Quasi-Experimental Shift-Share Research Designs

TLDR

Shift‑share (Bartik) instruments average shocks weighted by exposure shares and are widely used in empirical research. The paper introduces a new econometric framework for shift‑share instrumental variable regressions that permits endogenous exposure shares and demonstrates its practical insights using the Autor et al. setting. The framework relies on an equivalence between shift‑share orthogonality and shock‑level orthogonality, allowing SSIV coefficients to be derived from shock‑level regressions and motivating consistency conditions at the shock level.

Abstract

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.