Deriving Bounds and Inequality Constraints Using LogicalRelations Among Counterfactuals
This provides a general framework for causal inference researchers to derive bounds in non-identified scenarios, though it appears incremental as it builds on existing logical and graphical methods.
The paper tackles the problem of bounding causal parameters when unobserved confounding prevents point identification, developing a general method using probability rules and counterfactual restrictions from causal graphical models to recover bounds and inequality constraints from observed data. The approach recovers known sharp bounds and derives novel ones.
Causal parameters may not be point identified in the presence of unobserved confounding. However, information about non-identified parameters, in the form of bounds, may still be recovered from the observed data in some cases. We develop a new general method for obtaining bounds on causal parameters using rules of probability and restrictions on counterfactuals implied by causal graphical models. We additionally provide inequality constraints on functionals of the observed data law implied by such causal models. Our approach is motivated by the observation that logical relations between identified and non-identified counterfactual events often yield information about non-identified events. We show that this approach is powerful enough to recover known sharp bounds and tight inequality constraints, and to derive novel bounds and constraints.