Selection of the Truncation Lag in Structural Vars (or Vecms) with Long-Run Restrictions

The authors examine the issue of lag-length selection in the context of a structural vector autoregression (VAR) and a vector error-correction model with long-run restrictions. First, they show that imposing long-run restrictions implies, in general, a moving-average (MA) component in the stationary multivariate representation. Then they examine the sensitivity of estimates of the permanent and transitory components to the selection of the lag length required in a VAR system to approximate this MA component. In summary, they find that using a lag structure that is too short can lead to a significant estimation bias of the permanent and transitory components. In addition, in comparing four different lag-selection criteria, they find that the Schwarz information criterion systematically underperforms relative to the other tests. More generally, as the order of the VAR that best approximates the data-generating process increases, the sequence-based tests (Wald, likelihood ratio) tend to provide more reliable results than the information- based tests (Akaike, Schwarz)