Theoretical evolution of financial development and inclusive finance

Financial development has long been recognized as a driver of economic transformation, guided by classical theories such as financial intermediation [6] and the financial repression hypothesis [7]. In developing economies, financial deepening promotes growth and reduces poverty by improving capital allocation and lowering transaction costs, but its redistributive effects are conditional on institutional quality, governance and human capital [8,9]. Empirical studies indicate that without institutional safeguards, financial expansion may favor high-income urban groups, exacerbating inequality [9]. Nonlinear effects have also been documented: initial stages of financial deepening may narrow income gaps, whereas mature markets may reinforce disparities [10]. These findings motivate the emergence of inclusive finance, which explicitly addresses structural exclusion within conventional financial systems. Evidence shows that inclusive finance fosters poverty alleviation and regional equity, though spatial heterogeneity persists [11].

The transition from inclusive finance to DIF

The rise of ICT and fintech has transformed financial inclusion. Digital Inclusive Finance (DIF), encompassing mobile payments, digital credit, insurance, and data-driven risk assessment, reduces service barriers and broadens access for rural populations and microenterprises [12–14]. Comparative research highlights contrasting adoption patterns: advanced economies emphasize product innovation and regulatory adaptation, while developing economies rely on mobile platforms and agent-banking to overcome infrastructure deficits [15,16]. In China, DIF supports rural revitalization, agricultural modernization, and employment growth, with stronger effects in less-developed western provinces and diminishing returns in mature eastern regions [17–19]. Evidence from India confirms that digital financial inclusion reduces income inequality [20]. Yet potential downsides exist: unequal digital literacy and platform concentration may reinforce exclusion [21–24].

Despite this growing body of work, several gaps remain. First, most studies emphasize income distribution rather than broader dimensions of urban–rural integration (URI), including social-service equity, spatial mobility, and ecological sustainability. Second, the literature rarely considers nonlinear dynamics—for example, whether DIF only becomes effective beyond critical thresholds [25,26]. Third, regional heterogeneity is underexplored, particularly how local financial structures, policy environments, and demographic conditions shape DIF’s impact.

From DIF to URI: Theoretical linkages and research gaps

While most DIF research focuses on income or poverty outcomes, URI is multidimensional, encompassing economic convergence, equitable access to services, spatial connectivity, ecological sustainability, and demographic mobility [13,27]. Understanding DIF’s impact requires analyzing its transmission channels—credit expansion, digital payments, insurance, and platform services—within local institutional contexts. Nonlinear and threshold effects are increasingly recognized: DIF may only significantly influence URI beyond critical levels of technology diffusion or institutional readiness [25,26]. To address these gaps, this study decomposes DIF into coverage breadth, usage depth, and digitization level, applying a panel threshold regression model to examine regime-dependent effects across five URI dimensions using provincial data for China (2011–2023). This approach informs both China’s policy agenda and comparative analyses of inclusive digital transformation in developing economies.

Conceptual framework

URI involves coordinating economic structures, social services, population mobility, and spatial development across urban and rural areas. Achieving URI requires overcoming barriers in capital flows, institutional access, and infrastructure.

DIF offers opportunities to reshape urban–rural linkages by reducing financial frictions and expanding participation in formal financial systems [28,29]. Drawing on the inclusive innovation framework [30], DIF may enhance URI through two channels: (1) economic empowerment—facilitating credit access, lowering transaction costs, supporting rural entrepreneurship, and stimulating industrial upgrading; (2) social transformation—expanding digital platforms, improving e-commerce and tele-services, and integrating digitally mediated public infrastructure. DIF may also generate positive externalities that reinforce rural governance and environmental quality, indirectly supporting URI [17,18].

Hypothesis 1: Higher levels of DIF are associated with enhanced URI by improving financial access and enabling broader economic and institutional participation in rural areas.

Threshold effects and regional heterogeneity

The impact of DIF on URI is unlikely to be linear or uniform. In regions with low internet penetration or limited digital literacy, DIF’s effects may be constrained; as digital ecosystems mature, benefits may accelerate, suggesting threshold effects [27,29,31]. Prior studies emphasize that digital technologies often produce significant impacts only after surpassing critical levels of infrastructure and institutional capacity [25,26].

