Since the 21st century, global environmental pollution issues have become more prominent. Different regions choose various environmental indicators for EQ assessments based on their specific circumstances. For example, air quality index, carbon emission index, noise pollution index, etc. Some scholars integrate multiple environmental dimensions such as atmosphere, water, soil, ecology, and noise to establish a comprehensive evaluation index, thereby conducting a comprehensive assessment of regional EQ. According to the analysis of the impact paths of GI on regional EQ, it can be observed that currently, GI in China primarily focuses on industrial pollutant emissions, with minimal impact on residential pollution (Shi et al., 2023). In light of the mentioned characteristics, this paper draws extensively upon the contributions of scholars such as Miao in the research field (Miao et al., 2016). Ultimately, nine specific indicators were selected to establish a comprehensive EQ evaluation index from the critical dimensions of regional environmental carrying capacity and environmental governance level. The detailed interpretation of these indicators is presented in Table 1.

Evaluating regional EQ requires not only the establishment of an EQ evaluation index system but also the determination of weights for each indicator. In the academic realm, methods for determining indicator weights can be categorized into subjective and objective approaches. Subjective methods rely on personal judgment, such as expert scoring and the analytic hierarchy process (AHP). Objective methods, on the other hand, use data and mathematical models to determine weights, including the entropy method and principal component analysis. Objective weighting methods, relying on mathematical models and data analysis, are more scientific and objective, less susceptible to personal subjective views, and more flexible in dealing with complex issues and multi-criteria decision-making. Drawing on the research of scholars like Cheng, this paper applies the entropy method to further evaluate regional EQ (Cheng et al., 2023).

The entropy method is a mathematical approach used for multi-criteria decision analysis. It is primarily employed to determine the weights of each decision factor for a better understanding and evaluation of various alternative solutions. The steps in applying the entropy method include:

Step 1, data standardization processing. Standardize the data of each indicator in the EQ evaluation index. Ensure that the data for each indicator is within the same dimension and range of variation. The standardized processing formulas for positive and negative indicator data are shown in formula (1) and formula (2), respectively. x ij , = x ij − ⁡ min   x j max x j − ⁡ min   x j (1) x ij , = max x j − x ij max x j − ⁡ min   x j (2)

Step 2, calculate the entropy value. Calculate the entropy value of each indicator in the evaluation index system using the formula (3). Among them, p_ij is the proportion of the jth data under indicator i, and N is the number of samples in the dataset. The entropy value reflects the uncertainty and information content of the indicator, and the larger the value, the higher the information uncertainty. E i = − p ij ⁡ ln   p ij ln   N   p ij = x ij , ∑ i = 1 n x ij , (3)

Step 3, calculate the weights. Calculate the weight of the entropy value for each indicator, as shown in formula (4). Among them, k is the number of indicators. w i = 1 − E i k − ∑ i = 1 k E i (4)

Step 4, normalize weights. Normalize the calculated weights to ensure that the sum of weights for each indicator is 1.

Through a comprehensive review of existing research results on factors influencing EQ, we found a diverse range of factors affecting regional EQ, including economic, population, industrial, technological, energy, and policy factors. Combining the commonalities in the development of EQ across Chinese provinces, we systematically selected six key influencing factors, as shown in Table 2.

Interpreted variable: The EQ of various provinces in China is calculated based on the EQ evaluation index system constructed in the previous sections.

Core explanatory variable: The GI of various provinces in China is expressed by the proportion of environmental pollution liability insurance revenue to the total insurance revenue.

Control variables: (1) Selecting per capita GDP to reflect the regional economic development level. Regions with higher economic development levels may have more industrial activities and transportation, leading to increased emissions of pollutants such as exhaust gases and wastewater. Therefore, this indicator may decrease regional EQ (Lu et al., 2017). (2) Selecting total population to reflect the regional population level. Regions with large population concentrations may lead to higher levels of industrialization and urbanization, thereby increasing pollutant emissions. At the same time, the demand from a large population also drives more traffic and production activities, increasing pollutant emissions. Therefore, this indicator may decrease regional EQ (Li et al., 2019). (3) Selecting the proportion of the secondary industry to reflect regional industrial structure characteristics. The secondary industry, compared to the primary and tertiary industries, requires more production materials and may emit more pollutants. Therefore, this indicator may decrease regional EQ (Chen et al., 2021). (4) Selecting unit GDP energy consumption to reflect regional technological level. Advanced technological levels imply more efficient resource utilization, which can reduce fossil fuel consumption and even use clean energy. Therefore, this indicator may increase regional EQ (Mughal et al., 2022). (5) Selecting the proportion of investment in industrial pollution control to industrial value-added to reflect the level of environmental regulation. Reasonable environmental regulations can promote the upgrading of pollution control facilities by enterprises, reduce pollution emissions, and achieve improvement in regional EQ (Yang et al., 2018).

