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Atlanta Fed Working Papers


Indeterminacy in a Forward-Looking Regime-Switching Model

Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha
Working Paper 2006-19a
Revised September 2007

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This paper is about the properties of Markov-switching rational expectations (MSRE) models. We discuss possible solution concepts for MSRE models, distinguishing between stationary and bounded equilibria. For the case of models with one variable, we provide a necessary and sufficient condition for uniqueness of a bounded equilibrium, and we relate this condition to an alternative, the generalized Taylor principle suggested by Davig and Leeper. We provide examples of models with multiple bounded and multiple stationary equilibria which suggest that it may be more difficult to rule out nonfundamental equilibria in MSRE models than in the single-regime case where the Taylor principle is known to guarantee local uniqueness.

JEL classification: E5

Key words: policy rule, inflation, serial dependence, multiple equilibria, stationary equilibrium, bounded equilibrium


The authors thank Troy Davig, Jordi Galí, Eric Leeper, Julio Rotemberg, Tom Sargent, Chris Sims, Lars Svensson, Eric Swanson, Noah Williams, and Michael Woodford for helpful discussions. Farmer acknowledges the support of National Science Foundation grant #SES 0418074. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Roger E.A. Farmer, Professor, Department of Economics, University of California, Los Angeles, Box 951477, Los Angeles, CA 90095-1477, 310-825-6547, 310-825-9528 (fax), rfarmer@econ.ucla.edu; Daniel Waggoner, Research Economist and Associate Policy Adviser, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8278, daniel.f.waggoner@atl.frb.org; or Tao Zha, Research Economist and Senior Policy Adviser, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8353, tzha@earthlink.net.

For further information, contact the Public Affairs Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8020.