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Structural Vector Autoregressions: Checking Identifying Long-Run Restrictions Via Heteroskedasticity

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  • Helmut Lütkepohl
  • Anton Velinov

Abstract

Long-run restrictions have been used extensively for identifying structural shocks in vector autoregressive (VAR) analysis. Such restrictions are typically just-identifying but can be checked by utilizing changes in volatility. This paper reviews and contrasts the volatility models that have been used for this purpose. Three main approaches have been used, exogenously generated changes in the unconditional residual covariance matrix, changing volatility modelled by a Markov switching mechanism and multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models. Using changes in volatility for checking long-run identifying restrictions in structural VAR analysis is illustrated by reconsidering models for identifying fundamental components of stock prices.
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Suggested Citation

  • 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.
    • Handle: RePEc:bla:jecsur:v:30:y:2016:i:2:p:377-392
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    File URL: http://hdl.handle.net/10.1111/joes.2016.30.issue-2
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    Cited by:

    1. 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.
    2. 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.
    3. 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).
    4. Nestor Azcona, 2017. "Non-Traded Goods and Real Exchange Rate Fluctuations: A Structural VAR Analysis," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 23(2), pages 137-148, May.
    5. 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.
    6. 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.
    7. Fatih Chellai, 2021. "What Can SVAR Models Tell us About the Impact of Public Expenditure Shocks on Macroeconomic Variables in Algeria? A Slight Hint to the COVID-19 Pandemic," Folia Oeconomica Stetinensia, Sciendo, vol. 21(2), pages 21-37, December.
    8. Nikolay Arefiev & Ramis Khabibullin, 2018. "Bayesian identification of structural vector autoregression models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 49, pages 115-142.
    9. Martin Bruns & Helmut Lütkepohl, 2024. "Heteroskedastic Structural Vector Autoregressions Identified via Long-run Restrictions," Discussion Papers of DIW Berlin 2103, DIW Berlin, German Institute for Economic Research.
    10. Kiohos, Apostolos & Stoupos, Nikolaos, 2025. "Monetary alignment or divergence? - Exchange rates and economic dynamics in non-euro European countries," The Journal of Economic Asymmetries, Elsevier, vol. 32(C).
    11. 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.
    12. Helmut Lutkepohl & Fei Shang & Luis Uzeda & Tomasz Wo'zniak, 2024. "Partial Identification of Structural Vector Autoregressions with Non-Centred Stochastic Volatility," Papers 2404.11057, arXiv.org, revised Oct 2025.
    13. Puonti, Päivi, 2016. "Fiscal multipliers in a structural VEC model with mixed normal errors," Journal of Macroeconomics, Elsevier, vol. 48(C), pages 144-154.
    14. Anton Velinov & Wenjuan Chen, 2014. "Are There Bubbles in Stock Prices?: Testing for Fundamental Shocks," Discussion Papers of DIW Berlin 1375, DIW Berlin, German Institute for Economic Research.
    15. Helmut Lütkepohl & Aleksei Netšunajev, 2018. "The Relation between Monetary Policy and the Stock Market in Europe," Econometrics, MDPI, vol. 6(3), pages 1-14, August.
    16. 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.

    More about this item

    JEL classification:

    • 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

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