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Identification of the Linear Factor Model

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  • Benjamin Williams

    (The George Washington University)

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, 2018. "Identification of the Linear Factor Model," Working Papers 2018-002, The George Washington University, Department of Economics, H. O. Stekler Research Program on Forecasting.
    • Handle: RePEc:gwc:wpaper:2018-002
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    File URL: https://www2.gwu.edu/~forcpgm/2018-002.pdf
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    References listed on IDEAS

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    2. James J. Heckman & Tomáš Jagelka & Timothy D. Kautz, 2019. "Some Contributions of Economics to the Study of Personality," NBER Working Papers 26459, National Bureau of Economic Research, Inc.
    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. 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).
    5. Papageorge, Nicholas & Ronda, Victor & Zheng, Yu, 2014. "The Economic Value of Breaking Bad: Misbehavior, Schooling and the Labor Market," Economics Working Paper Archive 64574, The Johns Hopkins University,Department of Economics, revised 16 Jun 2020.
    6. Joachim Freyberger, 2021. "Normalizations and misspecification in skill formation models," Papers 2104.00473, arXiv.org, revised Jul 2022.
    7. James J. Heckman & John Eric Humphries & Gregory Veramendi, 2018. "The Nonmarket Benefits of Education and Ability," Journal of Human Capital, University of Chicago Press, vol. 12(2), pages 282-304.
    8. Ben-Moshe, Dan, 2018. "Identification Of Joint Distributions In Dependent Factor Models," Econometric Theory, Cambridge University Press, vol. 34(1), pages 134-165, February.

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    More about this item

    Keywords

    Latent variables; factor analysis;

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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