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The emergence of Big Data raises the question of how to model economicrelations when there is a large number of possible explanatory variables. Werevisit the issue by comparing the possibility of using dense or sparse modelsin a Bayesian approach, allowing for variable selection and shrinkage. Morespecifically, we discuss the results reached by Giannone, Lenza, and Primiceri(2020) through a "Spike-and-Slab" prior, which suggest an "illusion ofsparsity" in economic data, as no clear patterns of sparsity could be detected.We make a further revision of the posterior distributions of the model, andpropose three experiments to evaluate the robustness of the adopted priordistribution. We find that the pattern of sparsity is sensitive to the priordistribution of the regression coefficients, and present evidence that themodel indirectly induces variable selection and shrinkage, which suggests thatthe "illusion of sparsity" could be, itself, an illusion. Code is available ongithub.com/bfava/IllusionOfIllusion.

The Illusion of the Illusion of Sparsity: An exercise in prior sensitivity