  The widespread co-existence of misspecification and weak identification in
asset pricing has led to an overstated performance of risk factors. Because the
conventional Fama and MacBeth (1973) methodology is jeopardized by
misspecification and weak identification, we infer risk premia by using a
double robust Lagrange multiplier test that remains reliable in the presence of
these two empirically relevant issues. Moreover, we show how the
identification, and the resulting appropriate interpretation, of the risk
premia is governed by the relative magnitudes of the misspecification
J-statistic and the identification IS-statistic. We revisit several prominent
empirical applications and all specifications with one to six factors from the
factor zoo of Feng, Giglio, and Xiu (2020) to emphasize the widespread
occurrence of misspecification and weak identification.
