Maximum Entropy Estimation of Heterogeneous Causal Effects

For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the outcome. We assume a generalized version of the stable unit treatment value assumption, but we do not assume any version of strongly ignorable treatment assignment. Instead of conducting a sensitivity analysis, we utilize the principle of maximum entropy to estimate the distribution of causal effects. We develop a principled middle-way between extreme explanations of the observed data: we do not conclude that an observed association is wholly spurious, and we do not conclude that it is wholly causal. Rather, our conclusions are tempered and we conclude that the association is part spurious and part causal. In an example application we apply our methodology to analyze an observed association between marijuana use and hard drug use.