A team of Vietnamese researchers led by Thi Thao Pham and Khanh Cuong Le assembled a balanced panel covering all 63 Vietnamese provinces and centrally administered municipalities from 2010 to 2023, yielding 882 province-year observations. Their central instrument is a newly constructed Multidimensional Digital Transformation Indicator, or DTI, built from five dimensions: digital infrastructure such as fixed broadband subscriptions, digital adoption measured by active internet use, digital innovation captured through ICT-registered enterprises and e-commerce activity, digital governance based on provincial e-government readiness scores, and digital industry development reflecting the digital economy’s share of provincial GDP. The authors subjected the composite to an unusually thorough battery of diagnostics, including parallel analysis, reliability statistics such as McDonald’s omega of 0.89, and comparison against alternative weighting schemes, all of which supported its use as a regional capability measure.

The theoretical heart of the paper is a concept the authors call green capability infrastructure. Drawing on general-purpose technology theory, knowledge spillover theory, and absorptive capacity theory, they argue that digital transformation functions less like ordinary capital and more like an enabling layer for sustainability: it reduces the cost of searching for and transmitting knowledge, lowers barriers to adopting clean technologies, and helps shift economic activity toward less energy-intensive sectors. Crucially, the framework generates testable predictions that individual theories alone do not produce, namely that digital capability should correlate with green performance, that part of the relationship should travel through innovation, and that the association should strengthen once provinces accumulate enough digital capability to absorb and exploit new knowledge.

The empirical results are striking. In the preferred fixed-effects specification, a one-standard-deviation increase in the DTI corresponds to an energy-efficiency gain equal to roughly 10 percent of the sample mean. Energy efficiency here is measured as real GDP per unit of final energy consumption, a metric aligned with Vietnam’s National Energy Efficiency Program. The association survives a gauntlet of robustness checks: it holds when the index is rebuilt with entropy-weighted or equal-weight methods, when the outcome is switched to green total factor productivity computed with carbon dioxide treated as an undesirable output, and when the analysis is restricted to manufacturing energy intensity to rule out the possibility that service-heavy provinces are simply more efficient by composition.

Perhaps the most consequential finding concerns geography. Using a Spatial Durbin Model, the researchers decomposed the total association into direct and indirect components and found that approximately 37.5 percent of the fitted DTI-energy-efficiency relationship is indirect, meaning it operates through spatially neighboring provinces. Global Moran’s I statistics confirmed significant positive spatial autocorrelation in both digital capability and energy efficiency, with a high-high cluster centered on the Red River Delta and a persistent low-low cluster in the Northwestern Uplands. When the authors shuffled the spatial weight matrix at random, the fitted indirect effect collapsed to statistical insignificance while the direct effect remained intact, evidence that the spillover pattern depends on the actual geographic ordering of provinces rather than on the data’s marginal distribution alone.

The study also quantifies a plausible transmission mechanism. In sequential pathway models, stronger digital capability predicts higher patent activity, and patent activity in turn predicts better energy efficiency. The product-of-coefficients estimate implies that innovation accounts for an indicative 38 to 43 percent of the total digital-green association, a figure that remained stable when research and development intensity was substituted for patents. The authors are careful to note that their innovation measures are general rather than green-specific, so the evidence supports an innovation-consistent pathway rather than a proven green-innovation channel. Still, the magnitude suggests that digital infrastructure pays its largest environmental dividends when paired with functioning innovation ecosystems.

Nonlinearity adds a third layer to the story. Hansen panel threshold regression identifies a single breakpoint at a DTI value of 0.487, corresponding to the 60th percentile of the distribution. Below that threshold, the marginal association between digital capability and energy efficiency is modest; above it, the association more than doubles. The pattern is consistent with absorptive-capacity theory, which predicts that regions with sufficient complementary capabilities benefit disproportionately from knowledge flows. Comparisons with alternative threshold variables strengthen the interpretation: environmental regulation produces no significant threshold, and the digital-capability threshold remains evident after controlling for income per capita. The authors emphasize that the specific numerical cutoff is context-specific to Vietnam’s indicator scale, while the regime-testing framework itself is potentially transferable to other economies.

