A Continuous-Time Model of Monetary Policy and Inflation: A Stochastic Differential Game

Abstract

Cuckierman and Meltzer (1986) and Başar and Salmon (1988) have recently studied, in the discrete time, a stochastic model of monetary policy and inflation, that incorporates asymmetric information between the private sector and the monetary authority. In this model, the private sector is a passive player who simply forms conditional (rational) expectations of the current inflation rate, which constitutes the surprise component of the policy maker’s (the monetary authority) objective function. The policy maker strives to maximize the objective function by choosing a control policy which also affects the information carried to the passive player whose rational expectations in turn influence the performance of that policy. Under an asymmetric mode of decision making, the model leads to a stochastic control problem of the nonneutral type, whose solution involves active learning. The complete solution to this nonstandard dynamic optimization problem has been obtained by Başar (1988), by developing an indirect approach that necessitates the introduction of a sequence of zero-sum games. This solution corresponds to a Stackelberg solution for the original game, where the monetary authority is the leader. If instead, the roles of the decision makers are taken to be symmetric, while still retaining the asymmetry in the information structure, we obtain the Nash equilibrium solution, which is the one that was discussed by Cuckierman and Meltzer (1986); see also Başar and Salmon (1989) for a discussion of that point.