Advertisement

Computational Economics

, Volume 52, Issue 1, pp 167–193 | Cite as

Testing for Unit Roots in Dynamic Panels with Smooth Breaks and Cross-Sectionally Dependent Errors

  • Tolga Omay
  • Mübariz Hasanov
  • Yongcheol Shin
Article
  • 261 Downloads

Abstract

We develop the extended unit root testing procedure for dynamic panels characterised by slowly moving trends (SMT) and cross-section dependence (CSD). We allow SMT to follow the smooth logistic transition function and the components error terms to contain the unobserved common factors. We propose the two panel unit root test statistics, one derived by the extended common correlated effects (CCE) estimator and the other based on the Sieve bootstrap. We have conducted extensive simulation exercises and document that the failure to take into account SMT and CSD may lead to misleading inference. On the other hand, we find that both bootstrap and CCE-based tests maintain good power properties in small samples in the presence SMT and CSD. We apply our proposed tests to real interest rates for 17 OECD countries and find overwhelming evidence in favour of the Fisher hypothesis.

Keywords

Slow moving trends Cross-section dependence Common correlated estimator Bootstrap Panel unit root tests 

JEL Classification

C12 C22 O47 

Notes

Acknowledgements

We would like to thank the editor and two anonymous referees for most constructive and helpful comments and suggestions, which help us to greatly improve the quality of the paper. The usual disclaimer applies.

Supplementary material

10614_2017_9667_MOESM_ESM.docx (313 kb)
Supplementary material 1 (docx 312 KB)

