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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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    References listed on IDEAS

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    Cited by:

    1. repec:spr:empeco:v:53:y:2017:i:1:d:10.1007_s00181-016-1158-5 is not listed on IDEAS
    2. Simon Beyeler & Sylvia Kaufmann, 2016. "Factor augmented VAR revisited - A sparse dynamic factor model approach," Working Papers 16.08, Swiss National Bank, Study Center Gerzensee.
    3. 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.
    4. Francisco Corona & Pilar Poncela & Esther Ruiz, 2017. "Determining the number of factors after stationary univariate transformations," Empirical Economics, Springer, vol. 53(1), pages 351-372, August.
    5. 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 Publishing Ltd.
    6. Poncela, Pilar & Corona, Francisco & Ruiz Ortega, Esther, 2017. "Estimating non-stationary common factors : Implications for risk sharing," DES - Working Papers. Statistics and Econometrics. WS 24585, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Vegard H. Larsen & Leif Anders Thorsrud, 2018. "Business cycle narratives," Working Paper 2018/3, Norges Bank.
    8. repec:kap:jculte:v:42:y:2018:i:2:d:10.1007_s10824-017-9312-2 is not listed on IDEAS
    9. repec:eee:econom:v:210:y:2019:i:1:p:116-134 is not listed on IDEAS
    10. repec:eee:econom:v:202:y:2018:i:2:p:125-147 is not listed on IDEAS
    11. repec:rjr:romjef:v::y:2019:i:2:p:32-53 is not listed on IDEAS
    12. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    13. repec:eee:macchp:v2-415 is not listed on IDEAS

    More about this item

    Keywords

    High dimensional dynamic factor models; Identification; Rank conditions;

    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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