We propose a simplified approach to matching for causal inference that simultaneously optimizes balance (similarity between the treated and control groups) and matched sample size. Existing approaches either fix the matched sample size and maximize balance or fix balance and maximize sample size, leaving analysts to settle for suboptimal solutions or attempt manual optimization by iteratively tweaking their matching method and rechecking balance. To jointly maximize balance and sample size, we introduce the matching frontier, the set of matching solutions with maximum possible balance for each sample size. Rather than iterating, researchers can choose matching solutions from the frontier for analysis in one step. We derive fast algorithms (about one million times faster than the best existing approach) that calculate the matching frontier, for several commonly used balance metrics. We demonstrate with analyses of the effect of sex on judging and job training programs that show how the methods we introduce can extract new knowledge from existing data sets.
Software that implements all our ideas is available at http://projects.iq.harvard.edu/frontier.