Considering the availability and completeness of the data, this paper selects relevant data from 30 provinces in China for the period 2000-2021 to investigate the relationship between GI and EQ. The dataset does not include data from the regions of Hong Kong, Macao, Taiwan, and Tibet. GI data is obtained from the annual “China Insurance Yearbook,” while other data is collected from the annual “China Statistical Yearbook,” “China Environmental Statistical Yearbook,” and provincial statistical yearbooks. It is important to note that, to prevent the influence of non-stationarity of macro data on empirical results, all variables have been log-transformed. For missing data, we used either the mean imputation method or the nearest neighbor interpolation method for supplementation.

This article uses a quadratic regression model to test the hypothesis that the impact of GI on China’s EQ is an inverted “U” shape. The coefficients of the quadratic regression model bear an intuitive interpretation. The coefficient of the linear term variable signifies the slope of the linear relationship within the model, while the coefficient of the quadratic term variable reflects the concavity or convexity of the nonlinear relationship. This imparts a heightened level of intuitiveness and operability to the explication of the model outcomes. The underlying principle of the model unfolds as follows: when the coefficient of the quadratic term variable takes a negative value, the model manifests a inverted U-shaped form after the variable reaches a certain level. This configuration aligns with our conceptualization of an inverted U-shaped relationship, wherein the optimal EQ is attained when the GI level is moderate. Conversely, under excessively high or low GI levels, the EQ might experience a decline. A notably negative coefficient of the quadratic term variable indicates the presence of an inverted U-shaped relationship between GI and EQ.

To test the hypothesis that the impact of GI on EQ in China follows an inverted “U” shape, this paper introduces the quadratic term of GI (Haans et al., 2016). And introduce other variables that affect EQ, such as PGDP, TP, IS, TL, and ER. The complete nonlinear regression model for studying EQ is shown in Formula (5). In the Formula (5), i represents the ith province among the 30 provinces in China, and t represents the tth year from 2000 to 2021. For example, E Q i t represents the environmental quality level of province i in year t , and G I i t represents the green insurance level of province i in year t . Similarly, P G D P i t , T P i t , I S i t , T L i t respectively represent the per capita GDP, total population, industrial structure, technological level, and environmental regulation level of province i in year t . ln ⁡ E Q i t = α i + β 1 l n G I i t + β 2 l n G I i t 2 + β 3 l n P G D P i t + β 4 l n T P i t + β 5 l n I S i t + β 6 l n T L i t + β 7 l n E R i t + μ i t + ε it + δ it (5)

To further test the hypothesis that the impact of GI on EQ in China follows an inverted “U” shape, this paper employs Hansen’s proposed threshold panel model to analyze the influence of GI on EQ at different development stages. This paper constructs a regional environmental quality threshold regression model using GI as a threshold variable. The final model is shown in Formulas (6) and (7) (Lv and Xu, 2023). The meanings of each character in formulas (6) and (7) are consistent with those in formula (1). In addition, η represents the threshold value. l n E Q i t = α i + β 1 l n G I i t + β 2 l n P G D P i t + β 3 ⁡ ln ⁡ T P i t + β 4 l n I S i t + β 5 l n T L i t + β 6 l n E R i t + μ i t + ε it + δ it   l n G I ≤ η (6) l n E Q i t = α i + β 1 l n G I i t + β 2 l n P G D P i t + β 3 ⁡ ln ⁡ T P i t + β 4 l n I S i t + β 5 l n T L i t + β 6 l n E R i t + μ i t + ε it + δ it   l n G I > η (7)

The threshold regression model consists of two components: one capturing the linear relationship below the threshold and the other above the threshold. Such a model structure enhances the flexibility to depict the nonlinear impact of GI on EQ. It allows for modeling variations in EQ near the threshold. The pivotal aspect of the threshold regression model lies in the examination of the threshold. Through hypothesis testing on the threshold, it can be determined whether there exists a threshold for the impact of GI on EQ. This aids in comprehending at what level of GI the impact on EQ is optimized. The threshold regression model furnishes explanations for both stages below and above the threshold, enabling researchers to gain a clearer understanding of the mechanism through which GI affects EQ. Such interpretability holds practical guidance for policy formulation and operational practices.

