Robust inference in linear asset pricing models

We derive new results on the asymptotic behavior of the estimated parameters of a linear asset pricing model and their associated t-statistics in the presence of a factor that is independent of the returns. The inclusion of this \"useless\" factor in the model leads to a violation of the full rank (identification) condition and renders the inference nonstandard. We show that the estimated parameter associated with the useless factor diverges with the sample size but the misspecification-robust t-statistic is still well-behaved and has a standard normal limiting distribution. The asymptotic distributions of the estimates of the remaining parameters and the model specification test are also affected by the presence of a useless factor and are nonstandard. We propose a robust and easy-to-implement model selection procedure that restores the standard inference on the parameters of interest by identifying and removing the factors that do not contribute to improved pricing. The finite-sample properties of our asymptotic approximations and the practical relevance of our results are illustrated using simulations and an empirical application.