INTRODUCTION

The propensity score matching approach discussed in the previous chapter was aimed primarily at settings where the focus is on estimating treatment effects for the subset of treated units. The specific plan was to select a set of controls with a joint distribution of covariates similar to that for the treated units and discard the remaining controls. In the current chapter, we discuss a different approach to improving covariate balance. Starting with observations on covariates and treatment status for a sample of units with only limited overlap in terms of covariates, we construct a subsample that has a more substantial degree of overlap. We do so by discarding some units in the treatment group and some in the control group. For the resulting trimmed sample, we focus on estimating causal effects of the treatment versus control. By trimming the sample, this method generally alters the estimand, by changing the reference population. In that sense, this method sacrifices some external validity – the eventual estimators are less likely to be valid for typical (e.g., average) treatment effects in the original sample. The advantage is that the internal validity may be improved because estimators for causal effects in the trimmed sample are likely to be more credible and accurate than estimators for causal effects in the original, full sample. This primacy of internal validity, at the expense of external validity, is a general theme in this book as well as in the literature on design of randomized experiments. In studies of causal effects, there is often a trade-off between internal and external validity, with typically more focus on internal validity: given a well-defined population of interest, having a credible and precise answer for a subpopulation is often considered more important than a controversial (in the sense of relying on dubious assumptions) or imprecise answer for the full (original target) population.

The key to the trimming is the propensity score, the conditional probability of receiving the treatment given the pre-treatment variables.