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GMM Estimation for High-Dimensional Panel Data Models

Author

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  • Tingting Cheng
  • Chaohua Dong
  • Jiti Gao
  • Oliver Linton

Abstract

In this paper, we study a class of high dimensional moment restriction panel data models with interactive effects, where factors are unobserved and factor loadings are nonparametrically unknown smooth functions of individual characteristics variables. We allow the dimension of the parameter vector and the number of moment conditions to diverge with sample size. This is a very general framework and includes many existing linear and nonlinear panel data models as special cases. In order to estimate the unknown parameters, factors and factor loadings, we propose a sieve-based generalized method of moments estimation method and we show that under a set of simple identification conditions, all those unknown quantities can be consistently estimated. Further we establish asymptotic distributions of the proposed estimators. In addition, we propose tests for over-identification, specification of factor loading functions, and establish their large sample properties. Moreover, a number of simulation studies are conducted to examine the performance of the proposed estimators and test statistics in finite samples. An empirical example on stock return prediction is studied to demonstrate the usefulness of the proposed framework and corresponding estimation methods and testing procedures.

Suggested Citation

  • Tingting Cheng & Chaohua Dong & Jiti Gao & Oliver Linton, 2022. "GMM Estimation for High-Dimensional Panel Data Models," Monash Econometrics and Business Statistics Working Papers 11/22, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2022-11
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    File URL: https://www.monash.edu/business/ebs/research/publications/ebs/wp11-2022.pdf
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    References listed on IDEAS

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    1. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    2. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    3. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    4. Thompson, Samuel B., 2011. "Simple formulas for standard errors that cluster by both firm and time," Journal of Financial Economics, Elsevier, vol. 99(1), pages 1-10, January.
    5. Breitung, Jörg & Lechner, Michael, 1998. "Alternative GMM methods for nonlinear panel data models," SFB 373 Discussion Papers 1998,81, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Tomohiro Ando & Jushan Bai, 2017. "Clustering Huge Number of Financial Time Series: A Panel Data Approach With High-Dimensional Predictors and Factor Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1182-1198, July.
    7. Chaohua Dong & Jiti Gao & Bin Peng, 2021. "Varying-Coefficient Panel Data Models With Nonstationarity and Partially Observed Factor Structure," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 700-711, July.
    8. Breitung, J. & Lechner, M., 1995. "GMM-Estimation of Nonlinear Models on Panel Data," SFB 373 Discussion Papers 1995,67, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    10. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    11. Dong, Chaohua & Linton, Oliver & Peng, Bin, 2021. "A weighted sieve estimator for nonparametric time series models with nonstationary variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 909-932.
    12. Bai, Jushan & Liao, Yuan, 2017. "Inferences in panel data with interactive effects using large covariance matrices," Journal of Econometrics, Elsevier, vol. 200(1), pages 59-78.
    13. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    14. Arellano, Manuel & Carrasco, Raquel, 2003. "Binary choice panel data models with predetermined variables," Journal of Econometrics, Elsevier, vol. 115(1), pages 125-157, July.
    15. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    16. Dong, Chaohua & Linton, Oliver, 2018. "Additive nonparametric models with time variable and both stationary and nonstationary regressors," Journal of Econometrics, Elsevier, vol. 207(1), pages 212-236.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Linton, O. B. & Rücker, M. & Vogt, M. & Walsh, C., 2024. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Cambridge Working Papers in Economics 2467, Faculty of Economics, University of Cambridge.
    2. Oliver Linton & Maximilian Ruecker & Michael Vogt & Christopher Walsh, 2022. "Estimation and Inference in High-Dimensional Panel Data Models with Interactive Fixed Effects," Papers 2206.12152, arXiv.org, revised Nov 2024.

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    More about this item

    Keywords

    Generalized method of moments; high dimensional moment model; interactive effect; over-identification issue; panel data; sieve method;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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