The Q-Word As Red Herring: Why Disparate Impact Liability Does Not Induce Hiring Quotas

by Ian Ayres* and Peter Siegelman**

Forthcoming Texas Law Review (1996)

*William K. Townsend Professor of Law, Yale Law School.

**Research Fellow, American Bar Foundation and Olin Law and Economics Visiting Fellow, Yale Law School. Henry Hansmann made helpful comments, as did Keith Hylton on a much earlier version of some of the ideas. We also gratefully acknowledge many constructive discussions with members of the symposium on the future of employment law. Dawn Jeglum-Bartusch, Franklin Parlamis and Cathy Sharkey provided excellent research assistance.


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Introduction

The debates over the passage of Title VII of the 1964 Civil Rights Act were marked by passionate disagreement: conservatives objected to the legislation as an unwarranted interference with employers' freedom of contract, while liberal supporters considered it a first step toward racial justice. While disagreement about what employment discrimination law should do has continued--in much the same form--to this day, there has been surprising unanimity about the mechanism by which Title VII and other such laws actually work. Whether it is thought of as inadequate or excessive, Title VII is almost always presumed to promote the hiring of those it is designed to protect. The logic underlying this presumption is simple: by making employers liable for failures to hire based on race (or other forbidden grounds), the law raises the price of such discriminatory activity and produces less of it than would occur if employers were left completely free to hire whomever they wished.

As Donohue and Siegelman and others have recognized, however, there is a tension between protecting applicants against discrimination in hiring and protecting workers from discriminatory firing after they have been hired. Antidiscrimination law forbids both kinds of conduct, but the two prohibitions are inherently at odds. By making it harder to fire certain workers, employment discrimination law tends to make these workers less attractive prospects at the hiring stage. An employer would prefer to hire someone who can be easily fired (should that prove necessary) than an otherwise identical applicant whose firing would be subject to legal scrutiny. Thus, protection against discriminatory firing acts as a kind of tax on hiring those to whom it is extended.

While the tradeoff between "disparate treatment" hiring and firing protection has already been described, this article extends the analysis to the effects of "disparate impact" liability.McDonnel Douglas. Burdine, etc. Complications posed by mixed motives cases, Price-Waterhouse. 1991 Civil Rights Act partially overturns. Our major conclusion can be put succinctly: far from producing hiring quotas that induce employers to discriminate in favor of minorities, disparate impact liability may actually induce hiring discrimination against minorities (and other protected groups). Whether or not its net effect on minority employment is negative, disparate impact firing liability almost certainly blunts the positive incentives to hire minorities that Title VII was originally supposed to create.

Our thesis contradicts the common wisdom that disparate impact liability induces employers to hire "excessive" numbers of minorities. This quota theory of disparate impact liability has a long and distinguished pedigree. The Reagan administration sought to restrict disparate impact liability because of "its pressure toward quotas;" George Bush vetoed the 1990 Civil Rights Act because it was a "quota bill;" and a plurality of the Supreme Court in Watson v. Forth Worth Bank & Trust has enshrined the quota theory in its parsing of Title VII:

Respondent and the United States are thus correct when they argue that extending disparate impact analysis to subjective employment practices has the potential to create a Hobson's choice for employers and thus to lead in practice to perverse results. If quotas and preferential treatment become the only cost-effective means of avoiding expensive litigation and potentially catastrophic liability, such measures will be widely adopted.

Our thesis is that commentators have erred by only considering the effects of disparate impact hiring liability. There are strong theoretical and empirical reasons to believe that disparate impact firing liability is likely to have a much greater impact on employer behavior, and that this effect, far from inducing hiring quotas in favor of minorities, may induce hiring discrimination against these traditionally disadvantaged groups. As noted earlier, we argue that disparate impact liability should be modeled as a quota, but one that governs the racial composition of fired workers, not the composition of those hired.

Our argument is developed in three sections. In the first, we examine the evolution of disparate impact law, and the kinds of incentives it provides employers. Since 1990 only about one out of four disparate impact decisions involves hiring, and it is now considerably easier to establish a prima facie firing case than a hiring case. The reason is that the former requires only a simple comparison of the percentage of minorities fired with the percentage of minorities who are employed by the defendant. In contrast, plaintiffs seeking to establish disparate impact in hiring have a more difficult time establishing the relevant baseline, since the Supreme Court has rejected the use of general population statistics and requires proof of the qualified applicant pool. Accordingly, plaintiffs in disparate impact firing litigation can more easily prove a prima facie case and survive a defendant's summary judgement motion.

The second section explores how employers might behave if the stylized facts of the first section are indeed true. That is, assuming disparate impact in firing is scrutinized more closely than disparate impact in hiring, how are employers likely to respond? Specifically, this section solves a simple model of probationary hiring, in which an employer screens heterogenous prospective employees, hires some for a probationary period, and retains only those whose actual productivities are above the (fixed) wage. (Those who turn out to have low productivities are fired.) If one makes the plausible assumption that black workers are more variable in their productivity on the job than are whites, the model predicts that blacks will have higher firing rates in the absence of any law forbidding disparate impact in firing.

When disparate impact liability constrains the employer to fire the same proportion of whites and blacks, however, she will respond by hiring fewer blacks and more whites than she otherwise would have. By making it harder to fire protected workers, disparate impact liability discourages probationary employment generally, and might even lead employers to deliberately discriminate against protected workers at the hiring stage. In this model, disparate impact liability does produce a quota effect, but unlike the traditional theories, disparate impact liability induces a firing quota with an inverse quota at the hiring stage.

Our basic insight can also be put in other terms: probationary employment offers employers the equivalent of a financial option on the workers they hire. An employer's downside risk is limited, because an applicant who is hired and then turns out to produce less than the wage can be discharged quickly, limiting losses to the probationary period. A worker who is revealed to have high productivity can be retained for an additional period, at the same fixed wage. This means that employer profits are an increasing function of the variability of worker marginal product, because variability increases upside potential without proportionately increasing downside risk. Employers therefore have a preference for risk: Given two workers of equal expected productivity, a profit-maximizing employer will prefer the one whose productivity is more variable. This suggests that probationary hiring is especially likely to work to the advantage of black applicants, about whom employers may have more uncertainty.

