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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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    1. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, March.
    2. 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.
    3. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 665-696.
    4. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    5. Bekker, Paul A. & Pollock, D. S. G., 1986. "Identification of linear stochastic models with covariance restrictions," Journal of Econometrics, Elsevier, vol. 31(2), pages 179-208, March.
    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. Hannan, E J, 1971. "The Identification Problem for Multiple Equation Systems with Moving Average Errors," Econometrica, Econometric Society, vol. 39(5), pages 751-765, September.
    9. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    10. Bai, Jushan & Ng, Serena, 2013. "Principal components estimation and identification of static factors," Journal of Econometrics, Elsevier, vol. 176(1), pages 18-29.
    11. Zhongjun Qu & Denis Tkachenko, 2012. "Identification and frequency domain quasi‐maximum likelihood estimation of linearized dynamic stochastic general equilibrium models," Quantitative Economics, Econometric Society, vol. 3(1), pages 95-132, March.
    12. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    13. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    14. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    15. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    16. 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.
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    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 Group Publishing Limited.
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    11. Hauber, Philipp & Schumacher, Christian, 2021. "Precision-based sampling with missing observations: A factor model application," Discussion Papers 11/2021, Deutsche Bundesbank.
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    13. 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.
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    17. 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.
    18. 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.
    19. 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.
    20. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    21. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.

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    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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