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Adaptive estimation of the threshold point in threshold regression

Listed author(s):
  • Yu, Ping
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    This paper studies semiparametric efficient estimation of the threshold point in threshold regression. The classical literature of semiparametric efficient estimation rests on the fact that the maximum likelihood estimator is efficient in any parametric submodel for a large class of loss functions. However, in threshold regression, the maximum likelihood estimator is not efficient, while the Bayes estimators are efficient and different loss functions induce different efficient estimators. For an additively separable loss function that separates the efficiency problem of the threshold point from that of other parameters, we show that the semiparametric and parametric efficiency risk bounds coincide. Then we design a semiparametric empirical Bayes estimator to achieve this bound. In consequence, the threshold point can be adaptively estimated even under conditional moment restrictions. We also provide a valid confidence interval called the nonparametric posterior interval for the threshold point. Simulation studies show that the semiparametric empirical Bayes approach is substantially better than existing methods. To illustrate our procedure in practice, we apply it to an economic growth model for detecting different growth patterns.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615001888
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    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 189 (2015)
    Issue (Month): 1 ()
    Pages: 83-100

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    Handle: RePEc:eee:econom:v:189:y:2015:i:1:p:83-100
    DOI: 10.1016/j.jeconom.2013.09.002
    Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

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    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
    3. 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.
    4. Hall, Alastair R. & Han, Sanggohn & Boldea, Otilia, 2012. "Inference regarding multiple structural changes in linear models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 170(2), pages 281-302.
    5. Yu, Ping, 2014. "The Bootstrap In Threshold Regression," Econometric Theory, Cambridge University Press, vol. 30(03), pages 676-714, June.
    6. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(03), pages 497-521, June.
    7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    8. Oka, Tatsushi & Qu, Zhongjun, 2011. "Estimating structural changes in regression quantiles," Journal of Econometrics, Elsevier, vol. 162(2), pages 248-267, June.
    9. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    10. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    11. Durlauf, Steven N & Johnson, Paul A, 1995. "Multiple Regimes and Cross-Country Growth Behaviour," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(4), pages 365-384, Oct.-Dec..
    12. Powell, James L & Stock, James H & Stoker, Thomas M, 1989. "Semiparametric Estimation of Index Coefficients," Econometrica, Econometric Society, vol. 57(6), pages 1403-1430, November.
    13. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    14. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
    15. Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
    16. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
    17. Zhongjun Qu & Pierre Perron, 2007. "Estimating and Testing Structural Changes in Multivariate Regressions," Econometrica, Econometric Society, vol. 75(2), pages 459-502, March.
    18. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    19. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    20. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, 09.
    21. Caner, Mehmet, 2002. "A Note On Least Absolute Deviation Estimation Of A Threshold Model," Econometric Theory, Cambridge University Press, vol. 18(03), pages 800-814, June.
    22. Yu, Ping, 2013. "Inconsistency of 2SLS estimators in threshold regression with endogeneity," Economics Letters, Elsevier, vol. 120(3), pages 532-536.
    23. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    24. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
    25. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    26. Stoker, Thomas M, 1986. "Consistent Estimation of Scaled Coefficients," Econometrica, Econometric Society, vol. 54(6), pages 1461-1481, November.
    27. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(02), pages 186-199, June.
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