IDEAS home Printed from https://ideas.repec.org/p/diw/diwwpp/dp1707.html
   My bibliography  Save this paper

Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity

Author

Listed:
  • Helmut Lütkepohl
  • Tomasz Woźniak

Abstract

In order to identify structural shocks that affect economic variables, restrictions need to be imposed on the parameters of structural vector autoregressive (SVAR) models. Economic theory is the primary source of such restrictions. However, only over-identifying restrictions can be tested with statistical methods which limits the statistical validation of many just-identified SVAR models. In this study, Bayesian inference is developed for SVAR models in which the structural parameters are identified via Markov-switching heteroskedasticity. In such a model, restrictions that are just-identifying in the homoskedastic case, become over-identifying and can be tested. A set of parametric restrictions is derived under which the structural matrix is globally identified and a Savage-Dickey density ratio is used to assess the validity of the identification conditions. For that purpose, a new probability distribution is defined that generalizes the beta, F, and compound gamma distributions. As an empirical example, monetary models are compared using heteroskedasticity as an additional device for identification. The empirical results support models with money in the interest rate reaction function.

Suggested Citation

  • Helmut Lütkepohl & Tomasz Woźniak, 2017. "Bayesian Inference for Structural Vector Autoregressions Identified by Markov-Switching Heteroskedasticity," Discussion Papers of DIW Berlin 1707, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp1707
    as