China’s regional diversity in institutional quality, policy support, and human capital further implies spatial heterogeneity. For example, rural households may benefit more from digital financial access than urban counterparts [32], highlighting differentiated inclusion dynamics.

Hypothesis 2: The relationship between DIF and URI exhibits threshold characteristics. The early stages of DIF development have limited effects, while beyond a certain threshold, impacts strengthen substantially.

Fig 1 illustrates the proposed causal pathways and nonlinear dynamics between DIF and URI.

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Fig 1. Conceptual framework of DIF and URI.

Note: DIF includes three sub-indices (D1, D2, D3). Threshold effects are modeled for DIF, sub-indices, and traditional financial development (TF).

https://doi.org/10.1371/journal.pone.0342432.g001

Variable selection

Model specification

To estimate the impact of DIF on URI, we begin with a two-way fixed-effects specification that controls for time-invariant provincial characteristics and common temporal shocks. The baseline regression equation is formulated as follows:

(1)

where and denote province and year fixed effects, X_it is the vector of control variables (FCI, GOV, OPEN, EDU, MPP), and is the idiosyncratic error term. A fixed-effects estimator is preferred over random effects because regional governance quality, infrastructure, and economic structure are likely correlated with financial development, making the strict exogeneity assumption implausible.

While Eq (1) identifies the average association between DIF and URI, theoretical considerations and prior digital-finance research suggest that returns to digitalization may be nonlinear. Early-stage digital ecosystems suffer from low interoperability and limited digital literacy, whereas mature ecosystems generate stronger network and institutional complementarities. To capture this regime dependence, we apply Hansen’s (1999) panel threshold model:

(2)

where q_it is the threshold variable (DIF or one of its sub-indices), and , are estimated endogenously. Inference relies on bootstrap methods with 1,000 replications following Hansen (1999). MPP was excluded from threshold estimations because its strong correlation with DIF led to unstable regime classification in bootstrap iterations; excluding it does not materially affect the results.

By integrating fixed-effects and threshold approaches, our empirical strategy identifies not only the average effect of DIF on URI but also how this effect changes across stages of digital-financial development, enabling a more precise test of the nonlinear “digital maturity” hypothesis.

Descriptive statistics and multicollinearity diagnostics

Table 1 reports descriptive statistics for key variables. The URI index exhibits substantial cross-provincial variation (mean = 0.202; SD = 0.076), reflecting heterogeneous integration levels. The DIF index and its sub-indices also show broad dispersion, consistent with uneven digital development across regions. MPP is retained in its original unit to capture infrastructure capacity without information loss.

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Table 1. Descriptive statistics of key variables.

https://doi.org/10.1371/journal.pone.0342432.t001

Multicollinearity is assessed using VIFs; results are shown in Table 2. Most control variables have VIFs below 5. However, the DIF sub-indices (D1–D3) exhibit higher VIFs due to their shared origin in a composite index. To avoid mechanical multicollinearity, we exclude the composite DIF when estimating models with sub-indices and vice versa. Robustness checks excluding EDU or rescaling D1–D3 confirm that coefficients for DIF and D2 remain stable, indicating that collinearity does not drive our main findings.

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Table 2. Variance inflation factor (VIF) results.

https://doi.org/10.1371/journal.pone.0342432.t002

Baseline regression results

Table 3 reports the baseline regression results examining the association between DIF and URI. Model (1) includes only year and province fixed effects. The estimated coefficient for DIF is 0.1302 (p = 0.022), indicating a statistically significant and positive association with URI.

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Table 3. Benchmark regression results.

https://doi.org/10.1371/journal.pone.0342432.t003

Model (2) incorporates additional control variables—FCI, GOV, OPEN, EDU, and MPP. The DIF coefficient remains significant (, p = 0.003), underscoring its robust impact. The within-R² increases to 0.803, suggesting improved explanatory power.

Interestingly, the coefficients for OPEN and EDU are negative and statistically significant, suggesting potential structural asymmetries in how openness and education affect integration. This pattern warrants further exploration, which we address through decomposition and interaction analyses in “Decomposition Tests for OPEN and EDU”. Overall, the results confirm a robust and positive association between DIF and URI, though we refrain from asserting strict causality due to potential endogeneity concerns.

