Consistent Factor Estimation in Dynamic Factor Models with Structural Instability

Abstract

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent, and find that these instabilities can be larger than earlier theoretical calculations suggest. We further characterize the rate of convergence of the estimated factors as a function of the magnitude of the time variation in the factor loadings for general types of parameter instability, and provide numerical evidence that this consistency rate is tight in the special case of random walk parameter variation. We also discuss implications of these results for the robustness of regressions based on the estimated factors and of estimates of the number of factors in the presence of parameter instability.