🤖 AI Summary
This paper addresses sensitivity analysis for linear causal effect estimation under unobserved confounding and potential instrumental variables. Methodologically, it formalizes sensitivity analysis as a constrained stochastic optimization problem—the first such formulation—leverages algebraic rules of partial correlations to construct interpretable and easily calibratable bounds on omitted-variable bias, and develops a bootstrap-based algorithm for constructing sensitivity intervals with asymptotic confidence guarantees. Empirical evaluation in an education returns application and extensive numerical simulations demonstrates the method’s high coverage probability and robustness across diverse confounding scenarios. Furthermore, the paper releases an open-source, user-friendly interactive visualization tool that enhances interpretability and credibility of causal inference results.
📝 Abstract
Causal inference necessarily relies upon untestable assumptions; hence, it is crucial to assess the robustness of obtained results to violations of identification assumptions. However, such sensitivity analysis is only occasionally undertaken in practice, as many existing methods require analytically tractable solutions and their results are often difficult to interpret. We take a more flexible approach to sensitivity analysis and view it as a constrained stochastic optimization problem. This work focuses on sensitivity analysis for a linear causal effect when an unmeasured confounder and a potential instrument are present. We show how the bias of the OLS and TSLS estimands can be expressed in terms of partial correlations. Leveraging the algebraic rules that relate different partial correlations, practitioners can specify intuitive sensitivity models which bound the bias. We further show that the heuristic"plug-in"sensitivity interval may not have any confidence guarantees; instead, we propose a bootstrap approach to construct sensitivity intervals which performs well in numerical simulations. We illustrate the proposed methods with a real study on the causal effect of education on earnings and provide user-friendly visualization tools.
