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SPECIFICATION AND ESTIMATION OF SEMIPARAMETRIC MULTIPLE-INDEX MODELS

Published online by Cambridge University Press:  17 July 2008

Bas Donkers  and
Marcia Schafgans
Bas Donkers*
Affiliation:
Erasmus University Rotterdam
Marcia Schafgans
Affiliation:
London School of Economics
*
Address correspondence to Bas Donkers, Econometric Institute and Department of Business Economics, Erasmus University Rotterdam, P.O. Box 1738, NL-3000 DR Rotterdam, The Netherlands; e-mail: donkers@few.eur.nl
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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.

Type
Research Article
Information
Econometric Theory , Volume 24 , Issue 6 , December 2008 , pp. 1584 - 1606
Copyright
Copyright © Cambridge University Press 2008

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