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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 modeling, 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

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36817.

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Date of creation: 23 Dec 2011
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Handle: RePEc:pra:mprapa:36817

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

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References

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  1. Antonio Ciccone & Marek Jarociński, 2010. "Determinants of Economic Growth: Will Data Tell?," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 222-46, October.
  2. 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.
  3. 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.
  4. Theo Eicher & Chris Papageogiou & Adrian E Raftery, 2007. "Default Priors and Predictive Performance in Bayesian Model Averaging, with Application to Growth Determinants," Working Papers UWEC-2007-25-P, University of Washington, Department of Economics.
  5. Ley, Eduardo & Steel, Mark F.J., 2008. "On the Effect of Prior Assumptions in Bayesian Model Averaging with Applications to Growth Regression," MPRA Paper 6773, University Library of Munich, Germany, revised 06 Jan 2008.
  6. 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.
  7. 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.
  8. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics 0110002, EconWPA.
  9. Carmen Fernandez & Mark F. J. Steel, 2004. "Bayesian Regression Analysis with scale mixtures of normals," ESE Discussion Papers 27, Edinburgh School of Economics, University of Edinburgh.
  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.
  11. Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 31 Jul 1999.
  12. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  13. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers 15, Wisconsin Madison - Social Systems.
  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. 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.
  16. 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.
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Cited by:
  1. Feldkircher, Martin, 2014. "The determinants of vulnerability to the global financial crisis 2008 to 2009: Credit growth and other sources of risk," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 19-49.
  2. repec:cam:camdae:1324 is not listed on IDEAS
  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. Feldkircher, Martin & Horvath, Roman & Rusnak, Marek, 2013. "Exchange market pressures during the financial crisis: A Bayesian model averaging evidence," BOFIT Discussion Papers 11/2013, Bank of Finland, Institute for Economies in Transition.
  5. repec:dgr:uvatin:2011012 is not listed on IDEAS
  6. Gary Koop & Lise Tole, 2011. "Forecasting the European Carbon Market," Working Papers 1110, University of Strathclyde Business School, Department of Economics.

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