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A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models

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  • Martin Mugnier
Abstract
This paper introduces a new fixed effects estimator for linear panel data models with clustered time patterns of unobserved heterogeneity. The method avoids non-convex and combinatorial optimization by combining a preliminary consistent estimator of the slope coefficient, an agglomerative pairwise-differencing clustering of cross-sectional units, and a pooled ordinary least squares regression. Asymptotic guarantees are established in a framework where $T$ can grow at any power of $N$, as both $N$ and $T$ approach infinity. Unlike most existing approaches, the proposed estimator is computationally straightforward and does not require a known upper bound on the number of groups. As existing approaches, this method leads to a consistent estimation of well-separated groups and an estimator of common parameters asymptotically equivalent to the infeasible regression controlling for the true groups. An application revisits the statistical association between income and democracy.

Suggested Citation

  • Martin Mugnier, 2022. "A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models," Papers 2203.08879, arXiv.org, revised Sep 2024.
    • Handle: RePEc:arx:papers:2203.08879
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    References listed on IDEAS

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    1. Daron Acemoglu & Simon Johnson & James A. Robinson & Pierre Yared, 2008. "Income and Democracy," American Economic Review, American Economic Association, vol. 98(3), pages 808-842, June.
    2. Krasnokutskaya, Elena & Song, Kyungchul & Tang, Xun, 2022. "Estimating unobserved individual heterogeneity using pairwise comparisons," Journal of Econometrics, Elsevier, vol. 226(2), pages 477-497.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    4. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    5. Hyungsik Roger Moon & Martin Weidner, 2018. "Nuclear Norm Regularized Estimation of Panel Regression Models," Papers 1810.10987, arXiv.org, revised Jun 2023.
    6. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    7. Manuel Arellano & Stephen Bond, 1991. "Some Tests of Specification for Panel Data: Monte Carlo Evidence and an Application to Employment Equations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(2), pages 277-297.
    8. Karyne B. Charbonneau, 2017. "Multiple fixed effects in binary response panel data models," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 1-13, October.
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    Cited by:

    1. Daniel J. Lewis & Davide Melcangi & Laura Pilossoph & Aidan Toner‐Rodgers, 2023. "Approximating grouped fixed effects estimation via fuzzy clustering regression," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(7), pages 1077-1084, November.
    2. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    3. Thomas Wiemann, 2023. "Optimal Categorical Instrumental Variables," Papers 2311.17021, arXiv.org, revised May 2024.

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