    Download full text from publisher

    File URL: https://www.diw.de/documents/publikationen/73/diw_01.c.573492.de/dp1707.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Leeper, Eric M. & Zha, Tao, 2003. "Modest policy interventions," Journal of Monetary Economics, Elsevier, vol. 50(8), pages 1673-1700, November.
    2. Matthieu Droumaguet & Anders Warne & Tomasz Woźniak, 2017. "Granger Causality and Regime Inference in Markov Switching VAR Models with Bayesian Methods," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(4), pages 802-818, June.
    3. Helmut Lütkepohl & Mika Meitz & Aleksei Netšunajev & Pentti Saikkonen, 2021. "Testing identification via heteroskedasticity in structural vector autoregressive models," The Econometrics Journal, Royal Economic Society, vol. 24(1), pages 1-22.
    4. Michael T. Belongia & Peter N. Ireland, 2015. "Interest Rates and Money in the Measurement of Monetary Policy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 255-269, April.
    5. Velinov, Anton & Chen, Wenjuan, 2015. "Do stock prices reflect their fundamentals? New evidence in the aftermath of the financial crisis," Journal of Economics and Business, Elsevier, vol. 80(C), pages 1-20.
    6. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with heteroskedasticity: A review of different volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 2-18.
    7. Lanne, Markku & Lütkepohl, Helmut, 2010. "Structural Vector Autoregressions With Nonnormal Residuals," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 159-168.
    8. Dungey, Mardi & Milunovich, George & Thorp, Susan & Yang, Minxian, 2015. "Endogenous crisis dating and contagion using smooth transition structural GARCH," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 71-79.
    9. Helmut Lütkepohl & Anton Velinov, 2016. "Structural Vector Autoregressions: Checking Identifying Long-Run Restrictions Via Heteroskedasticity," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 377-392, April.
    10. Bernanke, Ben S & Blinder, Alan S, 1992. "The Federal Funds Rate and the Channels of Monetary Transmission," American Economic Review, American Economic Association, vol. 82(4), pages 901-921, September.
    11. Bacchiocchi, Emanuele & Castelnuovo, Efrem & Fanelli, Luca, 2018. "Gimme A Break! Identification And Estimation Of The Macroeconomic Effects Of Monetary Policy Shocks In The United States," Macroeconomic Dynamics, Cambridge University Press, vol. 22(6), pages 1613-1651, September.
    12. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    13. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2015. "Prior Selection for Vector Autoregressions," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 436-451, May.
    14. Eric M. Leeper & Jennifer E. Roush, 2003. "Putting \"M\" back in monetary policy," International Finance Discussion Papers 761, Board of Governors of the Federal Reserve System (U.S.).
    15. Herwartz, Helmut & Lütkepohl, Helmut, 2014. "Structural vector autoregressions with Markov switching: Combining conventional with statistical identification of shocks," Journal of Econometrics, Elsevier, vol. 183(1), pages 104-116.
    16. Sims, Christopher A., 1992. "Interpreting the macroeconomic time series facts : The effects of monetary policy," European Economic Review, Elsevier, vol. 36(5), pages 975-1000, June.
    17. J. B. Taylor & Harald Uhlig (ed.), 2016. "Handbook of Macroeconomics," Handbook of Macroeconomics, Elsevier, edition 1, volume 2, number 2.
    18. 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.
    19. Netsunajev, Aleksei, 2013. "Reaction to technology shocks in Markov-switching structural VARs: Identification via heteroskedasticity," Journal of Macroeconomics, Elsevier, vol. 36(C), pages 51-62.
    20. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
    21. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    22. 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.
    23. Satya Dubey, 1970. "Compound gamma, beta and F distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 16(1), pages 27-31, December.
    24. Christopher A. Sims, 1986. "Are forecasting models usable for policy analysis?," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 10(Win), pages 2-16.
    25. Fabio Canova & Fernando J. Pérez Forero, 2015. "Estimating overidentified, nonrecursive, time‐varying coefficients structural vector autoregressions," Quantitative Economics, Econometric Society, vol. 6(2), pages 359-384, July.
    26. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    27. Perrakis, Konstantinos & Ntzoufras, Ioannis & Tsionas, Efthymios G., 2014. "On the use of marginal posteriors in marginal likelihood estimation via importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 54-69.
    28. Barnett, William A., 2012. "Getting it Wrong: How Faulty Monetary Statistics Undermine the Fed, the Financial System, and the Economy," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262516888, April.
    29. Thomas Doan & Robert B. Litterman & Christopher A. Sims, 1983. "Forecasting and Conditional Projection Using Realistic Prior Distributions," NBER Working Papers 1202, National Bureau of Economic Research, Inc.
    30. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
    31. 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.
    32. Markku Lanne & Jani Luoto, 2016. "Data-Driven Inference on Sign Restrictions in Bayesian Structural Vector Autoregression," CREATES Research Papers 2016-04, Department of Economics and Business Economics, Aarhus University.
    33. Dmitry Kulikov & Aleksei Netsunajev, 2013. "Identifying monetary policy shocks via heteroskedasticity: a Bayesian approach," Bank of Estonia Working Papers wp2013-9, Bank of Estonia, revised 09 Dec 2013.
    34. Eric M. Leeper & Jennifer E. Roush, 2003. "Putting \\"M\\" back in monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 1217-1264.
    35. Emanuele Bacchiocchi & Luca Fanelli, 2015. "Identification in Structural Vector Autoregressive Models with Structural Changes, with an Application to US Monetary Policy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 761-779, December.
    36. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575.
    37. Helmut Lütkepohl & Aleksei NetŠunajev, 2014. "Disentangling Demand And Supply Shocks In The Crude Oil Market: How To Check Sign Restrictions In Structural Vars," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(3), pages 479-496, April.
    38. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    39. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    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. Thiago Drummond de Mendonça Giudici & Elcyon Caiado Rocha Lima, 2024. "The business cycle in Brazil: identification via heteroskedasticity," International Economics and Economic Policy, Springer, vol. 21(3), pages 649-684, July.
    2. Karin Klieber, 2023. "Non-linear dimension reduction in factor-augmented vector autoregressions," Papers 2309.04821, arXiv.org.
    3. Alfan Mansur, 2023. "Simultaneous identification of fiscal and monetary policy shocks," Empirical Economics, Springer, vol. 65(2), pages 697-728, August.
    4. Klieber, Karin, 2024. "Non-linear dimension reduction in factor-augmented vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 159(C).
    5. Jetro Anttonen & Markku Lanne & Jani Luoto, 2024. "Statistically identified structural VAR model with potentially skewed and fat‐tailed errors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 422-437, April.

