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 the structural function is partially identified when it is monotone or concave in the explanatory variable. D’Haultfœuille and Février (2015, Econometrica 83(3), 1199–1210) and Torgovitsky (2015, Econometrica 83(3), 1185–1197) prove the point identification of the structural function under a key assumption that the conditional distribution functions of the endogenous variable for different values of the instrumental variables have intersections. We demonstrate that, even if this assumption does not hold, monotonicity and concavity provide identification power. Point identification is achieved when the structural function is flat or linear with respect to the explanatory variable over a given interval. We compute the bounds using real data and show that our bounds are informative.