Confidence set for group membership

TL;DR

This paper introduces a confidence set for group membership in panel models that quantifies uncertainty and guarantees joint coverage, using high-dimensional statistical methods and validated through simulations and an empirical example.

Contribution

It develops a novel confidence set construction for group memberships that accounts for data-driven assignments and provides theoretical guarantees under large-sample asymptotics.

Findings

The confidence set achieves accurate coverage in finite samples.

Monte Carlo simulations validate the theoretical properties.

Application demonstrates practical usefulness in empirical settings.

Abstract

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.