Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions

TL;DR

This paper develops new methods for bounding and identifying joint probabilities of potential outcomes in causal inference with discrete treatments and outcomes, using monotonicity assumptions and linear programming.

Contribution

It introduces novel monotonicity assumptions and formulates the bounding problem as a linear program, enabling partial identification and potential full identification of joint probabilities.

Findings

New bounds for joint probabilities under monotonicity

Linear programming approach for bounding problems

Numerical validation with real-world data

Abstract

Evaluating joint probabilities of potential outcomes and observed variables, and their linear combinations, is a fundamental challenge in causal inference. This paper addresses the bounding and identification of these probabilities in settings with discrete treatment and discrete ordinal outcome. We propose new families of monotonicity assumptions and formulate the bounding problem as a linear programming problem. We further introduce a new monotonicity assumption specifically to achieve identification. Finally, we present numerical experiments to validate our methods and demonstrate their application using real-world datasets.