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We develop an omitted variable bias framework for sensitivity analysis of instrumental variable estimates that naturally handles multiple side effects (violations of the exclusion restriction assumption) and confounders (violations of the ignorability of the instrument assumption) of the instrument, exploits expert knowledge to bound sensitivity parameters and can be easily implemented with standard software. Specifically, we introduce sensitivity statistics for routine reporting, such as (extreme) robustness values for instrumental variables, describing the minimum strength that omitted variables need to have to change the conclusions of a study. Next, we provide visual displays that fully characterize the sensitivity of point estimates and confidence intervals to violations of the standard instrumental variable assumptions. Finally, we offer formal bounds on the worst possible bias under the assumption that the maximum explanatory power of omitted variables is no stronger than a multiple of the explanatory power of observed variables. Conveniently, many pivotal conclusions regarding the sensitivity of the instrumental variable estimate (e.g., tests against the null hypothesis of a 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). We apply our methods in a running example that uses proximity to college as an instrumental variable to estimate the returns to schooling. 

This tutorial introduces the package sensemakr for R and Stata, which implements a suite of sensitivity analysis tools for regression models developed in Cinelli and Hazlett (2020, 2022). Given a regression model, sensemakr can compute sensitivity statistics for routine reporting, such as the robustness value , which describes the minimum strength that unobserved confounders need to have to overturn a research conclusion. The package also provides plotting tools that visually demonstrate the sensitivity of point estimates and t-values to hypothetical confounders. Finally, sensemakr implements formal bounds on sensitivity parameters by means of comparison with the explanatory power of observed variables. All these tools are based on the familiar omitted variable bias framework, do not require assumptions regarding the functional form of the treatment assignment mechanism nor the distribution of the unobserved confounders, and naturally handle multiple, non-linear confounders. With sensemakr, users can transparently report the sensitivity of their causal inferences to unobserved confounding, thereby enabling a more precise, quantitative debate as to what can be concluded from imperfect observational studies.