“Valuing Diversity,” G. Loury & R. Fryer (2013)

The old chair of my alma mater’s economics department, Glenn Loury is, somehow, wrapped up in a kerfuffle related to the student protests that have broken out across the United States. Loury, who is now at Brown, wrote an op-ed in the student paper which to an economist just says that the major racial problem in the United States is statistical discrimination not taste-based discrimination, and hence the types of protests and desired recourse of the student protesters is wrongheaded. After being challenged about “what type of a black scholar” he is, Loury wrote a furious response pointing out that he is, almost certainly, the world’s most prominent scholar on the topic of racial discrimination and potential remedies, and has been thinking about how policy can remedy racial injustice since before the student’s parents were even born.

An important aspect of his work is that, under statistical discrimination, there is huge scope for perverse and unintended effects of policies. This idea has been known since Ken Arrow’s famous 1973 paper, but Glenn Loury and Stephen Coate in 1993 worked it out in greater detail. Imagine there are black and white workers, and high-paid good jobs, which require skill, and low-paid bad jobs which do not. Workers make an unobservable investment in skill, where the firm only sees a proxy: sometimes unskilled workers “look like” skilled workers, sometimes skilled workers “look like” unskilled workers, and sometimes we aren’t sure. As in Arrow’s paper, there can be multiple equilibria: when firms aren’t sure of a worker’s skill, if they assume all of those workers are unskilled, then in equilibrium investment in skill will be such that the indeterminate workers can’t profitably be placed in skilled jobs, but if the firms assume all indeterminate workers are skilled, then there is enough skill investment to make it worthwhile for firms to place those workers in high-skill, high-wage jobs. Since there are multiple equilibria, if race or some other proxy is observable, we can be in the low-skill-job, low-investment equilibrium for one group, and the high-skill-job, high-investment equilibrium for a different group. That is, even with no ex-ante difference across groups and no taste-based bias, we still wind up with a discriminatory outcome.

The question Coate and Loury ask is whether affirmative action can fix this negative outcome. Let an affirmative action rule state that the proportion of all groups assigned to the skilled job must be equal. Ideally, affirmative action would generate equilibrium beliefs by firms about workers that are the same no matter what group those workers come from, and hence skill investment across groups that is equal. Will this happen? Not necessarily. Assume we are in the equilibrium where one group is assumed low-skill when their skill in indeterminate, and the other group is assumed high-skill.

In order to meet the affirmative action rule, either more of the discriminated group needs to be assigned to the high-skill job, or more of the favored group need to be assigned to the low-skill job. Note that in the equilibrium without affirmative action, the discriminated group invests less in skills, and hence the proportion of the discriminated group that tests as unskilled is higher than the proportion of the favored group that does so. The firms can meet the affirmative action rule, then, by keeping the assignment rule for favored groups as before, and by assigning all proven-skilled and indeterminate discriminated workers as well as some random proportion of proven-unskilled discriminated workers, to the skilled task. This rule decreases the incentive to invest in skills for the discriminated group, and hence it is no surprise that not only can it be an equilibrium, but that Coate and Loury can show the dynamics of this policy lead to fewer and fewer discriminated workers investing in skills over time: despite identical potential at birth, affirmative action policies can lead to “patronizing equilibria” that exacerbate, rather than fix, differences across groups. The growing skill difference between previously-discriminated-against “Bumiputra” Malays and Chinese Malays following affirmative action policies in the 1970s fits this narrative nicely.

The broader point here, and one that comes up in much of Loury’s theoretical work, is that because policies affect beliefs even of non-bigoted agents, statistical discrimination is a much harder problem to solve than taste-based or “classical” bias. Consider the job market for economists. If women or minorities have trouble finding jobs because of an “old boys’ club” that simply doesn’t want to hire those groups, then the remedy is simple: require hiring quotas and the like. If, however, the problem is that women or minorities don’t enter economics PhD programs because of a belief that it will be hard to be hired, and that difference in entry leads to fewer high-quality women or minorities come graduation, then remedies like simple quotas may lead to perverse incentives.

