A Multiplicative Model of Investment in Human Capital

Abstract

The purpose of this paper is to analyze the effects of changes in exogenous parameters such as the interest rate, the length of the working period and initial endowments on the shape of the observed earnings profile. Though this problem can be treated in general, we shall restrict ourselves to the following "inverse optimal" problem: find a form of the trade-off function between current and future earnings which leads to a logarithmic earnings function. In the paper we demonstrate that logarithmic earning functions can be derived from optimal behavior. Specifically, the simple case which we analyze leads to piece wise linear log earnings functions. Such a derivation has the advantage that the effects on earnings of exogenous factors can be consistently analyzed. The model is sufficiently simple to allow a clear exposition of the basic elements which govern earnings in a static world. The same elements appear in the more complicated derivations currently available in the literature but it is more difficult to trace their impact. The multiplicative model provides additional information on the robustness of the results previously derived from the Ben-Porath specification. This is particularly important since the "production function" for human capital is not directly observable and alternative specification can only be compared in terms of their implications with respect to observed earnings.