References

  1. Amsler, C., & Lee, J. (1995). An LM test for a unit-root in the presence of a structural change. Econometric Theory, 11, 359–368.CrossRefGoogle Scholar
  2. Bacon, D. W., & Watts, D. G. (1971). Estimating the transition between two intersecting straight lines. Biometrika, 58, 525–534.CrossRefGoogle Scholar
  3. Bai, J., & Carrion-i-Silvestre, J. L. (2009). Structural changes, common stochastic trends, and unit roots in panel data. The Review of Economic Studies, 76, 471–501.CrossRefGoogle Scholar
  4. Bai, J., & Ng, S. (2004). A PANIC attack on unit roots and cointegration. Econometrica, 72, 1127–1177.CrossRefGoogle Scholar
  5. Bai, J., & Ng, S. (2010). Panel unit root tests with cross section dependence: A further investigation. Econometric Theory, 26, 1088–1114.CrossRefGoogle Scholar
  6. Baltagi, B. H., & Kao, C. (2000). Nonstationary panels, panel cointegration and dynamic panels. In B. Baltagi (Ed.), Advances in Econometrics (Vol. 15). New York: JAI.Google Scholar
  7. Banerjee, A. (1999). Panel data unit roots and cointegration: An overview. Oxford Bulletin of Economics and Statistics, 61, 607–629.CrossRefGoogle Scholar
  8. Banerjee, A., Marcellino, M., & Osbat, C. (2004). Some cautions on the use of panel methods for integrated series of macroeconomic data. Econometrics Journal, 7, 322–340.CrossRefGoogle Scholar
  9. Banerjee, A., Marcellino, M., & Osbat, C. (2005). Testing for PPP: Should we use panel methods? Empirical Economics, 30, 77–91.CrossRefGoogle Scholar
  10. Basawa, I. V., Mallik, A. K., McCormick, W. P., Reeves, J. H., & Taylor, R. L. (1991). Bootstrapping unstable first-order autoregressive processes. Annals of Statistics, 19, 1098–110.CrossRefGoogle Scholar
  11. Becker, R., Enders, W., & Lee, J. (2006). A stationarity test in the presence of an unknown number of smooth breaks. Journal of Time Series Analysis, 27, 381–409.CrossRefGoogle Scholar
  12. Bierens, H. J. (1997). Testing the unit root with drift hypothesis against nonlinear trend stationarity, with an application to the US price level and interest rate. Journal of Econometrics, 81, 29–64.CrossRefGoogle Scholar
  13. Brada, J. C. (1998). Exchange rates, capital flows, and commercial policies in transition economies. Journal of Comparative Economics, 26, 613–620.CrossRefGoogle Scholar
  14. Breitung, J., & Pesaran, M. H. (2005). Unit roots and cointegration in panels. In L. Matyas & P. Sevestre (Eds.), The Econometrics of Panel Data (3rd ed.). Berlin: Springer.Google Scholar
  15. Carrion-i-Silvestre, J. L., Del Barrio-Castro, T., & Lopez-Bazo, E. (2005). Breaking the panels: An application to GDP per capita. Econometrics Journal, 8, 159–175.CrossRefGoogle Scholar
  16. Chang, Y. (2004). Bootstrap unit root tests in panels with cross-sectional dependency. Journal of Econometrics, 120, 263–293.CrossRefGoogle Scholar
  17. Choi, I. (2001). Unit root tests for panel data. Journal of International Money and Banking, 20, 249–272.CrossRefGoogle Scholar
  18. Chortareas, G., & Kapetanios, G. (2009). Getting PPP right: Identifying mean-reverting real exchange rates in panels. Journal of Banking and Finance, 33, 390–404.CrossRefGoogle Scholar
  19. Chudik, A., Pesaran, M. H., & Tosetti, E. (2011). Weak and strong cross section dependence and estimation of large panels. Econometrics Journal, 14, C45–C90.CrossRefGoogle Scholar
  20. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimates for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.Google Scholar
  21. Driscoll, J. C., & Kraay, A. C. (1998). Consistent covariance matrix estimation with spatially dependent panel data. The Review of Economics and Statistics, 80, 549–560.CrossRefGoogle Scholar
  22. Garcia, R., & Perron, P. (1996). An analysis of the real rate of interest under regime shifts. The Review of Economics and Statistics., 78, 111–125.CrossRefGoogle Scholar
  23. Gengenbach, C., Palm, F. C., & Urbain, J.-P. (2009). Panel unit root tests in the presence of cross-sectional dependencies: Comparison and implications for modelling. Econometric Reviews, 29, 111–145.CrossRefGoogle Scholar
  24. Granger, C. W. J., & Teräsvirta, T. (1993). Modelling nonlinear economic relationships. New York: Oxford University Press.Google Scholar
  25. Greenaway, D., Leybourne, S. J., & Sapsford, D. (1997). Modelling growth and liberalisation using smooth transition analysis. Economic Inquiry, 35, 798–814.CrossRefGoogle Scholar
  26. Hadri, K. (2000). Testing for stationarity in heterogeneous panel data. Econometrics Journal, 3, 148–161.CrossRefGoogle Scholar
  27. Hadri, K., Larsson, R., & Rao, Y. (2012). Testing for stationarity with a break in panels where the time dimension is finite. Bulletin of Economic Research, 64(S1), 123–148.CrossRefGoogle Scholar
  28. Hadri, K., & Rao, Y. (2008). Panel stationarity test with structural breaks. Oxford Bulletin of Economics and Statistics, 70, 245–269.CrossRefGoogle Scholar
  29. Healy, P. M., & Palepu, K. G. (2001). Information asymmetry, corporate disclosure, and the capital markets: A review of the empirical disclosure literature. Journal of Accounting and Economics, 31, 405–440.CrossRefGoogle Scholar
  30. Im, K. S., Lee, J., & Tieslau, M. (2005). Panel LM unit-root tests with level shifts. Oxford Bulletin of Economics and Statistics, 67, 393–419.CrossRefGoogle Scholar
  31. Im, K. S., Pesaran, M. H., & Shin, Y. (1995). Testing for unit roots in heterogeneous panels. DAE working papers amalgamated series no. 9526. University of Cambridge.Google Scholar
  32. Im, K. S., Pesaran, M. H., & Shin, Y. (2003). Testing for unit roots in heterogeneous panels. Journal of Econometrics, 115, 53–74.CrossRefGoogle Scholar
