Conditional projection methods for large-scale Bayesian VARs

We develop methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. We define scenarios through distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with 37 variables for the US and ten structural shocks, identified by sign restrictions and internal instruments, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. Left to the model, the oil price path is read as an oil price shock accompanied by a demand boom; attributed to the structural oil price shock alone, a supply disruption, it implies higher inflation and slower growth.