The researchers are notably candid about the limits of their design. This is an observational study, not an experiment, and every result is framed as a robust association rather than a causal effect. An instrumental-variable strategy exploiting distance to pre-2009 fiber-optic trunk lines produced a larger estimate, but the authors decline to treat it as causal because historical fiber proximity may correlate with roads, electricity infrastructure, and administrative capacity. Reverse causality, omitted variables, and the coarse provincial unit of analysis all remain live concerns, and the paper’s mediation results are explicitly labeled mechanism-consistent rather than identified. That methodological honesty is itself part of the contribution: the study demonstrates how far carefully bounded spatial associations can be pushed without overclaiming causal certainty.

The policy implications are correspondingly measured but pointed. Because roughly a third of the fitted association is indirect, the results support evaluating shared digital infrastructure, regional data platforms, and inter-provincial coordination mechanisms jointly rather than province by province. The threshold finding suggests that provinces near the capability boundary, roughly 12 to 13 of the 63 provinces in the 40th to 60th percentile band, may gain the most from complementary investment in innovation and governance capacity, while lower-capability provinces concentrated in the Northern Uplands and Central Highlands still need foundational connectivity first. The authors caution that their estimates refer to Vietnam’s pre-2025 63-province geography and cannot be mapped mechanically onto the country’s newly consolidated 34-unit administrative structure.

For a world searching for affordable levers to accelerate decarbonization, the Vietnamese evidence carries a provocative message: the green transition may depend not only on solar panels and wind farms but on the invisible infrastructure of data, platforms, and digital governance that determines how quickly clean knowledge spreads. If the findings hold up under firmer identification, the digital and green transitions may be less parallel tracks than a single intertwined pathway, and the regions that invest early in both could find themselves crossing capability thresholds that make every subsequent environmental gain easier to achieve.

Subject of Research: Spatial and threshold effects of digital transformation indicators on green transition outcomes across Vietnamese provinces

Article Title: Digital transformation indicators for green transition: Spatial spillovers, innovation pathways, and regime heterogeneity in Vietnam

Article References: Pham, T. T., Nguyen, T. D., Luu, H. D., Tran, A. Q., Trinh, K. C., Le, K. C., & Nguyen, M. H. (2026). Digital transformation indicators for green transition: Spatial spillovers, innovation pathways, and regime heterogeneity in Vietnam. Environmental and Sustainability Indicators, 32, Article 101557. https://doi.org/10.1016/j.indic.2026.101557

Image Credits: AI Generated

DOI: 10.1016/j.indic.2026.101557

Keywords: digital transformation, green transition, Vietnam, spatial spillovers, energy efficiency, green total factor productivity, innovation pathway, absorptive capacity, threshold regression, spatial econometrics, sustainability indicators, digital governance

The study, conducted by Huong Thi Thu Pham of Hung Vuong University, Nga Thi Pham of Thai Nguyen University of Economics and Business Administration, Anh The Khuc and Anh Bao Nguyen of the National Economics University in Hanoi, set out to resolve a stubborn weakness in the banking literature. Most previous analyses of how net interest margins affect profitability assumed a linear relationship: every additional basis point of margin was presumed to add roughly the same amount of profit regardless of the bank’s size. Others divided banks into small, medium, and large categories using arbitrary cutoffs chosen by the researchers rather than by the data. Both approaches, the authors argue, risk missing the scale-dependent structural breakpoints that actually govern how banking business models perform.

To find where that breakpoint lies, the team turned to an endogenous panel threshold regression framework, a statistical technique that lets the data itself reveal the critical value at which the relationship between two variables changes. Rather than imposing a threshold chosen in advance, the model searches across possible asset levels and identifies the point that best splits the sample into two distinct regimes. Applied to a panel of 58 commercial banks across Southeast Asia observed from 2013 to 2025, the procedure converged on a specific total asset threshold of USD 1.3 billion, expressed in the model’s logarithmic scale as a size value of 14.0794. The precision of the estimate matters because it transforms an abstract question about economies of scale into an actionable benchmark that regulators and bank executives can actually use.

