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Likelihood estimation and inference in threshold regression

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  • Yu, Ping
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    Abstract

    This paper studies likelihood-based estimation and inference in parametric discontinuous threshold regression models with i.i.d. data. The setup allows heteroskedasticity and threshold effects in both mean and variance. By interpreting the threshold point as a “middle” boundary of the threshold variable, we find that the Bayes estimator is asymptotically efficient among all estimators in the locally asymptotically minimax sense. In particular, the Bayes estimator of the threshold point is asymptotically strictly more efficient than the left-endpoint maximum likelihood estimator and the newly proposed middle-point maximum likelihood estimator. Algorithms are developed to calculate asymptotic distributions and risk for the estimators of the threshold point. The posterior interval is proved to be an asymptotically valid confidence interval and is attractive in both length and coverage in finite samples.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 167 (2012)
    Issue (Month): 1 ()
    Pages: 274-294

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    Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:274-294

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Threshold regression; Structural change; Nonregular models; Boundary; Efficiency bounds; Bayes; Middle-point MLE; Compound Poisson process; Wiener–Hopf equation; Local asymptotic minimax; Credible set;

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    References

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    1. Savvides, A. & Stengos, T., 2000. "Income Inequality and Economic Development: Evidence from the Threshold Regression Model," Working Papers 2000-2, University of Guelph, Department of Economics and Finance.
    2. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
    3. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-25, April-Jun.
    4. Brenda L. Boetel & Ruben Hoffmann & Donald J. Liu, 2007. "Estimating Investment Rigidity within a Threshold Regression Framework: The Case of U.S. Hog Production Sector," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 89(1), pages 36-51.
    5. Sokbae Lee & Myung Hwan Seo, 2007. "Semiparametric estimation of a binary response model with a change-point due to a covariate threshold," LSE Research Online Documents on Economics 6806, London School of Economics and Political Science, LSE Library.
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    7. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    8. Savvides, Andreas & Stengos, Thanasis, 2000. "Income inequality and economic development: evidence from the threshold regression model," Economics Letters, Elsevier, vol. 69(2), pages 207-212, November.
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    12. Jesús Gonzalo & Michael Wolf, 2001. "Subsampling inference in threshold autoregressive models," Economics Working Papers 573, Department of Economics and Business, Universitat Pompeu Fabra.
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    14. Bai, Jushan, 1995. "Least Absolute Deviation Estimation of a Shift," Econometric Theory, Cambridge University Press, vol. 11(03), pages 403-436, June.
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    17. Durlauf, S.M. & Johnson, P.A., 1995. "Multiple Regimes and Cross-Country Growth Behavior," Working papers 9419r, Wisconsin Madison - Social Systems.
    18. Bwo-Nung Huang & Chin-Wei Yang, 2006. "Demand for cigarettes revisited: an application of the threshold regression model," Agricultural Economics, International Association of Agricultural Economists, vol. 34(1), pages 81-86, 01.
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    1. repec:wyi:journl:002203 is not listed on IDEAS
    2. repec:wyi:wpaper:002206 is not listed on IDEAS
    3. Kapetanios, George & Mitchell, James & Shin, Yongcheol, 2014. "A nonlinear panel data model of cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 179(2), pages 134-157.
    4. Haiqiang Chen, 2013. "Robust Estimation and Inference for Threshold Models with Integrated Regressors," SFB 649 Discussion Papers SFB649DP2013-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Donayre, Luiggi & Eo, Yunjong & Morley, James, 2014. "Improving Likelihood-Ratio-Based Confidence Intervals for Threshold Parameters in Finite Samples," Working Papers 2014-04, University of Sydney, School of Economics.

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