Approximating grouped fixed effects estimation via fuzzy clustering regression

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 clustering exponent $m$ approaches 1, the fuzzy clustering objective converges to the GFE objective, which we recast 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 offers improvements in terms of bias, classification accuracy, and computational speed.