using shares as weights.

Studies that use a shift-share instrument with explicit shocks as shifts include Kinnan et al. (2019), who study how rural-urban migration in China affects development in migrants’ rural origin areas. Their shift-share instrument uses shares based on prior dyadic rural-urban connections created by a government program, while the shifts are urban labor demand shocks and relaxations of urban in-migration restrictions. Another example is Khanna, Murathanoglu, Theoharides, and Yang (Khanna et al.), who study the impact of international migration income in Philippine migrant-origin areas. The share is the magnitude of a Philippine province’s baseline migrant income, and the shift is exchange rate shocks due to the 1997 Asian Financial Crisis.<sup>11</sup> In the Borusyak et al. (2022) framework, causal identification requires the assumption that the shifts are as good as randomly assigned. Conducting shift-share analyses in the framework of Borusyak et al. (2022) reveals ways to support this assumption. They suggest useful tests for the exogeneity of the shifts that are analogous to “balance tests” in analyses of randomized control trials. The framework also suggests that an important (and frequently omitted) type of control variable to include in the regression is appropriately-weighted averages of characteristics of the units generating the shocks (the units indexed by _j_ ). They also highlight that in cases with “incomplete shares” (cases where the sum of shares varies across observations), this sum of shares is likely to induce bias if omitted from the regression, so it is important to include it as a control variable as well.

The framework of Borusyak et al. (2022) also offers ways to potentially achieve credible causal inference in shift-share designs when one does not have an explicitly exogenous shock to use as the shift (e.g., the original Bartik (1991) study). In their framework, the key concern about such settings is that there may be a “mechanical” correlation between the shift-share instrument and outcomes driven by shocks in the _l_ units, that then get aggregated to the measure of _mj,t_ . In the case of equation 8 above, for example, the concern is that variation in aggregate U.S. immigration from country _j_ could be endogenous to changes in U.S. locations _l_ (e.g., demand for immigrant labor, and determinants thereof) that sum up to the aggregate change _mj,t_ .

Borusyak et al. (2022) describe conditions under which one may reasonably assume that the shift is exogenous.<sup>12</sup> First, if shocks in units _l_ in the study can be taken as spatially uncorrelated, the measure of aggregate flows from unit _j_ can use a “leave-one-out” estimator

> 11Household-level studies exploiting exchange rate shocks of migrant workers in different countries also involve shift-share approaches. Yang (2006) and Yang (2008) study how migrant return migration and origin-household outcomes are affected by overseas exchange rate shocks faced by migrants. The “shift” is the exchange rate shock in each particular destination, and the “share” is the fraction of a household’s migrants in a destination. Most households only have one migrant overseas (so that its share of migrants in any particular destination is 1 for one country and 0 for all other destinations), but a minority have multiple migrants, so that they nonzero shares in two or more destinations.

> 12See Borusyak et al. (2022) Section 4.1 and Appendix A.6 for a discussion of this in the context of the Bartik (1991) setting.

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