Analysing club convergence in sustainable total factor productivity using SBM based global Malmquist–Luenberger Productivity Index with undesirable outputs

This study evaluates the Sustainable Total Factor Productivity (STFP), by integrating ecological and social dimensions. We use biocapacity per capita as a measure of the regenerative capability of ecosystems, alongside other economic inputs such as labor, capital energy consumption. Also, we use the Human Development Index (HDI) as desirable output to capture socioeconomic progress, whereas undesirable externalities are represented by emissions of carbon dioxide (CO 2 ), methane (CH 4 ), and nitrous oxide (N 2 O). We used the DEA based Malmquist–Luenberger Productivity Index to evaluate the STFP, further the convergence was evaluated by the club convergence test. The results showed several important insights. First, around 53% of the countries experienced positive growth in STFP during the sample period, with technological innovation serving as the primary driver than technical efficiency change. Second, the countries that have strategically invested in sustainable technologies have emerged as top performers, showing significant gains in sustainable productivity. Third, our results showed no sign of overall global convergence in STFP, however, the results reveal the formation of three distinct convergent clubs. These clubs reflect the heterogeneous STFP paths, indicating that countries are merging into groups with similar productivity growth rather than converging uniformly.