Doubly Robust Estimation of Causal Effects Using Primal-Dual Optimization

• Activity Number: 33
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Qingyuan Zhao* and Daniel Percival
• Companies: Stanford University and Google
• Keywords: Causal Inference ; Entropy Balancing ; Double Robustness ; Convex Optimization

Abstract

In observational studies, the treatment is not randomly assigned, and so subjects in the treatment group may not be directly comparable to those in the control. Entropy Balancing (Hainmueller, 2011) is a recently proposed alternative to traditional estimators of mean causal effect for observational studies. It solves an entropy maximization problem under the constraints on the moments of covariates of each experimental group. In this paper, we show that Entropy Balancing (EB) is doubly robust, that is, it is consistent estimator of average treatment effect on the treated if the control outcome or the logs odds of the probability of selection for the treatment group are linear in the same covariate moments constrained by the EB optimization problem. Moreover, we show EB achieves the minimal asymptotic variance if both the outcome and log odds have the former linearity property. We show that this doubly robust property has an exact correspondence to the primal- dual optimization that is used to solve EB. We additionally compare Entropy Balancing with existing causal effect estimators using both simulations and real data.