Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-22T04:54:54.339Z Has data issue: false hasContentIssue false
  • English
  • Français

ENDOGENEITY IN SEMIPARAMETRIC THRESHOLD REGRESSION

Published online by Cambridge University Press:  27 May 2021

Andros Kourtellos ,
Thanasis Stengos  and
Yiguo Sun
Andros Kourtellos
Affiliation:
University of Cyprus
Thanasis Stengos
Affiliation:
University of Guelph
Yiguo Sun*
Affiliation:
University of Guelph
*
Address correspondence to Yiguo Sun, Department of Economics and Finance, University of Guelph, Guelph, Ontario N1G 2W1, Canada; E-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 3 , June 2022 , pp. 562 - 595
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The first author acknowledges that this research has received funding from Marie Skłodowska-Curie Actions (Work Programme 2016-17) of the Excellence Science Pillar of the Horizon 2020 Research and Innovation Programme of the European Union under REA grant agreement No. 707990. The authors would like to thank the editor, the co-editor, and the four anonymous referees for their patience and excellent comments that significantly improved the manuscript.

References

REFERENCES

Andrews, D. W. K. (1991) Asymptotic normality of series estimators for nonparametric and semiparametric regression models. Econometrica 59, 307–345.CrossRefGoogle Scholar
Blundell, R., Chen, X. & Kristensen, D. (2007) Semiparametric IV estimation of shape invariant engel curves. Econometrica 75, 1613–1669.CrossRefGoogle Scholar
Caner, M. & Hansen, B. (2004) Instrumental variable estimation of a threshold model. Econometric Theory 20, 813–843.CrossRefGoogle Scholar
Caner, M. & Hansen, B. E. (2001) Threshold autoregression with a unit root. Econometrica 69, 1555–1596.CrossRefGoogle Scholar
Chan, K. S. (1993) Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics 21, 520–533.CrossRefGoogle Scholar
Chen, X. (2007) Large sample sieve estimation of semi-nonparametric models. In Heckman, J. J. & Leamer, E. E. (eds.), Handbook of Econometrics, vol. 6B, pp. 5549–5632. Springer.CrossRefGoogle Scholar
Christopoulos, D., McAdam, P. & Tzavalis, E. (2021) Dealing with endogeneity in threshold models using copulas. Journal of Business and Economic Statistics 39, 166–178.CrossRefGoogle Scholar
Delgado, M. S., Ozabaci, D., Sun, Y. & Kumbhakar, S. C. (2020) Smooth coefficient models with endogenous environmental variables. Econometric Reviews 39, 158–180.CrossRefGoogle Scholar
Durlauf, S. N. (1996) A theory of persistent income inequality. Journal of Economic Growth 1, 75–93.CrossRefGoogle Scholar
Dzyadyk, V. K. & Shevchuk, I. A. (2008) Theory of Uniform Approximation of Functions by Polynomials, Walter de Gruyter.Google Scholar
Galor, O. & Zeira, J. (1993) Income distribution and macroeconomics. Review of Economic Studies 60, 35–52.CrossRefGoogle Scholar
Gao, J. & Anh, V. (2000) A central limit theorem for a random quadratic form of strictly stationary processes. Statistics and Probability Letters 49, 69–79.CrossRefGoogle Scholar
Gonzalo, J. & Pitarakis, J. Y. (2007) Inferring the predictability induced by a persistent regressor in a predictive threshold model. Journal of Business and Economic Statistics 35, 202–217.CrossRefGoogle Scholar
Gonzalo, J. & Wolf, M. (2005) Subsampling inference in threshold autoregressive models. Journal of Econometrics 127, 201–224.CrossRefGoogle Scholar
Hansen, B. E. (2000) Sample splitting and threshold estimation. Econometrica 68, 575–603.CrossRefGoogle Scholar
