Dynamic Network Productivity, Club Convergence, and Machine Learning Benchmarking: Evidence from Indian Banks across Ownership Groups

This paper examines the convergence patterns of risk-adjusted bank productivity across distinct ownership groups in the Indian banking industry by employing the state-of-the-art club convergence clustering procedure. To construct a comprehensive measure of bank productivity and its constituent components, we propose a three-stage dynamic network structure operationalised through the Dynamic Sequential Malmquist–Luenberger Productivity Index (DSMLPI), which adopts a holistic view of the bank production process by explicitly capturing the internal linkages among multiple divisions via intermediate processes and incorporating carryover flows across time periods to embed a meaningful temporal dimension in the analysis. Drawing on a balanced panel dataset spanning 2010–2017, our empirical results reveal that, in the absence of any discernible catching-up effect, the observed surge in bank productivity within the Indian banking industry is attributable entirely to technological progress rather than to improvements in productive efficiency. We identify distinct convergence clubs for overall bank productivity and its technical change component at both the aggregate industry level and the disaggregated ownership-group level; however, a single convergence club is detected for the efficiency change component across the industry as a whole. To rigorously validate these club convergence findings, we benchmark these results against unsupervised machine learning clustering algorithms, wherein tests of silhouette stability, seed sensitivity, and economic coherence collectively demonstrate that k-means clustering yields groupings that are ambiguous, unstable, and economically incoherent on our small banking panel, whereas the earlier procedure consistently produces stable, theoretically grounded clubs; thereby firmly establishing the methodological superiority of econometric convergence analysis over unsupervised machine learning for datasets of this scale and structure.