Semiparametric Estimation Of A Binaryresponse Model With A Change-Pointdue To A Covariate Threshold
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.
|Date of creation:||Feb 2007|
|Date of revision:|
|Contact details of provider:|| Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Nobuhiko Terui & Wirawan Dony Dahana, 2006. "Research Note—Estimating Heterogeneous Price Thresholds," Marketing Science, INFORMS, vol. 25(4), pages 384-391, 07-08.
- 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.
- Manski, Charles F. & Thompson, T. Scott, 1986. "Operational characteristics of maximum score estimation," Journal of Econometrics, Elsevier, vol. 32(1), pages 85-108, June.
- M. Hashem Pesaran & Andreas Pick, 2004.
"Econometric Issues in the Analysis of Contagion,"
CESifo Working Paper Series
1176, CESifo Group Munich.
- 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.
- Pesaran, M.H. & Pick, A., 2004. "Econometric Issues in the Analysis of Contagion," Cambridge Working Papers in Economics 0402, Faculty of Economics, University of Cambridge.
- 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.
- 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.
- Bruce E. Hansen, 1996.
"Sample Splitting and Threshold Estimation,"
Boston College Working Papers in Economics
319., Boston College Department of Economics, revised 12 May 1998.
- 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.
- 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.
- Kristin Forbes & Roberto Rigobon, 1999. "No Contagion, Only Interdependence: Measuring Stock Market Co-movements," NBER Working Papers 7267, National Bureau of Economic Research, Inc.
- Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
- Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
- 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.
- Oliver Linton & Myunghwan Seo, 2005. "A smoothed least squares estimator for threshold regression models," LSE Research Online Documents on Economics 4434, London School of Economics and Political Science, LSE Library.
- 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.
- Gonzalo, Jesus & Wolf, Michael, 2005.
"Subsampling inference in threshold autoregressive models,"
Journal of Econometrics,
Elsevier, vol. 127(2), pages 201-224, August.
- Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
- 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.
- 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.
- Horowitz, Joel L, 1992. "A Smoothed Maximum Score Estimator for the Binary Response Model," Econometrica, Econometric Society, vol. 60(3), pages 505-31, May.
When requesting a correction, please mention this item's handle: RePEc:cep:stiecm:/2007/516. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.