The Use of 'Reverse Regression' in Employment Discrimination Analysis
White, Paul F., Piette, Michael J., Journal of Forensic Economics
In cases of alleged employment discrimination, economists often utilize multiple regression techniques to demonstrate the presence or absence of discrimination on the basis of race, age, gender, or some other personal characteristic protected under the law. Typically, the dependent variables in these analyses are salary, hire status, promotion status, or termination status. The independent variables are chosen because they are believed to explain in part the variation in the dependent variable. Common independent variables include race, age, gender, and measures of worker productivity, such as education, training, and level of output.(1)
In the context of alleged racial discrimination, the typical approach to salary discrimination measures the impact of race and other independent variables on employees' salaries. The key question is: "for given qualifications and productivity levels, are non-white employees paid significantly different than white employees?" The results of this direct regression approach determine whether the white and non-white salaries are the same at given levels of productivity.
The process of determining salaries assumed by the direct regression approach is straightforward: An employer evaluates the qualifications of an individual and determines salary level that most closely matches the qualification level. The employee's qualifications are regarded as fixed, and the salary level can vary across all levels in the firm.
It is possible, however, that another employment process may also be considered.(2) In this alternative process, an employer reviews a group of candidates for a particular salary level and selects the candidate who appears to have the best qualifications for that salary. In this case, the salary level is fixed, while the qualification level varies across the eligible candidates. Proponents of this viewpoint, called reverse regression argue that the technique is most applicable to analyze this employment selection process.
The question asked by the reverse regression approach is, "for given salary levels, are minority employees more or less qualified than non-minority employees?" This technique involves the use of productivity as the dependent variable with salary and protected class membership as the independent variables. It is implied that salary discrimination also exists if minority employees are more qualified than equally-paid white employees.
The purpose of this paper is to apply the concept of reverse regression to an employment discrimination context, discussing the strengths and weaknesses of the method. Using a database from a large manufacturing company, we compare and contrast the features of the direct regression and the reverse regression approaches. This paper also provides examples of court cases where the reverse regression technique was included as part of the statistical liability analysis.
Section II of this paper provides a detailed description of the reverse regression approach. Section III applies the reverse regression methods to data from a large manufacturing company, highlighting the differences from the traditional, direct regression methods. Section IV discusses the advantages and disadvantages of reverse regression from the point of view of an economist who is considering the use of reverse regression in his or her analysis. Section V presents examples where the reverse regression technique was used in court proceedings. In Section VI, the paper concludes with suggestions and ideas for future research.
II. The Concept of Reverse Regression
For comparison purposes, we begin this section with a brief description of the traditional or direct regression approach, which is followed by a discussion of the reverse regression methodology.
A. Direct Regression
In the context of alleged salary inequities with respect to employee race, the traditional multiple regression approach is based upon the question, "are non-white employees paid less than equally-qualified white employees? …