On the small sample properties of weak exogeneity tests in cointegrated VAR models

We investigate the small sample properties of two types of weak exogeneity tests in cointegrated VAR models that are frequently used in applied work. The first one is the standard Likelihood Ratio (LR) test in the Johansen framework. The second test is based on mapping the cointegrated VAR model into VECM representation and then reducing the model using some model selection procedure before testing the significance of the alpha parameters. Results from Monte Carlo experiments indicate severe size distortions in both test types in small samples. We suggest a bootstrap version of the LR test, which can be used for size correction.