In testing the hypothesis that the impact relationship between green insurance and environmental quality is an inverted “U” shape using a nonlinear panel regression model, it is necessary to determine whether to use a fixed effects model or a random effects model. These two models handle heterogeneity among individuals in panel data differently. Therefore, this paper employs the Hausman test method to test the fixed effects model against the random effects model. The results are shown in Table 5. The test results indicate a chi-square value of 57.98, with a corresponding probability value of 0.0000. Consequently, this research rejects the random effects regression model and tends to choose the fixed effects regression model.

The results of the fixed effects regression model are shown in Table 6, with an R-squared equal to 0.893, indicating that the explanatory variables included in the model can effectively explain the variation in the dependent variable. The p-values corresponding to l n G I , l n G I 2 , l n P G D P , l n I S , l n T L , and l n E R are all less than 0.05, significantly affecting China’s EQ. However, at a significance level of 10%, TP did not have a significant impact on EQ.

The coefficient of l n G I on l n E Q is positive, with a value of 0.305, indicating that as the level of GI increases, the level of EQ also rises. The coefficient of l n G I 2 on l n E Q is −0.071, indicating that the impact of GI on EQ follows an inverted “U” shape. In the early stage of GI development, it can enhance the enterprise’s environmental risk management system and establish a scientific environmental protection strategy. It can promote increased environmental investment by implementing economic incentives and penalties. Through risk monitoring mechanisms and responsibility tracking mechanisms, it encourages companies to actively fulfill their environmental responsibilities. It can share the risk of technological innovation, promote the upgrade and application of green technologies. Financial support can guide investment direction and support the stable and rapid development of the green industry. Therefore, GI can reduce pollution emissions and promote the improvement of regional EQ. On the other hand, as the level of GI development continues to rise, when the market share of GI reaches saturation, the promotional effect of GI transforms into an inhibitory effect. The main reasons are that with the continuous development of the GI level, market competition intensifies, and related regulations become more stringent, forcing insurance companies to raise environmental standards and reduce insurance support for highly polluting enterprises. Additionally, as the GI market fully unfolds, excessive reliance on the EQ promotion effect of GI by the government, industry, and enterprises leads to a lowering of environmental standards by the government, a lack of market competitiveness in the green industry, and companies merely meeting the minimum environmental standards. This results in a decline in EQ. Existing research findings on the impact of GI on EQ have yielded contradictory results. Some studies posit a positive effect of GI on EQ, while others hold a contrary perspective. For instance, Rizwanullah et al., based on linear regression analysis, found a positive impact of GI on the EQ of BRICS (Rizwanullah et al., 2022). Conversely, Ahmed et al., utilizing linear regression analysis as well, discovered a negative impact of GI on the EQ of the United States (Ahmed et al., 2022). Through the revelation of an inverted U-shaped relationship in this study, not only can these conflicting results be elucidated, but it also expands the research perspective on the enhancement effects of GI on EQ. The discovery of such a nonlinear relationship provides a more profound and comprehensive understanding of GI research, offering insights into its nuanced impact on EQ.

Further calculations reveal that when the value of GI equals 8.567, the relationship between GI and EQ begins to show a turning point. That is, when GI is greater than 8.567, EQ decreases with the increase of GI. Spatial-temporal difference analysis of 30 provinces in China conducted in this study found that in 2016, the level of GI in Jiangsu Province first exceeded 8.567, followed by Beijing, Shanghai, Zhejiang, and Yunnan provinces. Combining with the development history of GI in China, we found that since the implementation of GI policies, the level of GI in China has continuously increased, growing from 4.42 in 2000 to 9.08 in 2021. In the initial stage, the introduction of GI effectively reduced pollutant emissions, leading to an improvement in regional EQ. However, the blind promotion of GI development has also brought a series of environmental pollution issues, inhibiting the improvement of EQ. Taking Jiangsu as an example. The GI and EQ of Jiangsu Province in 2000 were 4.41 and 0.466, respectively. With the continuous development of GI, EQ continued to rise, reaching the highest value of 0.768 by 2016. Then, Jiangsu Province’s EQ declined continuously with the growth of GI. By 2021, Jiangsu Province’s GI had grown to 9.13, and EQ had reduced to 0.658.

