What is required to correct the estimates of equation (4) for the bias from using P instead of Ps* is a variable that is correlated with productivity but uncorrelated with r|s, and that does not appear in equation (2). Because r|s is orthogonal to the information set Is, any variable that is in Is and correlated with productivity satisfies the first two criteria. However, to satisfy the third criteria, this variable has to be unrelated to starting wages conditional on expected productivity. Given that the null hypothesis is that there is taste discrimination, only variables that measure characteristics not subject to taste discrimination are valid instruments. The instruments considered include education, age, and training or experience. Age is potentially objectionable, given that there may well be age discrimination in the workplace (e.g., Johnson and Neumark, forthcoming). However, this is unlikely to be an issue in the present context, both because the sample consists of relatively young workers, and because most age discrimination claims concern discharges, layoffs, and hiring, rather than wage discrimination. website

Under statistical discrimination, a minority worker will earn less than an equally-productive white worker, as long as average productivity for minority workers is lower. But a minority and white worker with identical expected productivity will earn the same wage. Taste discrimination, on the other hand, implies that even with equal expected productivity, the minority worker will earn less. Therefore, at the one extreme of pure taste discrimination, the IV and OLS estimates of p will be identical, while at the other extreme of pure statistical discrimination, the IV estimate of P (bIV) will fall in absolute value to zero. Thus, a statistical test of whether race differences in wages reflect taste or statistical discrimination is obtained from a Hausman test for bias in the OLS estimate of the coefficient of R, which is a test of the null hypothesis of pure taste discrimination. A statistical test of the broader question of whether employers have accurate information about workers on which they base starting wages is obtained from a Hausman test for the “exogeneity” of P in equation (4), which is a test of the null hypothesis of complete information (under which the IV estimate of a (aIV) equals a^).