Optimal Cross-Sectional Regression

In the context of linear-beta pricing models, we develop a new class of two-pass estimators that are available in closed form and dominate existing two-pass estimators in terms of estimation efficiency. Importantly, we map our model into the generalized method of moments (GMM) framework and show our two-pass estimator is as efficient as the optimal GMM estimator, which is known to be semiparametrically efficient in the literature. Hence, contrary to popular belief, information loss does not need to occur when we go from the more methodical GMM approach to the simple-to-implement two-pass regressors. Intuitively, our estimator improves efficiency by disentangling the impacts of idiosyncratic and systematic return innovations on pricing errors in the second-stage cross-sectional regression. As an empirical application of the new two-pass estimators, we apply our approach to current factor models and shed new light on the Fama and French (2015) versus Hou, Xue, and Zhang (2015) debate.