Shift-Share Designs: Theory and Inference

Causal Question / Estimand

Methodological, focused on inference rather than point identification: are the standard errors reported in shift-share regressions (a regional outcome regressed on an exposure-weighted average of sectoral shocks) valid? The estimand is the shift-share regression coefficient; the question is how to build correctly sized confidence intervals for it.

Identification Strategy

The paper takes the shift-share design as given and studies its error structure. Because regions that share similar sectoral composition load on the same shocks, their regression residuals are correlated across regions with similar sector shares — regardless of geographic proximity. Conventional heteroskedasticity-robust or spatially-clustered standard errors ignore this dependence and badly over-reject. A placebo exercise — regressing actual U.S. commuting-zone labor outcomes on shift-share regressors built from randomly generated sectoral shocks — rejects the true null of no effect in up to 55% of samples at a nominal 5% level. Adão–Kolesár–Morales derive novel (AKM) standard errors, valid under arbitrary cross-regional correlation induced by the shares, treating the shocks as the source of design-based randomness (Design-Based-Inference).

Key Assumptions

• Shift-Share-Instrument — the outcome depends on an exposure-weighted average of sectoral shocks.
• Design-Based-Inference — inference is derived from the (quasi-random) sampling of the sectoral shocks, which induces the cross-regional dependence the new standard errors must accommodate.

Threats to Validity

n/a — theoretical/methodological. The paper’s subject is a threat: cross-regional residual correlation from shared sector shares, which invalidates conventional standard errors and produces severe over-rejection.

Setting / Data

Methodological. A placebo Monte Carlo over U.S. commuting zones with randomly generated sectoral shocks demonstrates the over-rejection; the corrected standard errors are then applied to popular published shift-share applications, where they widen confidence intervals substantially.

Key Claims

• Conventional standard errors in shift-share designs can massively over-reject (up to 55% at the 5% level) because residuals are correlated across regions with similar sector shares.
• The AKM standard errors restore correct size under arbitrary such correlation, at the cost of materially wider confidence intervals in real applications.

Connections

• Inference companion to BorusyakEtAl2022-QuasiExperimentalShiftShare: both adopt a shock-level, design-based reading of the Shift-Share-Instrument, and both complete the identification-focused GoldsmithPinkhamEtAl2020-BartikInstruments.
• Uses Design-Based-Inference; runs on the same commuting-zone data as AutorDornHanson2013-ChinaSyndrome.
• See also IV.

Citation

Adão, R., Kolesár, M., & Morales, E. (2019). Shift-Share Designs: Theory and Inference. Quarterly Journal of Economics, 134(4), 1949–2010.