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

Naoya Hashimoto, Yuta Kawakami, Jin Tian

TL;DR: We propose new families of monotonicity assumptions and study the bounding and identification problems for the joint probabilities of potential outcomes and observed variables.

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 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.

Submission Number: 1256