Daniel F. Waggoner and Tao Zha
Working Paper 2010-18a
Revised February 2012

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We estimate a Markov-switching mixture of two familiar macroeconomic models: a richly parameterized dynamic stochastic general equilibrium (DSGE) model and a corresponding Bayesian vector autoregression (BVAR) model. We show that the Markov-switching mixture model dominates both individual models and improves the fit considerably. Our estimation indicates that the DSGE model plays an important role only in the late 1970s and the early 1980s. We show how to use the mixture model as a data filter for estimation of the DSGE model when the BVAR model is not identified. Moreover, we show how to compute the impulse responses to the same type of shock shared by the DSGE and BVAR models when the shock is identified in the BVAR model. Our exercises demonstrate the importance of integrating model uncertainty and parameter uncertainty to address potential model misspecification in macroeconomics.

JEL classification: C52, E2, E4

Key words: Markov-switching mixture, heterogenous models, regime-dependent weights, model uncertainty, parameter uncertainty, impulse responses, policy analysis

For helpful discussions, the authors thank Dean Corbae, Frank Diebold, John Geweke, Lars Hansen, Bob King, Robert Kohn, Jianjun Miao, Frank Schorfheide, Chris Sims, Harald Uhlig, and seminar participants at the first European conference on Bayesian econometrics at Boston University and the conference "Macroeconomics and Policy Analysis after the Crisis in honor of Christopher Sims." This research is supported in part by the National Science Foundation grant no. SES-1127665. 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 Daniel F. Waggoner, Federal Reserve Bank of Atlanta, Research Department, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8278, daniel.f.waggoner@atl.frb.org, or Tao Zha, Federal Reserve Bank of Atlanta and Emory University, Research Department, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8353, tzha@earthlink.net.

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