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Multivariate Unit Root Tests and Testing for Convergence

Author

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  • Harvey, A.
  • Bates, D.

Abstract

We examine the properties of a multivariate Dickey-Fuller t-statistic designed to test for a unit root in a panel while taking account of cross-sectional dependence. The asymptotic distribution is presented and critical values provided. When intercepts are present, a modification along the lines of Elliot, Rothenberg and Stock (1996) can be implemented. The tests have invariance properties and can be carried out even if the number of series exceeds the number of time periods. Non-zero initial conditions actually boost the power of the (unmodified) Dickey-Fuller tests confirming that they are useful for testing the hypothesis that the series are in the process of converging. Typical applications are for a moderate number of series observed over a reasonably long period of time. The example given is for the per capital incomes of six US regions observed annually from 1950 to 1999.

Suggested Citation

  • Harvey, A. & Bates, D., 2003. "Multivariate Unit Root Tests and Testing for Convergence," Cambridge Working Papers in Economics 0301, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0301
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    Citations

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    Cited by:

    1. Eickmeier, Sandra, 2006. "Comovements and heterogeneity in the Comovements and heterogeneity in the dynamic factor model," Discussion Paper Series 1: Economic Studies 2006,31, Deutsche Bundesbank.
    2. Usman Khalid & Luke Okafor & Muhammad Shahbaz, 2022. "Economic reform and political stagnation: The inconsistent patterns of institutional change," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 30(4), pages 813-844, October.
    3. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2007. "Inflation Convergence and Divergence within the European Monetary Union," International Journal of Central Banking, International Journal of Central Banking, vol. 3(2), pages 95-121, June.
    4. Carvalho, Vasco M. & Harvey, Andrew C., 2005. "Growth, cycles and convergence in US regional time series," International Journal of Forecasting, Elsevier, vol. 21(4), pages 667-686.
    5. M. Hashem Pesaran, 2007. "A simple panel unit root test in the presence of cross-section dependence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(2), pages 265-312.
    6. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergence of Prices and Rates of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 863-877, December.
    7. David E.A. Giles & Hui Feng, 2003. "Testing For Convergence in Output and in 'Well-Being' in Industrialized Countries," Econometrics Working Papers 0302, Department of Economics, University of Victoria.
    8. Elliott, Graham & Muller, Ulrich K., 2006. "Minimizing the impact of the initial condition on testing for unit roots," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 285-310.
    9. Kristian Jönsson, 2005. "Cross‐sectional Dependency and Size Distortion in a Small‐sample Homogeneous Panel Data Unit Root Test," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(3), pages 369-392, June.
    10. Sandra Eickmeier, 2009. "Comovements and heterogeneity in the euro area analyzed in a non-stationary dynamic factor model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 933-959.
    11. Johan Lyhagen & Johanna Rickne, 2014. "Income inequality between Chinese regions: newfound harmony or continued discord?," Empirical Economics, Springer, vol. 47(1), pages 93-110, August.
    12. Breitung, Jörg & Pesaran, Mohammad Hashem, 2005. "Unit roots and cointegration in panels," Discussion Paper Series 1: Economic Studies 2005,42, Deutsche Bundesbank.
    13. Valérie Mignon & Christophe Hurlin, 2005. "Une synthèse des tests de racine unitaire sur données de panel," Économie et Prévision, Programme National Persée, vol. 169(3), pages 253-294.
    14. Alina M. Spiru, 2008. "Inflation Convergence In Central And Eastern European Economies," Romanian Economic Business Review, Romanian-American University, vol. 3(4), pages 14-34, Winter.
    15. Troy Lorde & Winston Moore, 2008. "Co-Movement in Tourist Arrivals in the Caribbean," Tourism Economics, , vol. 14(3), pages 631-643, September.
    16. Vasco M. Carvalho & Andrew C. Harvey, 2005. "Convergence in the trends and cycles of Euro‐zone income," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(2), pages 275-289.
    17. Usman Khalid, 2016. "Catch-up in Institutional Quality: An Empirical Assessment," Discussion Papers 2016-04, University of Nottingham, CREDIT.
    18. Fischer, Christoph, 2007. "An assessment of the trends in international price competitiveness among EMU countries," Discussion Paper Series 1: Economic Studies 2007,08, Deutsche Bundesbank.
    19. Fabio Busetti & Michele Caivano, 2017. "Low frequency drivers of the real interest rate: a band spectrum regression approach," Temi di discussione (Economic working papers) 1132, Bank of Italy, Economic Research and International Relations Area.
    20. Lorenzo Lucchese & Mikko Pakkanen & Almut Veraart, 2022. "The Short-Term Predictability of Returns in Order Book Markets: a Deep Learning Perspective," Papers 2211.13777, arXiv.org, revised Oct 2023.
    21. Ghassen El-Montasser & Roula Inglesi-Lotz & Rangan Gupta, 2015. "Convergence of greenhouse gas emissions among G7 countries," Applied Economics, Taylor & Francis Journals, vol. 47(60), pages 6543-6552, December.
    22. GRENADE, Kari & MOORE, Winston, 2008. "Co-Movements Between Foreign And Domestic Interest Rates In A Fixed Exchange Rate Regime: The Case Of The Eccu And The Us," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 8(1), pages 119-130.
    23. Christoph Fischer & Daniel Porath, 2010. "A reappraisal of the evidence on PPP: a systematic investigation into MA roots in panel unit root tests and their implications," Empirical Economics, Springer, vol. 39(3), pages 767-792, December.
    24. Alina M. Spiru, 2008. "Inflation Convergence In Central And Eastern European Economies," Journal of Information Systems & Operations Management, Romanian-American University, vol. 2(1), pages 289-316, July.

    More about this item

    Keywords

    balanced growth; cross-sectional dependence; Dickey-Fuller test; initials conditions; power envelope; stationarity tests;
    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
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General

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