Multi-dimensional latent group structures with heterogeneous distributions

This paper aims to identify the multi-dimensional latent grouped heterogeneity of distributional effects. We consider a panel quantile regression model with additive cross-section and time fixed effects. The cross-section effects and quantile slope coefficients are both characterized by grouped patterns of heterogeneity, but each unit can belong to different groups for cross-section effects and slopes. We propose a composite-quantile approach to jointly estimate multi-dimensional group memberships, slope coefficients, and fixed effects. We show that using multiple quantiles improves clustering accuracy if memberships are quantile-invariant. We apply the methods to examine the relationship between managerial incentives and risk-taking behavior.