Matrix Completion Methods for Causal Panel Data Models

In this article, 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 completio...

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Vydáno v:Journal of the American Statistical Association Ročník 116; číslo 536; s. 1716 - 1730
Hlavní autoři: Athey, Susan, Bayati, Mohsen, Doudchenko, Nikolay, Imbens, Guido, Khosravi, Khashayar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Alexandria Taylor & Francis 02.10.2021
Taylor & Francis Ltd
Témata:
Causal models
Causality
Completion
Control methods
Dependency
Dependency grammar
Estimators
Interactive fixed effects
Literature
Longitudinal studies
Low-rank matrix estimation
Matrices
Missing data
Panel data
Program evaluation
Regression analysis
Regularization
Social sciences
Statistical methods
Statistics
Synthetic controls
Time series
time series analysis
Unconfoundedness
ISSN:0162-1459, 1537-274X, 1537-274X
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Shrnutí:In this article, 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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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2021.1891924