Lecture Notes on Discrimination and Affirmative Actions | ECON 681, Study notes of Public finance

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Lectures Notes on Discrimination and Affirmative Actions Hanming Fang January 25, 2002 Contents 1 Introduction 2 2 Theoretical Models of Discrimination 2 2.1 Taste-Based Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Statistical Discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Phelps (AER, 1972) . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Arrow (1973) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.3 Coate and Loury (AER, 1993) . . . . . . . . . . . . . . . . . . . . . 8 2.3 Discrimination Due to Inter-Group Interactions . . . . . . . . . . . . . . . . 13 2.3.1 Moro and Norman (2001) . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Mailath, Samuelson and Shaked (AER, 2000) . . . . . . . . . . . . . 14 3 Affirmative Actions 16 3.1 Origins of Affirmative Action . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Theoretical Studies of the Effect of Affirmative Action . . . . . . . . . . . . 18 3.2.1 Coate and Loury’s Patronizing Equilibrium . . . . . . . . . . . . . . 18 3.2.2 Moro and Norman (2001) . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.3 Fang and Norman (2001) . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Evaluation of the Effects of Affirmative Action . . . . . . . . . . . . . . . . 24 3.3.1 Donohue and Heckman (1991) . . . . . . . . . . . . . . . . . . . . . 24 3.3.2 Moro (2001) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1 1 INTRODUCTION 2 4 Empirical Studies of Discrimination 26 4.1 Traditional Regression Analysis and Its Problems . . . . . . . . . . . . . . . 26 4.2 Market Test: Becker (1993) . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3 Audit Method and Its Problems . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.3.1 Ayres and Siegelman (1995) versus Goldberg (1996) . . . . . . . . . 34 5 Discussions 36 1 Introduction Wage inequality, and in particular, racial income inequality, is an important question in public economics. Numerous empirical studies have established that when wages are regressed on a bunch of variables that should matter for productivity (schooling, experience, union membership etc.) and dummy variables for race and sex, the coefficient for the dummies usually turn out to be significantly different from zero. While this type of analysis may under- or over- state the extend of racial discrimination, it motivates the theoretical studies on discrimination. [See Cain’s (1986) Handbook of Labor Economics survey article for more details of this empirical labor literature, and Section 4.1 for some problems in interpreting the results in this empirical literature.] Recently disparate treatment received by different racial and/or gender groups in hous- ing, mortgage lending, retailing, policing, judicial system, and even organ transfers have caused tremendous amount of publicity. It is important to know the extent of and the reasons for disparate treatments before the best policy to help the minorities can be made. 2 Theoretical Models of Discrimination 2.1 Taste-Based Discrimination The modern economics literature on discrimination started by Becker (1959) and his work is probably still the most well-known contribution. Becker studied several simple models of discrimination, which all had in common that the driving force behind discrim- ination are racist preferences (or racial animus) by some agents in the model. One simple version of the model (due to Arrow 1973) is as follows: 2 THEORETICAL MODELS OF DISCRIMINATION 5 6 -¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ " " " " "" " " " "" "" θ∗ = µa θ Wage WW (θ) WB (θ) Figure 1: Wage Offers in Phelps Model Hence if, σ2B > σ 2 W , (due, possibly, to the fact that most firms are White and they are better in interpreting signals generated by White workers), then we have the following implication: [See Figure 1 for an illustration] • Wages are lower for high scoring blacks than for high scoring whites (signals above the prior mean ability µa); • Wages are higher for low scoring blacks than for low scoring whites (signals below µa); • Average wages are equal for the two groups (unless if there are difference in the distribution of intrinsic ability a across the groups). We note that white workers with the same signals are treated differently depending on group identity, this may, or may not be viewed as discrimination. 2.2.2 Arrow (1973) Arrow (1973) is the first to lay out the necessary ingredients of a theory of “self-fulfilling prophecy” with endogenous skill acquisition decisions to interpret discriminatory outcomes. He mentioned the following important ingredients of such a statistical discrimination theory: (1) the employers should be able to costlessly observe a worker’s race; (2) the employers must incur some cost before he can determine the employee’s true productivity (otherwise, 2 THEORETICAL MODELS OF DISCRIMINATION 6 there is no need for surrogate information); (3) the employers must have some preconception of the distribution of productivity within each of the two groups of workers. Arrow then proposed the following model: • Each firm has two kinds of jobs, skilled and unskilled and they are complementary to each other. I think he means that the firm has a production function f (Ls, Lu) where Ls skilled labor and Lu is the unskilled labor, and f is a constant returns to scale production function • All workers are qualified to perform