Does a small cost share reflect a negligible role for energy in economic production? Testing for aggregate production functions including capital, labor, and useful exergy through a cointegration-based method

Neoclassical models disregard the role of energy in production, equating a factor's output elasticity with its cost share, but failing to explain growth without a residual term. In contrast, ecological economics acknowledges energy's importance in production, regardless of its cost share. The aggregate production function (APF) concept, central to neoclassical theory, is also disputed. We apply cointegration analysis to test for APFs between output, capital, and labor. We investigate the inclusion of energy inputs, measuring energy's capacity to generate productive work (useful exergy). Plausible APFs must verify cointegration and Granger-causality between output and inputs; and non-negative output elasticities. This method recognizes cases where: a) plausible APFs don't exist; b) energy impacts growth directly; c) energy impacts growth indirectly, through other inputs. We apply the method to Portugal (1960-2009), considering standard and quality-corrected capital and labor measures. Plausible APFs are rarely obtained for capital-labor models. When they are, the residual growth component is large, and output elasticities disagree with historical cost shares. However, the residual is virtually eliminated for capital-labor-energy models with two cointegration relationships: a) a capital-labor APF, with output elasticities matching historical cost shares; b) a function estimating capital from useful exergy. These models reconcile energy's significance in production with cost-share neoclassical assumptions.