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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 discuss the construction of 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 illustrate 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, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    • Handle: RePEc:eee:econom:v:231:y:2022:i:2:p:457-476
    DOI: 10.1016/j.jeconom.2021.05.010
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    1. Martin Eichenbaum & Charles L. Evans, 1995. "Some Empirical Evidence on the Effects of Shocks to Monetary Policy on Exchange Rates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(4), pages 975-1009.
    2. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    3. Baumeister, Christiane & Hamilton, James D., 2018. "Inference in structural vector autoregressions when the identifying assumptions are not fully believed: Re-evaluating the role of monetary policy in economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 100(C), pages 48-65.
    4. Kilian, Lutz & Zhou, Xiaoqing, 2022. "Oil prices, exchange rates and interest rates," Journal of International Money and Finance, Elsevier, vol. 126(C).
    5. Renée Fry & Adrian Pagan, 2011. "Sign Restrictions in Structural Vector Autoregressions: A Critical Review," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 938-960, December.
    6. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 665-696.
    7. 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.
    8. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    9. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    10. Haroon Mumtaz & Paolo Surico, 2009. "The Transmission of International Shocks: A Factor-Augmented VAR Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(s1), pages 71-100, February.
    11. Stefan Bruder & Michael Wolf, 2018. "Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 641-664, September.
    12. Lutz Kilian & Xiaoqing Zhou, 2020. "Does drawing down the US Strategic Petroleum Reserve help stabilize oil prices?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(6), pages 673-691, September.
    13. Juan Antolín-Díaz & Juan F. Rubio-Ramírez, 2018. "Narrative Sign Restrictions for SVARs," American Economic Review, American Economic Association, vol. 108(10), pages 2802-2829, October.
    14. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    15. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    16. Koop, Gary, 1996. "Parameter uncertainty and impulse response analysis," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 135-149.
    17. Andrew Mountford & Harald Uhlig, 2009. "What are the effects of fiscal policy shocks?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(6), pages 960-992.
    18. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2018. "Calculating joint confidence bands for impulse response functions using highest density regions," Empirical Economics, Springer, vol. 55(4), pages 1389-1411, December.
    19. Blanchard, Olivier Jean, 1989. "A Traditional Interpretation of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 79(5), pages 1146-1164, December.
    20. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    21. repec:zbw:bofrdp:2018_014 is not listed on IDEAS
    22. Atsushi Inoue & Lutz Kilian, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," Working Papers 2030, Federal Reserve Bank of Dallas.
    23. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    24. Cushman, David O. & Zha, Tao, 1997. "Identifying monetary policy in a small open economy under flexible exchange rates," Journal of Monetary Economics, Elsevier, vol. 39(3), pages 433-448, August.
    25. 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.
    26. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2015. "Confidence Bands for Impulse Responses: Bonferroni vs. Wald," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 800-821, December.
    27. Knut Are Aastveit & Hilde C. Bjørnland & Leif Anders Thorsrud, 2015. "What Drives Oil Prices? Emerging Versus Developed Economies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(7), pages 1013-1028, November.
    28. Jonas E. Arias & Juan F. Rubio‐Ramírez & Daniel F. Waggoner, 2018. "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications," Econometrica, Econometric Society, vol. 86(2), pages 685-720, March.
    29. Waggoner, Daniel F. & Zha, Tao, 2012. "Confronting model misspecification in macroeconomics," Journal of Econometrics, Elsevier, vol. 171(2), pages 167-184.
    30. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    31. Xiaoqing Zhou, 2020. "Refining the workhorse oil market model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 130-140, January.
    32. Jamie L. Cross & Bao H. Nguyen & Trung Duc Tran, 2022. "The role of precautionary and speculative demand in the global market for crude oil," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 882-895, August.
    33. Knut Are Aastveit & Hilde C. Bjørnland & Leif Anders Thorsrud, 2015. "What Drives Oil Prices? Emerging Versus Developed Economies," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(7), pages 1013-1028, November.
