Federal Reserve Bank of Atlanta

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 only evaluate an approximated likelihood associated to 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 ap-proximated policy function. Third, we find that the error in the approximated likelihood gets compounded with the size of the sample. Fourth, we discuss con-vergence of Bayesian and classical estimates. We complete the paper with three applications to document the quantitative importance of our results