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Joint Bayesian inference about impulse responses in VAR models

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  • Inoue, Atsushi
  • Kilian, Lutz

Abstract

We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.

Suggested Citation

  • Inoue, Atsushi & Kilian, Lutz, 2020. "Joint Bayesian inference about impulse responses in VAR models," CFS Working Paper Series 650, Center for Financial Studies (CFS).
    • Handle: RePEc:zbw:cfswop:650
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    Cited by:

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    6. Kilian, Lutz & Zhou, Xiaoqing, 2023. "Oil Price Shocks and Inflation," CEPR Discussion Papers 18416, C.E.P.R. Discussion Papers.
    7. Szafranek, Karol & Szafrański, Grzegorz & Leszczyńska-Paczesna, Agnieszka, 2024. "Inflation returns. Revisiting the role of external and domestic shocks with Bayesian structural VAR," International Review of Economics & Finance, Elsevier, vol. 93(PA), pages 789-810.
    8. Kilian, Lutz & Zhou, Xiaoqing, 2023. "A broader perspective on the inflationary effects of energy price shocks," Energy Economics, Elsevier, vol. 125(C).
    9. Güntner, Jochen & Reif, Magnus & Wolters, Maik H., 2024. "Sudden stop: Supply and demand shocks in the German natural gas market," Discussion Papers 22/2024, Deutsche Bundesbank.
    10. Kilian, Lutz & Zhou, Xiaoqing, 2022. "Oil prices, exchange rates and interest rates," Journal of International Money and Finance, Elsevier, vol. 126(C).
    11. Kilian, Lutz & Zhou, Xiaoqing, 2022. "The impact of rising oil prices on U.S. inflation and inflation expectations in 2020–23," Energy Economics, Elsevier, vol. 113(C).
    12. Gao, Jiti & Peng, Bin & Wu, Wei Biao & Yan, Yayi, 2024. "Time-varying multivariate causal processes," Journal of Econometrics, Elsevier, vol. 240(1).
    13. Diegel, Max & Nautz, Dieter, 2021. "Long-term inflation expectations and the transmission of monetary policy shocks: Evidence from a SVAR analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 130(C).
    14. Kilian, Lutz, 2023. "How to Construct Monthly VAR Proxies Based on Daily Futures Market Surprises," CEPR Discussion Papers 18348, C.E.P.R. Discussion Papers.
    15. Lukas Berend & Jan Pruser, 2024. "The Transmission of Monetary Policy via Common Cycles in the Euro Area," Papers 2410.05741, arXiv.org, revised Oct 2024.
    16. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Identification and Inference Under Narrative Restrictions," Papers 2102.06456, arXiv.org.
    17. Mohamad B. Karaki & Andrios Neaimeh, 2024. "Do higher global oil and wheat prices matter for the wheat flour price in Lebanon?," Agricultural Economics, International Association of Agricultural Economists, vol. 55(4), pages 559-571, July.
    18. Benk, Szilard & Gillman, Max, 2023. "Identifying money and inflation expectation shocks to real oil prices," Energy Economics, Elsevier, vol. 126(C).
    19. Ding, Shusheng & Wang, Anqi & Cui, Tianxiang & Du, Anna Min & Zhou, Xinmiao, 2024. "Commodity market stability and sustainable development: The effect of public health policies," Research in International Business and Finance, Elsevier, vol. 70(PB).
    20. Paul Carrillo‐Maldonado, 2023. "Partial identification for growth regimes: The case of Latin American countries," Metroeconomica, Wiley Blackwell, vol. 74(3), pages 557-583, July.
    21. Diab, Sara & Karaki, Mohamad B., 2023. "Do increases in gasoline prices cause higher food prices?," Energy Economics, Elsevier, vol. 127(PB).
    22. Finck, David & Tillmann, Peter, 2023. "The macroeconomic effects of global supply chain disruptions," IMFS Working Paper Series 178, Goethe University Frankfurt, Institute for Monetary and Financial Stability (IMFS).
    23. Bruns, Martin, 2021. "Proxy Vector Autoregressions in a Data-rich Environment," Journal of Economic Dynamics and Control, Elsevier, vol. 123(C).

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    More about this item

    Keywords

    Loss function; joint inference; median response function; mean response function; modal model; posterior risk;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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