What determines public support for affirmative action?

Levin, Andrew T.

Despite widespread recognition of the value of diversity, efforts to increase the number of minority professionals through race-sensitive admissions policies have never been fully accepted. As the competition to enter leading colleges and professional schools continued to intensify, this opposition became more vocal ... The U.S. economy is assigning more and more value to higher education as preparation for success in the workplace. As a result, the incentive to finish college is becoming stronger. This is surely one reason why the debate over who gains admission to the most selective schools has become so heated.

--from The Shape of the River, by W. G. Bowen and D. Bok (1998, pp. 13, 69) [emphasis added]

1. Introduction

Affirmative action, which came into effect in the United States in the late 1960s with the intent to eliminate racial, ethnic, and gender differences in access to economic opportunity, has arguably been one of the most contentious public policies implemented. (1) Although the civil rights struggle of the 1960s shifted public opinion in favor of affirmative action, opposition to such policies remained relatively high throughout the late 1960s and the 1970s. The Supreme Court's ruling on the 1978 Bakke v. the University of Ca1ifornia case, which prohibited the use of strict quotas but allowed the lawful consideration of race, gender, and ethnicity in college admissions, settled the issue temporarily--at least from a legal standpoint. In the 1990s, however, stronger opposition to affirmative action and the subsequent elimination in some states of such policies for college admissions, public procurement, and employment helped bring affirmative action to the forefront of the public policy forum once again. (2)

The three decades during which affirmative action policies were in effect also canvas a period with potentially relevant changes in academic trends and labor market outcomes: First, the disparity in the scores of Black and White takers of the Scholastic Assessment Tests narrowed fairly steadily between the mid-1970s and the late 1980s and held relatively steady thereafter. (3) In contrast, the disparity between Blacks and Whites with regard to job performance and labor productivity remained persistently and significantly lower than differences between Blacks and Whites with regard to average test scores during the whole period. (4) Second, after rising in the 1960s and declining in the 1970s, the returns to education, as well as other components of skill, started to increase rapidly in the early 1980s. In fact, the returns to education soared so impressively during the 1980s and the early 1990s that in 1994 it stood at roughly 35% above its value in 1963 (see Figure 1). Moreover, between the late 1970s and th e mid-1980s, when the return to education, experience, and other components of unobservable skill were rising, the increase in the education premium outpaced that in the returns to experience and other components of skill. (5)

For the most part, the debate about affirmative action revolves around assessing whether the impact and success of affirmative action policies to date justify their existence. But this debate also raises intriguing questions from a political economy standpoint. Why has political support for such policies begun to erode more rapidly in the 1990s? If indeed there are biases in screening, what role do they play in the political economy of affirmative action? And, more specifically, how are recent trends in public support for affirmative action linked to increases in the education premium and reductions in the test score gap in the last two decades?

In this paper, we present a political economy model of tax-financed public education. In the model, investment in education is indivisible, and as a result, demand for education can exceed its supply. Thus, a screening mechanism--such as a standardized test--is required for allocation. These tests can most accurately measure cognitive skills, but labor productivity depends on these skills as well as other immeasurable traits. In any given period, a majority vote determines the supply of education as well as whether to enact affirmative action policies. When voting, parents take into account not only the effect affirmative action has on the odds of admission of their own offspring, but also the social benefits of instituting these policies.

What are the potential social benefits of affirmative action? For one, to the extent that the majority and the minority are more similar in immeasurable traits than in measurable characteristics such that a selection system bias exists, affirmative action policies help to improve the efficiency of educational allocation. (6) Second, empirical and anecdotal evidence indicates that greater social diversity in access to education and employment generates aggregate economic benefits. (7) It is also clear that such social diversity can be achieved only through the maintenance of at least some degree of equal opportunity. In racially, ethnically, or culturally diverse societies, the benefits of diversity arise because greater representation of minorities in government, business, and the professions helps to produce more enlightened public policies and corporate choices. Moreover, for diverse societies to remain peaceful and economically efficient, access to economic opportunities and rewards need to be perceived to be open to all members of a society. (8)

Our results indicate that for a given amount of spending on public education, affirmative action policies may have two effects: First, they lower the odds of admission to a public school for applicants from majority households. Second, they alleviate the negative effect of the selection system bias on the allocation of education. Because of both these effects, changes in the returns to education as well as the relative test score distributions of the majority and the minority potentially affect the majority's political support for affirmative action. In periods in which the education premium is relatively low, the matching efficiency gains provided by affirmative action are relatively high compared with the opportunity cost of not acquiring education, and the majority supports affirmative action. In periods in which the returns to education are high, the majority's support for affirmative action declines as the opportunity cost of remaining uneducated increases relative to the matching efficiency gains provid ed by affirmative action policies. In contrast, changes in the test score gap have offsetting effects on the majority: On the one hand, a higher majority-minority test score gap suggests that the social benefits of affirmative action would be large. On the other hand, the institution of affirmative action policies would displace a number of the majority's offspring from the ranks of the college educated. Thus, in general, changes in the test score gap have ambiguous effects on the majority's political desire to support affirmative action. Nonetheless, for a sufficiently high test score gap, the social benefits of affirmative action outweigh the majority's utility cost of displacement from college such that they support affirmative action.

