??ࡱ?>?? qs????p??W???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????q` ??*?bjbjqPqP 8?::P&????????? ? ? ? RRRf.7.7.78f7?R8tf??x?8??<"?<?<F=~>?> ?>ބ????????????$?h??F??R?Hz>~>?H?H?? ^ D?<pF=4?^NNN?HdR pF=RF=ބN?HބNN??sD? ?RbwF=?8 P?????.7XI@u&„O?T??DuɊ?L ɊLbwɊRbw`?>?6A?NCtzDz?>?>?>???Md?>?>?>???H?H?H?Hfffd?'dfff?'fff? ? ? R R R ???? Why Retaining Racial Preferences in College Admissions May Yield a More-Able Student BodyByDong Li and Dennis L. Weisman *RRH: LI & WEISMAN: RACIAL PREFERENCES JEL classification: I20; I28Why Retaining Racial Preferences in College Admissions May Yield a More-Able Student BodyAbstractCritics of affirmative action policies contend that the elimination of racial preferences in college admissions would lead to a ?more-able? student body. We develop a simple model comprised of three classes of college admissions?merit, race and legacy?to show that a change in admissions policy that reduces racial preferences can lead to a ?less-able? student body. In fact, the change in admissions policy may serve only to ensure that more admissions are available for ?sale? to wealthy alumni through legacy preferences. The numerical simulations confirm the theoretical results. When there are multi-dimensional preferences, reducing or eliminating one dimension of preferences may result in a ?less-able? student body. Keywords: Education, Discrimination, Racial Preferences, Legacy Preferences Dong Li and Dennis L. WeismanDepartment of EconomicsKansas State UniversityManhattan, KS 66506-4001 I. IntroductionIn two recent landmark cases involving the University of Michigan, the U.S. Supreme Court affirmed that colleges may employ narrowly-tailored, race-based admissions policies if they contribute to the diversity of the student body. The Court indicated that it was primarily concerned with diversity of experience rather than diversity of color. The Court?s decisions satisfied neither side of the political spectrum?liberals contending that colleges should have broad discretion over admissions in order to enhance the overall educational experience of their students, conservatives contending that such preferences necessarily produce a ?less-able? student body. What is frequently overlooked in this debate is the fact that racial preferences represent only one of several types of preferences that prestigious colleges regularly employ in selecting their student bodies. Other types of preferences include those for talented athletes and the offspring of wealthy alumni, so-called legacy preferences. To date, there has been no serious challenge to these other types of preferences. This is curious because eliminating one type of preference?say racial preferences?while retaining other types of preferences could well produce a ?less-able? student body. This can occur, for example, if (i) the average ability of the students admitted under racial preferences exceeds that of the new group of students admitted under some other preference; or (ii) the average ability within the admissions subset decreases rapidly as the proportion of admissions drawn from that subset increases. Espenshade et al. (2004) and Espenshade and Chung (2005) find evidence that the athletes and legacy preferences are larger in magnitude than the racial preference while the racial preference is much more controversial. Fu (2006) shows that handicapping the stronger contestants may increase the competition, and that therefore racial preferences may help academic quality-oriented colleges increase the academic quality of their students. The format for the remainder of this paper is as follows. Section II formally derives sufficient conditions for the elimination of racial preferences to produce a ?less-able? student body. Simulations are provided in Section III. The conclusions and policy implications are discussed in Section IV. II. The ModelIn this section, we formally derive sufficient conditions for the elimination of racial preferences and the retention of legacy preferences to result inyield a ?less-able? student body. We begin with a simple numerical example to illustrate the nature of the problem and to motivate the formal analysis. Consider a pool of 10 applicants with academic abilities in descending rank order {10, 29, 38, ? ..., 102, 1}. Suppose that the racial applicant pool is {3,5} and that the legacy pool is {2,4}.  