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Matrix Completion Methods for Causal Panel Data Models

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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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    Citations

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    Cited by:

    1. Nicolaj N. Mühlbach, 2020. "Tree-based Synthetic Control Methods: Consequences of moving the US Embassy," CREATES Research Papers 2020-04, Department of Economics and Business Economics, Aarhus University.
    2. Ruoxuan Xiong & Susan Athey & Mohsen Bayati & Guido Imbens, 2019. "Optimal Experimental Design for Staggered Rollouts," Papers 1911.03764, arXiv.org, revised Aug 2020.
    3. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org.
    4. Irene Botosaru & Bruno Ferman, 2019. "On the role of covariates in the synthetic control method," Econometrics Journal, Royal Economic Society, vol. 22(2), pages 117-130.
    5. 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.
    6. Muhammad Jehangir Amjad & Devavrat Shah & Dennis Shen, 2017. "Robust Synthetic Control," Papers 1711.06940, arXiv.org.
    7. Jianqing Fan & Kunpeng Li & Yuan Liao, 2020. "Recent Developments on Factor Models and its Applications in Econometric Learning," Papers 2009.10103, arXiv.org.
    8. Anna Rita Bennato & Stephen Davies & Franco Mariuzzo & Peter Ormosi, 2019. "Mergers and Innovation: Evidence from the Hard Disk Drive Market," Working Paper series, University of East Anglia, Centre for Competition Policy (CCP) 2018-04v3, Centre for Competition Policy, University of East Anglia, Norwich, UK..
    9. 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.
    10. Chan, Mark K. & Kwok, Simon, 2020. "The PCDID Approach: Difference-in-Differences when Trends are Potentially Unparallel and Stochastic," Working Papers 2020-03, University of Sydney, School of Economics.
    11. Florian Gunsilius, 2020. "Distributional synthetic controls," Papers 2001.06118, arXiv.org, revised Mar 2020.
    12. Anil Kumar & Che-Yuan Liang, 2018. "Labor Market Effects of Credit Constraints: Evidence from a Natural Experiment," Working Papers 1810, Federal Reserve Bank of Dallas, revised 01 Sep 2018.
    13. Ruoxuan Xiong & Markus Pelger, 2019. "Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference," Papers 1910.08273, arXiv.org, revised Nov 2020.
    14. Victor Chernozhukov & Christian Hansen & Yuan Liao & Yinchu Zhu, 2019. "Inference for heterogeneous effects using low-rank estimations," CeMMAP working papers CWP31/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    15. Giulio Grossi & Patrizia Lattarulo & Marco Mariani & Alessandra Mattei & Ozge Oner, 2020. "Synthetic Control Group Methods in the Presence of Interference: The Direct and Spillover Effects of Light Rail on Neighborhood Retail Activity," Papers 2004.05027, arXiv.org, revised Jun 2020.

    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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