IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/100333.html
   My bibliography  Save this paper

Robust inference for threshold regression models

Author

Listed:
  • Hidalgo, Javier
  • Lee, Jungyoon
  • Seo, Myung Hwan

Abstract

This paper considers robust inference in threshold regression models when the practitioners do not know whether at the threshold point the true specification has a kink or a jump, nesting previous works that assume either continuity or discontinuity at the threshold. We find that the parameter values under the kink restriction are irregular points of the Hessian matrix, destroying the asymptotic normality and inducing the cube-root convergence rate for the threshold estimate. However, we are able to obtain the same asymptotic distribution as Hansen (2000) for the quasi-likelihood ratio statistic for the unknown threshold. We propose to construct confidence intervals for the threshold by bootstrap test inversion. Finite sample performances of the proposed procedures are examined through Monte Carlo simulations and an economic empirical application is given.

Suggested Citation

  • Hidalgo, Javier & Lee, Jungyoon & Seo, Myung Hwan, 2019. "Robust inference for threshold regression models," LSE Research Online Documents on Economics 100333, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:100333
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/100333/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    2. Bruce E. Hansen, 1999. "The Grid Bootstrap And The Autoregressive Model," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 594-607, November.
    3. Carmen M. Reinhart & Kenneth S. Rogoff, 2010. "Growth in a Time of Debt," American Economic Review, American Economic Association, vol. 100(2), pages 573-578, May.
    4. Bruce E. Hansen, 2000. "Sample Splitting and Threshold Estimation," Econometrica, Econometric Society, vol. 68(3), pages 575-604, May.
    5. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    6. Li, Dong & Ling, Shiqing, 2012. "On the least squares estimation of multiple-regime threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 167(1), pages 240-253.
    7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    8. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    9. Stephen G. Cecchetti & Sunil Mohanty & Fabrizio Zampolli, 2011. "Achieving growth amid fiscal imbalances: the real effects of debt," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 145-196.
    10. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    11. Yu, Ping, 2014. "The Bootstrap In Threshold Regression," Econometric Theory, Cambridge University Press, vol. 30(3), pages 676-714, June.
    12. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
    13. Hahn, Jinyong & Todd, Petra & Van der Klaauw, Wilbert, 2001. "Identification and Estimation of Treatment Effects with a Regression-Discontinuity Design," Econometrica, Econometric Society, vol. 69(1), pages 201-209, January.
    14. David Card & Alexandre Mas & Jesse Rothstein, 2008. "Tipping and the Dynamics of Segregation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(1), pages 177-218.
    15. Camille Landais, 2015. "Assessing the Welfare Effects of Unemployment Benefits Using the Regression Kink Design," American Economic Journal: Economic Policy, American Economic Association, vol. 7(4), pages 243-278, November.
    16. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    17. Joshua D. Angrist & Victor Lavy, 1999. "Using Maimonides' Rule to Estimate the Effect of Class Size on Scholastic Achievement," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(2), pages 533-575.
    18. Sokbae Lee & Hyunmin Park & Myung Hwan Seo & Youngki Shin, 2017. "Testing for a Debt‐Threshold Effect on Output Growth," Fiscal Studies, Institute for Fiscal Studies, vol. 38, pages 701-717, December.
    19. Stephen Cecchetti & Madhusudan Mohanty & Fabrizio Zampolli, 2011. "The real effects of debt," BIS Working Papers 352, Bank for International Settlements.
    20. J. Carpenter, 1999. "Test inversion bootstrap confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 159-172.
    21. Caner, Mehmet & Grennes,Thomas & Koehler-Geib, Fritzi, 2010. "Finding the tipping point -- when sovereign debt turns bad," Policy Research Working Paper Series 5391, The World Bank.
