Inference on Risk Premia in the Presence of Omitted Factors

Abstract

We propose a three-pass method to estimate the risk premia of observable factors in a linear asset pricing model, which is valid even when the observed factors are just a subset of the true factors that drive asset prices. Standard methods to estimate risk premia are biased in the presence of omitted priced factors correlated with the observed factors. We show that the risk premium of a factor can be identified in a linear factor model regardless of the rotation of the other control factors as long as they together span the space of true factors. Motivated by this rotation invariance result, our approach uses principal components to recover the factor space and combines the estimated principal components with each observed factor to obtain a consistent estimate of its risk premium. This methodology also accounts for potential measurement error in the observed factors and detects when such factors are spurious or even useless. The methodology exploits the blessings of dimensionality, and we therefore apply it to a large panel of equity portfolios to estimate risk premia for several workhorse linear models.