Up(and down)-skilling and directed technical change

In this paper we develop a dynamic general equilibrium analog to the Roy model. Specifically, the economy is populated by heterogeneous agents who differ in ability and sort into skilled and unskilled jobs. Because skilled jobs use ability with greater intensity, high (low) ability workers sort into skilled (unskilled) jobs. As in other frameworks, this endogenous cutoff ability depends on the economy's technology and distribution of workers. In contrast to existing' assignment' models, we incorporate endogenous skill- or, more aptly, ability - biased technical change. We use our framework to engage in a number of comparative statics. Our model fs tractability allows us to contrast the short and long-run effects of changes to the economy's fundamentals. We show that, for commonly used distributions, a first order stochastic dominance (FOSD) increase in the ability distribution raises the ability requirement to work in skilled jobs in the short run. In contrast, the long-run cutoff ability may actually decline. More generally, the technological response always dampens the increase in ability requirements.