Partial Identification of Nonseparable Models using Binary Instruments

TL;DR

This paper investigates how to partially identify structural functions in nonseparable models with continuous endogenous variables and binary instruments, especially under monotonicity or concavity assumptions, even without the intersection condition.

Contribution

It extends existing identification results by showing that monotonicity and concavity can provide partial identification without the intersection assumption.

Findings

Bounds are informative when structural function is flat or linear.

Monotonicity and concavity help identify the structural function.

Real data application demonstrates practical usefulness.

Abstract

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'Haultfoeuille and Fevrier (2015) and Torgovitsky (2015) 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 identifying 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.