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Partial Identification of Heteroskedastic Structural VARs: Theory and Bayesian Inference

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  • 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
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    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

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