    22. Jason Abrevaya & Jian Huang, 2005. "On the Bootstrap of the Maximum Score Estimator," Econometrica, Econometric Society, vol. 73(4), pages 1175-1204, July.
    23. Bruce E. Hansen, 2017. "Regression Kink With an Unknown Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 228-240, April.
    24. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
    25. Jessica Pan, 2015. "Gender Segregation in Occupations: The Role of Tipping and Social Interactions," Journal of Labor Economics, University of Chicago Press, vol. 33(2), pages 365-408.
    26. Anna Mikusheva, 2007. "Uniform Inference in Autoregressive Models," Econometrica, Econometric Society, vol. 75(5), pages 1411-1452, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lixiong Yang, 2023. "Variable selection in threshold model with a covariate-dependent threshold," Empirical Economics, Springer, vol. 65(1), pages 189-202, July.
    2. Segun Thompson Bolarinwa & Richard Olaolu Olayeni & Xuan Vinh Vo, 2021. "Is there a nonlinear relationship between nonperforming loans and bank profitability? Evidence from dynamic panel threshold," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(3), pages 649-661, April.
    3. Sokbae Lee & Yuan Liao & Myung Hwan Seo & Youngki Shin, 2020. "Desperate Times Call For Desperate Measures: Government Spending Multipliers In Hard Times," Economic Inquiry, Western Economic Association International, vol. 58(4), pages 1949-1957, October.
    4. V., Ernesto Guerra & H., Eugenio Bobenrieth & H., Juan Bobenrieth & Wright, Brian D., 2023. "Endogenous thresholds in energy prices: Modeling and empirical estimation," Energy Economics, Elsevier, vol. 121(C).
    5. Alfonso Mendoza-Velázquez & Heidi J. Smith & Diego Mendoza-Martínez, 2023. "Regional Growth, Debt Thresholds and Subnational Sustainability," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 18(2), pages 1-23, Abril - J.
    6. Konstantina Manou & Panagiotis Palaios & Evangelia Papapetrou, 2019. "Housing wealth, household debt and financial assets: are there implications for consumption?," Working Papers 263, Bank of Greece.
    7. Somlanare Romuald Kinda & Relwendé Sawadogo, 2023. "Does financial development really spur industrialization in sub‐Saharan African countries?," African Development Review, African Development Bank, vol. 35(4), pages 390-402, December.
    8. Chih‐Hao Chang & Kam‐Fai Wong & Wei‐Yee Lim, 2023. "Threshold estimation for continuous three‐phase polynomial regression models with constant mean in the middle regime," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 77(1), pages 4-47, February.
    9. Myung Hwan Seo & Sueyoul Kim & Young-Joo Kim, 2019. "Estimation of dynamic panel threshold model using Stata," Stata Journal, StataCorp LP, vol. 19(3), pages 685-697, September.
    10. Olaoye, Olumide O. & Eluwole, Oluwatosin O. & Ayesha, Aziz & Afolabi, Olugbenga O., 2020. "Government spending and economic growth in ECOWAS: An asymmetric analysis," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    11. Wayne Yuan Gao & Sheng Xu & Kan Xu, 2020. "Two-Stage Maximum Score Estimator," Papers 2009.02854, arXiv.org, revised Sep 2022.
    12. Sun, Yan & Wan, Chuang & Zhang, Wenyang & Zhong, Wei, 2024. "A Multi-Kink quantile regression model with common structure for panel data analysis," Journal of Econometrics, Elsevier, vol. 239(2).
    13. Yoonseok Lee & Yulong Wang, 2020. "Inference in Threshold Models," Center for Policy Research Working Papers 223, Center for Policy Research, Maxwell School, Syracuse University.
    14. Yaojie Zhang & Mengxi He & Danyan Wen & Yudong Wang, 2022. "Forecasting Bitcoin volatility: A new insight from the threshold regression model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(3), pages 633-652, April.
    15. Gregory Cox, 2022. "A Generalized Argmax Theorem with Applications," Papers 2209.08793, arXiv.org.
    16. Yan Sun & Wei Huang, 2024. "Estimation and testing of kink regression model with endogenous regressors," Computational Statistics, Springer, vol. 39(6), pages 3115-3135, September.
    17. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    18. Woosik Gong & Myung Hwan Seo, 2022. "Bootstraps for Dynamic Panel Threshold Models," Papers 2211.04027, arXiv.org, revised Sep 2024.