unskilled jobs; but only a proportion pw of whites and a proportion of pb of blacks are skilled. The firm must pay a cost r to find out whether the worker is skilled or not, and the firm knows eventually whether a worker is qualified or not. • Arrow’s model has some problem with the way he perceives the wage determination: his notion of a competitive wage in the skilled job is a contract that pays a worker from group j = b, w a wage wj > 0 if a worker is revealed to be qualified, and 0 otherwise; on the other hand the firm always pays a wage wu to any worker on the unskilled job. • Arrow claims that competition among firms will result in a zero profit condition, hence r = pw [f1 (Ls, Lu)−ww] r = pb [f1 (Ls, Lu)−wb] . Hence ww = pb pw wb + µ 1− pb pw ¶ f1 (Ls, Lu) . If for some reason pb < pw, then wb < ww. • The wage on the simple task for both groups is wu = f2 (Ls, Lu) . COMMENTS: I think Arrow had all the ideas right, but his model of wage determi- nation is simply not consistent: since wu > 0 and any unqualified worker who is hired on the skilled job will eventually get a wage 0, why would any unqualified worker agree to be hired on the skilled job in the first place? 2 THEORETICAL MODELS OF DISCRIMINATION 7 However, neglecting the above problems with the model, we have: • Blacks are paid a lower wage in the skilled task if they are believed to be qualified with a lower probability; • The explanation of discriminatory behavior is shifted from preferences to beliefs. Arrow then proceed to provide an explanation for why pw and pb differ in equilibrium even though there are no intrinsic differences between groups. Since Arrow’s model is problematic in details we will not go through the details, but he assumes that • A worker becomes qualified as a result of a costly (unobservable) investment; • Workers invest in skills if the gains of doing so outweighs the costs. Arrow takes the gains to be wj−wu (which is obviously inconsistent with the labor market equilibrium condition). Suppose the distribution of skill investment cost is given by G (·) . Then the proportion of skilled workers will be G (wj −wu) . And equilibrium requires that pj = G (wj (πj)−wu) . • Arrow then notes that the system can easily have symmetric as well as asymmetric equilibria. The intuition for the asymmetric equilibria is simple: if very few workers invest in a particular group, the firms will rationally perceive this group as unsuitable for the skilled task and equilibrium wages in the skilled task will be low, which will in turn give little incentive for the workers from this group to invest. Arrow is clearly aware of the logical inconsistency in his model: “I believe these results are only the barest fragment of what could be found with better and more detailed systems in which there is an interaction between reality and perception of it. One must consider still more precisely how indi- vidual employers acquire knowledge which will modify their initial estimates of distributions as differing between groups and in turn the effects of these percep- tions on the market and therefore on any incentives to modify those abilities.” 2 THEORETICAL MODELS OF DISCRIMINATION 10 while the profit is zero if it assigns the worker to the simple task. Hence the firm will assign this worker to the complex task if and only if p (θ;π)xq − [1− p (θ;π)]xu ≥ 0 ⇔ xq xu ≥ 1− π π fu (θ) fq (θ) . Since fq/fu is assumed to be monotonically increasing in θ, the above inequality holds if and only if θ ≥ θ̃ (π) where θ̃ (π) is determined as follows: • If the equation xq xu = 1− π π fu (θ) fq (θ) (1) has a solution [which will be unique due to MLRP], θ̃ (π) is the unique solution; • If xq/xu > (1− π) fu (θ) /πfq (θ) for all θ ∈ [0, 1] , then θ̃ (π) = 0; • Otherwise, θ̃ (π) = 1. It is clear that whenever θ̃ (π) is interior, we have dθ̃ (π) dπ = −l0 ³ θ̃ (π) ´ xu xq 1 π2 < 0. This is intuitive: the higher the prior probability that a worker is qualified, the firms will be more willing to give the benefit of doubts to the workers. TO SUMMARIZE: In the task assignment stage, the firm will follow a cutoff rule θ̃ (π) : workers with signal θ higher than θ̃ will be assigned to the complex task and those with signals lower than the cutoff will be assigned to the simple task. Moreover, the cutoff θ̃ (π) is weakly decreasing in π, the fraction of skilled which is weakly decreasing in π, the fraction of skilled workers in that group. Now we analyze the workers’ optimal skill investment decision at STAGE 2, given the firms’ sequentially rational behavior in STAGE 4. Suppose that in STAGE 4, the firms follow a cutoff rule at θ̃. If a worker with cost c decides to invest in skills, his expected payoff will be h 1− Fq ³ θ̃ ´i ω − c 2 THEORETICAL MODELS OF DISCRIMINATION 11 - 6 θ̃ B ³ θ̃ ´ 0 1 Figure 2: Benefits to Invest in Skills as a Function of the Cutoff θ̃ If he does not invest in skills, his expected payoff will beh 1− Fu ³ θ̃ ´i ω. Hence a worker with cost c will invest if and only if c ≤ B ³ θ̃ ´ ≡ h Fu ³ θ̃ ´ − Fq ³ θ̃ ´i ω. This implies that the fraction of workers who rationally invests in skills given a cutoff θ̃ is G ³ B ³ θ̃ ´´ = G ³h Fu ³ θ̃ ´ − Fq ³ θ̃ ´i ω ´ . (2) A few observations about the benefit function B (·) is useful. Note that B0 ³ θ̃ ´ = ω h fu ³ θ̃ ´ − fq ³ θ̃ ´i is positive if and only if l ³ θ̃ ´ < 1. Hence it is a single peaked function. Moreover, B (0) = B (1) = 0. The function B (·) is depicted in Figure 2. An equilibrium of the game is simply ³ θ̃ ∗ j ,π ∗ j ´ , j = B,W such that for each