Discussion of Preston, 'Learning About Monetary Policy Rules When Long-Horizon Expectations Matter'

Abstract

Abstract: The design of interest rate rules for conducting monetary policy have recently been examined for two key concerns. The first issue is determinacy of equilibria. Indeterminacy (multiplicity of stationary rational expectations equilibria) is a concern in models of monopolistic competition and price stickiness are currently a popular framework for the study of monetary policy. The second issue is stability of equilibria under adaptive learning. Some interest rate rules do not perform well when the expectations of the agents get out of equilibrium, e.g. as a result of structural shifts. 1 Background The design of interest rate rules for conducting monetary policy have recently been examined for two key concerns. The first issue is determinacy of equilibria. Indeterminacy (multiplicity of stationary rational expectations equilibria) is a concern in models of monopolistic competition and price stickiness are currently a popular framework for the study of monetary policy. The second issue is stability of equilibria under adaptive learning. Some interest rate rules do not perform well when the expectations of the agents get out of equilibrium, e.g. as a result of structural shifts. Both determinacy and learning stability can be seen criteria for good monetary policy. (1) The recent literature has shown that the form of the interest rate rule is important in facilitating the learning process of the private agents. In adaptive learning economic agents are assumed to use an econometric model to forecast the future and they update their forecast functions as new data becomes available. In any period, the forecasts are input to agents' behavioral rules. The decisions of the agents are obtained by combining the forecasts and the behavioral rules and these decisions lead to a temporary equilibrium, i.e. an equilibrium in the current period given the forecasts and the agent's decisions. The formulation of agents' behavioral rules outside equilibrium is a major issue in the learning approach. Much of the literature has assumed that Euler equations under subjective expectations, which are a key part of individual first-order optimality conditions, provide the behavioral rules of the agents. The behavioral rules based on Euler equations are forward-looking but they look forward only one period ahead. Nevertheless, these rules have often been used even if the horizon of the agents is in principle infinite. (2) One-step forward-looking behavioral rules are a relatively crude way for representing individual behavior under the changing circumstances in adaptive learning. The one-period ahead margin is a key margin of optimality but one can envisage that longer horizons can also matter. 2 Preston's Contribution The central contribution of (Preston 2003) is the reformulation of individual behavioral rules for standard models of monetary policy in a way that gives a role to long-horizon forecasting. This is a useful contribution even if earlier papers have done the same in other contexts (see footnote 2 above). Let me briefly outline Preston's methodology using a simple permanent-income model for illustration. (3) There are two parts to the description of the agent's behavior. The agent's current decisions in terms of forecasts is logically the first part. Preston's approach consists of the following steps. 1. Formulate the household decision problem over the infinite future and derive the standard optimality conditions, i.e. the Euler equation and the intertemporal budget constraint. 2. Linearize the Euler equation and the intertemporal budget constraint at a nonstochastic steady state. 3. Iterate the linearized Euler equation and compute planned consumption for each future period s as a function of current consumption and anticipated interest rates in periods up to s-1. 4. Substitute the iterated Euler equations into the linearized intertemporal budget constraint and solve for current consumption. …