An experimental study of statistical discrimination by employers.

• Author: Feltovich, Nick

1. Introduction

   This article reports results from an experiment that was motivated by the literature on labor market discrimination. Our aim for conducting this experiment was to investigate whether employers' initial perceptions of employee ability on the basis of group characteristics can lead to lower wages that persist for a long time. Under the maintained assumption that the employer learns about the group's ability through Bayesian updating, we examine how quickly he learns. The idea that inaccurate prior assessment by managers formed on the basis of an employee's group influences wages is one of many theories of labor market discrimination in economics. For economists, discrimination implies that workers in one group earn less than the competitive market rate for their labor, typically due to their gender or ethnic group. The economics literature contains many theories seeking to explain labor market discrimination and empirical work that attempts to test those theories and measure discrimination through observed wages (see, e.g., Altonji and Blank 1999, who provide a thorough survey of theoretical and empirical research on wage differences and discrimination, including statistical discrimination, as well as their probable causes).

   Economic models of discrimination were initially developed to address the empirical findings of many researchers that wages differ across groups and the widespread belief that wage differences stem in part from discrimination. Existing theoretical models of labor market discrimination fall into several distinct categories, according to the source of discrimination. First, there are theories based on tastes, such as Becker's (1972). According to such theories, employers have a preference for not hiring workers of a particular group, fellow employees have a preference for not working with workers of a particular group, or customers have a preference for not buying from firms hiring workers of a particular group. Second, there are theories based on market power (often in addition to tastes), such as labor-market monopsony (Robinson 1934), labor unions (Kessel 1958), and public-sector firms (Ross 1948). Third, there are theories that suppose social, legal, or institutional constraints crowd certain worker types into or out of particular occupations. Examples include the occupational exclusion models of Bergmann (1974) and Johnson and Stafford (1998). Finally, there are statistical theories pioneered by Phelps (1972) and Arrow (1973). Statistical theories of discrimination focus on the idea that, when a prospective employee's true ability is unobservable, the employer may rationally use the employee's ethnic group or gender as a proxy for his ability.

   Our study focuses on an extension to the basic statistical discrimination model. The initial model by Phelps (1972) simply argued that high-ability workers in groups with more variability in ability would earn less than high-ability members of other groups. Lundberg and Startz (1983) developed a more complex model to show that, even if two groups possessed the same average ability, a higher variance of ability in one group would lead to lower wages for members of that group relative to a low-variance group. Farmer and Terrell (1996) further extended this model to look at the possibility that inaccurate initial assessments of ability could become self-fulfilling prophecies. For example, lower initial assessments of worker ability by employers could diminish that worker's marginal returns to additional training or education and thus decrease his incentives to obtain skills. His ability would then remain low, reinforcing the employer's assessment.

   The empirical literature fails to produce a decisive conclusion on the sources of discrimination or even the extent to which it affects wages in the United States today. While average wages differ across groups, wage differences could simply reflect differences in worker ability. Explanations for differences in ability vary considerably. For example, Herrnstein and Murray's (1994) controversial book The Bell Curve: Intelligence and Class Structure in American Life asserts that races simply differ in inherent ability, while Card and Krueger (1992) argue that differences in quality of education for black and white workers explain a significant portion of the wage gap. A critical issue for empirical studies is that worker ability is unobserved. This makes it difficult to break wage differences across groups into one portion that is attributable to differences in ability and a second portion attributable to pure discrimination. Testing theories that explain discrimination or sources of differences in ability is even more difficult. (1)

   In this article, we turn to a laboratory experiment as a step toward understanding the impact of an employer's prior opinions formed on the basis of an employee's group on wages. The critical issue is how quickly employers learn about workers' true abilities through observing noisy information about their performance in the workplace. If prior opinions are weak, the employer will quickly update any group-based stereotypes with information from the workplace. However, if initial assessments are heavily weighted, the initial perception may lead to persistent differences in wages.

