Semiparametric estimation of a binary response model with a change-point due to a covariate threshold
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.
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- Jesús Gonzalo & Michael Wolf, 2001.
"Subsampling inference in threshold autoregressive models,"
Economics Working Papers
573, Department of Economics and Business, Universitat Pompeu Fabra.
- Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
- 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.
- Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, 07.
- 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.
- Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
- 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.
- 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.
- 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.
- 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.
- 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.
- Kristin Forbes & Roberto Rigobon, 1999.
"No Contagion, Only Interdependence: Measuring Stock Market Co-movements,"
NBER Working Papers
7267, National Bureau of Economic Research, Inc.
- 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.
- Nobuhiko Terui & Wirawan Dony Dahana, 2006. "Research Note—Estimating Heterogeneous Price Thresholds," Marketing Science, INFORMS, vol. 25(4), pages 384-391, 07-08.
- 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.
- 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.
- 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.
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