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The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions

Author

Listed:
  • Stypka, Oliver

    (Faculty of Statistics, Technical University Dortmund)

  • Wagner, Martin

    (Faculty of Statistics, Technical University Dortmund, Institute for Advanced Studies, Vienna and Bank of Slovenia, Ljubljana)

  • Grabarczyk, Peter

    (Faculty of Statistics, Technical University Dortmund)

  • Kawka, Rafael

    (Faculty of Statistics, Technical University Dortmund)

Abstract

The paper considers estimation and inference in cointegrating polynomial regressions, i. e., regressions that include deterministic variables, integrated processes and their powers as explanatory variables. The stationary errors are allowed to be serially correlated and the regressors are allowed to be endogenous. The main result shows that estimating such relationships using the Phillips and Hansen (1990) fully modified OLS approach developed for linear cointegrating relationships by incorrectly considering all integrated regressors and their powers as integrated regressors leads to the same limiting distribution as theWagner and Hong (2016) fully modified type estimator developed for cointegrating polynomial regressions. A key ingredient for the main result are novel limit results for kernel weighted sums of properly scaled nonstationary processes involving scaled powers of integrated processes. Even though the simulation results indicate performance advantages of the Wagner and Hong (2016) estimator that are partly present even in large samples, the results of the paper drastically enlarge the useability of the Phillips and Hansen (1990) estimator as implemented in many software packages.

Suggested Citation

  • Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    • Handle: RePEc:ihs:ihsesp:333
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    File URL: https://irihs.ihs.ac.at/id/eprint/4371
    File Function: First version, 2017
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    References listed on IDEAS

    as
    1. Wagner, Martin, 2012. "The Phillips unit root tests for polynomials of integrated processes," Economics Letters, Elsevier, vol. 114(3), pages 299-303.
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    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
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    11. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    12. Yandle, B. & Bhattarai, M. & Vijayaraghavan, M., 2004. "Environmental Kuznets Curves: a review of findings, methods, and policy implications. PERC Research study 02-1 update," IWMI Research Reports H044740, International Water Management Institute.
    13. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    14. Shin, Yongcheol, 1994. "A Residual-Based Test of the Null of Cointegration Against the Alternative of No Cointegration," Econometric Theory, Cambridge University Press, vol. 10(1), pages 91-115, March.
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    17. Liang, Hanying & Phillips, Peter C.B. & Wang, Hanchao & Wang, Qiying, 2016. "Weak Convergence To Stochastic Integrals For Econometric Applications," Econometric Theory, Cambridge University Press, vol. 32(6), pages 1349-1375, December.
    18. Kasparis, Ioannis, 2008. "Detection Of Functional Form Misspecification In Cointegrating Relations," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1373-1403, October.
    19. Saikkonen, Pentti, 1991. "Asymptotically Efficient Estimation of Cointegration Regressions," Econometric Theory, Cambridge University Press, vol. 7(1), pages 1-21, March.
    20. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    21. Martin Wagner, 2015. "The Environmental Kuznets Curve, Cointegration and Nonlinearity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(6), pages 948-967, September.
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    23. Jansson, Michael, 2002. "Consistent Covariance Matrix Estimation For Linear Processes," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1449-1459, December.
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    Cited by:

    1. Olimpia Neagu, 2019. "The Link between Economic Complexity and Carbon Emissions in the European Union Countries: A Model Based on the Environmental Kuznets Curve (EKC) Approach," Sustainability, MDPI, vol. 11(17), pages 1-27, August.
    2. Yicong Lin & Hanno Reuvers, 2020. "Cointegrating Polynomial Regressions with Power Law Trends: Environmental Kuznets Curve or Omitted Time Effects?," Papers 2009.02262, arXiv.org, revised Dec 2021.
    3. Stypka, Oliver & Wagner, Martin, 2019. "The Phillips unit root tests for polynomials of integrated processes revisited," Economics Letters, Elsevier, vol. 176(C), pages 109-113.

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    More about this item

    Keywords

    Cointegrating Polynomial Regression; Cointegration Test; Environmental Kuznets Curve; Fully Modified OLS Estimation; Integrated Process; Nonlinearity;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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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