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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. 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. 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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File URL: http://mpra.ub.uni-muenchen.de/31973/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26941.

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Date of creation: 22 Nov 2010
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Handle: RePEc:pra:mprapa:26941

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

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References

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  1. William A. Brock & Steven N. Durlauf & Kenneth D. West, 2003. "Policy Evaluation in Uncertain Economic Environments," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 34(1), pages 235-322.
  2. Antonio Ciccone & Marek Jarocinski, 2007. "Determinants of economic growth: Will data tell?," Economics Working Papers 1052, Department of Economics and Business, Universitat Pompeu Fabra, revised Sep 2009.
  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. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Gernot Doppelhofer & Ronald I. Miller & Xavier Sala-i-Martin, 2000. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," NBER Working Papers 7750, National Bureau of Economic Research, Inc.
  11. 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.
  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. 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.
  14. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  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. 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.
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Cited by:
  1. Gary Koop & Lise Tole, 2013. "Forecasting the European carbon market," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(3), pages 723-741, 06.
  2. Feldkircher, Martin & Horvath, Roman & Rusnak, Marek, 2014. "Exchange market pressures during the financial crisis: A Bayesian model averaging evidence," Journal of International Money and Finance, Elsevier, vol. 40(C), pages 21-41.
  3. repec:cam:camdae:1324 is not listed on IDEAS
  4. 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.
  5. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.
  6. repec:dgr:uvatin:2011012 is not listed on IDEAS

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