Towards estimation of individual causal effects: The use of a prior for the correlation between potential outcomes

Abstract

As people differ in how they react to events, properly modeling heterogeneous responses to treatment requires the estimation of individual causal effects (ICE). Under the potential outcomes framework, we may define ICE as the difference between Yi(1), the potential outcome for individual i where a manipulation is present, and Yi(0), the potential outcome of i where the manipulation is absent. The ICE for individiual i is thus simply calculated as: ICEi = Yi(1) ð€€€ Yi(0). Since only one of Yi(0) or Yi(1) can be observed, ICE is undefined from the data. Hence, estimation of ICE requires additional assumptions on the counterfactual (unobserved) condition. In the current paper we assess whether we can use multiple imputation for estimation of ICE, suggest the use a prior for the correlation between the potential outcomes to deal with the identification problem, and propose evaluation criteria to evaluate predictive performance of ICE estimation. We found that: a) multiple imputation can be used to estimate ICE, b) ICE estimation is affected by the correlation between Y (1) and Y (0), and c) the place of the missing potential outcome of i relative to the prior determines whether ICE estimation is feasible.