COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1151

Second-Order Approximation for Semiparametric Instrumental
Variable Estimators and Test Statistics

Oliver B. Linton

1997

We construct second-order asymptotic expansions to the first four cumulants of a kernel-based version of the nonlinear semiparametric instrumental variable estimator considered in Newey (1990) as well as a Wald statistic derived from it. The expansions are valid to order n^{-2 epsilon}, in distribution for some 0 < epsilon < 1/2, where depends on the smoothness and dimensionality of the data distribution. We use the expansions to define optimal bandwidth selection methods for both estimation and testing problems and apply our methods to simulated data.