The regression model in (12) is estimated separately in each Census year. To simplify the notation, I denote the adjusted wage of the “comparable” group of native workers by vn0t(/).u Consider initially the model where the standardizing vector X does not contain any variables. The vector of fixed effects in the immigrant population then gives the average log wage in each country-of-origin/year-of-migration/age-at-arrival cell, while the fixed effect in the native population gives the average log wage of natives in a particular age group. For example, v^it) may give the average 1970 log wage for Mexican immigrants who arrived between 1965 and 1969 and who were 25-34 years old as of 1970. The respective fixed effect vn0k(t) in the native population then gives the average 1970 log wage for natives who were 25-34 years old as of 1970.
Suppose we estimate the cross-section regression model in two different calendar years, say t and f. We can use the estimated fixed effects to calculate the rate of wage growth of immigrants over the calendar-time interval (t, t’) as:
If the vector X did not contain any standardizing variables, equation (13) defines the mean rate of wage growth for cohort (i,j, к), and equation (14) defines the cohort’s rate of wage growth relative to that observed in a comparably aged group of natives.
I restrict the study to the immigrant cohorts who arrived between 1960 and 1979. The Census data define four year-of-migration cohorts within this period: immigrants who arrived in 1960-64, 1965-69, 1970-74, and 1975-79. The immigrant cohorts will also be defined in terms of four age groups, where the age of the immigrant is observed at the time the Census is taken: immigrants who are 25-34, 35-44,45-54, and 55-64 years old.