Bayesian Analysis of the Prototypal Search Model

Bayesian analysis for a simple but widely applied dynamic programming model is obtained. The setting is the prototypal job-search model. The general case of wage and duration data, with potential censoring, is studied. The optimality condition implied by the dynamic programming setup is fully imposed. The posterior distribution reveals a “ridge” reflecting the characteristic nonstandard nature of the inference problem. Marginal distributions and moments are obtained in a canonical parameterization after a suitable approximation. The adequacy of the approximation is easily assessed. Simulation is applied to study alternative parameterizations and prior robustness and to facilitate prior elicitations. Finally, we illustrate the applicability of our methods by giving posterior distributions for the elasticities of unemployment durations and reemployment wages with respect to unemployment income. Our analysis is easy to implement and all computations are simple to perform.