Job Matching with Finite Horizon and Risk Aversion

Abstract

The consequences of introducing risk-averse workers with a known, finite retirement age into a simple job-matching framework are explored. The job-matching model includes two jobs. In the "primary" job, workers and firms learn about the worker's productivity by observing his output over time. In the "secondary" job, productivity of any worker is known with certainty at the outset. Workers start off in the primary job but, based on their observed performance, may choose to switch to the secondary job. The model is developed in two stages. First, the finite retirement age is introduced while the usual assumption of risk-neutral workers is retained. In this model it is shown that all workers who achieve at least a certain cumulative output record, denoted r*, by a certain age, denoted T, will thereafter remain in the primary job until retirement. Those who do not achieve r* by age T switch to the secondary job at or before age T and remain there. Second, risk aversion is introduced along with finite retirement age. Here the turnover aspects of the equilibrium are similar to the risk-neutral case, but firms provide workers with wage insurance. This takes the form of wages that are downward rigid. As a result, it may be optimal ex ante for workers to delegate the job choice decision to the employer, and, ex post, not all separations will be voluntary for the work r.