Topic: Contributed on Panel data models with common factors: Theory and applications Title: Shrinkage PCA for efficient estimation of large approximate factor models Authors:  Rachida Ouysse - University of New South Wales (Australia) [presenting]
Abstract: A new approach is developed for the efficient estimation of large dimensional approximate 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. A factor structure is approximate when the idiosyncratic errors are weakly correlated across the variables. 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 $N>T$, the sample covariance matrix is singular and accounting for cross-sectional dynamics is challenging without imposing a structure on these dynamics. We propose to use the approximate structure assumption of bounded cross-section correlation as a constraint in the PCA framework. The proposed penalized PCA can be interpreted as a shrinkage regression where the off diagonal elements of the covariance matrix are shrunk towards zero as $N$ grows large. The new approach performs well in a series of Monte carlo simulations against PCA and other competing alternatives.