We develop new tools for causal inference in settings where exogenous shocks affect the treatment status of multiple observations jointly, to different extents. In these settings researchers may construct treatments or instruments that combine the shocks with predetermined measures of shock exposure. Examples include measures of spillovers in social and transportation networks, simulated eligibility instruments, and shift-share instruments. We show that leveraging the exogeneity of shocks for identification generally requires a simple but non-standard recentering, derived from the specification of counterfactual shocks that might as well have been realized. We further show how specification of counterfactual shocks can be used for finite-sample inference and specification tests, and we characterize the recentered instruments that are asymptotically efficient. We use this framework to estimate the employment effects of Chinese market access growth due to high-speed rail construction and the insurance coverage effects of expanded Medicaid eligibility.

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