Two issues are noteworthy at the outset: First, although we identify returns to education as an important determinant of affirmative action policies, we do not claim that economic factors alone-- without reliance on sociological or cultural ones--can explain changes in the support for affirmative action. For example, one could argue that biases in screening for education and employment have been significantly reduced in the last three decades because of the Civil Rights Act and therefore that scaling back affirmative action policies is warranted. We do not take a position on this or any other similar argument. Rather, our sole intent is to explore the effects, if any, of economic factors on the determination and scope of affirmative action. Second, although the sole focus of this paper is affirmative action in higher education, it would be straightforward to extend this model to include affirmative action in employment. As will become apparent below, equilibrium affirmative action policies in education and em ployment should be perfectly correlated when such policies in education are based on the votes of a majority who take into account the private costs and benefits of affirmative action. In that context, the full benefits of affirmative action in education cannot accrue with continued biases in the labor market.

2. Related Literature

By design, this paper brings together the existing literature on public education and that on affirmative action. Fernandez and Rogerson (1995) examine political support for tertiary education. They do not consider the role of tests in the political economy outcomes but instead focus on subsidies whose sizes are determined by majority vote. Fernandez (1998) and Fernandez and Gali (1999) explore the role borrowing constraints play in the performance of exams versus that of markets as allocative mechanisms. In a model in which agents who differ in their initial wealth and ability are assigned to various investment opportunities or schools of various qualities, these authors show that exams dominate markets in terms of aggregate output. For sufficiently powerful (less-biased) exam technologies, exams are superior to markets in terms of aggregate consumption as well. Glomm and Ravikumar (1992) compare the income distribution and growth implications of public education with those of private education. Their model is one in which all agents in the economy demand educational services to various degrees and the quality of educational services depends on the total resources allocated to education. Glomm and Ravikumar find that private education, which will be chosen by higher-income individuals, results in less subsequent mobility but higher growth rates. In contrast, public education, which will be preferred by lower-income groups, leads to greater social mobility at the expense of long-run economic growth. As a result, to the extent that the median voter is poorer than the mean income voter, public education is chosen in a more unequal society. Gradstein and Justman (1997) focus on why public education should be more likely to be chosen over private education in a more democratic society that is unequal. They demonstrate that because rational voters internalize all possible positive externalities of an education system, these voters do not necessarily choose one with more redistribution--public education in particular-- over others that lead to higher long-run economic growth.

There are relatively fewer theoretical studies on affirmative action. Coate and Loury (1993a, b) develop models in which employers who harbor negative stereotypes of certain groups are likely to assign workers belonging to those groups to less rewarding jobs. They show that since this lowers the expected return for these workers on investments that make them more productive in more rewarding jobs, employers' negative beliefs can be self-confirming even when all groups are ex ante identical. Welch (1976) examines employment quotas in a setup in which employers discriminate. He shows how quotas may create a shortage of skilled minority workers. Thus, he argues that such quotas may lead unskilled minority workers to be assigned to skilled jobs as a result of firms' attempts to acquire the option of hiring additional skilled majority workers. Lundberg (1991) analyzes the problem of enforcing equal-opportunity laws when the regulators have imperfect information on employer personnel policies and on the relationshi p between workers' characteristics and their productiveness. She examines the social costs and benefits of two alternative regulatory regimes: one prohibiting the use of proxies for race, sex, or gender in the determination of worker wages, and the other requiring wages to depend on observed worker characteristics in the same way for each group. Chan and Eyster (2000), as noted above, study the potential effects of banning affirmative action on diversity and student quality. They find that eliminating affirmative action policies will reduce diversity and may also lower average student quality.

The remainder of this paper is organized as follows: In section 3, we define the economy and individuals' preferences. In section 4, we discuss the determination of affirmative action. We do this in two steps: First, we utilize a simple version of the model in which the share of resources devoted to education is fixed. Then, we relax this assumption and examine the joint determination of affirmative action and public education supply. In section 5, we conclude.

3. The Economy and Preferences

Consider an economy in which education is publicly provided. Let e (e > 0) denote the cost of education per pupil and y denote aggregate wealth in period 1. Then, the supply of educational services in the second period, S, will be given by

S = [[tau].sup.*]y/about, (1)

where [[tau].sup.*] represents the equilibrium tax rate.

There is a single consumption good and a continuum of parents of measure 1. The population comprises a majority, which accounts for p (a fraction of more than half of the population), and a minority, 1 - p. Parents live for two periods, and they get utility from their own consumption and the expected consumption of their offspring. There is no population growth, and each parent has one offspring who lives for one period. (9) In the first period of life, parents consume. They also vote on the share of resources to be allocated to public higher education and whether to adopt affirmative action in the following period. In the second period, these parents send their offspring to a public school if they are admitted.

At birth, individuals are endowed with some innate ability, which is lognormally distributed, with [a.sub.i] [equivalent to] log[A.sub.i] ~ N(0,1). (10) When voting on the share of resources to be allocated to public higher education, parents do not know the ability endowments of their children. (11) When the supply of public education, S, is less than its demand, applicants are admitted to schools on the basis of their measurable productive abilities. (12) Let [z.sub.i] ([z.sub.i] [equivalent to] log [Z.sub.i]: [R.sup.2] [right arrow] R) represent the log of labor productivity of parent i's offspring.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

where [alpha] ([alpha] [greater than or equal to] [alpha]) denotes the average productivity difference between the offspring of the majority and the offspring of the minority. (13)

The available screening technology is imperfect. It can accurately measure only a subset of the aggregate skills that determine labor productivity. Moreover, the traits that the test technology can measure are those for which minority children, on average, are at a particular disadvantage. Let [I.sub.i] ([I.sub.i]: [R.sup.2] [right arrow] R) denote the log of the labor productivity of parent i's offspring as measured with the available proxy. Then,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where [beta] ([beTa] [greater than or equal to] [alpha]) denotes the average difference between the test scores of the majority offspring and minority offspring.

