Impulse response analysis in vector autoregressions with unknown lag order

We show that the effects of overfitting and underfitting a vector autoregre ssive (VAR) model are strongly asymmetric for VAR summary statistics involv ing higher-order dynamics (such as impulse response functions, variance dec ompositions, or long-run forecasts). Underfit models often underestimate th e true dynamics of the population process and may result in spuriously tigh t confidence intervals. These insights are important for applied work, rega rdless of how the lag order is determined. In addition. they provide a new perspective on the trade-offs between alternative lag order selection crite ria. We provide evidence that, contrary to conventional wisdom, for many st atistics 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. Copyright (C) 2001 John Wiley & Sons, Ltd.