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Mixtures of g-priors for Bayesian Model Averaging with economic application

  • Ley, Eduardo
  • Steel, Mark F.J.

This paper examines the issue of variable selection in linear regression modeling, where there is 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. The main interest here is the effect of the prior on the results, such as posterior inclusion probabilities of regressors and predictive performance. The authors combine a Binomial-Beta prior on model size with a g-prior on the coefficients of each model. In addition, they 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, they examine the Zellner-Siow prior and a class of Beta shrinkage priors, which covers most choices in the recent literature. The authors 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. The authors examine the performance of the various priors in the context of simulated and real data. For the latter, they consider two important applications in economics, namely cross-country growth regression and returns to schooling. Recommendations for applied users are provided.

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Paper provided by The World Bank in its series Policy Research Working Paper Series with number 5732.

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Date of creation: 01 Jul 2011
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Handle: RePEc:wbk:wbrwps:5732
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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. 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.
  3. Carmen Fernandez & Eduardo Ley & Mark Steel, 2001. "Model uncertainty in cross-country growth regressions," Econometrics 0110002, EconWPA.
  4. Justin L. Tobias & Mingliang Li, 2004. "Returns to Schooling and Bayesian Model Averaging: A Union of Two Literatures," Journal of Economic Surveys, Wiley Blackwell, vol. 18(2), pages 153-180, 04.
  5. Brock,W.A. & Durlauf,S.N. & West,K.D., 2003. "Policy evaluation in uncertain economic environments," Working papers 15, Wisconsin Madison - Social Systems.
  6. David J. Nott & Robert Kohn, 2005. "Adaptive sampling for Bayesian variable selection," Biometrika, Biometrika Trust, vol. 92(4), pages 747-763, December.
  7. 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.
  8. 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.
  9. Carmen Fernández & Eduardo Ley & Mark F. J. Steel, . "Benchmark priors for Bayesian Model averaging," Working Papers 98-06, FEDEA.
  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. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
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