Sub-dimensional analysis of DIF

To explore underlying mechanisms, we decompose DIF into its three sub-indices—D1 (coverage breadth), D2 (usage depth), and D3 (digitalization degree)—and re-estimate the regression models. Table 4 presents the findings.

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Table 4. Results of DIF sub-indices.

https://doi.org/10.1371/journal.pone.0342432.t004

Only D2 and D3 are statistically significant and positively associated with URI, while D1 is not. This suggests that mere access to digital financial tools is insufficient; what matters more is active engagement and technological sophistication. These findings align with existing literature emphasizing usage over access in achieving meaningful financial inclusion outcomes.

D2 is positive and significant at the 1% level (p = 0.003), highlighting the importance of transaction frequency and sustained financial behavior. D3 is also significant (p = 0.005), pointing to the critical role of technological infrastructure and digital service quality. In contrast, D1 is not statistically significant (p = 0.252), indicating that expanded access without corresponding use may not contribute to URI.

These results reinforce the need for policies that promote not just access to, but also meaningful usage of, digital financial tools—especially in rural and underserved areas.

As shown in Table 2, the variance inflation factors (VIFs) for the sub-dimensions of DIF—particularly D1 and D2—exceed the conventional threshold of 10. This reflects their intrinsic interdependence, as these components originate from the same composite index and tend to evolve jointly in practice: wider coverage typically coincides with deeper usage and higher digitalization. To ensure robustness and interpretive reliability, we employ three complementary strategies.

(1) Stepwise regression comparison. The theoretical analysis does not rely solely on coefficient magnitudes within a single specification. Instead, we estimate stepwise regressions by introducing each sub-dimension separately and jointly to compare their relative effects. This approach reveals that D2 consistently exerts a positive and statistically significant influence on URI across all model specifications, while the signs and interpretations of D1 and D3 remain stable.

(2) Principal component adjustment. To control for shared variance among sub-dimensions, we apply principal component analysis (PCA) to extract their common component and re-estimate the baseline model. The resulting PCA-based index remains positive and significant at the 1% level (, p = 0.002). This consistency indicates that the observed effects of DIF on URI are not artifacts of multicollinearity.

(3) Ridge regression validation. Finally, we implement ridge regression using the optimal penalty parameter () determined via cross-validation. The ridge estimates preserve the same sign pattern as the OLS coefficients, with only minor magnitude adjustments (see S4 Table). This confirms that the positive association between DIF and URI remains stable even when multicollinearity is explicitly penalized.

Across all robustness checks, three conclusions emerge: (i) the positive effect of D2 is stable and significant in every model; (ii) when multiple sub-indices are included simultaneously, statistical significance declines slightly, but coefficient signs and economic interpretations remain unchanged; and (iii) PCA- and ridge-based estimations yield nearly identical substantive results.

Hence, while multicollinearity among sub-dimensions is acknowledged, it does not distort the estimated relationships or alter substantive conclusions. Retaining the sub-dimensional structure is theoretically justified, as it reveals the differentiated transmission mechanisms through which digital inclusive finance promotes URI.

Regional heterogeneity analysis

To capture the contextual diversity of DIF effects on URI, this section extends the baseline regressions to explore heterogeneity across multiple structural dimensions. Given space constraints, we focus on the two most theoretically salient sources of variation—regional differences and digital infrastructure levels—while briefly summarizing additional robustness tests. Detailed results are presented in Table 4 and (S5 Table 1–4).

