Instrument Rules, Inflation Forecast Rules and Optimal Control Rules When Expectations are Rational

Abstract

Over the last decade, as a number of industrialised countries¹ have gone over to the use of explicit inflation targets, there has been a resurgence of interest in the use of feedback rules to characterise monetary policy. In this paper we consider how the type of rule suggested by the methods of optimal control can be derived when the model we have of an economy is non-linear and the model contains forward-looking expectations. Although the literature in this area is voluminous, there is still considerable interest in seeking computational improvements to existing algorithms² and in deriving methods that can be applied to the highly non-linear, and analytically intractable, dynamic, stochastic general equilibrium models that have grown out of the original real business cycle methodology. Although the methods we describe in this paper could be applied to this class of model, we confine our attention here to non-linear models more in the Cowles Foundation tradition.³ One approach to the problem of dealing with non-linear, rational expectations models is to apply direct methods such as the Penalty Function method of Holly and Zarrop (1983), or the extended path methods associated with Anderson, Fair and Taylor used for solution and estimation, or for computing time consistent solutions (see Hall, 1986). The disadvantage of this approach, in the context of this paper, is that the solutions are in open-loop form; there is no explicit control rule that can be compared directly to other forms of rule existing in the literature.