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 that 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 pop-
ular belief, there need not be information loss 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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