case of the model with imperfect information, also explain the worker’s rank affiliation each
period.
To analyze the predictive power of these instruments, I performed a F-test for the joint
significance of the instruments when the instrumented variables (previous wage on the one
hand and current rank on the other) are regressed on the instruments and including all the
exogenous variables in the right-hand side of the wage equation. The Appendix D table shows
the results of the test. One can conclude from the table that rank affiliation either between
t - 1 and t or t - 2 and t - 1 are good instruments for the worker’s current job rank and the
previous period’s wage.
In terms of the validity of the instruments used to perform the estimation, note that in the
estimations with comparative advantage, the overidentification test rejects the hypothesis that
the instruments used are valid. Because this might be due to the importance of classification
errors in rank between two periods, I re-estimated the model using a second rather than a first
quasi-difference of the wage equation. 29 The idea is that if classification errors are important
and if they are serially uncorrelated, one can re-estimate the model and find similar results
when comparing observations in t and t - 2. Results are presented in table 5.
Results on the coefficients are similar to those of Table 4 implying that the preceding results
on comparative advantage and learning still hold. On the other hand, the result on the validity
of the instruments are better. The value of the statistic has substantially decreased suggesting
that it is sensitive to mis-classifications in rank.30 It also suggests that if there are errors in
rank classifications, they don’t seem to be serially correlated.
29 False classifications may affect the estimated value of the objective function through the estimation of the
weighting matrix as the covariance of the moments. See Altonji and Segal (1996) for an analysis of the small
sample properties of the GMM estimator when the weighting matrix is the variance of the moments. Since the
statistic of the overidentification test is a linear function of the value function, conclusions from the test may
be sensitive to the presence of classification errors in ranks.
30Another possibility is related to the model’s assumption of a single ability index to generate non random
selection and learning. Given the possibility of transitions between non consecutive ranks, there exists several
identification strategies to estimate the rank coefficients which leads to the failure of the overidentification test.
See Gibbons, Katz, Lemieux and Parent (2002) for a discussion of this point. Here however, there are too few
transitions between non consecutive ranks to consider this as a possible explanation for the high value of the
estimated objective function.
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