The term multi-valued treatment effects refers to a collection of population parameters capturing the impact of a treatment variable on an outcome variable when the treatment takes multiple values. For example, in labour training programmes participants receive different hours of training or in...

Empirical work on the wage impact of training has noted that unobserved heterogeneity of training participants should play a role. The expected return to training, which partly depends on unobservable characteristics, is likely to be a crucial criterion in the decision to take part in training...

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step, but retain a fully nonparametric specification in the first step. Such estimators exist in many economic applications, including a wide range of missing data and...

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment...

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...

A key assumption in regression discontinuity analysis is that units cannot manipulate the value of their running variable in a way that guarantees or avoids assignment to the treatment. Standard identification arguments break down if this condition is violated. This paper shows that treatment...

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...

Given a set of baseline assumptions, a breakdown frontier is the boundary between the set of assumptions which lead to a specific conclusion and those which do not. In a potential outcomes model with a binary treatment, we consider two conclusions: First, that ATE is at least a specific value...

We bound the distribution of treatment effects under plausible and testable assumptions on the joint distribution of potential outcomes, namely that potential outcomes are mutually stochastically increasing. We show how to test the empirical restrictions implied by those assumptions. The...

Outliers can be particularly hard to detect, creating bias and inconsistency in the semi-parametric estimates. In this paper, we use Monte Carlo simulations to demonstrate that semi-parametric methods, such as matching, are biased in the presence of outliers. Bad and good leverage point outliers...