Convergence Properties of the Likelihood of Computed Dynamic Models

52 Pages Posted: 3 Sep 2004

See all articles by Jesús Fernández-Villaverde

Jesús Fernández-Villaverde

University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)

Juan Francisco Rubio-Ramirez

Federal Reserve Bank of Atlanta - Research Department

Manuel Santos

Arizona State University (ASU) - Economics Department

Multiple version iconThere are 2 versions of this paper

Date Written: August 31, 2004

Abstract

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, economists approximate the policy functions of the agents in the model with numerical methods. But this implies that, instead of the exact likelihood function, the researcher can evaluate only an approximated likelihood associated with the approximated policy function. What are the consequences for inference of the use of approximated likelihoods? First, we show that as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we prove that the approximated likelihood converges at the same rate as the approximated policy function. Third, we find that the error in the approximated likelihood gets compounded with the size of the sample. Fourth, we discuss convergence of Bayesian and classical estimates. We complete the paper with three applications to document the quantitative importance of our results.

Keywords: computed dynamic models, likelihood inference, asymptotic properties

JEL Classification: C1, C5, E1

Suggested Citation

Fernández-Villaverde, Jesús and Rubio-Ramirez, Juan Francisco and Santos, Manuel, Convergence Properties of the Likelihood of Computed Dynamic Models (August 31, 2004). PIER Working Paper No. 04-034; FRB Atlatnta Working Paper No. 2004-27. Available at SSRN: https://ssrn.com/abstract=586781 or http://dx.doi.org/10.2139/ssrn.586781

Jesús Fernández-Villaverde (Contact Author)

University of Pennsylvania - Department of Economics ( email )

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National Bureau of Economic Research (NBER)

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Juan Francisco Rubio-Ramirez

Federal Reserve Bank of Atlanta - Research Department ( email )

1000 Peachtree Street, NE
Atlanta, GA 30309-4470
United States
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404-498-8956 (Fax)

HOME PAGE: http://www.econ.umn.edu/~rubio

Manuel Santos

Arizona State University (ASU) - Economics Department ( email )

Tempe, AZ 85287-3806
United States
(480) 965-0748 (Phone)

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