Model selection in factor-augmented regressions with estimated factors

This paper proposes two consistent model selection procedures for factor-augmented regressions (FAR) in finite samples. We first demonstrate that the usual cross-validation is inconsistent, but that a generalization, leave-d-out cross-validation, is consistent. The second proposed criterion is a generalization of the bootstrap approximation of the squared error of prediction to FARs. The paper provides the validity results and documents their finite sample performance through simulations. An illustrative empirical application that analyzes the relationship between the equity premium and factors extracted from a large panel of U.S. macroeconomic data is conducted.