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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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    3. 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.
    4. 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.
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    6. Yoonseok Lee & Yulong Wang, 2020. "Inference in Threshold Models," Center for Policy Research Working Papers 223, Center for Policy Research, Maxwell School, Syracuse University.
    7. 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.
    8. Varun Agiwal & Jitendra Kumar, 2020. "Bayesian estimation for threshold autoregressive model with multiple structural breaks," METRON, Springer;Sapienza Università di Roma, vol. 78(3), pages 361-382, December.
    9. Andros Kourtellos & Thanasis Stengos & Yiguo Sun, 2017. "Endogeneity in Semiparametric Threshold Regression," Working Paper series 17-13, Rimini Centre for Economic Analysis.
    10. Kai Yang & Dehui Wang & Boting Jia & Han Li, 2018. "An integer-valued threshold autoregressive process based on negative binomial thinning," Statistical Papers, Springer, vol. 59(3), pages 1131-1160, September.
    11. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(4), pages 778-810, August.
    12. Han Li & Kai Yang & Shishun Zhao & Dehui Wang, 2018. "First-order random coefficients integer-valued threshold autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 305-331, July.
    13. 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.
    14. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    15. 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.
    16. 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.
    17. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    18. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression asymptotics: From the compound Poisson process to two-sided Brownian motion," Economics Letters, Elsevier, vol. 172(C), pages 123-126.

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    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;
    All these keywords.

    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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