Tightening Bounds in Triangular Systems

This note discusses partial identification in a nonparametric triangular system with discrete endogenous regressors and nonseparable errors. Recently, [Jun, Pinkse and Xu (2011, JPX). Tighter Bounds in Triangular Systems. Journal of Econometrics 161(2), 122-128] provides 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