We model a labor market in which workers’ level of education might be a signal of skills. We show that whenever the wage premium for education increases over time – as it might happen under skill biased technological progress – the investment in education needed to sustain a separating equilibrium in which skilled workers perfectly signal their type, also increases. Hence, an increase in the education wage premium induces an education race. If the borrowing capacity of poor workers is lower than that of rich ones due to capital market imperfections, poor-skilled workers will finally fall behind in this race – and pool together with some unskilled ones – as the investment they would have to undertake to signal their type eventually becomes unaffordable to them. Such mechanism supports a supply side explanation for the joint long run trends of (i) the education wage premia, and (ii) the relative supply, of postgraduates and college graduates in the US labor market, which complements the demand based explanation for wage skill premia based on skill bias technological change hypothesis