The final section of the paper explores some normative implications of our analysis. We suggest a range of policies that illuminate the tradeoff between hiring and firing liability. None of our policy alternatives furthers all the goals underlying disparate impact liability. Nevertheless, we highlight some important factors that argue in favor of one or another of the policies we describe.

I. The Evolution of Disparate Impact Litigation

A. The Increasing Difficulty of Establishing A Disparate Impact in Hiring

Early disparate impact cases had two important characteristics. They were predominantly challenges to hiring practices, and they focussed on relatively objective practices such as "aptitude" tests, height or weight requirements, drug testing, criminal record checks, high school graduation requirements.

Over time, however, plaintiffs had increasing difficulty establishing prima facie evidence of disparate impact in hiring for two reasons. First, employers had an incentive to respond to the early hiring cases by abandonning testing and other objective practices in favor of subjective hiring standards that are less likely to give rise to disparate impact liaibility. Second, courts have toughened the requirement for establishing the relevant baseline against which disparities are to be assessed. Plaintiffs could no longer use the proportion of minorties or women in the general population as a benchmark. Instead of pointing to a simple population statistic, the Supreme Court in Hazelwood and subsequent opinions required plaintiffs to calculate the racial composition of "the qualified . . . population in the relevant labor market" or the "otherwise-qualified applicants."

In several respects, there are striking parallels between the evolution of disparate treatment and disparate impact law and the responses to each. As Donohue and Siegelman have shown, early disparate treatment cases were virtually all allegations of hiring discrimination. Relatively quickly, however, employers stopped engaging in obviously discriminatory hiring practices; either they continued to discriminate but covered their tracks, or actually cleaned up their act. In the absence of an obvious motive and/or a relevant comparison group, potential plaintiffs had a difficult time recognizing that disparate treatment in hiring had occurred, let alone convincing a court of that fact. Disparate treatment firing cases, however, typically do offer plaintiffs a relevant and accessible comparison group--other workers at the same firm who were not fired.

Much the same story can be told about disparate impact. In the early post-Griggs era, plaintiffs had a relatively easy time mounting disparate impact challenges to objective hiring practices such as tests and high school graduation requirements. Over time, employers responded to the threat of liability with defensive measures that made it harder for plaintiffs to devise a disparate impact hiring suit that could survive a motion for summary judgment. For example, it is relatively easy to substitute a subjective interview for an aptitude test at the hiring stage. Employers also have considerable latitude in defining the "qualified applicant pool" in such a way that the alleged hiring disparity disappears.

But given the current state of the law, it appears to be much harder for employers to avoid disparate impact in discharging workers. The racial composition of hired workers forms a clear baseline against which disparities in firing rates can easily be compared. An employer whose workforce is 5 percent black but whose fired workers are 10 percent black is thus likely to be an easy target for a disparate impact suit. This disparity constitutes powerful prima facie evidence that will almost certainly survive a summary judgment motion by the defendant. By contrast, an employer whose flow of newly hired workers is 10 percent black in an area where the population is 15 percent black can always argue that the "relevant" population (those who are qualified for and interested in the job under scrutiny) has a different racial composition from the overall population.

In sum, just as with the history of disparate treatment, it has become increasingly difficult for plaintiffs to prove a prima facie case of disparate impact in hiring. To the extent that employers today face a threat of disparate impact liability, it will not be for failing to hire a quota of minorities, but rather for firing a disproportionate number of those they have already hired.

B. The Changing Nature of Disparate Impact Litigation: An Empirical Assessment

This section attempts to quantify the number of disparate impact hiring and firing cases brought in Federal courts between 1971 and 1995. If our analysis of the changing doctrine and circumstances are correct, we would expect to see a Donohue/Siegelman-like shift in the composition of suits over time: hiring suits should fall and firing suits should increase.

Figure 1 plots the share of hiring and firing cases among all disparate impact cases, by year. These shares bounce around over time, so the figure shows the data in smoothed form by plotting 3-year moving averages. The figure shows that the relative importance of hiring cases among all disparate impact cases has fallen substantially since the early 1970s; by contrast, the proportion of firing cases has increased over this period. Although the total number of cases in any given year is relatively small, the overall trends are as predicted. The bottom line is that disparate impact firing cases have outnumbered hiring cases in every year since 1986, and since 1990, there have been almost three firing cases for every hiring case filed.

To further substantiate our claim that firings produce the most important form of disparate impact liability, we also calculated the proportion of cases that plaintiffs won. Overall we found that plaintiffs succeeded in 30.9% of the disparate impact firing cases -- which seems high enough to suggest that employers cannot simply ignore the increasingly important source of liability.

While these results are highly suggestive that hiring liability is less of a threat to employers than firing liability, they should be treated with caution for four reasons. First, the data come from a selected sample, since only those cases that generate a published opinion are eligible for inclusion in Westlaw. And the decision to write an opinion is not random. Non-random selection is only a problem when the selection criterion (whether or not to publish) is correlated with the variable(s) of interest (hiring vs firing case) as they evolve over time, however. There is no reason to think that hiring cases are differentially likely to generate published opinions over time in a way that could bias our results. Nevertheless, we also attempted to investigate the prevalence of hiring and firing disparate impact cases among unpublished cases, using a dataset of some 1200 unpublished employment discrimination cases collected by the American Bar Foundation. Unfortunately, the 1200-case sample contained only 6 identifiable disparate impact cases, so the data are essentially useless for these purposes.

A second caveat might be termed the "denominator problem." What employers care about is the probability of suit conditional on the practice being challenged. If firings are very common and hirings very rare, the mere fact that there are more hiring than firing suits is not very meaningful. Lacking data on the number of potential suit-generating incidents, it is hard to say anything concrete about how disparate impact liability actually affects employers. It is inconceivable that the total volume of new hiring has fallen substantially over the past 25 years, however, which implies that the number of disparate impact hiring suits per person hired has indeed fallen.

Third, the observed low proportion of hiring suits may be an endogenous artifact of the very quota effect that we argue is not present. Firms may have been so concerned about disparate impact hiring liability that they hired quotas of minorities to avoid hiring liability. While theoretically plausible, this explanation does not account for the high proportion of firing suits. Moreover, the low participation rate of minorities in so many job classifications is inconsistent with any widespread quota effect.

