Edgeworth approximations for semiparametric instrumental variable estimators and test statistics

摘要

We establish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable estimator considered in Newey (Econometrica 58 (1990) 809) as well as to the distribution of a Waldstatistic derived from it. We employ local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and (a version of) nearest neighbor estimates as special cases. Our expansions are valid to order n~(-2#epsilon#) for some 0 <#epsilon# < 1/2, where #epsilon# depends on the smoothness and dimensionality of the data distribution and on the order of the polynomial chosen by the practitioner. We use the expansions to define optimal bandwidth selection methods for both estimationand testing problems and apply our methods to simulated data.