Title: Making Sense of Sensitivity: Extending Omitted Variable Bias
Abstract:We extend the omitted variable bias framework with a suite of tools for sensitivity analysis in regression models that: (i) does not require assumptions about the treatment assignment nor the nature of confounders; (ii) naturally handles multiple confounders, possibly acting non-linearly; (iii) exploits expert knowledge to bound sensitivity parameters; and, (iv) can be easily computed using only standard regression results. In particular, we introduce two novel sensitivity measures suited for routine reporting. The robustness value describes the minimum strength of association unobserved confounding would need to have, both with the treatment and the outcome, to change the research conclusions. The partial R2 of the treatment with the outcome shows how strongly confounders explaining all the residual outcome variation would have to be associated with the treatment to eliminate the estimated effect. Next, we offer graphical tools for elaborating on problematic confounders, examining the sensitivity of point estimates, t-values, as well as “extreme scenarios”. Finally, we describe problems with a common “benchmarking” practice and introduce a novel procedure to instead formally bound the strength of confounders based on comparison to observed covariates. We apply these methods to a running example that estimates the effect of exposure to violence on attitudes toward peace.