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Atlanta Fed Working Papers

Estimating Nonlinear Dynamic Equilibrium Economies: A Likelihood Approach

Jesús Fernández-Villaverde and Juan Francisco Rubio-Ramírez
Working Paper 2004-1
January 2004

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This paper presents a framework to undertake likelihood-based inference in nonlinear dynamic equilibrium economies. The authors develop a sequential Monte Carlo algorithm that delivers an estimate of the likelihood function of the model using simulation methods. This likelihood can be used for parameter estimation and for model comparison. The algorithm can deal both with nonlinearities of the economy and with the presence of non-normal shocks. The authors show consistency of the estimate and its good performance in finite simulations. This new algorithm is important because the existing empirical literature that wanted to follow a likelihood approach was limited to the estimation of linear models with Gaussian innovations. The authors apply their procedure to estimate the structural parameters of the neoclassical growth model.

JEL classification: C63, C68, E37

Key words: dynamic equilibrium economies, likelihood function, nonlinear solution methods

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 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,

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