Palgrave Handbook of Econometrics: Applied Econometrics

Anindya Banerjee and Martin Wagner 701

lead to an estimator with a limiting covariance matrix proportional to the identity
matrix.

Pedroni (2001) considers a group mean D-OLS estimator. DenoteR ̃i,t=

[

̃x

′

i,t,Z ̃

′

i,t

]′

and estimate, for eachi=1,...,N,

[

βˆD,i

γˆi

]

=

⎛

⎝

∑N

i= 1

∑T

t= 1

R ̃i,tR ̃

′

i,t

⎞

⎠

− 1 ⎛

⎝

∑N

i= 1

∑T

t= 1

R ̃i,ty ̃i,t

⎞

⎠.

Then the group mean D-OLS estimator is given byβˆGD=N^1
∑N
i= 1 βˆD,i. The group
mean D-OLS estimator can also be computed in a normalized fashion.

13.3.2 Testing for cointegration and estimation of the cointegrating
vectors in systems

The analysis of multiple cointegrating vectors in panels is still very limited. The
analysis is plagued by problems of arriving at a proper, yet statistically tractable,
formulation of multiple cointegration (since one needs not only to consider the
cointegration possibilities within the units of a panel, but also to identify those
that link across the units of the panel). Estimation and inference are thus hampered
by theoretical difficulties, as well as dimensionality issues, even when the panel
dimensions are large.
Breitung (2005), Groen and Kleibergen (2003) and Larsson, Lyhagen and Löth-
gren (2001) have attempted analysis of this framework under restrictive assump-
tions such as a homogeneous cointegrating space (for the units of the panel) and,
more unrealistically, cross-sectional independence of the units of the panel. Some
of these methods are described in detail below.
If cross-unit cointegration is allowed then, as shown by Banerjee, Marcellino
and Osbat (2004), tests for cointegration in panels (in the presence of multiple co-
integrating vectors) suffer from size distortions and loss of power. Inference on the
full cointegration structure in such situations remains an extremely difficult exer-
cise and much further work is needed to understand the theoretical properties of
feasible estimators and their performance in finite and large samples. For a detailed
simulation study of some of the issues involved, see Wagner and Hlouskova (2007).
The established system methods are panel extensions of vector autoregressive
(VAR) cointegration analysis (see Johansen, 1995). Compared to the single-
equation methods several differences are worth mentioning. First, the systems
approach allows us to test for and model multiple cointegrating relationships.
Second, the cointegrated VAR approach allows for the incorporation of a richer
specification concerning (restricted) deterministic components which are consid-
ered relevant in the applied cointegration literature. Third, specifying a parametric
model incorporates the modeling of the short-run dynamics of the data, which are
treated as nuisance parameters in the single-equation methods.
Given that the system methods are based on VAR estimates, substantial biases
arise with short time series. Thus, for practical applications the time series dimen-
sion has to be sufficiently large, which is also required since the specification of a