IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v144y2008i2p492-499.html
   My bibliography  Save this article

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

Author

Listed:
  • 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'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 and are oracle-efficient in that and converge weakly to the distributions to which they would converge weakly if the other parameter(s) were known.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:144:y:2008:i:2:p:492-499
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(08)00042-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Nobuhiko Terui & Wirawan Dony Dahana, 2006. "Research Note—Estimating Heterogeneous Price Thresholds," Marketing Science, INFORMS, vol. 25(4), pages 384-391, 07-08.
    4. Pesaran, M. Hashem & Pick, Andreas, 2007. "Econometric issues in the analysis of contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 31(4), pages 1245-1277, April.
    5. John K. Dagsvik & Anders Karlström, 2005. "Compensating Variation and Hicksian Choice Probabilities in Random Utility Models that are Nonlinear in Income," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 57-76.
    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. 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. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    11. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
    12. Kristin J. Forbes & Roberto Rigobon, 2002. "No Contagion, Only Interdependence: Measuring Stock Market Comovements," Journal of Finance, American Finance Association, vol. 57(5), pages 2223-2261, October.
    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(1), pages 1-18, January.
    14. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
    15. Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-531, May.
    16. 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.
    17. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
    18. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    2. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2018. "Oracle Estimation of a Change Point in High-Dimensional Quantile Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1184-1194, July.
    3. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    4. Michael W. Robbins & Colin M. Gallagher & Robert B. Lund, 2016. "A General Regression Changepoint Test for Time Series Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 670-683, April.
    5. Wayne Yuan Gao & Sheng Xu & Kan Xu, 2020. "Two-Stage Maximum Score Estimator," Papers 2009.02854, arXiv.org, revised Sep 2022.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Le-Yu & Lee, Sokbae, 2018. "Best subset binary prediction," Journal of Econometrics, Elsevier, vol. 206(1), pages 39-56.
    2. Lahiri, Kajal & Yang, Liu, 2013. "Forecasting Binary Outcomes," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1025-1106, Elsevier.
    3. Jeremy T. Fox, 2018. "Estimating matching games with transfers," Quantitative Economics, Econometric Society, vol. 9(1), pages 1-38, March.
    4. Le-Yu Chen & Sokbae (Simon) Lee & Myung Jae Sung, 2013. "Maximum score estimation of preference parameters for a binary choice model under uncertainty," CeMMAP working papers CWP14/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. 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.
    6. Le‐Yu Chen & Sokbae Lee & Myung Jae Sung, 2014. "Maximum score estimation with nonparametrically generated regressors," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 271-300, October.
    7. D. F. Benoit & D. Van Den Poel, 2010. "Binary quantile regression: A Bayesian approach based on the asymmetric Laplace density," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/662, Ghent University, Faculty of Economics and Business Administration.
    8. Chen, Songnian & Zhang, Hanghui, 2015. "Binary quantile regression with local polynomial smoothing," Journal of Econometrics, Elsevier, vol. 189(1), pages 24-40.
    9. Sadikoglu, Serhan, 2019. "Essays in econometric theory," Other publications TiSEM 99d83644-f9dc-49e3-a4e1-5, Tilburg University, School of Economics and Management.
    10. Chen, Le-Yu & Oparina, Ekaterina & Powdthavee, Nattavudh & Srisuma, Sorawoot, 2022. "Robust Ranking of Happiness Outcomes: A Median Regression Perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 200(C), pages 672-686.
    11. Yan, Jin & Yoo, Hong Il, 2019. "Semiparametric estimation of the random utility model with rank-ordered choice data," Journal of Econometrics, Elsevier, vol. 211(2), pages 414-438.
    12. Hidalgo, Javier & Lee, Jungyoon & Seo, Myung Hwan, 2019. "Robust inference for threshold regression models," Journal of Econometrics, Elsevier, vol. 210(2), pages 291-309.
    13. Horowitz, Joel L., 2004. "Semiparametric models," Papers 2004,17, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    14. Shakeeb Khan & Fu Ouyang & Elie Tamer, 2021. "Inference on semiparametric multinomial response models," Quantitative Economics, Econometric Society, vol. 12(3), pages 743-777, July.
    15. Adam M. Rosen & Takuya Ura, 2019. "Finite Sample Inference for the Maximum Score Estimand," Papers 1903.01511, arXiv.org, revised May 2020.
    16. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Discussion Papers Series 626, School of Economics, University of Queensland, Australia.
    17. Dominic Coey & Bradley J. Larsen & Kane Sweeney & Caio Waisman, 2021. "Scalable Optimal Online Auctions," Marketing Science, INFORMS, vol. 40(4), pages 593-618, July.
    18. Chen, Le-Yu & Oparina, Ekaterina & Powdthavee, Nattavudh & Srisuma, Sorawoot, 2019. "Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth about Happiness Scales," IZA Discussion Papers 12152, Institute of Labor Economics (IZA).
    19. Jun, Sung Jae & Pinkse, Joris & Wan, Yuanyuan, 2015. "Classical Laplace estimation for n3-consistent estimators: Improved convergence rates and rate-adaptive inference," Journal of Econometrics, Elsevier, vol. 187(1), pages 201-216.
    20. Fu Ouyang & Thomas Tao Yang, 2022. "Semiparametric Estimation of Dynamic Binary Choice Panel Data Models," Papers 2202.12062, arXiv.org, revised Feb 2024.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:144:y:2008:i:2:p:492-499. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.