Assumptions and Bounds in the Instrumental Variable Model

TL;DR

This paper provides proofs for bounds and assumptions in the instrumental variable model with binary outcomes and treatments, extending previous results to instruments with multiple states.

Contribution

It offers rigorous proofs for bounds in the IV model with multi-state instruments, clarifying assumptions and extending prior theoretical results.

Findings

Validated bounds for binary IV models with multi-state instruments

Extended theoretical framework for IV assumptions

Clarified conditions under which bounds hold

Abstract

In this note we give proofs for results relating to the Instrumental Variable (IV) model with binary response $Y$ and binary treatment $X$, but with an instrument $Z$ with $K$ states. These results were originally stated in Richardson & Robins (2014), "ACE Bounds; SEMS with Equilibrium Conditions," arXiv:1410.0470.