تغییرات رژیم، یادگیری و سیاست پولی

Monetary policymakers should be concerned with potential changes in regime. In the model presented here, increasing returns in production creates the possibility of multiple expectationally stable steady states. The policymaker tries to achieve the two goals of smoothing fluctuations around the high output steady state, while trying to prevent the economy from slipping to the inferior, low output steady state. Agents use a learning rule to make forecasts and a key parameter in the rule provides an indication of the credibility of the policymaker. The greater the magnitude of the shocks and the lower the credibility of the policymaker, the more emphasis should be placed on stabilizing output.

Theoretical models with multiple equilibria have been used to address important issues in economics such as the causes of the great depression and the nature of development traps.1 Results from empirical methods such as Markov switching models, introduced in Hamilton’s (1989) study of GDP growth, imply that the economy does not necessarily fluctuate around a unique equilibrium, but could switch between multiple steady states. Diebold and Rudebusch (1996) stress that ignoring the possibility of regime shifts could lead to very poor policy recommendations, and they appeal for more applied work focusing on multiple equilibria. However, much of the literature on monetary policy concentrates on unique, rational expectations equilibria,2 possibly due to the modeling difficulties involved with multiple equilibria. The goal of this paper is to determine optimal monetary policy in an environment with potential regime shifts. The model presented here includes increasing returns in production that can lead to multiple steady states, similar to the approach of Evans and Honkapohja, 1993 and Evans and Honkapohja, 2001. For a given steady state we define the associated linear model and compute optimal policy under rational expectations. Simulations of the model with multiple steady states are then used to determine optimal policy in the non-linear case. In a model with multiple steady states, agents’ formation of expectations raises many subtle issues. Expectations should be able to respond quickly, if there is a regime shift, but they should also approach the equilibrium values associated with a steady state if the economy does not experience such drastic changes. To model such behavior, this paper uses the endogenous gain learning mechanism of Marcet and Niccolini (2004). The gain parameter shows the emphasis agents place on recent information when forming expectations and is allowed to vary depending on the state of the economy. Furthermore, the gain parameter provides an indication of the credibility of the policymaker. The monetary policymaker strives to stabilize the endogenous variables of the economy around the steady state with the highest level of output. Simulation results show that optimal policy depends on the magnitude of the shocks in the model and the credibility of the policymaker. For larger shocks and lower credibility, there is a greater danger of a shift to the neighborhood of a low output steady state. Hence, the policymaker should place more emphasis on output stabilization to minimize this possibility. For sufficiently small shocks and high credibility, optimal policy can be computed with the associated linear model under rational expectations, but for larger shocks and lower credibility this method is misleading. The model has full micro foundations. A money-in-the-utility function setup determines expectations-augmented IS and LM equations in the demand sector, similar to McCallum and Nelson (1999a). Increasing returns in the production function arise from productivity enhancing ideas, which depend on the aggregate quantity of labor. Firms maximize profits over labor but do not take into account the impact of their decision on aggregate labor. Therefore, the production externality is a possible source of multiple steady states. In the generic case, there are three steady states at different levels of output, but not all of them are relevant to the dynamics of the model. We provide a condition for expectationally stability (see Evans and Honkapohja, 2001) and show that the steady state at the intermediate level of output does not meet the criterion. The expectationally stable steady states are at the high and low levels of output. To focus on the impact of the production externality, the model is simplified in several ways. The policymaker’s instrument is the nominal money supply, and he has private information about the serially independent demand shock, which gives him the ability to stabilize endogenous variables under rational expectations. We abstract from growth, so the steady state values of these variables are constants. Hence, rational expectations of endogenous variables also take the form of constants. The policymaker seeks to keep the economy near the natural rate so there is no inflation bias as in Rogoff (1985). It follows that, since rational expectations are fixed, there is no tension between discretion and commitment. In the learning mechanism, agents update their estimates of the steady state values. Another important assumption is that the supply sector is deterministic, which is introduced since the interaction between a supply shock and the production externality greatly complicates the dynamics.3 In this environment, the usual trade-off between output and price (or inflation) stabilization does not exist. Including output deviations in the policymaker’s loss function captures his desire to stabilize prices and employment as well. The policymaker’s decision is one of output versus interest rate stabilization. Interest rate stabilization in monetary policy has been a topic of recent interest. Including interest rate deviations in the policymaker’s loss function goes back to Goodfriend (1991). The usual argument is that the policymaker does not want to shock financial markets with dramatic changes in interest rates. Woodford (2002) argues that interest rate smoothing could help to solve the commitment problem in monetary policy. Ravenna and Seppela (2005) construct a general equilibrium model to examine issues related to the yield curve, in particular, the failure of the expectations hypothesis. They show that the inclusion of interest rate smoothing in the monetary policy rule is crucial for their model to be able to reject the expectations hypothesis. There is some notable recent work on monetary policy in models with multiple equilibria, including Benhabib et al., 2001, Bullard and Cho, 2005 and Evans and Honkapohja, 2004. In these papers, a second, low inflation steady state, which is interpreted as a liquidity trap, arises due to the zero lower bound on interest rates. In contrast, the model in this paper has the same interest rate at both expectationally stable steady states and the multiplicity arises from real factors in production. The simulations concerning the credibility of the policymaker reported here use constant gain so that learning is always a determining factor in the dynamics. This approach follows Bullard and Cho, 2005 and Orphanides and Williams, 2002 who shows that optimal monetary policy under constant gain learning can differ from optimal policy computed under rational expectations. This result is clearly related to the present paper, though his model has a more empirical foundation. The paper is organized as follows. Section 2 describes the optimizing behavior underpinning the model. Section 3 presents the supply sector with increasing returns in production. Section 4 defines the linear versus the general non-linear model. Section 5 discusses the expectational stability of the steady states. Section 6 presents the learning mechanism and its interpretation in terms of credibility. Section 7 presents the problem facing the policymaker. Section 8 describes the calibration of the model, Section 9 the simulation results and Section 10 concludes.

