Symmetry and Separability in Two-Country Cointegrated VAR Models: Representation and Testing

Introducing the approach by Masanao Aoki (1981) to time series econometrics, we show that the dynamics of symmetric linear possibly cointegrated two-country VAR models can be separated into two autonomous subsystems: the country averages and country differences, where the latter includes the exchange rate. The symmetric two-country cointegrated VAR model is synchronized, ie the two countries are driven by the same common trends, if and only if the country-differences subsystem is stable. It is shown that separability carries over even under mild asymmetries such as difference in the size of the countries' economies. The possibilities of a recursive structural VECM representation under symmetry is evaluated. The derived conditions for symmetry and separability are easily testable and applied to nine-dimensional quarterly cointegrated VAR models for five different country pairs in the post-Bretton-Woods era. We find evidence for the symmetry of the cointegration space, which is of practical importance as it allows for the identification of the cointegration vectors in much smaller systems, and for the exchange rate equation in general.