  33. Kapetanios, G., Pesaran, M. H., & Yamagata, T. (2011). Panels with non-stationary multifactor error structures. Journal of Econometrics, 160, 326–348.CrossRefGoogle Scholar
  34. Kapetanios, G., Shin, Y., & Snell, A. (2003). Testing for unit root in the nonlinear STAR framework. Journal of Econometrics, 112, 359–379.CrossRefGoogle Scholar
  35. Karavias, Y., & Tzavalis, E. (2012). Testing for unit roots in short panels allowing for structural breaks. Computational Statistics and Data Analysis,. doi: 10.1016/j.csda.2012.10.014.Google Scholar
  36. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P. J., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root. Journal of Econometrics, 54, 159–78.CrossRefGoogle Scholar
  37. Levin, A., Lin, C. F., & Chu, C. S. J. (2002). Unit root tests in panel data: Asymptotic and finite-sample properties. Journal of Econometrics, 108, 1–24.CrossRefGoogle Scholar
  38. Leybourne, S., Newbold, P., & Vougas, D. (1998). Unit roots and smooth transitions. Journal of Time Series Analysis, 19, 83–97.CrossRefGoogle Scholar
  39. Lin, C. J., & Teräsvirta, T. (1994). Testing the constancy of regression parameters against continuous structural change. Journal of Econometrics, 62, 211–228.CrossRefGoogle Scholar
  40. Lundbergh, S., Teräsvirta, T., & van Dijk, D. (2003). Time-varying smooth transition autoregressive models. Journal of Business and Economic Statistics, 21, 104–12.CrossRefGoogle Scholar
  41. Maddala, G. S. (1977). Econometrics. New York: McGraw-Hill.Google Scholar
  42. Maddala, G. S., & Wu, S. (1999). A comparative study of unit root tests with panel data and a new simple test. Oxford Bulletin of Economics and Statistics, 61, 631–652.CrossRefGoogle Scholar
  43. Mishkin, F. S. (1992). Is the Fisher effect for real? A reexamination of the relationship between inflation and interest rates. Journal of Monetary Economics, 30, 195–215.CrossRefGoogle Scholar
  44. Moon, H. R., & Perron, B. (2004). Testing for a unit root in panels with dynamic factors. Journal of Econometrics, 122, 81–126.CrossRefGoogle Scholar
  45. Omay, T., & Emirmahmutoğlu, F. (2016). The comparison of power and optimization algorithms on unit root testing with smooth transition. Computational Economics. doi: 10.1007/s10614-016-9574-3.
  46. Omay, T., Çorakcı, A., & Emirmahmutoğlu, F. (2016). Real interest rate: Nonlinearity and structural break. Empirical Economics. doi: 10.1007/s00181-015-1065-1.
  47. Omay, T., Hasanov, M., & Ucar, N. (2014). Energy consumption and economic growth: Evidence from nonlinear panel cointegration and causality test. Applied Econometrics, 34(2), 36–55.Google Scholar
  48. Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica, 57, 1361–1401.CrossRefGoogle Scholar
  49. Perron, P. (1990). Testing for a unit root in a time series with a changing mean. Journal of Business and Economic Statistics, 8, 153–162.Google Scholar
  50. Perron, P., & Vogelsang, T. (1992). Nonstationarity and level shifts with an application to purchasing power parity. Journal of Business and Economic Statistics, 10, 301–320.Google Scholar
  51. Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 74, 967–1012.CrossRefGoogle Scholar
  52. Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence. Journal of Applied Econometrics, 22, 265–312.CrossRefGoogle Scholar
  53. Pesaran, M. H., Smith, L. V., & Yamagata, T. (2013). Panel unit root tests in the presence of a multifactor error structure. Journal of Econometrics, 175, 94–115.CrossRefGoogle Scholar
  54. Pesaran, M. H., & Tosetti, E. (2011). Large panels with common factors and spatial correlation. Journal of Econometrics, 161, 182–202.CrossRefGoogle Scholar
  55. Phillips, P. C. B. (2005). Econometric analysis of Fisher’s equation. The American Journal of Economics and Sociology, 64, 125–168.CrossRefGoogle Scholar
  56. Phillips, P. C. B., & Sul, D. (2003). Dynamic panel estimation and homogeneity testing under cross section dependence. Econometrics Journal, 6, 217–259.CrossRefGoogle Scholar
  57. Quah, D. (1994). Exploiting cross section variation for unit root inference in dynamic data. Economics Letters, 44, 9–19.CrossRefGoogle Scholar
  58. Rose, A. K. (1988). Is the real interest rate stable? Journal of Finance, 43, 1095–1112.CrossRefGoogle Scholar
  59. Schmidt, P., & Phillips, P. C. B. (1992). LM tests for a unit root in the presence of deterministic trends. Oxford Bulletin of Economics and Statistics, 54, 257–287.CrossRefGoogle Scholar
  60. Smith, R. P., & Fuertes, A. M. (2010). Panel Time Series. http://www.ems.bbk.ac.uk/faculty/smith/RSpanel.pdf.
  61. Smith, L. V., Leybourne, S., Kim, T. H., & Newbold, P. (2004). More powerful panel data unit root tests with an application to mean reversion in real exchange rates. Journal of Applied Econometrics, 19, 147–170.CrossRefGoogle Scholar
  62. Sollis, R. (2004). Asymmetric adjustment and smooth transitions: A combination of some unit-root tests. Journal of Time Series Analysis, 25, 409–417.CrossRefGoogle Scholar
  63. Stine, R. A. (1987). Estimating properties of autoregressive forecasts. Journal of the American Statistical Association, 82, 1072–1078.CrossRefGoogle Scholar
  64. Ucar, N., & Omay, T. (2009). Testing for unit root in nonlinear heterogeneous panels. Economics Letters, 104, 5–8.CrossRefGoogle Scholar
  65. Westerlund, J., Urbain, J. P. (2011). Cross sectional averages or principal components? Working paper no: RM/11/053. Maastricht University School of Business and Economics.Google Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of EconomicsAtılım University, Kızılcaşar Mahallesiİncek, Gölbaşı, AnkaraTurkey
  2. 2.Department of Banking and FinanceOkan UniversityIstanbulTurkey
  3. 3.Department of Economics and Related StudiesUniversity of YorkYorkUK

Personalised recommendations