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...

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...

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...

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...

Economics tends to define and measure discrimination as disparities stemming from the direct (causal) effects of protected group membership. But work in other fields notes that such measures are incomplete, as they can miss important systemic (i.e. indirect) channels. For example, racial...

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 shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while...

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...

We develop new tools for estimating the causal effects of treatments or instruments that combine multiple sources of variation according to a known formula. Examples include treatments capturing spillovers in social and transportation networks, simulated instruments for policy eligibility, and...