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Estimation and Inference of Threshold Regression Models with Measurement Errors

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  • Chong, Terence Tai Leung
  • Chen, Haiqiang
  • Wong, Tsz Nga
  • Yan, Isabel K.

Abstract

An important assumption underlying standard threshold regression models and their variants in the extant literature is that the threshold variable is perfectly measured. Such an assumption is crucial for consistent estimation of model parameters. This paper provides the first theoretical framework for the estimation and inference of threshold regression models with measurement errors. A new estimation method that reduces the bias of the coefficient estimates and a Hausman-type test to detect the presence of measurement errors are proposed. Monte Carlo evidence is provided and an empirical application is given.

Suggested Citation

  • Chong, Terence Tai Leung & Chen, Haiqiang & Wong, Tsz Nga & Yan, Isabel K., 2015. "Estimation and Inference of Threshold Regression Models with Measurement Errors," MPRA Paper 68457, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:68457
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    References listed on IDEAS

    as
    1. Chong, Terence Tai-Leung, 2001. "Structural Change In Ar(1) Models," Econometric Theory, Cambridge University Press, vol. 17(1), pages 87-155, February.
    2. Jushan Bai & Haiqiang Chen & Terence Tai-Leung Chong & Seraph Xin Wang, 2008. "Generic consistency of the break-point estimators under specification errors in a multiple-break model," Econometrics Journal, Royal Economic Society, vol. 11(2), pages 287-307, July.
    3. K. S. Chan & H. Tong, 1986. "On Estimating Thresholds In Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 7(3), pages 179-190, May.
    4. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    5. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    6. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    7. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    8. Jeong, Jinook & Maddala, G S, 1991. "Measurement Errors and Tests for Rationality," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 431-439, October.
    9. Jerry Hausman, 2001. "Mismeasured Variables in Econometric Analysis: Problems from the Right and Problems from the Left," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 57-67, Fall.
    10. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
    11. Haiqiang Chen & Terence Chong & Jushan Bai, 2012. "Theory and Applications of TAR Model with Two Threshold Variables," Econometric Reviews, Taylor & Francis Journals, vol. 31(2), pages 142-170.
    12. Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002. "Estimation and model selection based inference in single and multiple threshold models," Journal of Econometrics, Elsevier, vol. 110(2), pages 319-352, October.
    13. Astatkie, T. & Watts, D. G. & Watt, W. E., 1997. "Nested threshold autoregressive (NeTAR) models," International Journal of Forecasting, Elsevier, vol. 13(1), pages 105-116, March.
    14. Terence Tai-Leung Chong, 2003. "Generic consistency of the break-point estimator under specification errors," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 167-192, June.
    15. Amemiya, Yasuo, 1990. "Two-stage instrumental variables estimators for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 44(3), pages 311-332, June.
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    Cited by:

    1. Lixiong Yang & Chingnun Lee & I‐Po Chen, 2021. "Threshold model with a time‐varying threshold based on Fourier approximation," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 406-430, July.
    2. Lixiong Yang, 2023. "Variable selection in threshold model with a covariate-dependent threshold," Empirical Economics, Springer, vol. 65(1), pages 189-202, July.
    3. Ebrahimi Salari, Taghi & Naji Meidani, Ali Akbar & Shabani Koshalshahi, Zeinab & Ajori Ayask, Amir Abbas, 2022. "The threshold effect of HDI on the relationship between financial development and oil revenues," Resources Policy, Elsevier, vol. 76(C).

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    More about this item

    Keywords

    Threshold Model; Measurement Error; Hausman-type Test.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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