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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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    Cited by:

    1. Daniel J. Lewis & Davide Melcangi & Laura Pilossoph, 2019. "Latent Heterogeneity in the Marginal Propensity to Consume," Staff Reports 902, Federal Reserve Bank of New York.
    2. Mugnier, Martin, 2025. "A simple and computationally trivial estimator for grouped fixed effects models," Journal of Econometrics, Elsevier, vol. 250(C).
    3. Millimet, Daniel L. & Bellemare, Marc, 2023. "Fixed Effects and Causal Inference," IZA Discussion Papers 16202, Institute of Labor Economics (IZA).
    4. Pionati, Alessandro, 2025. "Latent grouped structures in panel data: a review," MPRA Paper 123954, University Library of Munich, Germany.

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    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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