Previous versions of this paper were presented at the 12th International Panel Conference in Copenhagen, at the Conference on Frontiers in Times Series Analysis in Olbia, at a seminar at the Econometric Institute in Rotterdam and at the NSF/NBER Time Series Conference in Heidelberg. The authors would like to thank conference and seminar participants and in particular Jörg Breitung, Josep Carrion-i-Silvestre, Peter Pedroni, Joakim Westerlund and three unknown referees for helpful comments and suggestions on a previous draft. The usual disclaimer applies.
Cointegration Testing in Panels with Common Factors*
Article first published online: 23 NOV 2006
Oxford Bulletin of Economics and Statistics
Volume 68, Issue Supplement s1, pages 683–719, December 2006
How to Cite
Gengenbach, C., Palm, F. C. and Urbain, J.-P. (2006), Cointegration Testing in Panels with Common Factors. Oxford Bulletin of Economics and Statistics, 68: 683–719. doi: 10.1111/j.1468-0084.2006.00452.x
- Issue published online: 23 NOV 2006
- Article first published online: 23 NOV 2006
Panel unit-root and no-cointegration tests that rely on cross-sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit-root tests using a common factor structure to model the cross-sectional dependence, but not much work has been done yet for panel no-cointegration tests. This paper proposes a model for panel no-cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non-stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual-based panel no-cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data-generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than as for independent panels. We then examine the possibilities of testing for various forms of no-cointegration by extracting the common factors and individual components from the observed data directly and then testing for no-cointegration using residual-based panel tests applied to the defactored data.