Testing "Discrimination Plus" Cases
Sarkar, Debojyoti, Journal of Forensic Economics
In employment litigation, statistical evidence now plays an increasingly important role in testing a charge of discrimination in various labor market related areas. The methodology of multiple regression analysis has come to be recognized as quite an effective analytical tool to perform such a task.
A variety of authors have explained the methodology and how to use it in an appropriate manner (Bloom & Killingsworth, 1982; McCabe, 1986; Finkelstein & Levin, 1990). The authors typically consider a single "discriminating" factor and explore how the methodology can be applied to test whether the relevant data support the charge of discrimination.
In some of the recent cases discrimination charges are based on more than one legally protected characteristic. Employees have complained that they have been discriminated against because of their race and gender (Foster v. Dalton); race and age (Coleman v. Runyon); gender and age (Walker v. Nationsbank of Florida); race, gender and age (Dewey v. PTT Telecom), etc. For the lack of a better term we will refer to these cases as "Discrimination Plus" cases.(1) Statistical tests relevant for these cases are more complex than the simple framework that we just described.
The objective of this article is to develop the appropriate multiple regression methodology to be applied in such discrimination plus cases. In particular, we consider only race and gender in a linear multiple regression analysis context, although the argument is generalizable to cases involving more than two discriminating factors as well as binary dependent variables. In section II we consider the single-factor discrimination cases whereas section III explores the discrimination plus case in greater details. Section IV explores the alternative "reduced" sample and "full" sample specifications that one may try in testing for these plus cases and comments on the relative merits of the full sample specification. Section V concludes.
II. Testing for Single-Factor Discrimination
To test for discrimination in earnings, an earnings function can be estimated with earnings as the dependent variable. The independent variables include a vector of productivity related characteristics and other appropriate variables ("other"), and an indicator variable for the discriminating factor.
Denoting earnings, the other variables and the indicator variable by Y, the vector X and I respectively, the above-mentioned specification can be expressed as:
1) Y = [[Beta].sub.0] [[Beta].sub.1].I+[X..sub.[Gamma]] + [Epsilon]
where [Epsilon] is an error term and [Gamma] is a vector of parameters.
If the estimate of [[Beta].sub.1] is negative and statistically significant, we can reject the null hypothesis of no earnings differential between the comparison group and the "plaintiff group", and conclude that the data supports the hypothesis of discrimination in earnings against the plaintiff group.
III. "Discrimination Plus" Cases
For the purposes of our discussion, assume that plaintiffs have brought charges of race and gender discrimination in earnings against their employer. Although the analysis can easily be extended to cases involving more than two race categories, for the sake of simplicity, assume that there are only whites and African-Americans (AA) present.
In most of such discrimination plus cases referred to earlier, the general methodology--not always statistical--used by the courts so far to test for discrimination has been first to test for discrimination arising from one factor and then to test for discrimination arising from the other factor.
However, the two separate tests do not directly answer the charges of race and gender discrimination brought forward: they answer the charges separately. They do not test for the fact that there are individuals who embody both the factors. …