Conditional projection methods for large-scale Bayesian VARs

2026-07-31

AI Summary

This study addresses the computational intractability and poor scalability of high-dimensional Bayesian vector autoregressive (VAR) models in conditional forecasting and structural scenario analysis. The authors propose a conditional projection framework that exploits a factor structure in the error terms, enabling separate distributional constraints on observed variables, structural shocks, and idiosyncratic components to facilitate efficient counterfactual prediction and scenario analysis. The resulting fast algorithm exhibits computational complexity cubic in the number of constraints but only linear in the system dimension, while endowing the latent factors with clear economic interpretations. Applied to a U.S. model featuring 33 macro-financial variables and 10 structural shocks, the framework successfully simulates the oil price trajectory under a hypothetical 2026 closure of the Strait of Hormuz, revealing that identical oil price shocks can generate outcomes ranging from mild fluctuations to severe stagflation depending on the underlying economic context.

Abstract

We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general 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. The scenarios are defined through separate 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 $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it.

Problem

• Bayesian VARs
• conditional forecasting
• structural scenario analysis
• high-dimensional
• computational efficiency

Innovation

• conditional projection
• Bayesian VAR
• factor structure
• structural scenario analysis
• high-dimensional forecasting