Factor-Based Imputation of Missing Values and Covariances in Panel Data of Large Dimensions

TL;DR

This paper introduces a factor-based method for imputing missing values in large panel datasets, ensuring consistent estimation of missing entries and covariances without iterative procedures, and demonstrates its effectiveness through simulations.

Contribution

It proposes a novel extsc{tall-project} algorithm that estimates factors from observed data blocks and imputes missing values efficiently in high-dimensional panel data.

Findings

Imputed values are consistent and asymptotically normal.

Covariance estimates are improved by resampling residuals.

Simulations confirm desirable finite sample properties.

Abstract

Economists are blessed with a wealth of data for analysis, but more often than not, values in some entries of the data matrix are missing. Various methods have been proposed to handle missing observations in a few variables. We exploit the factor structure in panel data of large dimensions. Our \textsc{tall-project} algorithm first estimates the factors from a \textsc{tall} block in which data for all rows are observed, and projections of variable specific length are then used to estimate the factor loadings. A missing value is imputed as the estimated common component which we show is consistent and asymptotically normal without further iteration. Implications for using imputed data in factor augmented regressions are then discussed. To compensate for the downward bias in covariance matrices created by an omitted noise when the data point is not observed, we overlay the imputed data with re-sampled idiosyncratic residuals many times and use the average of the covariances to estimate the parameters of interest. Simulations show that the procedures have desirable finite sample properties.