IDENTIFICATION AND ESTIMATION OF NONPARAMETRIC STRUCTURAL

Woocheol Kim

No 733, Econometric Society 2004 Far Eastern Meetings from Econometric Society

Abstract: This paper concerns a new statistical approach to instrumental variables (IV) method for nonparametric structural models with additive errors. A general identifying condition of the model is proposed, based on richness of the space generated by marginal discretizations of joint density functions. For consistent estimation, we develop statistical regularization theory to solve a random Fredholm integral equation of the first kind. A\ minimal set of conditions are given for consistency of a general regularization method. Using an abstract smoothness condition, we derive some optimal bounds, given the accuracies of preliminary estimates, and show the convergence rates of various regularization methods, including (the ordinary/iterated/generalized) Tikhonov and Showalter's methods. An application of the general regularization theory is discussed with a focus on a kernel smoothing method. We show an exact closed form, as well as the optimal convergence rate, of the kernel IV estimates of various regularization methods. The finite sample properties of the estimates are investigated via a small-scale Monte Carlo experiment

Keywords: Nonparametric Strucutral Models; IV estimation; Statistical inverse problems (search for similar items in EconPapers)
JEL-codes: C14 C20 (search for similar items in EconPapers)
Date: 2004-08-11
New Economics Papers: this item is included in nep-ecm
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