A Matching Model with Endogenous Skill Requirements

In this paper, we consider a labor market in which workers differ in their abilities and jobs differ in their skill requirements. We take the distribution of worker abilities as given (a fraction p of the workers is low-skill, a fraction 1-p is high-skill), but we model the determination of skill requirements by firms. High-skill jobs produce more output than low-skill jobs; however, high-skill jobs require high-skill workers and thus are more difficult to fill. We use a matching model together with a Nash bargaining approach to wage setting to determine the equilibrium mix of job types, along with the equilibrium relationship between worker/job characteristics and wages. We derive implications for the distributions of unemployment durations across workers and of vacancy durations across jobs. <br> We use this model to examine the comparative static effects of a relative increase in the productivity of high-skill jobs (interpreted as "skill-biased technical change") and of changes in the mix of worker types in the labor force. Specifically, we examine how these changes affect aggregate unemployment and wage inequality via their effects on the equilibrium distribution of skill requirements. We also examine the effects of policy interventions such as unemployment compensation on the equilibrium.