720 Panel Methods to Test for Unit Roots and Cointegration
Acknowledgments
We are very grateful to our students, colleagues and co-authors, whose insights and results we
share in the results reported in this chapter. Particular thanks go to Josep Carrion-i-Silvestre,
Jaroslava Hlouskova, Massimiliano Marcellino and Chiara Osbat for participating in research
projects on panel unit roots and cointegration with us over several years. AB also wishes to
thank Victor Bystrov for valuable research assistance and the Department of Economics of
the European University Institute for funding his research projects over the past eight years.
MW thanks the Jubiläumsfonds of the Oesterreichische Nationalbank for partially funding
his research over the last years. The help of Kerry Patterson and an anonymous referee is also
gratefully acknowledged. Responsibility for any errors that remain rests with us.
Notes
- Later in our chapter we illustrate the methods described by some other examples. These
include the frequently studied topic of purchasing power parity, but we also look at less
common examples such as the analysis of environmental Kuznets curves and exchange
rate pass-through. Further applications for which non-stationary panel methods have
been used include business-cycle synchronization, house price convergence, regional
migration and household income dynamics.
- The discussion in this subsection draws on Wagner (2008c) who considers the precise
econometric implications of several economic convergence definitions.
- Throughout our chapter, when referring toI(1) processes we refer to processes whose
stochastic component is integrated of order 1 and allow also for deterministic compo-
nents.
- Clearly, this definition leaves lots of possibilities, for example, multiple convergence
clubs, entirely unexplored. See Wagner (2008c) for a discussion of these issues.
- Remember that in the Granger representationrindicates the number of linearly indepen-
dent common stochastic trends, which in our case is 1 in the case of convergence. Clearly,
algebraically this single stochastic trend can be split intorcomponents in infinitely many
ways, that is, the constituent parts are not identified. An alternative way of formulating
the same thing is to simply remember the fact that forI(1) processes the sum of the dimen-
sion of the cointegrating space and the number of common trends equals the dimension
of the process.
- The discussion in EK at pp. 254–5 shows that the authors focus in their considerations on
potential correlation in the processesui,tbut ignore the potential of both the presence
of deterministic components as well as stochastic trends in the panel of seriesyi,t−yt.
The authors make the assumption that as the cross-sectional dimension tends to infinity
the seriesui,tbecome uncorrelated. This assumption, coupled with assuming that the
Dickey–Fuller regression also describes the DGP, with the seriesui,tbeing indeed white-
noise processes, then implies that there is no cointegration between the seriesyi,t−yt
under the null hypothesis of divergence.
- See Appendix B for further details.
- This formulation is similar to Bai and Carrion-i-Silvestre (2007), see also Bai and Ng
(2004).
- Breaks may of course coexist with cross-sectional independence. We merely look here at
the simplest cases first – that is, without dependence and without breaks – and introduce
some of the complications in later sub-sections.
- For both the unit root and cointegration tests consistency of the tests is established for the
case that the process is stationary under the alternative. This implies restrictions on the
coefficientsφikandρito ensureI(1) behavior under the null hypothesis and stationarity
under the alternative, which is the common framework in unit root and cointegration
analysis.