It is crucial at this juncture to explain what the specifications in Equations 2 and 3 imply. With a screening technology that could accurately measure all characteristics of lifetime productivity, there would be no selection bias and the allocation of education would be perfectly fair. For example, if labor. productivity depended only on cognitive skills, differences in test scores would fully reflect potential differences in productivity, and those with the highest potential would be admitted to schools. However, given that available tests most accurately measure some but not all of the traits that detennine productivity, the relevant issue is whether there exist screening biases that systematically leave members of certain cultural, racial, or ethnic groups at a disadvantage. (15) Equations 2 and 3 are designed to capture such biases, and the assumption [beta] [greater than or equal to] [alpha] [greater than or equal to] 0 guarantees that the formulation above is consistent with the empirical evidence.

We can verify that as [beta] [right arrow] [alpha], the available test technology becomes a better predictor of labor productivity:

[lim.sub.[beta][right arrow][alpha]] corr([I.sup.i], [z.sup.i]) = [lim.sub.[beta][right arrow][alpha]] = (1 + (1 - p)[alpha][beta]/[square root of (1 + p(1 - p)[[alpha].sup.2])] [square root of (1 + p(1 - p)[[beta].sup.2])]) = 1 (4)

Let [I.sup.*] denote the threshold score required for admission to a public school that is consistent with the equilibrium tax rate [[tau].sup.*]. If the measured ability level of parent i's offspring is greater than or equal to [I.sup.*], then i's offspring is admitted to a public school and earns [lambda](E)[Z.sub.i][w.sup.e] in the second period, where [lambda] denotes a labor productivity parameter, E denotes the aggregate efficiency units of educated labor, and [w.sup.e] denotes the wage rate per efficiency unit of educated labor. Otherwise, i's offspring remains uneducated and earns [lambda](E)[Z.sub.i][w.sup.u], where [w.sup.u] is the wage rate per efficiency unit of uneducated labor. We assume that [lambda] satisfies the standard Inada conditions, that is, [lambda]'(E) > 0, [lambda]"(E) < 0, [lim.sub.E[right arrow]0] [lambda]' = [infinity] and [lim.sub.E[right arrow][infinity] [lambda]] = 0.

Let [a.sub.p], and [a.sub.1-p], respectively, denote the relevant thresholds of admission for the children of the majority and the children of the minority that are consistent with [I.sup.*] Equation 3 implies that when no affirmative action policies are in effect, the same cutoff test score applies to all test takers. As a result [a.sub.p] = [I.sup.N] < [a.sub.1-p] = [I.sup.N] + [beta]. That is, the threshold ability necessary to gain admission for children of the majority is strictly less than that for children of the minority. Thus, when affirmative action is not adopted, the cutoff exam score required for admission, [I.sup.N], is given by

S = 1 - [psi]([I.sup.N]), (5)

where [psi]([I.sup.N]), [psi]([I.sup.N]) [equivalent to] p[PHI]([I.sup.N]) + (1 - p)[PHI]([I.sup.N] + [beta]), denotes the population c.d.f. and [PHI](*) denotes the log ability c.d.f.

When voters choose to enact affirmative action policies, however, we assume that higher-education admissions are carried out via a quota system (or some weak variant of it) under which the minority and the majority are admitted to schools on the basis of their representation in the population. In that case, [a.sub.p] = [a.sub.1-p] = [I.sup.A], and the threshold ability necessary to gain admission for majority children is equal to that for minority children. That is, [I.sup.A] is such that

S = 1 - [PHI]([I.sup.A]). (6)

Parent i's utility from his or her own consumption in period 1 and his or her offspring's consumption in period 2 has a log-linear form:

[u.sub.i] - [theta] ln([c.sub.i,1]) + (1 - [theta])E[ln([c.sub.i,2])]; 0 < [theta] < 1, (7)

where [c.sub.i,1] and [c.sub.i,2] denote parent i's consumption in period 1 and the consumption of i's offspring in period 2, respectively.

Given that the higher-education system is public and parents do not know their offspring's abilities when voting, the following constraints apply to maximizing Equation 7:

[c.sub.i,1] [less than or equal to] (1 - [[tau].sub.i])[y.sub.i],

E[ln([c.sub.i,2])] = [[integral].sup.ai.sub.-[infinity]] ln[exp([a.sub.i])[lambda](E)[w.sup.u]][phi](a) da + [[integral].sup.[infinity].sub.ai] ln[exp([a.sub.i])[lambda](E)[w.sup.e]][phi](a) da (8)

= ln [lambda](E) = [PHI]([a.sub.i]) ln([W.sup.u]) + [1 - [PHI]([a.sub.i])]ln([w.sup.e]),

where [phi](*) denotes the probability density function (p.d.f.) of the log-innate abilities, [y.sub.i] represents individual i's initial endowment, [[tau].sub.i] is i's preferred tax rate, and [a.sub.i], equals [a.sub.p], for majority voters and [a.sub.1-p] for minority voters.

4. Affirmative Action and Education Supply

Affirmative Action with Fixed Education Supply

In what follows, we present the simplest version of the model laid out above. Accordingly, the supply of education is fixed at S (i.e., the equilibrium tax rate, [[tau].sup.*] is predetermined at [tau]). The only decision that voters need to make is whether to enact affirmative action policies in the following period. As Equations 5 and 6 indicate, S = S [right arrow] [I.sup.A] > [I.sup.N].

