Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models

A method is presented for estimating nonlinear simultaneous equations and transformation models in the presence of disturbance distribution of unknown form. It asymptotically achieves the lower variance bound for instrumental variables estimates. The author avoids smoothed nonparametric estimation, his instruments averaging over the unsmoothed empirical distribution of preliminary residuals. He allows for stationary serial dependence. In various settings, estimates are proposed and large-sample inference rules justified, these being unaffected if the optimal instruments use only an arbitrarily small vanishing fraction of the residuals. The author investigates theoretically the effect of such computational savings on the goodness of the normal approximation.