Canonical Correlation Analysis in Panel Vector Error Correction Model. Performance Comparison

Abstract

Small sample properties of unrestricted and restricted canonical correlation
estimators of cointegrating vectors for panel vector autoregressive process are
considered when the cross-sectional dependencies occur in the process generating
nonstationary panel data. It is shown that the unrestricted Box-Tiao estimator
is slightly outperformed by the unrestricted Johansen estimator if the dynamic
properties of the underlying process are correctly specified. The comparison of
performance of the restricted canonical correlation estimator of cointegrating
vectors for the panel VAR and for the classical VAR applied independently for
each cross-section reveals that the latter performs better in small samples when
the cross-sectional dependence is limited to the error terms correlations, even
though it is inefficient in the limit, but it falls short in comparison to the former
when there are cross-sectional dependencies in the short-run dynamics and/or
in the long-run adjustments.