Credible Monetary Policy with Long-Lived Agents : Recursive Approaches

This paper develops recursive methods that completely characterize all the time-consistent equilibria of a class of models with long-lived agents. This class is large enough to encompass many problems of interest, such as capital- labor taxation and optimal monetary policy. The recursive methods obtained are intuitive and yield useful algorithms to compute the set of all time-consistent equilibria. These results are obtained by exploiting two key ideas derived from dynamic programming. The first developed by Abreu, Pearce, and Stachetti in the context of repeated games and by Spear and Srivastava and Green in the context of dynamic principal agent problems is that incentive constraints in infinite horizon models can be handled recursively by adding as a state variable the continuation value of the equilibrium. The second insight, due to Kydland and Prescott, is that the set of competitive equilibria of infinite horizon economies can often, in turn, be characterized recursively. I illustrate my methods by discussing optimal and credible monetary policy in a version of Calvo's (1978) model of time inconsistency. The set of time-consistent outcomes can be completely characterized as the largest fixed point of either of two well-defined operators, one motivated by Abreu, Pearce, and Stachetti (1990) and the other by Cronshaw and Luenberger (1994). In addition, recursive application of either of these two operators provides an algorithm that is shown to always converge to the set of time-consistent outcomes. Finally, the recursive method developed here yields valuable information about the nature of the time-inconsistency problem