The utility of a representative majority parent when there is no affirmative action, [u.sup.N.sub.p], is given by

[u.sup.N.sub.p] = [theta] ln[(1 - [tau])[y.sub.p]] + (1 - [theta]){ln [lambda][E([I.sup.N])] + [PHI]([I.sup.N]) ln([w.sup.u]) + [1 - [PHI]([I.sup.N])] ln([w.sup.e])}. (9)

The utility of a representative majority parent when there is affirmative action, [u.sup.A.sub.p], is given by

[u.sup.A.sub.p] = [theta] ln[(1 - [tau])[y.sub.p]] + (1 - [theta]){ln [lambda][E([I.sup.A])] + [PHI]([I.sup.A]) ln([w.sup.u]) + [1 - [PHI]([I.sup.A])] ln([w.sup.e])}. (10)

If [u.sup.A.sub.p] [less than or equal to] [u.sup.N.sub.p], the social benefit of affirmative action policies does not outweigh their costs to the majority (which accrue in the form of reduced odds of gaining entry to a college), and the majority votes against affirmative action. However, if [u.sup.A.sub.p] > [u.sup.N.sub.p], the benefit to the majority outweighs the costs, and the majority votes to adopt affirmative action. The likelihood that the utility of the majority with affirmative action will exceed that without it depends on how large the education premium, [w.sup.e]/[w.sup.u], is. This is more formally stated in the following proposition.

PROPOSITION 1. Ceteris paribus, an increase in the education premium, [w.sup.e]/[w.sup.u], reduces the likelihood that the majority will support affirmative action. That is, for [beta] = [beta] and [alpha] = [alpha], where [beta] > [alpha], [there exists] ([w.sup.e]/[w.sup.u]) such that [for all] [w.sup.e]/[w.sup.u] [greater than or equal to] ([w.sup.e]/[w.sup.u]), [u.sup.A.sub.p] [less than or equal to] [u.sup.N.sub.p], and [for all] [w.sup.e]/[w.sub.u] < ([w.sup.e]/[w.sup.u]), [u.sup.A.sub.p] > [u.sup.N.sub.p].

PROOF. Let F [equivalent to] [u.sup.A.sub.p] - [u.sup.N.sub.p] = ln{[lambda][E([I.sup.A])]/[lambda][E([I.sup.N])]} - ln([w.sup.e]/[w.sup.u][[PHI]([I.sup.A]) - [PHI]([I.sup.N]). Given that [I.sup.A] > [I.sup.N],

E([I.sup.A]) = p [[integral].sup.[infinity].sub.[I.sup.A]] exp(a)[phi](a) da + (1 - p) [[integral].sup.[infinity].sub.[I.sup.A]] exp(a - [alpha])[phi](a) da, (11)

and

E([I.sup.N]) = p [[integral].sup.[infinity].sub.[I.sup.N]] exp(a)[phi](a) da + (1 - p) [[integral]sup.[infinity].sub.[I.sup.N] + [betal]] exp(a - [alpha])[phi](a) da, (12)

[beta] > [alpha] [right arrow] E([I.sup.A]) > E([I.sup.N]). Thus, In {[lambda][E([I.sup.A])/[lambda][E([I.sup.N])]} > 0. Moreover, for any given pair ([beta], [alpha]), [there exists] ([w.sup.e]/[w.sup.u]) such that F = 0. It follows immediately from [partial]F/[partial]([w.sup.e]/[w.sup.u]) < 0 that [for all] [w.sup.e]/[w.sup.u] [greater than or equal to] ([w.sup.e]/[w.sup.u]), [u.sup.A.sub.p] [less than or equal to] [u.sup.N.sub.p], and [for all] [w.sup.e]/[w.sup.u] < ([w.sup.e]/[w.sup.u]), [u.sup.A.sub.p] > [u.sup.N.sub.p]. QED.

In the proof of the above proposition, the second term on the RHS of F represents the marginal cost of affirmative action to the majority voter, whereas the first term on the rhs of F represents its marginal benefit. The latter accrues through the positive externality of attaining a more efficient educational allocation, and the former is related positively to the marginal decline in the expected income of the majority's offspring,([w.sup.e]/[w.sup.u])[[PHI]([I.sup.A]) - [PHI]([I.sup.N])]. That, in turn, is related to the education premium, [w.sup.e]/[w.sup.u]. Thus, when there is an increase in the education premium, the net marginal benefit of majority voters' children being admitted to a college increases relative to that of affirmative action and raises the likelihood that majority voters will strike down affirmative action.

The extent to which the adoption of affirmative action displaces the majority offspring from college admissions also affects the expected income of the majority's offspring through the term [PHI]([I.sup.A]) - [PHI]([I.sup.M]). When the screening bias, [beta], is relatively small, fewer majority offspring are displaced when affirmative action is put in effect. Moreover, ceteris paribus, this manifests itself in a relatively unchanged admission score being required for the majority offspring under affirmative action, [I.sup.A]. This makes the private cost of affirmative action relatively low for the majority. Nonetheless, the positive externality of attaining a more efficient educational allocation is also smaller when [beta] is relatively small. As a result, we cannot establish whether the likelihood that affirmative action will be supported by majority voters is lower when screening biases are relatively small. Only when the screening biases are rather large can we conclude that the positive social externalit y of affirmative action outweighs the private costs to the majority voters. The next proposition formalizes this discussion.

