RDP 2025-03: Fast Posterior Sampling in Tightly Identified SVARs Using ‘Soft’ Sign Restrictions 6. Conclusion

We develop a new approach to posterior sampling in sign-restricted SVARs under the commonly used uniform prior for the orthonormal matrix. This approach can also be used when conducting prior-robust Bayesian inference. The key feature of the approach is that it samples from a target density that smoothly penalises parameter values that violate (or are close to violating) the identifying restrictions, which allows us to apply MCMC methods. Our approach is broadly applicable under a wide range of identifying restrictions, including elasticity and narrative restrictions. We provide evidence that our approach is more computationally efficient than brute force accept-reject sampling when the identified set for the orthonormal matrix is assigned small measure under the uniform prior. It is therefore likely to be particularly useful when rich sets of identifying restrictions are imposed.

Future work could investigate whether our approach could be made more efficient by using alternative MCMC samplers that exploit local information about the shape of the smoothed target density (e.g. gradients). It is also likely that the use of alternative MCMC samplers would be necessary in large models, since the slice sampler can become inefficient in high dimensions. A promising area for future work may be to extend our approach to allow for zero restrictions (e.g. Arias et al 2018; Giacomini and Kitagawa 2021a; Read 2022), which would further broaden its applicability.