Matching Bounds: How Choice of Matching Algorithm Impacts Treatment Effects Estimates and What to Do about It

Many major works in social science employ matching to make causal conclusions, but different matches on the same data may produce different treatment effect estimates, even when they achieve similar balance or minimize the same loss function. We discuss reasons and consequences of this problem. We present evidence of this problem by replicating ten papers that use matching and we find that different popular matching algorithms produce inconsistent results. We introduce Matching Bounds: a finite-sample, nonstochastic method that allows analysts to know whether a matched sample that produces different results with the same levels of balance and overall match quality could be obtained from their data. We apply Matching Bounds to a replication of two studies and show that in one case results are robust to this issue and in another they are not.