PROPOSITION 2. For [for all] [beta] > [alpha] [greater than or equal to] 0, the effect of higher test score biases, [beta], on the majority's support for affirmative action is ambiguous. For [for all] [alpha] [greater than or equal to] 0, the likelihood that the majority will support affirmative action approaches unity as [beta] [right arrow] [infinity].

PROOF. F [equivalent to] [u.sup.A.sub.p] - [u.sup.N.sub.p] = In {[lambda][E([I.sup.A])]/[lambda][E([I.sup.N])]} - In ([w.sup.e]/[w.sup.u])[[PHI]([I.sup.A]) - [PHI]([I.sup.N])]. Using Equation 5 and invoking the implicit function theorem, it is straightforward to show that [for all] [I.sup.N] > 0,

[partial][I.sup.N]/[partial][beta] = (1 - p)[phi]([I.sup.N] + [beta])/[psi]([I.sup.N]) < 0. (13)

Thus, [for all] [I.sup.N] > 0,

[partial][PHI]([I.sup.N])/[partial][beta] = [partial][PHI]([I.sup.N])/[partial][I.sup.N] [partial][I.sup.N]/[partial][beta] = (1 - p)[phi]([N.sup.N] + [beta])[phi]([I.sup.N])/[psi]([I.sup.N]) < 0. (14)

Moreover, using Equation 6, we can also establish that [for all] [I.sup.A] > 0, [partial][I.sup.A]/[partial][beta] = [partial][PHI]([I.sup.A])/[partial][beta] = 0. Thus, [partial][[PHI]([I.sup.A]) - [PHI]([I.sup.N])]/[partial][beta] = -[partial][PHI]([I.sup.N])/[partial][beta] > 0. In addition, using Equations 11 and 12, we also establish

[partial]In{[lambda][E([I.sup.A])]/[lambda][E([I.sup.N])}/[partial][b eta] = (1 - p) exp([I.sup.N] + [beta] - [alpha])[phi]([I.sup.N] + [beta])[lambda]'[E([I.sup.N])]/[lambda][E([I.sup.N])] > 0. (15)

Thus, [for all] [beta] > [alpha] [greater than or equal to] 0,

[partial]F/[partial][beta] = (1 - p)exp([I.sup.N] + [beta]) {exp([I.sup.N] + [beta] - [alpha])[lambda][E([I.sup.N])]/[lambda][E([I.sup.N])] - ln ([w.sup.e]/[w.sup.u]) [phi]([I.sup.N])/[psi]([I.sup.N])} >/< 0, (16)

where [psi]([I.sup.N]) [equivalent to] p[phi]([I.sup.N]) + (1 - p)[phi]([I.sup.N] + [beta]). For a sufficiently large [beta], the term in brackets in Equation 16 becomes strictly positive, since when [beta] [right arrow] [infinity], [phi]([I.sup.N] + [beta]) [right arrow] 0 (which implies in ([w.sup.e]/[w.sup.u])[[phi]([I.sup.N])/[psi]([I.sup.N])] [right arrow] in([w.sup.e]/[w.sup.u])/p) and exp([I.sup.N] + [beta] - [alpha]) [right arrow] [infinity] (which implies exp([I.sup.N] + [beta] - [alpha])[lambda]'E([I.sup.N])/[lambda]E([I.sup.N]) [right arrow] [infinity]). This suggests that [for all] [alpha] [greater than or equal to] 0, [there exists] large enough values of [beta] s.t. [partial]([u.sup.A.sub.p] - [u.sup.N.sub.p])/[partial][beta] > 0. QED.

Our second proposition implies that while the efficiency gains associated with the adoption of affirmative action policies are highest when screening biases are relatively large, its effect on the admissions criteria--and therefore on the offspring's admission odds--is also large. The implication of this is that smaller screening biases not only reduce the social benefit of affirmative action but also lower the cost to the majority because, at the margin, they displace fewer majority children from the ranks of the educated. Thus, we cannot generally and unambiguously establish what effect changes in the majority-minority test score gap might have on political support for affirmative action. As Proposition 2 shows, however, we can establish that the displacement effect diminishes as the test score bias gets large, whereas the social benefit of affirmative action increases. Hence, despite the generally ambiguous effect of the test score gap on support for affirmative action, we find that the public will favor a ffirmative action policies with sufficiently high test score biases. What remains unclear is what happens to that support when the test score gap declines.

Affirmative Action and Endogenous Education Supply

We now endogenize the share of resources devoted to education to demonstrate that such an extension preserves the results outlined above. In deciding on the optimal share of resources devoted to higher public education, parents maximize Equation 7 with respect to the tax rate [tau]. It is straightforward to show that majority parents prefer a tax rate [[tau].sup.*] that satisfies the following first-order condition

[partial][u.sub.p]/[partial][I.sup.*] = - [theta]/1 - [[tau].sup.*] [partial][[tau].sup.*]/[partial][I.sup.*] - (1 - [theta]) ln ([w.sup.e]/[w.sup.u]) [phi]([a.sub.p]) + (1 - [theta]) [lambda]'(E)/[lambda](E) [partial]E/[partial][I.sup.*] = 0, (17)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

and where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

The first term in Equation 17 denotes the marginal cost of lowering the admissions threshold and increasing the supply of public education, and the second and third terms represent the marginal benefit of doing so. While the first benefit term depends on the education premium, [w.sup.e]/[w.sup.u], and accrues only when the offspring gains admission to a public school, the second arises due to the productivity gains associated with a more educated labor force. Moreover, the former depends positively on the p.d.f. of the ability of parent i's offspring at that threshold, [phi]([a.sub.i]), but the cost of raising supply is related to the p.d.f. of abilities for the whole population. (16) In Equation 18, the latter term is given by the mixture density function [psi]([I.sup.*]). [psi]([I.sup.*]) is higher under affirmative action, which implies that the marginal cost of lowering the test-score threshold is also higher when affirmative action is in effect. Put differently, when the ratio of the majority voters' off spring density to population density is small (as is the case when affirmative action policies are in place), the net marginal benefit is low, since a larger share of the benefit of lowering the admissions threshold accrues to minority children. Equation 19 implies that when affirmative action policies are not in effect, a disproportionate number of educated workers come from majority households. Equation 20 indicates that the aggregate efficiency units of educated labor, E, depend negatively on the cutoff score [I.sup.*].

