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Nonparametric methods for inference in the presence of instrumental variables

Authors: Peter Hall and Joel L. Horowitz
Date: 01 December 2005
Type: Journal Article, Annals of Statistics, Vol. 33, No. 6, pp. 2904-2929

Abstract

We suggest two nonparametric approaches, based on kernel methods and orthogonal series, respectively, to estimating regression functions in the presence of instrumental variables. For the first time in this class of problems we derive optimal convergence rates, and show that they are attained by particular estimators. In the presence of instrumental variables the relation that identifies the regression function also defines an ill-posed inverse problem, the "difficulty" of which depends on eigenvalues of a certain integral operator which is determined by the joint density of endogenous and instrumental variables. We delineate the role played by problem difficulty in determining both the optimal convergence rate and the appropriate choice of smoothing parameter.

Previous version:
Peter Hall and Joel L. Horowitz April 2003, Nonparametric methods for inference in the presence of instrumental variables, cemmap Working Paper, CWP02/03, Institute for Fiscal Studies

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