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

  • Eduardo Ley

    ()

  • Mark F.J. Steel

    ()

We examine the issue of variable selection in linear regression have a potentially large amount of possible covariates and economic theory offers insufficient guidance on how to select the Model Averaging presents 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 addition, we assign a hyperprior to g, as the choice impact on the results. For the prior 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 selection. 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 appl economics, namely cross-country growth regression and returns to schooling. Recommendations to applied users are provided.

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Paper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws112116.

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Date of creation: Jul 2011
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Handle: RePEc:cte:wsrepe:ws112116
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  1. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers 15, Wisconsin Madison - Social Systems.
  2. Ciccone, Antonio & Jarocinski, Marek, 2007. "Determinants of Economic Growth: Will Data Tell?," CEPR Discussion Papers 6544, C.E.P.R. Discussion Papers.
  3. 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.
  4. Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach," OECD Economics Department Working Papers 266, OECD Publishing.
  5. 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.
  6. 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.
  7. Martin Feldkircher & Stefan Zeugner, 2012. "The impact of data revisions on the robustness of growth determinants—a note on ‘determinants of economic growth: Will data tell?’," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(4), pages 686-694, 06.
  8. Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 31 Jul 1999.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Carmen Fernandez & Mark F J Steel, 1999. "Bayesian Regression Analysis with scale mixtures of normals," ESE Discussion Papers 27, Edinburgh School of Economics, University of Edinburgh.
  14. 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.
  15. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  16. 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.
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