A New Metric for CO 2 Emissions Based on the Interaction Between the Efficiency Ratio Entropy/Marginal Product and Energy Use

Second Bwanakare (), Marek Cierpiał-Wolan and Daniel Rzeczkowski
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Second Bwanakare: Faculty of Socio-Economic Sciences, Institute of Economics and Finance, Cardinal Stephan Wyszynski University in Warsaw, ul. Kazimierza Wóycickiego 1/3/bud. 23, 01-938 Warsaw, Poland
Marek Cierpiał-Wolan: Institute of Economics and Finance, University of Rzeszow, ul. Mieczysławy Ćwiklińskiej 2, 35-601 Rzeszów, Poland
Daniel Rzeczkowski: Department of Market and Consumption, Institute of Economics and Finance, Faculty of Economic Sciences, University of Warmia and Mazury in Olsztyn, 1/327 Cieszyński Sq., 10-720 Olsztyn, Poland

Energies, 2025, vol. 18, issue 8, 1-22

Abstract: In an era of growing climate concerns and complex environmental policy challenges, novel approaches for accurate carbon emissions measurement are urgently needed. This article introduces an innovative approach for predicting carbon dioxide emissions by analyzing the interaction between energy consumption and production efficiency, measured through an entropy-to-marginal product ratio. Unlike conventional metrics such as Eurostat measurements or the Kaya identity, our framework establishes explicit connections to fundamental physical laws governing energy transformation while offering flexible elasticity parameters that capture non-linear relationships between efficiency improvements and emission reductions. The research combines theoretical modeling with empirical validation across ten European countries, demonstrating how the entropy-based methodology accounts for both production complexity and energy efficiency where traditional linear models fall short. Analysis reveals that energy-efficient countries demonstrate lower entropy maximization under stable conditions, indicating a direct relationship between operational efficiency and environmental impact. Although the model demonstrates strong predictive capabilities with an exceptional accuracy/information cost ratio, limitations exist in achieving accuracy in some country cases. This study concludes by evaluating these strengths and constraints, acknowledging the need for extended time series analysis and sector-specific applications, and providing clear directions for future research that bridge this promising theoretical contribution with practical environmental policy applications.

Keywords: economic production; economic efficiency; carbon dioxide emission metrics; power law (PL); maximum entropy principle; econometrics (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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