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Matrix Completion Methods for Causal Panel Data Models

Susan Athey, Mohsen Bayati, Nikolay Doudchenko, Guido Imbens, Khashayar Khosravi

arXiv 27 Oct 2017 · Mathematics — Statistics Theory · publishedJournal of the American Statistical Association (2018) · 118 citations (OpenAlex)

arXiv:1710.10251 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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

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63
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Alberto Abadie, Alexis Diamond, and Jens Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program1.00085100%
2Rahul Mazumder, Trevor Hastie, and Robert Tibshirani (2010) Spectral regularization algorithms for learning large incomplete matrices0.9507586%
3Emmanuel J Candès and Benjamin Recht (2009) Exact matrix completion via convex optimization0.92844100%
4Nikolay Doudchenko and Guido W Imbens (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis self0.92843100%
5Benjamin Recht (2011) A simpler approach to matrix completion0.8435360%
6Guido W Imbens and Donald B Rubin (2015) Causal Inference in Statistics, Social, and Biomedical Sciences self0.84333100%
7Donald B Rubin (2006) Matched sampling for causal effects0.84333100%
8Sahand Negahban and Martin J Wainwright (2012) Restricted strong convexity and weighted matrix completion: Optimal bounds with noise0.8307457%
9Jushan Bai and Serena Ng (2002) Determining the number of factors in approximate factor models0.81142100%
10Vladimir Koltchinskii, Karim Lounici, Alexandre B Tsybakov, et al (2011) Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion0.7374350%

Showing the top 10 of 63 scored citations.

Cited by, within the corpus

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12401.136651.00094
2When Can We Use Two-Way Fixed-Effects (TWFE): A Comparison of TWFE and Novel Dynamic Difference-in-Differences Estimators1.00093
3Covariate-Adjusted Deep Causal Learning for Heterogeneous Panel Data Models1.00083
4Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls1.00063
5Identification and Inference for Synthetic Controls with Confounding1.00063
6Low-Rank Approximations of Nonseparable Panel Models1.00053
7Causal Matrix Completion1.00054
8A Synthetic Business Cycle Approach to Counterfactual Analysis with Nonstationary Macroeconomic Data1.00053
9Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models0.969114
10Synthetic Difference in Differences0.95075