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...

This paper considers the role of school closures in the spread of the SARS-CoV-2 virus. To isolate the impact of the closures from other containment measures and identify a causal effect, we exploit variation in the start and end dates of the summer and fall school holidays across the 16 federal...

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...

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 develop a new approach to estimating flexible demand models with exogenous supply-side shocks. Our approach avoids conventional assumptions of exogenous product characteristics, putting no restrictions on product entry, despite using instrumental variables that incorporate characteristic...

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...

We develop a framework for difference-in-differences designs with staggered treatment adoption and heterogeneous causal effects. We show that conventional regression-based estimators fail to provide unbiased estimates of relevant estimands absent strong restrictions on treatment-effect...