Palgrave Handbook of Econometrics: Applied Econometrics

658 Panel Methods to Test for Unit Roots and Cointegration

in the IPS-type regressions, where the former are taken to act as a proxy for the
single common factor forNsufficiently large. Lags of the cross-sectional averages
may be utilized if necessary to take account of serial correlation in theui,tprocess.
Thus, using (for the case without linear trend),

yi,t=μi+ρiyi,t− 1 +ciyt+diyt+

∑pi

k= 1

φikyi,t−k

+νi,t,i=1, 2,...,N;t=pi+2,...,T, (13.12)

where the cross-sectional average of theyi,tterms is:

yt=

1

N

∑N

i= 1

yi,t, and

yt=

1

N

∑N

i= 1

yi,t,

theCIPSttest is given by:

CIPSt=

1

N

∑N

i= 1

CADFi,

withCADFidenoting the Dickey–Fullert-statistic for testingH 0 :ρi= 0 ∀iin
(13.12). This test harks back both to the idea of using group mean tests to allow for
heterogeneity of the autoregressive root under the alternative hypothesis and of
using cross-sectional averaging to allow for cross-sectional dependence across the
units. The latter may not be effective, depending on the nature of the dependence
being modeled.
Pesaran (2007) investigates the asymptotic null distribution of the individual
CADFistatistics as well as of the associatedCIPSttest statistic. The former allows
for the construction ofp-values for the individual (that is, unit by unit)CADFi
test statistics so that tests in the spirit of Maddala and Wu (1999) or Choi (2001)
can be constructed. The asymptotic distributions are derived both for sequential
asymptotics as well as joint asymptotics (NandTtending to infinity such that
N/T→k, wherekis a fixed finite non-zero positive constant). Pesaran shows
that theCADFistatistics do not depend on the factor loadings but are asymptot-
ically correlated through their dependence on the common factor. This has the
consequence that standard central limit theorems cannot be used to derive the
asymptotic distribution of eitherCIPStor of the pooledp-value tests. A truncated
CIPSttest statistic, denotedCIPSt∗, is also proposed with better properties. Critical
values for bothCIPStandCIPSt∗are presented for the three main specifications of
the deterministic components, and not just for the specification outlined here for
illustration.

Moon and Perron (2004)
A second specialization, somewhat less restrictive than Pesaran, is due to Moon
and Perron (2004), who consider a DGP of the following form (which may also be