Figures 2 and 3 show the log ability densities for the children of the two groups, [phi]([a.sub.i]), as well as the mixture p.d.f. for the whole population, [psi]([a.sub.i]). Figure 2 depicts the ease of no affirmative action when [beta] = 3. Note how at relatively high cutoff levels of the threshold indicator, [I.sup.i], the mixture density function lies below the density function of log abilities for the offspring of the majority voters. In contrast, at lower threshold levels the density of log abilities for majority offspring is below that for the population. Figure 3 shows the same variables for [beta] = 1. When screening biases are smaller, the ratio of the majority's offspring density to the population density is also smaller, which reflects the increase in the odds of admission to public schools of the children of the minority at the expense of those of the majority.

In the limiting case in which [alpha], [beta] [right arrow] 0, the ratio of the densities approach 1. In that case, neither screening biases, [beta], nor the fraction of the minority voters, 1 - p, has an influence on the equilibrium share of resources devoted to public education supply.

In order to highlight the role screening biases play in the majority's optimal choice of public education supply, let us now focus on the case in which affirmative action policies are not in effect. Then, the share of resources devoted to public education supply is an increasing function of the screening bias [beta]. More formally, let G [equivalent to] [partial][u.sub.p]/[partial][I.sup.N] = 0. Using the implicit function theorem, it is straightforward to show that

[partial][[tau].sup.N]/[partial][beta] = -[G.sub.[beta]]/[G.sub.[tau]]

= -p[phi]([I.sup.N] + [beta])/[G.sub.[tau]] [theta]/1-[[tau].sup.N] e/y [2([I.sup.N] + [beta]) + 1/1-[[tau].sup.N] c/y [psi]([I.sup.N])] + 1-[theta]/[G.sub.[tau]] [[lambda]'(E)/[lambda](E) [[partial].sup.2]E/[partial] [([I.sup.N]).sup.2] + [lambda]"(E)[lambda](E) - [lambda]'[(E).sup.2]/[lambda][(E).sup.2] [partial]E/[partial][I.sup.N]] [partial][I.sup.N]/[partial][beta]. (21)

The first term in Equation 21 shows the effect of a larger [beta] on the majority offspring's admission odds and on the majority voters' marginal cost: By assumption, [[tau].sup.N] is an interior solution to the maximization problem of a majority parent when affirmative action is not in effect. Thus, [G.sub.[tau]] is strictly negative. The term 2([I.sup.N] + [beta]) represents how a given supply of educational services benefits majority voters at the threshold [I.sup.N]. This effect arises because screening biases shift down the relative position of the minority applicants in the [I.sup.i] map and raise the majority voters' odds of admission when [I.sup.N] + [beta] > 0. A sufficient but not necessary condition for this effect to be positive is that resources allocated to public education are restrictive enough that the threshold score [I.sup.N] is nonnegative. The term [1/(1 - [[tau].sup.N])](e/y)[psi]([I.sup.N]) represents the effect on utility of a lower fraction of children born to minority voters qualifyi ng for admission at a given threshold [I.sup.N]. This effect arises because when biases are larger, fewer resources need to be devoted to public education supply, as a lower fraction of minority parents' offspring qualify for admission. This effect is unconditionally positive. The marginal utility and disutility of taxes are depicted in Figure 4. (17) Consistent with the above analysis, the utility of resources devoted to public education for majority voters peaks at lower threshold levels and higher tax rates when screening biases are larger.

The second term in Equation 21 denotes the marginal effect of screening biases on the productivity variable [lambda]. Given that a larger [beta] implies a less efficient allocation of education, this term too is unambiguously positive. Consequently, when [I.sup.N] + [beta] > 0, [[partial][tau].sup.N]/[partial][beta] > 0. The corollary is that when affirmative action policies are in effect, majority voters will choose to allocate a smaller share of total resources to the supply of education. That is, [for all] [beta] > [alpha] [greater than or equal to] 0, [[tau].sup.A] < [[tau].sup.N] [right arrow] [I.sup.A] > [I.sup.N].

Turning once again to the determination of affirmative action, the majority will vote to enact such policies if and only if > [u.sup.A.sub.P] > [u.sup.N.sub.P] Modifying the function F defined in the proof of Proposition 1, we get

F = 1n{1 - [[tau].sup.A])/(1 - [[tau].sup.N])} + 1n{[lambda][E([I.sup.A])]/[lambda] [E([I.sup.N])]} - 1n([w.sup.e]/[w.sup.u])[[PHI]([I.sup.A]) - [PHI]([I.sup.N])], (22)

where [[tau].sup.*] = d[1 - [PSI]([1.sup.*])]/y, * = N, A. From Equation 22, analogs of Propositions 1 and 2 follow.

