The propensity score plays an important role in causal inference with observational data. Once the propensity score is available, one can use it to estimate a variety of causal effects in a unified setting. Despite this appeal, a main practical difficulty arises because the propensity score is usually unknown, has to be estimated, and extreme propensity score estimates can lead to distorted inference procedures. To address these limitations, this article proposes to estimate the propensity score by fully exploiting its covariate balancing property. We call the resulting estimator the integrated propensity score (IPS) as it is based on integrated moment conditions. In sharp contrast with other methods that balance only some specific moments of covariates, the IPS aims to balance \textit{all} functions of covariates. Further, the IPS estimator is data-driven, does not rely on tuning parameters such as bandwidths, admits an asymptotic linear representation, and is $\sqrt{n}$-consistent an 查看全文>>