A Constructive GAN-based Approach to Exact Estimate Treatment Effect without Matching

Abstract

Matching has become the mainstream in counterfactual inference, with which selection bias between sample groups can be significantly eliminated. However in practice, when estimating average treatment effect on the treated (ATT) via matching, no matter which method, the trade-off between estimation accuracy and information loss constantly exist. Attempting to completely replace the matching process, this paper proposes the GAN-ATT estimator that integrates generative adversarial network (GAN) into counterfactual inference framework. Through GAN machine learning, the probability density functions (PDFs) of samples in both treatment group and control group can be approximated. By differentiating conditional PDFs of the two groups with identical input condition, the conditional average treatment effect (CATE) can be estimated, and the ensemble average of corresponding CATEs over all treatment group samples is the estimate of ATT. Utilizing GAN-based infinite sample augmentations, problems in the case of insufficient samples or lack of common support domains can be easily solved. Theoretically, when GAN could perfectly learn the PDFs, our estimators can provide exact estimate of ATT. To check the performance of the GAN-ATT estimator, three sets of data are used for ATT estimations: Two toy data sets with 1/2 dimensional covariate inputs and constant/covariate-dependent treatment effect are tested. The estimates of GAN-ATT are proved close to the ground truth and are better than traditional matching approaches; A real firm-level data set with high-dimensional input is tested and the applicability towards real data sets is evaluated by comparing matching approaches. Through the evidences obtained from the three tests, we believe that the GAN-ATT estimator has significant advantages over traditional matching methods in estimating ATT.