the sample of survivors in period 1 (that is, the average wage of those immigrants who chose to remain in the United States relative to the wage of natives in period 1). A fraction r of the immigrants will leave the United States between periods 0 and 1; assume that there is no sample attrition in the native population. We can then write the observed rate of wage convergence over this period for this particular cohort of immigrants as:
where w0S is the average relative entry wage of immigrants who remained in the United States; and w0R is the average relative entry wage of the immigrants who returned home. We can rewrite equation 3 as:
Equation 4 shows the relationship between the observed rate of wage growth and the true rate of wage growth (w1S - w0S) experienced by the sample of survivors.
Note that the observed rate of wage growth is a biased measure of the true rate as long as the sample of survivors differs from the sample of return migrants (that is, as long as w0S ≠ w0R).
No direct empirical evidence tells us about how much the entry wage of immigrants who remain in the United States differs from the entry wage of immigrants who do not. Equation 4 suggests, however, that the observed rate of wage convergence estimated by tracking cohorts across censuses cannot be far off the mark for reasonable parameter values. Suppose subsequent emigration rates are about 30 percent and out-migrants are the successes (they have higher wages than those who remain in the United States).22 If immigrants who leave earn about 30 percent more than those who stay, equation 4 then indicates that the true rate of wage convergence is about 9 percentage points higher than the observed rate of wage convergence. The data in Table 5.12 suggest, however, that even if we add 9 percentage points to the wage growth experienced by the surviving immigrants, the wage of recent immigrants will remain far below that of native workers.
Although most research focuses on wages of immigrants and natives, there are other salient labor market outcomes. One of the most important involves the likelihood of working. Trends in employment propensities for males are documented in Table 5.15, which lists employment rates for male immigrants relative to those of native-born men; Table 5.16 presents parallel evidence for women.
If the out-migrants are persons with relatively low wages, then the estimated rate of wage convergence reported in Table 5.12 overestimates the actual rate.