Primary Submission Category: Instrumental Variables
A Fully Stochastic Update to the Potential Outcome Framework: Never Too LATE
Authors: Hanti Lin,
Presenting Author: Hanti Lin*
Dawid (2000) raises a philosophical objection to the potential outcome framework along with its application to the local average treatment effect (LATE). His concern is that this framework makes a very strong assumption, that every individual’s potential outcomes are deterministic, which appears essential to the identification result about the LATE. I address this philosophical challenge by introducing a fully stochastic update to the potential outcome framework, which improves upon the partially stochastic account due to Small et al. (2017). Here is the idea: each individual’s potential outcomes are first rendered fully stochastic, following Robins and Greenland (1991), and their probabilities—called potential probabilities—are then treated as parameters of an appropriate causal Bayes net (which comes with the causal Markov assumption). Everyone has a degree of compliance, defined as a difference between two potential probabilities; defiers are refined to be those having a negative degree of compliance. I prove that, in this fully stochastic setting, if there are no defiers, then the usual IV estimand identifies a new quantity. This new quantity reduces to the LATE in the deterministic setting, where each individual’s potential probabilities are 0 or 1. I close by arguing that the proposed marriage between causal Bayes nets and the potential outcome framework is, in specific ways, superior to Pearl’s (2009) nonparametric structural equation models.