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Identification theory for high dimensional static and dynamic factor models

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  • Bai, Jushan
  • Wang, Peng

Abstract

High dimensional factor models can involve thousands of parameters. The Jacobian matrix for identification is of a large dimension. It can be difficult and numerically inaccurate to evaluate the rank of such a Jacobian matrix. We reduce the identification problem to a small rank problem, which is easy to check. The identification conditions allow both linear and nonlinear restrictions. Under reasonable assumptions for high dimensional factor models, the small rank conditions are shown to be necessary and sufficient for local identification.

Suggested Citation

  • Bai, Jushan & Wang, Peng, 2014. "Identification theory for high dimensional static and dynamic factor models," Journal of Econometrics, Elsevier, vol. 178(2), pages 794-804.
    • Handle: RePEc:eee:econom:v:178:y:2014:i:2:p:794-804
    DOI: 10.1016/j.jeconom.2013.11.001
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    Cited by:

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    4. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    5. Leif Anders Thorsrud, 2016. "Nowcasting using news topics Big Data versus big bank," Working Papers No 6/2016, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    6. Pilar Poncela & Esther Ruiz, 2016. "Small- Versus Big-Data Factor Extraction in Dynamic Factor Models: An Empirical Assessment," Advances in Econometrics, in: Dynamic Factor Models, volume 35, pages 401-434, Emerald Group Publishing Limited.
    7. Francisco Corona & Pilar Poncela & Esther Ruiz, 2020. "Estimating Non-stationary Common Factors: Implications for Risk Sharing," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 37-60, January.
    8. Maurizio Daniele & Julie Schnaitmann, 2019. "A Regularized Factor-augmented Vector Autoregressive Model," Papers 1912.06049, arXiv.org.
    9. Franco Peracchi & Claudio Rossetti, 2022. "A nonlinear dynamic factor model of health and medical treatment," Health Economics, John Wiley & Sons, Ltd., vol. 31(6), pages 1046-1066, June.
    10. Vegard H. Larsen & Leif Anders Thorsrud, 2018. "Business cycle narratives," Working Paper 2018/3, Norges Bank.
    11. Hauber, Philipp & Schumacher, Christian, 2021. "Precision-based sampling with missing observations: A factor model application," Discussion Papers 11/2021, Deutsche Bundesbank.
    12. Andrej Srakar & Vesna Čopič & Miroslav Verbič, 2018. "European cultural statistics in a comparative perspective: index of economic and social condition of culture for the EU countries," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 42(2), pages 163-199, May.
    13. Yuefeng Han & Cun-Hui Zhang & Rong Chen, 2021. "CP Factor Model for Dynamic Tensors," Papers 2110.15517, arXiv.org.
    14. Kaufmann, Sylvia & Schumacher, Christian, 2019. "Bayesian estimation of sparse dynamic factor models with order-independent and ex-post mode identification," Journal of Econometrics, Elsevier, vol. 210(1), pages 116-134.
    15. Martin Solberger & Erik Spånberg, 2020. "Estimating a Dynamic Factor Model in EViews Using the Kalman Filter and Smoother," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 875-900, March.
    16. Han, Xu, 2018. "Estimation and inference of dynamic structural factor models with over-identifying restrictions," Journal of Econometrics, Elsevier, vol. 202(2), pages 125-147.
    17. Dimitar EFTIMOSKI, 2019. "Improving Short-Term Forecasting of Macedonian GDP: Comparing the Factor Model with the Macroeconomic Structural Equation Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 32-53, June.
    18. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
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    More about this item

    Keywords

    High dimensional dynamic factor models; Identification; Rank conditions;
    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
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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