Optimal Cross-Sectional Regression

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See all articles by Zhipeng Liao

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics

Yan Liu

Purdue University

Date Written: October 26, 2020


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.

Keywords: Beta uncertainty, Efficient esetimation, Factor models, Fama-MacBeth, GMM, Idiosyncratic risk, Systematic risk, Two-pass regression, Errors-in-variables

JEL Classification: C14, C22

Suggested Citation

Liao, Zhipeng and Liu, Yan, Optimal Cross-Sectional Regression (October 26, 2020). Available at SSRN: https://ssrn.com/abstract=

Zhipeng Liao

University of California, Los Angeles (UCLA) - Department of Economics ( email )

8283 Bunche Hall
Los Angeles, CA 90095-1477
United States

Yan Liu (Contact Author)

Purdue University ( email )

West Lafayette, IN 47907-1310
United States

HOME PAGE: http://yliu1.com

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