  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.
