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's [Manski, Charles F., 1975. Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3 (3), 205-228; Manski, Charles F., 1985. Semiparametric analysis of discrete response. Asymptotic properties of the maximum score estimator. Journal of Econometrics 27 (3), 313-333] 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, [gamma]0, is n-1-consistent and the estimator of the remaining regression parameters, [theta]0, is n-1/3-consistent. Furthermore, we obtain the asymptotic distribution of the estimator. It turns out that both estimators and are oracle-efficient in that and converge weakly to the distributions to which they would converge weakly if the other parameter(s) were known.
Download Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. In case of further problems read
the IDEAS help
page. Note that these files are not on the IDEAS
site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 144 (2008) Issue (Month): 2 (June) Pages: 492-499 Download reference. The following formats are available: HTML
(with abstract),
plain text
(with abstract),
BibTeX,
RIS (EndNote, RefMan, ProCite),
ReDIF
Did you know? Citation analysis on IDEAS includes online papers that are freely accessible and whose text could be automatically analyzed, currently about 210000 papers.