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S-values and Bayesian weighted all-subsets regressions

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  • Leamer, Edward E.

Abstract

This paper compares and contrasts Bayesian variable-exclusion methods proposed by Eduardo Ley and coauthors with methods proposed by Raftery and Sala-i-Martin et al. and with the s-values proposed by myself. A distinction is drawn between estimation uncertainty which is the focus of Ley׳s research and model ambiguity which arises in Ley׳s work and is the focus of my own recent proposal. The discussion is organized around the prior covariance matrix, which needs to be diagonal to support all-subsets regressions. The basic question addressed here is: what aspects of the prior covariance matrix can be taken as known, what aspects can be estimated and what aspects require a sensitivity analysis because they are neither known nor estimable. When diagonality is in doubt, we are more-or-less forced into a model ambiguity sensitivity mode because the data are never rich enough credibly to estimate the full prior covariance matrix. When diagonality is assumed, the data evidence, though very limited, can help to estimate the diagonal elements, but this literature has not yet produced a compelling conventional treatment which will necessarily include both estimation uncertainty and model ambiguity as they relate both to the diagonal values and to the rest of the prior covariance matrix. But there has been a lot of progress.

Suggested Citation

  • Leamer, Edward E., 2016. "S-values and Bayesian weighted all-subsets regressions," European Economic Review, Elsevier, vol. 81(C), pages 15-31.
  • Handle: RePEc:eee:eecrev:v:81:y:2016:i:c:p:15-31
    DOI: 10.1016/j.euroecorev.2015.04.007
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Ley, Eduardo & Steel, Mark F.J., 2012. "Mixtures of g-priors for Bayesian model averaging with economic applications," Journal of Econometrics, Elsevier, vol. 171(2), pages 251-266.
    3. Carmen Fernandez & Eduardo Ley & Mark F. J. Steel, 2001. "Model uncertainty in cross-country growth regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(5), pages 563-576.
    4. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    5. Levine, Ross & Renelt, David, 1992. "A Sensitivity Analysis of Cross-Country Growth Regressions," American Economic Review, American Economic Association, vol. 82(4), pages 942-963, September.
    6. Theo S. Eicher & Chris Papageorgiou & Adrian E. Raftery, 2011. "Default priors and predictive performance in Bayesian model averaging, with application to growth determinants," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(1), pages 30-55, January/F.
    7. Sala-i-Martin, Xavier, 1997. "I Just Ran Two Million Regressions," American Economic Review, American Economic Association, vol. 87(2), pages 178-183, May.
    8. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    9. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-736, May.
    10. Liang, Feng & Paulo, Rui & Molina, German & Clyde, Merlise A. & Berger, Jim O., 2008. "Mixtures of g Priors for Bayesian Variable Selection," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 410-423, March.
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