This paper develops an IV-GMM approach that uses past beta estimates and firm characteristics as instruments for estimating ex-post risk premia while addressing the error in-variables problem in the two-pass cross-sectional regression method. The approach is developed in the context of large cross sections of individual stocks and short time series. We establish the N-consistency of the IV-GMM ex-post risk premia estimator and obtain its asymptotic distribution along with an estimator of its asymptotic variance-covariance matrix. These results are then used to develop new tests for asset pricing model implications.
Empirically, we examine a number of popular asset pricing models and fund support for the recent q-factor model
proposed by Hou, Xue, and Zhang (2015).