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

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. Copyright The American Finance Association 1998.

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