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
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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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Alberto Abadie, Alexis Diamond, and Jens Hainmueller (2010) Synthetic control methods for comparative case studies: Estimating the effect of california's tobacco control program | 1.000 | 8 | 5 | 100% |
| 2 | Rahul Mazumder, Trevor Hastie, and Robert Tibshirani (2010) Spectral regularization algorithms for learning large incomplete matrices | 0.950 | 7 | 5 | 86% |
| 3 | Emmanuel J Candès and Benjamin Recht (2009) Exact matrix completion via convex optimization | 0.928 | 4 | 4 | 100% |
| 4 | Nikolay Doudchenko and Guido W Imbens (2016) Balancing, regression, difference-in-differences and synthetic control methods: A synthesis self | 0.928 | 4 | 3 | 100% |
| 5 | Benjamin Recht (2011) A simpler approach to matrix completion | 0.843 | 5 | 3 | 60% |
| 6 | Guido W Imbens and Donald B Rubin (2015) Causal Inference in Statistics, Social, and Biomedical Sciences self | 0.843 | 3 | 3 | 100% |
| 7 | Donald B Rubin (2006) Matched sampling for causal effects | 0.843 | 3 | 3 | 100% |
| 8 | Sahand Negahban and Martin J Wainwright (2012) Restricted strong convexity and weighted matrix completion: Optimal bounds with noise | 0.830 | 7 | 4 | 57% |
| 9 | Jushan Bai and Serena Ng (2002) Determining the number of factors in approximate factor models | 0.811 | 4 | 2 | 100% |
| 10 | Vladimir Koltchinskii, Karim Lounici, Alexandre B Tsybakov, et al (2011) Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion | 0.737 | 4 | 3 | 50% |
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