A parametric approach to the estimation of cointegration vectors in panel data

root close to the unit circle (e.g. Schwert 1989, Perron and Ng 1996).

Another problem is that it is based on a single equation approach. There-
fore, it is assumed that there is only a single cointegration relationship. Fur-
thermore, the normalization of the cointegration vectors requires that the
dependent variable enters the cointegration relationship. This assumption is
however questionable if the cointegration vector is unknown (e.g. Boswijk
1996; Saikkonen, 1999).

For these reasons, a parametric approach may be a promising alternative,
in particular, for panels with a small number of time periods. In this paper a
vector error correction model (VECM) is employed to represent the dynamics
of the system. Our framework can be seen as a panel analog of Johansen’s
cointegrated vector autoregression, where the short-run parameters are al-
lowed to vary across countries and the long-run parameters are homogenous.
Unfortunately, in such a setup the ML estimator cannot be computed from
solving a simple eigenvalue problem as in Johansen (1988). Instead, in sec-
tion 2 we adopt a two-step estimation procedure that was suggested by Ahn
and Reinsel (1990) and Engle and Yoo (1991) for the usual time series model.
As in Levin and Lin (1993) the individual specific parameters are estimated
in a first step, whereas in a second step the common long-run parameters
are estimated from a pooled regression. The resulting estimator is asymp-
totically efficient and normally distributed. Furthermore, a number of test
procedures that are based on the two-step approach is considered in section
4 and extensions to more general models are addressed in section 5. The
results of a couple of Monte Carlo simulations presented in section 6 suggest
that the two-step estimator performs better than the FM-OLS estimator in
typical sample sizes. Some conclusions and suggestions for future work can
be found in section 7.

Finally, a word on the notational conventions applied in this paper. A
standard Brownian motion is written as Wi(a). Although there are different
Brownian motions for different cross section units i, we sometimes drop the
index i for convenience. This has no consequences for the final results since
they depend on the expectation of the stochastic functionals. Furthermore,
if there is no risk of misunderstanding, we drop the limits and the argument
a (or da). For example, the term ^R₀¹ aW_i(a)da will be economically written
as aW . As usual [b] is used to indicate the integer part of b.

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