Palgrave Handbook of Econometrics: Applied Econometrics

Anindya Banerjee and Martin Wagner 657

of the dynamic properties of these series (under the assumptions posited above).
That is, the tests for the number of common stochastic trends do not depend on
whether the idiosyncratic components are stationary, while the tests for whether
the errors are stationary do not depend on the presence or absence of common
stochastic trends.
To be set off against these advantages are the restrictions (for example, the restric-
tions with respect to cointegration discussed Appendix B) implied by modeling
dependence via common factors – and whether alternative approaches such as
GVAR models should be considered. In addition the finite sample properties of
factor-based methods, which have not always been shown to be encouraging, need
to be considered in more detail.

13.2.2.3 Specializations of the Bai and Ng (2004) framework

Three specializations of the Bai and Ng procedure may be considered briefly, since
they serve to illustrate some principles for dealing with cross-sectional dependence,
which have been explored in more general contexts (see, for example, Pesaran,
2006).

Pesaran (2007)
The first specialization, due to Pesaran (2007), allows for the dependence among
the cross-sectional units of the panel to derive only from onestationarycommon
factor in the disturbances of each unit, with this common factor entering into the
units with heterogeneous loadings.
His DGP takes the following form:

yi,t=( 1 −φi)μi+φiyi,t− 1 +ui,t

ui,t=πift+εi,t

i=1, 2,...,N;t=1, 2,...,T.

The following assumptions are put in place:

(i) The idiosyncratic errorsεi,tare independently distributed across bothiandt,
have mean zero, varianceσi^2 and finite fourth-order moment.
(ii) The common factorftis serially uncorrelated with mean zero, constant
varianceσf^2 and finite fourth-order moment.
(iii)εi,t,ftandπiare mutually independent groups.

The assumption of serially uncorrelated errorui,tcan be relaxed (see Pesaran, 2006,
for details).
The null and alternative hypotheses are as for the IPS test (remember that
ρi =φi− 1 ). Under the null hypothesis (φi =1,ρi = 0 )there is no trend in
the data. With this rather restrictive specification, Pesaran proposes the use of a
cross-sectionally augmented version of theIPSttest described above. The procedure
consists of including cross-sectional averages of the level and of lagged differences