Before proceeding with the empirical analysis, we must address the critical statistical assumptions underlying our spatial econometric models. First, we construct the spatial weights matrix based on economical contiguity, Furthermore, for model specifications, we assume that both the spatial lag coefficient ( ρ ) and spatial error coefficient ( λ ) lie within the interval (−1,1), which ensures model stability. Additionally, the matrix I − ρ W is required to be non-singular for consistent estimation. Third, regarding the error terms, we assume that the error terms are independent across different regions and periods. Based on these assumptions and following existing literature (Anselin, 1988; LeSage and Pace, 2009), we first construct a panel data model to examine the influence of MA on UER within the YRDr: U E R i t = α 0 + β 1 M A i t + β 2 M A 2 i t + ∑ n = 1 4 θ n Z n i t + μ n + v t + ε i t (1)

The subscripts i and t represent the prefecture-level cities and the year, respectively; U E R i t signifies the level of urban ecological resilience of city i; M A i t and M A 2 i t denote the degree of MA and its squared term of city i; μ n , v t are the area fixed effects and time fixed effects respectively; Z n i t encompasses a set of control variables, including urbanization level (UL), financial level (FL), population density (PD) and primary education level (PEL); ε i t represents the random error term, and α, β are the estimated coefficients of the relevant variables.

Consider that interregional activity does not occur in isolation and can be influenced by neighbouring areas due to interaction effects. In addition, considering that in economic reality, UER will be affected by the previous period’s level, there is time inertia, and the lag term can better overcome the endogeneity problem caused by omitted variables. Based on this, this paper extends Formula 1 to test the spatial spillover effect of MA using a spatial dynamic econometric model. The model is as follows: U E R i t = α 0 + β 0 U E R i t − 1 + ρ 1 ∑ i = 1 N W U E R i t + ρ 2 ∑ i = 1 N W U E R i t − 1 + β 1 M A i t + ρ 3 ∑ i = 1 N W M A i t + β 2 M A 2 i t + ρ 4 ∑ i = 1 N W M A 2 i t + ∑ n = 1 4 θ n Z n i t + τ ∑ i = 1 N W Z n i t + μ n + v t + ε i t (2) where ρ 1 , ρ 2 , ρ 3 , ρ 4 and τ mean the spatial-lag coefficient of each variable; W denotes the spatial weight, which denotes the spatial weight matrix. In this paper, we construct the economic distance spatial weight matrix W1 firstly and standardize it.

To further explore the influence mechanism of MA on UER, this paper refers to the classic mediation effect model (Chen and Lee, 2020) to test the mediation effect of GTI in MA and UER from green utility model patents (UtyGTI) and green invention-based patents (InvGTI): M = c X + e 2 (3)

In the context of this analysis, the paper redefines MA as X, and the process of GTI as M in Equation 3. To comprehensively assess the intricate dynamics between these elements, the study integrates a range of additional factors into the mediating effect model. These include control variables that capture other relevant influences, time-lagged terms of the explained variable (Y) to account for temporal continuities, and spatial-lagged terms of all variables to address the spatial dependencies and interactions among the units of analysis. G T I i t = b 0 + b 1 G T I i t − 1 + γ 1 ∑ i = 1 N W G T I i t + γ 1 ∑ i = 1 N W G T I i t − 1 + b 2 M A i t + γ 3 ∑ i = 1 N W M A i t + b 3 M A 2 i t + γ 4 ∑ i = 1 N W M A 2 i t + ∑ n = 1 4 θ n Z n i t + τ ∑ i = 1 N W Z n i t + μ n + v t + ε i t (4)

Following the principles of accessibility, comprehensiveness and comparability of the construction of the indicator system, combining the connotation of UER and referring to the results of previous studies (Martin and Sunley, 2015; Wu et al., 2020) this paper is based on the resistance-adaptation-resilience framework to construct a UER level evaluation index system in Table 1. This UER capacity characterizes the vulnerability and sensitivity of the city when it is impacted, the urban ecological adaptive capacity that characterizes the level of adjustment of the city when it faces disturbances, the urban ecological resilience capacity that embodies the speed of recovery and the degree of restoration of the city after experiencing perturbations, are included in the unified index system. Due to the different indicator units, this paper standardizes the individual indicators and then uses the entropy method Topsis to calculate the ecological resilience level of each city.

Since location entropy is conducive to eliminating endogenous effects due to regional scale differences (Zheng and Lin, 2018), this study employs location entropy to quantify the degree of manufacturing agglomeration within prefecture-level cities in YRDr.

As a quantitative tool, green patent application data can more intuitively measure the output of GTI activities (Shen et al., 2021). Compared with the number of patents granted, the number of patent applications reflects the current trend of technological innovation. It allows us to examine the impact of MA on the output of GTI activities in cities based on a more time-sensitive perspective. Therefore, this paper uses the Wanfang Data Knowledge Service Platform as the data source to obtain and construct a spatiotemporal database of green patent applications at the prefecture-level city level in the YRDr, and aggregate the total number of green invention patents and green utility model patents filed to assess the level of GTI, the unit of which is 1,000 pieces.

