TY  - JOUR
AU  - Fernandez-Villaverde,Jesus
AU  - Rubio,Juan
AU  - Santos,Manuel
TI  - Convergence Properties of the Likelihood of Computed Dynamic Models
JF  - National Bureau of Economic Research Technical Working Paper Series
VL  - No. 315
PY  - 2005
Y2  - October 2005
UR  - http://www.nber.org/papers/t0315
L1  - http://www.nber.org/papers/t0315.pdf
N1  - Author contact info:
Jesus Fernandez-Villaverde
University of Pennsylvania
160 McNeil Building
3718 Locust Walk
Philadelphia, PA 19104
Tel: 267/307-1068
E-Mail: jesusfv@econ.upenn.edu

Juan Rubio

Manuel Santos
Arizona State University
E-Mail: msantos@asu.edu
AB  - 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.
ER  -