Title: Semi-parametric estimation in a single index model with endogenous variables
Authors: Melanie Birke - University of Bayreuth (Germany) [presenting]
Sebastien Van Bellegem - Universite catholique de Louvain (Belgium)
Ingrid Van Keilegom - KU Leuven (Belgium)
Abstract: A semiparametric single-index model is considered where endogeneity is present in the explanatory variables. The presence of an instrument is assumed, that is noncorrelated with the error term. Endogeneity is a central issue when modeling statistical data coming from human or medical sciences and occurs when some of the independent variables in a regression model are correlated with the error term. It can arise when relevant explanatory variables are omitted from the model, as a result of sample selection errors or when unobserved subject selection occurs in experimental studies. When endogeneity is present, ordinary regression techniques produce biased and inconsistent estimators. A possible way out is to make use of the so-called instrumental variables. This approach is combined with the single-index model which is often used for dimension reduction. An estimator of the parametric component of the model is proposed, which is the solution of an ill-posed inverse problem. In a first step the unknown link function is estimated with kernel methods. In a second step this estimator is used to minimize a criterion function over a class of parameters. The estimator is shown to be asymptotically normal under certain regularity conditions common in empirical process theory. A simulation study is conducted to illustrate the finite sample performance of the proposed estimator.