    34. Rausser, Gordon & Stuermer, Martin, 2020. "A Dynamic Analysis of Collusive Action: The Case of the World Copper Market, 1882-2016," MPRA Paper 104708, University Library of Munich, Germany.
    35. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, October.
    36. Baumeister, Christiane & Hamilton, James, 2018. "Inference in Structural Vector Autoregressions When the Identifying Assumptions are Not Fully Believed: Re-evaluating the Role," CEPR Discussion Papers 12911, C.E.P.R. Discussion Papers.
    37. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2020. "Constructing joint confidence bands for impulse response functions of VAR models – A review," Econometrics and Statistics, Elsevier, vol. 13(C), pages 69-83.
    38. Herwartz, Helmut & Plödt, Martin, 2016. "The macroeconomic effects of oil price shocks: Evidence from a statistical identification approach," Journal of International Money and Finance, Elsevier, vol. 61(C), pages 30-44.
    39. Lutz Kilian & Daniel P. Murphy, 2014. "The Role Of Inventories And Speculative Trading In The Global Market For Crude Oil," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(3), pages 454-478, April.
    40. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2019. "Simultaneous confidence bands: Theory, implementation, and an application to SVARs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 1-17, January.
    41. Zha, Tao, 1999. "Block recursion and structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 90(2), pages 291-316, June.
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    Cited by:

    1. Finck, David & Tillmann, Peter, 2022. "The macroeconomic effects of global supply chain disruptions," BOFIT Discussion Papers 14/2022, Bank of Finland Institute for Emerging Economies (BOFIT).
    2. Atsushi Inoue & Lutz Kilian, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," Working Papers 2030, Federal Reserve Bank of Dallas.
    3. Berger, Tino & Richter, Julia & Wong, Benjamin, 2022. "A unified approach for jointly estimating the business and financial cycle, and the role of financial factors," Journal of Economic Dynamics and Control, Elsevier, vol. 136(C).
    4. Lutz Kilian & Nikos Nomikos & Xiaoqing Zhou, 2023. "A Quantitative Model of the Oil Tanker Market in the Arabian Gulf," The Energy Journal, , vol. 44(5), pages 95-114, September.
    5. Reichlin, Lucrezia & Ricco, Giovanni & Tarbé, Matthieu, 2023. "Monetary–fiscal crosswinds in the European Monetary Union," European Economic Review, Elsevier, vol. 151(C).
    6. Kilian, Lutz & Zhou, Xiaoqing, 2023. "Oil Price Shocks and Inflation," CEPR Discussion Papers 18416, C.E.P.R. Discussion Papers.
    7. Kilian, Lutz & Zhou, Xiaoqing, 2023. "A broader perspective on the inflationary effects of energy price shocks," Energy Economics, Elsevier, vol. 125(C).
    8. 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.
    9. Kilian, Lutz & Zhou, Xiaoqing, 2022. "Oil prices, exchange rates and interest rates," Journal of International Money and Finance, Elsevier, vol. 126(C).
    10. 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).
    11. Gao, Jiti & Peng, Bin & Wu, Wei Biao & Yan, Yayi, 2024. "Time-varying multivariate causal processes," Journal of Econometrics, Elsevier, vol. 240(1).
    12. 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).
    13. 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.
    14. 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.
    15. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Identification and Inference Under Narrative Restrictions," Papers 2102.06456, arXiv.org.
    16. 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.
    17. Benk, Szilard & Gillman, Max, 2023. "Identifying money and inflation expectation shocks to real oil prices," Energy Economics, Elsevier, vol. 126(C).
    18. 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.
    19. Diab, Sara & Karaki, Mohamad B., 2023. "Do increases in gasoline prices cause higher food prices?," Energy Economics, Elsevier, vol. 127(PB).
    20. 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).
    21. 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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