We study the interpretation of regressions with multiple treatments and flexible controls. Such regressions are often used to analyze stratified randomized control trials with multiple intervention arms, to estimate value-added (for, e.g., teachers) with observational data, and to leverage the...

We derive general, yet simple, sharp bounds on the size of the omitted variable bias for a broad class of causal parameters that can be identified as linear functionals of the conditional expectation function of the outcome. Such functionals encompass many of the traditional targets of...

Price theory says that the most important effects of policy and technological change are often found beyond their first point of contact. This appears opposed to econometric methods that rule out spillovers of one person's treatment on another's outcomes. This paper uses the industry model from...

Recent work shows that popular partially-linear regression specifications can put negative weights on some treatment effects, potentially producing incorrectly-signed estimands. We counter by showing that negative weights are no problem in design-based specifications, in which low-dimensional...

Many studies in economics use instruments or treatments which combine a set of exogenous shocks with other predetermined variables by a known formula. Examples include shift-share instruments and measures of social or spatial spillovers. We review recent econometric tools for this setting, which...

Pragmatic cancer screening trials mimic real-world scenarios in which patients and doctors are the ultimate arbiters of treatment. Intention-to-screen (ITS) analyses of such trials maintain randomization-based apples-to-apples comparisons, but differential adherence (the failure of subjects...

We study a difference-in-differences (DiD) framework where groups experience unequal treatment statuses in the pre-policy change period. This approach is commonly employed in empirical studies but it contradicts the canonical model's assumptions. We show that in such settings, the standard DiD...

We study two-way-fixed-effects regressions (TWFE) with several treatment variables. Under a parallel trends assumption, we show that the coefficient on each treatment identifies a weighted sum of that treatment's effect, with possibly negative weights, plus a weighted sum of the effects of the...

This article provides empirical researchers with an introduction and guide to research designs based on variation in judge and examiner tendencies to administer treatments or other interventions. We review the basic theory behind the research design, outline the assumptions under which the...

A growing number of central authorities use assignment mechanisms to allocate students to schools in a way that reflects student preferences and school priorities. However, most real-world mechanisms incentivize students to strategically misreport their preferences. In this paper, we provide an...