Endogeneity in Semiparametric Threshold Regression

Kourtellos, Andros; Stengos, Thanasis; Sun, Yiguo

doi:10.2139/ssrn.3080478

Cited by 6 publications

(6 citation statements)

References 15 publications

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“…We delay all the mathematical proofs in the Appendix. Supplementary proofs are given in Kourtellos, Stengos, and Sun (2017)-henceforth, we will refer to this as the Online Appendix.…”

Section: Introductionmentioning

confidence: 99%

Endogeneity in Semiparametric Threshold Regression

2021

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This paper estimates threshold regression models with an endogenous threshold variable using a nonparametric control function approach. Assuming diminishing threshold effects, we derive the consistency and limiting distribution of our proposed estimator constructed from the series approximation method for weakly dependent data. In addition, we propose a test for the endogeneity of the threshold variable, which is valid regardless of whether the threshold effects exist. We assess the performance of our methods using Monte Carlo simulations.

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“…We delay all the mathematical proofs in the Appendix. Supplementary proofs are given in Kourtellos, Stengos, and Sun (2017)-henceforth, we will refer to this as the Online Appendix.…”

Section: Introductionmentioning

confidence: 99%

Endogeneity in Semiparametric Threshold Regression

2021

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“…Second, working in Hansen's (2000) framework, Kourtellos, Stengos and Tan (2016) (KST hereafter) use a control function approach to deal with the case where q is also endogenous. 1 Their setup is parametric (see Kourtellos et al (2017) for a semiparametric extension) and the asymptotic theory is ‡awed. Speci…cally, Yu, Liao and Phillips (2018) (YLP hereafter) show that the structural threshold regression (STR) estimator of the threshold point in KST is not consistent unless the endogeneity level of the threshold variable is low compared to the threshold e¤ect.…”

Section: Introductionmentioning

confidence: 99%

Inference and Specification Testing in Threshold Regression with Endogeneity

Liao

Phillips

2019

SSRN Journal

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We propose three new methods of inference for the threshold point in endogenous threshold regression and two speci…cation tests designed to assess the presence of endogeneity and threshold e¤ects without necessarily relying on instrumentation of the covariates. The …rst 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 di¤erence kernel estimator in di¤erent ways and these methods do not require instrumentation. All three methods are applicable irrespective of endogeneity of the threshold variable. The two speci…cation tests are constructed using a score-type principle. The threshold e¤ect test extends conventional parametric structural change tests to the nonparametric case. A wild bootstrap procedure is suggested to deliver …nite sample critical values for both tests. Simulations show good …nite sample performance of these procedures and the methods provide ‡exibility in testing and inference for practitioners working with threshold models.

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“…Alternative methods to deal with the non-normality of the threshold variable were recently proposed by Kourtellos et al (2017) and Yu and Phillips (2017), who proposed semi-parametric and nonparametric estimators of the threshold parameter, respectively. Our method avoids the challenges of the semi-parametric and nonparametric estimators of the threshold or the remaining parameters of the model and, at the same time, it relies on a simple linear regression method of capturing the endogenous threshold variable bias effects on the estimates of these parameters.…”

Section: Introductionmentioning

confidence: 99%