Finally, there are problems of weighting. Most disparate treatment suits are brought by individuals, and from an employer's point of view are roughly similar in their effect on overall profits: we can be fairly sure that the effect on employers is roughly proportional to the number of suits filed. Disparate impact suits are much more heterogeneous, however. Most concern groups of individuals, of varying sizes; and they challenge a wide variety of practices, some of which are expensive or difficult for an employer to change while others are not. The raw number of suits filed is therefore not as good an indicator of the importance of disparate impact to employers as it would be for disparate impact suits. Moreover, it may be that the average disparate impact firing suit involves 20 employees and requires only a trivial adjustment to employer layoff policy to correct, while the typical hiring suit involves thousands of applicants and requires a major overall of personnel practices. While this is always a possibility, our results are at least strongly suggestive of a significant disparity in the effect of firing and hiring liability.

D. Conclusion

As with disparate treatment, early disparate impact suits were largely easy to win hiring cases. Once the disparate impact principle was articulated, however, an almost mechanical application was sufficient to strike down a whole host of hiring practices. These certain losses gave employers an incentive to change their hiring practices in a variety of ways to avoid such liability. Avoiding liability for disparate impact in firing, however, is more difficult because of the baseline and subjectivity problems we discussed earlier.

The empirical evidence, limited though it is, does support our thesis. Disparate impact hiring cases have become less common over time relative to others, while disparate impact firing cases have become more frequent, in a strong parallel with the evolution of disparate treatment cases. As a result, disparate impact firing suits are now more numerous than firing suits by a substantial margin.

Our bottom line conclusion is that rational employers have more to fear from racial disparities in firing than in hiring. Although an irrational fear of hiring liability could still force employers to react by hiring quotas of minorities, we attribute rational expectations to employers (at least in the long run). Accordingly, the next section models disparate impact liability as a constraint on employers' ability to fire workers.

II. The Effects of Disparate Impact Firing Liability

in A Simple Probationary Employment Model

A. An Overview of the Model

The actors in our model are a risk-neutral employer, and groups of workers of two races (black and white), with heterogeneous productivities. An extensive form representation of the timing of events in the model is depicted in Figure 2. In period zero--before the game starts--"Nature" determines each worker's productivity. In the first period, the employer forms an estimate of each applicant's productivity, compares it to the wage--which is fixed for all workers--and decides which applicants to hire. In the second period, the employer learns the true value of the worker's productivity, and either fires the worker or retains her for an additional period at the constant wage. By assumption, there are no costs to monitoring worker productivity, and no discounting. Workers are assumed to have no alternative occupation (except unemployment at a wage of zero), which means that employers' offers will always be accepted. The model thus depicts a stylized form of probationary employment, in which the worker is retained or fired depending on her productivity during an initial screening period. While we have choosen this model to highlight the influence of disparate impact liability on probationary employment, our general conclusion -- that disparate impact firing liability could induce discrimination against minorities in hiring -- would emerge from any labor demand model.

In our model, a worker's productivity on the job is the sum of two components, MP and . MP is observable to both the applicant and employer before hiring; is, however, not known by either player unless the worker is actually hired. However, the employer can observe the absolute value of before a hiring decision is made. In other words, the hiring decision is made on the basis of MP + | |, while the firing/retention decision is made on the basis of MP + , where the realized value of is equally likely to be +| |. This highly stylized characterization of uncertainty means that only the sign of is unknown before the worker is hired. Since PR( = +| |) = PR( = -| |) = , it follows that E( ) = 0 and that E(MP+ ) = MP. In this stylized example, we also assume equal numbers of black and white applicants.

We assume separate and independent distributions, for both MP and , for blacks and whites. For ease of exposition and calculation, all parameters are taken to follow uniform distributions. Specifically: MPw U[0,100]; MPb U[0,75]. | w| U[0,5], and | b| U[0,20/3], where the w and b subscripts refer to whites and blacks, respectively. Blacks therefore come from a population with lower mean productivity and greater uncertainty than whites. Our assumption that black applicants have a lower mean productivity is controversial, but not strictly necessary since a greater variance in is, by itself, sufficient to generate higher black firing rates. This greater black variance might in turn plausibly be explained by two factors: first, affirmative action in education means that any given level of achievement is a less precise signal for blacks than it is for whites. Second, since most employers are likely to be white, they may be unfamiliar with the relationship between "qualifications" and performance for minority job applicants.

B. Solving the Employer's Problem: The Unconstrained Case

A solution to the employer's problem takes the form of two optimal decision rules specifying which workers to hire, and of those hired, which to fire. To derive such a solution, we use the standard technique of solving backwards. In the last period, the employer must decide which workers to retain and which to fire in order to maximize his profits. Since the firing/retention decision takes place after the first period, there is no longer any uncertainty about | |. We can therefore express the employer's profit from any given worker i as

i = (MPi + i) - w.

Clearly, the employer should keep all workers for whom > 0 (or MP + > w), and fire the rest. Knowing this optimal second-period firing policy, which applicants should the employer decide to hire in period 1? Consider an applicant with an observable MP and | |; the employer knows that if hired, this applicant is equally likely to have a productivity of MP + | | or MP - | |. It is obvious that anyone for whom MP + | | < w should never be hired, since even in the best case, such an applicant will produce less than she costs the employer. Similarly, any applicant for whom MP - | | > w should obviously be hired--even in the worst case, this applicant will earn the employer a positive profit, and can be retained for two periods. For those applicants with intermediate values of (MP + | |), the employer's decision is somewhat more complicated. If, after hiring, the worker turns out to have a positive realization of , then the employer will earn positive profits, and will want to keep the worker for an additional period. If the worker turns out to have a negative realization of , however, the employer will earn negative profits, but only for one period, since the worker can be terminated at the end of the probationary period. It is this ability to fire after the first period if the worker turns out to have an unfavorable realization of (and to retain the worker for an additional period if turns out to be positive) that drives the probationary hiring decision.

The optimal first period hiring rule can thus be derived by simply noting that the employer should hire all applicants with a positive expected profit, given optimal firing behavior in the second-period. Since the employer has the option of firing employees who turn out to have low productivities ( < 0), this means the employer should hire anyone if the expected profit from two good periods (if > 0) is greater than the expected loss from one bad period (if < 0). In algebraic terms, this translates into hiring anyone for whom MPi > w - | i|/3. For example, this rule implies that with a fixed wage of 50, the employer should be willing to hire an applicant with MP = 48 and | | = 7. Even though this applicant has a one-period expected output (48) that is less than the wage, the employer would expect to earn a dollar profit from such an employee, because the employer has an equal chance of a single-period loss of (48-7-50 =) -9 and a two-period gain of [2(48+7-50) =] 10.

