Economic Predictions with Big Data: the Illusion of Sparsity

We compare sparse and dense representations of predictive models in macroeconomics, microeconomics and finance. To deal with a large number of possible predictors, we specify a prior that allows for both variable selection and shrinkage. The posterior distribution does not typically concentrate on a single sparse or dense model, but on a wide set of models. A clearer pattern of sparsity can only emerge when models of very low dimension are strongly favored a priori.