Semi-parametric estimation in a single-index model with endogenous variables

Birke, Mélanie [Universität Bayreuth, Germany] Van Bellegem, Sébastien [UCL] Van Keilegom, Ingrid [UCL]

We consider a semiparametric single-index model, and suppose that endogeneity is present in the explanatory variables. The presence of an instrument is assumed that is non-correlated with the error term. We propose an estimator of the parametric component of the model, which is the solution of an ill-posed inverse problem. The estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study is conducted to illustrate the finite sample performance of the proposed estimator.