Endogeneity in Semiparametric Threshold Regression

Kourtellos, Andros; Stengos, Thanasis; Sun, Yiguo

doi:10.1017/s0266466621000256

Cited by 10 publications

(4 citation statements)

References 39 publications

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“…, nonparametric estimators such as the IDKE in YP and YLP seem preferable because they do not require any instruments. 7 In summary, the parametric setup in this paper is not only preferable practically (not requiring series expansion on h 1 v qi and h 2 v qi as in Kourtellos et al (2022)), but also preferable theoretically when instruments are employed (given that nonparametric methods do not require instruments).…”

Section: Identification Of γ and Linear Endogeneity Formsmentioning

confidence: 99%

“…It seems that the first approach does not suffer from the curse of dimensionality compared with the second approach. Following this paper, Kourtellos et al (2022) do the semiparametric extension of CF-I, and their method may be applied to the extension of CF-II. We will not discuss semiparametric approaches in this paper because the key advantage of the CF approaches above is their parametric setup.…”

Section: Identification Of γ and Linear Endogeneity Formsmentioning

confidence: 99%

“…Recently, Kourtellos, Stengos and Sun (2022) extended g I (z,q;θ) in CF-I to a semiparametric setup where the CFs take nonparametric forms, whereas the other components of g I (z,q;θ) retain parametric forms; their approach can also be applied to CF-II. Section 3.2 provides detailed comparisons between the parametric setup of this paper and their semiparametric setup.…”

Section: Introductionmentioning

confidence: 99%

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New Control Function Approaches in Threshold Regression With Endogeneity

Liao

Phillips

2023

Econom. Theory

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This paper studies control function (CF) approaches in endogenous threshold regression where the threshold variable is allowed to be endogenous. We first use a simple example to show that the structural threshold regression (STR) estimator of the threshold point in Kourtellos, Stengos and Tan (2016, Econometric Theory 32, 827–860) is inconsistent unless the endogeneity level of the threshold variable is low compared to the threshold effect. We correct the CF in the STR estimator to generate our first CF estimator using a method that extends the two-stage least squares procedure in Caner and Hansen (2004, Econometric Theory 20, 813–843). We develop our second CF estimator which can be treated as an extension of the classical CF approach in endogenous linear regression. Both these approaches embody threshold effect information in the conditional variance beyond that in the conditional mean. Given the threshold point estimates, we propose new estimates for the slope parameters. The first is a by-product of the CF approach, and the second type employs generalized method of moment (GMM) procedures based on two new sets of moment conditions. Simulation studies, in conjunction with the limit theory, show that our second CF estimator and confidence interval for the threshold point together with the associated second GMM estimator and confidence interval for the slope parameter dominate the other methods. We further apply the new estimation methodology to an empirical application from international trade to illustrate its usefulness in practice.

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Section: Identification Of γ and Linear Endogeneity Formsmentioning

confidence: 99%

Section: Identification Of γ and Linear Endogeneity Formsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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New Control Function Approaches in Threshold Regression With Endogeneity

Liao

Phillips

2023

Econom. Theory

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“…Yu et al (2021) correct and expand Kourtellos et al (2016)'s method, assuming the endogeneity is known with a finite functional form. Kourtellos et al (2021) further relax Yu et al (2021)'s assumption on the known endogenous form and use a nonparametric approach to control for the unknown form of endogeneity. Chen et al (2012) consider a threshold regression model with two separate exogenous threshold variables, while further allow two thresholds to be endogenous.…”

Section: Introductionmentioning

confidence: 99%

Estimation and Inference for the Threshold Model with Hybrid Stochastic Local Unit Root Regressors

Chen

Stengos

2022

JRFM

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In this paper, we study the estimation and inference of the threshold model with hybrid local stochastic unit root regressors. Our main contribution is to propose an estimator that generalizes the threshold model with various forms of nonstationary regressors and to obtain its limiting distribution theory. In particular, our proposed model generalizes the threshold model with unit root, local-to-unity, and stochastic unit root regressors. We provide the estimation strategy for the least squares estimator and derive the asymptotic results for the proposed estimator. Depending on the diminishing rate of the threshold effect, we find that the limiting distribution of the threshold estimator takes different forms. Monte Carlo simulations are used to assess our proposed estimator’s finite sample performance, which is found to perform well.

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