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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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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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  1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, Biometrika Trust, vol. 97(2), pages 465-480.
  2. 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, American Statistical Association, vol. 103, pages 410-423, March.
  3. Justin L. Tobias & Mingliang Li, 2004. "Returns to Schooling and Bayesian Model Averaging: A Union of Two Literatures," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 18(2), pages 153-180, 04.
  4. Ciccone, Antonio & Jarociński, Marek, 2008. "Determinants of economic growth: will data tell?," Working Paper Series, European Central Bank 0852, European Central Bank.
  5. 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., John Wiley & Sons, Ltd., vol. 24(4), pages 651-674.
  6. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers, Wisconsin Madison - Social Systems 15, Wisconsin Madison - Social Systems.
  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. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, Elsevier, vol. 100(2), pages 381-427, February.
  9. 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.
  10. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics, EconWPA 0110002, EconWPA.
  11. Fern ndez, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(01), pages 80-101, February.
  12. 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.
  13. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, Biometrika Trust, vol. 92(4), pages 747-763, December.
  14. 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.
  15. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  16. 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, University of Salzburg 2010-12, University of Salzburg.
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Citations

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Cited by:
  1. Gary Koop & Dimitris Korobilis, 2014. "Model uncertainty in panel vector autoregressive models," Working Papers, University of Strathclyde Business School, Department of Economics 1408, University of Strathclyde Business School, Department of Economics.
  2. 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, Elsevier, vol. 43(C), pages 19-49.
  3. Martin Feldkircher & Roman Horvath & Marek Rusnak, 2013. "Exchange Market Pressures during the Financial Crisis: A Bayesian Model Averaging Evidence," Working Papers, Institut für Ost- und Südosteuropaforschung (Institute for East and South-East European Studies) 332, Institut für Ost- und Südosteuropaforschung (Institute for East and South-East European Studies).
  4. Gary Koop & Lise Tole, 2011. "Forecasting the European Carbon Market," Working Papers, University of Strathclyde Business School, Department of Economics 1110, University of Strathclyde Business School, Department of Economics.
  5. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, Springer, vol. 18(3), pages 253-283, September.
  6. repec:cam:camdae:1324 is not listed on IDEAS
  7. Koop, Gary & Tole, Lise, 2011. "Forecasting the European Carbon Market," SIRE Discussion Papers, Scottish Institute for Research in Economics (SIRE) 2011-20, Scottish Institute for Research in Economics (SIRE).
  8. repec:dgr:uvatin:2011012 is not listed on IDEAS

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