j, θ̃ ∗ j = θ̃ ¡ π∗j ¢ π∗j = G ³ B ³ θ̃ ∗ j ´´ , where θ̃ (·) and G (B (·)) are defined by (1) and (2) respectively. Equivalently, we could redefine the equilibrium of the model as π∗j , j = B,W, that satisfy π∗j = G ³ B ³ θ̃ ¡ π∗j ¢´´ . (3) 2 THEORETICAL MODELS OF DISCRIMINATION 12 6 θ̃ π 1 0 0 1 G ³ B ³ θ̃ ´´ inverse of θ̃ (·) ¡µ ¡ª - Figure 3: Multiple Equibria From the above definition of equilibirum, we see that the only way to rationalize dis- criminatory outcome for the blacks and whites is when the above equation has multiple solutions. In fact, nothing so far guarantees existence of non-trivial equilibria (equilibria where π∗j 6= 0). Coate and Loury then proceed to provide (not too special) circumstances under which the model admits discriminatory equilibria, hence it provides an explanation for discrimination with ex ante identical groups. [See Figure 3.] Proposition 1 If there exist θ̃ such that G ³ B ³ θ̃ ´´ > fu ³ θ̃ ´ /fq ³ θ̃ ´ xq/xu + fu ³ θ̃ ´ /fq ³ θ̃ ´ , then there exist at least two non-zero solutions to Equation (3). Thus Coate and Loury demonstrate that statistical discrimination is a logically consis- tent notion in their model. • Discrimination in this model can be viewed as a coordination failure: Removing dis- crimination is achieved if somehow blacks and the firms can all be coordinated on the good equilibrium. There is no conflict of interests among the whites and blacks concerning affirmative actions. 2 THEORETICAL MODELS OF DISCRIMINATION 15 • Workers differ in the opportunity cost of acquiring skills, c ≥ 0, and in the population c is distributed according to CDF G; • Each firm can hire at most one worker. If a firm employs a skilled worker, regardless of his color, a flow surplus of x is generated; the flow surplus from hiring an unskilled labor is 0; • Search Friction: Vacant firms (firms without employees) and unemployed workers match through searches. [The firm can choose to search both groups, or only one group, not the search intensity itself] — Suppose that a firm searches for both colors of workers, and suppose that the proportion of the skilled workers in the population is HW and the unemployment rate of skilled workers is ρW , then the process describing meetings between un- employed skilled workers and the searching firm follows a Poisson process with meeting rate λFρWHW where the parameter λF captures the intensity of firm search. — If instead, the firm searches only green workers with intensity λF , then the meet- ing rate between the firm and the green skilled workers is given by 2λFρGHG; — Unemployed skilled workers simultaneously search for vacant firms with intensity λW and the meetings generated by workers search follow a Poisson process with rate λWρF where ρF is the vacancy rate of the firms. • When an unemployed worker and a vacant firm match, they bargain over the wage with one of them randomly drawn to propose a take-it-or-leave-it offer. Besides the symmetric steady state equilibrium, they are interested in asymmetric steady state equilibrium. Suppose that firms search only for green workers. Hence skilled green workers will earn higher wages than skilled red workers not only because their match rate will be higher, but also because once matched with a firm, the green worker can demand, or will be offered, a higher wage because his continuation utility is higher. Hence the incentive to invest in skills are higher for the green workers. The question is, will firms find it optimal to only search for green workers? The trade-off is as follows: on the one hand, once a firm is matched with a skilled red worker, the wage a skilled red demands is lower, this will 3 AFFIRMATIVE ACTIONS 16 create incentive for searching for red workers; on the other hand, when the red workers’ incentive to invest in skills is low, the proportion of skilled red workers will be lower, so the probability of being matched with a red skilled worker if the firm searches also the red workers is low, this creates incentives against searching for red workers. They show that under some conditions asymmetric steady state equilibrium can be sustained. What are the differences from other papers? In the asymmetric equilibrium of MSS, the skilled red and green workers are equally productive (since their skills are perfectly observable), yet they are offered different wages (which is economic discrimination). 3 Affirmative Actions 3.1 Origins of Affirmative Action The affirmative action policy developed during the 1960s and 1970s in two phases that embodied conflicting traditions of government regulations: The first phase, culminating in the Civil Rights Act of 1964 and the Voting Rights Act of 1956, was shaped by the presidency and Congress and emphasized nondiscrimination under a “race-blind Constitution”. The second phase, shaped primarily by federal agencies and courts, witnessed a shift toward minority preferences during the Nixon administration. The development of two new agencies created to enforce the Civil Rights Act, the Equal Employment Opportunity Commission under Title VII and the Office of Federal Contract Compliance under Title VI, demonstrates the tensions between the two regulatory traditions and the evolution of federal policy from non-discrimination to minority preferences under the rubric of affirmative action. The results has strengthened the economic and political base of the civil rights coalition while weakening its moral claims in public opinion. CIVIL RIGHTS ACT OF 1964: The main intensions of Civil Rights Act of 1964 were “the destruction of legal segregation in the South and a sharp acceleration in the drive for equal rights for women”. Title VII [known as the Fair Employment Commission Title or FEPC title] of the Act would create the Equal Employment Opportunity Com- mission (EEOC) to police job discrimination in commerce and industry with the intension to destroy the segregated political economy of the South and enforce nondiscrimination throughout the nation. Title VI of the Act [known as the Contract Compliance Title] “pro- hibit discrimination in programs receiving funds from federal grants, loans or contracts.” 