Semiparametric estimation of a binary response model with a change-point due to a covariate threshold

Sokbae (Simon) Lee and Myung Hwan Seo

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: 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.

Keywords: Binary response model; maximum score estimation; semiparametric estimation; threshold regression; nonlinear random utility models. (search for similar items in EconPapers)
JEL-codes: C25 (search for similar items in EconPapers)
Pages: 24 pages
Date: 2007-02
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http://eprints.lse.ac.uk/6806/ Open access version. (application/pdf)

Related works:
Journal Article: Semiparametric estimation of a binary response model with a change-point due to a covariate threshold (2008)
Working Paper: SEMIPARAMETRIC ESTIMATION OF A BINARYRESPONSE MODEL WITH A CHANGE-POINTDUE TO A COVARIATE THRESHOLD (2007)
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