Convergence Properties of the Likelihood of Computed Dynamic Models

53 Pages Posted: 24 Jan 2007 Last revised: 12 Mar 2010

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: October 2005

Abstract

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.

Suggested Citation

Fernández-Villaverde, Jesús and Rubio-Ramirez, Juan Francisco and Santos, Manuel, Convergence Properties of the Likelihood of Computed Dynamic Models (October 2005). NBER Working Paper No. t0315. Available at SSRN: https://ssrn.com/abstract=827965

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 )

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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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