Matrix Completion with Fixed Effects for Treatment Effect Estimation

Thomas M. Menino Convention & Exhibition Center 

Matrix completion concerns the imputation of missing entries in a partially observed matrix. While its rapid development was originally motivated by applications in recommendation systems, it has also opened new possibilities in causal inference, where missing counterfactual outcomes can be imputed to estimate individual treatment effects.

In causal inference problems, the missingness pattern in potential outcomes is induced by the treatment adoption process. Although treatment assignment may satisfy the missing at random (MAR) assumption in randomized experiments and certain quasi-experimental designs, this assumption is often violated in observational studies. For instance, when a program is introduced at a particular time for a subset of units, the potential outcomes under control become unobserved for treated units after treatment adoption, creating a block missingness structure.

I present an inferential framework for matrix completion under missing not at random (MNAR) mechanisms and its application to treatment effect estimation. I also compare our approach with existing methods and discuss several promising extensions.