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Bank Efficiency & Risk: Entropy Meta Dynamic Model

November 15, 2025
in Social Science
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In an era where financial stability and sustainable growth are intertwined with technological innovation and risk management, a recent comprehensive study sheds new light on how different types of banks manage efficiency across multiple critical stages. Researchers have applied an advanced entropy meta two parallel three-stage dynamic Directional Distance Function (DDF) model to evaluate the efficiency of Chinese banks, dissecting its nuances not only by ownership type but also across critical operational dimensions—enterprise risk, operational performance, sustainability, and market presence. The findings reveal distinct patterns of strength and vulnerability among state-owned, joint-stock, urban, and rural commercial banks, presenting significant implications for policy makers, financial strategists, and the broader economic ecosystem.

At the heart of the study lies the categorization of banks into four groups: state-owned commercial banks, joint-stock commercial banks, urban commercial banks, and rural commercial banks. By examining the efficiency of these groups relative to both meta-frontier (MF) and group-frontier (GF) benchmarks, it becomes evident that the overarching frontier comprising pooled technological capabilities (GF) consistently outperforms the more restrictive group-specific frontier (MF). This result underscores the potential for banks to leverage cross-group innovations and shared technological advancements, potentially narrowing efficiency gaps through collaborative learning and technology diffusion.

State-owned commercial banks emerge as the unequivocal leaders in efficiency, consistently achieving or approaching optimal performance levels in operational and sustainability stages. Their resilience becomes particularly apparent in the aftermath of the COVID-19 pandemic, with marked improvements in market efficiency observed during 2022–2023 compared to earlier years. This rebound not only reflects an adaptive recovery trajectory but also highlights the relative robustness of state-owned institutions in absorbing economic shocks due to their stable capital structures, regulatory support, and better risk management frameworks. Their ability to blend risk control with resource allocation contributes to sustained competitiveness amid volatile market conditions.

Conversely, joint-stock commercial banks find themselves in a more precarious position. Although excelling in operational efficiency compared to sustainability and market stages, this group notably underperforms in sustainability efficiency, signaling challenges in integrating long-term environmental, social, and governance (ESG) criteria into their business models. This deficiency suggests a need for strategic realignment to embrace sustainability considerations more holistically, particularly as global financial regulations and investor expectations increasingly favor green and socially responsible investments.

Urban commercial banks echo this pattern but face their most significant hurdles in the market stage, where their efficiency is the lowest across all groups. This shortfall points to underlying issues in market adaptability, customer segmentation, and competitive strategy. Urban banks must refine their market engagement tactics by embracing innovative financial products, enhancing customer-centric services, and leveraging data analytics—all crucial for thriving in dynamic urban financial ecosystems characterized by intense competition and evolving consumer preferences.

Rural commercial banks represent the group with the highest enterprise risk and the greatest technology gaps, reflecting the inherent vulnerabilities linked to rural economic volatility, environmental challenges, and lower capital endowments. Despite exhibiting respectable performance in sustainability, likely due to their deep involvement in social welfare and rural development, these banks struggle to advance technologically and competitively in the short-term operational and market domains. Their traditional approaches and limited adoption of cutting-edge financial technologies restrict their capacity to enhance efficiency and market reach, leaving them exposed to systemic risks that could undermine their long-term viability.

A striking revelation of the study is the predominance of operational efficiency over sustainability and market efficiencies across most banks from a meta-frontier perspective. This difference illustrates the banks’ prioritization of short-term performance metrics over longer-term strategic goals, shedding light on the often observed dichotomy between immediate operational gains and sustained, responsible growth. Improving sustainability efficiency requires more than just financial investment; it necessitates institutional commitments to ESG principles, including green financing, risk monitoring, and incentive mechanisms that reshape operational mindsets toward enduring value creation.

The gap between sustainability and market efficiency further reveals a puzzling disparity rooted in market informational dynamics. Banks’ assets and ESG investments often carry long-term value that remains underappreciated by the market, which tends to reflect shorter-term pricing signals influenced by incomplete information. This asymmetry points to the inefficiencies in real-world financial markets and the limits of market efficiency theories, underscoring the importance of incorporating sustainability metrics into valuation frameworks to better capture banks’ comprehensive value propositions.

