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Econometrics Paper
Edgeworth Approximations for Semiparametric Instrumental Variable Estimators and Test Statistics
Oliver Linton
July 2000
Paper No' EM/2000/399:
Full Paper (pdf)

Tags: bandwidth selection; edgeworth approximation; instrumental viariables; kernel estimation; local polynomials.

We stablish the validity of higher order asymptotic expansions to the distribution of a version of the nonlinear semiparametric instrumental variable considered in Newey (1990) as well as to the distribution of a Wald statistic derived from it. We emply local polynomial smoothing with variable bandwidth, which includes local linear, kernel, and [a version of] nearest neighbour estimates as special cases. Our expansions are valid to order n ¿? for some 0 < ? < ½, where ? 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 estimation and testing problems and apply our methods to simulated data.