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Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

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  • Jushan Bai
  • Serena Ng

Abstract

This article proposes an imputation procedure that uses the factors estimated from a tall block along with the re-rotated loadings estimated from a wide block to impute missing values in a panel of data. Assuming that a strong factor structure holds for the full panel of data and its sub-blocks, it is shown that the common component can be consistently estimated at four different rates of convergence without requiring regularization or iteration. An asymptotic analysis of the estimation error is obtained. An application of our analysis is estimation of counterfactuals when potential outcomes have a factor structure. We study the estimation of average and individual treatment effects on the treated and establish a normal distribution theory that can be useful for hypothesis testing.

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  • Jushan Bai & Serena Ng, 2021. "Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1746-1763, October.
    • Handle: RePEc:taf:jnlasa:v:116:y:2021:i:536:p:1746-1763
    DOI: 10.1080/01621459.2021.1967163
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    1. Cahan, Ercument & Bai, Jushan & Ng, Serena, 2023. "Factor-based imputation of missing values and covariances in panel data of large dimensions," Journal of Econometrics, Elsevier, vol. 233(1), pages 113-131.
    2. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    3. Alexandre Belloni & Mingli Chen & Oscar Hernan Madrid Padilla & Zixuan & Wang, 2019. "High Dimensional Latent Panel Quantile Regression with an Application to Asset Pricing," Papers 1912.02151, arXiv.org, revised Aug 2022.
    4. Michael W. McCracken & Serena Ng, 2021. "FRED-QD: A Quarterly Database for Macroeconomic Research," Review, Federal Reserve Bank of St. Louis, vol. 103(1), pages 1-44, January.
    5. Anish Agarwal & Keegan Harris & Justin Whitehouse & Zhiwei Steven Wu, 2023. "Adaptive Principal Component Regression with Applications to Panel Data," Papers 2307.01357, arXiv.org, revised Oct 2023.
    6. Guido Imbens & Nathan Kallus & Xiaojie Mao, 2021. "Controlling for Unmeasured Confounding in Panel Data Using Minimal Bridge Functions: From Two-Way Fixed Effects to Factor Models," Papers 2108.03849, arXiv.org.
    7. Ruoxuan Xiong & Markus Pelger, 2019. "Large Dimensional Latent Factor Modeling with Missing Observations and Applications to Causal Inference," Papers 1910.08273, arXiv.org, revised Jan 2022.
    8. Joaqui-Barandica, Orlando & Manotas-Duque, Diego F. & Uribe, Jorge M., 2022. "Commonality, macroeconomic factors and banking profitability," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    9. Magnac, Thierry, 2023. "Capital humain et recherche d'emploi: un mariage heureux - Human Capital and Search Models: A Happy Match," TSE Working Papers 23-1489, Toulouse School of Economics (TSE).
    10. FATUM, Rasmus & YAMAMOTO, Yohei & CHEN, Binwei, 2023. "The Trend Effect of Foreign Exchange Intervention," Discussion paper series HIAS-E-132, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    11. Juho Koistinen & Bernd Funovits, 2022. "Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization," Papers 2202.00310, arXiv.org, revised Feb 2022.
    12. Alexandre Bonnet R. Costa & Pedro Cavalcanti G. Ferreira & Wagner Piazza Gaglianone & Osmani Teixeira C. Guillén & João Victor Issler & Artur Brasil Fialho Rodrigues, 2023. "Predicting Recessions in (almost) Real Time in a Big-data Setting," Working Papers Series 587, Central Bank of Brazil, Research Department.
    13. Yinchu Zhu, 2019. "How well can we learn large factor models without assuming strong factors?," Papers 1910.10382, arXiv.org, revised Nov 2019.
    14. Chan, Joshua C.C. & Poon, Aubrey & Zhu, Dan, 2023. "High-dimensional conditionally Gaussian state space models with missing data," Journal of Econometrics, Elsevier, vol. 236(1).
    15. Jungjun Choi & Hyukjun Kwon & Yuan Liao, 2023. "Inference for Low-rank Completion without Sample Splitting with Application to Treatment Effect Estimation," Papers 2307.16370, arXiv.org.
    16. Serena Ng & Susannah Scanlan, 2023. "Constructing High Frequency Economic Indicators by Imputation," Papers 2303.01863, arXiv.org, revised Oct 2023.
    17. Alberto Abadie & Anish Agarwal & Raaz Dwivedi & Abhin Shah, 2024. "Doubly Robust Inference in Causal Latent Factor Models," Papers 2402.11652, arXiv.org.
    18. Luis Costa & Vivek F. Farias & Patricio Foncea & Jingyuan (Donna) Gan & Ayush Garg & Ivo Rosa Montenegro & Kumarjit Pathak & Tianyi Peng & Dusan Popovic, 2023. "Generalized Synthetic Control for TestOps at ABI: Models, Algorithms, and Infrastructure," Interfaces, INFORMS, vol. 53(5), pages 336-349, September.
    19. Zongwu Cai & Ying Fang & Ming Lin & Zixuan Wu, 2023. "A Quasi Synthetic Control Method for Nonlinear Models With High-Dimensional Covariates," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202305, University of Kansas, Department of Economics, revised Aug 2023.
    20. Albert Chiu & Xingchen Lan & Ziyi Liu & Yiqing Xu, 2023. "What To Do (and Not to Do) with Causal Panel Analysis under Parallel Trends: Lessons from A Large Reanalysis Study," Papers 2309.15983, arXiv.org.
    21. Xingyu Li & Yan Shen & Qiankun Zhou, 2022. "Confidence Intervals of Treatment Effects in Panel Data Models with Interactive Fixed Effects," Papers 2202.12078, arXiv.org.
    22. Jungjun Choi & Ming Yuan, 2023. "Matrix Completion When Missing Is Not at Random and Its Applications in Causal Panel Data Models," Papers 2308.02364, arXiv.org.
    23. Xiong, Ruoxuan & Pelger, Markus, 2023. "Large dimensional latent factor modeling with missing observations and applications to causal inference," Journal of Econometrics, Elsevier, vol. 233(1), pages 271-301.
    24. Brantly Callaway, 2022. "Difference-in-Differences for Policy Evaluation," Papers 2203.15646, arXiv.org.

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