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

Lee, Sokbae and Seo, Myung Hwan (2007) Semiparametric estimation of a binary response model with a change-point due to a covariate threshold. Econometrics Papers (EM/2007/516). Suntory and Toyota International Centres for Economics and Related Disciplines, London, UK.

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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.

Item Type: Monograph (Discussion Paper)
Official URL:
Additional Information: © 2007 The Authors
Divisions: Economics
Subjects: H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
JEL classification: C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C25 - Discrete Regression and Qualitative Choice Models
Date Deposited: 09 Jul 2008 11:14
Last Modified: 14 Dec 2020 00:42

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