The raw data reveal substantial dispersion in the rate of wage convergence experienced by immigrants originating in different countries, arriving at different times, and at different ages. The remainder of the empirical analysis attempts to understand the source of these differences.
The dependent variable in this section is f), the rate of wage growth experienced by a particular immigrant cohort (from country i, arriving in year j, and at age к) over the intercensal ten-year period. The “cross-country” analysis is initially restricted to a sample that contains 85 countries (listed in the Appendix), four age groups, and 4 year-of-migration cohorts. The analysis “stacks” the data. The 85 countries used in the study are chosen because immigrants bom in these countries can be matched across two successive Censuses, and these countries have sufficiently large numbers of observations in the 1970,1980, and 1990 Censuses to allow reliable estimation of the first-stage regressions in equation (12). The issue of cell size will be discussed in more detail below. About 92 percent of the immigrants who entered the United States between 1960 and 1979 originate in one of these 85 countries.
As noted earlier, one can think of the data reported in Table 1 as being calculated from the model in equations (12)-(14) where there are no standardizing variables in the vector X. It is of interest to determine the sensitivity of the rate of wage growth in the immigrant population (relative to that of natives) to differences in human capital across the groups, particularly educational attainment. I estimated the regression model in (12) including a vector of dummy variables indicating the worker’s educational attainment. The dummy variables indicate if the worker has less than 9 years of schooling; 9 to 11 years; 12 years; 13 to 15 years; or 16 years or more. The fixed effects vijk were then computed at the mean level of educational attainment for the entire immigrant sample.
Table 2 reports the education-adjusted log wage levels and rate of wage growth (relative to natives). Not surprisingly, the wage gap between immigrants and natives falls when we control for differences in educational attainment between the two groups. For example, the entry wage of the immigrants who migrated in 1970-74 and were 35-44 years old in 1980 is 20 percent lower than that of natives in the same age group, but is only 15 percent lower than that of natives who have the same age and educational attainment. The data also suggest that there is faster wage convergence between immigrants and natives if we adjust for differences in educational attainment. The relative rate of wage growth for the immigrants who arrived in the late 1960s and were 25-34 years old in 1970 was 7 percentage points in the first ten years, and an additional 4 percentage points in the second ten years. The education-adjusted rate of wage growth was 9 percentage points in the first 10 years, and another 5 percentage points in the second ten years.
It is useful to begin by summarizing the broad trends in the rate of wage growth in the immigrant population over the 1970-90 period. The first three columns of Table 1 report the wage of immigrants—relative to that of comparably aged natives—for each of the year-of-migration/age-at-arrival cohorts (aggregated over all national origin groups). Consider the immigrants who arrived in the United States between 1965 and 1969, and were 25-34 years old at the time of the 1970 Census enumeration. These immigrants earned 13 percent less than natives who were 25-34 years old in 1970. By 1980, the wage gap between the two groups (who were ten years older) had narrowed to 6 percent, and by 1990 (when the two groups were 20 years older) to 3 percent. The last two columns of the table report the rate of wage convergence implied by these wage data (AviJk This particular cohort experienced a rate of wages convergence of 7 percentage points in the first 10 years after arrival, and of another 4 percentage points in the second 10 years.
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.
The potential relationships between the log entry wage and the rate of wage growth are illustrated in Figure 1. These cases can be used to construct simple empirical tests that might distinguish among the various possibilities and provide valuable information about the human capital production function faced by immigrants. For example, suppose that there is weak relative complementarity in the production function. The variables that increase the immigrant’s effective human capital at the time of entry would then have the same qualitative effect on the log entry wage and on the rate of wage growth. In contrast, if there were relative substitution, then variables that increase effective human capital would have a positive impact on the log entry wage but a negative impact on the rate of wage growth. The empirical analysis presented below suggests that the data is best summarized by a “weak” positive correlation between log entry wages and the rate of wage growth. Put differently, immigrants with high levels of effective human capital experience both higher entry wages and faster economic progress in the United States. This finding suggests that the immigrant human capital production function exhibits weak relative complementarity.
A higher discounting factor, therefore, reduces the log entry wage while raising the relative rate of wage growth. Equations (6) and (9) replicate the conceptual experiment where initial earnings vary among workers who have the same initial human capital. This experiment is the basis for many of the discussions of the human capital model. Human capital investment steepens the age-eamings profile by reducing entry wages, raising future wages, and effectively generating a negative correlation between the log entry wage and the rate of wage growth.
Equation (4) shows that the rate of human capital investment is positively related to the discounting factor, and that the relationship between the rate of human capital investment and initial human capital depends on the sign of a + p -1. Suppose that all workers have the same discounting factor p. Relative neutrality then implies that all persons allocate the same fraction of time to the production of human capital. Highly skilled workers invest more if there is relative complementarity (a + P >1) and invest less if there is relative substitutability (a + P < 1).
Most of the empirical work in the human capital literature focuses on the life cycle trends in log earnings, and analyzes the determinants of the rate of growth of earnings (rather than of the absolute change in earnings). It is, therefore, analytically convenient to define a different type of neutrality in the production function. In particular, rewrite equation (2) as:
Equation (3) relates the percentage increase in the human capital stock to the fraction of efficiency units that are used for investment purposes during the investment period. Define
“relative neutrality” to occur when the relative increase in the human capital stock (g) depends only on the fraction of time devoted to investment (s), and not on the initial level of effective capital. Relative neutrality then occurs when a + p = 1. If a + P > 1, the relative returns from the investment (for a given time input) depend positively on the initial level of effective capital, and there is “relative complementarity.” Conversely, if a + p < 1, the relative returns from the investment are negatively related to the level of initial capital, and there is “relative substitutability.” Not surprisingly, the sign of (a + P – 1) plays a crucial role in determining the relationship between the log entry wage of immigrants and the subsequent rate of wage growth.
An immigrant lives for two periods after arriving in the United States, the investment period and the payoff period. During the investment period, the immigrant devotes a fraction s of his efficiency units (or of his productive time) to the production of additional human capital. This allocation of effort might be worthwhile because it increases the number of efficiency units available in the payoff period by g x 100 percent. The present value of the immigrant’s income stream in the United States equals:
where p is the discounting factor. It is instructive to think of p not only as a function of the immigrant’s discount rate, but also as measuring the probability that the immigrant will stay in the United States (and hence collect the returns on the part of the investments that are U.S.-specific). The parameter p, therefore, is smaller when the immigrant has either a high discount rate or a high probability of out-migration.
Beginning with Chiswick (1978), practically all studies of the economic progress of immigrants use the human capital model as a point of departure. The typical discussion argues that immigrants have a relative wage disadvantage at the time of entry because immigrants lack the U.S.-specific skills that are rewarded in the labor market. Moreover, the costs of acquiring human capital in the post-migration period (such as becoming proficient in English) are mainly incurred as foregone earnings, so that these initial human capital investments further depress entry wages for immigrants. Over time, as the immigrants reduce their human capital acquisitions and collect the returns on earlier investments, they experience faster wage growth than natives.