Model Selection Criteria for Factor-Augmented Regressions

Factor-augmented regressions are often used as a parsimonious way of modeling a variable using information from a large data-set, through a few factors estimated from this data-set. But how does one determine the appropriate number of factors that are 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, these are not necessarily all relevant for modeling a specific dependent variable within a factor-augmented regression and have, in general, difficulties in determining the number of factors in a large data-set. This paper develops a number of theoretical conditions selection criteria have to fulfill in order to provide a consistent estimate of the factor dimension that is relevant for such a regression. Our framework takes into account factor estimation error and it does not depend on a specific factor estimation methodology. Our conditions indicate that standard model selection criteria, such as BIC, are not consistent for factor-augmented regressions, but they can be once we modify these such 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 appropriate factor-augmented regressions