Learning about which measure of inflation to target

Using a closed economy model with a flexible-price good and a sticky-price good we study the conditions under which interest rate rules induce real determinacy and, more importantly, the MSV solution is learnable in the E-stability sense proposed by Evans and Honkapohja (2001). We show that these conditions depend not only on how aggressively the rule responds to inflation but also on the measure of inflation included in the rule and on whether the flexible-price good and the sticky-price good are Edgeworth complements, substitutes or utility separable. We consider three possible measures of inflation: the flexible-price inflation, the sticky price inflation and the core inflation; and we analyze three different types of rules: a forward-looking rule, a contemporaneous rule and a backward-looking rule. Our results suggest that in order to guarantee a unique equilibrium whose MSV representation is learnable, the government should implement a backward looking rule that responds exclusively to the sticky-price inflation. Forward-looking and contemporaneous rules that respond to either the flexible-price inflation or the core-inflation are more prone to induce multiple equilibria and E-instability of the MSV solution. More importantly backward-looking rules that react to either the flexible-price inflation or the core inflation may guarantee a unique equilibrium but in these cases the fundamental solution (MSV representation) is not learnable in the E-stability senseInterest rate rules, Learning, E-stability, multiple equilibria, inflation

Learning About Inflation Measures for Interest Rate Rules

Empirical evidence suggests that goods are highly heterogeneous with respect to the degree of price rigidity. We develop a DSGE model featuring heterogeneous nominal rigidities across two sectors to study the equilibrium determinacy and stability under adaptive learning for interest rate rules that respond to inflation measures differing in their degree of price stickiness. We find that rules responding to headline inflation measures that assign a positive weight to the inflation of the sector with low price stickiness are more prone to generate macroeconomic instability than rules that respond exclusively to the inflation of the sector with high price stickiness. By this we mean that they are more prone to induce non-learnable fundamental-driven equilibria, learnable self-fulfilling expectations equilibria, and equilibria where fluctuations are unbounded. We discuss how our results depend on the elasticity of substitution across goods, the degree of heterogeneity in price rigidity, as well as on the timing of the rule.Learning; Expectational Stability; Interest Rate Rules; Multiple Equilibria; Determinacy; Multiple Sectors

Learning, monetary policy and housing prices

This paper evaluates different types of simple monetary policy rules according to the determinacy and learnability of rational expectations equilibrium criteria within a dynamic stochastic general equilibrium framework. Incorporating housing prices and collateralized borrowing into the standard model allow us to answer important policy questions. One objective is to investigate whether responding to housing prices affects determinacy and learnability of rational expectations equilibrium. For this purpose, we work with a New Keynesian model in which housing plays an accelerator role in business cycles as a collateralized asset. The results show that for current data rule, responding to asset prices does not improve learnable outcomes but for a monetary policy with lagged data and forward-looking rules we see improved learnable outcome if current housing prices are available to monetary authority. Moreover, we examine the effects of interest rate inertia and price stickiness on E-stability of REE.monetary policy rules, determinacy, learning, housing prices

Expectations Traps and Coordination Failures: Selecting among Multiple Discretionary Equilibria

Discretionary policymakers cannot manage private-sector expectations and cannot coordinate the actions of future policymakers. As a consequence, expectations traps and coordination failures can occur and multiple equilibria can arise. To utilize the explanatory power of models with multiple equilibria it is �first necessary to understand how an economy arrives to a particular equilibrium. In this paper, we employ notions of learnability, self-enforceability, and properness to motivate and develop a suite of equilibrium selection criteria. Central among these criteria are whether the equilibrium is learnable by private agents and jointly learnable by private agents and the policymaker. We use two New Keynesian policy models to identify the strategic interactions that give rise to multiple equilibria and to illustrate our equilibrium selection methods. Importantly, unless the Pareto-preferred equilibrium is learnable by private agents, we �find little reason to expect coordination on that equilibrium.Discretionary policymaking, multiple equilibria, coordination, equilibrium selection