1. Regional Heterogeneity
   Spatial differences in China remain the most fundamental dimension of economic and institutional variation. Subsample regressions for the eastern, central, and western regions reveal clear gradients in the effectiveness of DIF (see Table 4).
   In the eastern region, where digital and financial infrastructure is already mature, DIF’s overall effect on URI is positive but only marginally significant (, p = 0.062). This suggests diminishing marginal returns; incremental digital-finance expansion yields limited additional gains once access saturation has been achieved.
   In the central region, coefficients for all sub-dimensions are positive and significant, reflecting a “sweet spot” where digital finance interacts with improving infrastructure and growing rural demand to produce balanced integrative outcomes.
   In contrast, the western region shows the strongest effects (, p < 0.001) across all dimensions, indicating that DIF serves a substitutive function—compensating for physical and institutional deficits by enabling access, connectivity, and entrepreneurial opportunity.
   Overall, these results highlight a spatially stratified pattern. DIF yields the highest marginal benefits in transitional or lagging regions where traditional financial penetration remains low and digital technologies can leapfrog structural bottlenecks.
2. Heterogeneity by ICT Infrastructure
   To further test how technological readiness shapes the inclusivity of digital finance, provinces are divided into high-ICT and low-ICT groups based on internet penetration. Results (S5 Table2) indicate that DIF’s positive impact on URI is robust across both groups but substantially stronger in high-ICT provinces (, p < 0.01) than in low-ICT ones (, p < 0.05). The significant interaction term between DIF and ICT underscores a complementarity mechanism: advanced digital infrastructure amplifies the effectiveness of financial digitalization by improving transaction efficiency, lowering service costs, and facilitating real-time data verification.
   Among sub-indices, D2 and D3 display the highest sensitivity to ICT conditions, confirming that the transformative power of DIF depends not only on policy support but also on the technological ecosystem in which it operates.
3. Additional Heterogeneity Tests
   Three supplementary robustness checks further corroborate these findings:
   • Grouping provinces by economic development stage (per capita GDP) shows that DIF’s marginal effect strengthens with higher development levels, yet the “usage depth” channel remains significant even in low-income provinces.
   • Heterogeneity by industrial structure (service-sector share) suggests stronger DIF effects in service-oriented economies, where small-scale and digital-intensive activities dominate.
   • Analysis by fiscal support intensity reveals a positive interaction between public expenditure and DIF, implying that well-targeted fiscal programs can crowd in digital-finance participation rather than substitute for it.

Collectively, these tests confirm that DIF’s integrative impact is conditioned by both structural maturity and institutional coordination. Across all dimensions, two consistent findings emerge: (i) D2 remains the most stable and significant driver of URI, and (ii) DIF’s marginal returns rise with improvements in infrastructure, development level, and public support. These results demonstrate that digital finance is most transformative when embedded in an enabling technological and institutional environment.

Decomposition tests for OPEN and EDU

To further clarify the unexpected negative or insignificant coefficients on OPEN and EDU in the baseline results, we conduct decomposition and interaction analyses to explore whether these effects are driven by urban concentration rather than true “disbenefits” of openness or education.

Specifically, we proxy urban- and rural-oriented education by interacting total education investment with the provincial urbanization rate (edu_total × Urban_rate) and its complement (edu_total × (1 – Urban_rate)). We also construct an openness–urbanization interaction term (OPEN × Urban_rate) and an export-intensity variable (export_share = exports/GDP) to capture differences in the spatial concentration of trade activities.

The results are reported in S6 Table. Across all specifications, the main findings are consistent and intuitive:

• The coefficients on edu_urban_proxy and edu_x_urban are small and statistically insignificant, whereas the rural-oriented component (edu_rural_proxy) remains weakly negative. This pattern suggests that the overall negative EDU effect in the baseline regression stems largely from the urban bias of education investment and the associated outflow of human capital from rural areas. When accounting for urbanization heterogeneity, the education effect on URI becomes economically small and no longer significant, indicating that the negative sign does not reflect an inherently harmful role of education but rather resource diversion toward urban cores.
• Regarding openness, the coefficient on open_x_urban is strongly negative and highly significant (, p < 0.01), whereas the baseline OPEN effect becomes positive when this interaction is included (, p < 0.01). This confirms that the negative impact of openness is concentrated in provinces where trade and investment benefits accrue primarily to urbanized regions. Similarly, the export_share variable itself shows no robust association with URI once spatial concentration is controlled for, implying that trade intensity per se is not harmful, but its urban-centric distribution can temporarily inhibit province-level integration.
• The grouped regressions reinforce this mechanism: for provinces below the median urbanization or export concentration, the coefficients on OPEN and EDU are close to zero or slightly positive, whereas in highly urbanized or trade-concentrated provinces, the OPEN effect turns sharply negative. Taken together, these results support the interpretation that the apparent negative signs of OPEN and EDU are artifacts of urban concentration and center–periphery dynamics, not genuine detrimental effects on integration.

