Expectations and the Stability Problem for Optimal Monetary Policies

Abstract

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The Value of Interest Rate Stabilization Policies When Agents Are Learning

“…The relative weights assigned to output and interest rate stabilization are α x > 0 and α i > 0. The loss function differs from the one considered by Evans and Honkapohja (2003a, 2003b, 2006 by the inclusion of the third, interest rate stabilization element; Evans and Honkapohja have α i = 0. The three-element loss function we use has been given a micro-founded welfare-economic justification by Woodford (1999).…”

“…of this minimization problem is an optimal interest rate rule which is used together with equations describing private sector behavior to characterize the equilibrium of the economy. Evans and Honkapohja (2003a, 2003b, 2006 report that, regardless of whether the central bank operates under commitment or discretion, the REE of the system is always expectationally unstable when the policy rule is derived under the incorrect assumption that the private sector has rational expectations-they call the policy rule in this case the "fundamentals-based" policy rule. While the private sector is assumed to use a correctly specified model to form expectations, it does not initially possess knowledge of the REE parameterization of the model; instead it updates the parameters of its model in real time using all relevant data.…”

Debt, Policy Uncertainty, and Expectations Stabilization

“…For such rational expectations equilibria we are interested in asking under what conditions does an economy with learning dynamics converge to each equilibrium. Using stochastic approximation methods, Marcet and Sargent (1989b) and Evans and Honkapohja (2001) show that conditions for convergence are characterized by the local stability properties of the associated ordinary differential equation:…”

“…Within this class, policy rules are considered desirable if they have the additional property of stabilizing expectations under imperfect information, in the sense that expectations under learning dynamics converge to the rational expectations equilibrium associated with a given policy regime. This is adjudged by the property of expectational stability developed by Marcet and Sargent (1989b) and Evans and Honkapohja (2001). Good policy should be robust to both central bank and private agents' imperfect knowledge.…”

Learning with Expert Advice

“…25. In the terminology of Evans and Honkapohja (2001), LS α can achieve a "restricted perceptions" equilibrium. In a restricted perceptions equilibrium expectations are optimal within a restricted class of misspecified beliefs.…”