Instrumental regression in partially linear models

Jean-Pierre Florens, Jan Johannes and Sebastien Van Bellegem ()

No 2006025, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We consider the semiparametric regression X t +(Z) where and (r 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 . An incorrect parametrization of generally leads to an inconsistent estimator of , whereas consistent nonparametric estimators for 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 is ill-posed. In this paper, a n-consistent estimator for is derived under mild assumptions. One of these assumptions is given by the socalled 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 (search for similar items in EconPapers)
JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2006-03
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Related works:
Journal Article: Instrumental regression in partially linear models (2012)
Working Paper: Instrumental Regression in Partially Linear Models (2009)
Working Paper: Instrumental Regression in Partially Linear Models (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2006025

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