Coarsened confounding for causal effects: a large-sample framework

There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider coarsened exact matching, developed in Iacus et al. (2011). While they developed some statistical properties, in this article, we study the approach using asymptotics based on a superpopulation inferential framework. This methodology is generalized to what we termed as coarsened confounding, for which we propose two new algorithms. We develop asymptotic results for the average causal effect estimator as well as providing conditions for consistency. In addition, we provide an asymptotic justification for the variance formulae in Iacus et al. (2011). A bias correction technique is proposed, and we apply the proposed methodology to data from two well-known observational studi