 35 percent of their high school class. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 5 students interpret these bans as a signal that they are not welcome (Brown & Hirschman, 2006; Dickson, 2006). RACE-NEUTRAL AFFIRMATIVE ACTION POLICIES Some state university systems have responded to legislated bans on affirmative action either through increased recruitment of underrepresented students. The University of Washington, for example, was able to recover from a drop in applications from URM students with proactive recruitment (Brown & Hirschman, 2006). California, in response to Proposition 209, saw less successful results from a similar strategy (Gándara, 2012). Recruitment efforts work in part by making colleges seem more appealing to prospective students through additional, targeted contact with those students. Texas took efforts to make its campuses seem more appealing to underrepresented students one step further and, in addition to special recruitment and academic support programs, offered two special scholarships for enrollment in the Texas flagship universities to students from high schools in low-income areas with a low college-going tradition (Andrews, Imberman, & Lovenheim, 2016; Niu & Tienda, 2010). Only one of these programs increased enrollment among targeted students (Andrews, et al., 2016). Often, targeted recruitment is paired with “percent plan” admissions policies. Under percent plans, any student who graduates in some pre-specified top percentage of their high school class automatically gains admission to the public university system. Such plans leverage the existing racial segregation of high schools to increase the racial diversity of university admissions; any plan that takes the top portion of a school with a high minority population is bound to admit a sizeable number of minority students. Percent plans have been implemented in the three largest states—California, Texas, and Florida. Evaluations of these policies indicate that they have not been effective at maintaining racial diversity levels after state-wide bans on race-conscious affirmative action (e.g., Arcidiacono & Lovenheim, 2014; Bastedo & Jaquette, 2011; Horn & Flores, 2003; Lim, 2013; Long, 2004, 2007). CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 6 The failure of percent plans to deliver on their promise has prompted some scholars and colleges to propose an alternative race-neutral form of affirmative action, one that relies on SES instead of race to determine admissions preferences (Gaertner & Hart, 2013; Kahlenberg, 1996). Under SES-based affirmative action, students are given an admissions advantage because of their socioeconomic background rather than because of their race or ethnicity. The presumption is that such plans capitalize on the relationship between race and income in order to construct a socio-economically and racially diverse class of students. The potential effects of such policies are not clear. Some existing research suggests that substituting SES for race in college admissions decisions can at least partly maintain rates of URM enrollment while simultaneously increasing college access for economically disadvantaged students (Carnevale & Rose, 2004; Carnevale, Rose, & Strohl, 2014; Gaertner & Hart, 2013; Kahlenberg, 2012). Other research suggests that SES is not a sufficiently good proxy for race for SES-based policies to be effective at producing substantial racial diversity, at least without combining it with some form of raceawareness (Bowen, Kurzweil, & Tobin, 2005; Carnevale & Strohl, 2010; Espenshade & Radford, 2009; Kane, 1998; Long 2015; Reardon & Rhodes, 2011; Reardon, Yun, & Kurlaender, 2006; Xiang & Rubin, 2015). At the very least, SES-based affirmative action may help to increase socioeconomic diversity on college campuses, which in and of itself may be a desirable outcome for colleges. It is difficult to evaluate the effects of SES-based affirmative action in practice, however, because such plans are not widely used. Our aim in this paper is to, first, develop general intuition about SES-based affirmative action and the extent to which it can—alone or in combination with race-based recruiting—replicate or improve the levels of racial diversity evident in selective colleges under current admissions practices. Second, we attend to the effects that affirmative action policies at one or more colleges have on enrollment patterns at other schools. College admission and enrollment processes take place in an interrelated, dynamic system where admissions policies at one college might affect enrollment patterns at other colleges. For example, application patterns changed in Texas after the introduction of the state’s percent plan: nonCAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 7 flagship public universities in Texas saw an increase in the average test scores of their applicants, likely due to changes in application behavior of high-scoring students who were not eligible for automatic admission on the basis of their class rank (Long & Tienda 2010). Our aim is to expand such findings to examine how raceand SES-based affirmative action—arguably less-transparent than percent plans— might change application and enrollment patterns both at schools that use those policies and those that do not. Our simulations here provide insight into these potential system-wide, dynamic effects of affirmative action admissions policies. Finally, some critics of race-based affirmative action claim that it does a disservice to URM students because it places them in environments where their academic preparation systematically falls below that of their peers (e.g., Arcidiacono, Aucejo, Coate, & Hotz, 2014; Arcidiacono & Lovenheim, 2005; Sander, 2004). This mismatch might lead to within-college racial segregation based on academic background or a lower likelihood that URM students admitted under affirmative action will complete college (Arcidiacono, Khan, & Vigdor, 2011). Other studies, however, indicate no significant negative effects of academic mismatch (Bowen & Bok, 1998; Dillon & Smith, 2015). In order to inform this line of research, we use our simulations to assess the extent to which raceand SES-based affirmative action policies might place URM students in colleges where their achievement falls substantially below their peers. THE UTILITY OF AGENT-BASED SIMULATION We build intuition about the effects of different admissions policies using an agent-based model (ABM) that is grounded in real-world data and that incorporates a complex (though highly stylized) set of features of the college application, admission, and enrollment processes. Our model relies on a synthetic world of students and colleges created to mimic the salient characteristics of students and colleges in the real world. We give these actors rules to engage independently in a process that simulates college CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 8 admissions in the real world. By using an ABM, we can compare the effects of a range of policies on enrollment patterns in a way that takes into account how a policy would affect the full system of colleges. Our model allows us to investigate how diversity boosting policies might affect university composition in a world in which students (a) have idiosyncratic preferences about colleges, (b) have uncertainty about their own admissibility to each college, and (c) use their resources and limited information to strategically apply to a small subset of colleges, and in which colleges (a) differ in their use of affirmative action policies, (b) have idiosyncratic perceptions and preferences regarding students, and (c) strategically admit enough students to fill their seats under the expectation that not all students admitted will enroll. Many, but not all, of these features are present in previous, structural models of the college admissions process (for example, Fu, 2014; Howell, 2010). However, agent-based modeling in general, and our model design in particular, are well-suited for answering the policy questions that we address because we can observe behavior and outcomes for specific students and colleges at any given point in time. Although our model falls short of being completely realistic, it captures important, dynamic features of the application/ admissions/ enrollment processes that enable us to investigate the ways that affirmative action might affect enrollments. In addition, an important assessment of the validity of an ABM is whether it has “generative sufficiency;” whether it can reliably produce meaningful, macro-level outcomes similar to those observed in the real world given a set of realistic input parameters and rules for micro-level behaviors (Epstein, 1999). Reardon, Kasman, Klasik, and Baker (2016) demonstrate that a model with the stylized dynamics that we incorporate meets this condition and can replicate realistic patterns of application and enrollment. This simulation approach improves upon previous assessments of race and SES-based affirmative action in several important ways. First, unlike prior simulations, it models a dynamic system of students and colleges, rather than relying on static, regression-based or structural models. Nearly all previous studies of SES-based affirmative action have been based on simulations where regression-based CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 9 estimates of raceor legacy-based admissions boosts are simply added to the academic qualifications of low income students from the original data to create a new hypothetical class of admitted students (Bowen, Kurzweil, & Tobin, 2005; Carnevale & Strohl 2010; Espenshade & Radford, 2009). Second, many of the studies that model application and admissions decisions have not directly addressed the potential of SES-based affirmative action, (Arcidiacono 2005; Howell 2010; Long 2015). Arcidiacono (2005) and Howell (2010) use structural models of the college enrollment process to examine the effect of changes in affirmative action policies on college enrollment choices (Howell, 2010) and future earnings (Arcidiacono, 2005). None of the simulations, however, include SES-based affirmative action. Alternatively, Long (2015) simulates changes in college diversity if colleges could give admissions boosts to students based on predictions of a student’s race according to observable characteristics other than race, including measures of SES. Although these studies model application and admissions decisions explicitly, they too hinge on simply removing or adding various regression-estimated advantages to URM (or expected-URM) students in college admissions decisions. Third, none of these approaches provide intuition on how application and admission behavior might change in response to the simulated outcomes of the changes in policy. This is not a trivial omission. We know that, for example, UT Austin has had to add a cap to the number of students it admits under the Texas percent plan because demand for seats at the school is so high under the percent plan policy—a response that could not be modeled with structural approaches of prior affirmative action research. Although we establish certain parameters of our model in similar ways to earlier models (such as estimating the size of the admission boost that might be appropriate to use for an SES-based admission policy), repeated simulations in our model allow student and college behavior to adapt in response to different admission policies and the resulting changes in the size and composition of enrolling cohorts of students. Fourth, previous simulation studies are limited by the generalizability of their claims because of CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 10 the data they use. For example, some are based on relatively small subsets of the postsecondary system ranging from a single state university (Gaertner & Hart 2013), to a single state system (Long 2015; Long & Tienda, 2010), to the 193 “most selective” colleges (Carnevale & Strohl 2010). This focus makes sense when the goal is to understand how admissions policies affect admission and enrollment patterns at particular types of schools, but it is not clear how far these results generalize to other institutions. Other simulations are based on more complete national data, but these data are usually old and likely unable to speak to more recent trends in college choice. For example, Howell (2010) uses data from the high school class of 1992, while Arcidiacono (2005) uses data from the class of 1972. Our simulated system includes 40 simulated institutions, but—along with the students in our simulation—they are