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We characterize the instruments which optimally combine a set of exogenous shocks with some non-random measures of shock exposure, building on the framework of Borusyak and Hull (2023). Our characterization has implications for treatments capturing spillovers in social and transportation networks, simulated instruments for policy eligibility, and shift-share instruments. We show how significantly more precise estimates of Medicaid take-up and crowd-out effects can be obtained by combining policy expansion shocks with non-random variation in Medicaid eligibility.
