Determinacy, Learnability, And Plausibility In Monetary Policy Analysis: Additional Results

Abstract

In contrast with recent research in monetary policy analysis which has featured a great deal of work concerning conditions for determinacy, I have argued in recent publications that least-squares (LS) learnability is a compelling necessary condition for a rational expectations (RE) equilibrium to be considered plausible. As I have demonstrated in a previous paper, in a very wide class of linear RE models, determinacy implies LS learnability (but not the converse) when individuals have knowledge of current conditions available for use in the learning process. This strong result does not pertain, however, if individuals have available, in the learning process, only information regarding previous values of endogenous variables. One task of the present paper, accordingly, is to investigate the situation that is obtained when only lagged information is available. In particular, it is shown that models that are well formulated, often (but not invariably) possess the property of E-stability and hence LS learnability if current-period information is available in the learning process, even if determinacy does not prevail. Thus plausibility of a RE solution requires both that it be learnable and that the model at hand be well formulated. A sufficient condition for both of these to hold, requiring that certain matrices have positive dominant diagonals, is introduced and considered. Unfortunately, the situation in the case of lagged information is less favorable—that is, learnability can be assured only in special cases, for which no general characterization has been found.