constructed to represent the full system of degree-granting colleges and universities and the national population of high school students and is based on parameter estimates from 2004 and later. Finally, our simulation approach is more realistic than other simulations in some important ways. For example, whereas the simulation in Carnevale and Strohl (2010) assumed that all students apply to all colleges, our model, like Howell (2010), has students strategically applying to a small portfolio of colleges based on their (imperfect) assessments of both college quality and their likelihood of admission. Moreover, in the Carnevale and Strohl (2010) simulation of SES-based affirmative action, the model measures socioeconomic disadvantage using many variables not typically available to admissions officers (for example, the percentage of individuals in an applicant’s neighborhood who hold a college degree). Our model, in contrast, uses an index that is implicitly based on the types of factors (family income, parental education, parental occupation) that would be available to admissions officers. SIMULATING THE MECHANICS OF AFFIRMATIVE ACTION POLICIES Selective colleges generally try to admit classes of students that are both academically qualified and also diverse along numerous dimensions. These dimensions may include not only race or SES, but CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 11 also academic interests, extracurricular talents, geography, and other college-specific factors. For example, colleges may want to boost enrollment in an undersubscribed major or program or find talented players for their sports teams. Selective colleges across the country demonstrate admissions preferences for these students who will add to the different types of diversity of their campus. These preferences—as well as racial or socioeconomic diversity preferences—are typically enacted through a holistic review process in which the overall academic achievement of an applicant is assessed across a host of dimensions and one college’s assessment of the contribution of a student to the campus population might differ from another college’s assessment of the same student. Because it is part of a holistic process, the added weight given in the admissions process to students’ nonacademic characteristics such as race is not explicit or directly measurable. Indeed, by law it cannot be: The Supreme Court has prohibited colleges from assigning numeric values to race-based characteristics (Gratz v. Bollinger, 2003). That is not to say, however, that the net average admissions weight given to a characteristic like race (or athletic prowess, for that matter) cannot be quantified after the fact given the right data. One can ask, for example, how much higher, on average, are the grade point averages (GPAs) of admitted White students than those of admitted Black students. The answers to questions of this type provide a way of quantifying the weight given to race and factors associated with race in a holistic admissions process. However, a nonzero answer to this question does not imply that admissions officers simply add a certain number of GPA points to each Black student’s score and then admit all students simply on the basis of their (adjusted) GPA. To make the simulations in this paper realistic, we simulate a holistic admissions process in which race and/or SES are given more or less (or no) weight in admissions decisions. For this, we need a sense of the average weight given to these factors by actual selective colleges and universities so that the simulations produce patterns that are grounded in real-world data. Several existing papers have attempted to estimate the relative weight of race, SES, and CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 12 academic record in admissions decisions at selective colleges. A common strategy is to use data from a pool of applicants to one or more selective colleges to predict admission on the basis of race, academic, and other observable factors like SAT® exam scores and then compare the coefficients on the race variables with the coefficient on SAT® scores (see, for example, Kane, 1998 and Espenshade & Radford, 2009). For example, if a Black student’s probability of admission were 7 percent greater than an otherwise observationally identical White student, one can calculate what change in SAT® exam score would be needed to yield the same 7 percent boost in the probability of admission. We review these prior studies in some detail in Appendix B. Due to our concerns that the race weights estimated in these studies are likely too high, and because existing estimates do not describe the weight that colleges give to Hispanic students or to low-SES students, we also conduct our own simple analysis to estimate the relative weights given to race, SES, and academic performance in selective college admissions. Using data from Educational Longitudinal Study of 2002 (ELS), we estimate racial and SES admissions weights using a much more parsimonious version of the model fit by Espenshade and Radford (2009) and Kane (1998). We predict the probability of admission using only test scores and dummy variables for race or a standardized variable for SES.2 To account for the possibility that the implicit weights vary in magnitude along with the selectivity of the college, we repeated this analysis for admission to colleges in each of the six Barron’s Selectivity categories. The results of our analyses suggest that Black and Hispanic applicants to the most selective colleges receive an implicit admissions weight that is roughly equal to the weight given to a 1.3 standard deviation increase in academic performance (in other words, the difference in the probability of 2 In these analyses, we use SAT® scores because they are widely observable to colleges (unlike the tests administered as part of the ELS study) and they are standardized on a common scale (unlike GPA). Although colleges have access to other information about students, we use a single test score measure as a unidimensional proxy for students’ academic performance. The weights we estimate therefore should be understood as designed solely to provide information about the rough order of magnitude of the weights given to academic performance, race, and SES in admissions processes. They are not particularly useful as estimates of actual admissions processes. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 13 admission of White and Black or Hispanic students is roughly equal to the difference in the probability of admission of two students of the same race whose academic performance differs by 1.3 standard deviations). We find very little or no evidence of racial preferences in admissions to colleges in lower selectivity tiers (see Appendix Table B1). We find evidence of slight SES-based affirmative action in the most selective colleges—a standard deviation difference in family SES is roughly the same as a 0.15 standard deviation difference in academic record. However, lower-SES students applying to less selective colleges appear to be penalized in the admission process. In these colleges higher SES students were given implicit preference in admissions decisions. The SES weights are, however, relatively small in all cases. This heterogeneity perhaps reflects the fact that existing SES-based admissions preferences work in two directions: On the one hand, most colleges rely heavily on student tuition and must take ability to pay into account in admissions; on the other hand, many colleges, particularly very selective colleges, actively recruit and admit low-SES students (see Appendix Table B2). These findings suggest that race-based affirmative action plays (or played, in 2004) some role in admissions to highly selective colleges but SES-based affirmative action does not. We reiterate that our estimates are designed more to provide rough estimates of the average weight given to race in admissions processes than to precisely measure the impact of affirmative action policies. We use these estimates to determine the range of race and SES weights to use in the simulated affirmative action policies in our models. METHOD Model design We use a modification of the agent-based model of college application, admission, and enrollment developed and described in depth by Reardon, Kasman, Klasik, and Baker (2016). The model CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 14 includes two types of entities: students and colleges. We set up the model with 40 colleges and 10,000 new college-age students per simulated year.3 Students have three characteristics: race, a measure of high school academic achievement, and a measure of family resources. The race-specific distributions of academic achievement and resources, and race-specific correlations between resources and academic achievement were based on the real-world relationships between these variables observed in the Education Longitudinal Survey of 2002 (ELS), a nationally representative sample of high school students who would graduate in 2004. The achievement distribution is based on the standardized assessments of English language arts and mathematics administered to that sample in 10th grade. The family resource dimension is based on a composite measure of a student’s mother’s and father’s education, mother’s and father’s occupation, and family income generated by the National Center for Education Statistics. This measure captures the dimensions of class proposed by Kahlenberg (1996) for use in class-based affirmative action policies. The parameters used in our model are presented in Table 1. For simplicity, as well as the availability of real-world data, we limited our model to the four largest racial groups in the United States: White, Hispanic, Black, and Asian. Five percent of the students in the simulation are Asian, 15 percent are Black, 20 percent are Hispanic, and 60 percent are White, similar to actual proportions of the college-age population. The academic achievement characteristic represents the academic qualities that make a student attractive to a college (e.g., test scores, GPA, high school transcripts). We converted the scores from the original ELS test score scale to one that approximates the 1600-point SAT® exam scale (mean 1000, standard deviation 200) because of the ubiquity of this scale in general as well as its use in existing literature on affirmative action policies. The family resources measure is meant to represent the economic and social capital that a student can tap when engaging in the college application process (e.g., income, parental education, and knowledge of the 3 We conduct separate draws for each student cohort within a simulation run for two reasons. The first is that this is a realistic approach, as student cohorts can be expected to differ from one another. The second is that by doing so we gain confidence that our results are not driven by the attributes of a specific set of students. