In a dynamic framework in which generations are linked by educational background, we identify an intergenerational externality that is larger for disadvantaged groups. This provides an argument for affirmative action in higher education based on efficiency alone

Del Rey, Elena

Racionero, Maria

Revista Hacienda Pública Española

The Australian National University

   THE AUSTRALIAN NATIONAL UNIVERSITY   WORKING PAPERS IN ECONOMICS AND ECONOMETRICS   An efficiency argument for affirmative action in higher education  Elena Del Rey∗  and Maria Racionero†    Working Paper No. 447   September 13, 2004  ISBN: 086831 447 1  Abstract  In a dynamic framework in which generations are linked by educational background, we identify an intergenerational externality that is larger for disadvantaged groups. This provides an argument for affirmative action in higher education based on efficiency alone.   ∗ Department of Economics, Universitat de Girona, Spain. †Corresponding author: School of Economics, Australian National University, Australia.  Tel: + 61 2 61254466 Fax: + 61 2 61255124. Email: maria.racionero@anu.edu.au We gratefully acknowledge support from Fundación BBVA, Spain. Errors remain ours. An efficiency argument for affirmative actionin higher educationElena Del Rey∗ and Maria Racionero†September 13, 2004AbstractIn a dynamic framework in which generations are linked by educational background,we identify an intergenerational externality that is larger for disadvantaged groups. Thisprovides an argument for affirmative action in higher education based on efficiency alone.Keywords: affirmative action, intergenerational externalityJEL Classification: H21, I281 IntroductionAffirmative action in higher education is often explained by colleges and universities valuingdiversity of their student bodies (Chan and Eyster, 2003). However, it has been argued thatsuch preferences may imply efficiency costs, as resources are transferred from higher abilitystudents to lower ability students from disadvantaged groups.In contrast, efficiency enhancing properties of affirmative action have also been suggested.De Fraja (2002) provides an efficiency argument for reverse discrimination based on asymmetricinformation. Holzer and Neumark (2000) mention the likely existence of community externalitiesand, in particular, of role-model effects (i.e., educated members of a community may have apositive effect on the education of future generations). This suggests the existence of a positivecommunity-specific intergenerational externality that, to the best of our knowledge, has notbeen modeled before. Accounting for an externality of this type, and under the assumption thateducation levels the playing field for families of different background, we show that affirmativeaction can be justified exclusively on efficiency grounds.∗Department of Economics, Universitat de Girona, Spain.†Corresponding author: School of Economics, Australian National University, Australia. Tel: + 61 2 61254466.Fax: + 61 2 61255124. Email: maria.racionero@anu.edu.auWe gratefully acknowledge support from Fundación BBVA, Spain. Errors remain ours.2 The ModelWe consider two coexisting communities differentiated by race R (for instance, black B and whiteW ). Within each community, individuals differ both in their ability to benefit from educationand in their family educational background. Ability, denoted by a, is stochastically determinedat birth. For simplicity, we consider that a is uniformly distributed between 0 and 1 in bothcommunities. Educational background of an individual is represented by whether the parent isuneducated or educated: e−1 = 0, 1.Individuals live for one period. First, they decide whether or not to acquire higher education.Studying entails a financial cost that depends on their race, their ability to benefit from educationand on the education of their parents. We assume this cost to be γRe−1C (a). Belonging to adisadvantaged group, black individuals have to surpass more obstacles, which increases thecosts of acquiring higher education. However, we assume that education levels the playing field,so that children of educated parents of any race face identical costs.1 Accordingly, we positγB0 > γW0 > γB1 = γW1 = 1 to reflect the fact that education is more costly for children ofuneducated parents, and this effect is larger for black children. C (.) is a decreasing and convexfunction of ability (i.e., C0< 0, C00> 0).Productivity, and thus wages, depend on education alone. Higher education has a positiveeffect on wages, so that educated individuals earn higher wages (h) than uneducated individuals(`). Individuals inelastically supply one unit of labour.The decision to become educated or not is made by comparing income with and withouteducation. For each type, characterized by race R and educational background e−1 , it is possibleto determine a threshold value of ability above which individuals will acquire higher education.We denote by baRe−1 this ability level.