The Strength of Instrumental Variables and Their Sensitivity to Unobserved Biases
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*Dylan Small, University of Pennsylvania 

Keywords: instrumental variables, design sensitivity, observational studies, causal effects

We study the sensitivity of instrumental variable analyses to departures from the assumption that the instrument is independent of unmeasured confounding variables, with a particular focus on the effect of the strength of the instrumental variable on its sensitivity to bias. As a case study, we reanalyze Angrist and Krueger’s 1994 study of the effects of military service during World War II on subsequent earnings, in which birth cohorts of very similar but not identical age were differently encouraged to serve. In this study, we can create instruments of varied strength that may in fact be similarly biased. We show that studies with weak instruments are extremely sensitive to tiny biases, whereas those with stronger instruments can be insensitive to moderate biases.

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