Suppose that five applicants will be admitted and that there will be one racial admission and one legacy admission. The admission pool is {10,9,8,5,4} under both racial and legacy preferences. Suppose that we eliminate the racial admissions and expand the legacy admissions (i.e., three merit admissions and two legacy admissions), so that the admission pool is now {10,9,8,4,2}. In this case, the average ability declines after the elimination of racial preferences, contrary to the claims of the opponents of the affirmative action policy. The intuition is straightforward: you have towill go further down the distribution on one dimension when you remove another dimension of preferences. A. Assumptions and Definitions Suppose that there are Z applicants for N available admissions, where N < Z. The ability level of each applicant q is denoted by Sq, where q = 1, . . . , Z. The set of students applying for admission,{S}, can be partitioned into subsets {Sr}, {Sl} and {Sn}, where the superscripts r, l and n indicate, respectively, that the student is an under-represented, race-based minority, alumni offspring, or neither. Assumption 1. (Well-Ordering) The applicants for admission can be rank-ordered in descending order of ability level, {S1, . . . , SN, . . . , SZ}. Assumption 2. The set of rank-ordered admissions, {A}, can be partitioned into subsets of merit admissions, {Am}, racial-preference admissions, {Ar}, and legacy-preference admissions, {Al}. Definition 1. A preference-free admissions set is given by {A} = {S1, . . . , SN}.Definition 2. A merit admission is the admission  EMBED Equation.3  of any  EMBED Equation.3 Definition 3. A racial-preference admission is the admission  EMBED Equation.3  of any  EMBED Equation.3 Definition 4. A legacy-preference admission is the admission  EMBED Equation.3  of any  EMBED Equation.3 Assumption 3. (Continuity)  EMBED Equation.3 Assumption 4. The order of admissions within any subset,  EMBED Equation.3  proceeds sequentially in decreasing rank-order from ?most-able? to ?least-able.? In the benchmark case, the average ability of the student body is given by (1)  EMBED Equation.3 where  EMBED Equation.3  and  EMBED Equation.3  is the share of each of the three groups represented in the set of N admissions and  EMBED Equation.3  is the average ability level within the admissions subset. By Definitions 2-4,  EMBED Equation.3  and  EMBED Equation.3 respectively.Definition 5. An admissions policy consists of a three-tuple of admission shares  EMBED Equation.3 , with  EMBED Equation.3  and  EMBED Equation.3  for s = m, r and l. Definition 6. Let  EMBED Equation.3  s = m, r and l define the average-ability elasticities. B. Key Findings Consider now a ?small? change in the admissions policy that allows for a reduction in the share of racial preference admissions ( EMBED Equation.3 ) and an offsetting increase in the shares of merit and legacy preference admissions ( EMBED Equation.3 ). This implies that (2)  EMBED Equation.3  Proposition 1. The change in admissions policy leads to a ?less-able? student body when (3)  EMBED Equation.3 Proof: Taking the total differential of (1) implies that(4)  EMBED Equation.3  EMBED Equation.3 follows from (2). Substitution yields(5)  EMBED Equation.3 Setting  EMBED Equation.3  in (5) and appealing to Definition 6 yields(6)  EMBED Equation.3 Solving for  EMBED Equation.3  in (6) yields the result in (3). ?%Proposition 1 establishes a lower-bound for  EMBED Equation.3 sufficient for the change in education policy to lead to a  less-able student body. Lemma 1. The change in admissions policy leads to a ?more-able? student body when  EMBED Equation.3  Proof: When  EMBED Equation.3 , (4) reduces to(7)  EMBED Equation.3 Let  EMBED Equation.3 , then(8)  EMBED Equation.3 or(9)  EMBED Equation.3 The second and third terms on the right-hand side of (9) are non-negative. Also, since  EMBED Equation.3  and  EMBED Equation.3  for all i and j,  EMBED Equation.3 so the first term on the right-hand side of (9) is positive. It follows that  EMBED Equation.3  ?