Clustering for Multi-Dimensional Heterogeneity

Xu Cheng is an associate professor of economics at the University of Pennsylvania, Her research covers a wide range of topics in econometrics, such as identification issues of econometric models, likelihood and moment based estimation and inference, as well as shrinkage estimation.  Her research has appeared on Econometrica, Review of Economic Studies, Quantitative Economics, Journal of Econometrics, Econometric Theory, and Journal of Business & Economic Statistics, among others. She currently serves as the Co-editor of Econometric Theory, and an associate editor of Quantitative Economics, Econometrics Journal and Econometrics Review, and was an associate editor of Journal of Econometrics, Econometric Theory  and Journal of Business & Economic Statistics.

This paper provides a new multi-dimensional clustering approach for unobserved heterogeneity in panel data models. Each unit is associated with multiple clusters. For example, a firm can belong to the high productivity group and the low output elasticity group. In contrast, the standard one-dimensional clustering approach would be based on separate groups for each productivity-elasticity pair. Our approach provides substantial gains in estimation accuracy when unobserved features have sparse interactions, e.g., there are only a few firms with high productivity and low output elasticity. We propose an estimator for the unobserved group memberships and the group-specific and common parameters in a nonlinear GMM framework and derive its large sample properties. In particular, we provide the first classification consistency result in a nonlinear GMM setup. We re-evaluate the rise of aggregate markup in De Loecker, Eeckhout, and Unger (2018) by replacing their sector-specific production functions with a cluster-based one. We find that the upward trajectory persists, but the magnitude is less pronounced after accounting for multi-dimensional heterogeneity.