## Benchmark Priors Revisited: On Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging

_IMF Working Papers, September 1, 2009_

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## Bibliographic details
- Authors: Martin Feldkircher, Stefan Zeugner
- Published: September 1, 2009
- Series: IMF Working Papers
- DOI: https://doi.org/10.5089/9781451873498.001

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### Key findings
- Default prior choices fixing Zellner's g are predominant in the Bayesian Model Averaging literature but tend to concentrate posterior mass on a tiny set of models.
- The paper demonstrates a "supermodel effect" whereby fixed-g priors produce posterior distributions heavily concentrated on few models.
- A hyper-g prior is proposed to address the supermodel effect by providing data-dependent shrinkage that adapts posterior model distributions to data quality.
- An application to determinants of economic growth identifies several covariates whose robustness differs considerably from previous results based on default fixed-g priors.

### Analytical contributions
- Complements existing work on the hyper-g-prior by providing posterior expressions essential to:
  - fully Bayesian analysis, and
  - sound numerical implementation.
- Emphasizes that adaptive (data-dependent) shrinkage alters posterior model distributions relative to fixed-g benchmark priors.

### Methodology and experiments
- Analytical derivations of posterior expressions for the hyper-g-prior are provided to support implementation and interpretation.
- A simulation experiment is used to illustrate the implications of prior choice for posterior inference, highlighting differences between fixed-g and hyper-g priors.

### Implications for empirical practice
- Researchers using Bayesian Model Averaging should be aware that default fixed-g priors can concentrate posterior mass on a small subset of models (the supermodel effect), potentially overstating model robustness.
- Employing a hyper-g prior yields shrinkage that adapts to data quality, which can change posterior model weights and the assessed robustness of covariates.
- Reassessment of empirical findings (for example, determinants of economic growth) may be warranted when moving from fixed-g to hyper-g priors.

*IMF Working Paper — Benchmark Priors Revisited: On Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging (Martin Feldkircher and Stefan Zeugner, September 1, 2009).*

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