An Automated Approach to Causal Inference in Discrete Settings

Applied research conditions often make it impossible to point-identify causal estimands without untenable assumptions. Partial identification-bounds on the range of possible solutions-is a principled alternative, but the difficulty of deriving bounds in idiosyncratic settings has restricted its application. We present a general, automated numerical approach to causal inference in discrete settings. We show causal questions with discrete data reduce to polynomial programming problems, then present an algorithm to automatically bound causal effects using efficient dual relaxation and spatial branch-and-bound techniques. The user declares an estimand, states assumptions, and provides data-however incomplete or mismeasured. The algorithm then searches over admissible data-generating processes and outputs the most precise possible range consistent with available information-that is, sharp bounds-including a point-identified solution if one exists. Because this search can be computationally intensive, our procedure reports and continually refines non-sharp ranges guaranteed to contain the truth at all times, even when the algorithm is not run to completion. Moreover, it offers an $$ -sharpness guarantee, characterizing the worst-case looseness of the incomplete bounds. These techniques are implemented in our Python package, autobounds. Analytically validated simulations show the method accommodates classic obstacles-including confounding, selection, measurement error, noncompliance, and nonresponse. Supplementary materials for this article are available online.