These findings enrich our understanding of the role of structural asymmetries in digital and economic development. They underscore that openness and education can promote integration only when accompanied by mechanisms that channel their benefits beyond urban cores, such as rural education enhancement, balanced fiscal transfers, and inclusive trade-link infrastructure.

Replacing DIF with digital economy development

To assess robustness, we re-estimate the benchmark model by replacing the DIF index with a broader indicator of Digital Economy development (DE). Conceptually, DE and DIF are related but not interchangeable. The digital economy encompasses economy-wide digitalization—including ICT infrastructure, industrial digital transformation, e-commerce, and data-driven business models—whereas DIF refers specifically to the digitalization and diffusion of financial services. This hierarchical distinction is well established in the literature, which characterizes digital finance as a component within the broader digital economy system [37,38].

Thus, substituting DIF with DE constitutes an upper-category robustness test rather than a direct conceptual replacement. If both indicators yield similar signs and significance, this suggests that general digitalization and financial digitalization jointly promote URI; divergence would imply that DIF operates through mechanisms not captured by the broader DE construct. To avoid misinterpretation, we explicitly report DE as an alternative variable and interpret its coefficient as reflecting broad digitalization effects instead of financial-channel mechanisms.

Empirical results (Table 5) show that DE remains positively associated with URI (Coef. = 0.2174, p = 0.024), confirming that the main findings are not sensitive to how the digital transformation process is measured. This also supports the view that DIF plays a distinct and stable role within the broader digitalization landscape.

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Table 5. Regression using DE as the core explanatory variable.

https://doi.org/10.1371/journal.pone.0342432.t005

Excluding direct-administered municipalities

To address potential sample heterogeneity, we exclude the four direct-administered municipalities—Beijing, Shanghai, Tianjin, and Chongqing—which differ markedly from provinces in governance structure, economic scale, and urban-rural configurations. The results (Table 6) show that DIF remains significantly and positively associated with URI (Coef. = 0.0348, p < 0.01), and the within-R² rises to 0.9328. These findings confirm that the observed relationship is not driven by high-income outliers and holds across more homogeneous regional samples.

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Table 6.

Robustness Tests and Instrumental Variable (IV) Estimation Results

https://doi.org/10.1371/journal.pone.0342432.t006

Placebo test

To test for spurious correlation, we construct a placebo variable by randomly assigning DIF values to half the sample and setting the rest to zero. The placebo regression (Table 6) yields an insignificant coefficient (Coef. = 0.000137, p = 0.585), well above any standard significance threshold. This suggests that the relationship between DIF and URI in the main model is unlikely to result from random chance or omitted variable bias, further validating the causal interpretation of Hypothesis 1.

Addressing endogeneity through instrumental variables

To address potential endogeneity arising from reverse causality and omitted variables, we adopt an instrumental variable (IV) approach to reinforce the causal interpretation of the relationship between DIF and URI in the baseline fixed-effects and threshold models. Given the limited availability of strong external instruments, we adopt a two-stage least squares (2SLS) framework using lagged DIF values as internal instruments. This approach is widely accepted in macro-regional analyses where exogenous policy shocks are difficult to obtain [39].

Threshold identification and statistical significance

To examine potential nonlinearities in the relationship between DIF and URI, we adopt the non-linear panel threshold regression framework of Hansen (1999)[5]. Bootstrap-based inference is applied to ensure robustness against heteroskedasticity and small-sample bias. Each threshold test employs 1,000 bootstrap replications to obtain empirical p-values and 95 percent confidence intervals for threshold parameters.

Table 7 reports the threshold test results for DIF, its sub-indices (D1-D3), and TF. The results reveal strong and statistically significant threshold effects for DIF and most sub-indices. Both single- and double-threshold models for the composite DIF index are significant at the 1 percent level (F = 445.79 and 154.23, p = 0.000), whereas the triple-threshold model is rejected (p = 0.913). Similar patterns hold for D1 and D3, while only single thresholds are detected for D2 and TF. These findings support the existence of nonlinear, regime-dependent effects in the DIF–URI nexus.

