On the Identifying Content of Instrument Monotonicity

TL;DR

This paper investigates the conditions under which the instrument monotonicity assumption refines the identified set of potential outcome distributions in a binary outcome, treatment, and instrument model.

Contribution

It derives necessary and sufficient conditions for when the instrument monotonicity assumption narrows the identified set of potential outcomes.

Findings

Identifies conditions for strict subset relationships in potential outcome distributions.

Provides a theoretical framework for understanding the impact of instrument monotonicity.

Enhances understanding of the assumptions' implications in causal inference models.

Abstract

This paper studies the identifying content of the instrument monotonicity assumption of Imbens and Angrist (1994) on the distribution of potential outcomes in a model with a binary outcome, a binary treatment and an exogenous binary instrument. Specifically, I derive necessary and sufficient conditions on the distribution of the data under which the identified set for the distribution of potential outcomes when the instrument monotonicity assumption is imposed can be a strict subset of that when it is not imposed.