سیاست های پولی، عدم قطعیت پارامتر و یادگیری بهینه

Since central banks have limited information concerning the transmission channel of monetary policy, they are faced with the difficult task of simultaneously controlling the policy target and estimating the impact of policy actions. A tradeoff between estimation and control arises because policy actions influence estimation and provide information which may improve future performance. I analyze this tradeoff in a simple model with parameter uncertainty and conduct dynamic simulations of the policymaker's decision problem in the presence of the type of uncertainties that arose in the wake of German reunification. A policy that separates learning from control may induce a persistent upward bias in money growth and inflation, just as observed after unification. In contrast, the optimal learning strategy which exploits the tradeoff between control and estimation significantly improves stabilization performance and reduces the likelihood of inflationary bias.

Monetary policy is conducted in an uncertain economic environment where little is known about the exact relationship between policy instruments such as the short-term nominal interest rate and policy targets such as the rate of inflation. In fact, macroeconomists can at best provide a rough estimate of the economy's expected response to a specific policy action. As a consequence, monetary policymakers are confronted with a complex simultaneous control and estimation problem. On the one hand, they attempt to control target variables such as inflation as best as possible based on current knowledge and information. On the other hand, they have to examine and perhaps revise their view of how the economy responds to policy actions as soon as new information becomes available and then adjust policy accordingly. This is particularly important at times when the economy is undergoing structural changes such as, for example, following German unification or the formation of the European monetary union. Recent research on monetary policy and transition such as Bertocchi and Spagat (1993) and Balvers and Cosimano (1994) has emphasized that policymakers face a tradeoff between control and estimation whenever they are uncertain about parameters that influence policy effectiveness. This tradeoff arises because policy actions may provide new information about the relationship between policy instrument and target. In particular, it may be optimal to choose a policy setting that worsens current outcomes but yields new information that will make it possible to improve policy performance in the future. Thus, how quickly policymakers will learn about relevant parameters following structural changes such as German unification will depend, among other factors, on their own actions. For example, if the policymakers’ estimates are biased and policy is set without considering how it will affect these estimates, one might well expect to observe a persistent deterioration in stabilization performance. Alternatively, if policymakers take into account the informational effects of policy actions and learn optimally, long-lasting biases in target variables should be less likely. Such optimal policy may incorporate a significant degree of experimentation. This paper investigates the likelihood of a persistent bias in monetary policy due to parameter uncertainty and explores to what extent optimal policy improves the speed of learning. The analysis is based on a dynamic programming framework with Bayesian learning about unknown parameters. The asymptotic behavior of parameter estimates and policies in such a framework has been studied by Easley and Kiefer (1988) and Kiefer and Nyarko (1989). Wieland (2000) presents a numerical algorithm for computing the optimal policy in such a Bayesian learning model. Here, I use this methodology to study the quantitative implications of parameter uncertainty and learning for monetary policy. The practical relevance of such learning considerations in the aftermath of structural changes is shown by studying monetary policy after German unification. Economic union with East-Germany generated substantial uncertainties concerning the transmission of monetary policy and subsequent years witnessed a significant increase in money growth and inflation. I examine under what conditions learning dynamics could lead to such a persistent increase in inflation using a simple model of monetary policymaking. This exercise has a positive and a normative dimension. Actual central bank behavior under parameter uncertainty may be better represented by a policy that treats control and estimation separately. Such an approach corresponds to the cautious, gradualist policy recommended originally by Brainard (1967) and widely discussed in the policy literature (see for example Blinder, 1998). It implies that the policy action, which would be optimal given available estimates of the relationship between policy instrument and target, is adjusted to account for the degree of precision of these estimates. This approach involves learning albeit in a passive manner. Once new data become available the policy stance changes to account for changes in the parameter estimates and the associated degree of precision. This passive learning policy is myopic because it neglects the information effect of policy actions. Normative implications arise from a comparison to the optimal learning policy that exploits this information effect. The paper is structured as follows. Section 2 reviews related literature. Section 3 formulates the basic control problem with unknown parameters in a dynamic programming framework with Bayesian learning. Convergence of parameter estimates and policy actions is shown by Easley and Kiefer (1988) and Kiefer and Nyarko (1989). They also show that the limit beliefs of the decision maker need not coincide with the true parameter values generating the data. Using numerical methods I compute policy functions that map the policymaker's beliefs about the unknown parameters into policy actions. I consider two unknown parameters and model beliefs as a bivariate normal distribution. This specification is conducive to practical applications since it implies that the unknown parameters may be any real number from the perspective of the policymaker. The myopic, passive learning policy can be calculated analytically, while the optimal policy has to be approximated numerically, because Bayesian learning introduces a nonlinearity into the dynamic optimization problem.1Section 4 reviews the impact of German unification on money growth and inflation, the performance of the Bundesbank's monetary targeting strategy and the empirical evidence for structural changes in money demand and supply relationships. Section 5 provides an interpretation of the basic learning and control problem in terms of German monetary policy and describes the calibration of the learning model. Section 6 presents dynamic simulations of this model under passive and optimal learning policies. These simulations show that passive learning can result in a persistent upward bias in money growth and inflation due to mistaken beliefs about money demand and supply parameters. The optimal policy, which is approximated by numerical methods, substantially reduces the likelihood of such a policy bias, albeit at the expense of somewhat higher initial variability. I also provide a detailed sensitivity analysis. Section 7 concludes.

