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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 (2008) Semiparametric estimation of a binary response model with a change-point due to a covariate threshold. Journal of Econometrics, 144 (2). pp. 492-499. ISSN 0304-4076

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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’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, γ0, is n−1-consistent and the estimator of the remaining regression parameters, θ0, is n−1/3-consistent. Furthermore, we obtain the asymptotic distribution of the estimator. It turns out that both estimators View the MathML source and View the MathML source are oracle-efficient in that View the MathML source and View the MathML source converge weakly to the distributions to which they would converge weakly if the other parameter(s) were known.

Item Type: Article
Official URL:
Additional Information: © 2008 Elsevier
Library of Congress subject classification: H Social Sciences > HB Economic Theory
Journal of Economic Literature Classification System: C - Mathematical and Quantitative Methods > C2 - Econometric Methods: Single Equation Models; Single Variables > C25 - Discrete Regression and Qualitative Choice Models
Sets: Departments > Economics
Collections > Economists Online
Date Deposited: 23 Feb 2012 14:46

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