Time inconsistency and reputation in monetary policy : a strategic modelling in continuous time

This paper develops a reputation strategic model of monetary policy with a continuous finite or infinite time horizon. By using the optimal stopping theory and introducing the notions of sequentially weak and strong rational equilibria, we give the conditions under which the time inconsistency problem may be solved with trigger reputation strategies not only for stochastic but also for nonstochastic settings even with a finite horizon. We provide the conditions for the existence of stationary sequentially strong rational equilibrium, and also completely characterize the existence of stationary sequentially weak rational equilibrium. We show that, under the assumption of the public's weak rational expectation or the certainty setting, the government will keep the inflation at zero if and only if a(1 ¡ µ) < 2. This inequality is satisfied if the rate of the aggregate output gain from the unanticipated inflation, a, is small (less than 2) or the government puts more weight on stabilizing output than on stabilizing inflation (µ > 1). Furthermore, we investigate the robustness of the sequentially strong rational equilibrium behavior solution by showing that the imposed assumption is reasonable.