Marginal outcome tests compare the expected effects of a decision on individuals who are of different races but at the same indifference point of the decision-maker. I present a simple formalization of how such tests can detect racial bias, defined as a deviation from accurate statistical...

When estimating the effects of treatments defined by complex formulas, researchers often use simple functions of exogenous shocks as instruments. A leading example is "simulated instruments" for public policy eligibility, which capture variation in state-level policy generosity. We show how more...

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...

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...

Instrumental variable (IV) estimates may be difficult to interpret when there are multiple alternatives to treatment. I consider identification of counterfactual-specific local average treatment effects via interactions of the instrument and stratifying controls. Deriving general IV estimands, I...