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Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions

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  • Andrea Carriero
  • Todd E. Clark
  • Massimiliano Marcellino
Abstract
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR’s conditional mean. Even though the one-step-ahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs’ established performance for forecasting and structural analysis.

Suggested Citation

  • Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2020. "Capturing Macroeconomic Tail Risks with Bayesian Vector Autoregressions," Working Papers 20-02R, Federal Reserve Bank of Cleveland, revised 22 Sep 2020.
    • Handle: RePEc:fip:fedcwq:87375
    DOI: 10.26509/frbc-wp-202002r
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    Cited by:

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    2. Andrea Carriero & Todd E. Clark & Marcellino Massimiliano, 2020. "Nowcasting Tail Risks to Economic Activity with Many Indicators," Working Papers 20-13R2, Federal Reserve Bank of Cleveland, revised 22 Sep 2020.
    3. Hilde C. Bjørnland & Roberto Casarin & Marco Lorusso & Francesco Ravazzolo, 2023. "Fiscal Policy Regimes in Resource-Rich Economies," Working Papers No 13/2023, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    4. Gefang, Deborah & Koop, Gary & Poon, Aubrey, 2023. "Forecasting using variational Bayesian inference in large vector autoregressions with hierarchical shrinkage," International Journal of Forecasting, Elsevier, vol. 39(1), pages 346-363.
    5. Falconio, Andrea & Manganelli, Simone, 2020. "Financial conditions, business cycle fluctuations and growth at risk," Working Paper Series 2470, European Central Bank.
    6. Tamás Kiss & Stepan Mazur & Hoang Nguyen & Pär Österholm, 2023. "Modeling the relation between the US real economy and the corporate bond‐yield spread in Bayesian VARs with non‐Gaussian innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 347-368, March.
    7. Iseringhausen, Martin, 2024. "A time-varying skewness model for Growth-at-Risk," International Journal of Forecasting, Elsevier, vol. 40(1), pages 229-246.
    8. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Nowcasting tail risk to economic activity at a weekly frequency," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 843-866, August.
    9. Martin Gachter & Elias Hasler & Florian Huber, 2023. "A tale of two tails: 130 years of growth-at-risk," Papers 2302.08920, arXiv.org.
    10. Pfarrhofer, Michael, 2022. "Modeling tail risks of inflation using unobserved component quantile regressions," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    11. Adams, Patrick A. & Adrian, Tobias & Boyarchenko, Nina & Giannone, Domenico, 2021. "Forecasting macroeconomic risks," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1173-1191.
    12. Garratt, Anthony & Henckel, Timo & Vahey, Shaun P., 2023. "Empirically-transformed linear opinion pools," International Journal of Forecasting, Elsevier, vol. 39(2), pages 736-753.
    13. Schick, Manuel, 2024. "Real-time Nowcasting Growth-at-Risk using the Survey of Professional Forecasters," Working Papers 0750, University of Heidelberg, Department of Economics.
    14. Kevin Moran & Dalibor Stevanovic & Stephane Surprenant, 2024. "Risk Scenarios and Macroeconomic Forecasts," Working Papers 24-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management, revised Apr 2024.
    15. Kiss, Tamás & Nguyen, Hoang & Österholm, Pär, 2022. "The Relation between the High-Yield Bond Spread and the Unemployment Rate in the Euro Area," Finance Research Letters, Elsevier, vol. 46(PA).
    16. Deng, Chuang & Wu, Jian, 2023. "Macroeconomic downside risk and the effect of monetary policy," Finance Research Letters, Elsevier, vol. 54(C).
    17. Karlsson, Sune & Mazur, Stepan & Nguyen, Hoang, 2023. "Vector autoregression models with skewness and heavy tails," Journal of Economic Dynamics and Control, Elsevier, vol. 146(C).
    18. Mihail Yanchev, 2022. "Deep Growth-at-Risk Model: Nowcasting the 2020 Pandemic Lockdown Recession in Small Open Economies," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 7, pages 20-41.
    19. Leopoldo Catania & Alessandra Luati & Pierluigi Vallarino, 2021. "Economic vulnerability is state dependent," CREATES Research Papers 2021-09, Department of Economics and Business Economics, Aarhus University.
    20. Huang, Yu-Fan & Liao, Wenting & Luo, Sui & Ma, Jun, 2024. "Financial conditions, macroeconomic uncertainty, and macroeconomic tail risks," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).

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    More about this item

    Keywords

    downside risk; forecasting; asymmetries;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications
    • F47 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Forecasting and Simulation: Models and Applications

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