Working Paper: NBER ID: w24997
Authors: Kirill Borusyak; Peter Hull; Xavier Jaravel
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.
Keywords: shift-share; instrumental variables; quasiexperimental designs
JEL Codes: C18; C21; C26; F16; J21
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| shocks are uncorrelated with unobserved factors (C22) | SSIV estimator can identify a parameter of interest (C26) |
| shift-share instrument is uncorrelated with residuals from second-stage regression (C26) | orthogonality condition must hold (C29) |
| Chinese import shocks are independent from local labor supply shocks (F66) | SSIV framework can estimate effects of Chinese import competition on manufacturing employment (F17) |
| shocks are conditionally quasirandomly assigned (C90) | SSIV framework can be generalized (C36) |
| quasiexperimental shock variation is isolated through regression controls with shift-share structure (C21) | robustness of identification strategy (C20) |