Partial Identification of Nonseparable Models Using Binary Instruments

In this study, we explore the partial identification of nonseparable models with continuous endogenous and binary instrumental variables. We show that structural function is partially identified when it is monotone or concave in an explanatory variable. D'Haultfoeuille and Fevrier (2015) and Torgovitsky (2015) prove the point identification of the structural function under two key assumptions: (a) the conditional distribution functions of an endogenous variable given the instruments have intersections and (b) the structural function is strictly increasing in a scalar unobservable variable. However, we demonstrate that, even if the two assumptions do not hold, monotonicity or concavity provides an identifying power. Point identification is achieved when the structural function is flat or linear in explanatory variables in a given interval