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 15 college application process). The family resource measure is standardized to a mean of 0 and standard deviation of 1. Based on the findings of Reardon et al. (2016) and described more formally below, we structured the model to allow students’ family resources to influence the college application process in four ways. First, students’ resources and academic achievement are positively correlated. Second, students with more resources submit applications to more colleges than their lower-resource peers. Third, students with higher resources have higher quality information both about college quality and their own academic achievement relative to other students; this increases their likelihood of applying to colleges that are a good match for their academic records. Fourth, higher resource students are able to enhance their apparent academic records, visible to colleges as they make admissions decisions (analogous to engaging in test preparation or private tutoring, obtaining help writing college essays, or strategically participating in extracurricular activities). These features of the model are explained and calibrated in Reardon et al. (2016). Reardon et al. (2016) showed that, taken together, imperfect information, idiosyncratic preferences, strategic application behavior, and socioeconomic influences create patterns of college selection and enrollment that are similar to those in the real world. Each of the 40 colleges in our model has a target enrollment for each incoming class of 150 students, meaning there are a total of 6,000 seats available for each cohort of students. The ratio of total students to total college seats is roughly the same as the proportion of 2002 tenth graders who attended any type of college by 2006.4 The only attribute that colleges have is quality (perhaps better thought of as 4 Although all of the students in our model apply to colleges, roughly 40 percent are not admitted anywhere because there are fewer seats than students. An alternative model would be to model non-application based on parameters estimated from student observables and noise. Our results are not likely to be sensitive to this modeling choice, however, for two primary reasons: first, the students that would not apply at all are likely to be drawn from the pool of students in our simulation that do not receive acceptance to any college: low achievement students with poor information. Of course, some high achievement students would also likely not apply; this type of student is represented in our simulations as having idiosyncratic preferences for colleges. There are numerous examples of students with sufficiently high achievement to gain acceptance to some college that ultimately do not because they CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 16 reputation, though in the real world the two are generally conflated in public perception). Quality is operationalized as the three-year running average of academic achievement of students enrolled in the school. In the real world, this mean academic achievement is probably correlated with, but not the same as, the quality of educational experience for students at a given college. Quality is measured in the same units as student academic achievement. The model iterates through three stages during each simulated year: application, admission, and enrollment, detailed fully in Appendix C. During the application stage, a cohort of prospective students observes, with some uncertainty, the quality of each of the 40 colleges in a given year and selects a limited number of colleges to which to apply based on their uncertain and somewhat idiosyncratic perceptions of the utility of attending each college and of their probability of admission to each. During this stage, the model can allow some colleges to use race-based recruitment strategies that enhance the perceived utility of attending those colleges for targeted students. More formally, a student decides where to apply based on their perception of their own academic achievement, the perceived quality of a college, the utility of attending a college, and an estimation of the likelihood the student will be admitted to a college. A student perceives their own achievement according to AAss ∗ = AAss + bb ∙ rrrrrrrrrrrrrrrrrrss + rrss; rrss~NN(0,σσss), where AAss ∗ is the student’s estimate of how appealing she or he will be to colleges, AAss is the student’s actual academic achievement, and bb ∙ rrrrrrrrrrrrrrrrrrss represents the extent to which the student has enhanced his or her apparent academic achievement (e.g. via SAT® exam coaching or extracurricular participation); this enhancement parameter varies linearly with family resources. Students perceive their own academic achievement with some error, captured by rrss. This term also varies with family resources, prefer a different set of schools. Second, our results primarily focus on the top 10 percent of colleges; these schools pull students from the upper end of the achievement distribution, where complete non-application is uncommon. In effect the colleges in our model end up with very similar students using either approach. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 17 such that students with more family resources perceive their academic achievement with less error (i.e., σs is inversely related to resources). Students observe the quality of colleges according to QQccss ∗ = QQcc + rrccss; rrccss~NN(0, ττss) where QQccss ∗ is student rr’s perception of college rr’s quality, Qc is the actual quality of each college, and ucs is a random noise term drawn from a normal distribution whose variance is again a function of the student’s family resources. This noise captures idiosyncratic preferences for colleges (e.g., a student might be impressed by a college’s dormitories or the tour guide) as well as imperfect information on the part of students. Higher resource students perceive quality with less noise—they have better information and more uniform preferences about college quality. UUccss ∗ is the perceived utility of attending college c for student s. It is given by UUccss ∗ = aass + bbss(QQccss ∗ ) + RRsscc . Here aass and bbss are the intercept and slope of a linear utility function. RRsscc captures the result of racetargeted recruitment strategies on the part of colleges. This recruitment term is meant to represent the increase in perceived desirability of a college that has made special efforts to recruit Black and Hispanic students, whether through targeted visits to high-Black and -Hispanic high schools, strategic disbursement of financial aid, or other methods. RRsscc is the increase in student s’s perception of the utility of college c that comes from recruitment of s by c; this enhanced utility value is used by students when making application and enrollment decisions.5 A student’s estimation of her probability of admission to a given college c is given by PPccss = ff(AAss ∗ − QQccss ∗ ) 5 It may be that some students also have an explicit preference for racial diversity. The explicit modeling of this dimension of college choice is left for future work, however we can interpret a version of these preferences in the noisy perception of college quality. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 18 where ff is a logit function predicting admissions outcomes using the difference between a student’s true academic achievement and college quality for each submitted application over the prior 5 years.6 Students apply to the set of colleges CC1,CC2, ... ,CCnnss that maximizes ESS�CC1,CC2, ... ,CCnnss� , which can be calculated recursively as: ESS�CC1,CC2, ... ,CCnnss� = PPCCiissUUCCiiss ∗ + �1 − PPCCiiss�Ess(CC1,CC2, ... ,CCnnss\CCii). This recursive approach is similar to the sequential utility maximization of application choices used by Howell (2010). Although the model assumes all students are rational, utility-maximizing agents with enormous computational capacity, this rationality is moderated by the fact that the student agents in the model have both resource-related imperfect information and idiosyncratic preferences. This means that there is considerable variability in student application portfolios, even conditional on having the same true academic achievement, and that high-resource students choose, on average, more optimal application portfolios than lower-resource students. Both of these features mimic aspects of actual students’ empirical application decisions (e.g., Hoxby & Avery, 2012) and produce realistic patterns of application (Reardon et al., 2016). In the admission stage, colleges observe the academic records of students in their applicant pools and admit those they (noisily) perceive to be most qualified, up to a total number of students that colleges believe will be sufficient to fill their available seats based on yield information from previous years. In the calculation of how many students to admit, colleges consider the total number of seats they 6 We also attempted a simulation in which students knew which colleges were using affirmative action policies, but the resulting movement of Black and Hispanic students into affirmative action colleges was quite substantial so we omitted this condition from our analyses. This decision is warranted because real students likely have a vague sense that affirmative action will help their admissions chances, however the specifics of exactly which colleges offer how much additional consideration is relatively opaque. Although scholars have documented reductions in URM applications to colleges that have banned race-conscious policies (Brown & Hirschman, 2006), we argue the explicit, often highly publicized, prohibition of a policy is much more salient for decision making than a vague awareness of its presence. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 19 want to fill (150 in all cases) and a three-year running average of yield—the percentage of admitted students who enroll—and will admit as many students as they think they need to fill their seats exactly. Like students, colleges view the world with some uncertainty and idiosyncrasy. This means, for example, that colleges do not rank students identically, reflecting the reality that different colleges have different preferences for students. Formally, a college’s assessment of the admissions desirability of a given student is represented by AAccss ∗∗ = AAss + bb ∙ rrrrrrrrrrrrrrrrrrss + wwccss + TTcc[GG ∙ (BBBBaarrkkss|HHHHrrHHaaHHHHrrss) + HH ∙ rrrrrrrrrrrrrrrrrrss]; wwccss~NN(0, 1002). That is, a college perceives the actual academic achievement of a student, AAss, plus any strategic enhancement of the student’s academic achievement, bb ∙ rrrrrrrrrrrrrrrrrrss (described above), with a certain amount of noise wwccss. The standard deviation of this noise term is half a standard deviation of the academic achievement scale, implying that colleges detect and consider students’ academic achievement (including any enhancement effects) with a reliability of 0.8 (i.e. this noise reflects both a college’s uncertainty and idiosyncratic preferences). It is during the calculation of AAccss ∗∗ that colleges with an affirmative action policy apply additional weight to a student’s perceived admissions desirability in accordance with that policy. This additional weight is captured by the term TTcc[GG ∙ (BBBBaarrkkss|HHHHrrHHaaHHHHrrss) + HH ∙ rrrrrrrrrrrrrrrrrrss]. In this term, TTcc indicates whether a college has an affirmative action policy, GG is the size of the race weight given to a student if they are Black or Hispanic for colleges using race-based affirmative action. HH is the size of the weight given to students under SES-based affirmative action policies, which is applied linearly in accordance with the student’s resources, rrrrrrrrrrrrrrrrrrss. Finally, in the enrollment stage, students compare the colleges to which they have been admitted and enroll in the one with the greatest perceived utility (UUccss ∗ ). At the end of each simulated year, each CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 20 college’s quality (or reputation) is updated by taking a weighted average of prior college quality and the average academic achievement of the newest cohort of enrolled students (where prior quality has a weight of 0.9 and the new cohort has a weight of 0.1). Likewise, colleges update their yield estimates with the three most recent years of admissions data. These three stages are repeated in the next year with a new draw of 10,000 students and the same set of colleges. Model Application We allow the model to run for 30 simulated years in two 15-year phases. The simulation is not intended to represent 30 historical years; the analytic focus is on simulation end states, and not trends. The first 15 years are a conservatively long “burn-in” period in which no college used any affirmative action policy; this allowed the model to consistently settle into a state in which dynamic elements in the model (i.e. colleges’ quality values, colleges’ expected yield) are largely stable from one year to the next. After the 15-year burn-in period, specified colleges start to use affirmative action strategies, and the model then runs for an additional 15 years. Within five to eight years of using affirmative action strategies, college quality and enrollment patterns typically stabilize again (we discuss model stability in greater detail in Appendix C). We allow the model to run through year 30 and then use the average patterns of enrollment in the final five years (years 26 through 30) as our primary model output. In order to explore the effects of different affirmative action and recruitment policies, we run our model under different policy scenarios. Each of these scenarios is defined by four parameters: the magnitude of race-based affirmative action, the magnitude of SES-based affirmative action, the magnitude of race-based recruitment, and the number and rankings of colleges that use affirmative action. To account for potential idiosyncrasies within a given simulation run—particularly acknowledging that a given solution may not be unique—we simulate each of the scenarios that we describe in our primary results ten times, and average across these ten runs to capture the college and student outcomes of interest that we present. