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Inference and Specification Testing in Threshold Regression with Endogeneity

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Abstract

We propose three new methods of inference for the threshold point in endogenous threshold regression and two specification tests designed to assess the presence of endogeneity and threshold effects without necessarily relying on instrumentation of the covariates. The first inferential method is a parametric two-stage least squares method and is suitable when instruments are available. The second and third methods are based on smoothing the objective function of the integrated difference kernel estimator in different ways and these methods do not require instrumentation. All three methods are applicable irrespective of endogeneity of the threshold variable. The two specification tests are constructed using a score-type principle. The threshold effect test extends conventional parametric structural change tests to the nonparametric case. A wild bootstrap procedure is suggested to deliver finite sample critical values for both tests. Simulations show good finite sample performance of these procedures and the methods provide flexibility in testing and inference for practitioners working with threshold models.

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  • Ping Yu & Qin Liao & Peter C.B. Phillips, 2019. "Inference and Specification Testing in Threshold Regression with Endogeneity," Cowles Foundation Discussion Papers 2209, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2209
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    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d22/d2209.pdf
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    References listed on IDEAS

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    1. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(2), pages 1-21, June.
    2. Hsiao, Cheng & Li, Qi & Racine, Jeffrey S., 2007. "A consistent model specification test with mixed discrete and continuous data," Journal of Econometrics, Elsevier, vol. 140(2), pages 802-826, October.
    3. Yixiao Sun, 2005. "Adaptive Estimation of the Regression Discontinuity Model," Econometrics 0506003, University Library of Munich, Germany.
    4. Bai, Jushan, 1996. "Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach," Econometrica, Econometric Society, vol. 64(3), pages 597-622, May.
    5. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
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    Cited by:

    1. Rothfelder, Mario & Boldea, Otilia, 2016. "Testing for a Threshold in Models with Endogenous Regressors," Other publications TiSEM 40ca581a-e228-49ae-911f-e, Tilburg University, School of Economics and Management.
    2. Rothfelder, Mario P. & Boldea, Otilia, 2022. "Testing for a Threshold in Models with Endogenous Regressors," Other publications TiSEM 674deead-8826-450a-8f56-f, Tilburg University, School of Economics and Management.
    3. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.

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    More about this item

    Keywords

    Threshold regression; Endogeneity; Identification; Confidence interval; 2SLS; IDKE; Secification testing; Bootstrap; U-statistic;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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