Quasi-Experimental Shift-Share Research Designs

Causal Question / Estimand

Methodological: when is a shift-share IV (SSIV) valid, and what design justifies it? The target is a structural coefficient (e.g. the effect of Chinese import competition on local manufacturing employment) estimated via an exposure-weighted average of shocks.

Identification Strategy

The paper grounds SSIV in exogeneity of the shocks (shifters) rather than the shares, allowing exposure shares to be endogenous. The key move is an equivalence result: the orthogonality between a shift-share instrument and the regression residual is equivalent to the orthogonality between the underlying shocks and a shock-level unobservable. So SSIV coefficients can be recovered from an equivalent shock-level IV regression, weighted by exposure. Consistency then follows from shock-level conditions: the shocks are as-good-as-randomly assigned (Randomization), there are many shocks, and they are mutually (roughly) uncorrelated, so a law of large numbers purges the share-level confounding.

Key Assumptions

• Shift-Share-Instrument — analyzed as an exposure-weighted average of shocks.
• Randomization — quasi-random assignment of the shifters (shock exogeneity) is the identifying condition.
• Exclusion-Restriction — shocks are uncorrelated with the shock-level unobservable; they influence outcomes only through the exposure-weighted treatment.
• Many, mutually uncorrelated shocks — needed for the law of large numbers that makes endogenous shares innocuous.

Threats to Validity

Few or large shocks (no law of large numbers), shocks correlated across industries, and incomplete/ non-exhaustive shares all break consistency. The framework yields testable implications: check for shock-level balance and pre-trends, and use exposure-robust inference.

Setting / Data

Methodological; illustrated by re-analyzing AutorDornHanson2013-ChinaSyndrome — estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.

Key Claims

• SSIV can be valid even when exposure shares are endogenous, provided the underlying shocks are quasi-randomly assigned and numerous.
• The instrument is best understood, and diagnosed, at the shock level; provides a recentering procedure, shock-level balance tests, and exposure-robust standard errors.

Connections

• Direct counterpoint to GoldsmithPinkhamEtAl2020-BartikInstruments (share exogeneity) — the two poles of the Shift-Share-Instrument identification debate.
• Shares the design-based, shock-level view and inference concerns of AdaoEtAl2019-ShiftShareDesigns; re-analyzes AutorDornHanson2013-ChinaSyndrome.
• See also IV.

Citation

Borusyak, K., Hull, P., & Jaravel, X. (2022). Quasi-Experimental Shift-Share Research Designs. Review of Economic Studies, 89(1), 181–213.