An Omitted Variable Bias Framework for Sensitivity Analysis of Instrumental Variables

We develop an “omitted variable bias” framework for sensitivity analysis of instrumental variable (IV) estimates that is immune to “weak instruments,” naturally handles multiple “side-effects” (violations of the exclusion restriction assumption) and “confounders” (violations of the ignorability of the instrument assumption), exploits expert knowledge to bound sensitivity parameters, and can be easily implemented with standard software. Conveniently, many pivotal conclusions regarding the sensitivity of the IV estimate (e.g. tests against the null hypothesis of zero causal effect) can be reached simply through separate sensitivity analyses of the effect of the instrument on the treatment (the “first stage”) and the effect of the instrument on the outcome (the “reduced form”). More specifically, we introduce sensitivity statistics for routine reporting, such as robustness values for IV estimates, describing the minimum strength that omitted variables need to have to change the conclusions of an IV study. Next we provide visual displays that fully characterize the sensitivity of IV point-estimates and confidence intervals to violations of the standard IV assumptions. Finally, we offer formal bounds on the worst possible bias under the assumption that the maximum explanatory power of omitted variables are no stronger than a multiple of the explanatory power of observed variables. We apply our methods in a running example that uses instrumental variables to estimate the returns to schooling