Individual Factor Risk Premia Can Be Identified When the Vector Cannot

Abstract

A factor's risk premium can be point-identified even when the vector of risk premia is not. We derive the necessary and sufficient condition---the kernel-orthogonality (KO) condition---and show it is equivalent to the existence of a population mimicking portfolio. When KO fails, standard estimators converge to a random variable rather than a constant, and $t$-tests spuriously reject zero risk premia. We develop a test to determine \emph{which} individual factor risk premia are identified, not just whether the entire model is identified. Applying our methodology to well-known models, we find that certain factors (e.g., consumption growth, intermediary leverage) fail KO while others (e.g., the market) pass. 

Keywords: Linear factor models, Underidentification test, Risk premia

JEL Classification: G12, C12, C58