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

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  • Ley, Eduardo
  • Steel, Mark F.J.

Abstract

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.

Suggested Citation

  • Ley, Eduardo & Steel, Mark F.J., 2011. "Mixtures of g-priors for Bayesian Model Averaging with economic application," Policy Research Working Paper Series 5732, The World Bank.
  • Handle: RePEc:wbk:wbrwps:5732
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    References listed on IDEAS

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    1. 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, June.
    2. 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, April.
    3. 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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    5. 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.
    6. Antonio Ciccone & Marek Jarociński, 2010. "Determinants of Economic Growth: Will Data Tell?," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(4), pages 222-246, October.
    7. 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, pages 235-322.
    8. 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.
    9. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
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    11. 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.
    12. 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.
    13. Ley, Eduardo & Steel, Mark F. J., 2007. "On the effect of prior assumptions in Bayesian model averaging with applications to growth regression," Policy Research Working Paper Series 4238, The World Bank.
    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. 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.
    16. 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.
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    Cited by:

    1. Koop, Gary & Korobilis, Dimitris, 2016. "Model uncertainty in Panel Vector Autoregressive models," European Economic Review, Elsevier, vol. 81(C), pages 115-131.
    2. Rockey, James & Temple, Jonathan, 2016. "Growth econometrics for agnostics and true believers," European Economic Review, Elsevier, pages 86-102.
    3. repec:spr:testjl:v:26:y:2017:i:2:d:10.1007_s11749-016-0516-0 is not listed on IDEAS
    4. Salimans, Tim, 2012. "Variable selection and functional form uncertainty in cross-country growth regressions," Journal of Econometrics, Elsevier, vol. 171(2), pages 267-280.
    5. Devereux, John & Dwyer, Gerald P., 2016. "What determines output losses after banking crises?," Journal of International Money and Finance, Elsevier, vol. 69(C), pages 69-94.
    6. Havranek, Tomas & Horvath, Roman & Irsova, Zuzana & Rusnak, Marek, 2015. "Cross-country heterogeneity in intertemporal substitution," Journal of International Economics, Elsevier, vol. 96(1), pages 100-118.
    7. Joseph, Andreas & Osbat, Chiara, 2016. "How you export matters: the disassortative structure of international trade," Working Paper Series 1958, European Central Bank.
    8. 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.
    9. Kaffine, Daniel T. & Davis, Graham A., 2017. "A multi-row deletion diagnostic for influential observations in small-sample regressions," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 133-145.
    10. Leon-Gonzalez, Roberto & Vinayagathasan, Thanabalasingam, 2015. "Robust determinants of growth in Asian developing economies: A Bayesian panel data model averaging approach," Journal of Asian Economics, Elsevier, pages 34-46.
    11. Crespo Cuaresma, Jesus & Grün, Bettina & Hofmarcher, Paul & Humer, Stefan & Moser, Mathias, 2015. "A Comprehensive Approach to Posterior Jointness Analysis in Bayesian Model Averaging Applications," Department of Economics Working Paper Series 4493, WU Vienna University of Economics and Business.
    12. 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.
    13. 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, June.
    14. Kourtellos, Andros & Marr, Christa & Tan, Chih Ming, 2016. "Robust determinants of intergenerational mobility in the land of opportunity," European Economic Review, Elsevier, vol. 81(C), pages 132-147.
    15. Leamer, Edward E., 2016. "S-values and Bayesian weighted all-subsets regressions," European Economic Review, Elsevier, vol. 81(C), pages 15-31.
    16. Steel, Mark F. J., 2017. "Model Averaging and its Use in Economics," MPRA Paper 81568, University Library of Munich, Germany.
    17. León-González, Roberto & Montolio, Daniel, 2015. "Endogeneity and panel data in growth regressions: A Bayesian model averaging approach," Journal of Macroeconomics, Elsevier, pages 23-39.
    18. Paul Hofmarcher & Jesús Crespo Cuaresma & Bettina Grün & Kurt Hornik, 2015. "Last Night a Shrinkage Saved My Life: Economic Growth, Model Uncertainty and Correlated Regressors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(2), pages 133-144, March.
    19. Aart Kraay & Norikazu Tawara, 2013. "Can specific policy indicators identify reform priorities?," Journal of Economic Growth, Springer, vol. 18(3), pages 253-283, September.
    20. Ductor, Lorenzo & Leiva-Leon, Danilo, 2016. "Dynamics of global business cycle interdependence," Journal of International Economics, Elsevier, pages 110-127.
    21. Man, Georg, 2015. "Competition and the growth of nations: International evidence from Bayesian model averaging," Economic Modelling, Elsevier, vol. 51(C), pages 491-501.
    22. Poudineh, Rahmatallah & Jamasb, Tooraj, 2016. "Determinants of investment under incentive regulation: The case of the Norwegian electricity distribution networks," Energy Economics, Elsevier, vol. 53(C), pages 193-202.
    23. Feldkircher, Martin & Huber, Florian, 2016. "The international transmission of US shocks—Evidence from Bayesian global vector autoregressions," European Economic Review, Elsevier, vol. 81(C), pages 167-188.
    24. repec:cam:camdae:1324 is not listed on IDEAS

    More about this item

    Keywords

    Educational Technology and Distance Education; Arts&Music; Geographical Information Systems; Information Security&Privacy; Statistical&Mathematical Sciences;

    JEL classification:

    • O47 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - Empirical Studies of Economic Growth; Aggregate Productivity; Cross-Country Output Convergence
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General

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