Economic variable selection

Regression plays a central role in the discipline of statistics and is the primary analytic technique in many research areas. Variable selection is a classical and major problem for regression. This article emphasizes the economic aspect of variable selection. The problem is formulated in terms of the cost of predictors to be purchased for future use: only the subset of covariates used in the model will need to be purchased. This leads to a decision-theoretic formulation of the variable selection problems, which includes the cost of predictors as well as their effect. We adopt a Bayesian perspective and propose two approaches to address uncertainty about the model and model parameters. These approaches, termed the restricted and extended approaches, lead us to rethink model averaging. From an objective or robust Bayes point of view, the former is preferred. The proposed method is applied to three popular datasets for illustration.