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Mixtures of g-priors for Bayesian model averaging with economic applications

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  • Ley, Eduardo
  • Steel, Mark F.J.

Abstract

We examine the issue of variable selection in linear regression modelling, where we have a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the appropriate subset. In this context, Bayesian Model Averaging presents a formal Bayesian solution to dealing with model uncertainty. Our main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. We combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, we assign a hyperprior to g, as the choice of g has been found to have a large impact on the results. For the prior on g, we examine the Zellner-Siow prior and a class of Beta shrinkage priors, which covers most choices in the recent literature. We propose a benchmark Beta prior, inspired by earlier findings with fixed g, and show it leads to consistent model selection. The effect of this prior structure on penalties for complexity and lack of fit is described in some detail. Inference is conducted through a Markov chain Monte Carlo sampler over model space and g. We examine the performance of the various priors in the context of simulated and real data. For the latter, we consider two important applications in economics, namely cross-country growth regression and returns to schooling. Recommendations to applied users are provided.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 171 (2012)
Issue (Month): 2 ()
Pages: 251-266

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Handle: RePEc:eee:econom:v:171:y:2012:i:2:p:251-266

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Complexity penalty; Consistency; Model uncertainty; Posterior odds; Prediction; Robustness;

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References

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  1. Carmen Fernandez & E Ley & Mark F J Steel, 2004. "Benchmark priors for Bayesian models averaging," ESE Discussion Papers 66, Edinburgh School of Economics, University of Edinburgh.
  2. Ciccone, Antonio & Jarocinski, Marek, 2007. "Determinants of Economic Growth: Will Data Tell?," CEPR Discussion Papers 6544, C.E.P.R. Discussion Papers.
  3. Martin Feldkircher & Stefan Zeugner, 2009. "Benchmark Priors Revisited:on Adaptive Shrinkage and the Supermodel Effect in Bayesian Model Averaging," IMF Working Papers 09/202, International Monetary Fund.
  4. Fern ndez, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(01), pages 80-101, February.
  5. Li, Mingliang & Tobias, Justin, 2004. "Returns to Schooling and Bayesian Model Averaging: A Union of Two Literatures," Staff General Research Papers 12011, Iowa State University, Department of Economics.
  6. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics 0110002, EconWPA.
  7. 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.
  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. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers 15, Wisconsin Madison - Social Systems.
  10. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  11. Ley, Eduardo & Steel, Mark F. J., 2007. "On the effect of prior assumptions in Bayesian model averaging with applications to growth regression," Policy Research Working Paper Series 4238, The World Bank.
  12. Eduardo Ley & Mark F.J. Steel, 2009. "On the effect of prior assumptions in Bayesian model averaging with applications to growth regression This article was published online on 30 March 2009. An error was subsequently identified. This not," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(4), pages 651-674.
  13. 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.
  14. 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.
  15. Feldkircher, Martin & Zeugner, Stefan, 2010. "The Impact of Data Revisions on the Robustness of Growth Determinants - A Note on 'Determinants of Economic Growth. Will Data Tell?'," Working Papers in Economics and Finance 2010-12, University of Salzburg.
  16. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
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Cited by:
  1. Koop, Gary & Tole, Lise, 2011. "Forecasting the European Carbon Market," SIRE Discussion Papers 2011-20, Scottish Institute for Research in Economics (SIRE).
  2. Martin Feldkircher & Roman Horvath & Marek Rusnak, 2013. "Exchange Market Pressures during the Financial Crisis: A Bayesian Model Averaging Evidence," Working Papers 332, Institut für Ost- und Südosteuropaforschung (Institute for East and South-East European Studies).
  3. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.
  4. Tim Salimans, 2011. "Variable Selection and Functional Form Uncertainty in Cross-Country Growth Regressions," Tinbergen Institute Discussion Papers 11-012/4, Tinbergen Institute.
  5. Feldkircher, Martin, 2012. "The Determinants of Vulnerability to the Global Financial Crisis 2008 to 2009: Credit Growth and Other Sources of Risk," BOFIT Discussion Papers 26/2012, Bank of Finland, Institute for Economies in Transition.
  6. repec:cam:camdae:1324 is not listed on IDEAS

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