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...

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 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 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...