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Table 7. Threshold Effect Tests for DIF and Sub-indices

https://doi.org/10.1371/journal.pone.0342432.t007

Economic interpretation of threshold effects

The estimated thresholds carry distinct economic implications (see Table 8). For the overall DIF index, the lower threshold (2.8637) marks the emergence of basic digital finance infrastructure such as mobile payments and online banking; the upper threshold (4.1133) signals a mature digital ecosystem featuring platform interoperability and service diversification. Below the upper threshold, the marginal effect of DIF is modest (, p < 0.01); beyond it, the coefficient rises sharply to 0.2279 (p < 0.01), demonstrating super-linear returns once digital maturity is achieved.

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Table 8. Regime-specific coefficient estimates.

https://doi.org/10.1371/journal.pone.0342432.t008

Sub-indices analyses further clarify underlying mechanisms:

• D1 shows minimal impact below its threshold but a substantial gain after surpassing 4.1331 (, p = 0.083), reflecting scale-dependent improvements once coverage broadens.
• D2 remains effective even below 4.4379 (, p < 0.01), underscoring the role of active digital-service usage in promoting inclusivity through reduced transaction costs.
• D3 reveals significant nonlinearity, with coefficients jumping from 0.0084 to 0.0795 after the 4.4904 threshold (p < 0.01).
• For TF, the threshold at 0.0194 is only marginally significant (p = 0.060), and post-threshold effects are insignificant, suggesting that traditional finance lacks the transformative returns observed in digital domains.

Regime-specific estimates and data constraints

Table 8 presents regime-specific coefficient estimates for DIF and its components. For DIF, effects increase tenfold beyond the upper threshold, confirming strong nonlinearities. D1 exhibits similar patterns; D2 retains low-regime significance but has insufficient upper-regime data; D3 demonstrates robust double-threshold effects with statistical significance; TF shows no meaningful post-threshold gain.

Table 8 reports regime-specific coefficients with robust standard errors and 95% confidence intervals. Some upper-regime estimates are based on limited observations (e.g., only n = 19 for DIF >4.1133). To convey this uncertainty, we (i) report 95% confidence intervals for regime coefficients in Table 8, and (ii) plot coefficient estimates with 95% confidence bands in Fig 2. The wide intervals in high-regime segments signal low precision; therefore, although point estimates often imply large economic effects, we interpret these high-threshold magnitudes cautiously.

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Fig 2. Regime-specific coefficient estimates with 95% confidence intervals.

Notes: Each point denotes the estimated coefficient; horizontal bars show 95% confidence intervals based on province-level cluster-robust standard errors. Upper regimes (e.g., DIF >4.1133, n = 19) exhibit wider intervals due to limited sample size.

https://doi.org/10.1371/journal.pone.0342432.g002

Accordingly, these findings are interpreted conservatively: while statistical significance indicates regime-dependent effects, economic magnitudes remain imprecise and should be validated with longer time series or micro-level data. Bootstrap-based confidence intervals for threshold estimates are reported in S8 Appendix to further assess sampling variability.

Heterogeneity, data limitations, and mechanism differentiation.

The threshold regression results reveal strong nonlinearities in the DIF–URI relationship but also highlight important heterogeneity across dimensions and regimes. While the identified thresholds are statistically robust under 1,000 bootstrap replications, the distribution of observations is highly uneven—particularly in upper-threshold intervals (e.g., DIF >4.1133, D2 >4.4379, D3 >4.4904). These sparse upper regimes account for fewer than 5% of the total sample, reflecting the early and uneven stage of digital-finance development across Chinese provinces.

Consequently, although some upper-regime coefficient estimates are statistically significant, their economic magnitudes should be interpreted with caution due to limited precision and small sample sizes.

