These doubts are reinforced when we use an alternative instrument. We have three measures of the wage for the immigrants who arrived between 1960 and 1970. For these immigrants, we can observe their wage in 1970, 1980, and 1990. We can use this subsample of immigrants to estimate a convergence coefficient by regressing the 1980-90 rate of wage growth on the 1980 log wage. The data, however, also allow us to instrument the 1980 wage by the group’s 1970 wage. The resulting OLS and IV estimates are reported in the bottom panel of Table 5. The IV results show that the correlation between wage levels and wage growth remains positive even after we control for educational attainment.

In sum, there is a positive (although weak) correlation between the log entry wage and the subsequent rate of wage growth across immigrant cohorts. If anything, immigrants who earn high wages at the time of entry experience faster wage growth in the future. This correlation, however, turns negative when the analysis adjusts for differences in initial endowments of human capital, either by including measures of educational attainment or country-of-origin fixed effects. The results, therefore, seem to suggest that there exists conditional convergence in the immigrant population, in the sense that the wages of immigrant groups that have the same initial level of human capital converge over time. However, this finding is not robust to simple attempts to control for the bias introduced by measurement error.