Identification of Factor Risk Premia

Abstract

This paper a develops novel statistical test of whether individual factor risk premia are identified from return data in multi-factor models. We give a necessary and sufficient condition for population identification of individual risk premia, which we call the kernel-orthogonality condition. This condition is weaker than the standard rank condition commonly assumed for linear factor models. Under misspecification, our condition ensures point identification of the risk premium with minimal pricing error. We show how to test this restriction directly in reduced-rank models. Finally, we apply our test methodology to assess identification of risk premia associated with consumption growth and intermediary leverage.