Timing and Time Inconsistency in Search Models

We study how timing assumption matters for the commitment problem and time inconsistency in search models with unemployment insurance. We analyze the Markov equilibrium without commitment and the Ramsey policy with commitment under two different timings. The first timing is where consumption takes place before search within each period, and the second timing is where search takes place before consumption. We show that 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