Redirecting Reverse Regression
I am not sure that the imperfect correlation between workers' productivity and their measured qualifications creates, as Conway and Roberts suggest, a profound dilemma for the theory of distributive justice. On the other hand, I am fairly sure that it raises issues of statistical inference. And I am quite sure that statisticians are better equipped to resolve the latter than the former. So I will consider the choice of regression for inferring salary discrimination in the context of a causal model of employer behavior, rather than in the context of a philosophical model of fairness. I focus on the empirically relevant case where several qualification variables are observed. Suppose that employers assess productivity and then set salaries deterministically as