آموزش و سیاست پولی بهینه

To conduct policy efficiently, central banks must use available data to infer, or learn, the relevant structural relationships in the economy. However, because a central bank's policy affects economic outcomes, the chosen policy may help or hinder its efforts to learn. This paper examines whether real-time learning allows a central bank to learn the economy's underlying structure and studies the impact that learning has on the performance of optimal policies under a variety of learning environments. Our main results are as follows. First, when monetary policy is formulated as an optimal discretionary targeting rule, we find that the rational expectations equilibrium and the optimal policy are real-time learnable. This result is robust to a range of assumptions concerning private-sector learning behavior. Second, when policy is set with discretion, learning can lead to outcomes that are better than if the model parameters are known. Finally, if the private sector is learning, then unannounced changes to the policy regime, particularly changes to the inflation target, can raise policy loss considerably.

We study an economy in which households and firms must learn an equilibrium law of motion to form expectations and the central bank must learn structural parameters, such as those governing the short-run trade-off between inflation and output, to conduct policy. Using a stylized New Keynesian business cycle model as a laboratory, we investigate whether a central bank can learn to set policy optimally while updating its knowledge of the economy's structural parameters in real time, and we examine whether the need for households and firms to learn materially affects the central bank's ability to learn to set policy optimally. Focusing on real-time learning, we assess how central-bank learning affects policy loss and optimal policymaking over time and how optimal monetary policies bear on the learning process, and we examine the speed of learning. We apply simulation methods to study real-time learning dynamics in an economy in which private agents employ variants of least-squares learning (as in Tetlow and von zur Muehlen, 2001; Orphanides and Williams, 2005 and Orphanides and Williams, 2006; Aoki and Nikolov, 2004; Cogley and Sargent, 2005). The real-time learning approach refrains from assuming a stationary environment where beliefs are never updated. Further, in contrast to the E-stability literature, which focuses on asymptotic results, real-time learning allows us to study the transition path to the rational expectations equilibrium. Unlike previous studies, which have concentrated on the impact of private agents’ learning on monetary policy assuming the central bank has full information,1 we consider an economy in which both private agents and the central bank must learn. In our model, although a full understanding of the economy eludes private agents and the central bank, a realistic assumption in our view, their learning focuses on different aspects of the economy. Private agents, knowing their own preference/technology parameters but needing to forecast future outcomes, must learn the economy's equilibrium law of motion, which takes the form of a vector autoregression. In contrast, the central bank, knowing its policy objectives but needing to set monetary policy, must learn the parameters in the equations that constrain its policy decision. Since both the central bank and private agents are learning, we can assess the extent to which the two learning problems interact, study the role of central-bank and private-sector learning on the policy performance, and examine whether private sector learning helps or hinders central-bank learning. Importantly, because the central bank endeavors to implement an optimal policy, and must learn structural parameters to do so, our analysis departs from least-squares learning and formulates central-bank learning in terms of a decreasing gain (generalized) instrumental variables estimator, similar to Evans and Honkapohja, 2003a and Evans and Honkapohja, 2003b. A key feature of the learning process is that the central bank's parameter estimates, through their effect on monetary policy, affect economic outcomes and feed back into subsequent parameter estimates. Through this feedback, it is possible that the central bank may be unable to learn the model and that the real-time learnable equilibrium may correspond to a suboptimal policy, or simply not exist. Similarly, central-bank learning and private-agent learning may interact, with private-agent learning slowing or preventing the central bank from learning the rational expectations equilibrium. In these respects, although we do not analyze E-stability in any formal sense, we recognize that real-time learning behavior/outcomes need not converge to rational expectations (Evans and Honkapohja, 2001), and our simulations speak to this issue. Our results, however, indicate that the rational expectations equilibrium is real-time learnable, implying that the central bank can learn to set policy optimally. Moreover, the real-time learnability of the rational expectations equilibrium is robust to whether private agents are also learning, and to whether private agents employ a constant-gain or a decreasing-gain learning algorithm.2 This is not to say that private-sector learning is unimportant for policymaking. On the contrary, economic outcomes and the policy loss associated with the central bank's policy are both sensitive to learning, and in an unexpected way. Learning is slow, yet, when monetary policy is conducted under discretion, learning can distort monetary policy in ways that improve policy loss. Three important mechanisms appear to underlie this interesting result. First, when the central bank's estimate of the slope of the Phillips curve overstates the extent to which prices are rigid, then the central bank intervenes more aggressively. This more aggressive policy overstabilizes inflation and understabilizes the output gap relative to the full-information policy, thereby mitigating the magnitude of the discretionary stabilization bias (Dennis and Söderström, 2006).3 Second, the central bank will also tend to intervene more aggressively if it underestimates the elasticity of intertemporal substitution. Third, private-sector learning, by changing the persistence of inflation and the output gap, can assist stabilization. When only the central bank is learning, our simulations suggest that learning is detrimental more often than beneficial. However, when both the central bank and private agents are learning, with a non-negligible probability, the resulting policy loss can improve on the one obtained under discretion in the full-information economy. Of course, when agents employ decreasing-gain learning algorithms, this improvement in policy loss only occurs until the rational expectations equilibrium is learned. Interestingly, private-sector and central-bank learning generally affect policy loss in opposite directions – worsening loss in the case of the central bank, and improving loss in the case of the private sector. This latter result does not extend to unannounced changes in the policy regime. If private agents learn using a constant-gain algorithm, then a change in the level of the natural rate is relatively innocuous in terms of its effect on policy loss. In contrast, a change in the relative weight the central bank assigns to output stabilization is less innocuous and a change in the inflation target is importantly detrimental to policy loss. In the case of an unannounced one percentage point change in the inflation target, policy loss can be raised by as much as 10% while the new inflation target is being learned. Finally, the degree of interest rate smoothing in the policy loss function plays an important role in many of our results. Our paper is related to the work of Evans and Honkapohja, 2003a and Evans and Honkapohja, 2003b who also consider an economy in which both the central bank and private agents must learn. However, where Evans and Honkapohja focus on E-stability of the rational expectations equilibrium using a model simpler than ours, we consider the real-time learnability of the optimal discretionary policy and focus on the impact of learning on policy loss, issues that cannot be fully addressed by establishing E-stability of the rational expectations equilibrium. An interesting line of research examines the importance of real-time learning dynamics when only private agents are learning. Tetlow and von zur Muehlen (2001) examine the cost of private agents having to learn a new monetary policy rule. They focus on an environment in which only private agents must learn and in which monetary policy is conducted using simple instrument rules. Aoki and Nikolov (2004) analyze how alternative rules for implementing the optimal policy affect policy loss. They consider a stylized real-time learning environment in which expectations are observable and where private agents and the central bank share the same model and solve the same estimation problem. In contrast, we use a more realistic learning environment, and can examine the impact of private-sector and central-bank learning on the policy performance. Orphanides and Williams (2006) study a model with adaptive learning by households and firms and show that monetary policies designed to be efficient under rational expectations can perform poorly when knowledge is imperfect. They find that the costs of learning can be mitigated if the central bank adopts an explicit numerical inflation target, consistent with our findings. Finally, Ferrero (2007) uses a simple forward-looking New Keynesian model to analyze the speed of learning. Unlike our study, Ferrero (2007) assumes that the central bank conducts policy using a simple instrument rule and that only private agents must learn. The remainder of the paper is structured as follows. Section 2 introduces the New Keynesian business cycle model that we employ, presents the central bank's loss function, and describes how monetary policy would be implemented if all agents had full information and formed expectations rationally. Section 3 describes how agents learn and investigates real-time learnability of the rational expectations equilibrium, and hence of the optimal monetary policy, when the central bank and private agents are both learning. Section 3 also shows that the central bank can achieve a smaller policy loss when learning than if the model is known, a striking result that is possible because policy is set with discretion. The importance of private-agent learning is emphasized in 4 and 5. In Section 4 we show that the improvements in policy loss found in Section 3 stem largely from the fact that private agents are learning. Section 6 investigates the effect on policy loss of private agents having to relearn following changes to the natural rate, the inflation target, and the relative weight the central bank attaches to output stabilization. Section 7 concludes.