3 AFFIRMATIVE ACTIONS 17 It clearly bans discrimination: “No person in the United States shall, on the ground of race, color, or national origin, be excluded from participation in, be denied the benefits of, or be subject to discrimination under any program or activity receiving Federal financial assistance.” Contract compliance was backed by the authority to cancel the contracts of failed performers and ban the contractors from future contract work. Specter of bureaucrats telling businesses whom to hire under Title VII was raised during the congressional debates prior to the passage of the Civil Rights Act. Majority Leader of the time Hubert Humphrey promised to eat his hat if the civil rights bill ever led to racial preferences. The Civil Rights Act of 1964 was signed by President Lyndon Johnson into law on 2 July. AFFIRMATIVE ACTION: It turns out that Title VI of the Civil Rights Act of 1964 was the sleeper than leads to the affirmative action. In September 1965, President Johnson issued Executive Order 11246. This order intended to create new enforcement agencies to implement Title VI in the Civil Rights Act, and it repeated nondiscrimination. The Of- fice of Contract Compliance (OFCC) established by the Labor Department to implement Executive Order 11246. It designed a model of contract compliance based on a metropoli- tan Philadelphia plan, which requires that building contractors submit “pre-award” hiring schedules listing the number of minorities to be hired, with the ultimate goal to make the proportion of blacks in each trade equal to their proportion of metropolitan Philadelphia’s workforce (30%). This Philadelphia plan was ruled in November 1968 to violate federal contract law. But in 1971 under the Nixon administration, the Supreme Court affirmed that the minority preferences of the Philadelphia did not violate the Civil Rights Act. The EEOC who is in charge of the implementation of Title VII, followed a similar strategy, it issued guidelines to employers to use statistical proportionality in employee testing. In 1972, Congress extended the EEOC’s jurisdiction to state and local governments and education institutions (which were exempt in 1964). Affirmative action is full-blown. Contrary to its original content, Johnson’s Executive Order 11246 became known as the beginning of affirmative action. The original rationale for affirmative action was to right the historical wrong of insti- tutional racism and stressed its temporary nature. In 1978, in Regents of the University of California v. Bakke, Supreme Court Justice Harry Blackmun was apologetic about sup- porting a government policy of racial exclusion: “I yield to no one in my earnest hope that the time will come when an affirmative action program is unnecessary and is, in truth, only 3 AFFIRMATIVE ACTIONS 20 • The probability that a qualified worker gets an “unclear” score is pq = θu − θq 1− θq and that for an unqualified worker is pu = θu − θq θu • Suppose that the prior that a worker is qualified is π. Then the posterior probability that a worker with an unclear score is qualified is ξ = πpq πpq + (1− π) pu . Hence the employer will assign a worker with unclear scores to the complex task if and only if ξxq − (1− ξ)xu ≥ 0⇔ π ≥ π̂ = pu/pq xq/xu + pu/pq . We will say that a firm follows a liberal policy for group i if it assigns all group i workers with unclear test score to the complex task, i.e. if θ̃ = θq; we say that a firm follows a conservative policy for group i if it assigns all group i workers with unclear test to the simple task, i.e. if θ̃ = θu. • When can a liberal policy be an equilibrium? Under a liberal policy, the benefit from skill investment is given by B (θq) = ω (1− pu) because if he is skilled, he will be assigned with probability one to the complex task and if he is unskilled, the probability is pu. Hence the proportion of skilled workers in response to a liberal policy is πl = B (θq) = ω (1− pu) . Similarly, under a conservative policy, the benefit of skill investment is B (θu) = ω (1− pq) . Hence the proportion of skilled workers in response to a conservative policy is πc = B (θu) = ω (1− pq) . Hence the liberal policy is an equilibrium if πl ≥ π̂ and the conservative policy is an equilibrium if πc < π̂. 