Models with multiple equilibria can reproduce dramatic shifts in economic variables that reflect conditions often facing policymakers. Regime shifts can have many possible sources from a theoretical perspective, and macroeconomic data is well described by models that allow for multiple steady states. As discussed in the recent paper by Svensson (2003), policymakers are increasingly concerned with the proper approach to the possibility of large shifts in the economy. This paper develops a model of monetary policy that includes increasing returns in production and an endogenous gain learning mechanism. We introduce a modification of the production function in Evans and Honkapohja (1993) and use a learning rule from Marcet and Niccolini (2004), interpreting the gain parameter as an indication of the credibility of the policymaker. Modeling credibility in terms of learning offers a new approach to many policy issues. The model has two expectationally stable steady states at high and low levels of output, and is calibrated so that the difference in the two stable equilibria match regime shifting estimates for output and employment data. The policymaker attempts to keep the economy near the high output equilibrium and to dampen fluctuations of output and interest rates around this equilibrium. We compute optimal policy for a linear, single equilibrium version of the model assuming rational expectations. The primary results from the simulations of the model are as follows: • The greater the magnitude of the demand shock, the higher the possibility of a shift to the low output equilibrium and the more emphasis the policymaker should place on stabilizing output to insulate the economy from the negative impact of the externality in the supply sector. • The higher the credibility of the monetary authority, the less expectations contribute to the volatility of the endogenous variables, which implies that the policymaker can focus more on stabilizing interest rates. • For sufficiently small shocks and sufficiently high credibility, the optimal policy for the linear version of the model are valid. For larger shocks and lower credibility, however, the possibility of a regime shift invalidates the policy recommendations of the linear model. There are many avenues for future research in this area. Policy issues could be examined in light of many other potential sources of multiple equilibria. Alternative policy rules and loss functions could be examined in such an environment. The present paper takes an important step in connecting the literatures on complementarities, regime shifts and learning to current problems faced by monetary policymakers.