IDENTIFICATION AND ESTIMATION OF NONPARAMETRIC STRUCTURAL MODELS BY INSTRUMENTAL VARIABLES METHOD∗

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 con-vergence rates of various regularization methods, including (the ordinary/iterated/generalized) Tikhonov and Showalter’s methods. An application of the general regularization theory is dis-cussed with a focus on a kernel smoothing method. We show an exact closed form, as well ∗I would like to thank W. Härdle, O. Linton, W. Newey, P. Phillips, and V. Spokoiny for helpful discussions and comments