Semi‐parametric Estimation in a Single‐index Model with Endogenous Variables

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.