New Minimum Chi-Square Methods in Empirical Finance

This paper reviews recently developed simulation-based minimum chi-square estimators for structural models. Particular attention is paid to selection of the auxiliary model that defines the GMM-type criterion used in the minimum chi-square estimation. Considerations of statistical efficiency and behavior under misspecification make a strong case for using a very flexible, nonparametric approach to select the auxiliary model. To avoid a numerically ill-behaved GMM criterion function, the dynamic stability of the auxiliary model must also be verified, though, interestly, the dynamic stability of the structural model itself is automatically enforced and need not be imposed in estimation. The empirical application involves estimation of a single-fator diffusion model for the 30-day Eurodollar interest rate.