This paper has examined whether central banks can learn to set policy optimally when they are exposed to parameter uncertainty. Inevitably, central banks must formulate policy without knowing the true structure of the economy and this uncertainty can, and should, affect their policies. Although it is clearly desirable for a central bank to be able to learn the economy's underlying structure, the interaction, or feedback, between parameter estimates and economic outcomes that arises when central banks learn means that real-time learnability of the optimal policy is not assured. To uncover whether optimal policies are real-time learnable and to evaluate the impact of learning on the policymaker's loss, we employed a standard New Keynesian business cycle model, whose behavior is governed by both forward and backward dynamics. Since a central bank must know the economy's structural relationships rather than simply its reduced-form equilibrium relationships to formulate policy, we assumed that the central bank used recursive (generalized) instrumental variables to estimate perceived structural relationships, and studied the real-time learnability of the optimal rational expectations equilibrium when monetary policy was conducted according to an optimal discretionary targeting rule. Our main results are as follows. Provided the central bank's perceived model is correctly specified, the optimal rational expectations equilibrium and hence the optimal discretionary policy is real-time learnable. This result holds regardless of whether the central bank smooths interest rates or not; however, learning occurs more quickly and is less costly if the central bank does smooth interest rates. Our results also suggest that real-time learnability of the optimal discretionary policy occurs whether the private sector's expectations are rational or are formed using either recursive least squares or a constant-gain learning algorithm. Further, the impact of central-bank learning is small at the median. Although learning occurs slowly, this is largely due to the slow convergence properties of the central bank's learning algorithm and there appears to be little feedback from real-time policymaking to the speed of learning. While learning occurred slowly, the median cost of deviating from the rational expectations equilibrium was small. Yet, due to sampling variation in the central bank's parameter estimates, the variance in policy loss was large, implying that central-bank learning can have a potentially significant cost. At the same time, strikingly, with policy conducted under discretion, we found that central-bank learning could actually give rise to an equilibrium loss that improved on the optimal rational expectations equilibrium. This result obtains because the central bank's estimated constraints may lead it to formulate a policy that would be infeasible under discretion given the true constraints. When the private sector is also learning, the likelihood of improved outcomes is even higher. Interestingly, these declines in policy loss are reasonably large and are robust to changes in the monetary policy regime. We also studied how unannounced changes in the policy regime affect the economy's behavior and policy loss when the private sector is learning. Our results reveal that learning how the policymaker responds to shocks, that is, changes in how the central bank trades off the stability of output and inflation, has only a modest effect on policy loss. Similarly, changes in the natural rate of interest, while detrimental, led to only a relatively small deterioration in policy loss. In contrast, changes to the implicit inflation target that private agents must infer incurs a much higher cost in terms of policy loss. In other words, transparency regarding the inflation target in the policy objective function appears to be much more important for policy loss than transparency regarding how the central bank trades off output stability for inflation stability. One issue not addressed in this paper is how monetary policy is affected by the distributions of the parameter estimates. In our analysis, once the structural parameters are estimated they are taken to be fixed, clearly a simplifying assumption that could usefully be relaxed. It would also be interesting to allow the central bank to take into account the private-sector learning behavior when formulating its optimal policy (Gaspar et al., 2005). Although interesting and clearly relevant for real-time policymaking, both of these issues are left for future work