A revisited by-production technology for energy-carbon emission nexus in the OECD countries: Measuring the green productivity gains under alternative input specifications

The by-production (BP) model proposed by Murty et al. (2012) distinguishes between inputs that induce generation of the undesirable outputs (such inputs can include energy consumption) and those that do not contribute to generation of undesirable outputs (such inputs can include capital or labor). The BP model uses economic and environmental frontiers to approximate the production process and is considered to respect the materials balance principle. As the inputs contributing to generation of the undesirable outputs exhibit different roles (inequalities) across the two sub-technologies, construction of the input distance functions for construction of the productivity measures becomes cumbersome. To address this issue, the paper proposes a revision of the BP model where (i) the link between the two sub-technologies is improved and (ii) the role of the inputs that contribute to generation of the undesirable outputs is clarified. The revised model is fully compatible with popular productivity indices that incorporate input distance functions, such as the Luenberger-Hicks-Moorsteen indicator, making it practically applicable for assessing green productivity change. The empirical example of the energy-economy-environment nexus in the OECD countries is considered. The non-parametric environmental production technologies and productivity measures are compared based on the empirical example. The findings reveal substantial differences among the various methods and suggest that the proposed approach may serve as a viable alternative to existing approaches.