[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v230y2022i1p154-182.html
   My bibliography  Save this article

Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models

Author

Listed:
  • Petrova, Katerina
Abstract
Inaccurately imposing Gaussian distributional assumptions in standard multivariate time series models does not affect inference on the autoregressive coefficients but distorts both classical and Bayesian inference on the volatility matrix whenever the true error distribution has excess kurtosis relative to the multivariate normal density. Inference on the intercept is also affected whenever the innovations are generated from a non-symmetric distribution. As a result of distributional misspecification, Bayesian methods lead to asymptotically invalid posterior inference for the intercept and the volatility matrix and, consequently, invalid posterior credible sets for quantities such as impulse responses, variance decompositions and density forecasts. We propose a robust and computationally fast Bayesian procedure which delivers asymptotically correct posterior credible sets without the need for distributional assumptions. The proposed corrected Bayesian posteriors for the volatility matrix and the intercept vector are based on the asymptotic covariance of the QML estimators and admit a closed form. Implementation of the procedure requires consistent estimation of the multivariate skewness and kurtosis of the innovations, and we propose novel shrinkage estimators designed to shrink these large dimensional objects towards the skewness and kurtosis of a Gaussian vector. We extend our robust Bayesian analysis to accommodate non-Gaussian disturbances in the presence of parameter instability, by combining the estimators of the current paper with semi-parametric kernel-type methods. We demonstrate that our estimators deliver correct posterior coverage rates in an extensive Monte Carlo exercise under a variety of distributional specifications. Finally, we present empirical evidence that imposing Gaussianity or homoskedasticity assumptions on financial and uncertainty shocks is not justified and may lead to misleading empirical conclusions.