The coefficients on either side of that line tell a striking story. Below the threshold, each unit of net interest margin is associated with an estimated profitability coefficient of 0.2608. Above the threshold, the same coefficient rises to 0.4014—an increase of more than half. In practical terms, this means that once a bank crosses the critical asset scale, every increment of core intermediation income it generates contributes substantially more to its bottom line than the identical increment would at a smaller institution. Crucially, the study finds that crossing the threshold amplifies rather than reverses the profitability benefits of margins, countering any suggestion that oversized banks suffer diminishing returns on their core lending business in emerging markets.

The mechanism behind this asymmetry, the authors contend, lies in economies of scale. Larger banks can spread fixed operating costs—branch networks, core banking systems, compliance infrastructure, risk management platforms—across a much wider asset base. They typically enjoy stronger bargaining power in funding markets, allowing them to gather deposits and wholesale funding more cheaply. They can also invest in the technology and analytical capacity needed to price loans more accurately and manage credit risk more efficiently. Together, these advantages mean that interest income is generated with less waste, so a greater share of each unit of margin flows through to net profits. The threshold result captures the point at which these scale economies become decisive enough to visibly change the margin-to-profit relationship.

The timing of the study gives its findings particular weight. The 2013 to 2025 window spans a period of profound stress and transformation in Southeast Asian banking, including the disruptions of the pandemic era, shifting interest rate cycles, and accelerating digitalization. Sustainable profitability—the ability of banks to remain consistently profitable across such turbulence rather than enjoying isolated windfall years—is critical for emerging economies, where commercial banks supply the overwhelming majority of external financing for firms and households. When bank margins translate efficiently into profits, banks can absorb losses, maintain lending through downturns, and support the robust flow of economic credit that development strategies depend on.

For policymakers in emerging economies, the implications are direct. The authors argue that government support programs and banking consolidation strategies should explicitly target scale optimization rather than treating bank size as an afterthought. In many Southeast Asian markets, the banking sector remains fragmented, with dozens of small institutions competing in the same territories and duplicating infrastructure. The threshold evidence suggests that policies encouraging mergers, acquisitions, or organic growth up to and beyond the USD 1.3 billion mark could unlock measurable efficiency gains across the system. At the same time, the finding invites careful calibration: consolidation policy must balance the efficiency benefits of scale against the competition and systemic risk considerations that have long dominated the regulatory conversation.

Bank managers receive an equally concrete prescription. The study advises executives to prioritize asset growth and cost reduction in order to leverage the asymmetric benefits of net interest margin. For institutions still below the threshold, the message is that margin expansion alone will deliver only limited profit gains; the strategic payoff arrives when margin management is paired with a credible path across the critical scale. For banks already above the line, the results justify continued investment in scale-sensitive capabilities, from digital delivery channels to centralized credit underwriting, that deepen the economies of scale the threshold analysis reveals. Cost discipline, in this framing, is not merely housekeeping but a precondition for converting intermediation income into durable profitability.

Methodologically, the paper’s contribution lies in demonstrating what endogenous threshold modeling can uncover where linear panels cannot. By letting the breakpoint emerge from the data, the approach avoids the arbitrary size classifications that have fragmented earlier findings and provides a replicable template for studying scale effects in other regions and other financial systems. The framework could readily be applied to banking markets in other emerging economies, to different profitability measures such as return on average assets, or to other candidate thresholds defined by capitalization, deposit base, or loan book size. If the Southeast Asian pattern holds elsewhere, the notion of a universal, size-blind relationship between margins and profits may need to be retired altogether.

The study also carries a broader warning for the field of sustainable finance research. As attention shifts toward environmental and governance dimensions of banking stability, the new results are a reminder that the humble mechanics of intermediation—how efficiently a bank turns its interest spread into retained earnings—remain foundational. A banking sector whose small institutions struggle to convert margins into profits is a sector with thinner loss-absorbing buffers, weaker capacity to fund green transitions, and greater vulnerability to shocks. By pinpointing the exact asset scale at which that conversion becomes efficient, the research offers emerging economies a quantified target in the pursuit of resilient, sustainable financial systems, and gives the global debate over bank size a number worth arguing about.