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 21 As stated above, most of the parameters in our model are estimated directly from the nationally representative ELS data. These parameters include the specification of the joint distribution of race, SES, and academic achievement, and the amount of additional weight given to URMs under race-based affirmative action. Other parameters, like the racial composition of the students in the model, the ratio of college seats to total students are approximations that are grounded in real-world data, but are abstracted away out of necessity (because, for example, we do not include race groups other than White, Black, Hispanic, and Asian) and simplicity. Parameters such as the selectivity of colleges and, consequently, students’ assessments of their likelihood of admission, are determined by the model in accordance with the rules of the admissions process that the model dictates and, as a result, are accurate in the sense that they are the desired consequence of our agents responding to the model-defined system. Finally, some parameters, most notably the ones that give certain advantages to higher-resource students (like submitting more applications) were established and tested in Reardon et al. (2016). RESULTS We start by presenting the levels of racial diversity produced by of various combinations of SESbased affirmative action and race recruiting relative to the racial diversity of our simulated colleges using a race-based affirmative action policy whose strength is equivalent to our estimate of the strength of such policies in the real world. For this portion of the analysis, we focus on the scenarios when the top ten percent of colleges—the four with highest quality—use affirmative action policies. In Figure 2 we present results from sixteen scenarios: no, light, moderate and strong SES-affirmative action (corresponding to weights of 0, 50, 100, and 150 per standard deviation of resources); no, light, moderate and strong race-based recruiting (corresponding to weights of 0,25, 50, and 100), and all combinations thereof. In each cell, the light (dark) bar represents the proportion of Black (Hispanic) students enrolled in these four schools as a proportion of how many students enroll using the estimated real-world raceCAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 22 based affirmative action weight (weight of 260, results represented by the dotted line). The specific proportions of each race group achieved under each policy are presented in Appendix Figure A2. Increases in the strength of both policies increase the proportion of Black and Hispanic students relative to the baseline race-based policy. However, neither policy alone can recover the rates of Black and Hispanic enrollment we see using race-based affirmative action policies. To achieve these rates of diversity seen under our race-based policy, SES-based affirmative action and race recruiting need to be used at the strongest levels of our model. These simulations indicate that SES-based affirmative action and race recruiting together can replicate levels of racial diversity achieved by race-based policies, but it requires levels of SES-based affirmative action and race-recruiting that are quite large relative to current, observed admissions practices. [ Figure 2 here ] In Appendix Figures A3-A5, we present more detailed results of various raceand SES-based affirmative action and race recruiting policy simulations on the racial and socioeconomic composition of the participating schools. In short, they show similar findings to those presented in Figure 2, that SESbased affirmative action is not as effective as race-based affirmative action at generating racial diversity in the schools that use it unless it is used in conjunction with race recruiting (or race-based affirmative action itself). However, SES-based policies do create SES diversity in a way that race-based policies do not. Because students and colleges comprise an interconnected system, the effects of affirmative action policies will not be isolated to the colleges that use them. Colleges that do not use affirmative action policies are affected by the presence of such policies in other schools. Figure 3 illustrates these system dynamics—the effect of having the top four colleges using admissions policies (either SES-based affirmative action and race recruiting or race-based affirmative action) on the kinds of students (by CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 23 achievement and race) enrolled in all colleges.7 We present similar figures for the effects on achievement and proportion of low-resource students in Appendix D.8 In both panels, black arrows indicate the colleges that use affirmative action and gray arrows show colleges that do not. Each of the arrows starts at the location in the figure corresponding to the racial composition and average high school academic achievement of enrolled students in the college in the final year of the model’s burn-in period (year 15), before any college begins using affirmative action. The arrows end at the location corresponding to each college’s enrollment composition in the final year of the model (year 30), after some colleges in the model have been using admissions policies for 15 years. [ Figure 3 here ] A few results are immediately clear in Figure 3. First, colleges that use diversity-boosting admissions policies become more racially diverse and their students’ average achievement declines. Second, the slope of this change is quite steep, indicating that the changes in mean achievement are much less pronounced than the changes in the proportion of Black and Hispanic students. Evident in these graphs, and even more evident in the graphs in Appendix D (which gives similar graphs for changes in income diversity as well as for scenarios in which more than 4 colleges use affirmative action policies) the less selective colleges that use affirmative action experience the greatest changes in both diversity and average achievement—their lines move the farthest. This pattern is especially true for schools that use SES-based affirmative action in combination with race recruiting. This large movement for the less selective schools using these admissions policies is driven by race recruiting; when used alone (without SES-based affirmative action), we see a similar pattern of growth in the proportion of minority students 7 In this and the following analyses we use the “strong” versions of SES-based affirmative action and race recruiting that were the only policies, and only in combination, to reproduce levels of racial diversity achieved under our racebased affirmative action simulation. 8 We present the four college results because they are most analogous to patterns of affirmative action use in the real world. In Appendix D we present similar figures for the effects on Black and Hispanic and low-income enrollment of different numbers (four, ten, 20, and 40) of schools using affirmative action policies. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 24 for the less selective schools using the targeted recruitment policy (results showing the effects of racerecruiting and SES-based affirmative action alone are available upon request). Third, colleges that do not adopt affirmative action policies, but that are close in quality to those that do, also experience changes in diversity and average achievement, though in the opposite direction as those using affirmative action. That is, they become less diverse and the mean achievement of their enrolled students increases. Finally, the left-most arrow in each panel captures the characteristics of students in the model who end the process not enrolled in any college. In each panel, the introduction of diversity-boosting policies hardly moves these arrows. In other words, the margin of college attendance is generally unaffected by affirmative action policies; the characteristics of non-enrolled students remain mostly unchanged.9 Beyond the college-level consequences of affirmative action, we are also concerned with whether and how affirmative action policies affect the difference in academic achievement between the enrolled students and their peers. Figure 4 shows mean academic achievement of students’ classmates in college as a function of a student’s own achievement, race, and affirmative action type. Here again, only the top four colleges in the simulation use affirmative action or race recruiting. We first examine the effects of these policies on all students enrolled in colleges, because, as we just demonstrated, policies enacted at one college can affect enrollment across the system. Figure 4 also includes a 45-degree line, which indicates when a student’s own achievement is equal to the average achievement of his or her peers. A student’s own achievement falls below the average achievement of his or her peers when the lines of the figure are above the 45-degree line. Whether such overmatching is extreme enough that it leaves students academically over their head is beyond the scope of this paper. 9 In Appendix D, we show that this is true up until more than half of colleges use targeted admissions policies, then the population of students not enrolled in college includes notably fewer Black and Hispanic students and has higher mean achievement. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 25 [ Figure 4 here ] Under our simulation of race-based affirmative action, all Black and Hispanic students enroll in colleges where their peers have higher academic achievement than if no type of affirmative action were used (Figure 4, right panel). This policy simulation also results in the highest proportion of students enrolled in colleges where their achievement level falls below the average achievement of their peers. On average, Black and Hispanic students under our race-based policy are over matched if their achievement is roughly 1140 or lower. This results contrasts with our simulation with no diversity-boosting policy where the peers of Black and Hispanic students are generally lower, but it is the students with achievement below roughly 1060 that are over-matched. However, although fewer students are overmatched in the no-policy simulation, the results for the race-based simulation hew most closely to the 45degree line of all our policy simulations, indicating that this policy results in average peer achievement that aligns most closely with Black and Hispanic students’ own achievement. The race-neutral simulations that include SES-based affirmative action either on its own or in combination with race recruiting each perform between the extremes of no policy and race-based affirmative action. The combination policy results in higher average peer achievement for Black and Hispanic students than SES-based affirmative action on its own. Under both scenarios, Black and Hispanic students with achievement less than roughly 1080 are overmatched, on average. Race recruiting on its own leads to the lowest amount of overmatching—students below roughly 1050 achievement overmatch on average—but also tends to result in the lowest achieving peers for Black and Hispanic students out of all our simulated policies (including no policy at all). This lower peer achievement holds in the racerecruiting scenario for students with achievement less than about 1250. Above that point, students with higher achievement see better peers than they would under no policy and better than under all policies except race-based affirmative action for students at the highest end of the achievement distribution. In other words, race recruiting results in lower-achieving peers for lower achieving students, but higher CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 26 achieving peers than under many policies for higher achieving students. Figure 4 (left panel) also demonstrates, that our simulated policies have very little impact on the average peer achievement of white students, particularly those with achievement less than about 1250. Above that level, race recruiting and no affirmative action policy result in similarly high achieving peers for white students, while the other three policy simulations result in peers that, on average, are about 15 points lower performing. The results in Figure 4 are important if we are concerned with diversity-boosting polices as part of a broad higher education system. If, instead, we are concerned specifically with the students at institutions that use the policies, then we should focus on Figure 5, which presents these same comparisons as Figure 4, but only for students enrolled in the top four schools (i.e. within schools that use, or would use, affirmative action policies). Again, the 45-degree line indicates when a student’s own achievement is equal to the average achievement of his or her peers. For Black and Hispanic students in these most selective schools, all of the policy simulations with the exception of the SES-based affirmative action and race recruitment combination perform roughly similarly: under each of them students with achievement below anywhere from 1340-1360 overmatch (Figure 5, right panel). This is the same value at which White students tend to be overmatched under the no policy simulation, however a greater proportion of Black and Hispanic students than White students score below that threshold (Figure 5, left panel). In contrast, Black and Hispanic students under the combination policy have peers with achievement levels about 50 points lower, on average, than the other policy simulations. Although it exposes Black and Hispanic students to academically weaker students, the combination policy results in the lowest rate of overmatch—Black and Hispanic students with achievement below 1300 overmatch, on average, in the combination simulation. This result appears to be driven mostly by the fourth ranked school, which receives a large influx of lower-achieving Black and Hispanic students in the combination scenario. