Blocked Clusterwise Regression

Document pages: 46 pages

Abstract: A recent literature in econometrics models unobserved cross-sectionalheterogeneity in panel data by assigning each cross-sectional unit aone-dimensional, discrete latent type. Such models have been shown to allowestimation and inference by regression clustering methods. This paper ismotivated by the finding that the clustered heterogeneity models studied inthis literature can be badly misspecified, even when the panel has significantdiscrete cross-sectional structure. To address this issue, we generalizeprevious approaches to discrete unobserved heterogeneity by allowing each unitto have multiple, imperfectly-correlated latent variables that describe itsresponse-type to different covariates. We give inference results for a k-meansstyle estimator of our model and develop information criteria to jointly selectthe number clusters for each latent variable. Monte Carlo simulations confirmour theoretical results and give intuition about the finite-sample performanceof estimation and model selection. We also contribute to the theory ofclustering with an over-specified number of clusters and derive new convergencerates for this setting. Our results suggest that over-fitting can be severe ink-means style estimators when the number of clusters is over-specified.