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Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification

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  • Kaufmann, Sylvia
  • Schumacher, Christian

Abstract

Common variation in N series is extracted into k≪N dynamic factors. We induce sparsity by using a zero point mass–normal mixture prior distribution on the loadings. Estimation and rotational identification are independent of variable ordering. Sparsity helps identifying the factor space and the factors. Rotational identification, including factor order and sign, is obtained by processing the posterior output and based on factor draws rather than factor loading draws. Simulating data, we document sampler and estimation efficiency. To illustrate, we estimate the model for a large panel of Swiss macroeconomic and detailed price data. We identify 16 factors with a clear economic interpretation.

Suggested Citation

  • Kaufmann, Sylvia & Schumacher, Christian, 2019. "Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification," Journal of Econometrics, Elsevier, vol. 210(1), pages 116-134.
    • Handle: RePEc:eee:econom:v:210:y:2019:i:1:p:116-134
    DOI: 10.1016/j.jeconom.2018.11.008
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    4. Sylvia Fruhwirth-Schnatter, 2023. "Generalized Cumulative Shrinkage Process Priors with Applications to Sparse Bayesian Factor Analysis," Papers 2303.00473, arXiv.org.
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    8. Simon Beyeler & Sylvia Kaufmann, 2021. "Reduced‐form factor augmented VAR—Exploiting sparsity to include meaningful factors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(7), pages 989-1012, November.
    9. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    10. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    11. Simon Freyaldenhoven, 2020. "Identification Through Sparsity in Factor Models," Working Papers 20-25, Federal Reserve Bank of Philadelphia.
    12. Iacopini, Matteo & Poon, Aubrey & Rossini, Luca & Zhu, Dan, 2023. "Bayesian mixed-frequency quantile vector autoregression: Eliciting tail risks of monthly US GDP," Journal of Economic Dynamics and Control, Elsevier, vol. 157(C).
    13. Darjus Hosszejni & Sylvia Fruhwirth-Schnatter, 2022. "Cover It Up! Bipartite Graphs Uncover Identifiability in Sparse Factor Analysis," Papers 2211.00671, arXiv.org, revised Nov 2022.
    14. 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.
    15. Hauber, Philipp & Schumacher, Christian, 2021. "Precision-based sampling with missing observations: A factor model application," Discussion Papers 11/2021, Deutsche Bundesbank.
    16. Joshua Chan, 2023. "BVARs and Stochastic Volatility," Papers 2310.14438, arXiv.org.
    17. Hu, Guanyu, 2021. "Spatially varying sparsity in dynamic regression models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 23-34.
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    19. Florian Huber & Gary Koop, 2023. "Subspace shrinkage in conjugate Bayesian vector autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 556-576, June.
    20. Chan, Joshua C.C. & Poon, Aubrey & Zhu, Dan, 2023. "High-dimensional conditionally Gaussian state space models with missing data," Journal of Econometrics, Elsevier, vol. 236(1).
    21. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," PSE Working Papers halshs-03626503, HAL.
    22. Thomas Despois & Catherine Doz, 2021. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Working Papers halshs-02235543, HAL.
    23. Casarin, Roberto & Grassi, Stefano & Ravazzolo, Francesco & van Dijk, Herman K., 2023. "A flexible predictive density combination for large financial data sets in regular and crisis periods," Journal of Econometrics, Elsevier, vol. 237(2).
    24. Sylvia Fruhwirth-Schnatter & Darjus Hosszejni & Hedibert Freitas Lopes, 2023. "When it counts -- Econometric identification of the basic factor model based on GLT structures," Papers 2301.06354, arXiv.org.
    25. Sylvia Kaufmann & Markus Pape, 2023. "Bayesian (non-)unique sparse factor modelling," Working Papers 23.04, Swiss National Bank, Study Center Gerzensee.

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    More about this item

    Keywords

    Ex-post processing; Factor interpretation; Large dataset; Factor order permutation; Rotation;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: 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

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