Factor-based imputation of missing values and covariances in panel data of large dimensions

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 tall-project algorithm first estimates the factors from a tall block in which data for all rows are observed, and projections of unit specific sample size are then used to estimate the factor loadings. A missing value is imputed by its 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 sample covariance matrices created by an omitted noise in each imputed value, 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.