Unconfoundedness as an Information Constraint

This paper provides an information-theoretic characterization of unconfoundedness within a general class of models allowing for endogenous selection. We impose a conditional mutual information (CMI) restriction requiring that the information about treatment contained in a potential outcome, conditional on covariates, does not exceed that contained in its latent heterogeneity. Under the maintained model conditions, this restriction is equivalent to a multiplicative factorization of treatment probabilities into separate functions of latent heterogeneity and covariates. Although the CMI restriction permits endogenous selection, sufficiently rich variation in treatment probabilities across covariate values makes it equivalent to unconfoundedness for the corresponding potential outcome. For binary treatments, any nonconstant propensity score suffices; for multiple treatments, a full-rank condition on the second-moment matrix of the propensity-score vector is sufficient. State-specific restrictions bound residual selection and imply exogeneity for individual treatment states under boundary-support conditions. Extensions cover continuous treatments and instrument exogeneity.