Reverse Regression: The Algebra of Discrimination

How should discrimination in the marketplace be defined? The answer is less obvious than it might seem. As Conway and Roberts (1983) suggest, there are various definitions. The data may suggest that for given qualifications, in given jobs, women are paid less than men, suggesting discriminatory behavior. But the same data set may or may not suggest that at given salary levels, women and men have the same qualifications. What should we conclude in the case of a conflict? The is also possible, and it leaves the same problem. All of this may be moot, of course. Discrimination is what we say it is. As generally applied with respect to people already on the job, the law speaks in terms of wages for given qualifications in given jobs. The second form of discrimination mentioned here admits of no clear-cut remedy. As such, at least as commonly applied, the received wisdom defines discrimination (in the setting assumed here) in terms of equal pay. Nonetheless, the identification of the second form of discrimination might be of some interest. The more common view of discrimination fits neatly into a multiple-regression framework. Conway and Roberts (1983) and Kamlich and Polachek (1982) suggest an alternative regression strategy, reverse regression, for dealing with the second type. Some strong conclusions are drawn in the first of these studies, the primary one being that