%Because the ability of each additional merit admission exceeds the ability of each displaced racial-preference admission, the change in admissions policy necessarily leads to a  more-able student body. Lemma 2. The change in admissions policy when  EMBED Equation.3  leads to a ?less-able? student body whenever:a)  EMBED Equation.3  and  EMBED Equation.3 ; orb)  EMBED Equation.3  and  EMBED Equation.3  Proof: Under the conditions stated in the proposition, (3) reduces to (10) EMBED Equation.3  Equation (10) is satisfied if either condition a) or condition b) holds. ?%The change in admissions policy leads to a  less-able student body if (i) the average ability of legacy-preference admissions is lower than that of racial-preference admissions and the decrease in average ability is comparable across the two admissions subsets changes at a comparable rateas one moves further down the respective applicant pools; or (ii) the average ability levels are comparable across the two admissions subsets, but the average ability level of legacy-preference admissions decreases at a faster rate than that of racial-preference admissions. Proposition 2. There exists a change in admissions policy of the form  EMBED Equation.3 and  EMBED Equation.3  that leads to a ?less-able? student body whenever:a)  EMBED Equation.3  and  EMBED Equation.3 ; orb)  EMBED Equation.3  and  EMBED Equation.3  Proof: By Lemma 1, the change in admissions policy leads unequivocally to a ?more-able? student body when  EMBED Equation.3  By Lemma 2, the change in admissions policy leads to a ?less-able? student body when condition a) or condition b) holds. By continuity of ability within the admissions subsets (Assumption 3), there must exist a change in admissions policy of the form  EMBED Equation.3 and  EMBED Equation.3  that leads to a  less-able student body. ?%Due to the lack of real data, we resort to simulations in the next section to empirically examine theis issue. III. SimulationsIn this section we conduct simulations of the changes in admission policy. Values of the parameters are chosen to mimic a hypothetical selective college. It should be pointed out that the results are qualitatively similar when different values of the parameters are chosen. Assume that the ability of the three groups of applicants is randomly drawn from a tri-variate normal distribution N(?,?) where ?=[?m, ?r, ?l] is the mean ability vector of the three groups, ? is a 3 by 3 positively definite variance-covariance matrix. Assume that there are 10,000 applicants, of which 1,500 are racial applicants, 1,500 are legacy applicants, and 7,000 applicants are neither. Suppose that there are 1,500 admissions available. Under the current policy there are 1050 merit admissions, 225 racial-preference admissions, and 225 legacy-preference admissions. In the results presented below, we assume that if we eliminate the racial-preference admissions, there are 450 admissions for legacy preferences. In other words, the entirety of the racial-preference admission quota goes to the legacy-preference admissions. This iscorresponds to the case where  EMBED Equation.3  as in Lemma 2. Under each parameterization of the model, 1000 repetitions are carried out to compare the average student ability  under the current policy (with both racial-preference admissions and legacy-preference admissions) with that under the proposed policy (with only legacy-preference admissions). In each simulation, merit admissions are allocated purely based on the order of ability, regardless of racial or legacy status. Racial admissions and legacy admissions are subsequently allocated in the order of ability within the respective applicant pool. Of the 1000 repetitions, we calculate the probability that the average student ability under the current policy (with both racial and legacy admissions) is higher than that under the proposed policy (with only legacy admissions). We vary ? and ? in our simulations to find the break-even point in terms of average student ability for the two policies. Different parameterizations of ? and ? leads to different conditions analyzed in Section 3. For example, the conditions that ? is an identity matrix and ?l < ?r coincide with condition a) in Lemma 2. Similarly, the conditions that ?l = ?r and ?l > ?r with all covariances equal to zero coincide with condition b) in Lemma 2. In this case, the ability of