Diving deeper into enterprise risk performance exposes uneven distribution of risk-bearing capacities. Rural commercial banks suffered the most, with a majority maintaining optimal risk efficiency only in a few cases. In contrast, joint-stock and urban commercial banks showed moderate risk management efficacy, and state-owned banks demonstrated superior risk resilience. This stratification aligns with structural economic realities, where rural banks’ exposure to environmental shocks, commodity price volatility, and limited operational scale compounds risk, urging targeted policy interventions to bolster these institutions’ robustness.

Further validation comes from efficiency frontier analyses revealing vast discrepancies between technological levels within and across bank groups. Joint-stock and urban commercial banks, especially, manifested significant gaps between efficiencies calculated on meta-frontier versus group-frontier levels, indicating technological underutilization and missed opportunities for technology adoption to boost market and sustainability outcomes. By contrast, state-owned banks exhibited smaller, often statistically insignificant differences, reinforcing their advantage in technological maturity.

Statistical examinations, including Mann–Whitney U and Kruskal-Wallis tests, confirm the existence of significant heterogeneity in bank efficiencies and technology gaps, particularly highlighting where improvements are most critical. For example, the sustainability technology gap among joint-stock commercial banks is notably substantial, suggesting a focus area for strategic investment. Urban commercial banks, with noticeable market stage shortfalls, require a sharper orientation toward customer needs and competitive differentiation to close their efficiency deficits.

Encapsulating these insights, box plot visualizations illustrate cohort-specific technology gaps, painting a clear picture of performance landscapes. State-owned banks maintain a leading position across most efficiency dimensions, whereas joint-stock, urban, and rural banks struggle variably with operational technology, sustainability integration, and market competitiveness. These visual tools aid in pinpointing precise intervention points for improving banking sector robustness holistically.

The study’s revelations carry profound implications for the future trajectory of banking efficiency amidst escalating global economic uncertainties and the drive toward sustainable finance. For banks, embracing a balanced strategy that harmonizes short-term operational performance with long-term sustainability and market positioning is paramount. Policy-makers must tailor supportive frameworks that incentivize technology upgrades, risk management enhancement, and ESG commitment, particularly for vulnerable rural and mid-sized urban banks.

As the financial landscape evolves, technological innovation will remain a critical lever for improving efficiency and managing complex risk profiles. Investments in big data analytics, artificial intelligence for credit risk assessment, green finance technologies, and customer relationship management systems are essential to close the operational, sustainability, and market efficiency gaps highlighted in this research. Banks adopting such technologies early are better positioned to achieve sustainable competitive advantage, attract investment, and contribute to resilient economic systems.

Moreover, this research highlights the broader economic implications of banking efficiency disparities. The differential capacity of banks to manage risks and sustain growth affects credit availability, economic development, poverty alleviation, and environmental outcomes especially in underserved regions. Hence, addressing the disparities in efficiency and technological maturity is not merely an institutional concern but a societal imperative.

Ultimately, this landmark study provides a robust framework and empirical lens through which stakeholders can understand the multifaceted nature of bank efficiency. By confronting the interplay of risk, operations, sustainability, and market forces through rigorous modeling techniques, the research offers compelling evidence for strategic prioritization and innovation within the banking sector. Bridging these gaps holds promise for building financial institutions that are not only economically efficient but also socially responsible and economically inclusive in the years ahead.


Subject of Research: Bank efficiency estimation considering enterprise risk across different ownership types using an entropy meta two parallel three-stage dynamic Directional Distance Function model.

Article Title: Bank efficiency estimation considering enterprise risk: entropy meta two parallel three-stage dynamic DDF model.

Article References:
Fang, Z., Chen, Y., Chen, L. et al. Bank efficiency estimation considering enterprise risk: entropy meta two parallel three-stage dynamic DDF model. Humanit Soc Sci Commun 12, 1728 (2025). https://doi.org/10.1057/s41599-025-05991-6

Image Credits: AI Generated

DOI: https://doi.org/10.1057/s41599-025-05991-6

Tags: bank efficiency analysisChinese banking sector efficiencycross-group banking innovationsdirectional distance function modelentropy meta dynamic modelfinancial stability and growthmarket presence in bankingoperational performance evaluationrisk management in bankingstate-owned vs joint-stock bankssustainability in financial institutionstechnological advancements in finance
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