Convergence properties of the likelihood of computed dynamic models

Jesús Fernández-Villaverde, Juan F. Rubio-Ramírez, Manuel S. Santos

Research output: Contribution to journalArticle

32 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)93-119
Number of pages27
JournalEconometrica
Volume74
Issue number1
DOIs
StatePublished - Jan 1 2006
Externally publishedYes

Keywords

  • Computation
  • Convergence
  • Dynamic economic models

ASJC Scopus subject areas

  • Economics and Econometrics

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