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Recursive estimation in large panel data models: Theory and practice

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  • Jiang, Bin
  • Yang, Yanrong
  • Gao, Jiti
  • Hsiao, Cheng

Abstract

Bai (2009) proposes recursive estimation for panel data models with interactive effects. We study the behaviours of this recursive estimator. The recursive formula is established that shows the behaviours of recursive estimators depend on the initial estimator, the population structure and the iterative steps. Under some general scenarios, we find that the recursive estimator becomes consistent after the first iteration from any initials. We also obtain the optimal number of iterative steps under some prescribed conditions. The central limit theorem of the recursive estimator is established when the initial estimator is OLS. Various simulations are conducted to support our theoretical findings.

Suggested Citation

  • Jiang, Bin & Yang, Yanrong & Gao, Jiti & Hsiao, Cheng, 2021. "Recursive estimation in large panel data models: Theory and practice," Journal of Econometrics, Elsevier, vol. 224(2), pages 439-465.
    • Handle: RePEc:eee:econom:v:224:y:2021:i:2:p:439-465
    DOI: 10.1016/j.jeconom.2020.07.055
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    Cited by:

    1. Bin Peng & Liangjun Su & Joakim Westerlund & Yanrong Yang, 2021. "Interactive Effects Panel Data Models with General Factors and Regressors," Monash Econometrics and Business Statistics Working Papers 23/21, Monash University, Department of Econometrics and Business Statistics.
    2. Fei Liu & Jiti Gao & Yanrong Yang, 2019. "Nonparametric Estimation in Panel Data Models with Heterogeneity and Time Varyingness," Monash Econometrics and Business Statistics Working Papers 24/19, Monash University, Department of Econometrics and Business Statistics.
    3. Jiti Gao & Bin Peng & Yayi Yan, 2022. "Nonparametric Estimation and Testing for Time-Varying VAR Models," Monash Econometrics and Business Statistics Working Papers 3/22, Monash University, Department of Econometrics and Business Statistics.
    4. Gao, Jiti & Liu, Fei & Peng, Bin & Yan, Yayi, 2023. "Binary response models for heterogeneous panel data with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 1654-1679.
    5. Ruofan Xu & Jiti Gao & Tatsushi Oka & Yoon-Jae Whang, 2022. "Estimation of Heterogeneous Treatment Effects Using Quantile Regression with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 13/22, Monash University, Department of Econometrics and Business Statistics.
    6. Jiti Gao & Fei Liu & Bin peng, 2020. "Binary Response Models for Heterogeneous Panel Data with Interactive Fixed Effects," Monash Econometrics and Business Statistics Working Papers 44/20, Monash University, Department of Econometrics and Business Statistics.
    7. Guohua Feng & Jiti Gao & Bin Peng, 2021. "Productivity Convergence in Manufacturing: A Hierarchical Panel Data Approach," Papers 2111.00449, arXiv.org.
    8. Feng, Guohua & Gao, Jiti & Peng, Bin, 2022. "An integrated panel data approach to modelling economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 379-397.
    9. Guohua Feng & Jiti Gao & Bin Peng, 2022. "Multi-Level Panel Data Models: Estimation and Empirical Analysis," Monash Econometrics and Business Statistics Working Papers 4/22, Monash University, Department of Econometrics and Business Statistics.
    10. Guohua Feng & Jiti Gao & Bin Peng, 2019. "An Integrated Panel Data Approach to Modelling Economic Growth," Monash Econometrics and Business Statistics Working Papers 6/19, Monash University, Department of Econometrics and Business Statistics.
    11. Guowei Cui & Milda NorkutÄ— & Vasilis Sarafidis & Takashi Yamagata, 2022. "Two-stage instrumental variable estimation of linear panel data models with interactive effects [Eigenvalue ratio test for the number of factors]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 340-361.
    12. Chaohua Dong & Jiti Gao & Bin Peng, 2018. "Varying-coefficient panel data models with partially observed factor structure," Monash Econometrics and Business Statistics Working Papers 1/18, Monash University, Department of Econometrics and Business Statistics.
    13. Feng, Guohua & Peng, Bin & Su, Liangjun & Yang, Thomas Tao, 2019. "Semi-parametric single-index panel data models with interactive fixed effects: Theory and practice," Journal of Econometrics, Elsevier, vol. 212(2), pages 607-622.
    14. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

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    More about this item

    Keywords

    Factor model; Initial estimation; Multiplicative structure; Nonlinear optimization;
    All these keywords.

    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

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