Education race, Supply of Skills and the Wage Skill Premium

We model a competitive labor market populated by workers who are heterogeneous
in wealth and skills, in which education plays a signaling role. We show that
whenever the accumulation of factors of production such has technology results in a
wider wage premium for skills over time – as it might happen under skill biased
technological progress – the investment in education needed to sustain a talent
separating equilibrium, in which skilled workers are able to perfectly signal their
skills, also increases. Hence, increases in the wage skill premium induce an education
race as skilled individuals try and invest more to signal themselves. However, if due
to imperfect capital markets, the borrowing capacity of poor individuals is lower
than that of rich ones, such race will eventually come to an end as poor and skilled
individuals are no longer able to finance the amount of investment needed to signal
their talent, and end up pooled together with unskilled and rich at a lower level of
education. Hence, the behavior of the long run supply of skills with respect to an
increase in the wage-skill premium is sluggish. Such mechanism supports a supply
side explanation –which complements the skill bias technological change hypothesis
– for the long run trends of (i) The wage-skill differentials and (ii) The relative
supply of postgraduates and college graduates in the US labor market.