Working Paper: NBER ID: w25132
Authors: Susan Athey; Mohsen Bayati; Nikolay Doudchenko; Guido Imbens; Khashayar Khosravi
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.
Keywords: No keywords provided
JEL Codes: C01; C21; C23
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| matrix completion estimator (C51) | impute missing potential outcomes (C24) |
| observed outcomes from untreated units (C22) | impute missing potential outcomes for treated units (C32) |
| unconfoundedness approach (C90) | estimate missing potential outcomes (C51) |
| synthetic control approach (E61) | match treated units to control units (C78) |
| matrix completion method (C65) | improved estimation of treatment effects (C22) |
| traditional approaches (DID, synthetic control) (C90) | estimation of treatment effects (C22) |