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

Lee, S; Seo, MH; (2008) Semiparametric estimation of a binary response model with a change-point due to a covariate threshold. J ECONOMETRICS , 144 (2) 492 - 499. 10.1016/j.jeconom.2008.02.003. Green open access

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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'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.

Type: Article
Title: Semiparametric estimation of a binary response model with a change-point due to a covariate threshold
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jeconom.2008.02.003
Keywords: binary response model, maximum score estimation, nonlinear random utility models, semiparametric estimation, threshold regression, MAXIMUM SCORE ESTIMATOR, LEAST-SQUARES ESTIMATOR, CUBE ROOT ASYMPTOTICS, RANDOM UTILITY-MODELS, REGRESSION-MODEL, INFERENCE, CONTAGION, INCOME
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL SLASH
UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of SandHS > Dept of Economics
URI: http://discovery.ucl.ac.uk/id/eprint/16881
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