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Bartik Instruments: What, When, Why, and How -- by Paul Goldsmith-Pinkham, Isaac Sorkin, Henry Swift

The Bartik instrument is formed by interacting local industry shares and national industry growth rates. We show that the Bartik instrument is numerically equivalent to using local industry shares as instruments. Hence, the identifying assumption is best stated in terms of these shares, with the national industry growth rates only affecting instrument relevance. We then show how to decompose the Bartik instrument into the weighted sum of the just-identified instrumental variables estimators, where the weights sum to one, can be negative and are easy to compute. These weights measure how sensitive the parameter estimate is to each instrument. We illustrate our results through three applications: estimating the inverse elasticity of labor supply, estimating local labor market effects of Chinese imports, and using simulated instruments to study the effects of Medicaid expansions.
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