672 Panel Methods to Test for Unit Roots and Cointegration
covariance matrices of the first differences of the estimated idiosyncratic compo-
nents. Doing so (for details, see again Wagner, 2008a) indicates that even the
de-factored data do not appear to be uncorrelated. In this respect, note that the cor-
relation structure between the estimated idiosyncratic components depends upon
the number of factors chosen, which is intuitively clear because extracting too
many factors may actually induce cross-sectional dependence. Having this poten-
tial caveat in mind, for the idiosyncratic components the unit root hypothesis
is only rejected for the industrial country dataset. Thus, from the perspective of
the Bai and Ng (2004) approach, there is little support for stationarity in the RER
panels.
When the computations are performed with only one common factor as an
additional robustness check, the unit root null hypothesis is not rejected for this
common factor for the euro-area, CEEC and industrial countries datasets but is
rejected for the common factor in the worldwide dataset. With one common factor,
the panel unit root tests on the idiosyncratic components lead to no rejection of
the unit root null hypothesis.
The second-generation test results in Table 13.4 show that, much like for the
first-generation tests and for the more restrictive second-generation tests, the unit
root null hypothesis is by and large rejected for our datasets, with the exception of
the Chang (2002) test.
It is important to remember that these tests are designed for more restricted
DGPs than the Bai and Ng (2004) framework allows for. The Pesaran (2007) and
Choi (2006a) tests allow for only one common stationary serially uncorrelated
factor, with identical loadings for the latter test. The Moon and Perron (2004)
approach restricts the factors to be stationary under the alternative. Thus for all
these approaches key assumptions necessary for the panel unit root tests are most
likely violated, which is consistent with the rejections of the null hypothesis (com-
pare also Breitung and Das, 2008, and Gengenbach, Palm and Urbain, 2006).
Finally, it is unclear what drives the non-rejections of the unit root null hypoth-
esis obtained by applying the Chang (2002) test, since this is designed for panels
Table 13.4 Results of other second-generation panel unit root testsMPa MPb CIPS Cp CZ CL∗ NLEuro-area –9.67 –4.88 −1.96 5.08 –4.56 –4.43 1.52
CEEC –12.44 –7.86 –2.91 7.34 –4.57 –5.31 1.95
Industrial –15.81 –6.62 −1.85 9.87 –8.01 –8.04 1.50
Worldwide –20.77 –9.37 –2.43 18.05 –12.27 –13.67 −0.05Notes: The abbreviations are as in the discussion of the tests in section 13.2.2. Bold
entries indicate rejection of the unit root null hypothesis at the 5% critical level.
MPaandMPb: Moon and Perron tests in section 13.2.2.3.
CIPS: Pesaran test with cross-sectional demeaning in section 13.2.2.3.
Cp,CZandCL∗: Choi tests in section 13.2.2.3.
NL: Chang test in section 13.2.2.4.