Semiparametric Estimation Of A Binaryresponse Model With A Change-Pointdue To A Covariate Threshold
AbstractThis 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.
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Date of creation: Feb 2007
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Binary response model; maximum score estimation; semiparametricestimation; threshold regression; nonlinear random utility models.;
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 & Myung Hwan Seo, 2007. "Semiparametric estimation of a binary response model with a change-point due to a covariate threshold," LSE Research Online Documents on Economics 6806, London School of Economics and Political Science, LSE Library.
- C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-06-23 (All new papers)
- NEP-ECM-2007-06-23 (Econometrics)
- NEP-UPT-2007-06-23 (Utility Models & Prospect Theory)
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