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 27 [ Figure 5 here ] To assess the extent to which the results presented above are sensitive to assumptions that we make in the model (specifically, the use of resource-effect values like achievement enhancement that we take from Reardon et al. (2016)), we conduct a Latin Hypercube analysis (Bruch & Atwood 2012; SegoviaJuarez et al. 2004). This analysis consists of generating 100 random combinations of parameter values (within plausible ranges) that govern resource-effect pathways, affirmative action, and recruitment policies, and then running our simulation once using each of these. This ensures that, in expectation, the parameters used during a model run are not correlated with each other. We next run regressions predicting college-level outcomes of interest (averaged over the last five years of each simulation for schools using affirmative action) using the parameters that we vary; these outcomes include mean academic achievement and resources of enrolled students, college rank, and proportion of enrolled students who are low resource or Black or Hispanic. These regression results are presented in Table 2, and show both affirmative action and recruitment policy effects independent of the assumptions that we make about resource effect pathways as well as the influence of resource effect pathway values. Overall, policy effects in this sensitivity analysis are consistent with what we present above, and our findings are fairly robust to the assumptions that we make about resource effect pathways magnitude. As expected, the biggest impact of varying resource effect magnitudes is on levels of low-resource student enrollment in colleges, but the difference in this outcome between the highest and lowest parameter values that we explore never exceeds 10 percentage points. [ Table 2 here ] DISCUSSION The results of our simulations suggest at least three important patterns. First, within the range of values we investigate, neither SES-based affirmative action nor race recruiting policies on their own can CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 28 reproduce levels of racial diversity achieved by race-based affirmative action; however, SES-based affirmative action in combination with targeted recruitment shows the potential to yield racial diversity levels comparable to race-based affirmative action. The cost and magnitude of such policies might render such policies non-workable in practice, however. Second, the use of affirmative action policies by some colleges reduces the diversity of similar-quality colleges that do not have such policies. Third, overall, the combination of SES-based affirmative action and race recruiting results in slightly fewer Black and Hispanic students that are academically overmatched than under race-based affirmative action, but the schools that use the combination policy also see an overall reduction in the academic achievement of the students they enroll. The 2013 Fisher I decision requires universities to prefer “workable race-neutral alternatives” to race-based affirmative action. Suggesting one such alternative, Kahlenberg (1996) has argued that “classbased preferences provide a constitutional way to achieve greater racial and ethnic diversity” (p. 1064). However, our simulations suggest that unless SES-based affirmative action policies use a very strong preference for lower SES students, or are paired with effective race-based recruitment efforts, these policies are unlikely to result in the same racial composition in colleges as under current race-based affirmative action policies. These results are consistent with Sander (1997), who found that SES-based affirmative action at the UCLA law school did not produce the levels of racial diversity achieved under race-based affirmative action policies, and Long (2015) who found in Texas that that a number of race proxies could not reproduce the diversity achieved under race-based affirmative action. Race-based affirmative action likely leads to racial diversity because it can select directly the students who will contribute most to racial diversity on a campus. In contrast, SES-based affirmative action requires a strong relationship between SES and race in order to achieve racial diversity. Our analysis makes clear that the correlation currently observed in the real world is not high enough to make SES-based affirmative action a realistic alternative to race-conscious admissions policies (however, as CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 29 demonstrated in Appendix A, it is good at generating socioeconomic diversity). This is not to say that the correlation isn’t high—it is—however, it is not high enough that one can be used as a proxy for the other in affirmative action policies. This conclusion is consistent with the ineffectiveness of SES-based K-12 school integration policies at producing racial integration (Reardon et al., 2006; Reardon & Rhodes, 2011). Special recruitment efforts that target URM students may help increase the effectiveness of potential SES-based admissions policies, however, there are several reasons to believe that even with this help it is unlikely these policies would be “workable.” First, the level of additional weight necessary for SES-based policies to produce levels of racial diversity comparable to race-based policies would have to be exceptionally large, even with the help of race-targeted recruiting. Put in context, our empiricallybased race-based affirmative action model gives Black students a weight of 260 achievement points over White students. In contrast, the necessary SES-based approach in our model gives an additional weight of 150 points for each standard deviation of SES. This means that a student from two standard deviations below mean SES would have an admissions advantage 600 points higher than a student two standard deviations above mean SES, over two times larger than the weight we estimate is used in current racebased polices. Second, because SES-based affirmative action increases SES diversity, colleges who consider such policies will have to consider what those policies will mean in terms of the additional students who need financial aid. Currently, very few colleges are able to meet the full demonstrated financial need of the students they enroll without SES-based affirmative action, so an additional influx of lower-income students would likely stretch limited resources even more thinly. Moreover, our models assume that cost is not a barrier to enrollment for low-income admitted students. In the absence of additional financial aid, SES-based affirmative action policies will increase the number of low-income students who are admitted to a college, but may not have the same effect on enrollment patterns, because cost will be a barrier for some of the additionally-admitted low-income students. That is, our estimates may overstate the effects CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 30 of SES-based affirmative action policies unless such policies were coupled with increased financial aid. In contrast, race-based affirmative action alone yields higher proportions of URM students in the top colleges, although it produces relatively little additional socioeconomic diversity. In this respect, it is likely a less expensive and more direct means of increasing the racial diversity of colleges. Third, the addition of targeted race-based recruitment and outreach offers a tempting solution to bans on race-conscious admissions policies, but this recruitment likely only adds to the cost of achieving racial diversity, assuming it is even workable. Race targeted recruitment without SES-based affirmative action appears to have stemmed the loss of URM students at the University of Washington after the state banned race-conscious affirmative action in admissions (Brown & Hirschman 2006). However, the results of such efforts in California and Texas are less clear (Andrews, et al., 2016; Gándara, 2012; Geiser & Caspary 2005). In fact, despite doubling its recruitment budget, California still saw a substantial proportion of high-achieving URM students enroll in colleges outside the California system, even if they were admitted (Geiser & Caspary 2005). Such findings call into question whether outreach and recruitment efforts can sway URM students enough to make a difference to campus diversity. Our models assumed that, at a maximum, colleges could raise their appeal to students by 100 points (comparable to the average SAT® score at a college appearing 100 points higher—or, roughly the difference between Tulane and Cornell). Further, our model was 100 percent efficient—all Black and Hispanic students felt the effect of our recruitment mechanism. It is hard to judge whether these assumptions carry much veracity in the real world. At the very least, the effort required to boost URM student recruitment efforts will only add to the cost of SESbased affirmative action programs. In other words, SES-based affirmative action plus race-targeted recruitment and outreach is a race-neutral alternative to race-conscious affirmative action, but it is not clear whether institutional budgets at public universities make it “workable.” Affirmative action policies also affect all colleges, not just the colleges that use the policies. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 31 System dynamic effects are an important, and often overlooked, factor in affirmative action policies; because colleges and students are operating in an interconnected and interdependent system, the diversity-boosting policies tend to reduce the diversity of campuses with no policies. Building on the work of Long and Tienda (2010) in Texas, we find that these effects are particularly strong for colleges that are not using affirmative action policies but are close in quality to schools that are. This result could be a particularly important dynamic in states in which public colleges are unable to use race-based affirmative action but private colleges of similar quality continue to use race conscious admissions policies. This suggests that any complete assessment of affirmative action policies must attend to effects not only within colleges that use affirmative action, but also those that do not. Our models also suggest that affirmative action policies are unlikely to change the margin of college attendance. That is, they do not have much effect on who attends college, but only on which college they attend if they do. Unless affirmative action policies are targeted at much lower achieving students or are implemented much more widely than they currently are, these policies are unlikely to affect the overall racial and socioeconomic distribution of college attendees. Critics of race-based affirmative action have argued that it can lead to academic mismatch for URM students. We find that SES-based affirmative action, alone or in combination with race recruiting, lowers the average academic achievement of Black and Hispanic students’ peers relative to no diversityboosting policy or race-based affirmative action. This lowering of academic quality at colleges that use strong SES-based policies likely stems from the fact that colleges following these policies admit lowerachieving White students alongside Black and Hispanic students to achieve racial diversity. Our models do not presume that colleges would change their policies if their academic rank were falling. It is not clear that elite colleges in the real world would similarly want to lower their overall observable academic rank to the extent necessary to achieve racial diversity using race neutral policies, again suggesting that such policies may not be workable. