Title: Matrix Completion Methods for Causal Panel Data Models,
Abstract: In this paper we study methods for estimating causal effects in settings with
panel data, where a subset of units are exposed to a treatment during a subset
of periods, and the goal is estimating counterfactual (untreated) outcomes for
the treated unit/period combinations. We develop a class of matrix completion
estimators that uses the observed elements of the matrix of control outcomes
corresponding to untreated unit/periods to predict the "missing" elements of
the matrix, corresponding to treated units/periods. The approach estimates a
matrix that well-approximates the original (incomplete) matrix, but has lower
complexity according to the nuclear norm for matrices. From a technical
perspective, we generalize results from the matrix completion literature by
allowing the patterns of missing data to have a time series dependency
structure. We also present novel insights concerning the connections between
the matrix completion literature, the literature on interactive fixed effects
models and the literatures on program evaluation under unconfoundedness and
synthetic control methods.