Model selection in factor-augmented regressions with estimated factors

This paper proposes two consistent model selection procedures for factor-augmented regressions in finite samples. We first demonstrate that the usual cross-validation is inconsistent, but that a generalization, leave-d-out cross-validation, selects the smallest basis for the space spanned by the true factors. The second proposed criterion is a generalization of the bootstrap approximation of the squared error of prediction of Shao (1996) to factor-augmented regressions. We show that this procedure is consistent. Simulation evidence documents improvements in the probability of selecting the smallest set of estimated factors than the usually available methods. An illustrative empirical application that analyzes the relationship between expected stock returns and factors extracted from a large panel of United States macroeconomic and financial data is conducted. Our new procedures select factors that correlate heavily with interest rate spreads and with the Fama-French factors. These factors have strong predictive power for excess returns.