Instrumental Regression in Partially Linear Models

CORE Discussion Paper No. 2006/25

27 Pages Posted: 3 Aug 2006

See all articles by Jean-Pierre Florens

Jean-Pierre Florens

University of Toulouse

Jan Johannes

Ruprecht-Karls Universität Heidelberg

Sébastien Van Bellegem

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Date Written: December 2005

Abstract

We consider the semiparametric regression Xtβ + φ (Z) where β and φ(.) are unknown slope coefficient vector and function, and where the variables (X, Z) are endogeneous. We propose necessary and sufficient conditions for the identification of the parameters in the presence of instrumental variables. We also focus on the estimation of β. An incorrect parametrization of φ generally leads to an inconsistent estimator of β, whereas consistent nonparametric estimators for β have a slow rate of convergence. An additional complication is that the solution of the equation necessitates the inversion of a compact operator which can be estimated nonparametrically. In general this inversion is not stable, thus the estimation of β is ill-posed. In this paper, a √n -consistent estimator for β is derived under mild assumptions. One of these assumptions is given by the so-called source condition which we explicit and interpret in the paper. Finally we show that the estimator achieves the semiparametric efficiency bound, even if the model is heteroskedastic.

Keywords: Partially linear model, semiparametric regression, instrumental variables, endogeneity, ill-posed inverse problem, Tikhonov regularization, root-N consistent estimation, semiparametric efficiency bound

JEL Classification: C14, C30

Suggested Citation

Florens, Jean-Pierre and Johannes, Jan and Van Bellegem, Sébastien, Instrumental Regression in Partially Linear Models (December 2005). CORE Discussion Paper No. 2006/25, Available at SSRN: https://ssrn.com/abstract=921358 or http://dx.doi.org/10.2139/ssrn.921358

Jean-Pierre Florens (Contact Author)

University of Toulouse ( email )

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Jan Johannes

Ruprecht-Karls Universität Heidelberg ( email )

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Sébastien Van Bellegem

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

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B-1348 Louvain-la-Neuve, b-1348
Belgium