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 32 The models presented in this paper do not directly address issues of cost or financial aid. We do, however, indirectly include elements of race-targeted financial aid in our recruitment parameters: financial aid and other forms of tuition discounting are implied in efforts that would make a college more desirable to targeted students. However, it is likely that the direct inclusion of cost and financial aid considerations would mute some of the effects of affirmative action policies unless the policies are accompanied by increased financial aid or other greatly modified tuition structures. URM and low income students would presumably be discouraged from applying to expensive, selective colleges, limiting the ability of affirmative action policies of any type to be effective. Our results, therefore, may represent an upper bound on the potential effectiveness of various affirmative action polies. The complexities of this issue are worth exploring in future research and are an area to which policy makers should pay close attention. In Fisher I, the Supreme Court challenged states and universities to find race-neutral strategies that can achieve educationally-beneficial diversity and Fisher II pressed them to continue to evaluate the ongoing need for any race-conscious policies they use. Racial diversity is, the court has agreed, educationally beneficial (Grutter v. Bollinger, 2003). The question, then, is how best to achieve such diversity in constitutionally permissible ways. Perhaps the best way would be to eliminate racial gaps in high school achievement and graduation rates; doing so would certainly go a long way toward equalizing access to selective colleges and universities without the need for race-based affirmative action. Although these gaps have narrowed moderately in the last two decades (Reardon, Robinson-Cimpian, & Weathers, 2015; Murnane, 2013), they are still very large, without a clear indication that they will be eliminated any time soon. Until racial disparities in educational preparation are eliminated, colleges need other strategies to achieve diversity goals. Our analysis here suggests that affirmative action policies based on socioeconomic status are unlikely to reproduce levels of racial diversity achieved by race-based policies CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 33 unless they are paired with targeted race recruiting and provide admissions boosts larger than those used under race-based policies. That is not to say that socioeconomic affirmative action would not be valuable in its own right—it would increase socioeconomic diversity on university campuses and would benefit low-income college applicants—but only that it is not an effective or efficient means to achieving racial diversity. Race-conscious affirmative action does, however, increase racial diversity effectively at the schools that use it. Although imperfect, it may be the best strategy we currently have. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 34REFERENCESAndrews, R. J., Imberman, S. A., & Lovenheim, M. F. (2016). Recruiting and Supporting Low-Income, High-Achieving Students at Flagship Universities (Working Paper No. 22260). Cambridge, MA: NationalBureau of Economic Research.Arcidiacono, P., Aucejo, E., Coate, P., & Hotz, V. J. (2014). Affirmative action and university fit: Evidencefrom Proposition 209. IZA Journal of Labor Economics, 3, 7.Arcidiacono, P., Khan, S., & Vigdor, J. L. (2011). Representation versus assimilation: How do preferences incollege admissions affect social interactions? Journal of Public Economics, 95, 1–15.Arcidiacono, P., & Lovenheim, M. (2014). Affirmative action and the quality-fit tradeoff (Working PaperNo. 20962). Cambridge, MA: National Bureau of Economic Research.Backes, B. (2012). Do affirmative action bans lower minority college enrollment and attainment? Evidencefrom statewide bans. Journal of Human Resources, 47, 435-455.Bastedo, M. N., & Jaquette, O. (2011). Running in place: Low-income students and the dynamics of highereducation stratification. Educational Evaluation and Policy Analysis, 33, 318-339.Becker, B. J. (1990). Coaching for the Scholastic Aptitude Test: Further synthesis and appraisal. Review ofEducational Research, 60, 373-417.Bowen, W. G., & Bok, D. (1998). The Shape of the River: Long-term Consequences of Considering Race inCollege and University Admissions. Princeton, NJ: Princeton University Press.Bowen, W. G., Kurzweil, M. A., & Tobin, E. M (2005). Equity and Excellence in American Higher Education.Charlottesville, VA: University of Virginia Press.Brown, S. K., & Hirschman, C. (2006). The end of affirmative action in Washington State and its impact onthe transition from high school to college. Sociology of Education, 79, 106-130.Buchmann, C., Condron, D. J., & Roscigno, V. J. (2010). Shadow education, American style: Testpreparation, the SAT® and college enrollment. Social Forces, 89, 435-461. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 35Bruch, E., & Atwood, J. (2012). Agent-based models in empirical social research. Working paper.Carnevale, A. P., & Rose, S. J. (2004). Socioeconomic status, race/ethnicity, and selective collegeadmissions. In R. D. Kahlenberg (Ed.), America’s Untapped Resource: Low-Income Students inHigher Education (pp. 101–156). New York: Century Foundation Press.Carnevale, A. P., & Strohl, J. (2010). How increasing college access is increasing inequality, and what to doabout it. In R.D. Kahlenberg (Ed.) Rewarding Strivers: Helping Low-Income Students Succeed inCollege (pp. 71-190). New York: Century Foundation Press.Carnevale, A. P., Rose, S. J., & Strohl, J. (2014). Achieving racial and economic diversity with race-blindadmissions policy. In R. D. Kahlenberg (Ed.), The future of affirmative action: New paths to highereducation diversity after Fisher v. University of Texas (pp. 187–202). New York: Century FoundationPress.Dickson, L. M. (2006). Does ending affirmative action in college admissions lower the percent of minoritystudents applying to college?. Economics of Education Review, 25, 109-119.Dillon, E. W., & Smith, J. A. (2015). The consequences of academic match between students and colleges(IZA Discussion Paper No. 9080).Epstein, J. M. (1999). Agent-based computational models and generative social science. Complexity, 4,41-60.Espenshade, T. J., & Radford, A. W. (2009). No Longer Separate, Not Yet Equal: Race and Class in EliteAdmission and College Life. Princeton, NJ: Princeton University Press.Fisher v. University of Texas at Austin, 570 U.S.(2013).Fisher v. University of Texas at Austin, 579 U.S.(2016).Fu, C. (2014). Equilibrium tuition, applications, admissions and enrollment in the college market. Journalof Political Economy, 122, 225-281.Gaertner, M. N., & Hart, M. (2013). Considering class: College access and diversity. Harvard Law and CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 36Policy Review, 7, 367–403.Gandara, P. (2012). California: A case study in the loss of affirmative action. Los Angeles: The Civil RightsProject.Gratz v. Bollinger, 539 U.S. 244 (2003).Grutter v. Bollinger, 539 U.S. 306 (2003).Hinrichs, P. (2012). The effects of affirmative action bans on college enrollment, educational attainment,and the demographic composition of universities. Review of Economics and Statistics, 94, 712-722.Horn, C. L. & Flores, S. M. (2003). Percent plans in college admissions: A comparative analysis of threestates’ experiences. Cambridge, MA: The Civil Rights Project at Harvard University.Howell, J. S. (2010). Assessing the impact of eliminating affirmative action in higher education. Journal ofLabor Economics, 28, 113–166.Hoxby, C. M., & Avery, C. (2012). The missing “one-offs": The hidden supply of high-achieving, low incomestudents (Working Paper No. 18586). Cambridge, MA: National Bureau of Economic Research.Institute of Education Sciences (2012). NCES Common Core of Data. U.S. Department of Education,National Center for Education Statistics. Washington, DC.Kahlenberg, R. D. (1996). Class-based affirmative action. California Law Review, 84, 1037–1099.Kahlenberg, R. D. (2012). The future of school integration: Socioeconomic diversity as an educationreform strategy. New York, NY: Century Foundation Press.Kane, T. J. (1998). Racial and ethnic preferences in college admissions. In C. Jenks & M. Phillips (Eds.), TheBlack-White test score gap. Washington, DC: Brookings Institution Press.Lim, M. (2013). Percent plans: A workable, race-neutral alternative to affirmative action. Journal ofCollege and University Law, 39, 127-163.Long, M. C. (2004). Race and college admission: An alternative to affirmative action? The Review ofEconomics and Statistics, 86, 1020–1033. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 37Long, M. C. (2007). Affirmative action and its alternatives in public universities: What do we know? PublicAdministration Review, 67, 311–325.Long, M. C. (2015). Is there a “workable” race-neutral alternative to affirmative action in collegeadmissions?. Journal of Policy Analysis and Management, 34, 162-183.Murnane, R. (2013). U.S. high school graduation rates: Patterns and explanations. Journal of EconomicLiterature, 51, 370–422.Niu, S. X., & Tienda, M. (2010). The impact of the Texas top 10 percent law on college enrollment: Aregression discontinuity approach. Journal of Policy Analysis and Management, 29, 84-110.Powers, D. E., & Rock, D. A. (1999). Effects of coaching on SAT® I: Reasoning test scores. Journal ofEducational Measurement, 36, 93-118.Reardon, S. F., Baker, R., & Klasik, D. (2012). Race, income, and enrollment patterns in highly selectivecolleges, 1982-2004. Stanford Center on Poverty and Inequality, Stanford University. Retrievedfrom http://cepa.stanford.edu/content/race-income-and-enrollmentpatterns-highly-selective-colleges-1982-2004.Reardon, S. F., Kasman, M., Klasik, D., & Baker, R. B. (2016). Student resources and stratification amongcolleges: An agent-based simulation of five mechanisms of the college sorting process. Journal ofArtificial Societies and Social Simulation, 19(1), 8.Reardon, S. F., & Rhodes, L. (2011). The effects of socioeconomic school integration policies on racialschool segregation. In E. Frankenberg & E. DeBray (Eds.), Integrating schools in a changing society.Chapel Hill: University of North Carolina Press.Reardon, S., Robinson-Cimpian, J., & Weathers, E. (2015). Patterns and trends in racial/ethnic andsocioeconomic academic achievement gaps. In H. Ladd & M. Goertz (Eds.), Handbook of Researchin Education Finance and Policy. New York, NY: Routledge.Reardon, S. F., Yun, J. T., & Kurlaender, M. (2006). Implications of income-based school assignment CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 38policies for racial school segregation. Educational Evaluation and Policy Analysis, 28, 49–75.Sander, R. H. (1997). Experimenting with class-based affirmative action. Journal of Legal Education, 47,472–503.Sander, R. H. (2004). A systemic analysis of affirmative action in American law schools. Stanford LawReview, 57, 367–483.Segovia-Juarez, J. L., Ganguli, S., & Kirschner, D. (2004). Identifying control mechanisms of granulomaformation during M. tuberculosis infection using an agent-based model. Journal of TheoreticalBiology, 231 357–376. [doi:10.1016/j.jtbi.2004.06.031]Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: Cumulative representation ofuncertainty. Journal of Risk and Uncertainty, 5, 297-323.Xiang, A., & Rubin, D. B. (2015). Assessing the potential impact of a nationwide class-based affirmativeaction system. Statistical Science, 30, 297-327. