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Profile GMM estimation of panel data models with interactive fixed effects

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  • Hong, Shengjie
  • Su, Liangjun
  • Jiang, Tao

Abstract

This paper studies panel data models with interactive fixed effects where the regressors are allowed to be correlated with the idiosyncratic error terms. We propose a two-step profile GMM estimation procedure to estimate the parameters of interest. In the first step we obtain a preliminary consistent estimate of the slope coefficient via a nuclear-norm-regularization (NNR) based profile GMM procedure. In the second step, via an iterative procedure, we conduct post-NNR profile GMM estimation of the slope coefficient, factors, and factor loadings, with an improved convergence rate for the estimate of the slope coefficient. We establish the asymptotic properties of the preliminary estimates and the iterative estimates, and propose an efficient profile GMM estimator. We also study the determination of the number of factors and propose Hausman tests for the exogeneity of the regressor. Monte Carlo simulations suggest that the proposed estimation and testing methods work well in the determination of the number of factors, the estimation of the model parameters and the test for exogeneity. As an empirical application, we apply our model and method to study the price elasticity of U.S. imports.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:927-948
    DOI: 10.1016/j.jeconom.2022.07.010
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    Cited by:

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    3. Ruiqin Tian & Miaojie Xia & Dengke Xu, 2024. "Profile quasi-maximum likelihood estimation for semiparametric varying-coefficient spatial autoregressive panel models with fixed effects," Statistical Papers, Springer, vol. 65(8), pages 5109-5143, October.
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    7. Jan Ditzen & Yiannis Karavias, 2025. "Interactive, Grouped and Non-separable Fixed Effects: A Practitioner's Guide to the New Panel Data Econometrics," Papers 2507.19099, arXiv.org, revised Oct 2025.
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    9. Wang, Xia & Jin, Sainan & Li, Yingxing & Qian, Junhui & Su, Liangjun, 2025. "On time-varying panel data models with time-varying interactive fixed effects," Journal of Econometrics, Elsevier, vol. 249(PB).
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    13. Zhenhao Gong & Min Seong Kim, 2024. "Improved Inference for Interactive Fixed Effects Model under Cross-Sectional Dependence," Working papers 2024-02, University of Connecticut, Department of Economics.

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: 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
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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