Bartik Instruments: What, When, Why and How

With Isaac Sorkin and Henry Swift

nber.org/papers/w24408 or paulgp.github.io/papers/bartik_…
Bartik, or "shift-share," instruments are prevalent in a ton of papers now. You've almost certainly seen them in a recent paper or ten.

Haven't you ever wondered what the identifying assumptions are?
A famous recent example is Autor, Dorn and Hanson's work on China's effect on U.S. manufacturing jobs (the China Shock).
We show in the paper that you can even write simulated instruments in applications like Medicaid in the same formulation (for many cases).
Our paper, new and improved, provides three results:
1a) We argue that a key issue with these papers is that the necessary identifying empirical assumptions are usually not stated, and we formalize what assumptions are necessary.
1b) Just-identified two-stage least squares using a Bartik instrument can in fact be written as GMM with an overidentified set of instruments, where the weight matrix is the outer product of national growth rates.
1c) So while Bartik seems simple and clean, it is in fact carrying around the necessary assumption of the exogeneity of a whole set of industry shares!
2a) We next provide a statistic to decompose the Bartik instrument into those components that "matter" most.
2b) We do this by writing the estimator estimated via Bartik as the weighted sum of just-identified estimates, weighted by what we term a "Rotemberg" weight, alpha_k.
2b - aside) We discovered this way of writing out overidentified GMM estimates via this 1982 paper by Julio Rotemberg [RIP] that was never published and only ever self-cited.
2c) What is beautiful about these weights is that you can show that they are an elasticity version of Andrews, Gentzkow and Shapiro's (2017) misspecification parameters.
2d) Hence, say there are 100 instruments used in our Bartik estimator. We calculate the Rotemberg weights for this estimate. Each weight states how much bias the overall estimate would have if a given instrument (industry) were biased by X percent: alpha_k * X.
2e) This is particularly useful because, as we'll see, the weights are highly concentrated in a few empirical examples.
2f) Thus, we argue that researchers should report which industries are most "important" in their Bartik instruments, and identify whether this makes sense, given their story, and also try to assess the validity of this identifying assumption.
3a) Finally, we do three empirical examples:

the first is the canonical case of estimating labor supply elasticity;

the second is Autor, Dorn and Hanson's estimates of the impact of China's trade on U.S. manufacturing;

the third is simulated Medicaid eligibility.
3b) We highlight are how concentrated the weights are -- 40% weight is on the Top 5 industries for the China shock example. Hence, while there are many industries necessary for "true" exogeneity, much of the story can be told via these five industries.
3c) Second, while typically the national growth rate "weight" is typically view as the main factor, it only plays a partial role.
3d) In the ADH case, the main industries that are sensitive to misspecification are the booming tech sectors that experienced rapid growth in China + demand in the U.S.
3e) For those who work in health economics (or other fields!) that use simulated instruments, we also show how to break out the identifying variation across state and years using data very kindly provided by @SarahCohodes and co-authors.
3f) Similar to the China Shock case, we show which types of families and which state-year law changes have the highest Rotemberg weights.
3g) In this context, poor (below poverty line) families receive the highest weight, and the law changes had very different effects on poor vs rich families.
We provide Stata code to calculate the Rotemberg weights here: github.com/paulgp/bartik-…
To wrap up:
1) Bartik instrument is actually identified off of distribution of many instruments (industry shares) -> Single Instrument to many
2) We show how to find out which of these many industries actually "matter" -> Many instruments to few
3) We provide 3 examples + code
Let us know if you have comments, questions, thoughts!

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