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Matrix Completion Methods for Causal Panel Data Models

Author

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  • 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.

Suggested Citation

  • Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2018. "Matrix Completion Methods for Causal Panel Data Models," NBER Working Papers 25132, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:25132
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    References listed on IDEAS

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    Cited by:

    1. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org.
    2. Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," NBER Working Papers 24814, National Bureau of Economic Research, Inc.
    3. Muhammad Jehangir Amjad & Devavrat Shah & Dennis Shen, 2017. "Robust Synthetic Control," Papers 1711.06940, arXiv.org.
    4. Victor Chernozhukov & Kaspar Wüthrich & Yu Zhu, 2017. "An exact and robust conformal inference method for counterfactual and synthetic controls," CeMMAP working papers CWP62/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Kumar, Anil & Liang, Che-Yuan, 2018. "Labor Market Effects of Credit Constraints: Evidence from a Natural Experiment," Working Papers 1810, Federal Reserve Bank of Dallas, revised 01 Sep 2018.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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