Subject of Research: Threshold effects of bank size on the relationship between net interest margin and sustainable profitability in Southeast Asian emerging economies

Article Title: Threshold effects of net interest margin on bank sustainable profitability in emerging economies

Article References: Pham, H. T. T., Pham, N. T., Khuc, A. T., & Nguyen, A. B. (2026). Threshold effects of net interest margin on bank sustainable profitability in emerging economies. Discover Sustainability. https://doi.org/10.1007/s43621-026-04921-z

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04921-z

Keywords: net interest margin, bank profitability, threshold regression, economies of scale, Southeast Asia, emerging economies, commercial banks, banking consolidation, ROAA, sustainable finance, panel data, financial economics

The methodological architecture of the study is what gives its findings their weight. Rather than relying on a single regression model, Salami combines Ordinary Least Squares estimation with Newey–West heteroskedasticity and autocorrelation-consistent standard errors, a correction that ensures the statistical conclusions remain robust even when the data exhibit the volatility typical of developing economies. On top of this baseline, the analysis layers time-series threshold regression, which allows the inflation–growth relationship to shift abruptly at a critical value, and smooth transition regression, which instead models a gradual change in the relationship as inflation rises. The two approaches are complementary: threshold models capture sharp regime changes, while smooth transition models capture softer, more continuous adjustments. Comparing their results provides a way to test whether the inflation–growth link truly behaves differently at different levels of inflation, or whether any apparent shift is a statistical artifact.

The headline result is that inflation is negatively and statistically significantly associated with real GDP growth in Nigeria, and that the magnitude of this association varies across inflation regimes. The threshold model identifies the critical value at 12.22 percent, and, notably, the inflation coefficient is negative both below and above that line. This is an important nuance. Some countries exhibit a benign zone of low inflation where the relationship is positive or neutral, turning negative only at higher rates. In Nigeria’s case, the data suggest that inflation is already a burden even at moderate levels, and that crossing the 12.22 percent mark changes the intensity of the damage rather than its direction. For a country that has experienced inflation rates well into double digits in recent years, this finding implies that the economy has been operating on the wrong side of the threshold for extended periods.

Rigorous science demands sensitivity analysis, and the study delivers one that addresses a subtle data problem. The trade-openness series used in the analysis required a completion procedure for its three boundary observations, and any such imputation could in principle distort the estimated threshold. To check this, the author re-estimated the model excluding those three boundary observations. The result was reassuring: the 12.22 percent threshold survived intact, and the regime-specific coefficients were closely comparable to the baseline estimates. This means the central finding is not materially driven by the data-completion procedure, a conclusion that substantially strengthens confidence in the threshold estimate. In empirical macroeconomics, where results can hinge on small sample choices, this kind of robustness check is the difference between a suggestive correlation and a defensible policy benchmark.

The smooth transition model tells a more cautious story. It identifies a transition location of approximately 11.50 percent, remarkably close to the threshold estimate, but its transition parameters are not statistically significant. In practical terms, this means the evidence for a gradual, smooth adjustment of the inflation–growth relationship is weaker than the evidence for a discrete regime shift. The convergence of the two models on a similar location, around 11.5 to 12.2 percent, is itself informative, suggesting that something real happens to Nigerian growth dynamics as inflation approaches the low teens. But the statistical weakness of the transition parameters means the threshold model remains the more reliable guide, and policymakers should treat the smooth transition results as corroborating rather than independently conclusive.

Inflation does not operate in a vacuum, and the study’s treatment of Nigeria’s external and fiscal environment is one of its most valuable contributions. Exchange-rate depreciation and international Brent crude oil-price shocks are both negatively associated with growth in the baseline specification, a result that reflects Nigeria’s well-known vulnerabilities as an oil-dependent economy with a currency sensitive to external pressures. Intriguingly, however, the independent statistical significance of these external variables weakens once nonlinear inflation dynamics are incorporated into the model. This suggests that part of the damage inflicted by oil shocks and currency depreciation may operate through their effect on inflation itself, which then transmits to growth. In other words, inflation may be the channel through which Nigeria’s external shocks do much of their harm, making price stability not merely one policy goal among many but a central defensive mechanism.

