Subgroup Balancing Propensity Score

We investigate the estimation of subgroup treatment effects with observational data. Existing propensity score matching and weighting methods are mostly developed for estimating overall treatment effect. Although the true propensity score should balance covariates for the subgroup populations, the estimated propensity score may not balance covariates for the subgroup samples. We propose the subgroup balancing propensity score (SBPS) method, which selects, for each subgroup, to use either the overall sample or the subgroup sample to estimate propensity scores for units within that subgroup, in order to optimize a criterion accounting for a set of covariate-balancing conditions for both the overall sample and the subgroup samples. We develop a stochastic search algorithm for the estimation of SBPS when the number of subgroups is large. We demonstrate through simulations that the SBPS can improve the performance of propensity score matching in estimating subgroup treatment effects. We then apply the SBPS method to data from the Italy Survey of Household Income and Wealth (SHIW) to estimate the treatment effects of having debit card on household consumption for different income groups.