Confidence set for group membership

Our confidence set quantifies the statistical uncertainty from data-driven group assignments in grouped panel models. It covers the true group memberships jointly for all units with pre-specified probability and is constructed by inverting many simultaneous unit-specific one-sided tests for group membership. We justify our approach under $N, T \to \infty$ asymptotics using tools from high-dimensional statistics, some of which we extend in this paper. We provide Monte Carlo evidence that the confidence set has adequate coverage in finite samples.An empirical application illustrates the use of our confidence set.