the legacy applicants declines faster than that of the racial applicants. In the interest of economy of presentation, we present only the results based on ? as an identity matrix and various values for ? . Figures based on varying ? with fixed ? are qualitatively similar and are available upon request. [Figure 1 is inserted around here][Figure 2 is inserted around here] We fix ?m = 0 in all of the simulations. This is arbitrary and trivial for the results. The results are summarized in Figure 1. For example, when ?l = - 3 and ?r= - 1 (the top left point in the graph), abolishing the racial admissions leads to a less-able student body with 100% probability. When ?l = ?r the probability is still 100% or close to be 100%. Only when ?l is much larger than ?r does abolishing the racial admissions preference lead to a more-able student body. To better understand the graph, in Figure 2 we present a two dimensional cut of Figure 1 at ?l = 0. In Figure 2 we can see that the break-even point is around ?r= -1. This means that if the mean ability of the racial applicants is within one standard deviation less than the mean ability of the legacy applicants, the current policy dominates the proposed policy. Only if the mean ability of the racial applicants is significantly (more than one standard deviation) less than that of the legacy applicants does the proposed policy lead to a more-able student body. [Figure 3 is inserted around here][Figure 4 is inserted around here]To closely mimic reality, we also consider the case in which legacy admissions are not based on the order of ability among the legacy applicants. It is generally believed that selective colleges allocate racial admissions to the best minority applicants while they do not necessarily allocate legacy admissions to the best legacy applicants, but rather to the legacy applicants from more affluent families.,  Here we assume that legacy admissions are allocated randomly among the legacy applicants who have not been admitted based on merit. The results are presented in Figures 3 and 4. As one can see the results are even stronger than those in Figures 1 and 2. For example, Figure 4 shows that only if the mean ability of the racial applicants is more than two standard deviations lower than that of the legacy applicants does the proposed policy leads to a more-able student body. Our simulation results show that for a large parameter space, abolishing the racial- admissionspreference admissions leads to a less-able student body, contrary to what opponents of such policies may claim. The numerical simulations confirm the theoretical findings in Section 2. It should be pointed out that we maintain the assumption that the policy change would cause no behavior change in the applicants. For example, we assume in our simulations we assume that the number of applicants from each group remains the same regardless of policy changes. In practice, one might expect the policy change to induce some behavioral changes. For example, Long (2004a,b) finds that, as a in response to the elimination of affirmative action in California and Texas, minority students sent SAT reports to lower quality schools. Dickson (2006) reports similar findings, while Card and Krueger (2005) find no behavioral change in highly qualified black or Hispanic students. IV. ConclusionsThomas Paine observed more than 200 years ago that ?virtue is not hereditary? (Paine, 1776, p. 54). It is apparent that at least in some cases ability is not hereditary either. This has given rise to so-called legacy preferences whereby wealthy alumni are essentially able to ?buy? admissions for their less-able offspring. To date, legacy preferences have attracted relatively little attention as the focus has been on racial preferences and recent court decisions circumscribing its use. Critics of race-based admissions policies contend that eliminating racial preferences will necessarily lead to a ?more-able? student body. As the analysis in the previous sections attest, this need not be the case. In fact, the elimination of racial preferences in combination with the retention of legacy preferences could well lead to a ?less-able? student body. Hence, if the real intent of the policy change is to produce a ?more-able? student