Beyond data constraints, the heterogeneous regime behavior underscores multi-layered mechanisms through which digital finance affects URI:

• Coverage breadth (D1) operates via infrastructure accumulation: once sufficient reach is achieved, network externalities and scale economies emerge, amplifying integration effects.
• Usage depth (D2) functions through behavioral engagement: even at lower maturity levels, active participation in digital services reduces transaction costs and improves resource allocation.
• Digitalization level (D3) reflects technological sophistication: its high threshold (∼4.49) suggests that only advanced regions can fully leverage automation, AI-based credit scoring, and big-data analytics to enhance integration efficiency.

These differentiated pathways confirm that digital finance follows a staged, regime-dependent diffusion process rather than a linear progression. Early-stage gains stem from access expansion (D1), mid-stage gains from user adoption and service diversification (D2), and late-stage gains from technological upgrading and platform integration (D3). This pattern aligns with threshold theory, where marginal returns shift qualitatively upon crossing key enabling conditions such as institutional readiness or technological maturity.

Fig 3 visualizes the threshold effects for the composite DIF index and its sub-indices. The visible jumps at threshold points corroborate the presence of critical inflection levels, confirming that digital finance exhibits super-linear yet regime-bound effects on URI.

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Fig 3. Threshold effects of DIF and sub-dimensions on URI.

Notes: The red dashed vertical lines indicate estimated threshold values derived from Table 8. Blue lines represent estimated coefficients in lower and upper regimes; blue dots mark point estimates in each regime. The visible structural breaks reflect regime-dependent nonlinearities, reinforcing the presence of critical development inflection points in the DIF–URI relationship.

https://doi.org/10.1371/journal.pone.0342432.g003

While the results are robust to bootstrap resampling, upper-regime findings remain sensitive to data limitations. Future research should extend temporal coverage or utilize micro-level data to verify whether these super-linear effects persist in later stages of digital-finance evolution. Incorporating dynamic threshold estimation and regional spillover modeling would further enhance understanding of how digital finance interacts with local institutions, human capital, and technological ecosystems.

Policy implications and theoretical contributions

The empirical results, reinforced by 1,000 bootstrap replications, provide robust and nuanced policy implications.

First, verified threshold effects imply that developmental returns to digital finance are regime-dependent rather than linear. Bootstrap-based inference confirms the statistical stability of these nonlinearities, suggesting that policy interventions should be phased and region-specific rather than uniform nationwide. Provinces approaching critical DIF thresholds—especially those near 2.86 and 4.11—represent high-potential targets for catalytic investment and institutional support. Prioritizing transitional regions can yield disproportionately high payoffs once digital maturity is reached.

Second, sub-dimensional findings highlight complementary but asymmetric roles of DIF components:

• Expansion of coverage (D1) forms the infrastructural foundation;
• Usage depth (D2) ensures behavioral engagement;
• Digitalization level (D3) drives technology-enabled efficiency gains.

However, upper-regime estimates—though statistically significant—exhibit wide confidence intervals due to limited observations, implying that their economic magnitudes should be interpreted as potentially transformative yet less precise. Policymakers should adopt an evidence-sensitive sequencing strategy, combining infrastructure investment with capability-building and digital literacy programs.

Third, the analysis clarifies that improving access alone is insufficient. Sustainable integration requires deep digital engagement and institutional embedding of digital financial systems. The identification of threshold-dependent dynamics suggests that inclusive finance policies must evolve beyond “access-first” paradigms toward maturity-driven inclusion, where the interplay of technology, usage, and governance determines long-term outcomes.

From a theoretical standpoint, this study enriches the literature by empirically demonstrating the threshold-dependent and regime-specific nature of digital finance’s developmental impact. These results substantiate Hansen’s (1999) threshold theory in a digital economy context, illustrating how systemic returns change qualitatively once key technological or institutional parameters surpass critical levels. The observed multi-regime behavior aligns with theories of staged technological diffusion and endogenous financial modernization.

Moreover, by integrating bootstrap-based inference with multidimensional measurement of URI, this study advances methodological rigor in identifying nonlinear policy thresholds. It contributes to bridging the gap between linear empirical models and the complex realities of digital transformation.

Future research may extend this framework by exploring:

• Dynamic threshold shifts,
• Spatial spillovers,
• Interaction effects among digital, institutional, and human-capital dimensions.