1 Introduction

Few instruments have spread as widely across empirical economics as the shift-share, or Bartik, instrument. Originally deployed to isolate local labour demand shocks from supply responses, it now appears in studies of trade, immigration, technology adoption, credit supply, and health. Yet beneath the surface of a seemingly intuitive construction lies a surprisingly deep identification debate. Two research programmes have emerged with fundamentally different answers to the question: what makes a Bartik instrument valid?

 Goldsmith-Pinkham et al. [2020] show that the instrument's validity rests almost entirely on the exogeneity of the shares the pre-period industrial composition of each location- and develop a battery of specification tests to assess this. Borusyak et al. [2022] argue instead that the instrument is better understood as a quasi-experimental design in which the relevant randomness lies in the shocks the national industry growth rates and develop a wholly different estimator and inference procedure suited to that view. The two papers agree on surprisingly little, yet both have reshaped how applied economists use and defend Bartik-style instruments.

This feature article examines the classical Bartik construction, the theoretical underpinnings of each identification approach, the practical differences in estimation and inference, and what applied researchers should conclude.

2 The Classical Shift-Share Construction

The shift-share instrument was formalised by Bartik [1991] in a study of local labour market adjustment. Its defining formula is:‍


where l indexes locations (e.g. commuting zones), k indexes industries, sₗₖ is location l's share of employment in industry k at some pre-period baseline, and gₖ is a national-level shock typically industry-level employment or output growth computed in a "leave-one-out" fashion that excludes location l itself to avoid mechanical correlation. The instrument zₗ measures the predicted growth in local demand if each industry grew at its national rate, weighted by the local industrial mix. It is then used in a two-stage least squares regression for an endogenous outcome wages, employment, or trade exposure- where the first stage takes the form:‍


The workhorse application is Autor et al. [2013], where locations with higher pre-period employment shares in industries facing Chinese import competition experienced larger trade shocks an instrument for local manufacturing decline.

2.1 The Leave-One-Out Correction

Even before the recent theoretical debate, it was standard practice to compute the national growth rate excluding location l:‍


where Eₗₖ,ₜ is employment in location l, industry k, year t. This prevents correlation between the instrument and the local idiosyncratic error term, which would otherwise violate the exclusion restriction whenever a large location drives the national shock.

3 The Shares View: Goldsmith-Pinkham, Sorkin, and Swift (2020)

Goldsmith-Pinkham et al. [2020] decompose the Bartik instrument into a portfolio of industry-level just-identified IV estimators. The key insight is algebraic. The 2SLS coefficient using zₗ as the instrument for xₗ equals a weighted average of industry-specific IV estimators:‍


where β̂ₖ is the coefficient from an IV regression using sₗₖgₖ as the instrument for xₗ, and αₖ is the Rotemberg weight reflecting industry k's contribution to the first stage . From (3), the identifying variation comes from cross-sectional variation in the shares. The shocks gₖ enter only as scaling factors. This implies:

1. Exogeneity rests on the shares. The instrument is valid if and only if sₗₖ is uncorrelated with the structural error after conditioning on controls. Industries with large Rotemberg weights must have exogenous share variation.‍
2. The shocks can be treated as fixed constants. Under this view, variation over time in gₖ adds no identifying power beyond what is provided by the initial cross-sectional variation.‍
3. Testable implications. Because identification reduces to a set of industry-level IVs, standard pre-trends and balance tests can be conducted industry by industry, weighted by Rotemberg weights.

Goldsmith-Pinkham et al. [2020] provide an R package and Stata code that decomposes any Bartik instrument into its constituent industry IVs and computes Rotemberg weights. Applied researchers are then advised to scrutinise the top-weight industries: Are the shares in those industries plausibly exogenous?

4 The Shocks View: Borusyak, Hull, and Jaravel (2022)

Borusyak et al. [2022] take a fundamentally different perspective. They argue that the natural randomness in a shift-share design lies in the shocks gₖ, not the shares. Their reasoning is that shocks are generated by global or national market forces that plausibly vary quasi-randomly from the perspective of any individual location, whereas shares reflect historical location decisions that may be correlated with unobservable determinants of outcomes.

4.1 The Quasi-Experimental Framework

Under the shocks-based identification assumption, the shocks gₖ are conditionally independent of the error term given a set of industry-level controls hₖ:

where εₗₖ is the component of location l's error that is exposed to industry k's shock. The maintained assumption is that once industry-level controls capture systematic variation in gₖ, the residual shock variation is as-good-as-random across industries.

This framework yields a distinct estimator. Rather than running a location-level 2SLS regression, Borusyak et al. [2022] propose a two-step estimator that:

1. Regresses location-level outcomes and treatments on the shares interacted with industry controls, recovering a set of "residualised" industry-level outcome and treatment moments.
2. Instruments for the industry-level treatment moments using the industry shocks.

