This paper revisits testability of complementarity in economic models with multiple equilibria studied by Echenique and Komunjer (2009). We find that Echenique and Komunjer’s (2009) testable implications on extreme quantiles can be implied by a weaker version of their tail condition without...

This note applies large deviation-based optimality theory to evaluate treatment rules for treatment assignment problems. We find nearly optimal treatment rules whose asymptotic maximum large deviation risks can be arbitrary close to the corresponding minimax bounds.