Author and guest post by Eren Ocakverdi.
Vector Autoregression (VAR) is a standard tool for analyzing interactions among variables and making inferences about the historical evolution of a system (e.g., an economy). When doing so, however, interpreting the estimated coefficients of the model is generally neither an easy or useful task due to complicated dynamics of VARs. As Stock and Watson (2001) aptly puts it, impulse responses are reported as a more informative statistic instead.
The Impulse Response Function (IRF) measures the reaction of the system to a shock of interest. Unfortunately, when the underlying data generating process (DGP) cannot be well approximated by a VAR(p) process, IRFs derived from the model will be biased and misleading. Jordà (2005) introduced an alternative method for computing IRFs based on local projections that do not require specification and estimation of the unknown true multivariate dynamic system itself1.
The usual presentation of IRFs is through visualizing the dynamic propagation mechanism accompanied by error bands. In addition to marginal error bands, Jordà (2009) introduced two new sets of bands to represent uncertainty about the shape of the impulse response and to examine the individual significance of coefficients in a given trajectory. In this framework, it becomes straightforward to impose restrictions on impulse response trajectories and formally test their significance.
