Spanning Latent and Observable Factors

Abstract

Factor analysis is a widely used tool to summarize high dimensional panel data via a small dimensional set of latent factors. Applications, particularly in finance, are often focused on observable factors with an economic interpretation. The objective of this paper is to provide a formal test for the question whether the factor spaces of latent and observable (economic) factors are equal. We derive asymptotic properties and propose a bootstrap version of the test which has improved small sample properties.

Keywords: Latent pervasive factors, Observable factors, Canonical correlations, Spanning, PCA

JEL Classification: C23, C38, C55, C12, E32