Tightening bounds in triangular systems

•We study partial identification in a nonparametric triangular system.•We consider a triangular system with discrete endogenous regressors.•We propose a simple idea that allows to improve existing bounds in the literature.

This note discusses partial identification in a nonparametric triangular system with discrete endogenous regressors and nonseparable errors. Recently, Jun et al. (2011, JPX) provide bounds on the structural function evaluated at particular values using exclusion, exogeneity and rank conditions. We propose a simple idea that often allows to improve the JPX bounds without invoking a new set of assumptions. Moreover, we show how our idea can be used to tighten existing bounds on the structural function in more general triangular systems.