Empirical Asset Pricing and Statistical Power in the Presence of Weak Risk Factors
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Risk factors in many consumption-based asset pricing models display statistically weak correlation with the returns being priced. Some GMM procedures used to test these models have low power to reject misspecified stochastic discount factors (SDFs) when the covariance matrix of the asset returns with the risk factors has less than full column rank. Consequently, these estimators provide potentially misleading positive assessments of the SDFs. Two summary tests for failure of the rank condition have reasonable power, and lead to no Type I errors in Monte Carlo experiments.