The Illusion of the Illusion of Sparsity: the Effects of Using a Wrong Prior

Abstract

The emergence of Big Data raises the question of how to model statistical series when there is a big number of possible regressors. This monograph addresses the issue by comparing the possibility of using dense or sparse models in a Bayesian approach, allowing for variable selection and shrinkage. We discuss the results reached by Giannone, Lenza e Primiceri (2018) through a “Spike-and-Slab” prior, that suggest an “illusion of sparsity” in economic datasets, as no clear patterns of sparsity could be found. We make a further revision of the posterior distributions of the model, and propose three experiments to evaluate the robustness of the adopted prior distribution. We find that the model indirectly induces variable selection and shrinkage, what suggests that the “illusion of sparsity” is, itself, an illusion