This framework exploits the availability of comparable cross-sectional data from two different points in time, and the resulting regression analysis is very similar in spirit to that in Tables 7-3 through 7-6 in the previous section. Without strong restrictions, cross-sectional regressions cannot distinguish immigrant cohort and assimilation effects because, at any given point in time, variation across immigrants in years of U.S. residence arises only from differences in year of entry to the United States. With repeated cross sections, however, outcomes for immigrant arrival cohorts can be tracked over time, and the trick then becomes to isolate changes that are due to assimilation from changes that are caused by different economic conditions in the survey years being compared (i.e., period effects). The most popular solution to this problem, and the one adopted here, is to estimate period effects from the outcome changes experienced by an appropriate group of native workers. After netting out these estimates of the period effects, remaining changes for immigrant cohorts are attributed to assimilation.15
To be explicit, let ygj represent the outcome for worker j, where the superscript g takes on the values I for immigrants and N for natives. Pooling data from the 1980 and 1990 censuses, immigrant outcomes are determined by the equation
yIj = Cjλ1 + Ajδ1 + sπTj + (1-Tj)XjβI80 + TjXjβI90 + εIj, (1)
where the vector C is a set of mutually exclusive dummy variables identifying immigrant arrival cohorts, the vector A is a set of mutually exclusive dummy variables indicating duration of U.S. residence, T is a dummy variable marking observations from the 1990 Census, the vector X contains other determinants of outcomes, ε is a random error term, and the remaining parameters are the objects of estimation. This specification gives each immigrant arrival cohort its own intercept, and differences in these intercepts represent permanent outcome differentials between cohorts. The coefficients of the duration of U.S. residence dummies measure the effects of immigrant assimilation on the outcome variable. In addition, the coefficients of the variables in X are allowed to vary across census years, with the subscripts 80 and 90 indicating the survey year of a particular parameter vector.
The corresponding equation for natives is
yNj = αN + πTj + (1-Tj)XjβN80 + TjXjβN90 + εNj, (2)
where αN is the intercept for natives, and the immigrant arrival cohort and duration of U.S. residence variables are excluded from this equation because they are not relevant for U.S.-born workers.
To see the identification problem in equation (1), it is easiest to think of C, A, and T as being scalar variables denoting, respectively, year of entry to the United
A key assumption of this approach is that compositional changes in the subsample of an immigrant cohort observed in the U.S. labor market—such as those caused by emigration, mortality, and labor force entry and exit—do not bias measured outcome changes.