3 AFFIRMATIVE ACTIONS 21 • Hence in the absence of AA, if πc < π̂ < πl, then (πB,πW ) = (πc,πl) is an equilibrium outcome. In this equilibrium, firms hold a negative stereotype toward blacks. Affirmative Action: Suppose that we are in such an equilibrium and affirmative action policy in the form of employment quota is imposed. What happens? Compliance with the AA employment quota requires either more B’s or less W’s be assigned to the complex task. Given (πB,πW ) = (πc,πl) , if the firm assigns a failing B to complex task, it loses xu unit of profits; if the firm assigns an unclear W to the simple task, it loses πlpq πlpq + (1− πl) pu| {z } ≡ξl xq − (1− πl) pu πlpq + (1− πl) puxu. If λ [ξlxq − (1− ξl)xu] > (1− λ)xu, then the firm would rather put failing B’s into the complex task than putting unclear W’s to the simple task to satisfy the employment quota. Suppose that the firms still follow the following assignment policies: • for the whites, the original liberal policy, i.e. assign all pass or unclear W workers to the complex task. Under this policy, we still have πW = πl; • for the blacks the firms follow the following policy: assign all pass or unclear B workers to the complex task, and with probability α (πB) assign failing B workers to the complex task, where α (πB) is chosen to satisfy the employment quota requirement: πl + (1− πl) pu = πB + (1− πB) [pu + (1− pu)α (πB)] ⇔ α (πB) = πl − πB 1− πB . We say that the firms are “patronizing” the worker if he assigns a failing worker to the complex task. Hence the firms are patronizing the blacks. Now consider B’s best response to the firms’ assignment policy described above. An- ticipating being patronized with probability α, the return from investing in skills for a B worker is given by ω − [pu + (1− pu)α] = ω (1− α) (1− pu) = (1− α)πl Hence (πB,πl) (assuming πl > 1/2) can be sustained as an equilibrium under AA if and only if πB ≤ πl and πB satisfies πB = [1− α (πB)]πl = (1− πl)πl 1− πB . 3 AFFIRMATIVE ACTIONS 22 This equation has two solutions: πB = πl or πB = 1− πl. In the first solution, color-blind equilibrium (the employer is liberal toward both groups); in the second solution, the firms continue to see B’s as less productive and patronize the B’s to fulfil the AA mandates. 3.2.2 Moro and Norman (2001) Moro and Norman introduced affirmative action (in the form of employment quota as in CL) into their specialization-driven model of statistical discrimination. Because of the inherent interaction between these groups, affirmative action has redistributive consequences (which differs from the effect of affirmative action in CL, in which redistribution between the groups is absent: either blacks are made better off, or the whites are made worse off, but not at the same time.) Because in their model wages are endogenous, they can also study the effect of affirmative action on wages. In an admittedly styled model, they demonstrate the possibility that affirmative action may increase the inequality between groups. The rough intuition is as follows: the partial equilibrium effect of affirmative action (assuming that affirmative action does not affect the proportion of skilled workers in the population) typically is to reduce the wage in the unskilled job for the discriminated group and increase the wage in the unskilled job for the other group. Changes in investment behavior tend to mitigate the partial equilibrium effects, but nothing guarantees that the responses in terms of changes in human capital investments are large enough to reverse the initial effect. The message from Moro and Norman is similar to Coate and Loury: we need to worry about possible perverse effects of incentives of affirmative actions, as well as possible unin- tended consequences to the intended beneficiaries. 3.2.3 Fang and Norman (2001) We are motivated by the deteriorating (i.e. increasing) Chinese/Malay income inequality in Malaysia despite the fact that wide-ranging preferential policies are granted to the ethic Malays under the New Economic Policy from 1970. Why the preferentially treated Malays did not catch up the Chinese, but instead falls further behind? We make the following assumptions: • There are two sectors, a private sector and a government sector; 3 AFFIRMATIVE ACTIONS 25 To partially solve the first difficult, Donohue and Heckman focus on the comparison of the economic progress of the blacks in the South and in the other regions in the U.S. They reason as follows: by noting that black relative improvement was most rapid in the South, they can counter the argument that the laws themselves were mere manisfestation of preexisting social changes. Federal activity was imposed on the South and had its greatest apparent effect in the region that resisted it the most. To partially solve the second difficulty, Donohue and Heckman focus on cross-time vari- ation, in particular, the black economic progress in pre-1964 era and that after 1965. Their main findings on males are as follows • There is an upward jump in the time series of black earnings and wages beginning in the mid-1960s; • The South was the region of the greatest black economic advance in the period 1960- 1970, accounting for at least two-thirds of the increase in black economic status over the decade; • There is evidence of substantial desegregation of firms in the South during 1965-1970 period; • The black economic progress following the passage of Title VII coincided with a sharp drop in the outflow of blacks from the South and even led to black migration into that region between 1970 and 1980. • During the seventy-year period from 1920-1990, there are two periods of rapid relative black progress - the period of rebound from the Great Depression brought on by the World War II and the 1965-1975 period; • Regarding the mechanism underlying the episodic improvement of black economic status in the 1965-1975 period: — Black migration contributed little and relative increases in the quantity of black education contributed modestly to black progress after 1965; — The main cause of the observed black relative economic gains during this period are relative black increases in the returns to education. The reason for the increase in the returns to education could either be relative improvements in 4 EMPIRICAL STUDIES OF DISCRIMINATION 26 schooling quality for the blacks, or changes in the demand for black labor induced by declining racial discrimination, government civil rights policy, or tight labor markets. There is no consensus as to what caused the increase in the blacks’ returns to education. 