Timing and time inconsistency in search models

This paper studies how the timing assumption matters for the commitment problem and time inconsistency issue in search models with unemployment insurance. We analyze the Markov equilibrium without commitment and the Ramsey policy with commitment under two different timing assumptions. In the first timing, consumption takes place before search within each period; in the second, search takes place before consumption. Time inconsistency occurs mainly through search disincentive under the first timing, but only indirectly under the second timing. We show theoretically and numerically that the magnitude of time inconsistency is stronger under the first timing.