Matching estimators are widely used in statistical data analysis. However, the distribution of matching estimators has been derived only for particular cases (Abadie and Imbens, 2006). This article establishes a martingale representation for matching estimators. This representation allows the...

We offer a new strategy to identify the distribution of treatment effects using data from the Infant Health and Development Program (IHDP), a relatively understudied early-childhood intervention for low birth-weight infants. We introduce a new policy parameter, QCD, which denotes quantiles of...

Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using...

We derive nonparametric sharp bounds on average treatment effects with an instrumental variable (IV) and use them to evaluate the effectiveness of the Job Corps (JC) training program for disadvantaged youth. We concentrate on the population average treatment effect (ATE) and the average...

We consider inference in regression discontinuity designs when the running variable only takes a moderate number of distinct values. In particular, we study the common practice of using confidence intervals (CIs) based on standard errors that are clustered by the running variable. We derive...

In a treatment effect model with unconfoundedness, treatment assignments are not only independent of potential outcomes given the covariates, but also given the propensity score alone. Despite this powerful dimension reduction property, adjusting for the propensity score is known to lead to an...

This paper proposes a decomposition of the composition effect, i.e. the part of the observed between-group difference in the distribution of some economic outcome that can be explained by differences in the distribution of covariates. Our decomposition contains three types of components: (i) the...

This paper shows nonparametric identification of quantile treatment effects (QTE) in the regression discontinuity design. The distributional impacts of social programs such as welfare, education, training programs and unemployment insurance are of large interest to economists. QTE are an...

This paper assesses the effectiveness of unconfoundedness-based estimators of mean effects for multiple or multivalued treatments in eliminating biases arising from nonrandom treatment assignment. We evaluate these multiple treatment estimators by simultaneously equalizing average outcomes among...

An important goal when analyzing the causal effect of a treatment on an outcome is to understand the mechanisms through which the treatment causally works. We define a causal mechanism effect of a treatment and the causal effect net of that mechanism using the potential outcomes framework. These...