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Hierarchical shrinkage in time-varying parameter models


  • Miguel, Belmonte
  • Gary, Koop
  • Dimitris, Korobilis


In this paper, we forecast EU-area inflation with many predictors using time-varying parameter models. The facts that time-varying parameter models are parameter-rich and the time span of our data is relatively short motivate a desire for shrinkage. In constant coefficient regression models, the Bayesian Lasso is gaining increasing popularity as an effective tool for achieving such shrinkage. In this paper, we develop econometric methods for using the Bayesian Lasso with time-varying parameter models. Our approach allows for the coefficient on each predictor to be: i) time varying, ii) constant over time or iii) shrunk to zero. The econometric methodology decides automatically which category each coefficient belongs in. Our empirical results indicate the benefits of such an approach.

Suggested Citation

  • Miguel, Belmonte & Gary, Koop & Dimitris, Korobilis, 2011. "Hierarchical shrinkage in time-varying parameter models," MPRA Paper 31827, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31827

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    References listed on IDEAS

    1. Marta Bańbura, 2008. "Large Bayesian VARs," 2008 Meeting Papers 334, Society for Economic Dynamics.
    2. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    3. Cogley, Timothy & Morozov, Sergei & Sargent, Thomas J., 2005. "Bayesian fan charts for U.K. inflation: Forecasting and sources of uncertainty in an evolving monetary system," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1893-1925, November.
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    6. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    7. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2013. "Macroeconomic forecasting and structural change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 82-101, January.
    8. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423.
    9. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    10. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    11. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    12. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    13. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2009. "On the evolution of the monetary policy transmission mechanism," Journal of Economic Dynamics and Control, Elsevier, vol. 33(4), pages 997-1017, April.
    14. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    15. Stock, James H & Watson, Mark W, 1996. "Evidence on Structural Instability in Macroeconomic Time Series Relations," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 11-30, January.
    16. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 821-852.
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    Cited by:

    1. Florian Huber & Gregor Kastner & Martin Feldkircher, 2016. "Should I stay or should I go? Bayesian inference in the threshold time varying parameter (TTVP) model," Department of Economics Working Papers wuwp235, Vienna University of Economics and Business, Department of Economics.
    2. Prüser, Jan, 2017. "Forecasting US inflation using Markov dimension switching," Ruhr Economic Papers 710, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    3. Maheu, John M & Song, Yong, 2017. "An Efficient Bayesian Approach to Multiple Structural Change in Multivariate Time Series," MPRA Paper 79211, University Library of Munich, Germany.
    4. Eric Eisenstat & Joshua C. C. Chan & Rodney W. Strachan, 2016. "Stochastic Model Specification Search for Time-Varying Parameter VARs," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1638-1665, December.
    5. Michelle, Gilmartin, 2016. "A note on the identification and transmission of energy demand and supply shocks," MPRA Paper 76186, University Library of Munich, Germany.
    6. Kalli, Maria & Griffin, Jim E., 2014. "Time-varying sparsity in dynamic regression models," Journal of Econometrics, Elsevier, vol. 178(2), pages 779-793.
    7. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    8. Joscha Beckmann & Rainer Schüssler, 2014. "Forecasting Exchange Rates under Model and Parameter Uncertainty," CQE Working Papers 3214, Center for Quantitative Economics (CQE), University of Muenster.
    9. Gregor Kastner, 2016. "Sparse Bayesian time-varying covariance estimation in many dimensions," Papers 1608.08468,, revised Nov 2017.
    10. Korobilis, Dimitris, 2014. "Data-based priors for vector autoregressions with drifting coefficients," SIRE Discussion Papers 2014-022, Scottish Institute for Research in Economics (SIRE).
    11. Dufays, A. & Rombouts, V., 2015. "Sparse Change-Point Time Series Models," CORE Discussion Papers 2015032, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Damian Stelmasiak & Grzegorz Szafrański, 2016. "Forecasting the Polish Inflation Using Bayesian VAR Models with Seasonality," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 8(1), pages 21-42, March.
    13. Beckmann, Joscha & Schüssler, Rainer, 2016. "Forecasting exchange rates under parameter and model uncertainty," Journal of International Money and Finance, Elsevier, vol. 60(C), pages 267-288.
    14. Rangan Gupta & Shawkat Hammoudeh & Beatrice D. Simo-Kengne & Soodabeh Sarafrazi, 2014. "Can the Sharia-based Islamic stock market returns be forecasted using large number of predictors and models?," Applied Financial Economics, Taylor & Francis Journals, vol. 24(17), pages 1147-1157, September.
    15. Chan, Joshua C.C. & Grant, Angelia L., 2016. "Fast computation of the deviance information criterion for latent variable models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 847-859.
    16. Felix Abramovich & Vadim Grinshtein, 2013. "Estimation of a sparse group of sparse vectors," Biometrika, Biometrika Trust, vol. 100(2), pages 355-370.
    17. Ferroni, Filippo & Grassi, Stefano & Leon-Ledesma, Miguel A., 2017. "Selecting Primal Innovations in DSGE models," Working Paper Series WP-2017-20, Federal Reserve Bank of Chicago.
    18. Filippo Ferroni & Stefano Grassi & Miguel A. Leon-Ledesma, 2015. "Fundamental shock selection in DSGE models," Studies in Economics 1508, School of Economics, University of Kent.
    19. Joshua C.C. Chan, 2015. "Specification tests for time-varying parameter models with stochastic volatility," CAMA Working Papers 2015-42, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    20. Rangan Gupta & Mampho P. Modise & Josine Uwilingiye, 2016. "Out-of-Sample Equity Premium Predictability in South Africa: Evidence from a Large Number of Predictors," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 52(8), pages 1935-1955, August.
    21. Martin Feldkircher & Florian Huber & Gregor Kastner, 2017. "Sophisticated and small versus simple and sizeable: When does it pay off to introduce drifting coefficients in Bayesian VARs?," Papers 1711.00564,, revised Nov 2017.
    22. Matei, Florin, 2014. "An empirical examination of stock market integration in EMU," MPRA Paper 60717, University Library of Munich, Germany.
    23. Malefaki, Valia, 2015. "On Flexible Linear Factor Stochastic Volatility Models," MPRA Paper 62216, University Library of Munich, Germany.
    24. repec:eee:ecosta:v:3:y:2017:i:c:p:23-33 is not listed on IDEAS
    25. Joshua C.C. Chan & Eric Eisenstat, 2015. "Bayesian model comparison for time-varying parameter VARs with stochastic volatility," CAMA Working Papers 2015-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.

    More about this item


    Forecasting; hierarchical prior; time-varying parameters; Bayesian Lasso;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

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