THE ECONOMIC PROGRESS OF IMMIGRANTS: Conceptual Framework 4

iEquation (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).

Of course, we seldom have data on the fraction of time that workers allocate to human capital investments. However, we do observe the earnings histories of workers. Let Д be the relative wage growth experienced by an immigrant over his post-migration life cycle:
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Holding constant the immigrant’s initial endowment of human capital, the theory implies that immigrants with higher p’s (and hence lower discount rates or probabilities of out-migration) experience faster wage growth. The relationship between the rate of wage growth and the initial level of effective human capital, however, is more complicated:
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The correlation between the rate of wage growth and initial human capital depends on the sign of a + (3 – 1. If there is relative complementarity in the human capital production function, relative wage growth will be higher for immigrants who have higher levels of effective human capital. In contrast, if there is relative substitutability—and higher levels of effective human capital make it costly to acquire additional human capital—the most skilled immigrants experience less relative wage growth.
The model can be used to determine the correlation between log entry wages and the rate of wage growth. The log entry wage of the immigrant is:
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It is instructive to begin the discussion of the relationship between log w0 and A by considering the simpler case where the only exogenous variation in the immigrant population is in the discounting factor p. One can show that:
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