Unemployment and Human Capital∗

The paper explores the interaction between sector-specific human capital accumulation and sector-specific productivity or demand shocks. Our objective is to better understand the determinants of skill and experience premia, the costs of displacement for workers with long job tenure, and the nature of unemployment among such workers. For example, our model suggests why skilled workers can remain unemployed indefinitely even though low wage jobs are readily available and are acceptable to unskilled workers. We develop a version of the Lucas and Prescott (1974) search model with sector-specific human capital. Competitive firms in each sector hire skilled and unskilled workers to produce an intermediate good. The intermediate goods produced in different sectors are combined by a competitive final goods producer to generate a consumption good using a constant returns to scale technology. Unskilled workers are free to work in any sector, while skilled workers have sector-specific human capital, although they can always leave the sector to become unskilled. Skills are accumulated while working in a sector, with an unskilled worker becoming skilled at a constant rate. Finally, sectoral productivity is continuously buffeted by idiosyncratic shocks. Thus the state of a sector is described by its productivity and the number of skilled workers. We assume that log productivity follows a random walk, i.e. the growth rate of productivity is independent of its level. We show that equilibrium behavior depends on a single state variable ω, a linear combination of the sector’s log productivity and the log of the number of skilled workers (see also Alvarez and Shimer, 2009). The value of being a skilled worker is increasing in ω, as is the ratio of unskilled to skilled workers. An increase in the number