Clustering for Multi-Dimensional Heterogeneity with an Application to Production Function Estimation

This paper studies the estimation of multi-dimensional heterogeneous parameters in a nonlinear panel data model with endogeneity. These heterogeneous parameters are modeled with group patterns. Through estimating multiple memberships for each unit, the proposed method is robust to sparse interactions; in other words, certain combinations of unobserved features are less common compared to other combinations. We estimate the memberships along with the group-specific and common parameters in a nonlinear GMM framework and derive their large sample properties. Finally, we apply this approach to the estimation of production function and re-evaluate the trajectory of the aggregate markup.

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