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.

The human capital production function is:
where a < 1 because of diminishing marginal productivity to human capital investments. Beginning with Ben-Porath (1967), the value of the parameter p has been a matter of debate in the human capital literature. Highly skilled immigrants may be more adept at acquiring additional human capital. This complementarity between “pre-existing” human capital and the skills acquired in the post-migration period would suggest that (3 is positive. Because the costs of human capital investments are mostly foregone earnings, however, it may be that highly skilled workers find it very expensive to augment their human capital stock. This “substitutability” would then suggest that P is negative.
The Ben-Porath specification of the human capital production function assumes “neutrality,” so that the two effects cancel each other and P is zero. Holding p constant, the neutrality assumption states that all workers invest the same dollar amount in human capital, regardless of their initial endowment. All workers then get the same dollar increase in earnings in the payoff period. As a result, the dollar age-eamings profiles of different workers are parallel to each other. The neutrality assumption also implies that the log age-eamings profiles of different workers must converge because the payoff from human capital investment is relatively smaller for more skilled workers.