Explicit expressions for the reservation wage path and the unemployment duration density in nonstationary job search models

Generally, job search models used in empirical analyses of unemployment durations are taken to be stationary, which is unrealistic in most cases. Stationarity is adopted because it is thought that nonstationary models are intractable and any empirical implementation would generate formidable computational burdens. This paper shows that, given a restriction on some variables in the nonstationary model, explicit and tractable expressions can be derived for the reservation wage path, the time path of the exit rate out of unemployment, the unemployment duration density and the expected duration of unemployment, in a continuous-time setting.