Fast Posterior Sampling in Tightly Identified SVARs Using 'Soft' Sign Restrictions

2026-03-27

AI Summary

This study addresses the computational inefficiency of conventional Bayesian posterior sampling in structural vector autoregressive (SVAR) models when sign restrictions are tight. The authors propose an efficient Bayesian inference algorithm based on “soft” sign constraints, which smoothly penalizes parameter values violating the constraints and combines Markov chain Monte Carlo with importance sampling to generate posterior draws satisfying the original “hard” restrictions. The method substantially improves computational efficiency under tightly identified scenarios, facilitates prior robustness analysis, and demonstrates both high performance and broad applicability in an oil market SVAR model incorporating sign, elasticity, and narrative restrictions—reducing computation time dramatically.

Abstract

We propose algorithms for conducting Bayesian inference in structural vector autoregressions identified using sign restrictions. The key feature of our approach is a sampling step based on 'soft' sign restrictions. This step draws from a target density that smoothly penalises parameter values that violate the restrictions, facilitating the use of computationally efficient Markov chain Monte Carlo sampling algorithms. An importance-sampling step yields draws conditional on the 'hard' sign restrictions. Relative to standard accept-reject sampling, the method substantially speeds up sampling when identification is tight. It also facilitates implementing prior-robust Bayesian methods. We illustrate the broad applicability of the approach in an oil-market model identified using a rich set of sign, elasticity and narrative restrictions.

Problem

• structural vector autoregression
• sign restrictions
• Bayesian inference
• posterior sampling
• tight identification

Innovation

• soft sign restrictions
• Bayesian inference
• structural vector autoregression
• efficient posterior sampling
• importance sampling