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



1 Introduction

Since the papers by Levin and Lin (1992, 1993) and Pedroni (1995) it has be-
come popular to investigate long-run relationships by applying cointegration
techniques to multi-country data. The attractive feature of such an analysis
is that employing panel data with a substantial number of cross section units
(countries) takes advantage of a much richer data source than using pure
time series data.

An important problem with the analysis of panel data is its ability to cap-
ture heterogeneity due to country specific characteristics. The usual panel
cointegration framework therefore assumes that the mean (or trend) and the
short-run dynamics may differ across countries, whereas the long-run rela-
tionship is the same for all countries. The reason for assuming a homogenous
long-run relationship is that the underlying economic principles that are em-
ployed to establish the long-run equilibrium (for example the purchasing
power parity) should apply similarly in all economies, whereas the adjust-
ment process towards the long-run equilibrium may differ due to behavioral
and institutional characteristics.

Another important feature of the panel data model considered here is a
possible contemporaneous correlation among cross section units. In many
country studies this cross section correlation cannot be captured by a time-
specific random effect (e.g. O’Connell 1998). Thus, to allows for arbitrary
contemporaneous correlation among the errors, recent work employ simula-
tion techniques to mimic the cross-correlation pattern among the errors (e.g.
Chang 2001, Wu and Wu 2001).

Pedroni (1995, 2000) and Phillips and Moon (1999) suggest an asymp-
totically efficient estimation procedure that is based on the “fully-modified
OLS” (FM-OLS) approach suggested by Phillips and Hansen (1990). This
method employs kernel estimators of the nuisance parameters that affect the
asymptotic distribution of the OLS estimator. In order to achieve asymptotic
efficiency, the FM-OLS estimator accounts for a possible endogeneity of the
regressors and serial correlation of the errors. Although this nonparametric
approach is a very elegant way to deal with nuisance parameters, it may
be problematical especially in fairly small samples. Furthermore, it is well
known that nonparametric estimators may have poor properties in special
cases, for example if the process has a moving average polynomial with a



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