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Approximating Grouped Fixed Effects Estimation via Fuzzy Clustering Regression

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Abstract

We propose a new, computationally-efficient way to approximate the “grouped fixed-effects” (GFE) estimator of Bonhomme and Manresa (2015), which estimates grouped patterns of unobserved heterogeneity. To do so, we generalize the fuzzy C-means objective to regression settings. As the regularization parameter m approaches 1, the fuzzy clustering objective converges to the GFE objective; moreover, we recast this objective as a standard Generalized Method of Moments problem. We replicate the empirical results of Bonhomme and Manresa (2015) and show that our estimator delivers almost identical estimates. In simulations, we show that our approach delivers improvements in terms of bias, classification accuracy, and computational speed.

Suggested Citation

  • Daniel J. Lewis & Davide Melcangi & Laura Pilossoph & Aidan Toner-Rodgers, 2022. "Approximating Grouped Fixed Effects Estimation via Fuzzy Clustering Regression," Staff Reports 1033, Federal Reserve Bank of New York.
    • Handle: RePEc:fip:fednsr:94840
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    References listed on IDEAS

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    1. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    2. 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.
    3. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    4. Martin Mugnier, 2022. "Make the Difference! computationally Trivial Estimators for Grouped Fixed Effects Models," Working Papers 2022-07, Center for Research in Economics and Statistics.
    5. Martin Mugnier, 2022. "A Simple and Computationally Trivial Estimator for Grouped Fixed Effects Models," Papers 2203.08879, arXiv.org, revised Dec 2023.
    6. Jaeho Kim & Le Wang, 2019. "Hidden group patterns in democracy developments: Bayesian inference for grouped heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 1016-1028, September.
    7. Su, Liangjun & Ju, Gaosheng, 2018. "Identifying latent grouped patterns in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 554-573.
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    More about this item

    Keywords

    clustering; unobserved heterogeneity; panel data;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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