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 framework is centered around a numerical equivalence: conventional shift-share instrumental variable (SSIV) regression coefficients are equivalently obtained from a transformed regression where the shocks are used directly as an instrument. This equivalence implies a shock-level translation of the SSIV exclusion restriction, which holds when shocks are as-good-as-randomly assigned and large in number, with sufficient dispersion in their average exposure. We discuss and illustrate several practical insights delivered by this framework.
Replication archive: https://github.com/borusyak/shift-share
The ssaggregate Stata command is available from ssc