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A STUDY OF A SEMIPARAMETRIC BINARY CHOICE MODEL WITH INTEGRATED COVARIATES

Published online by Cambridge University Press:  23 May 2006

Emmanuel Guerre  and
Hyungsik Roger Moon
Emmanuel Guerre
Affiliation:
LSTA Université Paris 6 and CREST
Hyungsik Roger Moon
Affiliation:
University of Southern California
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Abstract

This paper studies a semiparametric nonstationary binary choice model. Imposing a spherical normalization constraint on the parameter for identification purposes, we find that the maximum score estimator and smoothed maximum score estimator are at least [square root of n]-consistent. Comparing this rate to the convergence rate of the parametric maximum likelihood estimator (MLE), we show that when a normalization restriction is imposed on the parameter, the Park and Phillips (2000, Econometrica 68, 1249–1280) parametric MLE converges at a rate of n3/4 and its limiting distribution is a mixed normal. Finally, we show briefly how to apply our estimation method to a nonstationary single-index model.The first draft of the paper was written while Guerre was visiting the economics department of the University of Southern California. We thank Peter C.B. Phillips, a co-editor, and three anonymous referees for helpful comments and John Dolfin for proofreading. Guerre thanks the economics department of the University of Southern California for its hospitality during his visit. Moon appreciates financial support of the University of Southern California faculty development award.

Type
MISCELLENEA
Information
Econometric Theory , Volume 22 , Issue 4 , August 2006 , pp. 721 - 742
Copyright
© 2006 Cambridge University Press

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