body, then consideration should perhaps be given to eliminating all preferences, not simply racial preferences (i.e., a preference-free admissions set). Admittedly, such policy prescriptions are unlikely to be popular with college administrators as they greatly limit their ability to extract contributions from wealthy alumni. Finally, it should be recognized that eliminating racial preferences while retaining legacy preferences may prove to be doubly-damning to minorities?possibly even reversing the laudable gains in college graduation rates that these groups have achieved over the last two decades (Bowen and Bok, 1998). The concern is that past discrimination in this country, inclusive of its implications for the distribution of wealth, may limit the degree to which minorities can avail themselves of legacy preferences. ReferencesBowen, William G. and Derek Bok. The Shape of the River: Long-Term Consequences of Considering Race in College and University Admissions. Princeton NJ: Princeton University Press, 1998. Card, David and Alan B. Krueger. ?Would the Elimination of Affirmative Action Affect Highly Qualified Minority Applicants? Evidence from California and Texas.? Industrial and Labor Relations Review, Volume 58, 2005, pp. 416-34. Dickson, Lisa. ?Does Ending Affirmative Action in College Admissions Lower the Percent of Minority Students Applying to College?? Economics of Education Review, Volume 25, 2006, pp. 109?119.Espenshade, Thomas J. and C.Y. Chung. ?The Opportunity Cost of Admission Preferences at Elite Universities.? Social Science Quarterly, Volume 86, 2005, pp. 293-305.Espenshade, Thomas J., C.Y. Chung, and J.L. Walling. ?Admission Preferences for Minority Students, Athletes, and Legacies at Elite Universities.? Social Science Quarterly, Volume 85, 2004, pp. 1422-46.Fu, Qiang. ?A Theory Of Affirmative Action in College Admissions.? Economic Inquiry, Volume 44, 2006, pp. 420?428.Golden, Daniel, The Price of Admission: How America?s Ruling Class Buys Its Way Into Elite Colleges?and Who Gets Left Outside the Gates. New York: Crown Publishers, 2006. Goldstein, Amy. ?Bush Hits ?Legacy? College Admissions; President Addresses Minority Journalists.? The Washington Post, Washingtonpost.com, August 7, 2004, Section A. Gratz et. al. v. Bollinger et. al., Case No. 02-516, Before The United States Supreme Court, Decided June 23, 2003. Grutter v. Bollinger et. al., Case No. 02-241, Before The United States Supreme Court, Decided June 23, 2003. Lipsey, R.G. and K. Lancaster. ?The General Theory of the Second Best.? Review of Economic Studies, Volume 24, 1956, pp. 11-32. Long, Mark C. ?College Applications and the Effect of Affirmative Action.? Journal of Econometrics, Volume 121, 2004a, pp. 319-342.Long, Mark C. ?Race and College Admissions: An Alternative to Affirmative Action??Review of Economics and Statistics, Volume 86, no. 4, 2004b, pp. 1020-33Loury, Glenn C. The Anatomy of Racial Inequality. Cambridge MA: Harvard University Press, 2002. Paine, Thomas. Common Sense, New York: Barnes and Noble, 1995 (Originally published in 1776).  PAGE PAGE 17* The authors are grateful to Alfred Kahn for helpful discussions and to Inung Jung and Daigyo Seo for expert research assistance. The usual caveat applies. Li: Associate Professor, Department of Economics, Kansas State University, Manhattan, KS 66506-4001, (785) 532-4572, dongli@ksu.edu. Weisman: Professor, Department of Economics, Kansas State University, Manhattan, KS 66506-4001, (785) 532-4588, weisman@ksu.edu.  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E7F7888888888 8"8&8(8*8.80828?8?8?8?8?8?8?;?;?;?;?;<<<<< <?<?<?<c>d>@@ @@@A??????????????????????????󚍩????u???????Hh3??fhW?h7-jh?J?0JUj*?hXT?h?J?EH??Uj?E h?J?CJUVaJjh?J?U?Hh????h(T%?h?J?h(TcHdhdhdh???? h?J?6?H*h?8Lh?J?6?H* h?J?5? h?8Lh?J?h?8Lh?J?5?h?J?h?8Lh?J?6?.AA$A&A0A2A4A?A?A?ABB B"B$B&B(B?B?B?B?B?B?B?B?B?B?B?B?B?B?B?C?C?D?D?DFEHEJE?E?E?E?E?EF?F?F?F?F?F GG?G?G?G?G?G?G?GIII?????????????????????????????????????????????????????? h??h?J? h?Dh?c?h?c? h00?h?J?h7- h?Dh?J? h?J?H*h?Dh?J?H*hO6yh?J?6? h?J?6?H*h?8Lh?J?6? h?J?5?h?8Lh?J?5?h?J??Hh???h(T=II I II?I?I?I?I?I?I?I"K$K(K?K?K?KnMoM?MLOMOOOPO{QQ?Q?Q?Q?Q?Q?Q?Q?QkRnR?R?R?R?R?R?R?R??????????????????????ij??????u?u?n?n?n?n? h"xh?J??Hh.??fh?!~-?h?J?h?!~cHcHcHdhdhdh/??f?Hh/??fh?!