Estimating Dynamic Equilibrium Economies: Linear versus Nonlinear Likelihood

Jesús Fernández-Villaverde and Juan Francisco Rubio-Ramírez
Working Paper 2004-3
February 2004

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This paper compares two methods for undertaking likelihood-based inference in dynamic equilibrium economies: a sequential Monte Carlo filter proposed by Fernández-Villaverde and Rubio-Ramírez (2004) and the Kalman filter. The sequential Monte Carlo filter exploits the nonlinear structure of the economy and evaluates the likelihood function of the model by simulation methods. The Kalman filter estimates a linearization of the economy around the steady state. The authors report two main results. First, both for simulated and for real data, the sequential Monte Carlo filter delivers a substantially better fit of the model to the data as measured by the marginal likelihood. This is true even for a nearly linear case. Second, the differences in terms of point estimates, even if relatively small in absolute values, have important effects on the moments of the model. The authors conclude that the nonlinear filter is a superior procedure for taking models to the data.

JEL classification: C63, C68, E37

Key words: dynamic equilibrium economies, likelihood function, the sequential Monte Carlo filter, the Kalman filter

The authors gratefully acknowledge Will Roberds, Tao Zha, and participants at several seminars for useful comments. They also thank the University of Minnesota Supercomputer Institute, which provided valuable computer assistance. 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 Jesús Fernández-Villaverde, Department of Economics, University of Pennsylvania, 160 McNeil Building, 3718 Locust Walk, Philadelphia, Pennsylvania 19104, 215-898-1504,, or Juan Francisco Rubio-Ramírez, Research Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8057,