Discussion of "Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models"

TL;DR

This paper discusses a novel matrix completion method for estimating causal effects in panel data with non-random missingness, highlighting its relation to existing estimators and addressing practical implementation challenges.

Contribution

It introduces a new perspective on applying matrix completion to causal panel data, connecting it with modern estimators and exploring practical issues.

Findings

Matrix completion can effectively estimate causal effects with structured missing data.

The approach relates to difference-in-differences and synthetic control methods.

Application to policy impact estimation demonstrates practical utility.

Abstract

Choi and Yuan (2025) propose a novel approach to applying matrix completion to the problem of estimating causal effects in panel data. The key insight is that even in the presence of structured patterns of missing data -- i.e. selection into treatment -- matrix completion can be effective if the number of treated observations is small relative to the number of control observations. We applaud the authors for their insightful and interesting paper. We discuss this proposal from two complementary perspectives. First, we situate their proposal as an example of a "split-apply-combine" strategy that underlies many modern panel data estimators, including difference-in-differences and synthetic control approaches. Second, we discuss the issue of the statistical "last mile problem" -- the gap between theory and practice -- and offer suggestions on how to partially address it. We conclude by considering the challenges of estimating the impacts of public policies using panel data and apply the approach to a study on the effect of right to carry laws on violent crime.