Matrix Completion Methods for Causal Panel Data Models

In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during periods and the goal is counterfactual (untreated) outcomes treated unit/period combinations. We propose class of matrix completion estimators that uses observed elements control corresponding untreated unit/periods impute "missing" outcome matrix, units/periods. This leads well-approximates original (incomplete) but has lower complexity according nuclear norm matrices. generalize results from literature by allowing patterns missing data have time series dependency structure common social science applications. present novel insights concerning connections between literature, on interactive fixed models literatures program evaluation under unconfoundedness synthetic methods. show all these can be viewed as focusing same objective function. They differ solely way they deal identification, cases through regularization (our proposed estimator) other primarily imposing hard restrictions (the approaches). The method outperforms unconfoundedness-based or simulations based real data.