Before proceeding to the IV estimation, a decision had to be made regarding which instrumental variables to use, choosing among the age, education, and job requirements variables. The maintained assumption is that at least one set of these variables can be excluded from the starting wage equation. The question that can be addressed empirically, however, is which set of instruments provides the most predictive power for the performance rating in the first-stage regression. To assess this, the first-stage regression was estimated using each set of instruments separately. For men, only the age variables were jointly significant in the first-stage regression; as reported in column (3), for the levels specification the p-value for the test of joint significance was .03 for the age variables, .58 for the education variables, and .47 for the job requirement variables, with qualitatively similar results for the log specification. Thus, for men the first set of instruments considered is the age variables. For women, only the education coefficients were jointly significant, with p-values of .00 in both the levels and log specifications. However, the p-values for the age variables are also relatively low (.17 and .21 in the two specifications); consequently, specifications using education and age as instruments are also reported for women.

0) (2) (3) (4) (5) (6) (7)
A. Usine linear performance ratine
Performance rating .0044(.0011) .0035(.0009) .009(.009) .0038(.001) .035(.015) .027(.011)
Black -.143(.032) -.126(.033) -.106(.047) -.178(.029) -.062(.081) -.091(.064)
Hispanic -.039(.030) -.006(.031) .020(.053) -.066(.034) .080(.089) .043(.067)
Schooling = 12 .120(.042) .187(.042) .184(.044)
Schooling = 13-15 .093(.049) .152(.050) .142(.054)
Schooling = 16+ .436(.054) .549(.053) .533(.060)
Age .050(.007)
Age2 x Ю’2 -.061(.010)
General experience required .026(.031) .043(.032) .051(.035)
Specific experience required .122(.034) .158(.035) .147(.040)
Vocational education/training required .264(.039) .292(.040) .303(.045)
R2 .384 .024 .347 .054
P-value from F-test of instruments in first-stage regression:
Age variables only .03
Education variables only .58
Job requirement variables only .47
Instruments Age Age Age, education, job requirements
F-statistic on instruments in
first-stage regression: 3.39 3.81 1.50
Overidentifying restrictions, p-value: .00
Bias in OLS estimates, p-value from Hausman test:
Performance rating .55 .04 .03
Black .56 .11 .09
Hispanic .56 .07 .06

Turning first to the results for men, columns (3) and (4) therefore report OLS estimates and IV estimates of the wage equation, using age and its square as instruments, in this case including the other variables (education and job requirements) in the wage equation. The OLS estimates of a, the coefficient of the productivity proxy, are similar to those in column (2). The IV estimate rises to .009 in the levels specification, but with the increased standard error becomes insignificant; in the log specification the IV estimate of a actually falls, also becoming insignificant. However, although the education and job requirements variables enter significantly in both the OLS and IV estimations, this model may be misspecified, and these variables may simply capture productivity differentials that would otherwise be captured in the performance rating..035