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A Class of Time-Varying Parameter Structural VARs for Inference under Exact or Set Identification

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Abstract
This paper develops a new class of structural vector autoregressions (SVARs) with time-varying parameters, which I call a drifting SVAR (DSVAR). The DSVAR is the first structural time-varying parameter model to allow for internally consistent probabilistic inference under exact?or set?identification, nesting the widely used SVAR framework as a special case. I prove that the DSVAR implies a reduced-form representation, from which structural inference can proceed similarly to the widely used two-step approach for SVARs: beginning with estimation of a reduced form and then choosing among observationally equivalent candidate structural parameters via the imposition of identifying restrictions. In a special case, the implied reduced form is a tractable known model for which I provide the first algorithm for Bayesian estimation of all free parameters. I demonstrate the framework in the context of Baumeister and Peersman?s (2013b) work on time variation in the elasticity of oil demand.

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  • Mark Bognanni, 2018. "A Class of Time-Varying Parameter Structural VARs for Inference under Exact or Set Identification," Working Papers (Old Series) 1811, Federal Reserve Bank of Cleveland.
    • Handle: RePEc:fip:fedcwp:1811
    DOI: 10.26509/frbc-wp-201811
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    References listed on IDEAS

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    2. Christiane Baumeister & Gert Peersman, 2013. "The Role Of Time‐Varying Price Elasticities In Accounting For Volatility Changes In The Crude Oil Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1087-1109, November.
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    10. Christiane Baumeister & Luca Benati, 2013. "Unconventional Monetary Policy and the Great Recession: Estimating the Macroeconomic Effects of a Spread Compression at the Zero Lower Bound," International Journal of Central Banking, International Journal of Central Banking, vol. 9(2), pages 165-212, June.
    11. Christiane Baumeister & James D. Hamilton, 2015. "Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information," Econometrica, Econometric Society, vol. 83(5), pages 1963-1999, September.
    12. 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.
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    14. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    15. Sims, Christopher A. & Waggoner, Daniel F. & Zha, Tao, 2008. "Methods for inference in large multiple-equation Markov-switching models," Journal of Econometrics, Elsevier, vol. 146(2), pages 255-274, October.
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    17. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    18. Jonas E. Arias & Juan F. Rubio‐Ramírez & Daniel F. Waggoner, 2018. "Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications," Econometrica, Econometric Society, vol. 86(2), pages 685-720, March.
    19. Arjun K. Gupta & Daya K. Nagar, 2000. "Matrix-variate beta distribution," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 24, pages 1-11, January.
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    Cited by:

    1. 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.
    2. Chan, Joshua C.C. & Yu, Xuewen, 2022. "Fast and Accurate Variational Inference for Large Bayesian VARs with Stochastic Volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 143(C).
    3. Qazi Haque & Leandro M. Magnusson & Kazuki Tomioka, 2021. "Empirical Evidence on the Dynamics of Investment Under Uncertainty in the U.S," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 83(5), pages 1193-1217, October.
    4. Joshua Chan & Eric Eisenstat & Xuewen Yu, 2022. "Large Bayesian VARs with Factor Stochastic Volatility: Identification, Order Invariance and Structural Analysis," Papers 2207.03988, arXiv.org.
    5. 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.
    6. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Waggoner, Daniel F., 2021. "Inference in Bayesian Proxy-SVARs," Journal of Econometrics, Elsevier, vol. 225(1), pages 88-106.
    7. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    8. Prüser, Jan, 2021. "The horseshoe prior for time-varying parameter VARs and Monetary Policy," Journal of Economic Dynamics and Control, Elsevier, vol. 129(C).
    9. Bognanni, Mark & Zito, John, 2020. "Sequential Bayesian inference for vector autoregressions with stochastic volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 113(C).
    10. Demetrescu, Matei & Salish, Nazarii, 2024. "(Structural) VAR models with ignored changes in mean and volatility," International Journal of Forecasting, Elsevier, vol. 40(2), pages 840-854.
    11. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Shin, Minchul, 2023. "Macroeconomic forecasting and variable ordering in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 235(2), pages 1054-1086.
    12. Laura Liu & Christian Matthes & Katerina Petrova, 2022. "Monetary Policy Across Space and Time," Advances in Econometrics, in: Essays in Honour of Fabio Canova, volume 44, pages 37-64, Emerald Group Publishing Limited.
    13. Etienne Vaccaro-Grange, 2019. "Quantitative Easing and the Term Premium as a Monetary Policy Instrument," AMSE Working Papers 1932, Aix-Marseille School of Economics, France.
    14. Christis Katsouris, 2023. "Structural Analysis of Vector Autoregressive Models," Papers 2312.06402, arXiv.org, revised Feb 2024.
    15. 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.
    16. Aymeric Ortmans, 2020. "Evolving Monetary Policy in the Aftermath of the Great Recession," Documents de recherche 20-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    17. Hartwig, Benny, 2020. "Robust inference intime-varying structural VAR models: The DC-Cholesky multivariate stochasticvolatility model," Discussion Papers 34/2020, Deutsche Bundesbank.
    18. Wu, Ping & Koop, Gary, 2023. "Estimating the ordering of variables in a VAR using a Plackett–Luce prior," Economics Letters, Elsevier, vol. 230(C).
    19. Mark Bognanni & John Zito, 2019. "Sequential Bayesian Inference for Vector Autoregressions with Stochastic Volatility," Working Papers 19-29, Federal Reserve Bank of Cleveland.
    20. Harrison, Andre & Liu, Xiaochun & Stewart, Shamar L., 2023. "Structural sources of oil market volatility and correlation dynamics," Energy Economics, Elsevier, vol. 121(C).

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    More about this item

    Keywords

    structural vector autoregressions; time-varying parameters; Gibbs sampling; stochastic volatility; Bayesian inference;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: 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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E4 - Macroeconomics and Monetary Economics - - Money and Interest Rates
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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