Multiple-Solution Indeterminacies in Monetary Policy Analysis

This paper discusses four current topics in monetary policy analysis, each of which hinges on the possibility of multiple solutions in rational expectations (RE) models. In three of these cases--involving inflation forecast targeting, the zero-lower bound deflation trap, and the fiscal theory of the price level--analysis based on E-stability and adaptive learnability of the solutions suggests that only one of them is a viable equilibrium candidate. Thus the dangers alleged to prevail, in these cases, are not ones with which actual policymakers need to be concerned. In the case of the Taylor principle, by contrast, policy behavior that violates the principle is genuinely undesirable, since all of the RE equilibria fail to be learnable.

Sunspots and monetary policy

A monetary economy subject to expectational sunspots is prone to instability, in the sense of multiple rational expectations equilibria. We show how to modify the policy rule to guarantee stability in the presence of expectational sunspots. The policy-maker must co-ordinate in ation dynamics by targeting each of lagged, current and expected in ation. We show that this solution maps directly into the timeless perspective by Woodford. Finally, we trace the responses in an arti cial sunspot economy to the adoption of our rule and illustrate the extent to which macroeconomic persistence is reduced

Learning About Monetary Policy Rules

We study macroeconomic systems with forward-looking private sector agents and a monetary authority that is trying to control the economy through the use of a linear policy feedback rule. A typical finding in the burgeoning literature in this area is that policymakers should be relatively aggressive in responding to available information about the macroeconomy. A natural question to ask about this result is whether policy responses which are too aggressive might actually destabilize the economy. We use stability under recursive learning (a la Evans and Honkapohja (2000)) as a criterion for evaluating monetary policy rules in this context. We find that considering learning can alter the evaluation of alternative policy rules.monetary policy rules; determinacy; expectational stability.

Multiple-Solution Indeterminacies in Monetary Policy Analysis

This paper discusses four current topics in monetary policy analysis, each of which hinges on the possibility of multiple solutions in rational expectations (RE) models. In three of these cases-involving inflation forecast targeting, the zero-lower bound deflation trap, and the fiscal theory of the price level-analysis based on E-stability and adaptive learnability of the solutions suggests that only one of them is a viable equilibrium candidate. Thus the dangers alleged to prevail, in these cases, are not ones with which actual policymakers need to be concerned. In the case of the Taylor principle, by contrast, policy behavior that violates the principle is genuinely undesirable, since all of the RE equilibria fail to be learnable.

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE.Robust control ; Monetary policy

Robustifying learnability

In recent years, the learnability of rational expectations equilibria (REE) and determinacy of economic structures have rightfully joined the usual performance criteria among the sought-after goals of policy design. Some contributions to the literature, including Bullard and Mitra (2001) and Evans and Honkapohja (2002), have made significant headway in establishing certain features of monetary policy rules that facilitate learning. However a treatment of policy design for learnability in worlds where agents have potentially misspecified their learning models has yet to surface. This paper provides such a treatment. We begin with the notion that because the profession has yet to settle on a consensus model of the economy, it is unreasonable to expect private agents to have collective rational expectations. We assume that agents have only an approximate understanding of the workings of the economy and that their learning the reduced forms of the economy is subject to potentially destabilizing perturbations. The issue is then whether a central bank can design policy to account for perturbations and still assure the learnability of the model. Our test case is the standard New Keynesian business cycle model. For different parameterizations of a given policy rule, we use structured singular value analysis (from robust control theory) to find the largest ranges of misspecifications that can be tolerated in a learning model without compromising convergence to an REE. In addition, we study the cost, in terms of performance in the steady state of a central bank that acts to robustify learnability on the transition path to REE. (Note: This paper contains full-color graphics) JEL Classification: C6, E5E-stability, learnability, Learning, monetary policy, robust control