Figure 3 depicts our analysis graphically. As derived above, the hiring line has a slope of -1/3. It represents those combinations of and MP for which the employer can expect to earn zero profits under optimal behavior. Applicants with (MP,| |) combinations below the line are not hired, while those above the line are.

The probationary line divides those initially hired into two groups: Employees above the line will have such high MP's that they will be retained (rehired in the second period) even if their turns out to be negative--we refer to these as the "Set" workers; those below this line are the true probationary hires, because they will be fired after the first period if the employer learns that their is negative.

Table 1 presents a numerical illustration of the model for the hypothetical parameter values listed earlier. The Table describes equilibria both with and without the disparate impact firing constraint. For the moment, we focus on the unconstrained equilibrium in column 1.

Table 1: The Effect of Disparate Impact Firing Liability on Employer Hiring and Firing Decisions

Unconstrained Employer Behavior

Employer Behavior Constrained

By Disparate Impact Firing Liability

% of White Applicants who are Hired

50.83%

51.29%

% of White Applicants who are Hired-Set

47.50%

46.50%

% of White Applicants who are Hired-Probation

3.33%

4.39%

% of White Applicants who are Hired-Doomed

0.00%

0.39%

% of Black Applicants who are Hired

34.81%

34.23%

% of Black Applicants who are Hired-Set

28.89%

30.77%

% of Black Applicants who are Hired-Probation

5.93%

3.46%

% of Black Applicants who are Hired-Doomed

0.00%

0.00%

% of Hired who are Black

40.65%

40.03%

% of Fired who are Black

64.00%

40.03%

% of Hired Whites who are fired

3.28%

5.05%

% of Hired Blacks who are fired

8.51%

5.05%

Expected Periods of Employment for Whites*

1.0000

0.9998

Expected Periods of Employment for Blacks*

0.6667

0.6673

Expected Wage Bill For Whites*

50

49.9875

Expected Wage Bill For Blacks*

33.3375

33.365

Expected Employer Profits

33.427

33.4127

Hired-Set = Hires with a 100% probability of being retained

Hired-Probation = Hires with a 50% probability of being retained

Hired-Doomed = Hires with a 0% probability of being retained

* Includes applicants who are not hired.

Given our assumption that whites' productivity has a lower variance and a higher mean, white applicants are more likely to be hired initially: although the labor force is 50 percent black, the hired workforce is only 40.6 percent black. Among those fired, however, blacks constitute a disproportionately large share, amounting to 64 percent. The reason for this disparity lies in the greater uncertainty surrounding black productivities. Since the typical black worker has a higher value of | |, she is more likely to be hired "on probation", and hence more likely to be fired.

C. Solving the Model: The Constrained Case

Until now, we have modeled behavior as if it were not subject to any employment discrimination law. For reasons discussed earlier, we propose that disparate impact liability can best be thought of as a constraint on employer firing behavior that nevertheless leaves the employer considerable leeway in making hiring decisions. To highlight the effects of disparate impact firing liability, we model disparate impact law as a restriction whose only effect is to forbid employers from disproportionately firing their minority workers. That is, if an employer's workforce is X% black, then her fired workers must also be no more than X% black. Put in this simplest possible terms, we are assuming that disparate impact liability requires employers to adopt minority firing quotas. The unconstrained equilibrium in our numeric example violates this mandate, because blacks made up 40.6% of the initial workforce, but 64% of those fired. Our goal in this section is to explore how rational employers would respond to the imposition of such a firing quota.

To abstract away from problems of enforcement, we assume the law to be absolutely binding and examine how an employer would go about complying with the legal constraint. The mathematics of this problem turn out to be complicated, without being particularly interesting. We therefore relegate the details to the Appendix and provide only a simple exposition here. Figures 4 and 5 graph the optimal (profit-maximizing) hiring and firing rules for blacks and whites, subject to the constraint that the employer must fire the same percentage of blacks and whites.

These figures show that an employer constrained by disparate impact firing liability will change her hiring and firing rules for both types of workers. To comply with the equal firing rates mandate, the employer expands her probationary hiring of whites while decreasing her probationary hiring of blacks.

Figure 4 shows that probationary firing for blacks decreases in two ways: first, the employer shifts up her hiring line, which means that she will hire fewer blacks in the first place. Probationary hiring is generally valuable to employers because they have the option of firing employees who turn out to have low productivity. But the civil rights constraint reduces the employer's ability to exercise this option, so that some black employees who would have been hireable in a world without disparate impact firing liability are no longer worth hiring. But the civil rights constraint has a second effect as well. Employers will also respond to the law by shifting down their probationary line. This increases the set of black workers who will be retained even if their turns out to be negative. To comply with the law, employers are even willing to retain some employees whose known productivity is less than the wage, because retaining these employees will allow the firm to fire even less productive blacks and to retain even more productive whites.

Figure 5 shows how firms change their hiring and firing decisions to increase the probationary hiring of whites. Initially, the firm lowers its hiring line to increase the number of white workers who are hired on probation. But the firm also changes its firing rules to comply with the civil rights constraint. The firm raises the probationary line, which increases the number of white employees who will be fired if their turns out to be negative. Figure 5 also shows that the constraint creates a new class of workers: the firm will hire some white workers merely so that they can be fired to help satisfy the civil rights constraint, even if these workers turn out have positive s. Figure 5 and Table 1 refer to these workers as the "Doomed" because they have 0 probability of being retained. Hiring whites who are then fired with certainty helps satisfy the disparate impact constraint by raising the white firing rate, and thus gives the firm more discretion to fire (more) unproductive black workers. All of these changes mean that the firm will be willing to fire white workers who turn out to have a known productivity higher than the wage, because firing these white workers will allow the firm to fire even more unproductive black workers and to retain even more productive white workers.

Table 1 provides a numeric comparison of the constrained and unconstrained results for blacks and whites. The civil right constraint forces the probability of being fired for blacks to equal the probability of being fired for whites (both are 5.05%), which implies that blacks make up the same proportion of hires as they do of fires (both are 40.03%). As expected, the civil rights constraint lowers the firm's expected profits (from 33.427 to 33.4127).

