IDEAS home Printed from https://ideas.repec.org/p/cwl/cwldpp/1251.html
   My bibliography  Save this paper

Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency

Author

Listed:
  • Yoosoon Chang

    (Dept. Economics, Rice University)

Abstract

We apply bootstrap methodology to unit root tests for dependent panels with N cross-sectional units and T time series observations. More specifically, we let each panel be driven by a general linear process which may be different across cross-sectional units, and approximate it by a finite order autoregressive integrated process of order increasing with T. As we allow the dependency among the innovations generating the individual panels, we construct our unit root tests from the estimation of the system of the entire N panels. The limit distributions of the tests are derived by passing T to infinity, with N fixed. We then apply the bootstrap method to the approximated autoregressions to obtain the critical values for the panel unit root tests, and establish the asymptotic validity of such bootstrap panel unit root tests under general conditions. The proposed bootstrap tests are indeed quite general covering a wide class of panel models. They in particular allow for very general dynamic structures which may vary across individual units, and more importantly for the presence of arbitrary cross-sectional dependency. The finite sample performance of the bootstrap tests is examined via simulations, and compared to that of the t-bar statistics by Im, Pesaran and Shin (1997), which is one of the commonly used unit root tests for panel data. We find that our bootstrap panel unit root tests perform well relative to the t-bar statistics, especially when N is small.

Suggested Citation

  • Yoosoon Chang, 2000. "Bootstrap Unit Root Tests in Panels with Cross-Sectional Dependency," Cowles Foundation Discussion Papers 1251, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1251
    as

