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Model Averaging

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The New Palgrave Dictionary of Economics
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Abstract

Model averaging estimates the distribution of quantities of interest across models. Model averaging can be used for inference, prediction and policy analysis to address model uncertainty. Three main approaches are discussed: Bayesian model averaging (BMA), empirical Bayes (EB) methods, and frequentist model averaging (FMA). Differences in prior specifications are contrasted using the example of normal, linear regression models. Finally, the article discusses implementation issues such as numerical simulation techniques and software for model averaging.

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Bibliography

  • Avramov, D. 2002. Stock return predictability and model uncertainty. Journal of Financial Economics 64: 423–458.

    Article  Google Scholar 

  • Bernardo, J.M., and A.F.M. Smith. 1994. Bayesian theory. New York: Wiley.

    Book  Google Scholar 

  • Brock, W.A., and S.N. Durlauf. 2001. Growth empirics and reality. World Bank Economic Review 15: 229–272.

    Article  Google Scholar 

  • Brock, W.A., S.N. Durlauf, and K. West. 2003. Policy evaluation in uncertain economic environments. Brookings Papers on Economic Activity 2003(1): 235–322.

    Article  Google Scholar 

  • Burnham, K.P., and D.R. Anderson. 2002. Model selection and multimodel inference: A practical information-theoretic approach. 2nd ed. New York: Springer.

    Google Scholar 

  • Carlin, B.P., and T.A. Louis. 2000. Bayes and empirical Bayes Methods for data analysis. 2nd ed. New York: Chapman & Hall.

    Book  Google Scholar 

  • Casella, G., and E.I. George. 1992. Explaining the Gibbs sampler. The American Statistician 46: 167–174.

    Google Scholar 

  • Chib, S. 2001. Markov chain Monte Carlo methods: Computation and inference. In Handbook of econometrics, ed. J. Heckman and E. Leamer, vol. 5. Amsterdam: North- Holland Pub. Co..

    Google Scholar 

  • Chib, S., and E. Greenberg. 1995. Understanding the Metropolis–Hastings algorithm. The American Statistician 49: 327–335.

    Google Scholar 

  • Chipman, H., E.I. George, and R.E. McCulloch. 2001. The practical implementation of Bayesian model selection. In Model selection. IMS lecture notes: Monograph series, ed. P. Lahiri. Beachwood: Institute of Mathematical Statistics.

    Google Scholar 

  • Clyde, M., H. Desimone, and G. Parmigiani. 1996. Prediction via orthogonalized model mixing. Journal of the American Statistical Association 91: 1197–1208.

    Article  Google Scholar 

  • Doppelhofer, G. and M. Weeks. 2007. Jointness of growth determinants. Journal of Applied Econometrics.

    Google Scholar 

  • Draper, D. 1995. Assessment and propagation of model uncertainty (with discussion). Journal of the Royal Statistical Society B 57: 45–97.

    Google Scholar 

  • Fernandez, C., E. Ley, and M.F.J. Steel. 2001a. Model uncertainty in cross-country growth regressions. Journal of Applied Econometrics 16: 563–576.

    Article  Google Scholar 

  • Fernandez, C., E. Ley, and M.F.J. Steel. 2001b. Benchmark priors for Bayesian model averaging. Journal of Econometrics 100: 381–427.

    Article  Google Scholar 

  • Garratt, A., K. Lee, M.H. Pesaran, and Y. Shin. 2003. Forecast uncertainties in macroeconomic modelling: An application to the U.K. economy. Journal of the American Statistical Association 98: 829–838.

    Article  Google Scholar 

  • George, E.I. 1999. Discussion of Bayesian model averaging and model search strategies by M.A. Clyde. Bayesian Statistics 6: 175–177.

    Google Scholar 

  • George, E.I., and D.P. Foster. 2000. Calibration and empirical Bayes variable selection. Biometrika 87: 731–747.

    Article  Google Scholar 

  • George, E., and R.E. McCulloch. 1993. Variable selection via Gibbs sampling. Journal of the American Statistical Association 88: 881–889.

    Article  Google Scholar 

  • Geweke, J. 1989. Bayesian inference in econometric models using Monte Carlo integration. Econometrica 57: 1317–1339.

