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Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension

Author

Listed:
  • Jushan Bai

    (Columbia University and Nankai University)

  • Kunpeng Li

    (Capital University of Economics and Business)

Abstract

An approximate factor model of high dimension has two key features. First, the idiosyncratic errors are correlated and heteroskedastic over both the cross-section and time dimensions; the correlations and heteroskedasticities are of unknown forms. Second, the number of variables is comparable or even greater than the sample size. Thus, a large number of parameters exist under a high-dimensional approximate factor model. Most widely used approaches to estimation are principal component based. This paper considers the maximum likelihood–based estimation of the model. Consistency, rate of convergence, and limiting distributions are obtained under various identification restrictions. Monte Carlo simulations show that the likelihood method is easy to implement and has good finite sample properties.

Suggested Citation

  • Jushan Bai & Kunpeng Li, 2016. "Maximum Likelihood Estimation and Inference for Approximate Factor Models of High Dimension," The Review of Economics and Statistics, MIT Press, vol. 98(2), pages 298-309, May.
    • Handle: RePEc:tpr:restat:v:98:y:2016:i:2:p:298-309
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    More about this item

    Keywords

    Factor analysis; Approximate factor models; Maximum likelihood; Principal components; Inferential theory;
    All these keywords.

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis

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