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A Gibbs Sampler for Efficient Bayesian Inference in Sign-Identified SVARs

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Abstract

We develop a new algorithm for inference based on structural vector autoregressions (SVARs) identified with sign restrictions. The key insight of our algorithm is to break from the accept-reject tradition associated with sign-identified SVARs. We show that embedding an elliptical slice sampling within a Gibbs sampler approach can deliver dramatic gains in speed and turn previously infeasible applications into feasible ones. We provide a tractable example to illustrate the power of the elliptical slice sampling applied to sign-identified SVARs. We demonstrate the usefulness of our algorithm by applying it to a well-known small SVAR model of the oil market featuring a tight identified set, as well as to a large SVAR model with more than 100 sign restrictions.

Suggested Citation

  • Jonas E. Arias & Juan F. Rubio-Ramirez & Minchul Shin, 2025. "A Gibbs Sampler for Efficient Bayesian Inference in Sign-Identified SVARs," Working Papers 25-19, Federal Reserve Bank of Philadelphia.
    • Handle: RePEc:fip:fedpwp:100040
    DOI: 10.21799/frbp.wp.2025.19
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    Keywords

    large structural vector autoregressions; sign restrictions; slice elliptical sampling;
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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