Bounds and Identification of Joint Probabilities of Potential Outcomes and Observed Variables under Monotonicity Assumptions
This work addresses a fundamental challenge in causal inference for researchers and practitioners, though it appears incremental as it builds on existing monotonicity assumptions.
The paper tackles the problem of bounding and identifying joint probabilities of potential outcomes and observed variables in causal inference with discrete treatment and ordinal outcomes, proposing new monotonicity assumptions and formulating the problem as linear programming, with validation through numerical experiments and real-world datasets.
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.