Policy-Dependent Parameters in the Presence of Optimal Learning: An Application of Kalman Filtering to the Fair and Sargent Supply-Side Equations

Abstract

Lucas' criticism was an important step in the development of rational expectations and the ensuing debate over policy-effectiveness. In a macro framework, where the main interest is on the effect of monetary policy on output, the Lucas criticism implies that changes in policy feedback rules will result in systematic changes in estimated models.' (See, for example, Barro (1977, 1978).) Kydland and Prescott (1977) and Calvo (1978) pointed out another implication of rational expectations for policy-making; if policy-makers are following a rule at time t, they may find it optimal to switch to another rule at some future time t + T, T > 0. Of course, a certain amount of parameter variability may be found in all econometric models. However, if the main source of parameter variability in the model is the lack of a learning mechanism about the behavior of the policy-maker, then the incorporation of a continuously-adjusting policy expectations mechanism would reduce parameter variation. Thus, if the rational expectations specification is the proper way to specify models, one may expect relatively less parameter variability in those models which make use of policy anticipations than those models which do not.2 This paper attempts to address the issues of parameter variability and parameter policy dependence by an analysis of two supply-side equations. One equation is from the Fair model, which does not incorporate rational expectations, and the other is from the Sargent model, which does. The parameter variability and parameter policy-dependence of these two equations are explored in three ways. First, the timevarying estimates in the Fair and Sargent supply-side equations are obtained with the Kalman filter algorithm, and the parameter variations of the two equations are compared. Second, Sargent's model is estimated with two different policy expectations mechanisms-one in which the expectation rule remains fixed during the sample period, and the other in which the expectation rule is allowed to adjust as new information becomes available. These estimates are compared to see if variation is reduced when expectations adjust at each time period. Finally, since the estimates themselves form well-defined stochastic processes, a series of Granger causality tests is presented to show if the variations in these estimated parameters are indeed caused' by changes in policy variables.