Parametric and Nonparametric Estimation of Covariate-Conditioned Average 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 and estimation of causal effects without requiring exogenous instruments, generalizing the classical structural equations approach; it relaxes the stable unit treatment value assumption of the treatment effect approach and provides significant insight into the selection of covariates; and it accommodates mutual causality, generalizing the DAG approach. We provide necessary and sufficient conditions for identification of covariate-conditioned average causal effects, parametric and nonparametric estimation results, and new tests for unconfoundedness