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.
JEL classification: E61, E52, C61
The author acknowledges particularly helpful discussions with Chris Phelan on the relation between this work and his independent work with Ennio Stachetti (Phelan and Stachetti 1996). He also thanks Costas Azariadis, Peter Ireland, Finn Kydland, Bruce Smith, Steve Williamson, and the participants of seminars at Cornell University and the 1996 SEDC meetings for useful comments. The views expressed here are those of the author and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the author's responsibility.
Please address questions of substance to Roberto Chang, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, N.W., Atlanta, Georgia 30303-2713, 404/498-8057, 404/498-8956 (fax), firstname.lastname@example.org.
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