The Effect of Statistical Discrimination on Black-White Wage Discrimination:
Estimating a Model with Multiple Equilibria

Andrea Moro, Universita Ca Foscari Di Venezia

The empirical literature on discrimination has consistently documented that blacks earn less than whites, even after controlling for observable characteristics. However, over the last 30 years the racial wage differential has narrowed considerably. Among the reason cited for the reduction in the differential are (1) a convergence in years of schooling; (2) a convergence in the quality of schooling, (3) the selective decline in the labor force participation of low-skilled blacks, (4) migration of black workers out of southern regions (5) affirmative action and other anti-discrimination legislation. Much of the debate has centered on the relative contributions of each of these explanations (there is a large literature on this topic. See, for example Card and Krueger (1991), Heckman (1989), Leonard (1984), Smith and Welch (1984, 1989)).

In their survey of the empirical literature, Donohue and Heckman\ (1991) argue that the first four explanations can account for at most 65% of the reduction in earnings inequality. Although better measurement of these factors could enhance their combined explanatory power, an additional explanation is that the unexplained portion of the decline reflects movements between different economy-wide equilibria that might result from the same fundamentals. In an environment where multiple equilibria co-exist, a reduction in inequality can be experienced if the economy moves from an equilibrium with high differentials to one with low differentials. Donohue and Heckman conjecture that such a phenomenon might have occurred in the past 30 years, perhaps as a result of anti-discrimination policy. But, they did not provide a structure within which an analysis of this conjecture could be conducted.

Theories of discrimination, pioneered by Arrow (1973) and Phelps (1972), provide a setting within which different outcomes are possible under the same set of primitives. These models do not provide an equilibrium selection mechanism. Nonetheless, recent studies have focused on the efficacy of anti-discrimination policies in reducing group disparities. They show that even if the effect of such policies is in general ambiguous, there are cases where such policies can eliminate the equilibria with discrimination and lead the economy towards group equality (See Coate and Loury (1993), Lundberg (1991), and Moro and Norman (1997)).

The starting point of this paper is the observation that while the empirical literature cannot account for all of the reduction in wage inequality based on changes in the fundamentals, the theoretical literature has demonstrated that under some circumstances wage inequality can be reduced even without such changes. This paper proposes and implements an estimation strategy capable of identifying both the fundamentals and the equilibrium chosen by the economic agents in a statistical discrimination model in which there may be multiple outcomes. By estimating the model in different time periods, it is possible to compare the pattern of the equilibria selected in the economy with the other equilibria that the model could have generated under the same fundamentals. This exercise can provide an answer about whether the reduction in wage inequality can be explained, at least in part, by the way equilibria were selected over time.

The model presented here builds on Arrow (1973), and is an extension of the model in Moro and Norman (1997). Production takes place using two different job-tasks of different complexity. Workers face a costly human capital investment decision, which, if undertaken, makes a worker productive in the complex task. Workers are heterogeneous in the cost of investment. Therefore, the fraction of workers who invest depends on how big the benefits from investing are. Firms decide how much to pay workers and how to allocate them between the tasks on the basis of a noisy signal of productivity. Equilibria with wage inequality can exist because if employers hold asymmetric expectations about aggregate human capital investment of members of different groups, workers belonging to the group with less productive people will be expected to be less productive than workers of the other group carrying the same signal. In this situation, higher signals of productivity will be differently rewarded for members of the two groups. This generates different incentives to invest. In such an equilibrium, one group will have less workers willing to undertake the costly human capital investment, which fulfills the employers' asymmetric expectations. In this context it is possible that multiple equilibria coexist with different levels of investment disparity, which implies different wage inequality and incentives to invest.

In general, the problem of estimating models with multiple equilibria stems from the fact that the equilibrium selection mechanism is unspecified. Although this is true here as well, the structure of the model is such that the selected equilibrium is nonetheless estimable. The idea behind the estimation strategy is the following. For a given set of fundamental parameters, the model yields different equilibrium wage distributions. However, given workers' human capital investment decision and firms' optimal responses in terms of wages and job allocation, the wage distribution is unique. The distinctive feature that allows the identification of the equilibrium is that there exists a representation of the model that uniquely relates the equilibrium wage distribution of one group of workers to the set of equilibrium choices made by the agents and a subset of the fundamental parameters. In the first stage of the estimation, this subset of the fundamentals and the sufficient statistics for workers and firms' equilibrium choices are considered as estimable parameters of the wage distribution. The other fundamental parameters, which refer essentially to the distribution of workers over investment costs, are recovered in a second stage. Identification requires merging the first stage results obtained for black and white male workers, and adopting functional form assumptions that replicate the equilibrium estimated in the first stage. Among these assumption, it is required that the two groups of workers possess the same distribution over costs of investment. After completing the estimation, it is possible to compute whether there are other equilibria that the model can generate under the same set of fundamentals and to evaluate whether there is a pattern in the way equilibria were selected over time.

The estimation was performed using wage data for ten three-year periods from 1963-65 to 1990-92. Results from the first estimation stage show that the estimated wage distributions essentially match the basic facts, such as the increased within-group wage inequality that occurred after the eighties. It is found that blacks invest in human capital on average 12.3% less than whites, although the difference declines over time. Consequently, relatively more blacks are employed in the simple task (92.9% vs. 79.1%). These differences cause a 23.6% average difference in mean wage between the two groups. As in the data, the predicted average wage difference between groups declined considerably until 1980, and stabilized afterwards.

For every year in which the estimation is performed, the model generates several equilibria. The equilibria that were selected in the economy over time (which from now on will be referred to as the "selected" equilibria) were those in which the mean wage differential was essentially the smallest. However, at the estimated parameters equilibria with higher wage inequality always existed. In some of them, blacks invest less than in the estimated equilibrium and receive a lower average wage, but are better off in terms of welfare than in the selected equilibrium because the reduced cost of investment compensates for the smaller wage. In another set of equilibria, blacks are better off than whites, because they invest more. In almost all of the equilibria of this type, whites are at a "corner solution," where none of them invest in human capital, and therefore are all placed in the simple task. Even though whites in these equilibria save the investment cost, their welfare is on average lower than in the selected equilibrium. This is a consequence of the fact that the larger group is not investing, which strongly affects the aggregate output of the economy.

These findings imply that statistical discrimination and self-fulfilling expectations about groups average productivities did not exacerbate wage differences in the U.S., and that the decline in wage differentials cannot be explained by a change in the way equilibria were selected over time. Therefore, anti-discrimination policies have not (and could not have) induced changes in the type of equilibrium selected in the economy after 1965.