Adaptive nonparametric instrumental variables estimation: empirical choice of the regularization parameter

Joel L. Horowitz ()
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Joel L. Horowitz: Institute for Fiscal Studies and Northwestern University

No CWP30/13, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: In nonparametric instrumental variables estimation, the mapping that identifies the function of interest, g say, is discontinuous and must be regularised (that is, modified) to make consistent estimation possible. The amount of modification is controlled by a regularisation parameter. The optimal value of this parameter depends on unknown population characteristics and cannot be calculated in applications. Theoretically justified methods for choosing the regularisation parameter empirically in applications are not yet available. This paper presents such a method for use in series estimation, where the regularisation parameter is the number of terms in a series approximation to g. The method does not required knowledge of the smoothness of g or of other unknown functions. It adapts to their unknown smoothness. The estimator of g based on the empirically selected regularisation parameter converges in probability at a rate that is at least as fast as the asymptotically optimal rate multiplied by (logn)1/2, where n is the sample size. The asymptotic integrated mean-square error (AIMSE) of the estimator is within a specified factor of the optimal AIMSE.

Keywords: ill-posed inverse problem. regularisatoin; sieve estimation; series estimation; nonparametric estimation (search for similar items in EconPapers)
JEL-codes: C13 C14 C21 (search for similar items in EconPapers)
Date: 2013-07-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (2)

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