Misspecification-robust bootstrap t-test for irrelevant factor in linear stochastic discount factor models

This paper examines the applicability of the bootstrap approach to test for irrelevant risk factors that are potentially useless in misspecified linear stochastic discount factor (SDF) models. In the literature, the misspecification-robust inference with useless factors is known to give rise to nonstandard limiting distributions bounded stochastically to compute critical values. We show how and to what extent the wild bootstrap yields a more accurate approximation of the distribution of $t$-statistics when testing for an unpriced factor in the context of linear SDF models. Simulation experiments and empirical tests are also used to document the relevance of the bootstrap method.