Thus, columns (5) and (6) omit the education and job requirement controls, retaining only the productivity proxy and the race/ethnicity variables that may, because of taste discrimination, affect wages independently of productivity. This seems the most appropriate specification of the starting wage equation with which to test for statistical versus taste discrimination. In the OLS regression, the R2 is considerably lower than in column (1) or (3). Of course, this may be partly attributable to the discrepancy between the performance rating P and expected productivity Ps\

Note that the F-statistic for the joint significance of the instruments in the first-stage regression is reasonably high (3.81 in the levels specification, and 2.92 in the log specification), indicating that small sample biases towards the OLS estimates are unlikely to be severe. The IV estimates of a are considerably higher than the OLS estimates, rising by a factor of eight or nine, and in both the linear and log specifications these estimates are statistically significant. As reported in the table, for both the levels and log specification the null hypothesis of no bias in the estimated coefficient of the actual performance rating is rejected (at the five-percent level in the levels specification, and the ten-percent level in logs). For the linear specification, a one-standard deviation in the performance rating is associated with an increase of .49 in the log wage, a bit higher than one standard deviation of the log wage. For the log specification, a one-standard deviation in the performance rating is associated with a .44 increase in the log wage, approximately the same result. Thus, the IV estimates appear to generate estimated coefficients of the productivity proxy that map into wage differentials relatively well.