Survey_OW_2003

Abstract

As a laboratory for our experiment, we employ a simple linear model of the U.S. economy with characteristics similar to more elaborate models frequently used to study optimal monetary policy. We assume that economic agents know the correct structure of the economy and form expectations accordingly. But, rather than endowing them with complete knowledge of the parameters of these functions—as would be required by imposing the rational expectations assumption—we posit that economic agents rely on finite memory least squares estimation to update these parameter estimates. This setting conveniently nests rational expectations as the limiting case corresponding to infinite memory least squares estimation and allows varying degrees of imperfection in expectations formation to be characterized by variation in a single model parameter. We consider a stylized model that gives rise to a nontrivial inflation-output variability tradeoff and in which a simple one-parameter policy rule represents optimal monetary policy under rational expectations. We begin by considering the “textbook” case of rational expectations with perfect knowledge in which private agents know both the structure of the economy and the central bank’s policy. In this case, expectations are rational in that they are consistent with the true data generating process of the economy (the model). As the perfect knowledge solution shows, private inflation forecasts depend on knowledge of the structural model parameters and of policymaker preferences. In addition, these parameters influence the expectations formation function nonlinearly. We now relax the assumption that private agents have perfect knowledge of all structural parameters and policymaker preferences. Instead, we posit that agents must somehow infer the information necessary for forming expectations by observing historical data, in essence acting like econometricians who know the correct specification of the economy but are uncertain about the parameters of the model. In particular, we assume that private agents update the coefficients of their model for forecasting inflation using least squares learning with finite memory. We focus on least squares learning because of its desirable convergence properties, straightforward implementation, and close correspondence to what real-world forecasters actually do. Estimation with finite memory reflects agents’ concern for changes in the structural parameters of the economy. To focus our attention on the role of imperfections in the expectations formation process itself, however, we deliberately abstract from the introduction of the actual uncertainty in the structure of the economy which would justify such concerns in equilibrium.