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Bayesian averaging, prediction and nonnested model selection

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  • Hong, Han
  • Preston, Bruce

Abstract

This paper studies the asymptotic relationship between Bayesian model averaging and post-selection frequentist predictors in both nested and nonnested models. We derive conditions under which their difference is of a smaller order of magnitude than the inverse of the square root of the sample size in large samples. This result depends crucially on the relation between posterior odds and frequentist model selection criteria. Weak conditions are given under which consistent model selection is feasible, regardless of whether models are nested or nonnested and regardless of whether models are correctly specified or not, in the sense that they select the best model with the least number of parameters with probability converging to 1. Under these conditions, Bayesian posterior odds and BICs are consistent for selecting among nested models, but are not consistent for selecting among nonnested models and possibly overlapping models. These findings have important bearing for applied researchers who are frequent users of model selection tools for empirical investigation of model predictions.

Suggested Citation

  • Hong, Han & Preston, Bruce, 2012. "Bayesian averaging, prediction and nonnested model selection," Journal of Econometrics, Elsevier, vol. 167(2), pages 358-369.
  • Handle: RePEc:eee:econom:v:167:y:2012:i:2:p:358-369
    DOI: 10.1016/j.jeconom.2011.09.021
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    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez, 2007. "Estimating Macroeconomic Models: A Likelihood Approach," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1059-1087.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. Sin, Chor-Yiu & White, Halbert, 1996. "Information criteria for selecting possibly misspecified parametric models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 207-225.
    4. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, September.
    5. Carroll Christopher Dixon, 2001. "Death to the Log-Linearized Consumption Euler Equation! (And Very Poor Health to the Second-Order Approximation)," The B.E. Journal of Macroeconomics, De Gruyter, vol. 1(1), pages 1-38, April.
    6. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    7. Lubik, Thomas A. & Schorfheide, Frank, 2007. "Do central banks respond to exchange rate movements? A structural investigation," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1069-1087, May.
    8. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    9. Frank Schorfheide, 2000. "Loss function-based evaluation of DSGE models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(6), pages 645-670.
    10. Juan F. Rubio-Ramirez & Jesus Fernández-Villaverde, 2005. "Estimating dynamic equilibrium economies: linear versus nonlinear likelihood," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(7), pages 891-910.
    11. Wright, Jonathan H., 2008. "Bayesian Model Averaging and exchange rate forecasts," Journal of Econometrics, Elsevier, vol. 146(2), pages 329-341, October.
    12. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    13. Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2004. "Estimating nonlinear dynamic equilibrium economies: a likelihood approach," FRB Atlanta Working Paper 2004-1, Federal Reserve Bank of Atlanta.
    14. Justiniano, Alejandro & Preston, Bruce, 2010. "Can structural small open-economy models account for the influence of foreign disturbances?," Journal of International Economics, Elsevier, vol. 81(1), pages 61-74, May.
    15. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    16. Orazio P. Attanasio & Hamish Low, 2004. "Estimating Euler Equations," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(2), pages 405-435, April.
    17. James H. Stock & Mark W.Watson, 2003. "Forecasting Output and Inflation: The Role of Asset Prices," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 788-829, September.
    18. Todd E. Clark & Michael W. McCracken, 2009. "Combining Forecasts from Nested Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(3), pages 303-329, June.
    19. Hong, Han & Preston, Bruce & Shum, Matthew, 2003. "Generalized Empirical Likelihood–Based Model Selection Criteria For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 19(6), pages 923-943, December.
    20. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    21. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    22. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    23. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    24. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    25. Andrews, Donald W. K. & Lu, Biao, 2001. "Consistent model and moment selection procedures for GMM estimation with application to dynamic panel data models," Journal of Econometrics, Elsevier, vol. 101(1), pages 123-164, March.
    26. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    27. Mark W. Watson & James H. Stock, 2004. "Combination forecasts of output growth in a seven-country data set," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(6), pages 405-430.
    28. Pötscher, B.M., 1991. "Effects of Model Selection on Inference," Econometric Theory, Cambridge University Press, vol. 7(2), pages 163-185, June.
    29. Fernandez-Villaverde, Jesus & Francisco Rubio-Ramirez, Juan, 2004. "Comparing dynamic equilibrium models to data: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 123(1), pages 153-187, November.
    30. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    5. Carlos Carvalho & Stefano Eusepi & Emanuel Moench & Bruce Preston, 2023. "Anchored Inflation Expectations," American Economic Journal: Macroeconomics, American Economic Association, vol. 15(1), pages 1-47, January.
    6. Mao, Guangyu, 2015. "Model selection of M-estimation models using least squares approximation," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 238-243.
    7. Alexander Vosseler & Enzo Weber, 2018. "Forecasting seasonal time series data: a Bayesian model averaging approach," Computational Statistics, Springer, vol. 33(4), pages 1733-1765, December.
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    9. Koetter, Michael & Poghosyan, Tigran, 2010. "Real estate prices and bank stability," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1129-1138, June.
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    12. Siddharta Chib & Minchul Shin & Anna Simoni, 2016. "Bayesian Empirical Likelihood Estimation and Comparison of Moment Condition Models," Working Papers 2016-21, Center for Research in Economics and Statistics.
    13. Minerva Mukhopadhyay & Sourabh Bhattacharya, 2022. "Bayes factor asymptotics for variable selection in the Gaussian process framework," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(3), pages 581-613, June.
    14. Mr. Alin T Mirestean & Mr. Charalambos G Tsangarides & Huigang Chen, 2009. "Limited Information Bayesian Model Averaging for Dynamic Panels with Short Time Periods," IMF Working Papers 2009/074, International Monetary Fund.
    15. Barbaglia, Luca & Frattarolo, Lorenzo & Onorante, Luca & Pericoli, Filippo Maria & Ratto, Marco & Tiozzo Pezzoli, Luca, 2023. "Testing big data in a big crisis: Nowcasting under Covid-19," International Journal of Forecasting, Elsevier, vol. 39(4), pages 1548-1563.
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    More about this item

    Keywords

    Model selection criteria; Nonnested; Posterior odds; BIC;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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