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The Role of the Prior in Estimating VAR Models with Sign Restrictions
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The Role of the Prior in Estimating VAR Models with Sign Restrictions

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  • Kilian, Lutz
  • Inoue, Atsushi

Abstract

Several recent studies have expressed concern that the Haar prior typically imposed in estimating sign-identified VAR models may be unintentionally informative about the implied prior for the structural impulse responses. This question is indeed important, but we show that the tools that have been used in the literature to illustrate this potential problem are invalid. Specifically, we show that it does not make sense from a Bayesian point of view to characterize the impulse response prior based on the distribution of the impulse responses conditional on the maximum likelihood estimator of the reduced-form parameters, since the the prior does not, in general, depend on the data. We illustrate that this approach tends to produce highly misleading estimates of the impulse response priors. We formally derive the correct impulse response prior distribution and show that there is no evidence that typical sign-identified VAR models estimated using conventional priors tend to imply unintentionally informative priors for the impulse response vector or that the corresponding posterior is dominated by the prior. Our evidence suggests that concerns about the Haar prior for the rotation matrix have been greatly overstated and that alternative estimation methods are not required in typical applications. Finally, we demonstrate that the alternative Bayesian approach to estimating sign-identified VAR models proposed by Baumeister and Hamilton (2015) suffers from exactly the same conceptual shortcoming as the conventional approach. We illustrate that this alternative approach may imply highly economically implausible impulse response priors.

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  • Kilian, Lutz & Inoue, Atsushi, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," CEPR Discussion Papers 15545, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:15545
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    Cited by:

    1. Kilian, Lutz, 2022. "Facts and fiction in oil market modeling," Energy Economics, Elsevier, vol. 110(C).
    2. Bruna, Karel & Van Tran, Quang, 2023. "Asymmetric effects of oil price shocks on EUR/USD exchange rate and structural shock decomposition in a BVAR model with sign restriction," Energy Economics, Elsevier, vol. 128(C).
    3. Khalil, Makram & Weber, Marc-Daniel, 2021. "Chinese supply chain shocks," MPRA Paper 110356, University Library of Munich, Germany.
    4. Luca Baldo & Elisa Bonifacio & Marco Brandi & Michelina Lo Russo & Gianluca Maddaloni & Andrea Nobili & Giorgia Rocco & Gabriele Sene & Massimo Valentini, 2021. "Inside the black box: tools for understanding cash circulation," Mercati, infrastrutture, sistemi di pagamento (Markets, Infrastructures, Payment Systems) 7, Bank of Italy, Directorate General for Markets and Payment System.
    5. Breitenlechner, Max & Georgiadis, Georgios & Schumann, Ben, 2022. "What goes around comes around: How large are spillbacks from US monetary policy?," Journal of Monetary Economics, Elsevier, vol. 131(C), pages 45-60.
    6. Drago Bergholt & Francesco Furlanetto & Etienne Vaccaro-Grange, 2023. "Did monetary policy kill the Phillips Curve? Some simple arithmetics," Working Paper 2023/2, Norges Bank.
    7. Katarzyna Budnik & Gerhard Rünstler, 2023. "Identifying structural VARs from sparse narrative instruments: Dynamic effects of US macroprudential policies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(2), pages 186-201, March.
    8. Kilian, Lutz, 2022. "Understanding the estimation of oil demand and oil supply elasticities," Energy Economics, Elsevier, vol. 107(C).
    9. Carrillo-Maldonado, Paul & Díaz-Cassou, Javier, 2023. "An anatomy of external shocks in the Andean region," The Journal of Economic Asymmetries, Elsevier, vol. 27(C).
    10. 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.
    11. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    12. Andres–Escayola, Erik & Berganza, Juan Carlos & Campos, Rodolfo G. & Molina, Luis, 2023. "A BVAR toolkit to assess macrofinancial risks in Brazil and Mexico," Latin American Journal of Central Banking (previously Monetaria), Elsevier, vol. 4(1).
    13. Lukas Boer & Mr. Andrea Pescatori & Martin Stuermer, 2021. "Energy Transition Metals," IMF Working Papers 2021/243, International Monetary Fund.
    14. Martin Stuermer, 2022. "Non-renewable resource extraction over the long term: empirical evidence from global copper production," Mineral Economics, Springer;Raw Materials Group (RMG);Luleå University of Technology, vol. 35(3), pages 617-625, December.
    15. 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.
    16. Ronicle, David, 2022. "Turning in the widening gyre: monetary and fiscal policy in interwar Britain," Bank of England working papers 968, Bank of England.
    17. 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).
    18. Herwartz, Helmut & Wang, Shu, 2023. "Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).

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    More about this item

    Keywords

    Prior; Posterior; Impulse response; Loss function; Joint inference; Absolute loss;
    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
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • Q43 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Energy - - - Energy and the Macroeconomy

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