یادگیری تطبیقی ​​و استفاده از پیش بینی در سیاست های پولی

This paper investigates monetary policy design when central bank and private-sector expectations differ. Private agents learn adaptively; the central bank has a possibly misspecified model of the economy. Successful implementation of optimal policy using inflation targeting rules requires the central bank to have complete knowledge of private agents’ learning behavior. If the central bank mistakenly assumes private agents to have rational expectations when in fact they are learning, then policy rules frequently lead to divergent learning dynamics. However, if the central bank does not correctly understand agents’ behavior, stabilization policy is best implemented by controlling the path of the price level rather than the inflation rate

How should forecasts be incorporated into optimal monetary policy design? The recent literature on implementing optimal monetary policy—see Svensson and Woodford, 2005, Svensson, 2003 and Giannoni and Woodford, 2002; Woodford, 2003, Chapter 7—characterizes the central bank's decision procedure in terms of specific targeting rules: such rules specify a relationship between one or more target variables that must be checked each time an interest-rate decision is made. The instrument setting is deemed appropriate if the specified ‘target criterion’ is satisfied. Since the target variables that appear in the criterion are usually not directly observable, to determine the instrument setting in any period the central bank requires a completely specified model of the economy to solve for the equilibrium path of endogenous variables. The targeting rule approach appears to be an effective way to implement optimal monetary policy and is argued to be robust to a range of assumptions concerning the nature of economic disturbances that affect the economy. To date, the literature on specific targeting rules rests on the assumption that the central bank is able to exploit the true structure of the economy—that it understands the true structural relations, and therefore the expectations held by private agents, when determining the instrument setting that is consistent with implementing its objectives.1 Furthermore, the literature typically rests on the assumptions of rational expectations and common information on the part of private agents and the central bank. This implies that both these economic actors necessarily hold common expectations about future macroeconomic conditions. But suppose the central bank does not know the true model of the economy. Or that the central bank and private agents hold differing beliefs about the future evolution of the economy—does this hinder the usefulness of specific targeting rules? And given uncertainty as to the true model, should optimal monetary policy be conditioned on private agents’ expectations and if so in what way? Or is it sufficient for the central bank's instrument choice to be conditioned solely on internally constructed forecasts using whatever model it may have at its disposal? This paper addresses these questions in a simple New-Keynesian model of output gap and inflation determination in which private agents must learn about the probability laws governing the evolution of state variables exogenous to their decision problems. Rational expectations are a nested special case of the proposed beliefs, and the analysis is centrally concerned with the conditions under which agents’ beliefs converge to those predicted by a rational expectations equilibrium analysis of the model. Introducing learning in this way permits the central bank and private agents to have differing beliefs about the evolution of the macroeconomy and allows examination of its implications for the design of optimal monetary policy. Because all economic actors will only hold identical believes if and when the learning process converges, the framework serves to coherently analyze robustness of rational expectations policy prescriptions to departures in underlying model assumptions; and specifically expectations formation. Following Giannoni and Woodford (2002), candidate targeting rules are variants of the consolidated first-order condition to the solution to the optimal commitment problem under the so-called “timeless perspective” of Woodford (1999) of a standard linear-quadratic policy problem. Two representations are analyzed. The first is a particular linear restriction on the inflation rate and the change in the output gap. The second, is an equivalent restriction on the price level and the contemporaneous output gap. 2 If the central bank can arrange for either of these relations to be met in all periods it will successfully implement the optimal monetary policy. The former will be referred to as the inflation targeting rule and the latter the price-level targeting rule. A policy is robust if agents’ beliefs converge to the rational expectations equilibrium associated with the policy. To implement such targeting criteria, the central bank requires a model of the economy. It follows that the central bank's knowledge of the economy will have consequences for its projection of the future path of economic variables and therefore the implementation and efficacy of any given targeting rule. Three decision procedures are considered that are equivalent in terms of the rational expectations equilibria they imply. Each represents the central bank's beliefs about the evolution of the economy. Of particular interest is whether learning dynamics provide ground for choosing among alternative approaches to implementing optimal monetary policy. First, the central bank implements the target criterion incorrectly assuming agents to have rational expectations and observing only lagged aggregate variables and fundamental disturbances. Thus the evolution of the economy is projected using a rational expectations model—that would obtain if agents’ solved their decision problems under rational expectations—and this implies a reaction function for the nominal interest rate that is a function only of the model's state variables and therefore independent of agents’ learning behavior.3 Second, the central bank implements the target criterion correctly understanding agents’ behavior. In contrast to the former decision procedure, this approach to monetary policy induces a strong dependence on agents’ forecasts—indeed agents’ long-horizon forecasts of macroeconomic conditions matter for the implementation of policy.4 Finally, since the above two decision procedures represent extreme informational assumptions on the part of the central bank, instrument rules that depend only on observed private one-period-ahead expectations are considered. If some dependency on private forecasts is desirable to implement optimal policy under learning dynamics, the use of one-period-ahead forecasts may be more feasible and effective than use of private forecasts into the indefinite future. For the inflation targeting rule, stability under learning dynamics depends on the central bank's model of the economy. If the monetary authority correctly understands agents’ behavior and projects the evolution of the economy on the basis of this model, then inflation targeting rules are always able to implement the optimal commitment equilibrium in the presence of learning dynamics. In contrast, if the central bank mistakenly assumes agents to have rational expectations, and projects the evolution of the economy under this assumption, the inflation targeting rule leads to instability for many empirically reasonable parameter values. The economy is, therefore, prone to self-fulfilling expectations of the type conjectured by Friedman (1968). A decision procedure that depends on one-period-ahead forecasts is similarly afflicted. Thus, successful implementation of optimal policy depends crucially on the central bank's forecasting procedure. For the price-level targeting rule, the central bank can also always successfully implement the optimal equilibrium given correct knowledge of agents’ behavior. However, in contrast to the inflation targeting rule, the price-level target criterion displays a degree of robustness to the model used by the central bank to construct projections. Even if the central bank mistakenly assumes agents to have rational expectations, the price-level targeting rule leads to stability under learning dynamics for many empirically reasonable parameter values. Important, stability obtains for a much larger region of the parameter space than under the analogous inflation targeting rule. This result is of considerable interest since, for appropriately chosen initial conditions, the two proposed targeting rules imply the same state-contingent evolution of model variables under rational expectations. The difference between these two rules, in the case of learning dynamics, is that the price-level targeting rule specifies a different kind of subsequent behavior when one finds that (because the private sector does not behave as they were projected to do) one has failed to achieve the target criterion precisely. Thus the difference between the two rules is a different commitment as to how one will react to seeing that one has missed one's target. The price-level targeting rule is more robust to learning dynamics and suggests optimal monetary policy might best be implemented by explicit reference to the path of the price level rather than the inflation rate. This paper builds on Preston (2005b) which proposes a framework for modeling learning in which agents face multi-period decision problems as in the microfoundations used in Bernanke and Woodford (1997), Clarida et al. (1999) and Woodford (1999) and is related to Preston (2006) which examines the efficacy of using forecasts in the design of simple instrument rules. This paper extends that analysis by considering decision procedures which require the central bank to adopt a completely specified model of the economy to implement monetary policy. It therefore seeks to learn what kind of model and information is useful to a central bank when charged with implementing optimal targeting rules. Moreover, it evaluates the merits of policies that control the path of the price level rather than the inflation rate. However, the analysis of this paper is closest in spirit to recent work by Evans and Honkapohja (2006) and Honkapohja and Mitra (2005). These papers assume a log-linear model of the monetary transmission mechanism where agents need to only forecast aggregate income and inflation one period in advance. The analysis of Honkapohja and Mitra (2005) examines a range of forecasting procedures (based on recursive learning algorithms) for the monetary authority and their implications for economic stability for a variety of common monetary policy rules. They show that internal forecast decision procedures of this kind often require stronger conditions for learnability than if the central bank responds to observed private-sector forecasts (when these forecasts are themselves formed under a least-squares learning algorithm). Evans and Honkapohja (2006) consider the question of implementing optimal monetary policy by use of an inflation targeting rule. This approach is shown to implement successfully the optimal equilibrium and therefore to eliminate instability due to self-fulfilling expectations. The present analysis revisits the question of implementing optimal monetary policy using a different approach to modeling learning than adopted in the papers by Evans and Honkapohja (2006) and Honkapohja and Mitra (2005). The current paper assumes agents face multi-period decision problems and use econometric models to learn about state variables that are beyond their control, so that long-horizon forecasts matter to the current determination of the economy's aggregate variables. This approach to modeling learning has the advantage that agents take proper account of their wealth and act optimally given their beliefs—ensuring that when private agents do learn the true probability laws predicted by a rational expectations analysis of the model, agents’ consumption decisions necessarily satisfy their intertemporal budget constraints. Importantly, this approach provides stronger evidence that a price-level targeting rule provides more robust learnability than does an analysis of learning in the economy where only one-period-ahead forecasts matter. This paper proceeds as follows. Section 2 outlines the model. Section 3 details the optimal monetary policy problem of the central bank. Section 4 then begins the analysis of monetary policy rules under learning dynamics. It considers an inflation targeting rule that is designed to implement the optimal commitment equilibrium under alternative assumptions on the central bank's knowledge. Section 5 turns to an analogous analysis of price-level targeting rules. Section 6 considers target criteria that depend on one-period-ahead forecasts. The final section concludes.

