Selecting the Relevant Variables for Factor Estimation in FAVAR Models

When specifying and estimating latent factor models, a common assumption made is one of factor pervasiveness, which requires that Γ'Γ/N converges to a positive definite matrix, as N → ∞, where Γ denotes the loading matrix of the factor model. This paper builds on the recent nascent literature that examines how to relax this assumption (see e.g., Giglio, Xiu, and Zhang (2021), Freyaldenhoven (2021a,b), and Bai and Ng (2021)) and analyzes the scenario where there is significant underlying heterogeneity in the sense that some of the variables load significantly on the underlying factors, while others are irrelevant. Consistent factor estimation turns out to be feasible, even under factor nonpervasiveness, if one first prescreens all available variables and prunes out the irrelevant ones. For this purpose, we introduce, within a factor-augmented VAR framework, a novel variable selection procedure that, with probability approaching one, correctly distinguishes between relevant and irrelevant variables. Our methodology enables the consistent estimation of conditional mean functions of factor-augmented forecast equations, even when the conventional assumption of factor pervasiveness is violated