Although the female percentage is reported in Table 3.9,

we exclude it from our equations because we think it represents at least partly the supply side. Proper econometric estimation of the joint (supply and demand) determination of the wage-effort offer curve with heterogeneous workers is beyond the scope of this paper. The data do indicate that females tend to be employed in labor-intensive (i.e. low wage-low hours) sectors.
Proper treatment of the human capital variable is another delicate task, which has been discussed more fully in Leamer(1996). Here we note that the model depicted in Figure 2.1 is based on the assumptions that workers are fully charged for the capital they use and that the wage we observe is total earnings net of all capital charges. To put it another way, we assume that workers do not bring their own tools to the workplace, and we assume also that workers have no other sources of wealth that can be used to finance consumption.

Both of these assumptions are violated by human capital, first because the wage that we observe is not net of the implicit human capital rental costs16 and second because human capital acquired in formal education is partly financed by the government and by the worker’s parents. Absent these two problems, we could simply combine human and physical capital into a single capital aggregate.

This is illustrated in Figure 3.9 which depicts three different jobs with differing fixed levels of human capital inputs and the same fixed level of physical capital inputs. One job uses physical capital only, the second job uses the same physical capital but also self-financed human capital, and the third job is the same as the second except that the human capital is provided without cost to the worker. The envelope of preferred contracts absent free education is the heavy wage-effort offer curve in Figure 3.9 which has the same character as the wage-effort offer curves that we have been discussing. Namely, the high-effort high (net) wage contracts are intensive in human capital. If the human capital is provided free of charge, then the offer line facing the educated worker has the slope of the original educated worker line but the intercept of the no-education line. This line of contracts with free-edu с at ion completely dominates the contracts if education is charged to the workers.

Empirically, there are a number of directions that this discussion of education could lead. One is nowhere. If education is free and everyone has the same ability, then the regressions of wages and hours on capital-intensity define the wage-effort offer curve. It may be that the educational requirements vary along the curve, but that is entirely immaterial because workers do not incur a cost for the education. If education is free, but ability is heterogeneous (and unobservable) and interacts with education, then we are in a lot of trouble and don’t want to talk about it.

If human capital is self-financed, then ideally we would amend equation (3.1) and (3.2) by aggregating human with physical capital, and by subtracting from weekly wages a term that is proportional to human capital and that represents the human capital rental charges. We don’t know how to aggregate years of education with dollars of physical capital and we don’t know what is the implicit rental rate of human capital to net from wages. What we do is add the human capital variable to our equations, and hope for the best, recognizing that our wage equation is gross of human capital rental charges but net of physical capital rent.. We plan on revisiting the issues of educational financing and heterogeneity in ability in subsequent work. legitimate payday loans