How to conduct joint Bayesian inference in VAR models?

When economic analysis requires simultaneous inference across multiple variables and time horizons, this paper shows that conventional pointwise quantiles in Bayesian structural vector autoregressions significantly understate the uncertainty of impulse responses. The performance of recently proposed joint inference methods, which produce noticeably different error band estimates, is evaluated, and calibration routines are suggested to ensure that they achieve the intended nominal probability coverage. Two practical applications illustrate the implications of these findings: (i) within a structural vector autoregression, the fiscal multiplier exhibits error bands that are 51% to 91% wider than previous estimates, and (ii) a pseudo-out-of-sample projection exercise for inflation and gross domestic product shows that joint inference methods could effectively summarize uncertainty for forecasts as well. These results underscore the importance of using joint inference methods for more robust econometric analysis.