Detecting Common Dynamics in Transitory Components

This paper considers VECMs for variables exhibiting cointegration and common features in the transitory components. While the presence of cointegration between the permanent components of series reduces the rank of the long-run multiplier matrix, a common feature among the transitory components leads to a rank reduction in the matrix summarizing short-run dynamics. The common feature also implies that there exists linear combinations of the first-differenced variables in a cointegrated VAR that are white noise and traditional tests focus on testing for this characteristic. An alternative, however, is to test the rank of the short-run dynamics matrix directly. Consequently, we use the literature on testing the rank of a matrix to produce some alternative test statistics. We also show that these are identical to one of the traditional tests. The performance of the different methods is illustrated in a Monte Carlo analysis which is then used to re-examine an existing empirical study. Finally, this approach is applied to provide a check for the presence of common dynamics in DSGE models.