Statistical discrimination

Abstract: My recent book, Inflation Policy and Unemployment Theory, introduces what is called the statistical theory of racial (and sexual) discrimination in the labor market.' The theory fell naturally out of the non-Walrasian treatment there of the labor "market" as operating imperfectly because of the scarcity of information about the existence and characteristics of workers and jobs. A paradigm for the theory is the traveller in a strange town faced with choosing between dinner at the hotel and dinner somewhere in the town. If he makes it a rule to dine outside the hotel without any prior investigation, he is said to be discriminating against the hotel. Though there will be instances where the hotel cuisine would have been preferable, the rule represents rational behavior it maximizes expected utilityif the cost of acquiring evaluations of restaurants is sufficiently high and if the hotel restaurant is believed to be inferior at least half the time. In the same way, the employer who seeks to maximize expected profit will discriminate against blacks or women if he believes them to be less qualified, reliable, long-term, etc. on the average than whites and men, respectively, and if the cost of gaining information about the individual applicants is excessive. Skin color or sex is taken as a proxy for relevant data not sampled. The a priori belief in the probable preferability of a white or a male over a black or female candidate who is not known to differ in other respects might stem from the employer's previous statistical experience with the two groups (members from the less favored groups might have been, and continue to be, hired at less favorable terms); or it might stem from prevailing sociological beliefs that blacks and women grow up disadvantaged due to racial hostility or at least prejudices toward them in the society (in which latter case the discrimination is self-perpetuating). The theory is applicable to the class of "liberal" employers and workers who have no distaste for hiring and working alongside black or female workers. By contrast, the theory of discrimination originated by Gary Becker is based on the factor of racial taste. The pioneering work of Gunnar Myrdal et al. also appears to center on racial (and, in an appendix, sexual) antagonism. Some indications of interest in the new theory, and the independent discovery of the same statistical theoryby Kenneth Arrow, convince me that it is time for a formalization of the theory in terms of an exact statistical model. Though what follows is very simple, it may be useful to those who like exact models and it may stimulate others to develop the theory further. An employer samples from a population of job applicants. The employer is able to measure the performance of each applicant in some kind of test, yi, which, after suitable scaling, may be said to measure the applicant's promise or degree of qualification, qi, plus an error term, ps.