IDEAS home Printed from https://ideas.repec.org/p/diw/diwwpp/dp2081.html
   My bibliography  Save this paper

Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference

Author

Listed:
  • Helmut Lütkepohl
  • Fei Shang
  • Luis Uzeda
  • Tomasz Woźniak

Abstract

We consider structural vector autoregressions identified through stochastic volatility. Our focus is on whether a particular structural shock is identified by heteroskedasticity without the need to impose any sign or exclusion restrictions. Three contributions emerge from our exercise: (i) a set of conditions under which the matrix containing structural parameters is partially or globally unique; (ii) a statistical procedure to assess the validity of the conditions mentioned above; and (iii) a shrinkage prior distribution for conditional variances centred on a hypothesis of homoskedasticity. Such a prior ensures that the evidence for identifying a structural shock comes only from the data and is not favoured by the prior. We illustrate our new methods using a U.S. fiscal structural model.

Suggested Citation

  • Helmut Lütkepohl & Fei Shang & Luis Uzeda & Tomasz Woźniak, 2024. "Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference," Discussion Papers of DIW Berlin 2081, DIW Berlin, German Institute for Economic Research.
    • Handle: RePEc:diw:diwwpp:dp2081
    as

    Download full text from publisher

    File URL: https://www.diw.de/documents/publikationen/73/diw_01.c.900011.de/dp2081.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lütkepohl, Helmut & Velinov, Anton, 2016. "Structural Vector Autoregressions : Checking Identifying Long-Run Restrictions via Heteroskedasticity," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 30, pages 377-392.
    2. Markku Lanne & Helmut Lütkepohl, 2008. "Identifying Monetary Policy Shocks via Changes in Volatility," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(6), pages 1131-1149, September.
    3. 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.
    4. Christina D. Romer & David H. Romer, 2010. "The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks," American Economic Review, American Economic Association, vol. 100(3), pages 763-801, June.
    5. 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.
    6. Joshua C. C. Chan, 2018. "Specification tests for time-varying parameter models with stochastic volatility," Econometric Reviews, Taylor & Francis Journals, vol. 37(8), pages 807-823, September.
    7. Lütkepohl, Helmut & Meitz, Mika & Netšunajev, Aleksei & Saikkonen, Pentti, 2021. "Testing identification via heteroskedasticity in structural vector autoregressive models," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 24(1), pages 1-22.
    8. 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.
    9. Mertens, Karel & Ravn, Morten O., 2014. "A reconciliation of SVAR and narrative estimates of tax multipliers," Journal of Monetary Economics, Elsevier, vol. 68(S), pages 1-19.
    10. Roberto Rigobon & Brian Sack, 2003. "Measuring The Reaction of Monetary Policy to the Stock Market," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(2), pages 639-669.
    11. Joshua C. C. Chan & Gary Koop & Xuewen Yu, 2024. "Large Order-Invariant Bayesian VARs with Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 825-837, April.
    12. Timothy Cogley & Thomas J. Sargent, 2005. "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 262-302, April.
    13. Waggoner, Daniel F. & Zha, Tao, 2003. "Likelihood preserving normalization in multiple equation models," Journal of Econometrics, Elsevier, vol. 114(2), pages 329-347, June.
    14. 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.
    15. Callealta Barroso, Francisco Javier & García-Pérez, Carmelo & Prieto-Alaiz, Mercedes, 2020. "Modelling income distribution using the log Student’s t distribution: New evidence for European Union countries," Economic Modelling, Elsevier, vol. 89(C), pages 512-522.
    16. 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.
    17. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    18. 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.
    19. Daniel J Lewis, 2021. "Identifying Shocks via Time-Varying Volatility [First Order Autoregressive Processes and Strong Mixing]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(6), pages 3086-3124.
    20. Sentana, Enrique & Fiorentini, Gabriele, 2001. "Identification, estimation and testing of conditionally heteroskedastic factor models," Journal of Econometrics, Elsevier, vol. 102(2), pages 143-164, June.
    21. Todd E. Clark & Francesco Ravazzolo, 2015. "Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 551-575, June.
    22. Neville Francis & Valerie A. Ramey, 2009. "Measures of per Capita Hours and Their Implications for the Technology-Hours Debate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(6), pages 1071-1097, September.
    23. Joshua C. C. Chan & Eric Eisenstat, 2018. "Bayesian model comparison for time‐varying parameter VARs with stochastic volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(4), pages 509-532, June.
    24. 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.
    25. 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.
    26. Kastner, Gregor & Frühwirth-Schnatter, Sylvia, 2014. "Ancillarity-sufficiency interweaving strategy (ASIS) for boosting MCMC estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 408-423.
    27. Bitto, Angela & Frühwirth-Schnatter, Sylvia, 2019. "Achieving shrinkage in a time-varying parameter model framework," Journal of Econometrics, Elsevier, vol. 210(1), pages 75-97.
    28. Eddelbuettel, Dirk & Sanderson, Conrad, 2014. "RcppArmadillo: Accelerating R with high-performance C++ linear algebra," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1054-1063.
    29. Waggoner, Daniel F. & Zha, Tao, 2003. "A Gibbs sampler for structural vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 349-366, November.
    30. Frühwirth-Schnatter, Sylvia & Wagner, Helga, 2010. "Stochastic model specification search for Gaussian and partial non-Gaussian state space models," Journal of Econometrics, Elsevier, vol. 154(1), pages 85-100, January.
    31. Annalisa Cadonna & Sylvia Frühwirth-Schnatter & Peter Knaus, 2020. "Triple the Gamma—A Unifying Shrinkage Prior for Variance and Variable Selection in Sparse State Space and TVP Models," Econometrics, MDPI, vol. 8(2), pages 1-36, May.
    32. Hogg, Robert V. & Klugman, Stuart A., 1983. "On the estimation of long tailed skewed distributions with actuarial applications," Journal of Econometrics, Elsevier, vol. 23(1), pages 91-102, September.
    33. Lütkepohl, Helmut & Milunovich, George, 2016. "Testing for identification in SVAR-GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 73(C), pages 241-258.
    34. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    35. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano, 2019. "Large Bayesian vector autoregressions with stochastic volatility and non-conjugate priors," Journal of Econometrics, Elsevier, vol. 212(1), pages 137-154.
    36. Markku Lanne & Jani Luoto, 2021. "GMM Estimation of Non-Gaussian Structural Vector Autoregression," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 69-81, January.
    37. Darjus Hosszejni & Gregor Kastner, 2019. "Modeling Univariate and Multivariate Stochastic Volatility in R with stochvol and factorstochvol," Papers 1906.12123, arXiv.org, revised Feb 2021.
    38. repec:cup:cbooks:9781316647332 is not listed on IDEAS
    39. repec:oup:emjrnl:v:24:y:2021:i:1:p:1-22. is not listed on IDEAS
    40. repec:cup:cbooks:9781107196575 is not listed on IDEAS
    41. Roberto Rigobon, 2003. "Identification Through Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 85(4), pages 777-792, November.
    Full references (including those not matched with items on IDEAS)