    Article  Google Scholar 

  • Geweke, J., and C. Whiteman. 2006. Bayesian forecasting. In Handbook of economic forecasting, ed. G. Elliott, C.W.J. Granger, and A. Timmermann, vol. 1. Amsterdam: North-Holland.

    Google Scholar 

  • Gilks, W., S. Richardson, and D. Spiegelhalter. 1996. Markov Chain Monte Carlo in practice. New York: Chapman & Hall.

    Google Scholar 

  • Hansen, B.E. 2007. Least squares model averaging. Econometrica 75: 1175–1189.

    Article  Google Scholar 

  • Hjort, N.L., and G. Claeskens. 2003. Frequentist model averaging. Journal of the American Statistical Association 98: 879–899.

    Article  Google Scholar 

  • Hoeting, J.A., D. Madigan, A.E. Raftery, and C.T. Volinsky. 1999. Bayesian model averaging: A tutorial. Statistical Science 14: 382–417.

    Article  Google Scholar 

  • Jeffreys, H. 1961. Theory of probability. 3rd ed. Oxford: Clarendon Press.

    Google Scholar 

  • Kass, R.E., and A.E. Raftery. 1995. Bayes factors. Journal of the American Statistical Association 90: 773–795.

    Article  Google Scholar 

  • Kass, R.E., and L. Wasserman. 1995. A reference Bayesian test for nested hypotheses and its relationship to the Schwarz criterion. Journal of the American Statistical Association 90: 928–934.

    Article  Google Scholar 

  • Klein, R.W., and S.J. Brown. 1984. Model selection when there is ‘minimal’ prior information. Econometrica 52: 1291–1312.

    Article  Google Scholar 

  • Koop, G. 2003. Bayesian econometrics. Chichester: Wiley.

    Google Scholar 

  • Leamer, E. 1978. Specification searches. New York: Wiley.

    Google Scholar 

  • Levin, A.T., and J.C. Williams. 2003. Robust monetary policy with competing reference models. Journal of Monetary Economics 50: 945–975.

    Article  Google Scholar 

  • Madigan, D., and J. York. 1995. Bayesian graphical models for discrete data. International Statistical Review 63: 215–232.

    Article  Google Scholar 

  • Mitchell, T.J., and J.J. Beauchamp. 1988. Bayesian variable selection in linear regression. Journal of the American Statistical Association 83: 1023–1032.

    Article  Google Scholar 

  • Raftery, A.E. 1995. Bayesian model selection in social research. Sociological Methodology 25: 111–163.

    Article  Google Scholar 

  • Raftery, A.E., D. Madigan, and J.A. Hoeting. 1997. Bayesian model averaging for linear regression models. Journal of the American Statistical Association 92: 179–191.

    Article  Google Scholar 

  • Raftery, A.E., D. Madigan, and C.T. Volinsky. 1996. Accounting for model uncertainty in survival analysis improves predictive performance. Bayesian Statistics 5: 323–349.

    Google Scholar 

  • Sala-i-Martin, X., G. Doppelhofer, and R.M. Miller. 2004. Determinants of economic growth: A Bayesian averaging of classical estimates (BACE) approach. American Economic Review 94: 813–835.

    Article  Google Scholar 

  • Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–464.

    Article  Google Scholar 

  • Wasserman, L. 2000. Bayesian model selection and model averaging. Journal of Mathematical Psychology 44: 92–107.

    Article  Google Scholar 

  • Yang, Y. 2001. Adaptive regression by mixing. Journal of the American Statistical Association 96: 574–588.

    Article  Google Scholar 

  • Yuan, Z., and Y. Yang. 2005. Combining linear regression models: When and how? Journal of the American Statistical Association 100: 1202–1214.

    Article  Google Scholar 

  • Zellner, A. 1986. On assessing prior distributions and Bayesian regression analysis with g-prior distributions. In Bayesian inference and decision techniques: Essays in honor of Bruno de Finetti, ed. P.K. Goel and A. Zellner. Amsterdam: North-Holland.

    Google Scholar 

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Doppelhofer, G. (2018). Model Averaging. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2075

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