Under the shocks assumption, this estimator is consistent even when shares are endogenous, provided the shocks are exogenous after conditioning on industry-level covariates.

4.2 Inference with Many Weak Shocks

A critical innovation in Borusyak et al. [2022] concerns inference. Because a typical Bartik instrument aggregates hundreds or thousands of industries, asymptotic approximations depend on the number of shocks K → ∞ rather than the number of locations L → ∞. Standard location-clustered standard errors are invalid when identification comes from shock-level variation. Instead, BHJ propose standard errors that cluster at the shock (industry) level and account for the exposure-weighted nature of the aggregation.

5 A Tale of Two Decompositions

The two frameworks illuminate different possible sources of invalidity. As Table 1 shows, the two papers agree that identification requires some form of exogeneity, but they disagree on what is random. The practical implication is stark: an instrument that passes the GPS diagnostic (exogenous shares) might fail the BHJ diagnostic (endogenous shocks), and vice versa.

Consider the Autor et al. [2013] China shock instrument. The shares reflect historical Chinese export competition exposure pre-1990 industry composition in each commuting zone.

GPS would ask: is that pre-period industrial structure exogenous? BHJ would ask: conditional on broad industry-level trends, are the growth rates of Chinese export competition quasi-random? Both are defensible research designs under different maintained assumptions, and the two papers arrive at broadly similar estimates for the China shock application but this need not hold in general.

6 The SSIV Literature and Further Extensions

A parallel literature has developed the shift-share instrumental variable (SSIV) framework beyond the original labour market application. Borusyak et al. [2022] apply their method to estimate the effect of immigrant labour supply on native wages, using industry-level immigrant inflows instrumented by historical settlement patterns (shares) times national arrival rates (shocks). The same structure appears in studies of bank credit supply, technology adoption, and agricultural productivity.

Recent extensions address several limitations:

• Multiple endogenous variables. When both the treatment and a confound have shift-share structure, additional identifying restrictions are needed. Borusyak et al. [2022] provide conditions under which separate SSIV estimates can be combined .

• Panel settings. Most SSIV applications use a cross-section, but panel versions with location and time fixed effects require modified estimators to account for within-location serial correlation in shares.

• Non-linear models. The standard SSIV framework is linear. Goldsmith-Pinkham et al. [2020] note that their decomposition extends to GMM estimators, and recent work has applied SSIV-style instruments in count-data models .

7 Guidance for Practitioners

Given the two frameworks, what should an applied researcher do?

• Report both perspectives. It is good practice to present results from both the GPS and BHJ frameworks. Alignment between the two provides reassurance; divergence signals that identification is sensitive to which source of variation is treated as exogenous.

• Conduct Rotemberg diagnostics. The GPS decomposition identifies which industries drive identification. For the top-weighted industries, researchers should test for pre-trends in shares against lagged outcomes and present covariate balance statistics.

• Use BHJ-corrected standard errors. When K (the number of industries) is large relative to L (the number of locations), and especially when some industries have large exposures, BHJ standard errors are preferred. These are available in the ssaggregate Stata package and can be constructed manually in R.

• Assess the plausibility of the maintained assumption. Neither shares nor shocks exogeneity is automatically satisfied. The researcher must make a substantive case for whichever source of variation is exploited, supported by institutional knowledge and diagnostic tests.

8 Conclusion

The Bartik instrument is one of applied economics' workhorses, but its theoretical foundations are more complex than its simple formula suggests. Goldsmith-Pinkham et al. [2020] and Borusyak et al. [2022] have sharpened our understanding by deriving the implicit identifying assumptions from two distinct directions. The shares view frames the problem as a portfolio of industry-level instruments and demands exogenous share variation. The shocks view frames the design as quasi-experimental randomisation of shocks and demands that national industry growth rates are as-good-as-randomly assigned across industries. Both perspectives have enriched applied practice. Researchers who understand both frameworks are better equipped to defend their designs, anticipate threats to validity, and conduct the diagnostic tests that will persuade sceptical readers. The Bartik instrument is not going away but the days of deploying it without a rigorous identification argument are over.

References

1. Autor, D. H., Dorn, D., and Hanson, G. H. (2013). The China syndrome: Local labor market effects of import competition in the United States. American Economic Review, 103(6):2121-2168.
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3. Borusyak, K., Hull, P., and Jaravel, X. (2022). Quasi-experimental shift-share research designs. Review of Economic Studies, 89(1):181-213.
4. Goldsmith-Pinkham, P., Sorkin, I., and Swift, H. (2020). Bartik instruments: What, when, why, and how. American Economic Review, 110(8):2586-2624.
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