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Many empirical studies leverage shift-share (or "Bartik") instruments that average a set of observed shocks with shock exposure weights. We derive a necessary and sufficient shock-level orthogonality condition for these instruments to identify causal effects. We then show that orthogonality holds when observed shocks are as-good-as-randomly assigned and growing in number, with the average shock exposure sufficiently dispersed. Quasiexperimental shift-share designs may be implemented with new shock-level procedures, which help visualize the identifying variation, correct standard errors, choose appropriate specifications, test identifying assumptions, and optimally combine multiple sets of quasi-random shocks. We illustrate these ideas by revisiting Autor et al. (2013)'s analysis of the labor market effects of Chinese import competition.

We characterize the factors that determine who becomes an inventor in the United States, focusing on the role of inventive ability ("nature") vs. environment ("nurture"). Using de-identified data on 1.2 million inventors from patent records linked to tax records, we first show that children's chances of becoming inventors vary sharply with characteristics at birth, such as their race, gender, and parents' socioeconomic class. For example, children from high-income (top 1%) families are ten times as likely to become inventors as those from below-median income families. These gaps persist even among children with similar math test scores in early childhoodwhich are highly predictive of innovation ratessuggesting that the gaps may be driven by differences in environment rather than abilities to innovate. We then directly establish the importance of environment by showing that exposure to innovation during childhood has significant causal effects on children's propensities to invent. Children whose families move to a high-innovation area when they are young are more likely to become inventors. These exposure effects are technology-class and gender specific. Children who grow up in a neighborhood or family with a high innovation rate in a specific technology class are more likely to patent in exactly the same class. Girls are more likely to invent in a particular class if they grow up in an area with more women (but not men) who invent in that class. These gender-and technology class-specific exposure effects are more likely to be driven by narrow mechanisms such as role model or network effects than factors that only affect general human capital accumulation, such as the quality of schools. Consistent with the importance of exposure effects in career selection, women and disadvantaged youth are as under-represented among highimpact inventors as they are among inventors as a whole. These findings suggest that there are many "lost Einsteins" -individuals who would have had highly impactful inventions had they been exposed to innovation in childhood -especially among women, minorities, and children from low-income families.

A broad empirical literature uses "event study," or "difference-in-differences with staggered rollout," research designs for treatment effect estimation: settings in which units in the panel receive treatment at different times. We show a series of problems with conventional regressionbased two-way fixed effects estimators, both static and dynamic. These problems arise when researchers conflate the identifying assumptions of parallel trends and no anticipatory effects, implicit assumptions that restrict treatment effect heterogeneity, and the specification of the estimand as a weighted average of treatment effects. We then derive the efficient estimator robust to treatment effect heterogeneity for this setting, show that it has a particularly intuitive "imputation" form when treatment-effect heterogeneity is unrestricted, characterize its asymptotic behavior, provide tools for inference, and illustrate its attractive properties in simulations. We further discuss appropriate tests for parallel trends, and show how our estimation approach extends to many settings beyond standard event studies.

Many studies use shift-share (or “Bartik”) instruments, which average a set of shocks with exposure share weights. We provide a new econometric framework for shift-share instrumental variable (SSIV) regressions in which identification follows from the quasi-random assignment of shocks, while exposure shares are allowed to be endogenous. The framework is motivated by an equivalence result: the orthogonality between a shift-share instrument and an unobserved residual can be represented as the orthogonality between the underlying shocks and a shock-level unobservable. SSIV regression coefficients can similarly be obtained from an equivalent shock-level regression, motivating shock-level conditions for their consistency. We discuss and illustrate several practical insights of this framework in the setting of Autor et al. (2013), estimating the effect of Chinese import competition on manufacturing employment across U.S. commuting zones.