SEMIPARAMETRIC ESTIMATION OF A BINARYRESPONSE MODEL WITH A CHANGE-POINTDUE TO A COVARIATE THRESHOLD

Sokbae (Simon) Lee and Myung Hwan Seo

STICERD - Econometrics Paper Series from Suntory and Toyota International Centres for Economics and Related Disciplines, LSE

Abstract: This paper is concerned with semiparametric estimation of a threshold binaryresponse model. The estimation method considered in the paper is semiparametricsince the parameters for a regression function are finite-dimensional, whileallowing for heteroskedasticity of unknown form. In particular, the paper considersManski (1975, 1985)'s maximum score estimator. The model in this paper isirregular because of a change-point due to an unknown threshold in a covariate.This irregularity coupled with the discontinuity of the objective function of themaximum score estimator complicates the analysis of the asymptotic behavior ofthe estimator. Sufficient conditions for the identification of parameters are givenand the consistency of the estimator is obtained. It is shown that the estimator ofthe threshold parameter is n-consistent and the estimator of the remainingregression parameters is cube root n-consistent. Furthermore, we obtain theasymptotic distribution of the estimators. It turns out that a suitably normalizedestimator of the regression parameters converges weakly to the distribution towhich it would converge weakly if the true threshold value were known andlikewise for the threshold estimator.

Keywords: Binary response model; maximum score estimation; semiparametricestimation; threshold regression; nonlinear random utility models. (search for similar items in EconPapers)
JEL-codes: C25 (search for similar items in EconPapers)
Date: 2007-02
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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 binary response model with a change-point due to a covariate threshold (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:cep:stiecm:516

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