Perhaps the most policy-relevant finding concerns the interaction between inflation and fiscal conditions. The study finds a positive and statistically significant interaction between inflation and the fiscal balance, indicating that improved fiscal positions can attenuate, though not eliminate, the adverse association between inflation and growth. The mechanism is intuitive: when a government’s budget is healthier, it is better able to cushion households and firms against price shocks, avoid inflationary deficit financing, and maintain public investment that supports productive capacity. The crucial caveat is the word attenuate. Sound fiscal management softens the blow of inflation but cannot substitute for monetary control of prices. The finding underscores the study’s overarching conclusion that Nigeria’s growth stability depends on coordinated monetary, fiscal, and exchange-rate policies rather than on any single lever pulled in isolation.

The temporal dimension of the analysis reveals how Nigeria’s macroeconomic history is written into the data. Structural-break tests identify breaks in 2016, 2020, and 2023, corresponding to the country’s recession, the COVID-19-related economic disruption, and the exchange-rate liberalisation reforms respectively. These are not abstract statistical artifacts but recognizable chapters in Nigeria’s recent economic narrative. The 2016 recession followed the collapse of oil prices and foreign-exchange shortages; the 2020 break captures the pandemic’s simultaneous supply and demand shocks; and the 2023 break reflects the liberalisation measures that reshaped the currency regime. That the econometric tests independently detect these episodes lends credibility to the modeling framework, while also reminding analysts that parameter stability cannot be assumed in an economy subject to such repeated structural upheaval.

Complementary evidence comes from quantile regression, which examines how the inflation–growth relationship varies across the distribution of growth outcomes rather than only at the mean, and from machine-learning techniques applied in an explicitly exploratory role. Random Forest and XGBoost models were assessed using chronologically ordered hold-out validation, a demanding test that trains models on earlier data and evaluates them on later periods. The results indicated limited temporal generalisation, meaning the machine-learning models struggled to predict growth in unseen future periods. Consequently, their feature-importance and SHAP outputs are interpreted as exploratory nonlinear evidence rather than independent predictive or causal confirmation. This is a methodologically honest stance. Machine-learning tools can reveal complex interaction patterns that linear models miss, but without demonstrated out-of-sample predictive power, their outputs cannot be elevated to causal claims. The study’s willingness to constrain its own machine-learning findings is a model of restraint in a field often tempted by algorithmic overreach.

Taken together, the findings paint a coherent and sobering picture of Nigeria’s post-shock macroeconomic environment. The inflation–growth relationship is negative, regime-sensitive, and conditioned by fiscal and external circumstances. Trade openness is positively associated with growth, offering a rare bright spot, while broad money growth exhibits a negative baseline relationship, though these effects vary across specifications. Parameter-stability diagnostics, including CUSUM and CUSUMSQ tests, confirm that the baseline model’s coefficients and residual variance remain within statistical bounds, indicating no systematic instability that would undermine the estimates. For Nigerian policymakers, the practical message is clear: keeping inflation below the estimated 12.22 percent threshold, strengthening fiscal balances to buffer the inflation–growth nexus, and managing exchange-rate and oil-price exposures through coordinated policy are not competing objectives but interlocking requirements. For economists studying other emerging economies, the study offers a template for combining classical threshold econometrics with modern machine-learning diagnostics while respecting the limits of each. As global inflation pressures persist, the Nigerian experience serves as a reminder that the cost of letting prices drift upward is not abstract; it is measured in forgone growth, and the price of that mistake becomes steeper with every percentage point past the line.

Subject of Research: The nonlinear threshold relationship between inflation and economic growth in Nigeria

Article Title: Inflation threshold, fiscal conditions and growth stability in Nigeria’s post-shock macroeconomic environment

Article References: Salami, R. A. (2026). Inflation threshold, fiscal conditions and growth stability in Nigeria’s post-shock macroeconomic environment. Discover Sustainability. https://doi.org/10.1007/s43621-026-04682-9

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04682-9

Keywords: inflation, economic growth, Nigeria, inflation threshold, fiscal balance, exchange rate, oil prices, threshold regression, quantile regression, machine learning, macroeconomics, structural breaks