Approximating Grouped Fixed Effects Estimation via Fuzzy Clustering Regression

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Staff Reports

Approximating Grouped Fixed Effects Estimation via Fuzzy Clustering Regression

Number 1033
September 2022

JEL classification: C23, C63

Authors: Daniel J. Lewis, Davide Melcangi, Laura Pilossoph, and Aidan Toner-Rodgers

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.

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Author Disclosure Statement(s)

Daniel Lewis
The author declares that (s)he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.

Davide Melcangi
I declare that I have no relevant or material financial interests that relate to the research described in this paper.

Laura Pilossoph
I, Laura Pilossoph, declare that I have no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.

Aidan Toner-Rodgers
The author declares that (s)he has no relevant or material financial interests that relate to the research described in this paper. Prior to circulation, this paper was reviewed in accordance with the Federal Reserve Bank of New York review policy, available at https://www.newyorkfed.org/research/staff_reports/index.html.

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