2. The Model

   In order to motivate our experiment, we discuss a model based on Farmer and Terrell (1996) and Lewis and Terrell (2001), who examine a statistical discrimination framework with Bayesian updating of employers' beliefs. A large number of employers hire workers for one period from a large pool of potential employees. The labor market is competitive, so that workers are paid their expected marginal product in each period, [w.sub.it] = E([y.sub.it]). The marginal output of worker i in period t is given by the following production technology:

   (1) [y.sub.it] = [[A.sup.[alpha].sub.i][e.sup.[epsilon]it]], where [[epsilon].sub.it], ~ N(0,[[sigma].sup.2]) i.i.d.

   The random variable A reflects the ability of all workers with the same observable characteristics as worker i, while the random variable [epsilon] is an individual-specific component that is normally distributed and i.i.d, across workers. (2) The values of A and [epsilon] are unobservable to the employer, but A can be gradually learned over time. Note that, because of our assumption about the distribution of [epsilon], one can generate the log-normal distribution of wages initially observed by Mincer (1974). Taking logarithms in Equation 1 yields

   log [y.sub.it] = [alpha] log[A.sub.i] + [[epsilon].sub.it].

   Without loss of generality, we assume that [alpha] = 1, so that [Y.sub.it], = [A.sub.i][e.sup.[epsilon]it] and log [y.sub.it] = log [A.sub.i] + [[epsilon].sub.it]. The normality assumption on e implies that the distribution of log output conditional on group log ability is normal and given by

   (log [y.sub.it] | log [A.sub.i]) ~ N(log [A.sub.i], [[sigma].sup.2]),

   or more explicitly,

   f(log [y.sub.it] | log [A.sub.i]) = 1/[square root of 2[pi][[sigma].sup.2] exp[-1/2[[sigma].sup.2][(log [y.sub.it] - log [A.sub.i]).sup.2]].

   We further assume that the (representative) employer gradually learns about the ability of an employee type by making T sequential observations of employees' output. This assumption is at the heart of our investigation in examining the persistence of the employers' priors about employees' abilities that are initially unobservable. This assumption, along with the independence property of the assumed error distribution, implies

   f(log [y.sub.i1], ..., log [y.sub.iT] | log [A.sub.i] = 1/[(2[pi] [[sigma].sup.2]).sup.T/2] exp [-1/2[[sigma].sup.2] [T.summation over (t=1)] [(log [y.sub.it] - log [A.sub.i]).sup.2]].

   The employer's initial beliefs about employees' ability is characterized by the prior distribution function given by

   (log [A.sub.i]) ~ N([bar.[mu]], [[bar.[sigma]].sup.2]),

   where [bar.[mu]] is the mean of a normal prior reflecting the best guess about employees' group ability, and [[bar.[sigma]].sup.2] is a measure of certainty of prior beliefs. [bar.[mu]] and [[bar.[sigma]].sup.2] are allowed to vary across groups as employers' priors depend on employees' group. Employers are assumed to use Bayesian updating when forming beliefs about the ability of workers. So, beliefs at time T are calculated as

   f(log [A.sub.i] | log [y.sub.i1], ..., log [y.sub.iT]) = f(log [y.sub.i1], ..., log [y.sub.iT] | log [A.sub.i)f(log [A.sub.i]/f(log [y.sub.i1], ..., log [y.sub.iT].

   This in turn implies

   (log [A.sub.i] | log [y.sub.i1], ..., log [y.sub.iT]) ~ N([[mu].sub.T], [[sigma].sup.2.sub.T]),

   where

   [[mu].sub.T] = [[sigma].sup.2.sub.T][[summation].sup.T.sub.t=1] log [y.sub.it]/[[sigma].sup.2] + [bar.[mu]]/[[bar.[sigma]].sup.2] and [sigma].sup.2.sub.T] = [[T/[[sigma].sup.2] + 1/[[bar.[sigma]].sup.2]].sup.-1].

   The mean of the updated distribution for...