Efficient estimation of large approximate factor models using constrained principal components analysis

Abstract: 

This paper develops a new approach to the estimation of the number of factors, factors and factor loadings in large dimensional factor models. Efficient estimation of factor models is attracting considerable attention because recent empirical evidence suggests the estimates are adversely affected by the inability to account for the cross-sectional dynamics.

Principal components analysis (PCA) provides consistent estimation of the factor structure and efficiency can be achieved using robust econometric tools such as generalized PCA and quasi maximum likelihood. However when the number of variables is larger than the number of observations., the sample covariance matrix is singular and accounting for cross-sectional dynamics is challenging without imposing a structure on these dynamics. This paper uses the approximate structure assumption of bounded cross-sectional correlation as a constraint in the PCA framework. The proposed constrained PC can be interpreted as a shrinkage regression where the off diagonal elements of the covariance matrix are shrunk towards zero as the number of variables grows large. The new approach performs well in a series of Monte carlo simulations against PCA and other alternatives that make use of a known covariance structure. The results are appreciable for estimating the factor space, estimating the number of factors, but less significant in terms of forecasts performance.