Instrumental identification of interventional distribution via moment recovery in a parametric outcome model

Purpose Many economic and policy decisions require the full interventional outcome distribution (e.g. tails, dispersion and asymmetry), not just average treatment effects. We study cases where that distribution is identifiable in instrumental variables (IV) settings with endogenous treatment and latent confounding. We focus on coupling additive mean structure with parametric outcome model assumptions to enable estimation of distributional treatment effects. Design/methodology/approach We posit outcome families that admit summary features that can recover confounder moments. A parsimonious distribution (e.g. discrete or common parametric families) can then be fit to match those moments and combined with the posited outcome model to construct the interventional distribution. Examples include Gaussian outcomes with multiplicative noise, Poisson counts and Gamma outcomes. Findings The moment-recovery scheme accurately reconstructs the low-order moments of the confounder and the interventional distribution in simulations, including a skewed confounding with multiplicative noise. Originality/value The paper provides a transparent pathway from the classical IV assumptions to the full identification of the interventional distribution, clarifying the feasibility conditions and offering a simple, practical workflow.