Palgrave Handbook of Econometrics: Applied Econometrics

Anindya Banerjee and Martin Wagner 671

Table 13.3 Results of Bai and Ng (2004) analysis

Factors BNN BNχ 2 MQc(m)MQf(m)

Euro-area 6 0.17 23.14 6 6

CEEC 5 1.24 30.25 5 5

Industrial 4 1.93 78.76 44

Worldwide 4 0.25 117.78 3 3

Notes: Bold entries indicate rejection of the unit root null hypoth-

esis at the 5% critical level;BNNandBNχ 2 denote the Bai and

Ng tests on the estimated idiosyncratic components described in

section 13.2.2.2; andMQc(m)andMQf(m)are the Bai and Ng tests

for common trends in section 13.2.2.2.

Further evidence concerning the cross-sectional dependence structure in the RER
panels is collected by applying the Bai and Ng (2004) methodology for computing
common factors and the results are reported in Table 13.3. The second column
contains the estimated number of common factors chosen according to the infor-
mation criterion BIC 3 of Bai and Ng (2002), while the third and fourth columns
provide the results of tests on the idiosyncratic components based on using the
pooled inverted normal test and the Maddala and Wu test respectively. The fifth
and sixth columns give the number of common trends amongst the common
factors according to the two different tests described previously.
These results reflect a well-known weakness of the information criteria to deter-
mine the number of common factors (see the second column), which tend to favor
large numbers of estimated common factors (given that the upper bound for the
number of common factors is six). For the euro-area six factors are selected, five
factors are selected for the CEEC panel and four for the other two datasets. Onatski
(2006) reports simulations showing that correlation between the idiosyncratic com-
ponents of the individual units (for which evidence is presented in Wagner, 2008a,
for the RER panels at hand) leads to overestimation of the number of common
factors when using the information criteria of Bai and Ng (2002). Thus, the results
concerning thenumberof common factors should be interpreted with caution,
given that the cross-sectional dimensions are rather small in the panels.
The second striking feature is that the number of common trends is selected to
be equal to the number of common factors, with the exception of the worldwide
dataset where the number of common trends in the common factors is selected to
be three (that is, a lot of evidence for unit roots in the common factors). Simulations
performed by the authors indicate a tendency of the tests to lead to too large a
number of common trends unless, for example, the time series dimensionTis
very large. Hence, the results concerning the number of common trends also have
to be interpreted with some caution.
The Bai and Ng (2004) panel unit root tests are designed for cross-sectionally inde-
pendent data. In order to verify whether the de-factored data are cross-sectionally
independent, one can again look at the cross-correlation functions or the long-run