Understanding Markov-Switching Rational Expectations Models

Roger E.A. Farmer, Daniel F. Waggoner, and Tao Zha
Working Paper 2009-5
March 2009

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We develop a set of necessary and sufficient conditions for equilibria to be determinate in a class of forward-looking Markov-switching rational expectations models, and we develop an algorithm to check these conditions in practice. We use three examples, based on the new Keynesian model of monetary policy, to illustrate our technique. Our work connects applied econometric models of Markov switching with forward-looking rational expectations models and allows an applied researcher to construct the likelihood function for models in this class over a parameter space that includes a determinate region and an indeterminate region.

JEL classification: E5

Key words: stability, nonlinearity, unique equilibrium, cross-regime indeterminacy, expectations formation, necessary and sufficient conditions

This paper is a thorough revision of the earlier draft titled "Understanding the New-Keynesian Model When Monetary Policy Switches Regimes" (NBER Working Paper no. 12965). The authors thank the referees and editors for thoughtful comments and Zheng Liu, Richard Rogerson, Eric Swanson, and John Williams for helpful discussions. They are grateful to Jacob Smith for excellent research assistance. This study is supported in part by National Science Foundation grant no. 0720839. 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, UCLA, 8283 Bunche Hall, 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.

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