Bias-Reduced Estimation of Finite Mixtures: An Application to Latent Group Structures in Panel Data

TL;DR

This paper introduces a bias-reduction method for finite mixture models in econometrics, improving parameter estimates especially in small samples and overlapping components, with theoretical and empirical validation.

Contribution

It proposes a novel estimation approach using a classification-based likelihood that reduces finite-sample bias in finite mixture models.

Findings

Bias in standard MLE diminishes with larger samples or more distinct components.

The proposed method outperforms standard MLE in simulations regarding bias and mean squared error.

Empirical application shows a 17.6% reduction in out-of-sample prediction error.

Abstract

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias in all parameters under mild regularity conditions. The bias arises from the influence of outliers in component densities with unbounded or large support and increases with the degree of overlap among mixture components. I show that maximizing the classification-mixture likelihood function, equipped with a consistent classifier, yields parameter estimates that are less biased than those obtained by standard maximum likelihood estimation (MLE). I then derive the asymptotic distribution of the resulting estimator and provide conditions under which oracle efficiency is achieved. Monte Carlo simulations show that conventional mixture MLE exhibits pronounced finite-sample bias, which diminishes as the sample size or the statistical distance between component densities tends to infinity. The simulations further show that the proposed estimation strategy generally outperforms standard MLE in finite samples in terms of both bias and mean squared errors under relatively weak assumptions. An empirical application to latent group panel structures using health administrative data shows that the proposed approach reduces out-of-sample prediction error by approximately 17.6% relative to the best results obtained from standard MLE procedures.