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 39Table 1. Agent-Based Simulation Model (ABM) Parameters ParameterValueSourceNumber of students10,000n/apercent White60 percentNCES Common Core of Data,2012percent Black15 percentNCES Common Core of Data,2012percent Hispanic20 percentNCES Common Core of Data,2012percent Asian5 percentNCES Common Core of Data,2012Number of colleges40n/aCollege capacity150 students/collegen/aStudent academic achievementELSWhiteachievement ~N(1052, 186)Blackachievement ~N(869, 169)Hispanicachievement ~N(895, 185)Asianachievement ~N(1038, 202)Student resourcesELSWhiteresources~N(.198, .657)Blackresources~N(-.224, .666)Hispanicresources~N(-.447, .691)Asianresources~N(.012, .833)Resources-achievement correlationsELSWhiter=0.395Blackr=0.305Hispanicr=0.373Asianr=0.441Quality reliability(how well students see college quality)0.7 + a(resources); a=0.1Reardon et al., 2016 Own achievement reliability(how well students see their ownachievement)0.7 + a(resources); a=0.1Reardon et al., 2016 Achievement reliability(how well colleges see student achievement)0.8Reardon et al., 2016 Apparent achievement (perceivedachievement, increased or decreasedthrough achievement enhancement)perceived achievement +b(resources); b=0.1Becker, 1990; Buchmann,Condron, & Roscigno, 2010;Powers & Rock, 1999;Reardon et al., 2016Number of applications4 + INT[c(resources)]; c=0.5ELSUtility of college attendanced + e(perceived quality); d=-250, e=1 Reardon et al., 2016Note. Quality and achievement reliability bound by minimum values of 0.5 and maximum values of 0.9. ELS =Educational Longitudinal Study. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 40Table 2. Latin Hypercube Analysis Model/Dependent Variable Independent VariableCollegeQualityMean CollegeResourcesCollegeQuality RankPercent LowResourcePercentBlack/HispanicIndependent Variable Rangesb/(se)b/(se)b/(se)b/(se)b/(se)Mean Min Max Information Reliability91.572*** 0.397*** 4.111-16.052*** -15.641.10.2(16.600) (0.077)(2.641)(4.181)(8.651)Resource-Apps Corr.5.269** 0.078*** 0.493-4.779*** -3.386***102(1.599)(0.007)(0.254)(0.403)(0.833)Utility Slope2.1650.0110.284-0.688-1.487102(1.622)(0.008)(0.258)(0.409)(0.846)Resource-App Enhancement36.411* 0.961*** 2.358-47.376*** -2.072.10.2(16.003) (0.074)(2.546)(4.030)(8.340)SES AA Weight-0.372*** -0.004*** -0.043*** 0.186*** 0.174***750150(0.022)(0.000)(0.003)(0.005)(0.011)Race AA Weight-0.366*** -0.002*** -0.041*** 0.086*** 0.234***150 0300(0.011)(0.000)(0.002)(0.003)(0.006)Race Recruit Weight-0.154*** -0.001*** -0.019*** 0.047*** 0.122***100 0200(0.016)(0.000)(0.003)(0.004)(0.008)constant1375.603*** 0.767*** 102.009*** 5.886*** -9.407***(4.753)(0.022)(0.756)(1.197)(2.477)N100100100100100R-Sqr0.9410.9700.8850.9610.957Note. “Percent Low Resource” is defined as the percentage of students from the bottom two quintiles of the resources distribution. Coefficients give the changein the given outcome associated with varying the given parameter between the extremes listed to the right of the table. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 41Figure 1. The racial composition of postsecondary destinations for the high school class of 2004. Notes. Reproduced from Reardon, Baker, & Klasik (2012). Figure shows the postsecondary enrollment status ofmembers of the high school class of 2004 by race and type of college or university. In particular, we break collegeenrollment into enrollment in a less-than-four-year college and, if a student is enrolled in a four-year college, wedivide schools according to the Barron’s selectivity rating of the school (from the least selective [6] to most selective[1]). The width of each bar represents the percentage of the college-age population enrolled in different types ofcolleges and universities (or not enrolled in any college, in the case of the leftmost bars); the vertical dimensiondescribes the racial composition of students enrolled in each type of postsecondary institution. Source: EducationalLongitudinal Study, 2002. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 42Figure 2. Black and Hispanic Enrollment in Colleges using SES-Based Affirmative Action and Race-BasedRecruitment, as a share of estimated Black and Hispanic enrollment under race-based affirmative action(using estimated real-world affirmative action weight) Notes. Figure 2 shows Black and Hispanic enrollment as a share of estimated Black and Hispanic enrollment underrace-based affirmative action, where colleges use the estimated real world race-based affirmative action weight of260. Black and Hispanic enrollment is shown by affirmative action style and strength for the four highest rankedcolleges, which all use SES-based affirmative action and/or recruitment. SES-based affirmative action strength is 0,50, 100, and 150 corresponding to “None”, “Light”, “Moderate”, and “Strong”, respectively. Race recruitmentstrength is 0, 25, 50, and 100 corresponding to “None”, “Light”, “Moderate”, and “Strong”, respectively. As anexample of how to read this figure, consider the third box from the left on the top: in this simulation, the collegesthat use affirmative action use “Strong” SES-based affirmative action and “Moderate” race-based recruitment. Thiscombination results in nearly 80% of the Black student enrollment as race-based affirmative action (using real worldweight), and results in over 100% of Hispanic enrollment, relative to race-based affirmative action. SES issocioeconomic status. Source: authors’ simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 43Figure 3. Mean achievement and proportion minority by type of admission policies used by top fourschools. Notes. The left panel gives the results of the scenario where strong socioeconomic-based affirmative action andrace-recruiting policies are used by the top four schools. The right panel gives the results of the scenario where thetop four schools use strong race-based affirmative action policies. Arrows start at a school’s position in year 15when it was not using affirmative action, and end at the school’s position in year 30. The left-most arrow capturesstudents who do not enroll in college in our simulation. Source: authors’ simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 44Figure 4. Mean achievement of students in own college by race and affirmative action type, all students;top four ranked schools use affirmative action. Notes. Figure 4 shows the mean peer achievement of students in own college by race and affirmative action type forall schools and students in the simulation; only the four highest ranked colleges use affirmative action orrecruitment. Consider White students (left panel) with achievement scores of 1400. This figure shows that thesestudents attend schools where their peers’ average achievement is approximately 1340 when there is no affirmativeaction or recruitment used. These same students have peers with a marginally lower mean achievement under thecombination of SES-based affirmative action and race recruiting. When these lines are below the 45-degree line,students have higher achievement than the average achievement of their peers; conversely, when these lines areabove the 45-degree line, students are in settings where their own achievement is lower than the averageachievement of their peers. SES is socioeconomic status. Strong SES affirmative action corresponds to 150; strongrace-based recruitment corresponds to 100; “real world” race-based affirmative action is 260. Source: authors’simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 45Figure 5. Mean achievement of students in own college by race and affirmative action type, only studentsin affirmative action schools; top four ranked schools use affirmative action. Notes. Figure 5 shows the mean peer achievement of students in own college by race and affirmative action type forschools that use affirmative action; only the four highest ranked colleges use affirmative action or recruitment.Consider White students (left panel) with achievement scores of 1400. This figure shows that these students attendschools where their peers’ average achievement is approximately 1340 when there is no affirmative action orrecruitment used. Under the combination of strong SES-based affirmative action and strong race-based recruitment,the same students experience peers with an average achievement of approximately 1310. When these lines arebelow the 45-degree line, students have higher achievement than the average achievement of their peers;conversely, when these lines are above the 45-degree line, students are in settings where their own achievement islower than the average achievement of their peers. SES is socioeconomic status. Strong SES affirmative actioncorresponds to 150; strong race-based recruitment corresponds to 100; “real world” race-based affirmative action is260. Source: authors’ simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 46APPENDIX A. SOCIOECONOMIC AND RACIAL COMPOSITION OF REAL-WORLD AND SIMULATED COLLEGESIn Appendix A we provide figures representing the student composition of real-world post-secondary destinations (Figure A1) and simulated colleges under a range of admissions policies (FiguresA2-A5). In the results presented in the main text we focus on testing the effects of SES-based affirmativeaction and race-based recruiting strategies, as compared to race-based affirmative action policies, on thestudent composition (in terms of both race and achievement). Our goal is to provide an extended view ofthe effects of our simulated admissions policies and again compare them to the effects of race-basedaffirmative action.In Figure A2 we extend Figure 2 by showing the full racial composition of schools using variouscombinations of SES-based affirmative action and race-based recruiting. We again see the importantcomplementary effects of these policies, and the small effect that SES-based affirmative action can haveon racial diversity if it is not combined with race recruiting. In Figure A3 we show the effects of thesesame policies on the SES composition of schools. Unsurprisingly, race recruiting has little effect on the SEScomposition of schools, and SES-based affirmative action has a large effect.In Figures A4 and A5 we provide the racial and SES compositions of schools using variouscombinations of raceand SES-based affirmative action policies. These figures provide an extension toFigure 2 and allow us to examine the effects of using SESand race-based affirmative action policies aloneand in combination. Both in terms of racial composition and SEScomposition, the affirmative actionpolicies have interactive effects: schools are more diverse when the policies are used in tandem. But,each policy has a much greater effect on its focal group than it does on the other (e.g. SES-basedaffirmative has a much smaller effect on the racial diversity of a school than the SES diversity of a school).SES-based affirmative action has little effect on the racial diversity of schools unless it is used with a race-targeted policy. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 47Figure A1: Income Composition of Postsecondary Destinations, Class of 2004 Notes: Figure A1 shows the postsecondary enrollment status of members of the high school class of 2004 by familyincome and type of college or university. The width of each bar represents the percentage of the college-agepopulation enrolled in different types of colleges and universities (or not enrolled in any college, in the case of theleftmost bars); the vertical dimension describes the income composition of students enrolled in each type ofpostsecondary institution. Source: Educational Longitudinal Study, 2002. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 48Figure A2. The racial composition of colleges using SES-based affirmative action and race-basedrecruitment, by affirmative action and recruitment strength. Notes. Simulated population proportions are: 60 percent White, 20 percent Hispanic, 15 percent Black, and 5percent Asian. Moderate and strong SES-based affirmative action scenarios utilize a weight equivalent to 75 and 150achievement points per standard deviation of resources. Recruitment weights are: light, 25 points; moderate, 50points; strong, 100 points. SES is socioeconomic status. Source: authors’ simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 49Figure A3: The socioeconomic composition of colleges using SES-based affirmative action and race-basedrecruitment, by affirmative action and recruitment strength. Notes. Moderate and strong SES-based affirmative action scenarios utilize a .375 and .75 weight, respectively,equivalent to 75 and 150 achievement points. Recruitment weights are: light, 25 points; moderate, 50 points;strong, 100 points. SES is socioeconomic status. Source: authors’ simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 50Figure A4. The racial composition of colleges using affirmative action, by affirmative action type. Notes. Simulated population proportions are: 60 percent White, 20 percent Hispanic, 15 percent Black, and 5percent Asian. Moderate and strong race-based affirmative action scenarios utilize a weight equivalent to 150 and300 achievement points. Moderate and strong SES-based affirmative action scenarios utilize a weight equivalent to75 and 150 achievement points per standard deviation of resources. Bar 3 is most analogous to using the estimatedreal world affirmative action race weight of 260 achievement points. SES is socioeconomic status. Source: authors’simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 51Figure A5. The socioeconomic composition of colleges using affirmative action, by affirmative action type. Notes. Moderate and strong race-based affirmative action scenarios utilize a weight equivalent to 150 and 300achievement points. Moderate and strong SES-based affirmative action scenarios utilize a weight equivalent to 75and 150 achievement points per standard deviation of resources. Bar 3 is most analogous to using the estimatedreal world affirmative action race weight of 260 achievement points. SES is socioeconomic status. Source: authors’simulation. