Dynamic Factor Models

Macroeconometricians face a peculiar data structure. On the one hand, the number of years for which there is reliable and relevant data is limited and cannot readily be increased other than by the passage of time. On the other hand, for much of the postwar period statistical agencies have collected monthly or quarterly data on a great many related macroeconomic, financial, and sectoral variables. Thus macroeconometricians face data sets that have hundreds or even thousands of series, but the number of observations on each series is relatively short, for example 20 to 40 years of quarterly data. This chapter surveys work on a class of models, dynamic factor models (DFMs), which has received considerable attention in the past decade because of their ability to model simultaneously and consistently data sets in which the number of series exceeds the number of time series observations. Dynamic factor models were originally proposed by Geweke (1977) as a time-series extension of factor models previously developed for cross-sectional data. In early influential work, Sargent and Sims (1977) showed that two dynamic factors could explain a large fraction of the variance of important U.S. quarterly macroeconomic variables, including output, employment, and prices. This central empirical finding that a few factors can explain a large fraction of the variance of many macroeconomic series has been confirmed by many studies; see for example Giannone, The aim of this survey is to describe, at a level that is specific enough to be useful to researchers new to the area, the key theoretical results, applications, and empirical findings in the recent literature on DFMs. Bai and Ng (2008) and Stock and Watson 2 (2006) provide complementary surveys of this literature. Bai and Ng's (2008) survey is more technical than this one and focuses on the econometric theory and conditions; Stock and Watson (2006) focus on DFM-based forecasts in the context of other methods for forecasting with many predictors. The premise of a dynamic factor model is that a few latent dynamic factors, f t , drive the comovements of a high-dimensional vector of time-series variables, X t , which is also affected by a vector of mean-zero idiosyncratic disturbances, e t. These idiosyncratic disturbances arise from measurement error and from special features that are specific to an individual series (the effect of a Salmonella scare on restaurant employment, for example). The latent factors follow a time series process, which is …