3.3.2 Moro (2001) Mor (2001) wants to ask the following question: after 1964, the relative economic status of blacks have improved substantially. Was the improvement of the black economic status is a result of the blacks being coordinated on a less discriminatory equilibrium due to the Civil Rights policies? To this end, Moro estimated a structural model of labor market discrimination for different points in time after 1964 (namely, 1965, 1980, 1995). His structural model is an extension of Moro and Norman’s theoretical model allowing for ability heterogeneity. With the estimates of the structural parameters, Moro numerically solves for the other equilibria that can be admitted under these parameter estimates, and ask what equilibrium corresponds to the actual outcome? Is it the least discriminatory, or most discriminatory, or anything in the middle? In particular, has there been change in the severity of discrimination in the selected equilibrium in the three points in time? He finds that it has always been the equilibrium with the least wage inequality that have been selected whenever estimated parameters are consistent with multiple equilibria. He then concludes that self-fulfilling expectations did not exacerbate wage differentials in the U.S. and that the decline in wage inequalities experienced in the U.S. economy can not be attributed to changes in equilibrium selection, but rather changes in fundamentals of the economy is responsible. 4 Empirical Studies of Discrimination 4.1 Traditional Regression Analysis and Its Problems See for example, the Boston Fed study: “Mortgate Lending in Boston: Interpreting HMDA Data”, by Alicia Munnell, Geoffrey Tootell, Lynn Browne and James McEneaney, AER March 1996. 4 EMPIRICAL STUDIES OF DISCRIMINATION 27 4.2 Market Test: Becker (1993) Gary Becker, in a op-ed piece for Business Week in 1993 criticizes the Fed-Boston study on mortgage discrimination against black and Hispanic applicants by banks. The Fed- Boston study examine whether rates of denial to minority applicants for mortgage exceed those to whites with similar income, credit histories, and various other characteristics. They found that after controlling for these observable characteristics, black and Hispanic applicants are more likely denied mortgage. Becker argued that omitted variables, such as record indicating chronic late payments, could very well explain the differences in lending rates between groups. Becker seems to view discrimination only those motivated by racial animus: “An employer discriminates when he refuses to hire applicants from a group even though they would produce more profit than those who are hired. Em- ployees discriminate if they refuse to work alongside members of a group even though they can earn more by doing that. The corollary here is that if a company chooses not to hire members of a group, its decisions may not be discriminatory if hiring others who are cheaper or more productive results in more profits.” He then proposed an approach to detect if there is racial animus (or taste baste discrim- ination) in bank lending: “If banks do discriminated against blacks and other groups, they would im- pose stricter standards on loan to them than to whites with truly compara- ble credit backgrounds. The banks would be willing to finance only the most profitable of African-American applications. Were that the case, the mortgage loans approved for minority applications should be more profitable than loans to whites, not less profitable or even equally profitable.” He then suggests that we look at the average default rates of accepted loans for blacks, Hispanics and whites. If the average default rate for the blacks are smaller than for the whites, then it is a market outcome indication of discrimination against the blacks: the banks are imposing a higher standard on the blacks than that on the whites. CRITIQUE: There is no doubt that Becker raised a very creative way of detecting discrimination by looking at the market outcomes. However, his suggestion of looking at 4 EMPIRICAL STUDIES OF DISCRIMINATION 30 Different from the mortgage market, the bail bond context has a nondichotomous, non- censoring decision variable and under the null hypothesis the court’s goal is to equalize the probability of flight across all defendants. The judge’s ability to individually vary the bail among in a sense makes every defendants marginal and thus avoids the inframarginal problem that has plagued the application of outcome tests to the mortgage context. One may directly apply Becker’s idea to compare the probability of flee for black defendants and white defendants in detecting if there is racial discrimination. But the defendant flight information is hard to get. The novelty of Ayres and Waldfogel paper is to look at the bond rates charged by bond dealers to defendants as a measure of the flight risk perceived by the competitive market. They provide some evidence that the New Haven bail bond market they study is competitive. The model is simple. Let R be the total non-refundable fees charged by the bond dealer, p be the flight probability, f be the