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Impulse Response Diagnostics for Priors on Parameters in Structural Vector Autoregressions

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  • Lutz Kilian

Abstract

Structural impulse response functions may be estimated based on priors about the parameters of the structural VAR presentation. Even when such priors appear seemingly reasonable, they may imply an unintentionally informative prior for the structural impulse responses. Rather than pretending that the posterior of the impulse responses does not depend on this prior, the proposal in this paper is to verify that the prior distribution of the vector of impulse responses of interest is not unintentionally informative. Moreover, if the impulse response prior is intentionally informative, this point must be conveyed, so the reader can properly evaluate the reported conclusions. This paper discusses easy-to-use diagnostic tools that help practitioners address these concerns.

Suggested Citation

  • Lutz Kilian, 2025. "Impulse Response Diagnostics for Priors on Parameters in Structural Vector Autoregressions," Working Papers 2507, Federal Reserve Bank of Dallas.
    • Handle: RePEc:fip:feddwp:99620
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    References listed on IDEAS

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    1. Kilian, Lutz, 2022. "Facts and fiction in oil market modeling," Energy Economics, Elsevier, vol. 110(C).
    2. James D. Hamilton, 2009. "Causes and Consequences of the Oil Shock of 2007-08," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 40(1 (Spring), pages 215-283.
    3. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    4. Casoli, Chiara & Manera, Matteo & Valenti, Daniele, 2024. "Energy shocks in the Euro area: Disentangling the pass-through from oil and gas prices to inflation," Journal of International Money and Finance, Elsevier, vol. 147(C).
    5. Christiane Baumeister & James D. Hamilton, 2019. "Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks," American Economic Review, American Economic Association, vol. 109(5), pages 1873-1910, May.
    6. Christiane Baumeister & James D. Hamilton, 2015. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, Econometric Society, vol. 83(5), pages 1963-1999, September.
    7. Robert B. Barsky & Lutz Kilian, 2002. "Do We Really Know That Oil Caused the Great Stagflation? A Monetary Alternative," NBER Chapters, in: NBER Macroeconomics Annual 2001, Volume 16, pages 137-198, National Bureau of Economic Research, Inc.
    8. Ana María Herrera & Sandeep Kumar Rangaraju, 2020. "The effect of oil supply shocks on US economic activity: What have we learned?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(2), pages 141-159, March.
    9. Robin Braun, 2023. "The importance of supply and demand for oil prices: Evidence from non‐Gaussianity," Quantitative Economics, Econometric Society, vol. 14(4), pages 1163-1198, November.
    10. Lutz Kilian & Daniel P. Murphy, 2012. "Why Agnostic Sign Restrictions Are Not Enough: Understanding The Dynamics Of Oil Market Var Models," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 1166-1188, October.
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    More about this item

    Keywords

    VAR; prior; posterior; impulse response; inference;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • 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
    • Q43 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy and the Macroeconomy

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