Identification and estimation of average causal effects when treatment status is ignorable within unobserved strata

Abstract

This paper extends matching and propensity-score reweighting methods to settings in which unobserved variables influence both treatment assignment and counterfactual outcomes. Identification proceeds under the assumption that counterfactual outcomes are independent of treatment status conditional on observed covariates and membership in one of a finite set of latent classes. Individuals are first assigned to latent classes according to posterior probabilities of class membership derived from a finite-mixture model that relates a set of auxiliary variables to latent class membership. Average causal effects are then identified by comparing outcomes among treated and untreated individuals assigned to the same class, correcting for misclassifications arising in the first step. The identification procedure suggests computationally attractive latent-class matching and propensity-score reweighting estimators that obviate the need to directly estimate the distributions of counterfactual outcomes. In Monte Carlo studies, the resulting estimates are centered around the correct average causal effects with minimal loss of precision compared to competing estimators that misstate those effects. I apply the methods to estimate the effect of gang membership on violent delinquency.