~%?h?J?h?!~cHdhdhdh.??f ?jHh????h?(0JU?Hh????h?(H*jh?J?0JUh?c? hr&ih?J? h?J?6?H*h?8Lh?J?6?hO6yh?J?6?h?J?+?M2QMRUUWZ\\?\?\?]?]{^|^!_"_?_?_??????????????????$a$gdy?$a$gd?>\$a$gdO0?$a$gd? ? $d?a$gdL $d?a$gd?eA $d??xa$gd.|O$??d?`??a$gd& ?$??d?`??a$gd?^[^\^]^m^n^r^y^z^{^|^?^?^?^?^?^?^?^__ __ _!_"_6_7_8_????????????????????????????????????????????????»»´¬?´´¨¨hy?h>?h>?6? h>?h>? hy?h>?h>? h?>\h?>\h?>\h?>\6?h?>\hO0?hO0?hO0?6?h.y h.yh.yht#?hnm6hnm66?hnm6A8_9_>_E_H_I_N_U_?_?_?_?_?_?_?_?_?_?_?_?_?_`-`0`@`B`E`H`S`W`^```q`?`a a aaara?a?a?b?bcc c%c-c.c/c7c8cLc?????????????????????????????????ž??ڥ??????????????h??h?}?h>z\ h? ?6?h? ?h h??6?h?? h_s?h?Jz5?B*OJQJph?h_s? h?qOh?Jzh?qO h?Jz6?h?JzhT?hT?6? hT?hT?hT?h I?h?>\hT?hy?6?hy? hy?hy?5?_``a`aa?a?a-b.b?b?bc c?c?c?cAdBd?d?deeee e????????????????????????$a$gdEr?$a$gd?$a$gd?7gd?}?$a$gd?Jz$a$gd? ?LcMcVcWcbcjckc?c?c?c?c?c?c?c?c?cdBdRdrd?d?d?d?deeeeeeeeeeeeeeeeeee e!e#e$e&e?????????????????????????û????????????????h?bjh?bUh?q'j??h??Uh?C4h??j?3h??Uj?h?E?Uh?E?h+hnm6ja?h?E?Uh?d?h?'W h?6?h? h>z\h>z\ h>z\6?h>z\ht#?h?76?h?7h??h?}?6?h?}?h??/ e e e eeeeeeeeeeeeee e"e#e%e&e/e0e1e=e>e???????????????????????????x????&`#$gd?C4$a$gdEr?&e'e-e.e/e1e2e8e9e;ee?e@e?eef?f?g????&?_??????J?n?ƾ???? ??????????????????????????????gd%k?gds)?gd?($a$gd?j(gd?^Ggd?q'?x(2006) for a provocative account of the pervasive use of legacy preferences in college admissions at many prestigious colleges.  Recently, President Bush called for an end to legacy preferences in college admissions. See Goldstein (2004).  This corresponds to condition a) in Lemma 2. These include Blacks, Hispanics and Native Americans.  This assumption essentially says that the difference in ability between any two adjacent admissions in any well-ordered admissions subset is ?small.?  As Loury (2002, p. 132) observes, ?Selective institutions will naturally try to reject the least qualified of the otherwise admissible nonblack applicants while admitting the most qualified of those black applicants who would otherwise have been rejected.? Note that if university admissions officers can be ?bribed? to violate Assumption 4,  EMBED Equation.3  will increase in absolute value and the sufficient conditions for Lemma 2 are more likely to be satisfied, ceteris paribus.  Note that we adopt this numerical assumption to simplify the presentation. We experimented with a more realistic assumption wherein both merit admissions and legacy-preference admissions share the eliminated quota of the racial-preference admissions. The results are qualitatively similar, though not as pronounced, and hence are not reported here.  Of course, one does not have to use the average student ability to measure the quality of student body. Other measurements can be easily used here in the simulations. We chose to use the average/mean ability to be consistent with the theoretical model presented in the previous section.  Admittedly there may be a correlation between family background and student ability.  Consider, for example, a university administrator with a utility function containing two arguments?the average ability of the student body (A) and the university?s financial endowment (E). Suppose further that the administrator?s utility function takes the simple form  EMBED Equation.3  where  EMBED Equation.3  How much would the university administrator require in additional E to compensate for a one unit reduction in A? This is given by the marginal rate of substitution of A for E, or MRSA-E =  EMBED Equation.3  Hence, the larger the value of  EMBED Equation.3 , the greater the contribution to the endowment alumni would have to make in order to compensate the administrator for the decline in the average ability of the student body resulting from the admission of less-able students. This may explain why prestigious universities, those with relatively large values of  EMBED Equation.3 , are able to extract large financial contributions from wealthy alumni who wish to gain admission for their less-able offspring.  This, of course, is a variation on the General Theory of the Second Best?eliminating only one of multiple constraints can [actually] lead to a lower level of social welfare. See Lipsey and Lancaster (1956).  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