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Choosing Prior Hyperparameters

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Abstract
Bayesian inference is common in models with many parameters, such as large VAR models, models with time-varying parameters, or large DSGE models. A common practice is to focus on prior distributions that themselves depend on relatively few hyperparameters. The choice of these hyperparameters is crucial because their influence is often sizeable for standard sample sizes. In this paper we treat the hyperparameters as part of a hierarchical model and propose a fast, tractable, easy-to-implement, and fully Bayesian approach to estimate those hyperparameters jointly with all other parameters in the model. In terms of applications, we show via Monte Carlo simulations that in time series models with time-varying parameters and stochastic volatility, our approach can drastically improve on using fixed hyperparameters previously proposed in the literature.

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  • Pooyan Amir-Ahmadi & Christian Matthes & Mu-Chun Wang, 2016. "Choosing Prior Hyperparameters," Working Paper 16-9, Federal Reserve Bank of Richmond.
    • Handle: RePEc:fip:fedrwp:16-09
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    References listed on IDEAS

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    1. Koop, Gary & Leon-Gonzalez, Roberto & Strachan, Rodney W., 2011. "Bayesian inference in a time varying cointegration model," Journal of Econometrics, Elsevier, vol. 165(2), pages 210-220.
    2. Luca Benati & Thomas A. Lubik, 2014. "The Time-Varying Beveridge Curve," Dynamic Modeling and Econometrics in Economics and Finance, in: Frauke Schleer-van Gellecom (ed.), Advances in Non-linear Economic Modeling, edition 127, pages 167-204, Springer.
    3. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    4. Koop, Gary & Korobilis, Dimitris, 2010. "Bayesian Multivariate Time Series Methods for Empirical Macroeconomics," Foundations and Trends(R) in Econometrics, now publishers, vol. 3(4), pages 267-358, July.
    5. Canova, Fabio & Gambetti, Luca, 2009. "Structural changes in the US economy: Is there a role for monetary policy?," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 477-490, February.
    6. Korobilis, Dimitris, 2014. "Data-based priors for vector autoregressions with drifting coefficients," SIRE Discussion Papers 2014-022, Scottish Institute for Research in Economics (SIRE).
    7. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    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. Martin Kliem & Alexander Kriwoluzky & Samad Sarferaz, 2016. "On the Low‐Frequency Relationship Between Public Deficits and Inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 566-583, April.
    11. Pooyan Amir‐Ahmadi & Christian Matthes & Mu‐Chun Wang, 2016. "Drifts and volatilities under measurement error: Assessing monetary policy shocks over the last century," Quantitative Economics, Econometric Society, vol. 7(2), pages 591-611, July.
    12. Cooley, Thomas F & Prescott, Edward C, 1976. "Estimation in the Presence of Stochastic Parameter Variation," Econometrica, Econometric Society, vol. 44(1), pages 167-184, January.
    13. 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.
    14. Colin Ellis & Haroon Mumtaz & Pawel Zabczyk, 2014. "What Lies Beneath? A Time‐varying FAVAR Model for the UK Transmission Mechanism," Economic Journal, Royal Economic Society, vol. 0(576), pages 668-699, May.
    15. Thomas A. Lubik & Christian Matthes & Andrew Owens, 2016. "Beveridge Curve Shifts and Time-Varying Parameter VARs," Economic Quarterly, Federal Reserve Bank of Richmond, issue 3Q, pages 197-226.
    16. Diebold, Francis X. & Schorfheide, Frank & Shin, Minchul, 2017. "Real-time forecast evaluation of DSGE models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 201(2), pages 322-332.
    17. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    18. Todd E. Clark & Stephen J. Terry, 2010. "Time Variation in the Inflation Passthrough of Energy Prices," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1419-1433, October.
    19. 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.
    20. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    21. Timothy Cogley & Thomas J. Sargent, 2015. "Measuring Price-Level Uncertainty and Instability in the United States, 1850–2012," The Review of Economics and Statistics, MIT Press, vol. 97(4), pages 827-838, October.
    22. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    23. Luca Benati & Thomas A. Lubik, 2014. "Sales, Inventories And Real Interest Rates: A Century Of Stylized Facts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1210-1222, November.
    24. Thomas J. Sargent & Paolo Surico, 2011. "Two Illustrations of the Quantity Theory of Money: Breakdowns and Revivals," American Economic Review, American Economic Association, vol. 101(1), pages 109-128, February.
    25. Lopes, Hedibert Freitas & Moreira, Ajax R. Bello & Schmidt, Alexandra Mello, 1999. "Hyperparameter estimation in forecast models," Computational Statistics & Data Analysis, Elsevier, vol. 29(4), pages 387-410, February.
    26. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    27. Frank Schorfheide & Dongho Song & Amir Yaron, 2018. "Identifying Long‐Run Risks: A Bayesian Mixed‐Frequency Approach," Econometrica, Econometric Society, vol. 86(2), pages 617-654, March.
    28. Baumeister, Christiane & Liu, Philip & Mumtaz, Haroon, 2013. "Changes in the effects of monetary policy on disaggregate price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 543-560.
    29. Antonello D'Agostino & Paolo Surico, 2012. "A Century of Inflation Forecasts," The Review of Economics and Statistics, MIT Press, vol. 94(4), pages 1097-1106, November.
    30. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
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    Cited by:

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    2. Simon Beyeler, 2019. "Streamlining Time-varying VAR with a Factor Structure in the Parameters," Working Papers 19.03, Swiss National Bank, Study Center Gerzensee.
    3. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    4. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Shin, Minchul, 2023. "Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1054-1086.
    5. Peersman, Gert & Rüth, Sebastian K. & Van der Veken, Wouter, 2021. "The interplay between oil and food commodity prices: Has it changed over time?," Journal of International Economics, Elsevier, vol. 133(C).
    6. Hartwig, Benny, 2020. "Robust inference intime-varying structural VAR models: The DC-Cholesky multivariate stochasticvolatility model," Discussion Papers 34/2020, Deutsche Bundesbank.
    7. Korobilis, Dimitris & Landau, Bettina & Musso, Alberto & Phella, Anthoulla, 2021. "The time-varying evolution of inflation risks," Working Paper Series 2600, European Central Bank.
    8. Reusens Peter & Croux Christophe, 2017. "Detecting time variation in the price puzzle: a less informative prior choice for time varying parameter VAR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(4), pages 1-18, September.
    9. Nikolay Hristov & Oliver Hülsewig & Thomas Siemsen & Timo Wollmershäuser, 2019. "Restoring euro area monetary transmission: Which role for government bond rates?," Empirical Economics, Springer, vol. 57(3), pages 991-1021, September.
    10. Markus Heinrich & Magnus Reif, 2020. "Real-Time Forecasting Using Mixed-Frequency VARS with Time-Varying Parameters," CESifo Working Paper Series 8054, CESifo.
    11. Jan Prüser & Alexander Schlösser, 2020. "On the Time‐Varying Effects of Economic Policy Uncertainty on the US Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(5), pages 1217-1237, October.
    12. Prüser, Jan & Schlösser, Alexander, 2018. "On the time-varying effects of economic policy uncertainty on the US economy," Ruhr Economic Papers 761, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    13. Prüser, Jan & Schlösser, Alexander, 2017. "The effects of economic policy uncertainty on European economies: Evidence from a TVP-FAVAR," Ruhr Economic Papers 708, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.

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