Impulse response analysis in vector autoregressions with unknown lag order

We show that the effects of overfitting and underfitting a vector autoregressive (VAR) model are strongly asymmetric for VAR summary statistics involving higher-order dynamics (such as impulse response functions, variance decompositions, or long-run forecasts). Underfit models often underestimate the true dynamics of the population process and may result in spuriously tight confidence intervals. These insights are important for applied work, regardless of how the lag order is determined. In addition, they provide a new perspective on the trade-offs between alternative lag order selection criteria. We provide evidence that, contrary to conventional wisdom, for many statistics of interest to VAR users the point and interval estimates based on the AIC compare favourably to those based on the more parsimonious Schwarz Information Criterion and Hannan–Quinn Criterion.