سیاست های پولی، یادگیری و سرعت همگرایی

Under the assumption of bounded rationality, economic agents learn from their past mistaken predictions by combining new and old information to form new beliefs. The purpose of this paper is to investigate how the policy-maker, by affecting private agents’ learning process, determines the speed at which the economy converges to the rational expectation equilibrium. I find that by reacting strongly to private agents’ expected inflation, a central bank increases the speed of convergence and shortens the length of the transition to the rational expectation equilibrium. I use speed of convergence as an additional criterion for evaluating alternative monetary policies. I find that a fast convergence is not always desirable.

The recent literature on monetary policy has emphasized that while rational expectations is an important and useful benchmark, a policy-maker should consider the robustness of any equilibrium reached under a particular monetary policy to deviations from rational expectations. In the presence of structural changes, in fact, agents in the economy may need time in order to learn about the new environment1: in the early stages of this process, previously held beliefs could lead to biased predictions. Thus, a relevant issue concerns the conditions under which learning agents end up forming rational expectations. A common way to carry out this topic is to employ the least-squared learning approach of Marcet and Sargent, 1989a and Marcet and Sargent, 1989b and Evans and Honkapohja (2001), assuming that agents in the model form expectations via econometric forecasts. In this environment, Evans and Honkapohja, 2003a and Evans and Honkapohja, 2003b and Bullard and Mitra (2002) suggest that economic policies should be designed to be conducive to long-run convergence of private expectations to rational expectations. Failing to do so gives rise to an equilibrium which is not robust to small expectational errors. In accordance with this literature, ‘good’ policies are those that induce a determinate and learnable rational expectations equilibrium (REE) (see Bullard and Mitra, 2002). Another small but growing body of research is concerned with the properties of the convergence along the learning process. Evans and Honkapohja (1993), Timmerman (1996), Sargent (1999) and Marcet and Nicolini (2003) make use of learning models not only to study the asymptotic properties of the equilibrium attainable under learning, but as a compelling alternative to study economic behaviors in the short and medium-run. The works of Giannitsarou (2003), Aoki and Nikolov (2006) and Orphanides and Williams (2004) analyze the transition to the REE in the context of policy decisions, addressing the question of whether all policies that produce learnability and determinacy are equally good from a learning perspective. I take up this point by adapting theoretical results of Benveniste et al. (1990) and Marcet and Sargent (1995). I first examine how the policy-maker, by affecting the private agents’ learning process, can influence the transition to the REE (i.e. the speed of learning). I show that by reacting strongly to expected inflation, a central bank can shorten the length of the transition and increase the speed of convergence to the REE. Next, I consider the case where the central bank has a stabilization objective on inflation and output gap and I focus on the optimal discretionary policy described in Evans and Honkapohja (2003a), EH policy. I show that this policy, even though it meets all of the objectives listed above (determinacy and stability under learning) and is optimal under rational expectations, is not suitable from the perspective of the speed of learning, as it implies a very slow transition. Therefore, I show how a policy-maker who wants to reach in the long run the same REE determined as under the EH policy, can manipulate the speed of learning of the private sector. Finally, I analyze the welfare implications of converging to a given REE at different speeds. My main conclusion is that fast learning is not always desirable. In the absence of an inflation bias, fast learning always increases social welfare. In the presence of such a bias, however, the relation between speed of convergence and welfare is not as straightforward. If the initial expected inflation is higher than in the REE, the policy-maker by inducing a fast learning has room to substantially increase social welfare. If, instead, perceived inflation is initially lower, a slow transition might be preferable, as inflation would remain closer to the first best for a longer period of time. The paper is organized as follows. Section 2 presents the monetary policy problem and describes the learning dynamics under a restricted set of expectations-based policy rules. Section 3 considers the optimal policy under discretion described in Evans and Honkapohja (2003a), as a specific policy in this set. The section ends showing that the EH policy determines a very slow convergence to the REE. In Section 4, I study policies that allow the central bank to shorten (or extend) the transition period without affecting the long-run equilibrium and I analyze how social welfare is influenced under these policies. Section 5 presents robustness checks. Section 6 describes some points that deserve further analysis. Section 7 summarizes and concludes.

In this paper I have shown that considering learning in a model of monetary policy design is particularly important in order to describe not only the asymptotic properties of the REE to which the economy could converge, but also to describe the dynamics that characterize the transition to this equilibrium. The central message of the paper is that policy-makers should look at monetary policies which lead to determinate and E-stable equilibria. However, since policies that produce learnable equilibria may imply very different transitions, the policy-maker should also take into account how his decisions affect the speed at which agents’ beliefs converge to rational expectations. Therefore, the aim of this paper is twofold: it helps to explain some facts described in the literature and it shows new results. From the first side, it makes it possible to explain why policies that would be optimal under rational expectations can perform poorly when knowledge is imperfect. Under some policies, the REE is stable under learning, but it could be located near the borderline between stability and instability. In this case the period needed to converge to the REE could be incredibly long. I have shown that by reacting strongly to expected inflation, a central bank can shorten the transition and increase the speed of convergence to the REE. From the other side, I show that a policy-maker who considers his role in determining the dynamics of the agents’ learning process could choose a policy rule that induces agents to learn at a given speed, affecting the welfare of society along the transition. In particular, if the policy-maker knows that after a regime change private agents’ perceived inflation would be higher than in the REE, by choosing a policy that reacts strongly to expected inflation he would determine a fast convergence and increase social welfare. If, instead, perceived inflation is initially lower than in the REE, a slow transition is preferred only when the output gap target is greater than zero. This conclusion points out how crucial it is for the design of monetary policies to obtain good data about the state of markets’ expectations.