SPECIFICATION AND ESTIMATION OF SEMIPARAMETRIC MULTIPLE-INDEX MODELS

We propose an easy to use derivative-based two-step estimation procedure for semiparametric index models, where the number of indexes is not known a priori+ In the first step various functionals involving the derivatives of the unknown function are estimated using nonparametric kernel estimators, in particular the average outer product of the gradient ~AOPG!+ By testing the rank of the AOPG we determine the required number of indexes+ Subsequently, we estimate the index parameters in a method of moments framework, with moment conditions constructed using the estimated average derivative functionals+ The estimator readily extends to multiple equation models and is shown to be root-N-consistent and asymptotically normal+