Hastie, T. & Tibshirani, R. (1993) Varying parameter models. Journal of the Royal Statistical Society, Series B 55, 757–796.Google Scholar
Horn, S. D., Horn, R. A. & Duncan, D. B. (1975) Estimating heteroscedastic variances in linear model. Journal of the American Statistical Association 70, 380–385.CrossRefGoogle Scholar
Kapetanios, G. (2010) Testing for exogeneity in threshold models. Econometric Theory 26, 231–259.CrossRefGoogle Scholar
Kourtellos, A., Stengos, T. & Tan, C. M. (2016) Structural threshold regression. Econometric Theory 32, 827–860.CrossRefGoogle Scholar
Lee, S., Seo, M. H. & Shin, Y. (2016) The lasso for high dimensional regression with a possible change point. Journal of the Royal Statistical Society. Series B 78, 193–210.CrossRefGoogle ScholarPubMed
Li, D. & Ling, S. (2012) On the least squares estimation of multiple regime threshold autoregressive models. Journal of Econometrics 167, 240–253.CrossRefGoogle Scholar
Newey, W. K. (1997) Convergence rates and asymptotic normality for series estimators. Journal of Econometrics 79, 147–168.CrossRefGoogle Scholar
Newey, W. K. (2009) Two-step series estimation of sample selection models. The Econometrics Journal 12, 217–229.CrossRefGoogle Scholar
Newey, W. K. & McFadden, D. (1994) Large Sample Estimation and Hypothesis Testing (Vol. IV. Elsevier Science B.V., pp. 2111–2245).Google Scholar
Reinhart, C. M. & Rogoff, K. S. (2010) Growth in time of debt. American Economic Review 100, 573–578.CrossRefGoogle Scholar
Seber, G. A. F. (2008) A Matrix Handbook for Statisticians. Wiley.Google Scholar
Seo, M. H. & Linton, O. (2007) A smoothed least squares estimator for threshold regression models. Journal of Econometrics 141, 704–735.CrossRefGoogle Scholar
Seo, M. H. & Shin, Y. (2016) Dynamic panels with threshold effect and endogeneity. Journal of Econometrics 195, 169–186.CrossRefGoogle Scholar
Terasvirta, T., Granger, W. J. & Nelson, R. R. (1986) Aspects of modelling nonlinear time series. In Terasvirta, T., Granger, W. J., & Nelson, R. R. (eds.), Handbook of Econometrics, pp. 2917–2957. Elsevier.Google Scholar
Tong, H. (1990) Nonlinear Time Series: A Dynamical System Approach. Oxford University Press.Google Scholar
White, H. (2001) Asymptotic Theory for Econometricians. Academic Press.Google Scholar
Wooldridge, J. M. & White, H. (1988) Some invariance principles and central limit theorems for dependent heterogeneous processes. Econometrica 4, 210–230.Google Scholar
Xiang, S. (2012) Asymptotics on Laguerre or Hermite polynomial expansions and their applications in gauss quadrature. Journal of Mathematical Analysis and Applications J393, 434–444.CrossRefGoogle Scholar
Yu, P. (2012) Likelihood estimation and inference in threshold regression. Journal of Econometrics 167, 274–294.CrossRefGoogle Scholar
Yu, P. (2015) Adaptive estimation of the threshold point in threshold regression. Journal of Econometrics 189, 83–100.CrossRefGoogle Scholar
Yu, P., Liao, Q., & Phillips, P.C.B. (2020) New Control Function Approaches in Threshold Regression with Endogeneity, Working paper, University of Hong Kong. http://web.hku.hk/~pingyu/WorkingPapers/EndoTR_CF.pdf Google Scholar
Yu, P. & Phillips, C. B. (2018) Threshold regression with endogeneity. Journal of Econometrics 203, 50–68.CrossRefGoogle Scholar
Supplementary material: PDF

Kourtellos et al. supplementary material

Kourtellos et al. supplementary material

Download Kourtellos et al. supplementary material(PDF)
PDF 308.5 KB