Suggested Citation

  • Petrova, Katerina, 2022. "Asymptotically valid Bayesian inference in the presence of distributional misspecification in VAR models," Journal of Econometrics, Elsevier, vol. 230(1), pages 154-182.
    • Handle: RePEc:eee:econom:v:230:y:2022:i:1:p:154-182
    DOI: 10.1016/j.jeconom.2020.12.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407621000865
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2020.12.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    2. Gary M. Koop, 2013. "Forecasting with Medium and Large Bayesian VARS," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(2), pages 177-203, March.
    3. 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.
    4. Gouriéroux, Christian & Monfort, Alain & Renne, Jean-Paul, 2017. "Statistical inference for independent component analysis: Application to structural VAR models," Journal of Econometrics, Elsevier, vol. 196(1), pages 111-126.
    5. James Berger & Elías Moreno & Luis Pericchi & M. Bayarri & José Bernardo & Juan Cano & Julián Horra & Jacinto Martín & David Ríos-Insúa & Bruno Betrò & A. Dasgupta & Paul Gustafson & Larry Wasserman &, 1994. "An overview of robust Bayesian analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 3(1), pages 5-124, June.
    6. Siddhartha Chib & Minchul Shin & Anna Simoni, 2018. "Bayesian Estimation and Comparison of Moment Condition Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1656-1668, October.
    7. Caldara, Dario & Fuentes-Albero, Cristina & Gilchrist, Simon & Zakrajšek, Egon, 2016. "The macroeconomic impact of financial and uncertainty shocks," European Economic Review, Elsevier, vol. 88(C), pages 185-207.
    8. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    9. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    10. Robinson, P M, 1988. "Using Gaussian Estimators Robustly," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(1), pages 97-106, February.
    11. Chernozhukov, Victor & Hong, Han, 2003. "An MCMC approach to classical estimation," Journal of Econometrics, Elsevier, vol. 115(2), pages 293-346, August.
    12. Christopher A. Sims & Tao Zha, 2006. "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, American Economic Association, vol. 96(1), pages 54-81, March.
    13. Timothy Cogley & Giorgio E. Primiceri & Thomas J. Sargent, 2010. "Inflation-Gap Persistence in the US," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 43-69, January.
    14. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    15. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    16. Jon Faust, 1998. "The robustness of identified VAR conclusions about money," International Finance Discussion Papers 610, Board of Governors of the Federal Reserve System (U.S.).
    17. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    18. repec:ulb:ulbeco:2013/13388 is not listed on IDEAS
    19. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Large Vector Autoregressions with Stochastic Volatility and Flexible Priors," Working Papers (Old Series) 1617, Federal Reserve Bank of Cleveland.
    20. Marta Banbura & Domenico Giannone & Lucrezia Reichlin, 2010. "Large Bayesian vector auto regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(1), pages 71-92.
    21. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    22. Alessio Moneta & Doris Entner & Patrik O. Hoyer & Alex Coad, 2013. "Causal Inference by Independent Component Analysis: Theory and Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(5), pages 705-730, October.
    23. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    24. Phillips, P C B, 1991. "To Criticize the Critics: An Objective Bayesian Analysis of Stochastic Trends," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(4), pages 333-364, Oct.-Dec..
    25. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    26. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Applications to Poisson Models," Econometrica, Econometric Society, vol. 52(3), pages 701-720, May.
    27. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    28. Christopher A. Sims, 1991. "Comment on 'To Criticize the Critics,' by Peter C. B. Phillips," Cowles Foundation Discussion Papers 985, Cowles Foundation for Research in Economics, Yale University.
    29. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, September.
    30. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    31. Giraitis, L. & Kapetanios, G. & Yates, T., 2014. "Inference on stochastic time-varying coefficient models," Journal of Econometrics, Elsevier, vol. 179(1), pages 46-65.
    32. Kalli, Maria & Griffin, Jim E., 2018. "Bayesian nonparametric vector autoregressive models," Journal of Econometrics, Elsevier, vol. 203(2), pages 267-282.
    33. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    34. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, September.
    35. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    36. Petrova, Katerina, 2019. "A quasi-Bayesian local likelihood approach to time varying parameter VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 286-306.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    2. Philippe Andrade & Filippo Ferroni & Leonardo Melosi, 2023. "Identification Using Higher-Order Moments Restrictions," Working Paper Series WP 2023-28, Federal Reserve Bank of Chicago.
    3. Valeria Gargiulo & Christian Matthes & Katerina Petrova, 2024. "Monetary Policy across Inflation Regimes," Staff Reports 1083, Federal Reserve Bank of New York.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Herwartz, Helmut & Rohloff, Hannes & Wang, Shu, 2022. "Proxy SVAR identification of monetary policy shocks - Monte Carlo evidence and insights for the US," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    2. Dominik Bertsche & Robin Braun, 2022. "Identification of Structural Vector Autoregressions by Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 328-341, January.
    3. Petrova, Katerina, 2019. "A quasi-Bayesian local likelihood approach to time varying parameter VAR models," Journal of Econometrics, Elsevier, vol. 212(1), pages 286-306.
    4. Magnus Reif, 2020. "Macroeconomics, Nonlinearities, and the Business Cycle," ifo Beiträge zur Wirtschaftsforschung, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, number 87.
    5. Herwartz, Helmut & Rohloff, Hannes & Wang, Shu, 2020. "Proxy SVAR identification of monetary policy shocks: MonteCarlo evidence and insights for the US," University of Göttingen Working Papers in Economics 404, University of Goettingen, Department of Economics.
    6. Cordoni, Francesco & Dorémus, Nicolas & Moneta, Alessio, 2024. "Identification of vector autoregressive models with nonlinear contemporaneous structure," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    7. 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).
    8. Lanne, Markku & Lütkepohl, Helmut & Maciejowska, Katarzyna, 2010. "Structural vector autoregressions with Markov switching," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 121-131, February.
    9. Maxand, Simone, 2020. "Identification of independent structural shocks in the presence of multiple Gaussian components," Econometrics and Statistics, Elsevier, vol. 16(C), pages 55-68.
    10. Herwartz, Helmut & Lange, Alexander & Maxand, Simone, 2019. "Statistical identification in SVARs - Monte Carlo experiments and a comparative assessment of the role of economic uncertainties for the US business cycle," University of Göttingen Working Papers in Economics 375, University of Goettingen, Department of Economics.
    11. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    12. Marek Rusnak & Tomas Havranek & Roman Horvath, 2013. "How to Solve the Price Puzzle? A Meta‐Analysis," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(1), pages 37-70, February.
    13. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    14. Lutz Kilian, 2013. "Structural vector autoregressions," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 22, pages 515-554, Edward Elgar Publishing.
    15. Belongia, Michael T. & Ireland, Peter N., 2016. "The evolution of U.S. monetary policy: 2000–2007," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 78-93.
    16. Laura Liu & Christian Matthes & Katerina Petrova, 2022. "Monetary Policy Across Space and Time," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 37-64, Emerald Group Publishing Limited.
    17. Helmut Herwartz & Alexander Lange & Simone Maxand, 2022. "Data‐driven identification in SVARs—When and how can statistical characteristics be used to unravel causal relationships?," Economic Inquiry, Western Economic Association International, vol. 60(2), pages 668-693, April.
    18. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    19. Helmut Herwartz, 2022. "Modelling interaction patterns in a predator-prey system of two freshwater organisms in discrete time: an identified structural VAR approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 63-85, March.
    20. Hauzenberger, Niko, 2021. "Flexible Mixture Priors for Large Time-varying Parameter Models," Econometrics and Statistics, Elsevier, vol. 20(C), pages 87-108.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:230:y:2022:i:1:p:154-182. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.