Bartik Instruments: What, When, Why, and How

Causal Question / Estimand

Methodological: what identifying assumption does a Bartik (shift-share) IV actually rely on, and what parameter does it estimate? The illustrative estimands are the elasticity of labor supply and the elasticity of substitution between immigrants and natives.

Identification Strategy

The Bartik instrument interacts local industry shares with national industry growth rates. The paper’s central result is an equivalence: using the Bartik instrument is numerically identical to a GMM estimator that uses the industry shares themselves as instruments, with national growth rates as the weighting matrix. Hence the canonical Bartik design is a pooled-exposure design whose identification rests on exogeneity of the shares — not the shocks. Because the design is over-identified, the Bartik estimate is a weighted sum of the just-identified share-IV estimands, with Rotemberg weights that reveal which industries drive identification, expose sensitivity to misspecification, and diagnose Treatment-Effect-Heterogeneity.

Key Assumptions

• Shift-Share-Instrument — treated as a set of share instruments interacted with a common shock.
• Exclusion-Restriction at the share level — industry exposure shares are uncorrelated with the structural error (share exogeneity), the binding identifying assumption in the pooled design.
• Treatment-Effect-Heterogeneity — with over-identification the estimand is a Rotemberg-weighted average of heterogeneous share-specific effects; negative weights signal trouble.

Threats to Validity

Shares may be correlated with unobserved local trends or level determinants of the outcome; a few high-Rotemberg-weight industries can dominate the estimate; negative weights can make the aggregate uninterpretable. The paper supplies plausibility checks: correlate high-weight shares with observables, test for pre-trends, and inspect over-identification.

Setting / Data

Methodological, with two worked applications — estimating the labor supply elasticity, and estimating the elasticity of substitution between immigrants and natives (a Card-style enclave design).

Key Claims

• The typical use of a Bartik instrument is a share-exogeneity research design; the shocks provide the weights, the shares provide identification.
• Rotemberg weights decompose the estimate and pinpoint which shocks/industries the identification actually leans on.
• Provides a concrete diagnostic toolkit for assessing the plausibility of shift-share designs.

Connections

• Direct counterpoint to BorusyakEtAl2022-QuasiExperimentalShiftShare, which grounds the same instrument in shock exogeneity — the defining share-vs-shock debate for the Shift-Share-Instrument.
• Formalizes the designs in Card2001-ImmigrantInflows and BlanchardKatz1992-RegionalEvolutions; inference concerns overlap with AdaoEtAl2019-ShiftShareDesigns.
• See also IV.

Citation

Goldsmith-Pinkham, P., Sorkin, I., & Swift, H. (2020). Bartik Instruments: What, When, Why, and How. American Economic Review, 110(8), 2586–2624.