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Identification of the linear factor model

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  • Benjamin Williams

Abstract

This paper provides several new results on identification of the linear factor model. The model allows for correlated latent factors and dependence among the idiosyncratic errors. I also illustrate identification under a dedicated measurement structure and other reduced rank restrictions. I use these results to study identification in a model with both observed covariates and latent factors. The analysis emphasizes the different roles played by restrictions on the error covariance matrix, restrictions on the factor loadings and the factor covariance matrix, and restrictions on the coefficients on covariates. The identification results are simple, intuitive, and directly applicable to many settings.

Suggested Citation

  • Benjamin Williams, 2020. "Identification of the linear factor model," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 92-109, January.
    • Handle: RePEc:taf:emetrv:v:39:y:2020:i:1:p:92-109
    DOI: 10.1080/07474938.2018.1550042
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    Citations

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    Cited by:

    1. Belzil, Christian & Pernaudet, Julie & Poinas, François, 2021. "Estimating Coherency between Survey Data and Incentivized Experimental Data," IZA Discussion Papers 14594, Institute of Labor Economics (IZA).
    2. Gallegos, Sebastián & García, Jorge Luis, 2024. "Childcare and parenting in the production of early life skills," Economics of Education Review, Elsevier, vol. 101(C).
    3. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    4. James J. Heckman & Bridget Galaty & Haihan Tian, 2023. "The Economic Approach to Personality, Character and Virtue," NBER Working Papers 31258, National Bureau of Economic Research, Inc.
    5. Botosaru, Irene, 2023. "Time-varying unobserved heterogeneity in earnings shocks," Journal of Econometrics, Elsevier, vol. 235(2), pages 1378-1393.
    6. 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.
    7. Matthew Harding & Carlos Lamarche & Chris Muris, 2022. "Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data," Papers 2203.03051, arXiv.org.
    8. John Eric Humphries & Juanna Schrøter Joensen & Gregory F. Veramendi, 2024. "The Gender Wage Gap: Skills, Sorting, and Returns," AEA Papers and Proceedings, American Economic Association, vol. 114, pages 259-264, May.
    9. 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.
    10. Joachim Freyberger, 2021. "Normalizations and misspecification in skill formation models," Papers 2104.00473, arXiv.org, revised Jul 2022.
    11. Gregory Cox, 2022. "Weak Identification in Low-Dimensional Factor Models with One or Two Factors," Papers 2211.00329, arXiv.org, revised Mar 2024.
    12. Giorgio Calzolari & Roxana Halbleib & Christian Mucher, 2023. "Sequential Estimation of Multivariate Factor Stochastic Volatility Models," Papers 2302.07052, arXiv.org.
    13. Rueben Ellul & Germano Ruisi, 2022. "Nowcasting the Maltese economy with a dynamic factor model," CBM Working Papers WP/02/2022, Central Bank of Malta.

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