Statistics

Econometrics

Economics

Geometry

Consistency (knowledge bases)

Mathematics

Regression

Algorithm

Residual

Shock (circulatory)

Discrete mathematics

Internal medicine

Instrumental variable

Orthogonality

Equivalence (formal languages)

Unobservable

Medicine

The Review of Economic Studies

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 shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor et al. (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.

Quasi-Experimental Shift-Share Research Designs