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.
Before proceeding to an analysis of the model, it is worth noting that relative neutrality implies human capital complementarity in the Ben-Porath sense. After all, if the log age-eamings profiles are parallel across different workers, more skilled workers must be investing more in human capital. An empirical finding of relative neutrality or relative complementarity, therefore, would necessarily imply “Ben-Porath complementarity” in the production of human capital.
Workers choose the rate of human capital investment (5) that maximizes the present value of earnings. The first-order condition to the maximization problem implies that: