The key question, however, is whether the coefficient A estimates the unconditional rate of convergence (0) or the conditional rate of convergence (0*). To see the relationship among the various parameters, rewrite the log entry wage and the rate of wage growth for the (/, k, s) cohort as:
where and xs are fixed effects giving the “returns to schooling” for the log entry wage and the rate of wage growth, respectively; and eiks and ziks are i.i.d. random variables that are uncorrelated with the other right-hand-side variables in (18) and (19). The convergence regression in (17) can be rewritten as:
where со’ = (£>iks + Xeiks – e,b, and an observation is an (i, k, s) cell. Let pik(s) be the fraction of the population that has s years of schooling in the immigrant cohort that migrated from country i at age k, and aggregate across schooling groups within this cohort.16 This aggregation yields:
Equation (21) shows that the convergence regression that uses schooling groups to define the cohort is equivalent to a regression that aggregates across schooling groups but includes variables that indicate the educational attainment of the cohort. As a result, the coefficient к estimates the extent of conditional convergence across immigrant cohorts, 0*. It is not surprising, therefore, that Duleep and Regets (1997b) find a great deal of wage convergence across immigrant cohorts since they are implicitly holding constant the human capital endowment at the time of entry.
The second panel of Table 4 shows a related way of controlling for educational attainment.