This paper shows that the tradeoff between control and estimation which arises in the presence of parameter uncertainty can have quantitatively important implications for monetary policymaking. Parameter uncertainty, of course, is most prevalent following changes in the structure of the economy. Taking the example of German unification, a careful reading of the Bundesbank's monthly reports from this period suggests that central bankers were particulary uncertain whether the increase in money growth and inflation observed after unification was driven by temporary or permanent factors. Furthermore, the proliferation of studies on money demand following unification and the substantial range of findings indicates that the high degree of uncertainty regarding the determinants of money growth persisted for many years after unification. The paper then uses a simple model with Bayesian learning about two unknown parameters to describe the decision problem of a central bank in the presence of such uncertainty. Dynamic simulations of this model indicate that a passive learning strategy, which does not take into account that current policy actions influence the speed of learning, is likely to induce a persistent inflationary bias due to misspecified beliefs about the impact of policy on money growth and inflation. This bias may well be of similar magnitude as the increase in inflation observed after unification. A detailed sensitivity analysis confirms that the likelihood of such a policy-induced bias is significant under a wide range of initial beliefs and values of the underlying parameters. The fully optimal strategy which takes into account the learning channel, however, is found to experiment with tighter monetary policy and substantially reduce the likelihood of a sustained policy bias due to incorrect beliefs. This finding shows that optimal learning can have important quantitative implications for stabilization policy. Of course, given the simplifying assumptions regarding the underlying macroeconomic model, this finding should not be interpreted as an empirical test of the optimality of German monetary policy. Finally, note that the intrinsic nonlinearity of the learning problem precludes analytical solution. The numerical algorithm that is used in this paper to approximate the optimal policy allows for more complicated learning dynamics than previous studies on learning by central banks and could be used to investigate decision problems under parameter uncertainty in many other areas.18 Several new questions arise from this research. First, the tradeoff between control and estimation may be relevant for monetary policymaking during other episodes of structural change. An example that immediately comes to mind is the European Central Bank's policy in the new European monetary union. As far as U.S. monetary policy is concerned one could think of the so-called `missing money’ period in the mid-1970s, or more recently, of uncertainty about the natural unemployment rate (see Staiger et al., 1997) and the possibility of improvements in productivity trends. Second, the dynamic simulations in this paper show that parameter uncertainty and learning by the policymaker may induce nonstationary behavior in economic observables such as money growth and inflation. This effect is usually neglected in econometric studies of macroeconomic relationships even though it would call standard estimation results into question. An exception is the study by Horvath (1991).19 Third, questions regarding central bank credibility and the interaction between the private sector's and the policymaker's learning behavior, especially when they do not share the same information set and have different beliefs, would seem to be of special interest.