γRe−1C(baRe−1 ) = h− ` R = B,W ; e−1 = 0, 1 (1)At the threshold ability level baRe−1 , the cost of education equals the gain, in terms of earnings,of attaining higher education. Children with given R and e−1 whose ability is larger than baRe−1 willinvest in higher education. Individuals of ability a < baRe−1 will not. From (1) and the assumptionsmade about γRe−1 , baW1 = baB1 < baW0 < baB0 .1This assumption is made for simplicity of presentation. The weaker assumption γB1 −γW1 <¡γB0 − γW0¢ γB1 γW1γB0 γW0is sufficient, although not necessary, to yield the same qualitative results.2At the end of the period each individual gives birth to another one and dies. Populationis thus constant. Given that a is uniformly distributed between 0 and 1, baRe−1 denotes theprobability of remaining uneducated depending on parental educational background and race.Under the assumptions made we can conclude that, children of educated parents are more likelyto gain tertiary education than those of non-educated ones and, among children of uneducatedparents, black children are less likely to gain tertiary education than white children of the sameability. The evolution over time of the proportions of educated and uneducated people of raceR in this economy can be described by a Markov chain with the following transition matrix:PR =µ baR0 1− baR0baR1 1− baR1¶. (2)Let πR0 and πR1 denote, respectively, the proportions of uneducated and educated people ofrace R in each generation. Once the steady state has been reached, the proportion of educatedand uneducated people of each group replicates itself: (πR0 ,πR1 ) = (πR0 ,πR1 )PR. The vector ofsteady state probabilities is then:2πR0 =baR11− baR0 + baR1 and πR1 = 1− baR01− baR0 + baR1 . (3)3 The First BestLet yRe−1,e be the net income of an individual of race R, family education e−1 and educatione. We define the first best proportions of educated and uneducated individuals of each race R,ãR0 and ãR1 , as those which provide the highest aggregate net income. The government thenmaximizes πR0 EyR0 + πR1 EyR1 , where:EyRe−1 = baR0 ye−1,0 + Z 1baR0 yRe−1,1(a)da (4)stands for the expected utility of children of educational background e−1 and race R. After somerearrangements, the optimality condition for interior ãRe−1 is:γRe−1C(ãRe−1)) = h− `+EyR1 −EyR01− ãR0 + ãR1(5)Since C is decreasing, ãR0 > ãR1 . Thus, at the first best, a higher proportion of children ofeducated than of uneducated parents undertake higher education within each group. The reasonfor this result is that the education of the children of uneducated parents is more costly.2We assume that costs associated to education are such that baRe−1 is interior for all R and e−1.3On the other hand, since, at the laissez-faire, the expected utility is larger for children ofeducated parents (EyR1 > EyR0 ), all individuals who make their educational choice in the absenceof government intervention end up consuming too little education.Finally, since the difference in participation between children of educated and uneducatedparents is larger for B and the difference in the costs they face is also larger, EyB1 − EyB0 >EyW1 − EyW0 . Therefore, the difference between first best and decentralized threshold ability islarger for black people.In other words, the individual decision to undertake education is inefficient because peoplefail to account for the fact that their getting higher education increases the chances that theirchildren also will gain access to higher education. This intergenerational externality is higher forblack people, since the difference in expected income for children of uneducated and educatedindividuals is larger within this group.4 Optimal subsidiesThe government may subsidize education in order to internalize the externality. We assume thatsubsidies can be dependent on race or ethnicity but not on the education decision previouslymade by parents. To finance this policy, it levies a lump-sum tax T on all workers.The objective of the government is to maximizeXRXe−1πRe−1ÃbaRe−1 (`− T ) + Z 1baRe−1³h− γRe−1C(a) + SR − T´da!subject to the budget constraint 2T =PR πR1 SR, where SR, R = B,W , represents the subsidy.The optimal policy is characterized by the first order conditions corresponding to the lumpsum tax T and subsidies SW and SB. The optimality condition for T yields λ = 1 (i.e.,the marginal cost of raising one unit is one since lump-sum taxes are non-distortionary). Theoptimality condition for each SR is:∂πR0∂SR£EyR0 −EyR1¤+ πR0∂EyR0∂SR+ πR1∂EyR1∂SR−µπR1 + SR ∂πR1∂SR¶= 0.After some manipulation, these conditions becomeSR = EyR1 −EyR0 .Since EyB1 − EyB0 > EyW1 − EyW0 , it follows that SB > SW . Hence, individuals from thedisadvantaged community receive a larger Pigouvian subsidy.45 ConclusionsIn this note, we have considered a dynamic framework in which generations are linked by fam-ily background, which is determined both by family education and appurtenance or not to adisadvantaged group. We have identified an intergenerational externality that is larger for dis-advantaged groups provided that education levels out the playing field (i.e., existing differencesacross groups are smaller for educated individuals). This externality can be internalized bymeans of Pigouvian subsidies, equal to the size of the externality in each case. Therefore, largersubsidies for students that belong to disadvantaged groups can be justified on efficiency groundsalone.References[1] Chan, J. and E. Eyster, 2003, Does banning affirmative action lower college student quality?American Economic Review 93(3), 858-872[2] De Fraja, G., 2002, Affirmative action and efficiency in education, CEPR Discussion PaperNo 3357 (forthcoming International Economic Review).[3] Holzer, H. and D. Neumark, 2000, Assessing affirmative action, Journal of Economic Liter-ature 38(3), 483-568.5

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