Model selection criteria for factor-augmented regressions

In a factor-augmented regression, the forecast of a variable depends on a few factors estimated from a large number of predictors. But how does one determine the appropriate number of factors relevant for such a regression? Existing work has focused on criteria that can consistently estimate the appropriate number of factors in a large-dimensional panel of explanatory variables. However, not all of these factors are necessarily relevant for modeling a specific dependent variable within a factor-augmented regression. This paper develops a number of theoretical conditions that selection criteria must fulfill in order to provide a consistent estimate of the factor dimension relevant for a factor-augmented regression. Our framework takes into account factor estimation error and does not depend on a specific factor estimation methodology. It also provides, as a by-product, a template for developing selection criteria for regressions that include standard generated regressors. The conditions make it clear that standard model selection criteria do not provide a consistent estimate of the factor dimension in a factor-augmented regression. We propose alternative criteria that do fulfill our conditions. These criteria essentially modify standard information criteria so that the corresponding penalty function for dimensionality also penalizes factor estimation error. We show through Monte Carlo and empirical applications that these modified information criteria are useful in determining the appropriate dimensions of factor-augmented regressions.