forfeiture rate, B be the bail amount set by the state and C be the collateral requirement set by the bond dealer. Assuming C = αB, i.e. a collateral proportional to the bond amount is required. Then competitive bail bond market requires zero profit, i.e. R− p (fB − αB) = R− pB (f − α) ⇐⇒ r ≡ R B = p (f − α) where r is the bond rate. Their empirical finding is that bail setting produces lower probabilities of flight among minorities, which is inconsistent with the statutory mandate that bail be set to limit flight probability to a constant maximum level for all bailees. Knowles, Persico and Todd (2001) Knowles, Persico and Todd (2001) applied the idea of outcome test to investigate if there is taste based discrimination against minorities in highway police searches. The novelty of this paper is that they propose a model in which motorists react to the polices’ potential racially biased search behavior and show that in equilibrium the probability that a marginal driver carries contraband are the same as that of an average driver. THE MODEL • r ∈ {A,W}: race of the motorist, observable by the police officer; 4 EMPIRICAL STUDIES OF DISCRIMINATION 31 • c : all characteristics other than race that are potentially used by the officer in the decision to search cars; researcher may or may not observe c; c is distributed in the population according to F (c|W ) and F (c|A) . • A motorist of characteristic (c, r) chooses to whether to carry a contraband or not. The payoff is v (c, r) if not searched by a police; and −j (c, r) if searched; • Police officers decide whether to search motorists to maximize the total number of convictions minus a search cost. Normalize the benefit of each arrest to one, and let the cost of searching a white drive be tW and that of searching a black driver be tA. • Hence the game between a driver of characteristic (c, r) and the police is a “matching penny” game: carry drug not carry drug search 1− tr,−j (c, r) −tr, 0 not search 0, v (c, r) 0, 0 • The equilibrium is in mixed strategies: a driver of characteristics (c, r) carries drug with probability P ∗ (G|c, r) = tr and the police searches the motorist with probability γ∗ (c, r) = v (c, r) v (c, r) + j (c, r) . • This gives them the following test for prejudice: for race r, conditional on being searched, the average probability of a driver being guilty is given by D (r) = Z P ∗ (G|c, r) γ ∗ (c, r) f (c|r)R γ∗ (s, r) f (s|r)dsdc = tr. Hence if there is no racial prejudice, i.e. if tA = tW = t, then D (W ) = D (A) = t. Nice feature of this test is that the researcher is not required to know the other characteristics c in applying this test. 4 EMPIRICAL STUDIES OF DISCRIMINATION 32 EMPIRICAL FINDINGS: They applied the above test to a data set collected by Maryland state troopers on Interstate 95. They use a Pearson’s χ2 test to see D (W ) = D (A) holds. They find that the hypothesis that D (W ) = D (A) is not rejected, indicating no taste-driven racial profiling. But when they test whether the probabilities of being guilty conditional on being searched are equal for all racial and ethnic groups, the null hypothesis is rejected, in fact they find prejudice against the Hispanics: the Hispanics have lower guilty rates than Blacks and Whites. COMMENTS: This is a nice attempt to have a model in which the marginal driver is the same as an average driver. The role played by the police is really deterrence: they search blacks more simply because blacks have a higher propensity to carry drugs if they are not searched more. The main problems are: • In practice, some of the characteristics that police officers use to decide whether to search or not is endogenous, for example, a driver is more likely to be nervous when being stopped if he/she carries contraband. [This suggests a model along the lines in the labor market discrimination literature.] • Are the police force monolithic? The national spotlight on racial profiling is largely due to the exposure of white policemen searching black drivers. Is it possible, since the authors did not control for the race of the police, that black officers and white officers have reverse prejudice and in the aggregate they cancel out? • What about fairness? Should the police officer also be concerned about the cost imposed on innocent drivers when they are searched? 4.3 Audit Method and Its Problems Main reference here is Heckman and Siegelman. The major criticism against regression analysis of the differential treatments of agents controlling for observable characteristics is the omitted variable bias. Audits were suppose to present evidence that two individuals, identical as much as possible, except for race and/or gender, are disparately treated. One of the advantage of audit method over regression analysis is that in audits, because the audit pairs are chosen by the investigators, more characteristics can be controlled for than what can be achieved in typical data sets; the second advantage of audit method is 4 EMPIRICAL STUDIES OF DISCRIMINATION 35 • Age: all testers were twenty-four to twenty-eight years old; • Education: All testers had three or four years of college education; • Dress: All testers were dressed similarly during the negotiations. Testers wore casual sportswear. • Transportation: All testers drove to the dealerships in similar used rental cars of the same model and year. Using similar modes of transportation prevented the dealers from making inferences based on the kind of car the tester drove or the way the tester reached the dealership; • Economic