Matrix Completion Methods for Causal Panel Data Models

2017/10/27 by Susan Athey, Mohsen Bayati, Nikolay Doudchenko +3 · 1 voice
Economics, Econometrics and Finance · Mathematics · #Advanced Causal Inference Techniques #Algorithm #Artificial intelligence #Computer science #Contrast (vision) #Counterfactual thinking #Econometrics #Estimator #Health Systems, Economic Evaluations, Quality of Life #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix completion #Missing data #Panel data #Regression #Regression analysis #Spatial and Panel Data Analysis #Statistics #econ.EM #math.ST #stat.TH

paper · pdf · doi:10.1080/01621459.2021.1891924

published as Journal of American Statistical Association (JASA), Journal of American Statistical Association (JASA), Vol 116 (536), 2021 · 42 pages, 10 figures

arxiv published 2017/10/27 · openalex publication_date 2018/10/01 · arxiv created 2022/04/21 · arxiv updated 2022/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Chapter 22 Panel data
• Atomic Decomposition by Basis Pursuit
• User-Friendly Tail Bounds for Sums of Random Matrices
• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• A Simpler Approach to Matrix Completion
• Estimating causal effects of treatments in randomized and nonrandomized studies.
• Longitudinal data analysis using generalized linear models
• The central role of the propensity score in observational studies for causal effects
• Recovering Low-Rank Matrices From Few Coefficients in Any Basis
• Comparative Politics and the Synthetic Control Method
• Double/Debiased Machine Learning for Treatment and Causal Parameters
• Principal Components and Regularized Estimation of Factor Models
• Robust Synthetic Control
• The Elements of Statistical Learning: Data Mining, Inference, and Prediction
• Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption
• Nuclear norm penalization and optimal rates for noisy low rank matrix\n completion
• Recent Developments in the Econometrics of Program Evaluation
• Generalized Synthetic Control Method: Causal Inference with Interactive Fixed Effects Models
• Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure
• Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score
• Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program

Discussions

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