A Discrete-Time Stochastic Model of Job Matching

Abstract

In this Paper, an explicit micro scenario is developed which yields a well-defined aggregate job-matching function. In particular, a stochastic model of job-matching behavior is constructed in which the system steady state is shown to be approximated by an exponential-type matching function, as the population becomes large. This steady-state approximation is first derived for fixed levels of both wages and search intensities, where it is shown (without using a free-entry condition) that there exists a unique equilibrium. It is then shown that if job searchers are allowed to choose their search intensities optimally, then this model is again consistent with a unique steady state. Finally, the assumption of a fixed wage is relaxed, and an optimal "offer wage" is derived for employers.

Keywords: Matching function, large population approximation, optimal search intensity

JEL Classification: D83, J41, J61