<p>Threshold Effect Tests for DIF and Sub-indices</p>

This paper examines the nonlinear effects of Digital Inclusive Finance (DIF) on urban–rural integration (URI) using a provincial panel for mainland China (31 provinces, 2011–2023). We construct a multidimensional URI index and decompose DIF into coverage breadth (D1), usage depth (D2) and digitalization level (D3). Estimation proceeds with two-way fixed-effects models and Hansen-style panel threshold regressions with bootstrap inference; robustness checks include placebo tests and instrumental-variable specifications. The evidence shows that DIF’s impact on URI is regime-dependent: marginal returns are limited at low development levels but increase sharply once DIF and complementary institutional conditions cross empirically identified thresholds. Disaggregation reveals that usage depth (D2) consistently promotes integration, whereas the benefits of coverage (D1) and digitalization (D3) materialize mainly in digitally mature regimes. Traditional finance exhibits declining marginal contribution beyond its effective range, underlining the catalytic role of digital systems. We document heterogeneity across regions and show that negative baseline coefficients on openness and education reflect spatial concentration rather than intrinsic harms. The findings reconcile mixed results in prior work and imply that policy should be threshold-aware: prioritize foundational access where coverage is low, while in advanced contexts emphasize usage, platform interoperability, and regulatory safeguards to manage platform concentration and distributional risks.本研究基于中国内地31个省份2011—2023年的省级面板数据，考察数字普惠金融（Digital Inclusive Finance, DIF）对城乡融合（urban–rural integration, URI）的非线性影响。我们构建了多维城乡融合指数，并将数字普惠金融拆解为覆盖广度（D1）、使用深度（D2）与数字化程度（D3）三个维度。实证估计采用双向固定效应模型与带有Bootstrap推断的汉森型面板门槛回归模型；稳健性检验涵盖安慰剂检验与工具变量设定。 实证结果表明，数字普惠金融对城乡融合的影响呈区制依赖特征：在发展水平较低阶段，其边际效应较为有限；唯有当数字普惠金融与配套制度条件跨过经验识别出的门槛值后，边际效应才会显著提升。 分维度拆解结果显示，使用深度（D2）始终能显著促进城乡融合，而覆盖广度（D1）与数字化程度（D3）的积极效应主要在数字化成熟区制中显现。 传统金融在超出有效作用区间后，其边际贡献呈递减趋势，这凸显了数字技术系统的催化作用。 本研究还揭示了显著的区域异质性，并发现开放程度与教育水平的基准负向系数实则反映了空间集聚特征，而非其本身具有内在危害性。本研究调和了此前相关研究中存在的不一致结论，并表明政策制定应具备门槛意识：在覆盖广度较低的地区优先推进基础普惠接入，而在数字化成熟场景中则应侧重使用深度提升、平台互联互通建设与监管保障，以应对平台垄断与分配风险。