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Principal components estimation and identification of static factors

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  • Bai, Jushan
  • Ng, Serena

Abstract

It is known that the principal component estimates of the factors and the loadings are rotations of the underlying latent factors and loadings. We study conditions under which the latent factors can be estimated asymptotically without rotation. We derive the limiting distributions for the estimated factors and factor loadings when N and T are large and make precise how identification of the factors affects inference based on factor augmented regressions. We also consider factor models with additive individual and time effects. The asymptotic analysis can be modified to analyze identification schemes not considered in this analysis.

Suggested Citation

  • Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    • Handle: RePEc:eee:econom:v:176:y:2013:i:1:p:18-29
    DOI: 10.1016/j.jeconom.2013.03.007
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    References listed on IDEAS

    as
    1. Bai, Jushan & Ng, Serena, 2010. "Instrumental Variable Estimation In A Data Rich Environment," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1577-1606, December.
    2. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    3. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    4. James Algina, 1980. "A note on identification in the oblique and orthogonal factor analysis models," Psychometrika, Springer;The Psychometric Society, vol. 45(3), pages 393-396, September.
    5. Ricardo Reis & Mark W. Watson, 2010. "Relative Goods' Prices, Pure Inflation, and the Phillips Correlation," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(3), pages 128-157, July.
    6. Paul Bekker, 1986. "A note on the identification of restricted factor loading matrices," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 607-611, December.
    7. Jushan Bai, 2003. "Inferential Theory for Factor Models of Large Dimensions," Econometrica, Econometric Society, vol. 71(1), pages 135-171, January.
    8. Jushan Bai & Serena Ng, 2006. "Confidence Intervals for Diffusion Index Forecasts and Inference for Factor-Augmented Regressions," Econometrica, Econometric Society, vol. 74(4), pages 1133-1150, July.
    9. Emanuel Moench & Serena Ng, 2011. "A hierarchical factor analysis of U.S. housing market dynamics," Econometrics Journal, Royal Economic Society, vol. 14(1), pages 1-24, February.
    10. Marc Hallin & Roman Liska, 2008. "Dynamic Factors in the Presence of Block Structure," Economics Working Papers ECO2008/22, European University Institute.
    11. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    12. Chris Heaton & Victor Solo, 2004. "Identification of causal factor models of stationary time series," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 618-627, December.
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    More about this item

    Keywords

    Diffusion indices; FAVAR; Rotation; Factor space; Skew-symmetric matrices;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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