Instrumental Regression in Partially Linear Models

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

No 10-167, TSE Working Papers from Toulouse School of Economics (TSE)

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 parameterization of φ may generally lead to an inconsistent estimator of β, whereas even consistent nonparametric estimators for φ imply a slow rate of convergence of the estimator of β. An additional complication is that the solution of the equation necessitates the inversion of a compact operator that has to 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 that is explicitly interprated in the paper. Finally we show that the estimator achieves the semiparametric efficiency bound, even if the model is heteroscedastic. Monte Carlo simulations demonstrate the reasonable performance of the estimation procedure on finite samples.

JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2009-09
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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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 (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:tse:wpaper:22820

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