5. Conclusion

This paper presents a political economy model of affirmative action for higher education. In the model, there are positive social externalities associated with admitting applicants to public schools according to their ability, and the demand for education exceeds supply because of indivisibility in educational investment. Therefore, a screening mechanism, which may potentially be biased against minorities, is required to choose the student body. The results indicate that the returns to education affect the support for affirmative action policies. In periods in which the education premium is relatively low, the matching efficiency gains provided by affirmative action are relatively high compared with the opportunity cost of not acquiring education, and the majority supports broader affirmative action. In contrast, in periods in which the returns to education are high, the majority's support for affirmative action declines as the opportunity cost of not getting educated increases relative to the matching effici ency gains provided by affirmative action policies. Unlike the role of the education premium in determining the political outcome, a higher test score bias has a generally ambiguous effect on political support for affirmative action. Nonetheless, the social benefits of affirmative action are large enough to sustain political support for affirmative action when the test score gap is sufficiently large.

Appendix: Some Gallup Survey Results on Affirmative Action (18)

* Question: (Would you be more likely or less likely to vote for a candidate who took the following positions or would it not affect your opinion either way?) ... Favored affirmative-action plans that guarantee minorities and women access to education and jobs.

Responses:

More likely: 63%

Less likely: 19%

No effect: 14%

Don't know: 4%

Population: National adult

Population size: 1009

Interview method: Telephone

Survey date: January-February 1982.

* Question: Do you generally favor or oppose affirmative-action programs for women and minorities?

Responses:

Favor: 55%

Oppose: 34%

No opinion: 11%

Population: National adult

Population size: 1220

Interview method: Telephone

Survey date: March 1995.

* Question: When affirmative-action programs were first adopted almost thirty years ago, do you think they were needed to help women and racial minorities overcome discrimination, or were they not needed thirty years ago?

Responses:

Needed: 86%

Not needed: 12%

No opinion: 2%

Population: National adult

Population size: 1003

Interview method: Telephone

Survey date: February 1995.

* Question: (As I read you each of the following issue positions, please tell me if you would be more likely or less likely to vote for a presidential candidate taking this position--or if it would not make much difference.)... What if the candidate favored strengthening affirmative-action laws for women and minorities?

Responses:

More likely: 51%

Less likely: 26%

Not much difference: 18%

Don't know/refused: 5%

Population: National adult

Population size: 1421

Interview method: Telephone

Survey dote: January 1992.

* Question: Do you favor or oppose strengthening affirmative-action laws for women and minorities?

Responses:

Favor: 49%

Oppose: 43%

Don't know/refused: 9%

Population: National adult

Population size: 1022

Interview method: Telephone

Survey date: September 1994.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

Received December 2000; accepted March 2002.

(1.) The Civil Rights Act, which prohibits discrimination on the basis of race, gender, or ethnicity, was enacted in 1964. Executive orders 11246 and 11375, which set the currently applicable standards of affirmative action policies in federal procurement, employment, and education, were signed in 1965 and 1967, respectively.

(2.) In 1995, the U.S. Court of Appeals for the Fifth Court approved eliminating the consideration of race for admissions to public colleges in Texas. In 1996, a majority of California voters cast their ballots in favor of Proposition 209, which called for ending the consideration of race, ethnicity, or gender in admissions to public colleges and universities in California.

According to Gallup polls, opposition to affirmative action policies in education stood at a much higher level in the mid1990s than in the early 1980s--the earliest period for which the opinion polls exist. In 1982, 63% of the representative subsample of the U.S. adult population responded that they would be more likely to vote for a presidential candidate who favored affirmative action in education and employment for women and minorities. In contrast, only 55% of the respondents to a national poll in 1995 said that they generally favored affirmative action programs. At least an striking, 86% of those surveyed in 1995 thought that affirmative action programs were needed when they were first adopted in the late 1960s. (For more details, see the Appendix.)

(3.) Bowen and Bok (1998) document that the score gap for both the verbal and the math sections of the test declined by approximately 25% between 1975-1976 and 1989 and that it held steady or even widened modestly in recent years.

(4.) The standard deviation for test scores averages around 1. but that of job performance does not exceed 0.4.

Jencks (1998) points out that this difference is indicative of a "selection system bias" in higher-education screening. Such a bias occurs because while available screening tests measure mostly--if not purely--cognitive skills, test scores explain only 10-20% of the variation in job performance. Moreover, Blacks are far less disadvantaged in noncognitive determinants of productivity than in cognitive ones.

(5.) See Juhn, Murphy. and Pierce (1993), Murphy (1997), and Autor, Katz, and Krueger (1998).

(6.) Chan and Eyster (2000) show, for example, that banning affirmative action always reduces diversity and, in some cases, may also reduce average student quality. Moreover, Holzer and Neumark (1999) find no evidence of weaker job performance among most minority groups, although they find that the educational qualifications of minorities hired under affirmative action are lower.

(7.) Some indirect empirical evidence is provided by numerous studies on the long-run adverse economic consequences of income inequality. See, for example, Galor and Zeira (1993) and Persson and Tabellini (1994).

(8.) See Bowen and Bok (1998, pp. 11-12).

(9.) This assumption is clearly nonessential. Whether the offspring live for one period or two periods is irrelevant, since, in this context, we do not focus on the dynamics of public education finance and affirmative action.

10.) We employ the lognormal probability density function (p.d.f.) for expositional convenience only. In fact, the results we present below are not dependent on the exact specification of the p.d.f. To the extent that the simple trade-off between the private costs and the social gains of affirmative action exist for decisive voters, our results would--at least qualitatively--go through.