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 52APPENDIX B. ESTIMATES OF THE RELATIVE ADMISSIONS WEIGHT GIVEN TO RACE, SOCIOECONOMIC STATUS(SES), AND ACADEMIC PERFORMANCEIn this appendix we examine past efforts to estimate the relative weights given to race, SES, andacademic performance in selective college admissions processes and provide more details on our ownanalyses. The existing methods for calculating relative admissions weights given to applicants’ race, andthe weights these results yield, are variable and sometimes misleading. For example, simply comparingthe average academic records (such as GPAs or SAT® scores) of students of different races enrolled atselective colleges can be misleading for a number of reasons. First, because of racial disparities in gradesand test score distributions, we would expect the mean scores of admitted Black and White students tobe different even if a college admitted solely on the basis of test scores.10 Second, this approach cannotdisentangle differences in average scores that are due to differential admission criteria from differencesin scores that are due to racial differences in application or enrollment patterns. A better approach to estimating average affirmative action weights is to use data on a pool ofapplicants to one or more selective colleges and to estimate the relationship between race/SES and theprobability of admissions. This approach was taken by Kane (1998) and Espenshade and Radford (2009).The idea of this approach is to predict admission on the basis of race, academic, and other observablefactors and then compare the coefficients on the race variables with the coefficient on SAT® scores. BothKane and Espenshade and Radford estimated the implicit weight given to race (being Black, specifically, intheir models) in the admission process at selective colleges as roughly equivalent to the weight given toan additional 300−400 SAT® points (as measured on the 1600 point SAT® scale that was in use at thetime). 10 This may seem counterintuitive, but it results from the fact that racial differences in mean test scores mean thatthere are more URM students with very low scores and more White students with very high scores. If a collegesimply admitted every student with an SAT® score above, say, 1200, the mean score for White students in this groupwould be higher than that of URM students because of the higher proportion of White students with very highscores. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 53It is important to note that these estimates apply only to the most selective colleges anduniversities. Espenshade and Radford’s (2009) data set contained only seven selective, 4-year colleges oruniversities. Kane’s (1998) data set came from an analysis of the top 20 percent of 4-year colleges interms of selectivity. His models based on all 4-year colleges yield estimated weights one-third as large.Such findings are in keeping with the patterns in Figure 1 that suggest there is greater use of race-basedaffirmative action at the most selective colleges. Even taking into account the fact that they are based on a limited set of colleges, the Kane (1998)and Espenshade and Radford (2009) SAT-equivalent weight estimates are likely too high. Their modelsinclude a number of control variables, such as high school GPA and extracurricular involvement. Becausethese variables are positively correlated with SAT® scores, their inclusion in the model will tend toattenuate the coefficient on the SAT® score variable. This, in turn, will exaggerate the SAT-equivalentweight (because it is a ratio of the coefficient on race to the coefficient on SAT® scores). Another way tosee this is to realize that two students who differ by 300−400 SAT® score points will tend to differ also onmany other factors that affect college admission, so the average difference in admission probabilitiesbetween two students who differ by 300−400 SAT® points will be much larger than that implied by theSAT® coefficient alone. This means that a smaller difference in SAT® points (along with the otherdifferences in correlated characteristics) will yield an average difference in admission probability equal tothat implied by the race coefficient. Because of these concerns, and because existing estimates do not describe the weight thatcolleges give to Hispanic students or to low-SES students, we conducted our own simple analysis of recentcollege admission data. Using data from the 2002 ELS, we estimated racial and SES admissions weightsusing methods similar to those of Espenshade and Radford (2009) and Kane (1998). We fit a much moreparsimonious models than they do, however: we predict the probability of admission using only test CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 54scores and dummy variables for race or a standardized variable for SES.11 To account for the possibilitythat the implicit weights vary in magnitude along with the selectivity of the college, we repeated thisanalysis for admission to each of the six Barron’s Selectivity categories. Similar to Kane (1998), we find notable racial admissions preferences only in the top Barron’scategory, which represents approximately 10 percent of 4-year colleges that are not open admission. Weestimate significant positive admissions preferences for both Black and Hispanic students applying tothese most selective colleges. We estimate that Black and Hispanic students are given an implicit weightthat is roughly equivalent to that given to students with a test score roughly 1.3 standard deviationshigher than another student. We find very little or no evidence of racial preferences in admissions tocolleges in lower selectivity tiers (for details, see Table B1).We conducted a similar analysis to estimate the average implicit weight given to low-SES studentsin admissions. Here we find evidence of slight SES-based affirmative action in the most selective colleges(the weight given to a standard deviation difference in family SES is roughly the same as given to a 0.15standard deviation test score difference). Moreover, the evidence indicates that students applying to lessselective colleges were penalized for their lower SES in the admission process (in these colleges higherSES students were given implicit preference in admissions). The SES weights are, however, relatively smallin all cases (for details, see Table B2). In sum, it appears that, in 2004, affirmative action or other related policies at the most selectivecolleges increased the probability of minority students’ admission substantially by an amount that may beas high as the difference between students whose academic records differ by over a standard deviation. 11 In these analyses, we use SAT® scores, which are reported in the ELS data, as a standardized test score measure.We use them because they are widely observable to colleges (unlike the tests administered as part of the ELSstudy) and they are standardized on a common scale (unlike GPA). Although colleges of course have access to otherinformation about students when making admissions decisions, we use a single standardized test score measure asa unidimensional proxy for students’ academic performance so that we can roughly quantify the implicit weightsgiven to race or SES in college admissions. The weights we estimate therefore should be understood as designedsolely to provide information about the rough order of magnitude of the weights given to academic performance,race, and SES in admissions processes. They are not particularly useful as estimates of actual admissions processes. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 55SES-based affirmative action policies, however, appear to have been much less prevalent. On average,low-SES applicants appear to have received little or no admissions preference at most colleges. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 56Table B1. Estimates of Implicit Weight Given to Minority Students in Admissions Process, High School Classof 2004 All schools Barron’s 4 Barron’s 3 Barron’s 2 Barron’s 1SAT® 0.076*** 0.079*** 0.09*** 0.093*** 0.115***(0.002) (0.003) (0.003) (0.005) (0.006)Asian -0.004 -0.028 0.026 0.006 0.007(0.011) (0.022) (0.021) (0.029) (0.024)-5.26 -35.44 28.89 6.45 6.09Black -0.04*** -0.098*** -0.044* -0.028 0.303***(0.010) (0.016) (0.021) (0.034) (0.040)-52.63 -124.05 -48.89 -30.11 263.48Hispanic 0.024* -0.025 0.01 0.037 0.294***(0.010) (0.018) (0.021) (0.031) (0.034)31.58 -31.65 11.11 39.79 255.65Intercept -0.015 0.038 -0.197 -0.376 -1.102(0.019) (0.033) (0.038) (0.061) (0.080)N23,000 6,700 5,000 2,800 2,700+ p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.001Source: Authors’ calculations from ELS 2002 study. Standard errors are adjusted for clustering. Estimates are from alinear probability model predicting acceptance to a given selectivity of school as a function of SAT® score anddummy variables for race. SAT® scores are divide by 100. Sample sizes have been rounded to the nearest 100. Theimplicit admissions weight (in SAT® points) is included in italics below the standard error for each model. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 57Table B2. Implicit Weight Given to Socioeconomic Status (SES) in Admissions Process, High School Class of2004All schools Barron’s 4 Barron’s 3 Barron’s 2 Barron’s 1SAT® 0.076*** 0.083*** 0.092*** 0.094*** 0.09***(0.002) (0.003) (0.003) (0.005) (0.006)SES 0.01* 0.027*** 0.003 0.001 -0.033*(0.004) (0.007) (0.008) (0.013) (0.014)13.2 32.5 3.2 1.1 -36.6Intercept -0.025 -0.026 -0.216 -0.381 -0.716(0.017) (0.030) (0.035) (0.057) (0.073)N23,000 6,700 5,000 2,800 2,700+ p < 0.10, * p < 0.05, ** p < 0.01, *** p < 0.001Source: Authors’ calculations from ELS 2002 study. Standard errors are adjusted for clustering. Estimates are froma linear probability model predicting acceptance to a given selectivity of school as a function of SAT® score and theELS SES variable (continuous and standardized). SAT® scores are divide by 100. Sample sizes have been rounded tothe nearest 100. The implicit admissions weight (in SAT® points) is included in italics below the standard error foreach model. CAN SOCIOECONOMIC STATUS SUBSTITUTE FOR RACE? 58APPENDIX C. DETAILED EXPLANATION OF AGENT-BASED MODELInitializationFor each scenario of the model, we generate J colleges with m available seats per year (for thesake of simplicity, m is constant across colleges). During each year of the model run, a new cohort of Nstudents engages in the college application process. Initial college quality (Q) is normally distributed, asare race-specific distributions of student achievement (A) and student resources (R). We allow for race-specific correlations between A and R. The values used for these parameters, and their sources, arespecified in Table 1. We select these values to balance computational speed and distribution density (e.g.,for number of colleges and students), real-world data (e.g., for achievement and resource distributions),and based on the original version of the model (ELS 2002; Reardon et al., 2016).SubmodelsApplication. During this stage of our model, students generate an application portfolio, with eachstudent selectingHHss colleges to which they will apply. Every student observes each college’s quality(QQcc)with some amount of uncertainty(rrccss), which represents both imperfect information and idiosyncraticpreferences.QQccss∗ = QQcc + rrccss; rrccss~NN(0, ττss).(C.1)The error in students’ perceptions of college quality has a variance that depends on a students’resources; students from high-resources families have better information about college quality.Specifically, ττss =Var(QQcc)�1 − ρρssQQρρssQQ �,