# THE ECONOMIC PROGRESS OF IMMIGRANTS: Wage Convergence 7

There are a number of technical problems with the convergence regressions reported in Table 4 that deserve some discussion. First, many of the cells in the analysis contain relatively few observations. The dependent variable in each cell is constructed from wages reported in two different Censuses. Because the 1980 and 1990 immigrant extracts form a 5 percent random sample of the population (and because the immigrant population has grown rapidly over time), the sample size used in the construction of wage levels for the various cells is reasonable for most national origin groups. In particular, 19 observations were used to calculate the 1980 wage for the average cohort, and 24 observations were used to calculate the 1990 wage. The smaller size of the 1970 immigrant extract, however, implies that only 11 observations were used to calculate the 1970 wage for the average cohort.

# THE ECONOMIC PROGRESS OF IMMIGRANTS: Wage Convergence 6

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.

# THE ECONOMIC PROGRESS OF IMMIGRANTS: Wage Convergence 5

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:

# THE ECONOMIC PROGRESS OF IMMIGRANTS: Wage Convergence 4

Although the Census data do not offer precise measures of the cohort’s effective human capital at the time of entry, we have information on the average educational attainment of the cohort at time t. Table 4 reveals that the coefficient 0* is strongly negative when the regression adds the cohort’s educational attainment, and becomes even more negative if the regression includes country-of-origin fixed effects (which can also be interpreted as determining effective human capital). Holding initial human capital constant, therefore, there is convergence among the various immigrant groups. Moreover, the rate of convergence is economically significant. The regression coefficient of suggests that wage differences among the various immigrant groups (holding initial skills constant) narrow by 32.2 percent within the first decade. If this rate of convergence remained constant over the immigrant’s working life, over two-thirds of the initial wage differential would vanish within 30 years. This finding, of course, mirrors the well-known conditional convergence result in the economic growth literature (Barro, 1997).

# THE ECONOMIC PROGRESS OF IMMIGRANTS: Wage Convergence 3

The top panel of Table 4 reports the relevant coefficients from the convergence regressions. The simplest specification (reported in the first column) reveals a positive, though insignificant, correlation between the unadjusted rate of wage growth and the log entry wage of immigrant cohorts. This weak correlation is consistent with the raw data summarized in Table 1 more recent cohorts, who have much lower entry wages, experience roughly the same rate of wage growth as earlier cohorts. Therefore, there is little reason to expect that the earnings of immigrants who belong to different national origin groups and arrive at different times will converge as they assimilate in the United States. If we take the positive point estimate of 0 at face value, the data, in fact, suggest that there might be some divergence over time: the immigrants with the highest entry wages are also the ones who experience the most rapid wage growth. In the context of the model, there seems to be some weak relative complementarity between the skills that immigrants bring into the United States and the skills that they acquire in the post-migration period. This result resembles Mincer’s (1974) finding of complementarity between investments in school and investments in on-the-job training.