Abstract :
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+
