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

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  • 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
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    2. Karin Klieber, 2023. "Non-linear dimension reduction in factor-augmented vector autoregressions," Papers 2309.04821, arXiv.org.
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    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.

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    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

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