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Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies

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  • Yoosoon Chang
  • Wonho Song

Abstract

An IV approach, using as instruments non-linear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of co-integration across cross-sectional levels. Unbalanced panels and panels with differing individual short-run dynamics and cross-sectionally related dynamics are also permitted. We also more carefully formulate the unit root hypotheses in panels. In particular, using order statistics, we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV t-ratios, which are the bases of our tests, are asymptotically and normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual average statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, whereas other existing tests fail to perform properly. As an illustration, we apply our tests to the panels of real exchange rates, and find no evidence for the purchasing power parity hypothesis, which is in sharp contrast with the previous studies. Copyright , Wiley-Blackwell.

Suggested Citation

  • Yoosoon Chang & Wonho Song, 2009. "Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 903-935.
  • Handle: RePEc:oup:restud:v:76:y:2009:i:3:p:903-935
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    File URL: http://hdl.handle.net/10.1111/j.1467-937X.2009.00549.x
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    Cited by:

    1. Francesca Iorio & Stefano Fachin, 2014. "Savings and investments in the OECD: a panel cointegration study with a new bootstrap test," Empirical Economics, Springer, vol. 46(4), pages 1271-1300, June.
    2. Hwang, Eunju & Shin, Dong Wan, 2015. "Stationary bootstrapping for semiparametric panel unit root tests," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 14-25.
    3. Mauro Costantini & Claudio Lupi, 2013. "A Simple Panel-CADF Test for Unit Roots," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(2), pages 276-296, April.
    4. Vishal Chandr Jaunky & Robert Lundmark, 2015. "Are Shocks to Wood Fuel Production Permanent? Evidence from the EU," Energies, MDPI, Open Access Journal, vol. 8(11), pages 1-11, November.
    5. Dimitris Christopoulos & Peter Mcadam, 2017. "On the Persistence of Cross‐Country Inequality Measures," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 49(1), pages 255-266, February.
    6. Iorio, Francesca Di & Fachin, Stefano, 2014. "Savings and investments in the OECD, 1970–2007: A test of panel cointegration with regime changes," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 59-76.
    7. Christopoulos, Dimitris & McAdam, Peter, 2017. "Do financial reforms help stabilize inequality?," Journal of International Money and Finance, Elsevier, vol. 70(C), pages 45-61.
    8. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2011. "Cross-sectional dependence robust block bootstrap panel unit root tests," Journal of Econometrics, Elsevier, vol. 163(1), pages 85-104, July.
    9. Snaith, Stuart, 2012. "The PPP debate: Multiple breaks and cross-sectional dependence," Economics Letters, Elsevier, vol. 115(3), pages 342-344.
    10. Matei Demetrescu & Christoph Hanck & Adina I. Tarcolea, 2014. "Iv-Based Cointegration Testing In Dependent Panels With Time-Varying Variance," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 393-406, August.
    11. Kaddour Hadri & Eiji Kurozumi & Daisuke Yamazaki, 2015. "Synergy between an Improved Covariate Unit Root Test and Cross-sectionally Dependent Panel Data Unit Root Tests," Manchester School, University of Manchester, vol. 83(6), pages 676-700, December.
    12. Kang, Wensheng, 2011. "Housing price dynamics and convergence in high-tech metropolitan economies," The Quarterly Review of Economics and Finance, Elsevier, vol. 51(3), pages 283-291, June.
    13. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    14. Matei Demetrescu & Christoph Hanck, 2013. "Nonlinear IV panel unit root testing under structural breaks in the error variance," Statistical Papers, Springer, vol. 54(4), pages 1043-1066, November.
    15. Eiji Kurozumi & Daisuke Yamazaki & Kaddour Hadri, 2012. "Covariate Unit Root Test for Cross-Sectionally Dependent Panel Data," Global COE Hi-Stat Discussion Paper Series gd12-256, Institute of Economic Research, Hitotsubashi University.
    16. Ho, Tsung-wu, 2015. "Income inequality may not converge after all: Testing panel unit roots in the presence of cross-section cointegration," The Quarterly Review of Economics and Finance, Elsevier, vol. 56(C), pages 68-79.
    17. Yiannis Karavias & Elias Tzavalis, 2014. "Testing for unit roots in panels with structural changes, spatial and temporal dependence when the time dimension is finite," Discussion Papers 14/03, University of Nottingham, Granger Centre for Time Series Econometrics.
    18. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Stephan Smeekes, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 398-415, May.
    19. Jaunky, Vishal Chandr, 2013. "A cointegration and causality analysis of copper consumption and economic growth in rich countries," Resources Policy, Elsevier, vol. 38(4), pages 628-639.
    20. Qaiser Munir & Sook Ching Kok & Kasim Mansur, 2019. "External Shocks, Structural Breaks And Unemployment Hysteresis In Selected Asian Countries," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 64(03), pages 575-600, June.
    21. Joakim Westerlund, 2015. "Rethinking the Univariate Approach to Panel Unit Root Testing: Using Covariates to Resolve the Incidental Trend Problem," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 430-443, July.
    22. Jaunky, Vishal Chandr, 2013. "Are Shocks To Aluminium Consumption Transitory Or Permanent?," Review of Applied Economics, Lincoln University, Department of Financial and Business Systems, vol. 9(1-2), January.
    23. Jaunky, Vishal Chandr, 2012. "Is there a material Kuznets curve for aluminium? evidence from rich countries," Resources Policy, Elsevier, vol. 37(3), pages 296-307.
    24. Vishal Jaunky, 2013. "Democracy and economic growth in Sub-Saharan Africa: a panel data approach," Empirical Economics, Springer, vol. 45(2), pages 987-1008, October.

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