出版社：Suntory Toyota International Centre for Economics and Related Disciplines
摘要：This paper is concerned with semiparametric estimation of a threshold binary
response model. The estimation method considered in the paper is semiparametric
since the parameters for a regression function are finite-dimensional, while
allowing for heteroskedasticity of unknown form. In particular, the paper considers
Manski (1975, 1985)¡¯s maximum score estimator. The model in this paper is
irregular because of a change-point due to an unknown threshold in a covariate.
This irregularity coupled with the discontinuity of the objective function of the
maximum score estimator complicates the analysis of the asymptotic behavior of
the estimator. Sufficient conditions for the identification of parameters are given
and the consistency of the estimator is obtained. It is shown that the estimator of
the threshold parameter is n-consistent and the estimator of the remaining
regression parameters is cube root n-consistent. Furthermore, we obtain the
asymptotic distribution of the estimators. It turns out that a suitably normalized
estimator of the regression parameters converges weakly to the distribution to
which it would converge weakly if the true threshold value were known and
likewise for the threshold estimator.
关键词：Binary response model, maximum score estimation, semiparametric
estimation, threshold regression, nonlinear random utility models.
