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.