Exploiting Equality Constraints in Causal Inference

February, 2021

Abstract

Assumptions about equality of effects are commonly made in causal inference tasks. For example, the well-known “differencein-differences” method assumes that confounding remains constant across time periods. Similarly, it is not unreasonable to assume that causal effects apply equally to units undergoing interference. Finally, sensitivity analysis often hypothesizes equality among existing and unaccounted for confounders. Despite the ubiquity of these “equality constraints,” modern identification methods have not leveraged their presence in a systematic way. In this paper, we develop a novel graphical criterion that extends the well-known method of generalized instrumental sets to exploit such additional constraints for causal identification in linear models. We further demonstrate how it solves many diverse problems found in the literature in a general way, including differencein-differences, interference, as well as benchmarking in sensitivity analysis.