Energy Use Efficiency in G20 Economies under Carbon Emissions Constraints: A Variable-Returns-to-Scale Allocative Luenberger Indicator Approach

Abstract Energy-use efficiency is an important indicator of primary-energy performance, but it does not show whether energy, labor, and capital are moving toward a minimum-value feasible input mix. The objective of this study is to assess energy-use efficiency and factor-allocation change jointly for 18 Group of Twenty(G20) economies over 2008–2022. We develop a biennial variable-returns-to-scale Allocative Luenberger indicator that evaluates adjacent years against a common production technology while holding carbon emissions at observed levels. Using country-year valuation coefficients on a common purchasing-power-parity basis, the indicator decomposes full-input benchmark-value change into value-share-weighted technical and benchmark-relative allocation components; a matched energy-only direction measures change in the energy gap. Under the baseline input definitions, equal-country cumulative energy-use efficiency change is 0.0389. Full-input benchmark-value change is 0.0607, comprising a technicalLuenberger component of 0.0889 and an allocation component of −0.0282. These baseline results show improvements in energy-use efficiency and full-input technical performance over the sample period, whereas factor allocation moved away from the benchmark input mix. The allocation result is sensitive to input definitions, aggregation choices, and frontier composition.