    Download full text from publisher

    File URL: https://cowles.yale.edu/sites/default/files/files/pub/d12/d1251.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Shao, Q. M., 1995. "Strong Approximation Theorems for Independent Random Variables and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 107-130, January.
    2. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    3. Yoosoon Chang & Robin C. Sickles & Wonho Song, 2017. "Bootstrapping unit root tests with covariates," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 136-155, March.
    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    5. Im, Kyung So & Pesaran, M. Hashem & Shin, Yongcheol, 2003. "Testing for unit roots in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 115(1), pages 53-74, July.
    6. Suzanne McCoskey & Chihwa Kao, 1998. "A residual-based test of the null of cointegration in panel data," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 57-84.
    7. Quah, Danny, 1994. "Exploiting cross-section variation for unit root inference in dynamic data," Economics Letters, Elsevier, vol. 44(1-2), pages 9-19.
    8. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    9. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation for Research in Economics, Yale University.
    10. Pesaran, M. Hashem & Smith, Ron, 1995. "Estimating long-run relationships from dynamic heterogeneous panels," Journal of Econometrics, Elsevier, vol. 68(1), pages 79-113, July.
    11. Yoosoon Chang & Joon Y. Park, 2003. "A Sieve Bootstrap For The Test Of A Unit Root," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(4), pages 379-400, July.
    12. Chang, Yoosoon & Park, Joon Y. & Song, Kevin, 2006. "Bootstrapping cointegrating regressions," Journal of Econometrics, Elsevier, vol. 133(2), pages 703-739, August.
    13. Yoosoon Chang & Joon Park, 2002. "On The Asymptotics Of Adf Tests For Unit Roots," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 431-447.
    14. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    15. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    16. Boozer, Michael A., 1997. "Econometric Analysis of Panel DataBadi H. Baltagi Wiley, 1995," Econometric Theory, Cambridge University Press, vol. 13(5), pages 747-754, October.
    17. Park, Joon Y., 2002. "An Invariance Principle For Sieve Bootstrap In Time Series," Econometric Theory, Cambridge University Press, vol. 18(2), pages 469-490, April.
    18. Banerjee, Anindya, 1999. "Panel Data Unit Roots and Cointegration: An Overview," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 607-629, Special I.
    19. Levin, Andrew & Lin, Chien-Fu & James Chu, Chia-Shang, 2002. "Unit root tests in panel data: asymptotic and finite-sample properties," Journal of Econometrics, Elsevier, vol. 108(1), pages 1-24, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. António Afonso & Christophe Rault, 2010. "What do we really know about fiscal sustainability in the EU? A panel data diagnostic," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(4), pages 731-755, January.
    2. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
    3. António Afonso & Christophe Rault, 2010. "What do we really know about fiscal sustainability in the EU? A panel data diagnostic," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(4), pages 731-755, January.
    4. António Afonso & Christophe Rault, 2010. "What do we really know about fiscal sustainability in the EU? A panel data diagnostic," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 145(4), pages 731-755, January.
    5. Joerg Breitung & M. Hashem Pesaran, 2005. "Unit Roots and Cointegration in Panels," CESifo Working Paper Series 1565, CESifo.
    6. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    7. Peter Phillips & Hyungsik Moon, 2000. "Nonstationary panel data analysis: an overview of some recent developments," Econometric Reviews, Taylor & Francis Journals, vol. 19(3), pages 263-286.
    8. Breitung, Jörg & Pesaran, Mohammad Hashem, 2005. "Unit roots and cointegration in panels," Discussion Paper Series 1: Economic Studies 2005,42, Deutsche Bundesbank.
    9. Trapani, Lorenzo & Urga, Giovanni, 2010. "Micro versus macro cointegration in heterogeneous panels," Journal of Econometrics, Elsevier, vol. 155(1), pages 1-18, March.
    10. 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.
    11. MUSOLESI, Antonio, 2006. "Recherche, productivité et externalités internationales : une analyse économétrique sur données de panel pour un groupe de pays de l'OCDE," LEG - Document de travail - Economie 2006-07, LEG, Laboratoire d'Economie et de Gestion, CNRS, Université de Bourgogne.
    12. Hyungsik Roger Moon & Peter C. B. Phillips, 2004. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Econometrica, Econometric Society, vol. 72(2), pages 467-522, March.
    13. Stephan Smeekes, 2013. "Detrending Bootstrap Unit Root Tests," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 869-891, November.
    14. Ling, Tai-Hu & Venus, Khim-Sen Liew & Syed Khalid Wafa, Syed Azizi Wafa, 2008. "Does Fisher hypothesis hold for the East Asian Economies? an application of panel unit root tests," MPRA Paper 21601, University Library of Munich, Germany, revised Jan 2010.
    15. Andreas Dietrich, 2012. "Does growth cause structural change, or is it the other way around? A dynamic panel data analysis for seven OECD countries," Empirical Economics, Springer, vol. 43(3), pages 915-944, December.
    16. Karikallio, Hanna, 2015. "Cross-commodity Price Transmission and Integration of the EU Livestock Market of Pork and Beef: Panel Time-series Approach," 2015 Conference, August 9-14, 2015, Milan, Italy 211832, International Association of Agricultural Economists.
    17. Imed Drine & Christophe Rault, 2008. "Purchasing Power Parity For Developing And Developed Countries. What Can We Learn From Non‐Stationary Panel Data Models?," Journal of Economic Surveys, Wiley Blackwell, vol. 22(4), pages 752-773, September.
    18. Chihwa Kao & Min-Hsien Chiang, 1997. "On the Estimation and Inference of a Cointegrated Regression in Panel Data," Econometrics 9703001, University Library of Munich, Germany.
    19. Maria Elena Bontempi & Roberto Golinelli, 2012. "The effect of neglecting the slope parameters’ heterogeneity on dynamic models of corporate capital structure," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1733-1751, November.
    20. Ibhagui, Oyakhilome W., 2019. "Does the long-run monetary model hold for Sub-Saharan Africa? A time series and panel-cointegration study," Research in International Business and Finance, Elsevier, vol. 47(C), pages 279-303.

    More about this item

    Keywords

    Panels with cross-sectional dependency; unit root tests; sieve bootstrap; AR approximation;
    All these keywords.

    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
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cwl:cwldpp:1251. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Matthew Regan (email available below). General contact details of provider: https://edirc.repec.org/data/cowleus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.