But what are the effects on black and white workers? The central result of the model is that disparate impact firing liability can induce disparate treatment against blacks in hiring. Firms responded to the constraint by hiring fewer blacks and by hiring more whites. The disparate shifts in the hiring lines in Figures 4 and 5 mean that similarly situated applicants will be treated differently because of their race. Specifically, blacks will be worse off at the hiring stage. But the model also suggests that disparate impact firing liability induces disparate treatment in favor of blacks in retention.

The changes in the firm's hiring and firing decisions mean that some blacks will benefit from the constrain while others will suffer. As shown in Table 1, the civil rights constraint reduces the proportion of black applicants who will be hired (from 34.81 to 34.23%), but those who are hired have a higher probability of being retained for two periods. In general, it is impossible to know which effect dominates: in our example, the firing constraint increases the expected number of periods that an average black applicant will be employed, but for other parameter values the disemployment effect could outweigh the retention effect.

The constraint also has varying effects on white welfare. Somewhat surprisingly, disparate impact firing liability helps some white applicants by causing them to be hired when they would not be in the unconstrained equilibrium. It disadvantages other whites by increasing the probability that they will be fired. These effects are seen in Table 1: the constraint increases the percentage of white applicants who are hired (from 50.8% to 51.3%), but reduces their expected length of employment.

D. Some Cautions and Additional Evidence

1. Empirical Evidence on Firing Rates

The model analyzed above predicts a relatively small effect of firing liability on the hiring decision. For example, imposition of the equal firing rates constraint lowers the proportion of blacks hired by only about 1.7 percent (from 34.8 to 34.23 percent). Moreover, in their "back-of-the-envelope" calculations, Donohue and Siegelman suggested that the hiring effect of disparate treatment firing liability should be quite small. Thus, it is reasonable to ask whether disparate impact firing liability is actually a serious problem for employers. It is impossible to answer this question directly, but we suggest that the answer is "Yes," for four reasons.

First, the magnitude of all of the effects in our model depends crucially on the highly unrealistic simplifying assumptions we made. We could have generated larger effects with different distributional and parametric assumptions.

Second, it is clear that if workers are only rarely fired, employers will not need to worry about firing liability at the time they make hiring decisions. But the best evidence suggests that a typical employer can expect to terminate roughly 8 percent of her workforce each year in a manner that might give rise to disparate impact liability.

Third, the evidence from Europe--where there has been more substantial experience with job security laws--suggests that firing costs do influence hiring behavior. Daniel Hamermesh summarizes the body of work on this subject as follows:

[Nearly all of] the evidence shows that employment responds more rapidly to output or cost shocks in North America than elsewhere [Europe or Japan]. There are many easy explanations of why employment demand reacts more rapidly in North America than elsewhere. The lack of restrictive laws and penalties against rapid dismissals is a common explanation.

Finally, probationary employment regimes such as the one we describe--in which applicants are hired, evaluated for a relatively brief period, and discharged if their productivities turn out to be lower than the wage--appear to be quite common. Evidence on the prevalence of probationary employment comes from 2 studies. Harry Holzer uses data from the large EOPP survey. He finds that 64 percent of the firms surveyed used probationary employment. Groshen and Loh used the EOPP and 2 other datasets. They find that 72% of firms in the EOPP sample had a "formal" probationary period. Surveys by The Conference Board and the Federal Reserve Bank of Cleveland find 76 percent and 60 percent of firms using probationary hiring.

The possibility of future firing thus seems large enough to cast a shadow on the hiring decision, although the exact size of this effect is an empirical question. We are confident that disparate impact liability is more likely to constrain employers' firing decisions than their hiring decisions -- hence are conclusion that firing quotas are much more likely than hiring quotas. But there remains a possibility that neither type of legal liability is salient enough to change employer behavior. While our analysis of the law and of the available evidence suggests that disparate impact firing liability is more salient than hiring liability, the threat of firing liability may not be sufficient to induce the perverse hiring behavior outlined in our model.

III. Policy recommendations

A. Firing Liability Does Not Further the Traditional Justifications For Disparate Impact

The first part of this article suggested that, in practice, disparate impact liability tends to be invoked by plaintiffs largely to challenge employers' firing decisions. The second part demonstrated the plausible consequences of this pattern of enforcement: employers responding to a disparate impact firing constraint will fire fewer blacks (and more whites), but will also hire fewer blacks (and more whites) as well. This section now takes up the difficult question of what, if anything, we ought to do about the situation we have just described.

We begin by inquiring about the theoretical justifications for disparate impact liability. What is disparate impact law supposed to do; and if it works as we have just described it, how compatible is disparate impact with these objectives? The second half of this section then takes up the question of how we might refocus the law of disparate impact so as to better achieve these goals.

For our purposes, it is convenient to think of two broad classes of justifications for disparate impact liability. The first sees it as a way of improving the economic opportunities of traditionally disadvantaged groups. The second justification is as a deterrent to disparate treatment, to be used as a supplement to the traditional attack on intentional discrimination when the latter is too difficult to prove.

1. Enhancing Minority Economic Outcomes

According to this view, disparate impact liability can be justified either because the purpose of Title VII is to "ensure proportionate distribution of economic resources among...groups" or to remedy past discrimination. For our purposes, the distinction between disparate impact as a forward-looking means of achieving a fairer division of the employment benefits controlled by employers or as a backward-looking remedy for past discrimination against a group is not particularly important. Under either principle, the goal for disparate impact liability is to enhance minority employment outcomes.

Does disparate impact, as we have described it, contribute to a more equal division of resources between blacks and whites? The answer is a qualified "No." Table 1 compares the equilibria with and without the disparate impact firing constraint. In particular, Rows 9 and 10 show the expected wage bill, by race, with and without disparate impact. The table reveals that disparate impact liability can lower the toal earnings of whites (including both those who are unemployed and those who hold a job), but can increase the total earnings of blacks. The reason is that although more whites are hired, more are also fired, so that the expected length of employment falls (row 7) when firms are subject to the disparate impact firing constraint. The reverse is true for blacks: fewer are hired when disparate impact firing liability constrains employers, but the expected length of employment increases by more than the hiring rate falls, leading to an increase in earnings for blacks as a group.