    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. Dmitry Kulikov & Aleksei Netsunajev, 2016. "Identifying Shocks in Structural VAR models via heteroskedasticity: a Bayesian approach," Bank of Estonia Working Papers wp2015-8, Bank of Estonia, revised 19 Feb 2016.
    2. Justyna Wr'oblewska & {L}ukasz Kwiatkowski, 2024. "Identification of structural shocks in Bayesian VEC models with two-state Markov-switching heteroskedasticity," Papers 2406.03053, arXiv.org, revised Jun 2024.
    3. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with heteroskedasticity: A review of different volatility models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 2-18.
    4. Michael T. Belongia & Peter N. Ireland, 2015. "Interest Rates and Money in the Measurement of Monetary Policy," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 255-269, April.
    5. Helmut Lütkepohl & Anton Velinov, 2016. "Structural Vector Autoregressions: Checking Identifying Long-Run Restrictions Via Heteroskedasticity," Journal of Economic Surveys, Wiley Blackwell, vol. 30(2), pages 377-392, April.
    6. Helmut Lutkepohl & Fei Shang & Luis Uzeda & Tomasz Wo'zniak, 2024. "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference," Papers 2404.11057, arXiv.org.
    7. Fritsche, Jan Philipp & Klein, Mathias & Rieth, Malte, 2021. "Government spending multipliers in (un)certain times," Journal of Public Economics, Elsevier, vol. 203(C).
    8. Michael T. Belongia & Peter N. Ireland, 2016. "Money and Output: Friedman and Schwartz Revisited," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 48(6), pages 1223-1266, September.
    9. Mengheng Li & Ivan Mendieta-Munoz, 2019. "The multivariate simultaneous unobserved components model and identification via heteroskedasticity," Working Paper Series 2019/08, Economics Discipline Group, UTS Business School, University of Technology, Sydney.
    10. Michael T. Belongia & Peter N. Ireland, 2021. "A Classical View of the Business Cycle," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 53(2-3), pages 333-366, March.
    11. 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.
    12. Annika Camehl & Tomasz Wo'zniak, 2023. "Time-Varying Identification of Monetary Policy Shocks," Papers 2311.05883, arXiv.org, revised May 2024.
    13. John W. Keating & Logan J. Kelly & A. Lee Smith & Victor J. Valcarcel, 2019. "A Model of Monetary Policy Shocks for Financial Crises and Normal Conditions," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(1), pages 227-259, February.
    14. Lütkepohl, Helmut & Netšunajev, Aleksei, 2017. "Structural vector autoregressions with smooth transition in variances," Journal of Economic Dynamics and Control, Elsevier, vol. 84(C), pages 43-57.
    15. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    16. Marek A. Dąbrowski & Łukasz Kwiatkowski & Justyna Wróblewska, 2020. "Sources of Real Exchange Rate Variability in Central and Eastern European Countries: Evidence from Structural Bayesian MSH-VAR Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(4), pages 369-412, December.
    17. 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.
    18. 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.
    19. Helmut Lütkepohl & Thore Schlaak, 2018. "Choosing Between Different Time‐Varying Volatility Models for Structural Vector Autoregressive Analysis," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 80(4), pages 715-735, August.
    20. Hess Chung & Troy Davig & Eric M. Leeper, 2007. "Monetary and Fiscal Policy Switching," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 809-842, June.

    More about this item

    Keywords

    Identification through heteroskedasticity; Markov-Switching models; Savage-Dickey Density Ratio; monetary policy shocks; Divisia Money;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:diw:diwwpp:dp1707. 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: Bibliothek (email available below). General contact details of provider: https://edirc.repec.org/data/diwbede.html .

    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.