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Theory and methods of panel data models with interactive effects

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  • Bai, Jushan
  • Li, Kunpeng

Abstract

This paper considers the maximum likelihood estimation of the panel data models with interactive effects. Motivated in economics and other social sciences, a notable feature of the model is that the explanatory variables are correlated with the unobserved effects. The usual within-group estimator is inconsistent. Existing methods for consistent estimation are either designed for panel data with short time periods or are less efficient. The maximum likelihood estimator has desirable properties and is easy to implement, as illustrated by the Monte Carlo simulations. This paper develops the inferential theory for the maximum likelihood estimator, including consistency, rate of convergence and the limiting distributions. We further extend the model to include time-invariant regressors and common regressors (cross-section invariant). The regression coefficients for the time-invariant regressors are time-varying, and the coefficients for the common regressors are cross-sectionally varying.

Suggested Citation

  • Bai, Jushan & Li, Kunpeng, 2010. "Theory and methods of panel data models with interactive effects," MPRA Paper 43441, University Library of Munich, Germany, revised Dec 2012.
    • Handle: RePEc:pra:mprapa:43441
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    References listed on IDEAS

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    Cited by:

    1. Arteaga-Molina, Luis A. & Rodríguez-Poo, Juan M., 2019. "Empirical likelihood based inference for a categorical varying-coefficient panel data model with fixed effects," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 110-124.
    2. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    3. Li, Kathleen T. & Bell, David R., 2017. "Estimation of average treatment effects with panel data: Asymptotic theory and implementation," Journal of Econometrics, Elsevier, vol. 197(1), pages 65-75.
    4. Jia Chen, 2019. "Estimating latent group structure in time-varying coefficient panel data models," The Econometrics Journal, Royal Economic Society, vol. 22(3), pages 223-240.
    5. Archer Gong Zhang & Jiahua Chen, 2023. "Optimal Estimation under a Semiparametric Density Ratio Model," Papers 2309.09103, arXiv.org.
    6. Degui Li & Junhui Qian & Liangjun Su, 2016. "Panel Data Models With Interactive Fixed Effects and Multiple Structural Breaks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1804-1819, October.

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    More about this item

    Keywords

    factor error structure; factors; factor loadings; maximum likelihood; principal components; within-group estimator; simultaneous equations;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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