Abstract: In structural econometric models featuring individual-specific parameters, managing dimensionality and enhancing interpretability often involves clustering the population and estimating the model within these clusters. This paper examines a scenario where individuals are grouped but retain heterogeneity within each group, an issue that may persist asymptotically. We address the challenge of interpreting estimations from oracle estimators that assume within-group homogeneity, as this assumption can lead to inaccuracies due to potential misspecification. Instead, we suggest focusing on group-specific average marginal effects.
Our approach integrates established methods: the mean-group estimator and the correction for clustering bias, both of which are common in nonlinear panel data models. The novelty of our work lies in synthesizing these techniques to conduct post-clustering inference. We introduce a debiased mean-group estimator that performs robustly regardless of within-group heterogeneity, making it a valuable tool when such heterogeneity is uncertain.
Additionally, we contribute to the literature by establishing the consistency and non-asymptotic bounds of a convex clustering algorithm in the context of econometrics, where individual-specific parameters are estimated with sampling error. We demonstrate that while sampling error can obscure group structures in finite samples, it does not undermine clustering consistency provided that $T$ grows faster than a polynomial of $\log(n)$. Our results also imply that the debiased mean-group estimator can be applied with other clustering methods, such as the popular K-means algorithm.