Our analysis therefore suggests that disparate impact firing liability does reduce average inequality between black and white workers. But it does so at the cost of increasing inequality within the black community. As a result of disparate impact firing liability, fewer blacks are hired, but those who do find a job can expect to be employed for longer, and thus to have higher earnings. While average black earnings are higher under the disparate impact regime, the variance of earnings is also larger. If they are risk-neutral and have to vote before they know anything about what their productivity will turn out to be, blacks should prefer the disparate impact regime. But if they are sufficiently risk averse, blacks will prefer the unconstrained equilibrium. Put another way, if we care about differences in average utility rather than average earnings, disparate impact firing liability may exacerbate black-white differences, rather than lessening them.

If disparate impact liability turns out in practice to be firing liability, and if blacks are sufficiently risk-neutral, then disparate impact may be consistent with the "group rights" justification we described earlier. But in reducing differences between the average black and white workers, disparate impact simultaneously increases differences within the black community and may lower average utility. As a method for equalizing outcomes between blacks and whites, therefore, disparate impact (firing liability) seems critically flawed.

2. Deterring Disparate Treatment

Even though motive is formally irrelevant in establishing liability under a disparate impact standard, one possible justification for disparate impact is as a means to create liability in cases in which we believe an employer intended to discriminate but her intent is impossible to prove. That is, when intentional discrimination is hard to prove directly, disparate impact provides an alternative route to the same result, with a lower evidentiary burden on plaintiffs. Disparate impact would then serve to deter at least some instances of explicit or intentional discrimination that could not be attacked via a "normal" disparate treatment claim.

Until now, we have taken disparate impact at face value by assuming that it occurred even though the employer had no intent to discriminate. There are obviously some discriminatory employers in the world, however, and it is useful to re-examine our model to see how the introduction of discriminatory motives might change our conclusions about how employers behave. In doing so, we find it useful to distinguish between several different kinds of discriminatory behavior.

a. "Non-Standard" Theories

It might at first seem that firing discrimination is incompatible with rational behavior by employers. After all, why would an employer discriminate against someone at the firing stage, when she could more easily have done so by not hiring them in the first place?

There are theories of disparate treatment that predict that employers will discriminate in firing, even in the absence of hiring discrimination, however. For example, suppose that discriminatory employers get pleasure from inflicting harm on black workers--such preferences have been termed "Consequential Animus," since employers care about the consequences of their behavior on those it is designed to harm. Consistent with the large literature on the importance of endowment effects, it seems plausible that workers might suffer more from losing a job they already have than they would from not getting the job in the first place. This implies that racist employers might find they could hurt blacks more effectively by hiring and then firing them than by not hiring them at all.

Richard McAdams' status-based model of discrimination might also predict firing discrimination even in the absence of hiring discrimination. If firing blacks is a way for a white employer to increase his own status, and if he can do so more effectively by firing than by not hiring, we are in a similar situation to consequential animus. Finally, an employer could practice what might be called "role-based" discrimination. Such an employer would be willing to hire black workers as long as they conformed to certain stereotypes or roles such as acting with "appropriate servility" or speaking with a white accent. Black workers who failed to play their "assigned" roles on the job would then be subject to discriminatory firing, even though the employer was willing to hire them in the first place.

In addition to these "non-standard" theories of discrimination, both of the traditional economic theories (associational animus and statistical discrimination) also predict that disparate treatment in firing is possible, although under these theories it only occurs in conjunction with hiring discrimination.

b. Associational Animus

Animus-based discrimination was first analyzed by Gary Becker, who modeled it as a psychological distaste on the part of white employers for associating with black workers. Formally, this means that instead of a market wage of w, discriminatory employers see a wage of w+ when they hire a black worker, with representing the psychological cost per period of associating with blacks. Although there are problems with this formulation, it is worth thinking about its implications for firing discrimination.

In our probationary employment model, employers with a distaste for associating with blacks behave identically to those who are race-neutral, with one exception. An employer's associational animus shifts up the black firing and hiring lines, so that their new intercept is w+ instead of w. (This is a straightforward implication of the fact that the true wage faced by a discriminatory employer when hiring a black applicant is w+ , not w.) This upward shift of both the hiring and probationary lines lowers the number of blacks hired, leaves probationary employment unchanged, and lowers the number of "set" (guaranteed two-period) hires. A greater proportion of probationary hires obviously increases the firing rate for blacks, which in turn increases the disparity between black and white firing rates.

c. Statistical Discrimination

Employers might consider the race of applicants in making hiring decisions not because they care about race per se, but because race contains information about (is correlated with) some other characteristic that is not directly observable. In our model, race is correlated with average productivity (MP) and average | |, but since both are directly observable, race does not convey any additional information to employers. Suppose, however, that we alter the model slightly and now think of MP as a test score that is observable to employers before hiring. Suppose further that for any observed value of MP, blacks' "true" productivity on the job will always be 10 points lower than whites with the identical score, but productivity itself is not directly observable until the end of the second period. In this case, race would tell the employer something useful about future productivity, so employers would have an incentive to make race-conscious hiring decisions. And they would also make race-conscious firing decisions: since race and the MP score perfectly predicts true productivity, employers absent civil liability would fire some blacks in period 1 who would have been retained had they been white.

d. Can Disparate Impact Firing Liability Deter Disparate Treatment?

If disparate treatment in firing is at least theoretically possible, we must then ask whether disparate impact firing liability is an appropriate or effective legal remedy for this problem. Briefly, the answer is, "No." By forcing employers to fire fewer blacks and more whites than they would if they were given free rein, disparate impact firing liability does push employers towards non-discriminatory conduct at the firing stage: firing liability exacerbates the distorted hiring practices of discriminatory employers. At least under many of the theories surveyed above, these employers will already hire fewer black applicants because of their tastes for discrimination; in any case they will be prompted to hire even fewer because of the effects of disparate impact firing liability at the hiring stage. In short, disparate impact firing liability can protect workers who have already have a job from discriminatory firing, but only at the cost of further reducing the ability of such workers to get hired in the first place. Moreover, if we believe that only some employers engage in intentional firing discrimination, disparate impact liability will be over broad. It will influence the hiring behavior of all employers, including those who do not practice disparate treatment in firing.

B. Ameliorating the Perverse Effects of Current Disparate Impact Enforcement

The core perversity of the current enforcement regime is that forcing firms to discriminate in favor of minorities in deciding whether to rehire may induce firms to discriminate against minorities in deciding whether to hire originally. To ameliorate this legally induced disparate treatment in hiring, legal reforms might broadly attempt to:

decrease the cost of firing minorities (relative to firing whites); or

increase the cost of failing to hire minorities (relative to failing to hire whites).

