Statistics Department Seminar Series: Luke Miratrix, Professor, Department of Statistics, Harvard Graduate School of Education

Matching promises simple and transparent causal inferences for observational data, making it an attractive approach in many settings, especially given its easily communicated and intuitive rationale. Matching methods “match” treated units to control units with similar covariates, with the goal of achieving joint covariate balance between treated and control units, as would be expected in a randomized experiment. In practice, however, standard matching methods often perform poorly compared to more recent approaches such as response-surface modeling and balancing. Finding close matches for treated units becomes particularly challenging when there are many covariates and overlap is low, which can lead to imbalanced matched treatment groups, biased effect estimates, or low effective sample sizes. Building on a host of literature, including synthetic control methods, classic matching approaches, and coarsened exact matching, we propose Caliper Synthetic Matching (CSM) to address challenges with finding quality matches while preserving simple and transparent matching diagnostics. CSM, a version of radial matching, is an adaptive caliper matching method that utilizes locally built synthetic controls to adjust for inexact matches. By combining adaptive calipers and synthetic controls, CSM produces data-driven bounds on potential extrapolation biases while exploiting local linearity to interpolate in a principled manner. Due to the local nature of CSM, we can also detect which units are more difficult to match and assess degree of overlap. We can even locally adapt caliper width to more tightly control bias in information dense regions. We show that CSM belongs to the monotonic imbalance bounding (MIB) class of matching methods, and that it improves upon the bias bounds for popular MIB methods such as coarsened exact matching. We finally give theoretical results on an inferential strategy that allows for reuse of controls by different treated units (matching with replacement).