An Asymptotic Theory for Estimating Beta‐Pricing Models Using Cross‐Sectional Regression

ABSTRACT Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two‐stage cross‐sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t ‐value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta‐pricing model is misspecified, the t ‐values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross‐sectional regressions for detecting model misspecification.