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Empirical Bayesian Density Forecasting in Iowa and Shrinkage for the Monte Carlo Era

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  • Kurt F. Lewis
  • Charles H. Whiteman

Abstract

The track record of a sixteen-year history of density forecasts of state tax revenue in Iowa is studied, and potential improvements sought through a search for better performing "priors" similar to that conducted two decades ago for point forecasts by Doan, Litterman, and Sims (Econometric Reviews, 1984). Comparisons of the point- and density-forecasts produced under the flat prior are made to those produced by the traditional (mixed estimation) "Bayesian VAR" methods of Doan, Litterman, and Sims, as well as to fully Bayesian, "Minnesota Prior" forecasts. The actual record, and to a somewhat lesser extent, the record of the alternative procedures studied in pseudo-real-time forecasting experiments, share a characteristic: subsequently realized revenues are in the lower tails of the predicted distributions "too often". An alternative empirically-based prior is found by working directly on the probability distribution for the VAR parameters, seeking a betterperforming entropically tilted prior that minimizes in-sample mean-squared-error subject to a Kullback-Leibler divergence constraint that the new prior not differ "too much" from the original. We also study the closely related topic of robust prediction appropriate for situations of ambiguity. Robust "priors" are competitive in out-of-sample forecasting; despite the freedom afforded the entropically tilted prior, it does not perform better than the simple alternatives.
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Suggested Citation

  • Kurt F. Lewis & Charles H. Whiteman, 2015. "Empirical Bayesian Density Forecasting in Iowa and Shrinkage for the Monte Carlo Era," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(1), pages 15-35, January.
  • Handle: RePEc:wly:jforec:v:34:y:2015:i:1:p:15-35
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    Cited by:

    1. P. A. Nazarov & Kazakova, Maria, 2014. "Theoretical Basis of Prediction of Main Budget Parameters of Country," Published Papers r90221, Russian Presidential Academy of National Economy and Public Administration.
    2. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
    3. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2015. "Bayesian VARs: Specification Choices and Forecast Accuracy," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 46-73, January.
    4. Fabian Krüger & Todd E. Clark & Francesco Ravazzolo, 2017. "Using Entropic Tilting to Combine BVAR Forecasts With External Nowcasts," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 470-485, July.
    5. P. A. Nazarov & Kazakova, Maria, 2014. "Development of Prediction Model of Basic Budget Parameters in Russian Federation," Published Papers r90220, Russian Presidential Academy of National Economy and Public Administration.
    6. P. A. Nazarov & Kazakova, Maria, 2014. "Methodological Principles of Prediction of Tax Revenues of Budgetary System," Published Papers r90219, Russian Presidential Academy of National Economy and Public Administration.

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