A Joint Impulse Response Function for Vector Autoregressive Models

Many applications call for measuring the response due to shocks from several variables at once. We introduce a joint impulse response function (jIRF) that is independent of the order of the variables and allows for simultaneous shocks from multiple variables in the VAR, rather than one at a time as in the generalized IRF. The proposed jIRF controls for the cross-correlations of the several simultaneous shocks. As an application of the jIRF, we study the effect of the COVID-19 pandemic on trans-Atlantic volatility transmissions across large financial institutions and show that simply summing the generalized IRFs overestimates volatility transmissions.