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...

Studies of racial discrimination often condition on endogenous measures of race or on earlier decisions that might themselves be affected by discrimination. We develop quasi-experimental tools for estimating the impact of racial misclassification on measures of unwarranted disparity, and for...

Black children in the U.S. are twice as likely as white children to spend time in foster care. Such racial disparities raise concerns of discrimination, but might also reflect differences in the underlying need for intervention. This paper estimates unwarranted disparities (UDs)--racial...

A recent econometric literature shows two distinct paths for identification with shift-share instruments, leveraging either many exogenous shifts or exogenous shares. We present the core logic of both paths and practical takeaways via simple checklists. A variety of empirical settings illustrate...

The ISCHEMIA Trial randomly assigned patients with ischemic heart disease to an invasive treatment strategy centered on revascularization with a control group assigned non-invasive medical therapy. As is common in such "strategy trials," many participants assigned to treatment remained untreated...

Many studies use shift-share (or "Bartik") instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for such designs in which identification follows from the quasi-random assignment of shocks, allowing exposure shares to be endogenous. This...

We develop new tools for causal inference in settings where exogenous shocks affect the treatment status of multiple observations jointly, to different extents. In these settings researchers may construct treatments or instruments that combine the shocks with predetermined measures of shock...

Competition in health insurance markets may fail to improve health outcomes if consumers are not willing to pay for high quality plans. We document large differences in the mortality rates of Medicare Advantage (MA) plans within local markets. We then show that when high (low) mortality plans...

We develop new quasi-experimental tools to measure racial discrimination, due to either racial bias or statistical discrimination, in the context of bail decisions. We show that the omitted variables bias in observational release rate comparisons can be purged by using the quasi-random...

There is growing concern that the rise of algorithmic decision-making can lead to discrimination against legally protected groups, but measuring such algorithmic discrimination is often hampered by a fundamental selection challenge. We develop new quasi-experimental tools to overcome this...