Confidence Set for Group Membership

 Associate professor of Economics, NYU Shanghai

OKUI, Ryo's curriculum vitae

We consider panel models in which heterogeneity is driven by a latent group structure. We propose procedures for calculating a confidence set for group membership. Recently, Bonhomme and Manresa (2015) develop methods to simultaneously estimate group memberships and group-specific parameters. Our confidence sets can be used to quantify the uncertainty inherent in these estimated group mem- berships. We consider uniform confidence sets that cover the true group membership for all units with a pre-specified probability as well as unitwise confidence sets. Our approach exploits the fact that the problem of sorting units into groups can be characterized by a large number of moment inequalities. Building on recent work by Chernozhukov, Chetverikov and Kato (2014), we develop procedures for testing the group membership of all units simultaneously. The confidence sets are derived by inverting this test. We use analytical critical values obtained from the theory of self-normalized sums as well as bootstrap critical values. The theoretical justification of our methods is based on large N, T asymptotics, where T can be very small compared to N. For both analytical and bootstrap critical values, we suggest a finite sample adjustment that is motivated by the finite sample behavior of the test statistic under normal errors. This adjustment gives confidence sets that have good coverage even for very small T and for non-normal errors. To illustrate their empirical relevance, we apply our methods to the classification of countries according to their respective paths towards democratization. The application illustrates that our procedures can yield an informative confidence set even if the panel is very short.