This paper applies the framework of Preston (2005b) to understand how private-sector forecasts should be incorporated into the design of optimal monetary policy rules. The analysis finds that targeting rules can guarantee the successful implementation of the optimal equilibrium from the timeless perspective under learning dynamics if the central bank has correct knowledge of the true model of the economy—that is, it understands the exact nature of private-sector behavior and its implications for aggregate dynamics. In contrast, an inflation targeting rule fails to be robust to learning dynamics, in the sense that if the central bank implements the policy under the mistaken assumption that private agents have rational expectations, the policy leads to the propagation of self-fulfilling expectations for many empirically reasonable parameter values. However, this instability appears far less severe for price-level targeting rules for the parameter values considered. It follows that, if the central bank nonetheless attempts to implement a targeting rule under the mistaken assumption that agents have rational expectations, it is best that the decision procedure be cast in terms of arranging for a desired path for the price level rather than the inflation rate. By anchoring policy in terms of the price level, the central bank can better restrain agents’ expectations, and therefore eliminate the possibility of self-fulfilling expectations for many parameter values. Importantly, not all uses of private forecasts in the conduct of monetary policy help to improve learnability. The inflation and price-level targeting rules in this paper require the central bank to use its information about private forecasts in order to offset the effects of those forecasts on the variables that it is targeting, just as it uses its information about other disturbances in order to offset the effects of those disturbances. But forecast-based instrument rules of the kind often discussed in the literature may instead strengthen the effects of private forecasts on the economy's evolution, by making the central bank behavior as well as private behavior respond to them; and in this case the central bank's behavior makes it easier for expectations to be a source of instability.