A Survey of Non-radial Directional Distance Function and Global Malmquist-Luenberger Index in Assessing Carbon Emission Performance of Urban Agglomerations

This survey paper explores an advanced analytical framework that integrates non‑radial directional distance functions (NDDF) and the Global Malmquist‑Luenberger (GML) productivity index to assess carbon emission performance and environmental efficiency in urban agglomerations. The study underscores the significance of evaluating carbon emissions, given the substantial contribution of urban centers to global greenhouse gas emissions. By accommodating undesirable outputs, NDDF offer a comprehensive assessment of environmental productivity—crucial for effective policy formulation in urban settings. Integration with the GML index enhances the evaluation of green total factor productivity, offering insights into the interplay between economic growth and environmental sustainability. The paper outlines the methodological framework and discusses case studies that illustrate the practical application of these tools in Chinese urban agglomerations. Challenges such as data availability, methodological limitations, and the integration of socioeconomic factors are addressed, highlighting the need for refined methodologies and policy innovations. The findings emphasize the importance of technological advancements and targeted policies in promoting sustainable urban development. By leveraging these methodologies, urban planners and policymakers can develop effective strategies to enhance environmental efficiency and support the transition towards sustainable urban futures.