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Estimation of Nonlinear Error CorrectionModels

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  • Myung Hwan Seo

Abstract

Asymptotic inference in nonlinear vector error correction models (VECM) thatexhibit regime-specific short-run dynamics is nonstandard and complicated. Thispaper contributes the literature in several important ways. First, we establish theconsistency of the least squares estimator of the cointegrating vector allowing forboth smooth and discontinuous transition between regimes. This is a nonregularproblem due to the presence of cointegration and nonlinearity. Second, we obtainthe convergence rates of the cointegrating vector estimates. They differ dependingon whether the transition is smooth or discontinuous. In particular, we find that therate in the discontinuous threshold VECM is extremely fast, which is n^{3/2},compared to the standard rate of n: This finding is very useful for inference onshort-run parameters. Third, we provide an alternative inference method for thethreshold VECM based on the smoothed least squares (SLS). The SLS estimatorof the cointegrating vector and threshold parameter converges to a functional of avector Brownian motion and it is asymptotically independent of that of the slopeparameters, which is asymptotically normal.

Suggested Citation

  • Myung Hwan Seo, 2007. "Estimation of Nonlinear Error CorrectionModels," STICERD - Econometrics Paper Series 517, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  • Handle: RePEc:cep:stiecm:517
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    7. Anton Skrobotov, 2021. "Structural breaks in cointegration models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 63, pages 117-141.
    8. Chen, Pei-Fen & Lee, Chien-Chiang & Zeng, Jhih-Hong, 2014. "The relationship between spot and futures oil prices: Do structural breaks matter?," Energy Economics, Elsevier, vol. 43(C), pages 206-217.
    9. Daniel Ordoñez-Callamand & Luis F. Melo-Velandia & Oscar M. Valencia-Arana, 2017. "Current Account Sustainability in Latin America Considering Nonlinearities," Borradores de Economia 987, Banco de la Republica de Colombia.
    10. Lynda Atil & Hocine Fellag & Ana E. Sipols & M. T. Santos-Martín & Clara Simón Blas, 2024. "Non-linear Cointegration Test, Based on Record Counting Statistic," Computational Economics, Springer;Society for Computational Economics, vol. 64(4), pages 2205-2230, October.
    11. Dreger, Christian & Gerdesmeier, Dieter & Roffia, Barbara, 2020. "The impact of credit for house price overvaluations in the euro area: Evidence from threshold models," MPRA Paper 99523, University Library of Munich, Germany.
    12. Lukáš Frýd, 2020. "Alternativní pojetí Feldsteinova-Horiokova modelu za předpokladu proměnlivých parametrů: studie dopadu vstupu České republiky do Evropské unie [Alternative Concept of the Feldstein-Horioka Model un," Politická ekonomie, Prague University of Economics and Business, vol. 2020(2), pages 121-141.
    13. Jesús Gonzalo & Jean-Yves Pitarakis, 2013. "Estimation and inference in threshold type regime switching models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 8, pages 189-205, Edward Elgar Publishing.
    14. Dennis Kristensen & Anders Rahbek, 2007. "Likelihood-Based Inference in Nonlinear Error-Correction Models," CREATES Research Papers 2007-38, Department of Economics and Business Economics, Aarhus University.
    15. Kai-Yin Woo & Shu-Kam Lee & Cho-Yiu Joe Ng, 2018. "An Investigation Into The Dynamic Relationship Between Cpi And Ppi: Evidence From The Uk, France And Germany," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 64(05), pages 1081-1100, July.
    16. Novella Maugeri, 2014. "Some Pitfalls in Smooth Transition Models Estimation: A Monte Carlo Study," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 339-378, October.
    17. James A. Duffy & Sophocles Mavroeidis & Sam Wycherley, 2022. "Cointegration with Occasionally Binding Constraints," Papers 2211.09604, arXiv.org, revised Feb 2025.
    18. Ranjit Kumar Paul & Tanmoy Karak, 2022. "Asymmetric Price Transmission: A Case of Wheat in India," Agriculture, MDPI, vol. 12(3), pages 1-17, March.
    19. Deokwoo Nam, 2011. "The Roles of Nominal Exchange Rate and Relative Price Adjustments in PPP Reversion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(4), pages 775-785, June.
    20. Miguel Ángel Mendoza González, 2020. "Sensibilidad y asimetrías ante choques de ingreso en el consumo privado de México, 1995-2017. (Sensitivity and asymmetries of income shocks in Mexico's private consumption, 1995-2017)," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(1), pages 21-58, May.
    21. Mert Demir & Terrence F. Martell & Jun Wang, 2019. "The trilogy of China cotton markets: The lead–lag relationship among spot, forward, and futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(4), pages 522-534, April.

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    More about this item

    Keywords

    Threshold Cointegration; Smooth Transition Error Correction; Least Squares; Smoothed Least Squares; Consistency; Convergence Rate.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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