    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. Karamysheva, Madina & Skrobotov, Anton, 2022. "Do we reject restrictions identifying fiscal shocks? identification based on non-Gaussian innovations," Journal of Economic Dynamics and Control, Elsevier, vol. 138(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. Carriero, Andrea & Clark, Todd E. & Marcellino, Massimiliano, 2021. "Using time-varying volatility for identification in Vector Autoregressions: An application to endogenous uncertainty," Journal of Econometrics, Elsevier, vol. 225(1), pages 47-73.
    4. 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).
    5. 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.
    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. 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.
    8. 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.
    9. Yu Bai & Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2022. "Macroeconomic forecasting in a multi‐country context," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1230-1255, September.
    10. Alfan Mansur, 2023. "Simultaneous identification of fiscal and monetary policy shocks," Empirical Economics, Springer, vol. 65(2), pages 697-728, August.
    11. Luis Gruber & Gregor Kastner, 2022. "Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!," Papers 2206.04902, arXiv.org, revised Jul 2023.
    12. 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.
    13. 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.
    14. Helmut Lütkepohl & Aleksei Netšunajev, 2015. "Structural Vector Autoregressions with Heteroskedasticity - A Comparison of Different Volatility Models," CESifo Working Paper Series 5308, CESifo.
    15. 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.
    16. Lütkepohl, Helmut & Velinov, Anton, 2016. "Structural Vector Autoregressions : Checking Identifying Long-Run Restrictions via Heteroskedasticity," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 30, pages 377-392.
    17. Fengler, Matthias & Polivka, Jeannine, 2021. "Identifying structural shocks to volatility through a proxy-MGARCH model," Economics Working Paper Series 2103, University of St. Gallen, School of Economics and Political Science, revised May 2021.
    18. Lütkepohl, Helmut & Woźniak, Tomasz, 2020. "Bayesian inference for structural vector autoregressions identified by Markov-switching heteroskedasticity," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    19. Emanuele Bacchiocchi & Efrem Castelnuovo & Luca Fanelli, 2014. "Gimme a break! Identification and estimation of the macroeconomic effects of monetary policy shocks in the U.S," "Marco Fanno" Working Papers 0181, Dipartimento di Scienze Economiche "Marco Fanno".
    20. Sascha A. Keweloh & Mathias Klein & Jan Pruser, 2023. "Estimating Fiscal Multipliers by Combining Statistical Identification with Potentially Endogenous Proxies," Papers 2302.13066, arXiv.org, revised May 2024.

    More about this item

    Keywords

    Identification through heteroskedasticity; stochastic volatility; non-centred parameterisation; shrinkage prior; normal product distribution; tax shocks;
    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
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory

    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:dp2081. 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.