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 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.
The (unheralded) first step in many applications of automated text analysis involves selecting keywords to choose documents from a large text corpus for further study. Although all substantive results depend on this choice, researchers usually pick keywords in ad hoc ways that are far from optimal and usually biased. Paradoxically, this often means that the validity of the most sophisticated text analysis methods depend in practice on the inadequate keyword counting or matching methods they are designed to replace. Improved methods of keyword selection would also be valuable in many other areas, such as following conversations that rapidly innovate language to evade authorities, seek political advantage, or express creativity; generic web searching; eDiscovery; look-alike modeling; intelligence analysis; and sentiment and topic analysis. We develop a computer-assisted (as opposed to fully automated) statistical approach that suggests keywords from available text without needing structured data as inputs. This framing poses the statistical problem in a new way, which leads to a widely applicable algorithm. Our specific approach is based on training classifiers, extracting information from (rather than correcting) their mistakes, and summarizing results with Boolean search strings. We illustrate how the technique works with analyses of English texts about the Boston Marathon Bombings, Chinese social media posts designed to evade censorship, among others.