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Partial Identification of Heteroskedastic Structural Vector Autoregressions: Theory and Bayesian Inference

Author

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

Abstract

We consider structural vector autoregressions that are identified through stochastic volatility. Our analysis focuses on whether a particular structural shock can be identified through heteroskedasticity without imposing any sign or exclusion restrictions. Three contributions emerge from our exercise: (i) a set of conditions that ensures the matrix containing structural parameters is either partially or globally unique; (ii) a shrinkage prior distribution for the conditional variance of structural shocks, centred on the hypothesis of homoskedasticity; and (iii) a statistical procedure for assessing the validity of the conditions outlined in (i). Our shrinkage prior ensures that the evidence for identifying a structural shock relies predominantly on the data and is less influenced by the prior distribution. We demonstrate the usefulness of our framework through a fiscal structural model and a series of simulation exercises.

Suggested Citation

  • Helmut Lütkepohl & Fei Shang & Luis Uzeda & Tomasz Woźniak, 2025. "Partial Identification of Heteroskedastic Structural Vector Autoregressions: Theory and Bayesian Inference," Staff Working Papers 25-14, Bank of Canada.
    • Handle: RePEc:bca:bocawp:25-14
    DOI: 10.34989/swp-2025-14
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    References listed on IDEAS

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    1. 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.
    2. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, Enero-Abr.
    3. 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.
    4. 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.
    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. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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    Cited by:

    1. Fei Shang & Tomasz Wo'zniak, 2026. "Identification Verification for Structural Vector Autoregressions with Sparse Heterogeneous Markov Switching Heteroskedasticity," Papers 2603.16035, arXiv.org.

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    Keywords

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    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

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