Columns (4) and (5) report results from using the average unemployment rate experienced by each entry cohort, in each year, rather than the unemployment rate experienced by the individual, in order to obtain a more exogenous instrument. The first-stage results in column (4) are quite similar, suggesting that early unemployment raises longest tenure attained in the immediate post-schooling period, and later unemployment lowers it, again by less. Note also that the estimated effects of unemployment are larger in column (4) than in column (2), consistent with a migration response to local unemployment rates that biases the estimates in column (2) towards weaker effects of variation in labor market conditions. The IV estimate of the effect of longest tenure attained on the wage (.08) is again considerably above the OLS estimate, and statistically significant. The specification test results are also similar, although in this case-perhaps reflecting the greater aggregation (and exogeneity) of the cohort average unemployment rates-the p-values for the overidentification tests are higher, and the restrictions are not rejected whether or not the minimum unemployment rate is excluded from the wage equation. In addition, the exogeneity of longest tenure attained is rejected, with a p-value of .02. review
The estimates in columns (6) and (7) use both the cohort average unemployment rates, and the deviations of the individual rates from these, as instruments. Again, the wage equation results are very similar to those in columns (2)-(5), with the estimated effect of longest tenure attained positive (.07) and statistically significant. In this specification, the overidentification test has a stronger interpretation, since it seems reasonable to assume that the cohort average unemployment rates provide valid instruments a priori, and to interpret the test as informative with respect to the individual-level deviations. As long as the minimum unemployment rate on the current job is included in the wage equation, the instruments easily pass the overidentification test. However, the evidence from the first-stage regressions indicates that only the cohort average unemployment rates have significant effects on early job stability.