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The optimal control approach to monetary policy has garnered increased attention in recent years. Optimal control policies, however, are designed for the specific features of a particular model and therefore may not be robust to model misspecification. One important source of potential misspecification is how agents form expectations. Specifically, whether they know the complete structure of the model as assumed in rational expectations or learn using a forecasting model that they update based on incoming data. Simulations of an estimated model of the U.S. economy show that the optimal control policy derived under the assumption of rational expectations can perform poorly when agents learn. The optimal control approach can be made more robust to learning by deemphasizing the stabilization of real economic activity and interest rates relative to inflation in the central bank loss function. That is, robustness to learning provides an incentive to employ a “conservative” central banker. In contrast to optimal control policies, two types of simple monetary policy rules from the literature that have been found to be robust to model misspecification in other contexts are shown to be robust to learning.

For nearly as long as macroeconomic models have existed, economists have been drawn to the idea of applying optimal control theory to the problem of monetary policy (see Chow, 1976, for an early example). Support for the use of optimal control for policy has waxed and waned, reflecting in part swings in economists’ confidence in macroeconometric models. Recently, interest in the optimal control approach to monetary policy among academics and central banks has re-emerged, as spelled out in contributions by Svensson (2002), Svensson and Woodford (2003), Woodford (2003), Giannoni and Woodford (2005), and others. As described in Svensson and Tetlow (2006), analytical and computational advances now make it possible to operationalize this approach using the Federal Reserve Board's large-scale nonlinear macroeconomic model and other models. One potential shortcoming of the optimal control approach is that it ignores uncertainty about the specification of the model. Although in principle one could incorporate various types of uncertainty into the analysis of optimal policy, in practice this is infeasible given current methods and computational power. As a result, existing optimal control policy analysis is done using a single reference model. Levin and Williams (2003) found that optimal control policies can perform very poorly if the central bank's reference model is badly misspecified. Given the prominence accorded to optimal control in the monetary policy literature and increasingly at central banks, it seems an especially propitious moment to examine more closely the robustness properties of optimal control and other monetary policies when the reference model may be misspecified. This paper examines the robustness of optimal control policies derived under the assumption of rational expectations to potential model misspecification with respect to how private agents form expectations.1 This approach takes seriously the informational problems facing economic agents, which may cause expectations to deviate from those implied by the model of the economy they inhabit (see Taylor, 1975, for an early analysis of this issue and Sargent, 2007, for a recent discussion). Evidence that survey measures of expectations are inefficient and display significant dispersion at each point in time (see, for example, Mankiw et al., 2003, Williams, 2003a and D’Amico and Orphanides, 2006) suggests that the process of expectations formation is an important source of model uncertainty. As an alternative to rational expectations, agents are assumed to learn about the economy by reestimating a forecasting model as new data become available. A range of plausible learning models are considered, each of which yields good forecasts in our model economy and represents a relatively modest departure from the rational expectations benchmark. Unlike the existing literature in this area, including Orphanides and Williams, 2007a and Orphanides and Williams, 2007b, which has focused exclusively on simple monetary policy rules that are generalizations of the Taylor (1993) rule, this paper analyzes the robustness of optimal control policies to learning. The optimal control policy derived assuming rational expectations can perform poorly in an estimated model of the U.S. economy when agents do not possess perfect knowledge of the economy but instead must learn. To evaluate the optimal policy, the central bank is assumed to minimize the weighted unconditional variances of the deviation of the inflation rate from its target, the deviation of the unemployment rate from the natural rate, and the first difference of the nominal interest rate. The optimal control policy brings inflation gradually back to target while smoothing swings in the unemployment rate and interest rate. This policy works extremely well when private expectations are perfectly aligned with those implied by rational expectations; however, if agents are learning, expectations can deviate from those implied by rational expectations, and the finely tuned optimal control policy can go awry. In particular, by implicitly assuming that inflation expectations are always well anchored, the optimal control policy responds insufficiently strongly to movements in inflation, which results in highly persistent and large deviations of the inflation rate from its target. The lack of robustness of the optimal policy derived under rational expectations can be corrected by assigning the central bank a policy objective that places significantly less weight on stabilization of the real economy and interest rates relative to inflation than that implied by society's true objective function. Thus, robustness to learning provides a rationale for hiring a “conservative” central banker (in the parlance of Rogoff, 1985). The optimal bias to the weights in the loss function are quite large, implying that the central bank should act as if it put up to 10 times greater weight on inflation than implied by society's true loss function. The optimal control policy derived under the biased objective function responds more strongly to inflation, anchoring inflation expectations and performing well under the models of learning that we consider. The performance of the optimal control policy is then compared to two types of simple monetary policy rules that have been found to be robust to model uncertainty in the literature. The first is a forward-looking version of a Taylor-type rule, which Levin et al. (2003) found to perform very well in a number of estimated rational expectations models. The second is a rule proposed by Orphanides and Williams (2007a) that differs from the first rule in that policy responds to the change in the measure of economic activity, rather than to the level. This type of rule has been shown to perform very well in a counterfactual analysis of monetary policy during 1996–2003 undertaken by Tetlow (2006). Both rules are parsimonious in that they have only two free parameters. These two simple monetary policy rules, where the parameters are chosen to be optimal under rational expectations, perform very well under learning. Indeed, these rules outperform the optimal control policies derived under rational expectations with the society's true loss when agents learn, and yield comparable performance to the optimal control policy derived under the biased objective function. The remainder of the paper is organized as follows. Section 2 describes the model and reports the estimation results. Section 3 describes the central bank objective and optimal control policy. Section 4 describes the models of expectations formation. Section 5 discusses the simulation methods. Section 6 reports and analyzes economic outcomes for optimal control policies under rational expectations and under learning. Section 7 examines the performance of simple monetary policy rules, and Section 8 concludes.

Current techniques for determining optimal control and robust control monetary policies rely on the assumption that the policymaker possesses a very good reference model, an assumption that is untenable in practice. This paper focuses on one facet of model misspecification and uncertainty associated with the formation of expectations. The main finding is that optimal control policies are not in general robust to this form of model uncertainty, providing a warning about the potential pitfalls of optimal control policies. The lack of robustness of optimal control policies can be partially mitigated by assigning to the central bank an objective that places more weight on inflation stabilization relative to unemployment and interest rate stabilization. Simple policy rules that are robust to other types of model uncertainty are shown to be robust as well to uncertainty about how expectations are formed. Under learning, these rules perform as well or better than optimal control policies derived under rational expectations, even after biasing the central bank loss to maximize performance. Until feasible methods are developed that allow for the derivation of optimal monetary policy under a realistic range of model uncertainty including models with learning, the alterative approach of “stress testing” parsimonious policy rules across a wide set of models provides a practical and productive method of identifying which characteristics of monetary policies are robust and which are fragile.15 Of course, robustness of any policy cannot be definitively “proved” because the policy may perform poorly in an alternative model that has yet be considered. As Carlson and Doyle(2002) warn: “They are robust, yet fragile, that is, robust to what is common or anticipated but potentially fragile to what is rare or unanticipated.” Recognition of this suggests a need for continuing research into the robustness properties of all monetary policy strategies