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

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  • Lee, Sokbae
  • Seo, Myung Hwan

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 (1975, 1985)’s 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 is n-consistent and the estimator of the remaining regression parameters is cube root n-consistent. Furthermore, we obtain the asymptotic distribution of the estimators. It turns out that a suitably normalized estimator of the regression parameters converges weakly to the distribution to which it would converge weakly if the true threshold value were known and likewise for the threshold estimator.

Suggested Citation

  • Lee, Sokbae & Seo, Myung Hwan, 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.
  • Handle: RePEc:ehl:lserod:6806
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    References listed on IDEAS

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    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
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    6. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
    7. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    8. Joseph A. Herriges & Catherine L. Kling, 1999. "Nonlinear Income Effects in Random Utility Models," The Review of Economics and Statistics, MIT Press, vol. 81(1), pages 62-72, February.
    9. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    10. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
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    12. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
    13. Horowitz, Joel L., 1993. "Optimal Rates of Convergence of Parameter Estimators in the Binary Response Model with Weak Distributional Assumptions," Econometric Theory, Cambridge University Press, vol. 9(01), pages 1-18, January.
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    Citations

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    Cited by:

    1. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    2. Mayer Walter J. & Wu Chen, 2013. "A maximum score test for binary response models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(5), pages 619-639, December.
    3. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2016. "Oracle Estimation of a Change Point in High Dimensional Quantile Regression," Papers 1603.00235, arXiv.org, revised Dec 2016.

    More about this item

    Keywords

    Binary response model; maximum score estimation; semiparametric estimation; threshold regression; nonlinear random utility models.;

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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