Stochastic Potential Choices and Outcomes

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 discrete subgroup: the estimand averages effects over the population, weighing each individual 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. Finally, repeated choices give the stable-kernel formulation empirical content: short panels identify moments of individual treatment probabilities, while long panels identify the joint dependence between treatment effects and the probability movements induced by an instrument or policy.