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Many major works in social science employ matching to make causalconclusions, but different matches on the same data may produce differenttreatment effect estimates, even when they achieve similar balance or minimizethe same loss function. We discuss reasons and consequences of this problem. Wepresent evidence of this problem by replicating ten papers that use matchingand we find that different popular matching algorithms produce inconsistentresults. We introduce Matching Bounds: a finite-sample, nonstochastic methodthat allows analysts to know whether a matched sample that produces differentresults with the same levels of balance and overall match quality could beobtained from their data. We apply Matching Bounds to a replication of twostudies and show that in one case results are robust to this issue and inanother they are not.

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