    19. Alfonso Mendoza-Velazquez & Heidi J. Smith & Diego Mendoza-Martinez, 2022. "Subnational Regional Growth, Debt Thresholds and Sustainability," Working Paper Series Sobre México 2022001, Sobre México. Temas en economía.
    20. Chen, Yining, 2020. "Jump or kink: note on super-efficiency in segmented linear regression break-point estimation," LSE Research Online Documents on Economics 103488, London School of Economics and Political Science, LSE Library.
    21. Lihua Hu & Yuanyuan Chen & Tao Fan, 2022. "The Influence of Government Subsidies on the Efficiency of Technological Innovation: A Panel Threshold Regression Approach," Sustainability, MDPI, vol. 15(1), pages 1-21, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel J. Henderson & Christopher F. Parmeter & Liangjun Su, 2017. "M-Estimation of a Nonparametric Threshold Regression Model," Working Papers 2017-15, University of Miami, Department of Economics.
    2. Yu, Ping & Phillips, Peter C.B., 2018. "Threshold regression with endogeneity," Journal of Econometrics, Elsevier, vol. 203(1), pages 50-68.
    3. Miao, Ke & Li, Kunpeng & Su, Liangjun, 2020. "Panel threshold models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 219(1), pages 137-170.
    4. Yu, Ping, 2015. "Adaptive estimation of the threshold point in threshold regression," Journal of Econometrics, Elsevier, vol. 189(1), pages 83-100.
    5. Martins, Luis F., 2021. "The US debt–growth nexus along the business cycle," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    6. Alfonso Mendoza-Velazquez & Heidi J. Smith & Diego Mendoza-Martinez, 2022. "Subnational Regional Growth, Debt Thresholds and Sustainability," Working Paper Series Sobre México 2022001, Sobre México. Temas en economía.
    7. Rothfelder, Mario & Boldea, Otilia, 2016. "Testing for a Threshold in Models with Endogenous Regressors," Discussion Paper 2016-029, Tilburg University, Center for Economic Research.
    8. Seo, Myung Hwan & Linton, Oliver, 2007. "A smoothed least squares estimator for threshold regression models," Journal of Econometrics, Elsevier, vol. 141(2), pages 704-735, December.
    9. Javier Hidalgo & Jungyoon Lee & Myung Hwan Seo, 2017. "Robust Inference and Testing of Continuity in Threshold Regression Models," STICERD - Econometrics Paper Series 590, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    10. Law, Siong Hook & Ng, Chee Hung & Kutan, Ali M. & Law, Zhi Kei, 2021. "Public debt and economic growth in developing countries: Nonlinearity and threshold analysis," Economic Modelling, Elsevier, vol. 98(C), pages 26-40.
    11. Bruce E. Hansen, 2017. "Regression Kink With an Unknown Threshold," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(2), pages 228-240, April.
    12. Chung-Ming Kuan & Christos Michalopoulos & Zhijie Xiao, 2017. "Quantile Regression on Quantile Ranges – A Threshold Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 99-119, January.
    13. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    14. Seo, Myung Hwan & Shin, Yongcheol, 2016. "Dynamic panels with threshold effect and endogeneity," Journal of Econometrics, Elsevier, vol. 195(2), pages 169-186.
    15. Imbens, Guido W. & Lemieux, Thomas, 2008. "Regression discontinuity designs: A guide to practice," Journal of Econometrics, Elsevier, vol. 142(2), pages 615-635, February.
    16. Lee, Yoonseok & Wang, Yulong, 2023. "Threshold regression with nonparametric sample splitting," Journal of Econometrics, Elsevier, vol. 235(2), pages 816-842.
    17. Lee, Sokbae & Seo, Myung Hwan, 2008. "Semiparametric estimation of a binary response model with a change-point due to a covariate threshold," Journal of Econometrics, Elsevier, vol. 144(2), pages 492-499, June.
    18. Christian Richter & Sara El Asy, 2019. "Is Public Debt Always Harmful to Economic Growth," Working Papers 52, The German University in Cairo, Faculty of Management Technology.
    19. Chaoyi Chen & Yiguo Sun, 2018. "Monte Carlo Comparison for Nonparametric Threshold Estimators," JRFM, MDPI, vol. 11(3), pages 1-15, August.
    20. Kourtellos, Andros & Stengos, Thanasis & Tan, Chih Ming, 2013. "The effect of public debt on growth in multiple regimes," Journal of Macroeconomics, Elsevier, vol. 38(PA), pages 35-43.

    More about this item

    Keywords

    Change point; Cube root; Grid bootstrap; Kink;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:100333. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.