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Reducing dimensions in a large TVP-VAR

Author

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  • Joshua C.C. Chan
  • Eric Eisenstat
  • Rodney W. Strachan

Abstract

This paper proposes a new approach to estimating high dimensional time varying parameter structural vector autoregressive models (TVP-SVARs) by taking advantage of an empirical feature of TVP-(S)VARs. TVP-(S)VAR models are rarely used with more than 4-5 variables. However recent work has shown the advantages of modelling VARs with large numbers of variables and interest has naturally increased in modelling large dimensional TVP-VARs. A feature that has not yet been utilized is that the covariance matrix for the state equation, when estimated freely, is often near singular. We propose a specification that uses this singularity to develop a factor-like structure to estimate a TVP-SVAR for 15 variables. Using a generalization of the re-centering approach, a rank reduced state covariance matrix and judicious parameter expansions, we obtain efficient and simple computation of a high dimensional TVP-SVAR. An advantage of our approach is that we retain a formal inferential framework such that we can propose formal inference on impulse responses, variance decompositions and, important for our model, the rank of the state equation covariance matrix. We show clear empirical evidence in favour of our model and improvements in estimates of impulse responses.

Suggested Citation

  • Joshua C.C. Chan & Eric Eisenstat & Rodney W. Strachan, 2018. "Reducing dimensions in a large TVP-VAR," CAMA Working Papers 2018-49, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
  • Handle: RePEc:een:camaaa:2018-49
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    File URL: https://cama.crawford.anu.edu.au/sites/default/files/publication/cama_crawford_anu_edu_au/2018-10/49_2018_eisenstat_chan_strachan.pdf
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    References listed on IDEAS

    as
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    Cited by:

    1. Simon Beyeler, 2019. "Streamlining Time-varying VAR with a Factor Structure in the Parameters," Working Papers 19.03, Swiss National Bank, Study Center Gerzensee.
    2. Philippe Goulet Coulombe, 2020. "The Macroeconomy as a Random Forest," Papers 2006.12724, arXiv.org, revised Mar 2021.
    3. Jim Hart & Bernardino D'Amico & Francesco Pomponi, 2021. "Whole‐life embodied carbon in multistory buildings: Steel, concrete and timber structures," Journal of Industrial Ecology, Yale University, vol. 25(2), pages 403-418, April.
    4. Philippe Goulet Coulombe, 2021. "The Macroeconomy as a Random Forest," Working Papers 21-05, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management.
    5. Zhao, Jing, 2023. "Time-varying impact of geopolitical risk on natural resources prices: Evidence from the hybrid TVP-VAR model with large system," Resources Policy, Elsevier, vol. 82(C).
    6. Philippe Goulet Coulombe, 2020. "Time-Varying Parameters as Ridge Regressions," Papers 2009.00401, arXiv.org, revised Apr 2023.

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    More about this item

    Keywords

    Large VAR; time varying parameter; reduced rank covariance matrix;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation

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