(11.) The results of our model are based on the premise that by the time parents vote on the supply of public higher education, there exists some uncertainty about the innate academic ability of the voters' offspring. While we employ a stricter version of this notion by assuming that at the time of voting parents have no information on their children's academic potential, the results below would hold under alternative specifications where there is some degree of uncertainty at the time of the vote.

(12.) Note that in our simple framework, the demand for education equals 1, as the second-period wage earnings for educated labor are higher than those for uneducated labor for all ability levels. Note also that for the sake of simplicity, we abstract from any cost associated with screening.

(13.) We allow for the possibility that there is a positive productivity gap between the majority and the minority on the grounds that there exist accumulable factors, such as social capital and connections, that influence labor productivity. As some argue, there can be historical precedents to suggest that biases in social practices and policies have led to gaps between the minority and the majority in the accumulation of such factors. That noted, whether [alpha] is strictly positive or not is inconsequential for the results below.

(14.) In our view, a more comprehensive version of Equation 3 ought to include a measurement error term. Although we abstract from it in the version provided here, the qualitative nature of our results is robust to a specification of Equation 3 that includes such an error term.

(15.) Jencks (1998) identifies five such potential biases in testing and concludes that two of those--labeling and selection system biases--significantly harm minorities. He shows how choosing students at least in part on the basis of test technologies that measure cognitive skills leads to biases even if the technology exhibits no systematic prediction errors. The reason is that available tests measure those traits for which differences across groups tend to be larger than those for other unmeasured determinants of productivity (see footnote 4). According to Jencks's definitions, labeling bias arises when a test claims to measure one thing but actually measures something else. Selection system bias occurs when (i) labor productivity depends only partly on cognitive skills, (ii) it is easy to measure cognitive skills relative to other skills that affect performance, and (iii) the racial disparity in cognitive skills is larger than that in other unmeasured traits that influence performance.

(16.) Note that the concavity of voter's utility function manifests itself in a precautionary supply of public education. This effect is implicit in both the second and the third terms of Equation 17. In the former it is reflected in ln([w.sup.e]/[w.sup.u]), and in the latter it is reflected in [lambda]'(E)/[lambda](E).

(17.) To simplify the exposition. Figure 4 has been drawn under the assumption that there are no externalities of educated labor on the level of technology.

(18.) The margin of error on all listed surveys is [+ or -]3%.

References

Autor, David, Lawrence Katz, and Alan Krueger. 1998. Computing inequality: Have computers changed the labor market? Quarterly Journal of Economics 113:1169-214.

Bowen, William G., and Derek Bok. 1998. The shape of the river. Princeton, NJ: Princeton University Press.

Chan, Jimmy, and Erik Eyster. 2000. Does banning affirmative action harm college student quality? Unpublished paper, Johns Hopkins University.

Coate, Steven, and Glenn Loury. 1993a. Antidiscrimination enforcement and the problem of patronization. American Economic Review 83:92-8.

Coate, Steven, and Glenn Loury. 1993b. Will affirmative-action policies eliminate negative stereotypes? American Economic Review 83:1220-40.

Fernandez, Raquel. 1998. Education and borrowing constraints: Tests vs. prices. Unpublished paper, New York University.

Femander, Raquel, and Jordi Gali. 1999. To each according to ...? Markets, tournaments, and the matching problem with borrowing constraints. Review of Economic Studies 66:199-824.

Fernandez, Raquel, and Richard Rogerson. 1995. On the political economy of education subsidies. Review of Economic Studies 62:249-62.

Galor, Oded, and Joseph Zeira. 1993. income distribution and macroeconomics. Review of Economic Studies 60:35-52.

Glomin, Gerhard, and B. Ravikumar. 1992. Public versus private investment in human capital: Endogenous growth and income inequality. Journal of Political Economy 100:818-34.

Gradstein, Mark, and Moshe Justman, 1997. Democratic choice of an education system: Implications for growth and income distribution. Journal of Economic Growth 2:169-83.

Hoizer, Harry, and David Neumark. 1999. Are affirmative action hires less qualified? Evidence from employer-employee data on new hires. Journal of Labor Economics 17:534-69.

Jencks, Christopher. 1998. Racial bias in testing. in The Black-White test score gap, edited by C. Jencks and M. Phillips. Washington, DC: Brookings institution Press, pp. 55-85.

Juhn, Chinhui, Kevin M. Murphy, and Brooks Pierce. 1993. Wage inequality and the rise in returns 10 skill. Journal of Political Economy 101:410-42.

Lundberg, Shelly J. 1991. The enforcement of equal opportunity laws under imperfect information: Affirmative action and alternatives. Quarterly Journal of Economics 106:309-26.

Murphy, Kevin M. 1997. Skills and earnings inequality: The supply side. AEI Seminar Series on Understanding Economic Inequality. Working Paper No. 7375.

Persson. Torsten, and Guido Tabellini. 1994. Is inequality harmful for growth? American Economic Review 84:600-621.

Murat F. Iyigun *

Welch, Finis. 1976. Employment quotas for minorities. Journal of Political Economy 84:S105-39.

* Department of Economics, University of Colorado, Campus Box 256, Boulder, CO 80309-0256, USA; E-mail murat.iyigun@colorado.edu; corresponding author.

Andrew T. Levin +

+ Board of Governors of the Federal Reserve System, 20th and C Streets, Washington, DC 20551, USA; E-mail levina@frb.gov.

For useful suggestions we thank two anonymous referees and seminar participants at Brown University and the Federal Reserve Board. All remaining errors are our own. This paper represents the views of the authors and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff.