Matrix Completion Methods for Causal Panel Data Models

50 Pages Posted: 8 Oct 2018

See all articles by Susan Athey

Susan Athey

Stanford Graduate School of Business

Mohsen Bayati

Stanford Graduate School of Business

Nikolay Doudchenko

Stanford University

Guido W. Imbens

Stanford Graduate School of Business

Khashayar Khosravi

Stanford University

Date Written: October 2018

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.

Suggested Citation

Carleton Athey, Susan and Bayati, Mohsen and Doudchenko, Nikolay and Imbens, Guido W. and Khosravi, Khashayar, Matrix Completion Methods for Causal Panel Data Models (October 2018). NBER Working Paper No. w25132, Available at SSRN: https://ssrn.com/abstract=3262395

Susan Carleton Athey (Contact Author)

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Mohsen Bayati

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

HOME PAGE: http://web.stanford.edu/~bayati/

Nikolay Doudchenko

Stanford University ( email )

Stanford, CA 94305
United States

Guido W. Imbens

Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States

Khashayar Khosravi

Stanford University

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