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When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures

Author

Listed:
  • Sylvia Frühwirth-Schnatter

    (Department of Finance, Accounting, and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria)

  • Darjus Hosszejni

    (Department of Finance, Accounting, and Statistics, WU Vienna University of Economics and Business, 1020 Vienna, Austria)

  • Hedibert Freitas Lopes

    (School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85281, USA
    Insper Institute of Education and Research, São Paulo 04546-042, Brazil)

Abstract

Despite the popularity of factor models with simple loading matrices, little attention has been given to formally address the identifiability of these models beyond standard rotation-based identification such as the positive lower triangular (PLT) constraint. To fill this gap, we review the advantages of variance identification in simple factor analysis and introduce the generalized lower triangular (GLT) structures. We show that the GLT assumption is an improvement over PLT without compromise: GLT is also unique but, unlike PLT, a non-restrictive assumption. Furthermore, we provide a simple counting rule for variance identification under GLT structures, and we demonstrate that within this model class, the unknown number of common factors can be recovered in an exploratory factor analysis. Our methodology is illustrated for simulated data in the context of post-processing posterior draws in sparse Bayesian factor analysis.

Suggested Citation

  • Sylvia Frühwirth-Schnatter & Darjus Hosszejni & Hedibert Freitas Lopes, 2023. "When It Counts—Econometric Identification of the Basic Factor Model Based on GLT Structures," Econometrics, MDPI, vol. 11(4), pages 1-30, November.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:4:p:26-:d:1283993
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    References listed on IDEAS

    as
    1. Bekker, Paul A., 1989. "Identification in restricted factor models and the evaluation of rank conditions," Journal of Econometrics, Elsevier, vol. 41(1), pages 5-16, May.
    2. A. Bhattacharya & D. B. Dunson, 2011. "Sparse Bayesian infinite factor models," Biometrika, Biometrika Trust, vol. 98(2), pages 291-306.
    3. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    4. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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