Table 3 Theoretical premises for the selection of indicators for the QAP model.

Spatial adjacency

According to the theory of spatial spillovers, geographical proximity fosters economic interdependence and intensifies financial linkages across regions. Spatial adjacency among provinces fosters strong interconnections, with reduced geographical distance further strengthening linkages in the real economy (Wu et al., 2019). These enhanced interconnections contribute to the integration of regional financial markets, amplify the contagion of financial risks, and intensify their correlation and spillover effects within the spatial financial risk network (Allen and Gale, 2000). To capture these dynamics, a spatial adjacency matrix is constructed, where adjacent provinces are assigned a value of 1 and non-adjacent provinces are assigned a value of 0.

Economic Intensity

The stability of macroeconomic operation is a critical factor influencing the occurrence of financial risks (Yartey 2010). The intensity of economic radiation significantly impacts fluctuations in financial risks across provinces (Li et al., 2021). From the perspective of regional growth theory, provinces with stronger economic radiation tend to exert spillover effects on neighboring regions, thereby shaping the evolution of financial risk contagion (Bernanke and Gertler, 2000). To quantify economic radiation intensity, per capita GDP is employed as a measurement metric (Guo and Shi 2023), and a difference matrix of economic radiation intensity is constructed to capture spatial variations.

Financial Size

Financial size, reflecting the scale of the regional financial sector, further shapes systemic risk. While a larger financial sector can support credit expansion, resource allocation, and economic growth, excessive expansion may amplify systemic vulnerabilities, increase interconnectedness, and facilitate rapid propagation of financial shocks (Acemoglu et al., 2015). The ratio of financial industry added value to industrial added value is used as a proxy for financial size, and a corresponding difference matrix is developed to reflect provincial heterogeneity.

Current Ratio

Corporate financial performance constitutes a crucial micro-foundation for systemic risk. According to the financial accelerator theory, deterioration of firms’ balance sheets exacerbates financing constraints, amplifying shocks during economic downturns (Bernanke and Gertler, 2000; Ma and He, 2021). Liquidity shortages not only affect enterprise stability but can also transmit risks across broader financial networks through capital market channels (Shen et al., 2019). Based on this metric, a current ratio difference matrix is constructed to capture spatial variations and assess its role in the propagation of financial risks.

Fiscal Regulation

Effective financial supervision is essential to mitigate systemic vulnerabilities. Procyclical regulatory practices can amplify financial cycles, whereas countercyclical tools, such as capital buffers, can alleviate systemic risk (Vazquez and Federico, 2015). Excessive government intervention may induce moral hazard, consistent with soft budget constraint theory (KORNAI, 1986). To analyze the role of fiscal oversight, local fiscal and financial supervision expenditures are utilized to construct a fiscal supervision difference matrix, providing insights into regional variations in financial governance.

Household Credi

Household credit enables families to participate in financial markets, but high leverage may increase sensitivity to external shocks, thereby exacerbating systemic risk (Mian and Sufi, 2014). Following the life-cycle hypothesis, household consumption-to-income ratios reflect financial vulnerability and risk exposure (Modigliani and Brumberg, 2013). To assess household lending behavior, the ratio of urban residents’ expenditure to income is used as a proxy, and a household credit spread matrix is constructed based on this measure.