Matching Strategies for Observational Multilevel Data

When randomized experiments cannot be conducted in practice, propensity score (PS) techniques for matching treated and control units are frequently used for estimating causal treatment effects. Despite the popularity of PS techniques, they are not yet well studied for matching multilevel data where selection into treatment takes place at the lowest level. Two main strategies for matching level-one units can be distinguished: (i) within-cluster matching where level-one units are matched within clusters and (ii) acrosscluster matching where treatment and control units may be matched across clusters. Using a simulation study, we show that both matching strategies are able to produce consistent estimates of the average treatment effect. We also demonstrate that a lack in overlap between treated and control units within clusters cannot directly be compensated by switching to an across-cluster matching strategy.