Confidence set for group membership

Our confidence set quantifies the statistical uncertainty from data-driven cluster assignment in clustered panel models. It covers the true cluster 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 or develop in this paper. We provide an empirical application as well as Monte Carlo evidence that the confidence set has adequate coverage in finite samples.