Robust monetary policy with imperfect knowledge

Abstract

We examine the performance and robustness properties of monetary policy rules in an estimated macroeconomic model in which the economy undergoes structural change and where private agents and the central bank possess imperfect knowledge about the true structure of the economy. Policymakers follow an interest rate rule aiming to maintain price stability and to minimize fluctuations of unemployment around its natural rate but are uncertain about the economy's natural rates of interest and unemployment and how private agents form expectations. In particular, we consider two models of expectations formation: rational expectations (RE) and learning. We show that in this environment the ability to stabilize the real side of the economy is significantly reduced relative to an economy under RE with perfect knowledge. Furthermore, policies that would be optimal under perfect knowledge can perform very poorly if knowledge is imperfect. Efficient policies that take account of private learning and misperceptions of natural rates call for greater policy inertia, a more aggressive response to inflation, and a smaller response to the perceived unemployment gap than would be optimal if everyone had perfect knowledge of the economy. We show that such policies are quite robust to potential misspecification of private sector learning and the magnitude of variation in natural rates.

Introduction

To paraphrase Clausewitz, monetary policy is conducted in a fog of uncertainty. Our understanding of many key features of the macroeconomic landscape remains imperfect, and the landscape itself evolves over time. As emphasized by McCallum (1988) and Taylor (1993), a crucial requirement for a monetary policy rule is that its good performance be robust to various forms of model misspecification. In this view, it is not enough for a monetary policy rule to be optimal in one specific model, but instead it must be “stress tested” in a variety of alternative model environments before one can conclude with any confidence that the policy is likely to perform well in practice.¹ In this paper, we examine the performance and robustness of monetary policy rules in the context of fundamental uncertainty related to the nature of expectations formation and structural change in the economy. Our goal is to identify characteristics of policy rules that are robust to these types of imperfect knowledge, as well as to identify those that are not.

The first form of uncertainty facing the policymaker that we consider relates to the way in which agents form expectations. There is a growing literature that analyzes a variety of alternative models of expectations formation. The key conclusion we take from our reading of this literature is that there is a great deal of uncertainty regarding exactly how private expectations are formed. In particular, the standard assumption of rational expectations (RE) may be overly restrictive for monetary policy analysis, especially in the context of an economy undergoing structural change. But, the available evidence does not yet provide unequivocal support for any other single model of expectations formation. Therefore, fundamental uncertainty about the nature of expectations formation appears to be an unavoidable aspect of the policy environment facing central banks face today.

In this paper, we consider two popular alternative models of private expectations formation. Our approach can easily be extended to incorporate other alternative models of expectations as well, but for reasons of tractability, we leave this for future research. One model is RE, which assumes that private agents know all the parameters of the model and form expectations accordingly. This, of course, is the model used in much of the recent monetary policy rule literature. The second model is perpetual learning, where it is assumed that agents do not know the true parameters of the model, but instead continuously reestimate a forecasting model (see Sargent, 1999, Evans and Honkapohja, 2001 for expositions of this model). This form of learning represents a relatively modest, and arguably realistic, deviation from RE. An advantage of the perpetual learning framework is that it allows varying degrees of deviations in expectations formation relative to the RE benchmark, which are characterized by variation in a single model parameter. As shown in Orphanides and Williams, 2005a, Orphanides and Williams, 2005b, Orphanides and Williams, 2005c), perpetual learning on the part of economic agents introduces an additional layer of interaction between monetary policy, expectations, and economic outcomes.

The second source of uncertainty that we consider is unobserved structural change, which we represent in the form of low-frequency variation in the natural rates of unemployment and interest. The equilibrium of our model economy is described in terms of deviations from these natural rates. In particular, the inflation rate is in part determined by the unemployment gap, the deviation of the unemployment rate from its natural rate. Similarly, the unemployment rate gap is determined in part by the real interest rate gap, the difference between the real short-term interest rate and the real natural rate of interest. We assume that the central bank does not observe the true values of the natural rates and, indeed, is uncertain about the processes generating the natural rates.

Natural rate uncertainty presents a difficulty for policymakers who follow an interest rate rule with the goal of maintaining price stability and minimizing fluctuations of unemployment around its natural rate. With perfect knowledge of natural rates, the setting of policy would ideally account for the evolution of the economy's natural rates. But, if policymakers do not know the values of the natural rates of interest and unemployment when they make policy decisions, they must either rely on inherently imprecise real-time estimates of these rates for setting the policy instrument, or, alternatively, eschew natural rates altogether and follow a policy rule that does not respond to natural rate estimates.

The evidence suggests there exists considerable uncertainty regarding the natural rates of unemployment and interest and ambiguity about how best to model and estimate natural rates, even with the benefit of hindsight.²${}^{,}$³ Indeed, the measurement of the natural rate of output has been a key issue in U.S. monetary policy debates in both the 1970s and 1990s, and uncertainty about the natural rate of interest has been the topic of increasing discussion. The evidence indicates that substantial misperceptions regarding the economy's natural rates may persist for some time, before their presence is recognized. In the meantime, policy intended to be contractionary may actually inadvertently be overly expansionary, and vice versa. Moreover, in an environment where the private sector is learning, the learning process can interact with the policy errors and feed back to economic outcomes, as pointed out by Orphanides and Williams, 2005a, Orphanides and Williams, 2005b, Orphanides and Williams, 2005c and Gaspar et al. (2006).

We examine the effects and policy implications of imperfect knowledge of expectations formation and unknown time-varying natural rates using a quarterly model of the U.S. economy estimated over 1981–2004. We first consider the performance and robustness characteristics of simple operational monetary policy rules under perfect and imperfect knowledge. We then analyze the characteristics and performance of policy rules optimized taking into account model uncertainty about expectations formation and natural rate uncertainty. We approach this problem of optimal policy under uncertainty from Bayesian and Min–Max perspectives and compare the results.

Our analysis yields several key findings. First, the scope for stabilization of the real economy in our model with imperfect knowledge is significantly reduced relative to the economy under perfect knowledge (where private agents and the central bank are assumed to know all features of the model). Second, monetary policies that would be optimal under perfect knowledge can perform very poorly when knowledge is imperfect. Third, the optimal Bayesian policy under uncertainty performs very well across all of our model specifications and is therefore highly robust to the types of model uncertainty that we examine here. This policy features greater policy inertia, a larger response to inflation, and a smaller response to the perceived unemployment gap than would be optimal under perfect knowledge.

The remainder of the paper is organized as follows. Section 2 discusses the problems for monetary policy caused by natural rate mismeasurement. Section 3 briefly describes the estimated macro model. Section 4 describes the class of monetary policy rules that we study. Section 5 presents the models of expectations formation and natural rate estimation. Section 6 provides details on the simulation method. Section 7 analyzes monetary policy under different models of expectations formation, but assuming constant natural rates. Section 8 explores the joint effects of alternative models of expectations and time-varying natural rates. Section 9 examines the optimal Bayesian and Min–Max policies. Section 10 concludes.