Semiparametric estimation of a binary response model with a change-point due to a covariate threshold
AbstractThis 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 (gamma) over cap and (theta) over cap are oracle-efficient in that n((gamma) over cap (n) - gamma(0)) and n(1/3)((theta) over cap (n) - theta(0)) converge weakly to the distributions to which they would converge weakly if the other parameter(s) were known. (C) 2008 Elsevier B.V. All rights reserved.
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Bibliographic InfoPaper provided by University College London in its series Open Access publications from University College London with number http://discovery.ucl.ac.uk/16881/.
Date of creation: Jun 2008
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Publication status: Published in J ECONOMETRICS (2008-06) v.144, p.492-499
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Other versions of this item:
- Lee, Sokbae & Seo, Myung Hwan, 2008. "Semiparametric estimation of a binary response model with a change-point due to a covariate threshold," Journal of Econometrics, Elsevier, vol. 144(2), pages 492-499, June.
- Sokbae Lee & Myunghwan Seo, 2007. "Semiparametric Estimation Of A Binaryresponse Model With A Change-Pointdue To A Covariate Threshold," STICERD - Econometrics Paper Series /2007/516, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
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