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Convergence Properties of the Likelihood of Computed Dynamic Models

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  • Jesus Fernandez-Villaverde

    ()
    (Department of Economics, University of Pennsylvania)

  • Juan F. Rubio-Ramirez

    ()
    (Federal Reserve Bank of Atlanta)

  • Manuel Santos

    ()
    (College of Business, Arizona State University)

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.

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Bibliographic Info

Paper provided by Penn Institute for Economic Research, Department of Economics, University of Pennsylvania in its series PIER Working Paper Archive with number 04-034.

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Length: 56 pages
Date of creation: 31 Aug 2004
Date of revision:
Handle: RePEc:pen:papers:04-034

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Keywords: computed dynamic models; likelihood inference; asymptotic properties;

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