Working Paper

Design-based identification with formula instruments: A review


Kirill Borusyak, Peter Hull, Xavier Jaravel

Published Date

28 June 2023


Working Paper (CWP12/23)

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 leverage the assignment process of the exogenous shocks and the structure of the formula for identification. We compare this design-based approach with conventional estimation strategies based on conditional unconfoundedness, and contrast it with alternative strategies that leverage a model for unobservables.