A wide variety of legal instruments could be fashioned to further these goals, some by extending potential civil rights liability for hiring decisions and others by reducing potential civil rights liability for firing decisions. Changing firms' regulatory environment beyond Title VII might also mitigate the asymmetric enforcement effect. We will begin by simply cataloging a number of possible reforms that might mitigate the perverse effects of lopsided disparate impact enforcement. We then assess which reforms best advance the traditional justifications for our civil rights laws. Rather than thinking simply about antidiscrimination rules that would apply to all employment decisions, we would do better to distinguish between hiring and firing decisions in fashioning liability rules.

1. Decreasing the Cost of Firing Minorities

The most direct way to reduce the perverse effects of disparate impact protection for minority firing would be to reduce firms' potential legal liability. Such a reduction could be accomplished by making it more difficult for plaintiffs to establish the relevant pool of qualified firees, or by making it easier for defendants to establish their business necessity defense to charges of discriminatory firing. A more modest, but strongly justified, reform would reduce potential liability by overturning a troubling aspect of Connecticut v. Teal. Suppose a firm's qualified applicant pool is 20 percent black, its labor force is 25 percent black, but its fired workers during some period are 32 percent black. Perversely, the firm woulf probably be liable under Teal's "no bottom-line defense" holding -- even if black share of the firm's labor force after the firing was still above the 20% (the minority share of the qualified applicant pool). A firm's very success in hiring minorities inequitiably increases its exposure to disparate impact firing claims. In place of the Teal standard, we propose allowing defendants a "stock" defense: a firm should be able to fire minority workers without fear of disparate impact liability as long as the minority proportion of its workforce stock remains above the minority share of the qualified applicant pool.

A firm's expected legal liability might also be lowered by reducing the potential for disparate treatment firing suits. While disparate treatment is not the focus of this article, Table 2 shows that in the American Bar Foundation sample of recent Title VII suits, a substantial proportion of disparate treatment firing suits (more than one-third) are brought by employees who were working for the defendant for less than two years (and more than one-quarter are brought by those who have been employed less than a year). It is difficult to calculate the analogous percentage for disparate impact suits--both because disparate impact suits are more likely to be class actions with multiple plaintiffs and because there have been relatively few disparate impact filings. But the substantial proportion of firing suits brought by plaintiffs who might plausibly still be completing a probationary period might particularly deter firms from taking chances on minority hiring.

Table 2: The Proportion of Disparate Treatment Firing Suits Brought By Arguably Probationary Employees (Observed in a Random Sample of 396 Cases)

Number of Months Plaintiff Was Employed Before Firing

Cumulative Percent

< 3

7.3

< 6

13.4

< 9

17.7

< 12

26.0

< 18

31.3

< 24

37.1

The large number of suits brought by recently hired employees gives us grounds to worry that the benefits of deterring discrimination in firing could be less than the costs of the disparate treatment in hiring that this firing protection may induce. To reduce the potential shadow that firing liability casts on probationary hiring, firms and their employees might be allowed to contract out of disparate impact or disparate treatment firing liability for a short period of time. Such an opt-out provision would give firms the freedom to take chances with probationary employment of minorities without exposing themselves to the risk of civil rights liability for subsequent discharge.

2. Increasing the Cost of Firing Whites

Another way for law to decrease the relative cost of firing minorities is to increase the cost of firing whites. One way to accomplish this would be to expand wrongful discharge liability. If discharged employees could generally challenge the firm's firing rationale for firing them, firms would have less reason to hire whites or minority workers on a probationary basis. Any law which enhances employees' job security generally (or white job security in particular) will tend to mitigate the effect of disparate impact firing liability on initial hiring decisions. Accordingly, a wide-range of reforms such as plant closing laws or replacement worker regulations may effect firms' incentive to substitute toward white probationary employment. Paradoxically, minorities should find Title VII's "pseudo just cause" firing protection more attractive if whites also have such protection, because employers would no longer have an incentive to substitute away from blacks at the hiring stage.

3. Increasing the Cost of Failing to Hire Minorities

There are several alternatives that might raise an employer's cost of failing to hire a minority applicant. Employment audits using matched pairs of minority/white testers, based on the Fair Housing model, have attracted considerable attention. While there are legal and other problems with the use of employment testing, it holds considerable promise as a means of detecting hiring discrimination. We might also consider adjusting the lodestar used to calculate attorney's fees in hiring (but not firing) cases in order to make hiring cases more attractive to bring (and more expensive to defend). Finally, tax subsidies for hiring minorities would also raise the costs of failure to hire. Inner-city enterprise zones are one example of how such programs could be implemented. Many of these alternatives, if applied to disparate impact hiring liability, would push us towards the hiring quotas that conservatives have long decried. But now, the rationale behind a hiring quota would be to counter-balance the perverse effects of a firing quota. As hiring regulations become increasingly binding on employers, the combination of quotas on the flows of people hired and fired would in essence create a quota on the stock of minority employment. A fine exploration of the benefits of such a regime is provided in a recent article by David Strauss.

We have placed on table a variety of reforms. Which of these policies one prefers will be informed by one's views of the purposes of disparate impact law and about the amount and kind of disparate treatment in the world.

For example, decreasing the costs of firing blacks will be much more problematic if you believe that this will unleash a great deal of disparate treatment in firing. While the prevalence of "pure" firing discrimination (without discrimination in hiring) is implausible under standard theories of discrimination based on statistical inference or associational animus, this threat may be much more salient under other theories (consequential animus and role- or status-based discrimination).

Alternatively, enhancing disparate impact hiring liability would probably help blacks but would induce disparate treatment against whites in both hiring and firing, and would thus be inconsistent with the process rationale for disparate impact.

While it is hard to identify a silver bullet, we tentatively suggest some movement on both the hiring and firing margins might be warranted. Besdies repealing Teal, we suggest that augmenting attorneys fees for disparate treatment hiring cases and state-sponsored testing might be combined with a reduction in disparate impact firing liability. This might be an appealing tradeoff for both advocates and opponents of the civil rights regime. But in the limited space allowed us in this symposium our goal is primarilly to bury the hiring quota theory which has for too long distorted our discussion about disparate impact liability. Refocusing on firing liability changes the terms of the debate.

