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

TL;DR

This paper critically examines the robustness of the perceived sparsity in Bayesian economic models, revealing that the illusion of sparsity is highly sensitive to prior assumptions and may not reflect true data patterns.

Contribution

It revises previous Bayesian models with alternative priors and demonstrates that the supposed sparsity pattern is an artifact of prior sensitivity, challenging prior conclusions.

Findings

Sparsity patterns are highly sensitive to prior distributions.

Model induces variable selection and shrinkage indirectly.

The illusion of sparsity may be an artifact of prior choices.

Abstract

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.