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Atlanta Fed Working Papers


Minimal State Variable Solutions to Markov-Switching Rational Expectations Models

Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha
Working Paper 2008-23a
Revised September 2010

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We develop a new method for deriving minimal state variable (MSV) equilibria of a general class of Markov-switching rational expectations models and a new algorithm for computing these equilibria. We compare our approach to previously known algorithms, and we demonstrate that ours is both efficient and more reliable than previous methods in the sense that it is able to find MSV equilibria that previously known algorithms cannot. Further, our algorithm can find all possible MSV equilibria in models where there are multiple MSV equilibria. This feature is essential if one is interested in using a likelihood-based approach to estimation.

JEL classification: C61, C62

Key words: regime switching, rational expectations, MSV, iterative algorithm, policy changes


This research was supported by National Science Foundation grant. The authors thank Michel Juillard and Junior Maih for helpful discussions. 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, Department of Economics, University of California, Los Angeles, Box 951477, Los Angeles, CA 90095-1477, 310-825-6547, rfarmer@econ.ucla.edu; Daniel F. Waggoner, 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 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.