Equilibrium Search with Time‐Varying Unemployment Benefits

Abstract

We show how time-varying unemployment benefits can generate equilibrium wage dispersion when identical firms post wages and homogeneous risk-averse workers search for jobs. We model a two-tier system similar to real-world UI programmes. The unemployed initially receive benefit b. Eventually, if a worker does not find a job, the benefit falls to s. The duration of high benefits is treated as an exponential random variable, so the model is stationary. We characterise the equilibrium and derive the comparative statics effects of changes in the two benefit levels and the expected duration of the high-benefit state on equilibrium wages and unemployment. In this article, we analyse the implications of time-varying unemployment insurance in an equilibrium search model. We consider a two-tier system, i.e., a system with a high and a low benefit level. This is the form taken by most real-world UI programmes. Unemployed workers initially receive unemployment compensation but eventually, if a worker does not find a job in the meantime, this benefit is terminated. The worker then has access only to lower social assistance benefits or in some countries to no benefits at all. Specifically, we consider an economy in which newly unemployed workers initially receive unemployment benefits at rate b. Eventually, if a worker does not find and accept a job in the meantime, the unemployment benefit falls to a lower level, s. We assume the event that triggers the fall from b to s occurs at Poisson rate k. 1 This allows us to do our equilibrium analysis in a stationary framework while focusing on the most important aspect of time-varying unemployment compensation, namely, that after some point the benefit falls. This representation of time-varying unemployment compensation enables us to derive a two-point equilibrium wage distribution in a simple stationary setting. We derive this equilibrium distribution using a wage-posting model of sequential search. We allow for free entry and exit of jobs and for matching frictions in the sense that the rate at which unemployed workers and vacant jobs contact one another depends on overall labour market tightness. The use of a matching function to determine the job contact rate for workers (and the worker contact rate for jobs) is relatively unusual in wage-posting models, which typically assume a fixed contact rate. Our model can thus be viewed * We thank participants at the Tinbergen Institute’s Conference on Search and Assignment for useful comments. In particular, we thank Gerard van den Berg, who shared notes with us on an alternative approach to the topic of this paper. We also thank Lucas Navarro for valuable research assistance. 1 Our model can be interpreted as one in which the search activity of unemployed workers is imperfectly monitored by a government agency. Suppose unemployed workers are punished by a reduction in their benefits from b to s when found to be putting forth less search effort than required and that detection of insufficient search effort occurs at Poisson rate k. If all workers choose to put forth less than the required effort ‐ and this is a plausible assumption, given that workers are homogeneous ‐ then this sanctions model is equivalent to our model with time-varying benefits. That is, our model can