Centralized school assignment algorithms must distinguish between applicants with the same preferences and priorities. This is done with randomly assigned lottery numbers, nonlottery tie-breakers like test scores, or both. The New York City public high school match illustrates the latter, using...

We present a unifying identification strategy of dynamic average treatment effect parameters for staggered interventions when parallel trends are valid only after controlling for interactive fixed effects. This setting nests the usual parallel trends assumption, but allows treated units to have...

We provide evidence on the least biased ways to identify causal effects in situations where there are multiple outcomes that all depend on the same endogenous regressor and a reasonable but potentially contaminated instrumental variable that is available. Simulations provide suggestive evidence...