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

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  • Eduardo Ley

    ()

  • Mark F.J. Steel

    ()

Abstract

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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Bibliographic Info

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

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References

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  1. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics 0110002, EconWPA.
  2. Ciccone, Antonio & Jarocinski, Marek, 2007. "Determinants of Economic Growth: Will Data Tell?," CEPR Discussion Papers 6544, C.E.P.R. Discussion Papers.
  3. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers 15, Wisconsin Madison - Social Systems.
  4. Carmen Fernandez & Eduardo Ley & Mark F.J. Steel, 1998. "Benchmark Priors for Bayesian Model Averaging," Econometrics 9804001, EconWPA, revised 31 Jul 1999.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  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. 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.
  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. 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.
  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. 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.
  15. 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.
  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. Tim Salimans, 2011. "Variable Selection and Functional Form Uncertainty in Cross-Country Growth Regressions," Tinbergen Institute Discussion Papers 11-012/4, Tinbergen Institute.
  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. 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.
  4. Gary Koop & Lise Tole, 2011. "Forecasting the European Carbon Market," Working Papers 1110, University of Strathclyde Business School, Department of Economics.
  5. repec:cam:camdae:1324 is not listed on IDEAS
  6. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.

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