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Likelihood estimation and inference in threshold regression

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  • Yu, Ping

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.

Suggested Citation

  • Yu, Ping, 2012. "Likelihood estimation and inference in threshold regression," Journal of Econometrics, Elsevier, vol. 167(1), pages 274-294.
  • Handle: RePEc:eee:econom:v:167:y:2012:i:1:p:274-294
    DOI: 10.1016/j.jeconom.2011.12.002
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(04), pages 778-810, August.
    2. 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.
    3. repec:bla:jtsera:v:38:y:2017:i:1:p:99-119 is not listed on IDEAS
    4. Li, Dong & Tong, Howell, 2016. "Nested sub-sample search algorithm for estimation of threshold models," LSE Research Online Documents on Economics 68880, London School of Economics and Political Science, LSE Library.
    5. Donayre Luiggi & Eo Yunjong & Morley James, 2018. "Improving likelihood-ratio-based confidence intervals for threshold parameters in finite samples," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 22(1), pages 1-11, February.
    6. Andros Kourtellos & Thanasis Stengos & Yiguo Sun, 2017. "Endogeneity in Semiparametric Threshold Regression," University of Cyprus Working Papers in Economics 10-2017, University of Cyprus Department of Economics.
    7. Pavlos Almanidis & Giannis Karagiannis & Robin Sickles, 2015. "Semi-nonparametric spline modifications to the Cornwell–Schmidt–Sickles estimator: an analysis of US banking productivity," Empirical Economics, Springer, vol. 48(1), pages 169-191, February.
    8. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    9. repec:wyi:journl:002203 is not listed on IDEAS
    10. Porter, Jack & Yu, Ping, 2015. "Regression discontinuity designs with unknown discontinuity points: Testing and estimation," Journal of Econometrics, Elsevier, vol. 189(1), pages 132-147.
    11. Daniel J. Henderson & Christopher F. Parmeter & Liangjun Su, 2017. "M-Estimation of a Nonparametric Threshold Regression Model," Working Papers 2017-15, University of Miami, Department of Economics.
    12. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    13. Fitzpatrick, Luke & Parmeter, Christopher F. & Agar, Juan, 2017. "Threshold Effects in Meta-Analyses With Application to Benefit Transfer for Coral Reef Valuation," Ecological Economics, Elsevier, vol. 133(C), pages 74-85.

    More about this item

    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;

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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