The regressions in this panel use earnings data that are adjusted for education in the first stage. In particular, the individual-level regressions in equation (12) include educational attainment as an independent variable.

As a result, the log entry wage (yljk) and the rate of wage growth (Av,-^) are measured for the worker with the “average” level of schooling. This approach to controlling for differences in educational attainment across the groups, therefore, is roughly similar to the Duleep-Regets approach. Not surprisingly, the regression coefficients reported in the second panel of Table 4 show that the correlation between the rate of wage growth and the log entry wage is strongly negative, regardless of the variables that are included in the regression.

Although interesting, it is important not to “over-interpret” the practical significance of the finding of conditional convergence. Conditional convergence does not suggest that immigrant cohorts with lower entry wages experience faster wage growth in the United States. There is, in fact, no convergence among the various national origin groups that make up the immigrant population. The observed wage gap among the various immigrant cohorts will not narrow over time, but might even increase.
The lesson is clear: the choice of a base group is crucial in any discussion of immigrant economic progress or “assimilation.” Immigrants who start out with similar endowments of human capital tend to end up with roughly similar wages. But immigrants originating in different countries, in fact, have very different human capital endowments, and will tend to end up in very different places in the income distribution.