A hierarchical Bayesian regression model that reduces uncertainty in material demand predictions

Predictions of metal consumption are vital for criticality assessments and sustainability analyses. Although demand for a material varies strongly by region and end-use sector, statistical models of demand typically predict demand using regression analyses at an aggregated global level (“fully pooled models”). “Un-pooled” regression models that predict demand at a disaggregated country or regional level face challenges due to limited data availability and large uncertainty. In this paper, we propose a Bayesian hierarchical model that can simultaneously identify heterogeneous demand parameters (like price and income elasticities) for individual regions and sectors, as well as global parameters. We demonstrate the model's value by estimating income and price elasticity of copper demand in five sectors (Transportation, Electrical, Construction, Manufacturing, and Other) and five regions (North America, Europe, Japan, China, and Rest of World). To validate the benefits of the Bayesian approach, we compare the model to both a “fully pooled” and an “un-pooled” model. The Bayesian model can predict global demand with similar uncertainty as a fully pooled regression model, while additionally capturing regional heterogeneity in income elasticity of demand. Compared to un-pooled models that predict demand for individual countries and sectors separately, our model reduces the uncertainty of parameter estimates by more than 50%. The hierarchical Bayesian modeling approach we propose can be used for various commodities, improving material demand projections used to study the impact of policies on mining sector emissions and informing investment in critical material production.