A probability index of the robustness of a causal inference

Causal inference is an important, controversial topic in the social sciences, where it is difficult to conduct experiments or measure and control for all confounding variables. To address this concern, the present study presents a probability index to assess the robustness of a causal inference to the impact of a confounding variable. The information from existing covariates is used to develop a reference distribution for gauging the likelihood of observing a given value of the impact of a confounding variable. Applications are illustrated with an empirical example pertaining to educational attainment. The methodology discussed in this study allows for multiple partial causes in the complex social phenomena that we study, and informs the controversy about causal inference that arises from the use of statistical models in the social sciences.