class: Testers volunteered that they could finance the car themselves; • Occupation: If asked by a salesperson, each tester said that he or she was a young urban professional (for example, a systems analyst for First Chicago Bank); • Address: If asked by the salesperson, each tester gave a fake name and an address in an upper-class, Chicago neighborhood; • Attractiveness: Applicants were subjectively ranked for average attractiveness. In the training session, each tester was given a script of how to negotiate, and then mock negotiation sessions were conducted to make sure of the testers’ spoken as well as non-verbal behavior uniformity. Ayres and Siegelman study revealed systematic disparate treatment. Dealerships offered white males significantly lower prices than blacks and women. The average prices offered white women were more than $200 higher than the offers to white men, the offers to black women were more than $400 higher than those to white men, and the offers to black men were more than $900 higher. And these differences are statistically significant. Their audits uncovered very little evidence of outright refusals to bargain and no evidence that dealerships were less likely to bargain with non-white male testers. [Note, however, Ayres and Siegelman do not establish that the disparate treatment is due to animus (or taste).] How should we understand Ayres and Siegelman findings? Does the disparate treatment found in the audit study of dealership offers provide much evidence of the economic injury 5 DISCUSSIONS 36 born by blacks who in equilibrium might in a variety of ways mitigate its impact? Heckman claims that: “[Audit evidence of disparate racial treatment] is entirely consistent with lit- tle or no market discrimination at the margin. Purposive sorting within markets eliminates the worse form of discrimination. There may be evil lurking in the hearts of firms that is never manifest in consummated market transactions.” Heckman’s claim relies on the existence of dealerships with varying degrees of racial treatment differences. But in Ayres and Siegelman’s audit, testers in the controlled exper- iment visit various dealerships in the Chicago area, some of which are located in poorer areas or in black neighborhoods, yet there is no evidence of any difference in the treatment minorities receive in such locations. But in actual bargaining, blacks and whites may use a different bargaining strategy that differs from the strategy that was imposed to the testers. It is then important to know whether blacks pay more in actual consummated transactions. Goldberg (1996) conducted such an analysis using Consumer Expenditure Survey (CES) of approximately 1300 new car purchases drawn randomly from the nation. [The CES data set is created by the Bureau of Labor Statistics to compute the Consumer Price Index.] For years 1983-1987, Goldberg created a data set of approximately 1300 reliable new car purchases. She constructed a measure of the discount from the dealer’s sticker price (from Automobile News Market Data Book) and regressed this variable on a host of consumer characteristics including race and gender. She found that variables referring to race and sex have no explanatory power: the hypothesis that whites and blacks, or men and women, receive the same discounts cannot be rejected at any reasonable significance level. Reconciling The Differences Between AS and Goldberg: Leave it to you. 5 Discussions Is the market discrimination in the labor market still the main obstacle for black’s improvement in their economic status? This is the question that we have to ask more than 20 years after the enactment affirmative actions policies. Answers to this question may lead to better policies to help the minorities. 5 DISCUSSIONS 37 Neal and Johnson (JPE 1996) use NLSY data to run the following simple regression: log wage regressed on a score from a test administered as teenagers (18 or younger) prepared to leave high school and embark on work careers or postsecondary education, and race, gender. What they found is that this one test score explains all of the black-white wage gap for young women and much of the gap for young men. From this, they conclude that for today’s young adults, the black-white wage gap primarily reflects a skill gap, which in turn they trace, at least in part, to observable differences in the family backgrounds and school environments of black and white children. Neal and Johnson’s approach differs significantly from earlier attempts to measure the labor market discrimination, which run wage regression controlling for education, experience etc. Neal and Johnson’s criticism of the earlier approach is that education, experience, career choices etc. in these earlier regressions are endogenous and themselves could be affected by market discrimination. Keane andWolpin (Careers Choices of Young Men 1996) also found in a structural model that most of the variation in the wages can only be explained by unobserved heterogeneities at age 14. Neither of the studies in any way imply that genetic differences are the reason for racial wage inequality. Instead, they seem to point out that the obstacles blacks face have changed from market discrimination to the obstacles in productivity skill acquisition for the children. Government policies to help the blacks can be more effective if they are directed to improving blacks’ primary, and secondary education, improving the social norms in black neighborhoods, etc.. What is your view on this issue?