Estimation of Approximate Factor Models: Is it Important to have a Large Number of Variables?

The use of principal component techniques to estimate approximate factor models with large cross-sectional dimension is now well established. However, recent work by Inklaar, Jacobs and Romp (2003) and Boivin and Ng (2005) has cast some doubt on the importance of a large cross-sectional dimension for the precision of the estimates. This paper presents some new theory for approximate factor model estimation. Consistency is proved and rates of convergence are derived under conditions that allow for a greater degree of cross-correlation in the model disturbances than previously published results. The rates of convergence depend on the rate at which the cross-sectional correlation of the model disturbances grows as the cross-sectional dimension grows. The consequences for applied economic analysis are discussed.