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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, S
  • Seo, MH

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.

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Bibliographic Info

Paper provided by University College London in its series Open Access publications from University College London with number http://discovery.ucl.ac.uk/16881/.

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Date of creation: Jun 2008
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Publication status: Published in J ECONOMETRICS (2008-06) v.144, p.492-499
Handle: RePEc:ner:ucllon:http://discovery.ucl.ac.uk/16881/

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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. Hashem Pesaran & Andreas Pick, 2004. "Econometric Issues in the Analysis of Contagion," Money Macro and Finance (MMF) Research Group Conference 2004 67, Money Macro and Finance Research Group.
  3. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
  4. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-29, July.
  5. 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.
  6. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
  7. Lee, Stephen M.S. & Pun, M.C., 2006. "On m out of n Bootstrapping for Nonstandard M-Estimation With Nuisance Parameters," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1185-1197, September.
  8. Delgado, Miguel A. & Hidalgo, Javier, . "Nonparametric Inference on Structural Breaks," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/2446, Universidad Carlos III de Madrid.
  9. 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.
  10. Nobuhiko Terui & Wirawan Dony Dahana, 2006. "Research Note—Estimating Heterogeneous Price Thresholds," Marketing Science, INFORMS, vol. 25(4), pages 384-391, 07-08.
  11. Gonzalo, Jesús & Wolf, Michael, . "Subsampling inference in threshold autoregressive models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3218, Universidad Carlos III de Madrid.
  12. Manski, Charles F., 1975. "Maximum score estimation of the stochastic utility model of choice," Journal of Econometrics, Elsevier, vol. 3(3), pages 205-228, August.
  13. repec:bla:restud:v:72:y:2005:i:1:p:57-76 is not listed on IDEAS
  14. John K. Dagsvik & Anders Karlstr�m, 2005. "Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 57-76.
  15. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
  16. Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
  17. 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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