Stochastic Potential Choices and Outcomes

2026-07-23

AI Summary

This study addresses a key limitation of traditional instrumental variable (IV) models, which assume deterministic relationships between treatment selection and potential outcomes under an instrument, thereby failing to capture stochastic decision-making in real-world settings. To overcome this restriction, the paper develops a micro-founded framework in which both potential outcomes and treatment choices exhibit individual-level randomness. Response types are redefined as state-dependent treatment probabilities coupled with distributions of potential outcomes, grounded in expected utility maximization subject to information constraints. Within this framework, conventional IV estimands are reinterpreted not merely as local average treatment effects for compliers, but as population-weighted averages of treatment effects, where weights correspond to individual changes in treatment probability induced by the instrument. This approach yields a more flexible and interpretable characterization of treatment effect heterogeneity.

Abstract

Applied econometricians typically model each individual as having fixed outcomes under treatment and control and, in instrumental-variables (IV) settings, fixed treatment decisions under each value of the instrument. This paper asks what changes when outcomes and treatment allocations or choices are stochastic at the individual level. In the model, each individual has a stable (but possibly stochastic) response type consisting of two objects: a treatment choice probability under each state and a potential outcome distribution under each treatment-state pair. These stochastic potential outcomes change the interpretation of some familiar estimators. For instance, in the deterministic IV model, the estimand identifies treatment effect only for compliers - those whose treatment status switches with the instrument. Under stochastic treatment allocation or choice there is no such subgroup: the estimand averages effects over all individuals, weighting each by how much the instrument, policy, or assignment rule moves their probability of treatment. The paper then gives an information-based foundation for stochastic choice, in which individuals act on expected gains given their information.

Problem

• stochastic potential outcomes
• instrumental variables
• treatment effect
• stochastic choice
• compliers

Innovation

• stochastic potential outcomes
• instrumental variables
• treatment effect heterogeneity
• randomized choice
• information-based decision