NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

Convergence Properties of the Likelihood of Computed Dynamic Models

Jesus Fernandez-Villaverde, Juan Rubio, Manuel Santos

NBER Technical Working Paper No. 315
Issued in October 2005
NBER Program(s):   TWP

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.

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Document Object Identifier (DOI): 10.3386/t0315

Published: 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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