A Unified Framework for Defining and Identifying Causal Effects

This paper unifies three complementary approaches to defining, identifying, and estimating causal effects: the classical structural equations approach of the Cowles Commision; the treatment effects framework of Rubin (1974) and Rosenbaum and Rubin (1983); and the Directed Acyclic Graph (DAG) approach of Pearl. The settable system framework nests these prior approaches, while affording significant improvements to each. For example, the settable system approach permits identification of causal effects without requiring exogenous instruments; instead, a weaker conditional exogeneity condition suffices. It removes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates. It generalizes the DAG approach by accommodating mutual causality and attributes. We provide a variety of results ensuring structural identification of general covariate-conditioned average causal effects, laying the foundation for parametric and nonparametric estimation of effects of interest and new tests for structural identification. Acknowledgments: The authors are indebted to Jinyong Hahn, James Heckman, Kei Hirano, Kevin Hoover, Meng Huang, Massimiliano Marinucci, Rosa Matzkin, and Rosalind Wu for helpful discussions and suggestions. Any errors remain the authors’ responsibility JEL Classificiation Numbers: .