The Illusion of the Illusion of Sparsity: An exercise in prior sensitivity
This addresses the problem of model robustness in high-dimensional economic data analysis for researchers, but it is incremental as it builds on prior work.
The paper revisits the 'illusion of sparsity' in economic data by analyzing prior sensitivity in Bayesian models, finding that sparsity patterns depend heavily on the prior distribution of regression coefficients, suggesting the original illusion might itself be an illusion.
The emergence of Big Data raises the question of how to model economic relations when there is a large number of possible explanatory variables. We revisit the issue by comparing the possibility of using dense or sparse models in a Bayesian approach, allowing for variable selection and shrinkage. More specifically, we discuss the results reached by Giannone, Lenza, and Primiceri (2020) through a "Spike-and-Slab" prior, which suggest an "illusion of sparsity" in economic data, as no clear patterns of sparsity could be detected. 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 pattern of sparsity is sensitive to the prior distribution of the regression coefficients, and present evidence that the model indirectly induces variable selection and shrinkage, which suggests that the "illusion of sparsity" could be, itself, an illusion. Code is available on github.com/bfava/IllusionOfIllusion.