Matrix Completion, Counterfactuals, and Factor Analysis of Missing Data

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...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 116; no. 536; pp. 1746 - 1763
Main Authors: Bai, Jushan, Ng, Serena
Format: Journal Article
Language:English
Published: Alexandria Taylor & Francis 02.10.2021
Taylor & Francis Ltd
Subjects:
Convergence
Counterfactual thinking
Counterfactuals
EM algorithm
Error analysis
Estimation
Factor analysis
Hypothesis testing
mathematical theory
Matrices
Missing data
Missing-at-random
Normal distribution
Nuclear-norm regularization
Regression analysis
Regularization
Statistical methods
Statistics
Synthetic controls
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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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ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2021.1967163