Determining the Number of Factors in Approximate Factor Models

In this paper we develop some econometric theory for factor models of large dimensions. The focus is the determination of the number of factors, which is an unresolved issue in the rapidly growing literature on multifactor models. We propose some panel C(p) criteria and show that the number of factors can be consistently estimated using the criteria. The theory is developed under the framework of large cross-sections (N) and large time dimensions (T). No restriction is imposed on the relation between N and T. Simulations show that the proposed criteria yield almost precise estimates of the number of factors for configurations of the panel data encountered in practice.