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Abstract:
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Social scientists frequently aim to assess the causal effect of treatments that cannot ethically or practically be randomized. While quasi-experimental designs can estimate causal effects under a "no unobserved confounding" assumption, this assumption is often suspect. Sensitivity analyses seek to illuminate (i) what qualities would an unobservable confounder need to have to substantively change our answer, and (ii) how difficult is it to believe such an unobservable exists? Existing sensitivity analyses remain largely underutilized, perhaps due to their strong assumptions, difficulties in implementation, or difficulties in interpretation. We aim to produce a simple sensitivity analysis, by elaborating on the familiar "omitted variable bias" framework. This approach assumes a linear outcome model, but makes no assumptions on the treatment assignment model, nor on the distribution of the unobserved confounder. It applies when there may be one or many unobserved sources of confounding, and whether they influence the outcome linearly or not. We provide several different parameterizations and visualizations of the results to maximize interpretability.
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