Convergence Properties of the Likelihood of Computed Dynamic Models
University of Pennsylvania - Department of Economics; National Bureau of Economic Research (NBER)
Juan Francisco Rubio-Ramirez
Duke University - Department of Economics; Federal Reserve Bank of Atlanta - Research Department
Arizona State University (ASU) - Economics Department
August 31, 2004
PIER Working Paper No. 04-034; FRB Atlatnta Working Paper No. 2004-27
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.
Number of Pages in PDF File: 52
Keywords: computed dynamic models, likelihood inference, asymptotic properties
JEL Classification: C1, C5, E1working papers series
Date posted: September 3, 2004
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