Useful Exergy Is Key in Obtaining Plausible Aggregate Production Functions and Recognizing the Role of Energy in Economic Growth: Portugal 1960-2009

The role of energy in economic growth is controversial. Models based on aggregate production functions (APF) range from the neoclassical, which downplay energy due to a cost-share theorem, but typically rely on exogenous total factor productivity (TFP), to the ecological economic, which acknowledge energy's importance. The validity of the APF concept itself is questioned. Here, we apply cointegration analysis to identify APFs between output, capital, labor, and possibly energy, measured as primary energy or useful exergy. We test for TFP growth by including a time trend. We require that plausible APFs verify cointegration, non-negative output elasticities, and Granger-causality linking inputs to output. Our method recognizes cases where: a) plausible APFs do not exist (thereby addressing the APF critique); b) energy impacts growth directly; c) energy impacts growth indirectly, through capital and labor. We apply the method to Portugal (1960-2009), considering standard and quality-adjusted capital/labor measures. With a time trend or disregarding energy, plausible APFs are never found. Without a trend, plausible APFs are found only when considering capital-energy-labor combinations. Within these, with quality-adjusted capital and labor and useful exergy, results are consistent with the cost-share theorem but energy plays a central role, through a constraint on all factors of production.