Investigating the Effect of the Optimality Constraint on Parameter Estimates in a Job Search Model

Abstract

In a standard job search model, an unemployed worker maximizes the expected present discounted value of his income stream while facing a stationary environment. It can be shown that the optimal policy for the worker to follow is a reservation wage policy. This involves the worker accepting wages above a certain cut-off wage called the reservation wage and rejecting others. The implicit equation defining this reservation wage is termed the optimality constraint in the job search literature. The optimality constraint implies a specific relationship between the reservation wage, the arrival rate of offers, the wage distribution, the discount rate and the unemployment benefit. The goal of this paper is to study the effect of the imposition of the optimality constraint in a simple job search model. I compare estimates of parameters obtained when the optimality constraint is imposed to those obtained when the constraint is not imposed. This constraint is also tested for a given set of data. Although it is difficult to impose, this constraint has been used to identify the parameters of a job search model. Some studies, including Lancaster and Chesher(1988) use the optimality constraint to deduce the effect of the unemployment benefit on the reservation wage and the mean duration of unemployment. Studies that do not use the optimality constraint often assume that the reservation wage is a linear function of explanatory variables and deduce elasticities using a regression approach as in Ehrenberg and Oaxaca(1976). Studies so far do not compare parameters estimates obtained with and without the optimality constraint, which is the contribution of my paper.