Conclusion

The disparate impact rhetoric of both liberals and conservatives traditionally focuses on hiring decisions: for example, the debate over the 1991 Civil Rights Act centered on disparate impacts in hiring. The paucity of attention given to firing liability may be a result of the Supreme Court's reluctance to review disparate impact firing cases: Even though we detailed the dominance of firing cases in the district courts' docket, a similar analysis of the Supreme Court reveals a continuing focus on hiring decisions in cases such as Wards Cove. We suggest, however, that this focus on hiring is wrongheaded: disparate impact liability is likely to be more salient for firing decisions than hiring decisions. Among disparate impact opinions as a whole, there are 4 judicial opinions in firing cases for every 1 hiring opinion. This disparity is probably caused by the simple fact that it is much easier for plaintiffs to prove a prima facie case of disparate impact in firing than to prove disparate impact in hiring. While our data are not conclusive, the empirical and doctrinal evidence in support of this "asymmetric scrutiny" hypothesis at the very least warrants a refocussing of Title VII scholarship toward the likely effects of disproportionate judicial scrutiny of firing decisions.

An immediate byproduct of this revised focus is the insight that disparate impact liability is unlikely to induce firms to increase the employment of traditionally disadvantaged groups. Far from pushing firms towards minority hiring quotas, the current salience of firing liability might induce employers to discriminate against minorities in hiring.

The implausibility of the hiring quota critique does not, however, suggest that the current pattern of disparate impact liability is well tailored to further Title VII's implicit goals. First, current disparate impact enforcement is not well suited to reduce disparate treatment. While the current emphasis on disparate impact firing liability may deter some preexisting disparate treatment against minorities in firing, this will only come at the cost of increasing disparate treatment in hiring.

Second, current disparate impact enforcement is not well-suited to increase minority employment prospects. Although disparate impact firing liability is likely to increase the chance that hired minorities will be retained, we have shown that it decreases the probability that they will be hired initially. In many cases, this latter effect will dominate to reduce the minority wage bill or utility level. And even when the hiring effect does not dominate, disparate impact firing liability only succeeds by increasing the variance in minority outcomes. Some minorities are never hired so that others can achieve better job security.

These troubling side-effects of the current disparate impact regime suggest two complementary strategies for legal reform: either to increase scrutiny of firms' hiring decisions or to decrease scrutiny of firing decisions. We suggested several means by which these strategies might be accomplished, and the reader can probably think of many more. In any case, the major point is that we need to begin thinking about hiring and firing liability as separate policy instruments, with different effects. We should be wary of using the same rules to regulate discrimination in hiring and firing when the two kinds of behavior have such different consequences.

Mathematical Appendix

Optimal employer behavior in the probationary employment model without disparate impact firing liability was fully described in the text. Briefly, given a wage fixed at w for all workers, employers should hire all applicants for whom MP - | |/3 > w. After learning the exact value of in the first period, employers should retain all workers for whom MP + > w for an additional period, and should fire all those for whom this condition is not met. These two rules were graphed in Figure 3; both are linear, and have an intercept of w, the wage; their slopes are -1/3 and 1 for the hiring and probationary lines respectively. Even if, as we assume, the black and white population distributions of MP and | | are different, the unconstrained employer will choose the same hiring and firing rules for the two groups.

This appendix demonstrates the optimal hiring and firing rules when employers are constrained to fire the same proportion of white and black workers. The problem becomes more complicated with the addition of this constraint, because employers must now choose the same firing rates for both races, but are allowed to adjust their hiring behavior at the same time. We begin by defining 4 parameters that shift the hiring and firing lines for each race. Specifically:

New Parameter Definition

x1 Shifts down the (first-period) hiring line for whites.

x2 Shifts up the (second-period) firing line for whites.

y1 Shifts the (first-period) hiring line for blacks.

y2 Shifts down the (second-period) firing line for blacks.

The shifts in the hiring and firing lines caused by these new parameters are illustrated in Figures 4 and 5.

We now show that the constrained optimum hiring and firing rules can be defined in terms of these four parameters. Both the hiring and the probationary lines are isoprofit curves. The hiring line represents the set of applicants that an employer is indifferent between hiring and not hiring. In the unconstrained case, the indifference curve has an intercept of 50 and a slope of -1/3. But with the disparate impact firing constraint, this isoprofit hiring line will have a horizontal component for both blacks and whites. For blacks, the shifts in the firm's hiring and probationary lines mean that some of the marginal hires will be retained with probability 1. One can readily show that the expected profits from all employees on the new kinked hiring line are equal. For whites, the shifts in the firms' hiring and probationary lines means that in the constrained equilibrium some of the marginal hires will be retained with probability 0. Again one can show that the expected profits from all hires along this kinked hiring lines are equal given the employer's optimal firing decisions in the second period.

Having demonstrated that the employer's optimal hiring and firing rules in the constrained case can be characterized by the (old) unconstrained rules with the four new shift-parameters just introduced, we now move to calculating the actual values of these new choice variables, given the distributional and other assumptions we made in setting up the model. To do so, we write down the (cumbersome but not theoretically difficult) expressions for expected profits on black and white hires, and then choose the values of x1, x2, y1, and y2 that maximize total profits, subject to the equal firing rates constraint. Since expected profits are a discontinuous function of MP and | |, we need separate expressions for each relevant region in (MP,| |) space. For whites, the employer's problem is:

Subject to

where

For blacks, the problem is:

subject to

where

These two maximization problems yield expression w*(k) and b*(k). To maximize profits subject to the constraint the firm must then maximize w*(k) + b*(k) with respect to k, yielding an optimal k*. Using Mathematica to solve the initial integrals, we performed a numeric grid search to locate the optimal shifts in the hiring firing lines which maximized profits given this constraint. In equilibrium the optimum values of the 4 shift parameters are: x1 =.9824; x2 = 1; y1 = .5; y2 = 1.6. The effects of these shifts on the proportions of blacks hired and fired are reported in Table 1.

As a check on our results, we also considered, but do not report, the mathematics of the less-complicated intermediate case, in which the employer is assumed to be unable to adjust his hiring decisions, so that the constraint can only be satisfied by a change in firing behavior. As one might expect, this intermediate or "naive" problem requires more of an adjustment in firing rates than is the case when the employer is free to adjust both hiring and firing policies in order to satisfy the disparate impact constraint.


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