Optimal formula instruments - Kirill Borusyak; Peter Hull (Centre for Microdata Methods and Practice (cemmap), The Institute for Fiscal Studies (IFS))
When estimating the effects of treatments defined by complex formulas, researchers often use simple functions of exogenous shocks as instruments. A leading example is "simulated instruments" for public policy eligibility, which capture variation in state-level policy generosity. We show how more powerful instruments can be constructed by incorporating heterogeneous shock exposure while using a recentering procedure to avoid bias. We characterize the asymptotically efficient instruments in this class and propose an algorithm for constructing feasible approximations to them. Compared to a simulated instrument approach, our approach yields a 44% smaller standard error on the private insurance crowd-out effect of Medicaid enrollment from the 2014 Affordable Care Act expansions.
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