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Determining the Number of Factors in Approximate Factor Models


  • Jushan Bai

    () (Dept. of Economics, Boston College, U.S.A.)

  • Serena Ng

    () (Dept. of Economics, Johns Hopkins University, Baltimore, U.S.A.)


In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors ("r"), which is an unresolved issue in the rapidly growing literature on multifactor models. We first establish the convergence rate for the factor estimates that will allow for consistent estimation of "r". We then propose some panel criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections ("N") and large time dimensions ("T"). No restriction is imposed on the relation between "N" and "T". Simulations show that the proposed criteria have good finite sample properties in many configurations of the panel data encountered in practice. Copyright The Econometric Society 2001.

Suggested Citation

  • Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:1:p:191-221

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    References listed on IDEAS

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation


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