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Response surface regressions for critical value bounds and approximate p-values in equilibrium correction models

Author

Listed:
  • Sebastian Kripfganz

    (University of Exeter)

  • Daniel C. Schneider

    (Max Planck Institute for Demographic Research)

Abstract

Single-equation conditional equilibrium correction models can be used to test for the existence of a level relationship among the variables of interest. The distributions of the respective test statistics are nonstandard under the null hypothesis of no such relationship and critical values need to be obtained with stochastic simulations. We compute more than 95 billion F -statistics and 57 billion t-statistics for a large number of specifications of the Pesaran, Shin, and Smith (2001, Journal of Applied Econometrics 16: 289Ð326) bounds test. Our large-scale simulations enable us to draw smooth density functions and to estimate response surface models that improve upon and substantially extend the set of available critical values for the bounds test. Besides covering the full range of possible sample sizes and lag orders, our approach notably allows for any number of variables in the long-run level relationship by exploiting the diminishing effect on the distributions of adding another variable to the model. The computation of approximate p-values enables a fine-grained statistical inference and allows us to quantify the finite-sample distortions from using asymptotic critical values. We find that the bounds test can be easily oversized by more than 5 percentage points in small samples.

Suggested Citation

  • Sebastian Kripfganz & Daniel C. Schneider, 2019. "Response surface regressions for critical value bounds and approximate p-values in equilibrium correction models," Discussion Papers 1901, University of Exeter, Department of Economics.
  • Handle: RePEc:exe:wpaper:1901
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    File URL: http://people.exeter.ac.uk/RePEc/dpapers/DP1901.pdf
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    References listed on IDEAS

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    1. MacKinnon, James G & Haug, Alfred A & Michelis, Leo, 1999. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 563-577, Sept.-Oct.
    2. Mills, Terence C. & Pentecost, Eric J., 2001. "The real exchange rate and the output response in four EU accession countries," Emerging Markets Review, Elsevier, vol. 2(4), pages 418-430, December.
    3. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
    4. Presno, Maria Jose & Lopez, Ana Jesus, 2003. "Response surface estimates of stationarity tests with a structural break," Economics Letters, Elsevier, vol. 78(3), pages 395-399, March.
    5. Sephton, Peter S., 1995. "Response surface estimates of the KPSS stationarity test," Economics Letters, Elsevier, vol. 47(3-4), pages 255-261, March.
    6. Pesaran, M. Hashem & Shin, Yongcheol & Smith, Richard J., 2000. "Structural analysis of vector error correction models with exogenous I(1) variables," Journal of Econometrics, Elsevier, vol. 97(2), pages 293-343, August.
    7. Athina Kanioura & Paul Turner, 2005. "Critical values for an F-test for cointegration in a multivariate model," Applied Economics, Taylor & Francis Journals, vol. 37(3), pages 265-270.
    8. Jesús Otero & Jeremy Smith, 2012. "Response surface models for the Leybourne unit root tests and lag order dependence," Computational Statistics, Springer, vol. 27(3), pages 473-486, September.
    9. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of a Modified Dickey-Fuller Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 57(3), pages 411-419, August.
    10. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-1072, June.
    11. Uwe Hassler & Jürgen Wolters, 2006. "Autoregressive distributed lag models and cointegration," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 90(1), pages 59-74, March.
    12. Neil R. Ericsson & James G. MacKinnon, 2002. "Distributions of error correction tests for cointegration," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 285-318, June.
    13. Carrion i Silvestre, Josep Lluis & Sanso i Rossello, Andreu & Artis Ortuno, Manuel, 1999. "Response surfaces estimates for the Dickey-Fuller unit root test with structural breaks," Economics Letters, Elsevier, vol. 63(3), pages 279-283, June.
    14. Peter Sephton, 2017. "Finite Sample Critical Values of the Generalized KPSS Stationarity Test," Computational Economics, Springer;Society for Computational Economics, vol. 50(1), pages 161-172, June.
    15. Peter Sephton, 2008. "Critical values of the augmented fractional Dickey–Fuller test," Empirical Economics, Springer, vol. 35(3), pages 437-450, November.
    16. S Cook, 2001. "Finite-sample critical values of the Augmented Dickey-Fuller statistic: a note on lag order," Economic Issues Journal Articles, Economic Issues, vol. 6(2), pages 31-46, September.
    17. M. Hashem Pesaran & Yongcheol Shin & Richard J. Smith, 2001. "Bounds testing approaches to the analysis of level relationships," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 289-326.
    18. Cheung, Yin-Wong & Lai, Kon S, 1995. "Lag Order and Critical Values of the Augmented Dickey-Fuller Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 277-280, July.
    19. Jesús Otero & Jeremy Smith, 2017. "Response surface models for OLS and GLS detrending-based unit-root tests in nonlinear ESTAR models," Stata Journal, StataCorp LP, vol. 17(3), pages 704-722, September.
    20. Robert McNown & Chung Yan Sam & Soo Khoon Goh, 2018. "Bootstrapping the autoregressive distributed lag test for cointegration," Applied Economics, Taylor & Francis Journals, vol. 50(13), pages 1509-1521, March.
    21. MacKinnon, James G, 1996. "Numerical Distribution Functions for Unit Root and Cointegration Tests," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(6), pages 601-618, Nov.-Dec..
    22. MacKinnon, James G, 1994. "Approximate Asymptotic Distribution Functions for Unit-Root and Cointegration Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 167-176, April.
    23. Jesús Otero & Christopher F Baum, 2017. "Response surface models for the Elliott, Rothenberg, and Stock unit-root test," Stata Journal, StataCorp LP, vol. 17(4), pages 985-1002, December.
    24. Paul Turner, 2006. "Response surfaces for an F-test for cointegration," Applied Economics Letters, Taylor & Francis Journals, vol. 13(8), pages 479-482.
    25. Sebastian Kripfganz & Daniel Schneider, 2018. "ardl: Estimating autoregressive distributed lag and equilibrium correction models," London Stata Conference 2018 09, Stata Users Group.
    26. James G. MacKinnon, 2010. "Critical Values For Cointegration Tests," Working Paper 1227, Economics Department, Queen's University.
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    Cited by:

    1. Tarek Tawfik Yousef Alkhateeb & Haider Mahmood, 2019. "Energy Consumption and Trade Openness Nexus in Egypt: Asymmetry Analysis," Energies, MDPI, Open Access Journal, vol. 12(10), pages 1-10, May.
    2. Haider Mahmood & Nabil Maalel & Olfa Zarrad, 2019. "Trade Openness and CO 2 Emissions: Evidence from Tunisia," Sustainability, MDPI, Open Access Journal, vol. 11(12), pages 1-14, June.
    3. Sebastian Kripfganz & Daniel Schneider, 2018. "ardl: Estimating autoregressive distributed lag and equilibrium correction models," London Stata Conference 2018 09, Stata Users Group.
    4. Usman, Ojonugwa & Alola, Andrew Adewale & Sarkodie, Samuel Asumadu, 2020. "Assessment of the role of renewable energy consumption and trade policy on environmental degradation using innovation accounting: Evidence from the US," Renewable Energy, Elsevier, vol. 150(C), pages 266-277.
    5. Nduka, Eleanya K., 2018. "Modeling the Long-Run Relationship Between Exchange Rate-Tourism Pass-Through and Growth: The Case of Nigeria?," MPRA Paper 86584, University Library of Munich, Germany.

    More about this item

    Keywords

    Bounds test; Cointegration; Error correction model; Generalized Dickey-Fuller regression; Level relationship; Unit roots;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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