Moving beyond perverse incentives, there is also the question of how affirmative action programs should be designed if we want to equate outcomes across groups that face differential opportunities. This question is taken up in “Valuing Diversity”, a recent paper Loury wrote with recent John Bates Clark medal winner Roland Fryer. Consider dalits in India or African-Americans: for a variety of reasons, from historic social network persistence to neighborhood effects, the cost of increasing skill may be higher for these groups. We have an opportunity which is valuable, such as slots at a prestigious college. Simply providing equal opportunity may not be feasible because the social reasons why certain groups face higher costs of increasing skill are very difficult to solve. Brown University, or even the United States government as a whole, may be unable to fix the persistence social difference in upbringing among blacks and whites. So what to do?

There are two natural fixes. We can provide a lower bar for acceptance for the discriminated group at the prestigious college, or subsidize skill acquisition for the discriminated group by providing special summer programs, tutoring, etc. If policy can be conditioned on group identity, then the optimal policy is straightforward. First, note that in a laissez faire world, individuals invest in skill until the cost of investment for the marginal accepted student exactly equates to the benefit the student gets from attending the fancy college. That is, the equilibrium is efficient: students with the lowest cost of acquiring skill are precisely the ones who invest and are accepted. But precisely that weighing of marginal benefit and costs holds within group if the acceptance cutoff differs by group identity, so if policy can condition on group identity, we can get whatever mix of students from different groups we want while still ensuring that the students within each group with the lowest cost of upgrading their skill are precisely the ones who invest and are accepted. The policy change itself, by increasing the quota of slots for the discriminated group, will induce marginal students from that group to upgrade their skills in order to cross the acceptance threshold; that is, quotas at the assignment stage implicitly incentivize higher investment by the discriminated group.

The trickier problem is when policy cannot condition on group identity, as is the case in the United States under current law. I would like somehow to accept more students from the discriminated against group, and to ensure that those students invest in their skill, but the policy I set needs to treat the favored and discriminated against groups equally. Since discriminated-against students make up a bigger proportion of those with a high cost of skill acquisition compared to students with a low cost of skill acquisition, any “blind” policy that does condition on group identity will induce identical investment activity and acceptance probability among agents with identical costs of skill upgrading. Hence any blind policy that induces more discriminated-students to attend college must somehow be accepting students with higher costs of skill acquisition than the marginal accepted student under laissez faire, and must not be accepting students whose costs of skill acquisition were at the laissez faire margin. Fryer and Loury show, by solving the relevant linear program, that we can best achieve this by allowing the most productive students to buy their slots, and then randomly assigning slots to everyone else.

Under that policy, very low cost of effort students still invest so that their skill is high enough that buying a guaranteed slot is worth it. I then use either a tax or subsidy on skill investment in order to affect how many people find it worth investing in skill and then buying the guaranteed slot, and hence in conjunction with the randomized slot assignment, ensuring that the desired mixture across groups that are accepted is achieved.

This result resembles certain results in dynamic pricing. How do I get people to pay a high price for airplane tickets while still hoping to sell would-be-empty seats later at a low price? The answer is that I make high-value people worried that if they don’t buy early, the plane may sell out. The high-value people then trade off paying a high price and getting a seat with probability 1 versus waiting for a low price by maybe not getting on the plane at all. Likewise, how do I induce people to invest in skills even when some lower-skill people will be admitted? Ensure that lower-skill people are only admitted with some randomness. The folks who can get perfect grades and test scores fairly easily will still exert effort to do so, ensuring they get into their top choice college guaranteed rather than hoping to be admitted subject to some random luck. This type of intuition is non-obvious, which is precisely Loury’s point: racial and other forms of injustice are often due to factors much more subtle than outright bigotry, and the optimal response to these more subtle causes do not fit easily on a placard or a bullhorn slogan.

Final working paper (RePEc IDEAS version), published in the JPE, 2013. Hanming Fang and Andrea Moro have a nice handbook chapter on theoretical explorations of discrimination. On the recent protests, Loury and John McWhorter have an interesting and provocative dialog on the recent student protests at Bloggingheads.

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2 thoughts on ““Valuing Diversity,” G. Loury & R. Fryer (2013)

  1. a m says:

    Wow, cited in a blog, now I can retire satisfied. Ps there’s a typo in the second part, you should substitute coate with fryer

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