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Convergence Properties of the Likelihood of Computed Dynamic Models

Jesus Fernandez-Villaverde (), Juan F Rubio-Ramirez () and Manuel Santos ()

No 315, NBER Technical Working Papers from National Bureau of Economic Research, Inc

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.

JEL-codes: C11 C15 D9 E10 E32 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-dge and nep-mac
Date: 2005-10
Note: TWP
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Published as Fernández-Villaverde, Jesus, Juan F. Rubio-Ramírez, and Manuel S. Santos. "Convergence Properties of the Likelihood of Computed Dynamic Models." Econometrica 74, 1 (2006): 93-119.

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Journal Article: Convergence Properties of the Likelihood of Computed Dynamic Models (2006) Downloads
Working Paper: Convergence properties of the likelihood of computed dynamic models (2004) Downloads
Working Paper: Convergence Properties of the Likelihood of Computed Dynamic Models (2004) Downloads
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