To minimize the potential issue of omitted variable bias beyond the core and mechanism variables, this study draws on relevant literature and economic theory (Ma et al., 2024; Jiang et al., 2024), incorporating the following control variables into the model: including urbanization level (UL), measured by the ratio of the urban resident population to the total resident population; financial level (FL), measured as the logarithm of total deposits at the end of the year in regional financial institutions; population density (PD), calculated as the logarithm of the total year-end population of each city divided by its administrative area size; and the primary education level (PEL): expressed as the logarithm of the number of people enrolled in primary school. To mitigate potential multicollinearity between MA and its quadratic term, we applied standardization to both MA and MA2. The statistical characteristics of the main variables are shown in Table 2.

Before proceeding with the empirical analysis, we conduct multicollinearity diagnostics for our model. Table 3 presents the results of VIF (Variance Inflation Factor) tests after centering the variables. The VIF test results suggest no severe multicollinearity problems in the model, as all VIF values are well below the conventional threshold of 5.

Because traditional panel econometric model estimates ignore possible spatial spillovers, they are prone to biased error in the results. To assess the presence of spatial correlation between MA and UER, this paper employs the global Moran’s I test. Subsequently, this paper refers to Equations 2, 4 in turn through the LM test, the RLM test, the WALD test and the Hausman test, and finds that all the tests passed the significance test, so this paper adopts the fixed effects of the spatial Durbin model (SPDM).

In addition to using the dynamic SPDM model, this paper reports the FE and static SAR models’ results. Before interpreting the results, we verify the statistical assumptions in Section 4.1. As shown in Table 4, the estimated spatial lag coefficient ( ρ ) is around 0.18 (significant at 1% level), which lies within the stable range (−1,1), confirming our model stability assumption. The spatial weights matrix (W) is properly row-standardized based on geographic contiguity, and tests for error term independence are satisfactory. These results validate the reliability of our spatial econometric specifications.

The coefficient of the primary term of MA estimated by the FE model in the model (1) is significantly negative at the 1% level. The coefficient of the secondary term is significantly positive at the 1% level, which indicates that there is an apparent positive U-shaped relationship between MA and UER, i.e., with the increase of the level of MA, the impact of the MA on the UER will be changed from negative to positive. That is the impact of MA on UER shifts from negative to positive as the level of MA increases. Initially, the negative impact of MA on UER may reflect the early-stage environmental pressures associated with manufacturing agglomeration, such as increased pollution, resource depletion, and ecosystem disruption. As MA levels increase, the positive impact likely stems from technological advancements, improved environmental management practices, and the adoption of cleaner production methods, ultimately enhancing the city’s ecological resilience. The coefficients of the primary and secondary terms of MA estimated by the static SPDM and dynamic SDM models in models (2) and model (3) also passed the 10% significance test, which is consistent with the estimation results of the non-spatial econometric model.

Further analysis of the coefficients of MA in the model reveals that the coefficients of the primary term and the coefficients of the quadratic term of MA in model (1) are more significant than the coefficients of MA in models (2) and (3), which suggests that if spatial correlation and endogenous correlation are ignored, the impact of MA on UER may be overestimated. This overestimation highlights the importance of considering spatial spillover effects in assessing the impact of MA on UER. It suggests that a city’s ecological resilience is influenced by its manufacturing agglomeration and neighbouring areas, emphasizing the need for regional coordination in environmental policies and industrial planning. Therefore, the results of the subsequent analyses in this paper are based on the dynamic SPDM model that considers the explanatory variables’ endogeneity, spatial correlation and time lag effect.

To measure the impact of MA on UER, this paper carried out a spatial effect decomposition, and the results of the effect Decomposition for Dynamic SPDM are shown in Table 5. In the short term, the coefficient of MA is −0.0274 and MA2 is 0.0071, indicating significant spatial linkage effects. In the long run, the coefficient of MA is −0.0275 and MA2 is 0.0071. The results show that both MA and MA2 are significant at the 5% level in both periods, indicating the stability of MA’s impact on UER over time. The inflection points are 1.930 and 1.937 for short-term and long-term respectively, suggesting a consistent inverted U-shaped relationship between MA and UER. The increased values of spatial effects from short-term to long-term (such as UL from 4.2986 to 4.3481, FL from 5.4896 to 5.6051) suggests that over time, the environmental practices and policies associated with MA have an even more pronounced impact on the broader region. This could be attributed to the gradual diffusion of eco-friendly technologies and management practices across cities and the cumulative effects of environmental policies on regional ecosystems.”

The analysis further delineates that MA impedes UER when its level is below 1.930 in the short term, suggesting a threshold effect where MA initially acts as a barrier to UER. Conversely, once MA surpasses this threshold, it markedly enhances UER, illustrating a transformative shift in its impact. Similarly, as presented in Table 5, long-term effects also exhibit an inverted U-shaped relationship between MA and UER, with the long-term inflection point slightly higher at 1.937 compared to the short-term. This consistent inverted U-shaped relationship across both time frames underscores the nuanced dynamics between MA and UER. Notably, the higher inflection point in the long-term analysis (1.937 versus 1.930) indicates that the beneficial impacts of MA on UER are sustained longer over extended periods. This temporal shift suggests that the positive contributions of MA to UER become more enduring as the temporal horizon extends, affirming the stable and evolving nature of this relationship.

The previous empirical analyses of the benchmark regression used a model that controls for regional time and regional fixed effects, which, to a specific extent, controls for the impact of omitted variable factors that may come from different levels. To further verify and enhance the reliability of the estimation results, this paper will use the following methods to conduct the robustness test based on applying control variables.