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.
However, this negative correlation can potentially break down when the entry wage is lower because the effective level of human capital is itself lower. In particular:
The positive sign of the first term inside the brackets of (10) indicates that the larger level of effective human capital raises entry wages simply because the additional skills are valued by American employers. At the same time, the larger human capital endowment alters the rate of human capital investment. Define к* as:
By definition, the log entry wage is independent of the initial endowment of human capital when a + p – 1 = к*. Figure 1 illustrates the four cases that summarize the potential relationship between log entry wages and the rate of wage growth of immigrants:
1. Relative substitution between pre- and post-migration human capital (a + P < 1). Immigrants endowed with a substantial level of effective human capital find it expensive to augment their stock in the United States. There is then a negative correlation between log entry wages and the rate of wage growth. Skilled immigrants invest less, earn more at the time of entry, and have a smaller rate of wage growth.
2. Relative neutrality in the human capital production function (a + p = 1). All workers have the same rate of investment (s). The correlation between the log entry wage and the rate of wage growth is zero.
3. Weak relative complementarity in human capital (0 < a + p – 1 < к*). Skilled immigrants then invest more in human capital, have higher entry wages, and also have a higher rate of wage growth. There is, therefore, a positive correlation between the log entry wage and the rate of wage growth.
4. Strong relative complementarity in human capital (0 < к* < a + P – 1). Skilled immigrants invest so much in human capital that they actually earn less at the time of entry, but experience faster wage growth. There is again a negative correlation between the log entry wage and the rate of wage growth.