Consistent Estimation, Variable Selection, and Forecasting in FAVAR Models

In the context of latent factor models that are widely used in economics, a common assumption made is one of factor pervasiveness, which implies that all available predictor or informative variables in a dataset, with the possible exception of a negligible number of them, load significantly on the underlying factors. In this paper, we analyze the more likely 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, in the sense that they do not share any common dynamic structure with each other or with the relevant variables in the data set. We show that, even in such a setting, consistent factor estimation can be achieved if one pre-screens the variables and successfully prunes out the irrelevant ones. To do so, we introduce a new variable selection procedure that, with probability approaching one, correctly distinguishes between relevant and irrelevant variables. We study this problem within a factor-augmented VAR (FAVAR) framework, and show that by using variables selected via our pre-screening procedure to estimate the underlying factors and then inserting these factor estimates into -step ahead forecasting equations implied by the FAVAR model, we can obtain consistent estimates of the conditional mean function of said equations. In particular, our methodology allows the conditional mean function of a factor augmented forecast equation to be consistently estimable in a wide range of situations, including cases where violation of factor pervasiveness is such that consistent estimation is precluded in the absence of variable pre-screening