Analyze the impact of each control variable on EQ in detail. (1) The impact coefficient of PGDP on EQ is −0.212, indicating a significant inhibitory effect of PGDP on EQ. Currently, China’s rapid economic growth relies predominantly on high-energy-consuming and pollution-intensive heavy industries and manufacturing. The development of these traditional industries often accompanies substantial energy consumption and environmental pollution emissions, leading to deteriorating EQ. Hence, the improvement of EQ in China exhibits a suppressing effect due to PGDP. Existing research outcomes on the influence of PGDP on Chinese EQ have yielded conflicting results. Some studies suggest a positive effect of PGDP on EQ, while others hold the opposite view. Song et al. found that, influenced by high-energy-consuming and high-emission industries, Chinese EQ declines with the growth of PGDP, consistent with the findings of this study (Song et al., 2020). However, Awan et al. focused on Shanghai and discovered that with economic development, an increase in per capita GDP leads people to be more inclined towards investing in environmental protection and improvement measures, thereby enhancing EQ (Awan and Azam, 2022). (2) The significant negative impact coefficient of IS indicates that for every increase of 1 unit in IS, EQ decreases by 0.17 units, demonstrating a notable inhibitory effect of IS on EQ. China’s secondary industry primarily comprises industries such as manufacturing and heavy manufacturing, which often exhibit high energy consumption and pollution characteristics. With the increasing proportion of the secondary industry, the development of industries such as manufacturing may lead to significant energy consumption and emissions of environmental pollutants, thereby exerting adverse effects on EQ. Yin and Song conducted an empirical analysis on the impact of industrial structure on regional EQ in China. The results consistently indicate a decline in regional EQ with the increase in the proportion of the secondary industry, aligning with the conclusions of this study (Song et al., 2022; Yin et al., 2024). (3) The significant positive impact coefficient of TL indicates that for every increase of 1 unit in TL, EQ increases by 0.121 units, demonstrating a noteworthy promoting effect of TL on EQ. In recent years, China has witnessed rapid development and widespread adoption of renewable and clean energy technologies, reducing reliance on traditional fossil fuels, and consequently lowering carbon emissions and other pollutants, thereby benefiting EQ. Furthermore, China’s advancements in production technology have continuously elevated resource utilization efficiency, reducing wastage and consumption of resources effectively. This has also led to a reduction in pollutant emissions during the production process, thereby alleviating environmental pressures. Villanthenkodath and Chishti respectively studied India and the BRICS economies, empirically analyzing the impact of technological levels on regional EQ. The results consistently demonstrate an improvement in regional EQ with the enhancement of technological levels, aligning with the conclusions of this study (Chishti and Sinha, 2022; Villanthenkodath and Mahalik, 2022). (4) The impact factor of ER is significantly positive. For every one-unit increase in ER, EQ increases by 0.263 units, indicating a significant promoting effect of ER on EQ. Environmental regulations in China enforce emission standards and restrictions on enterprises, compelling them to take measures to reduce pollutant emissions. This fosters enhanced clean production and technological innovation within enterprises and can also elevate public and corporate awareness of environmental protection, thereby driving improvements in EQ. Tang and Feng respectively focus on China and the Yangtze River Economic Belt as their study subjects, empirically analyzing the influence of environmental regulations on regional EQ. The results consistently demonstrate that regional EQ improves with the enhancement of environmental regulations, corroborating the findings of this study (Tang et al., 2020; Feng et al., 2023).

To further verify the inverted “U” relationship between Chinese GI and EQ, this paper examines the threshold variable l n G I under three different threshold conditions. Specifically, we investigated the cases where l n G I has no threshold, has one threshold, and has two thresholds. The F-statistics and p-values for each threshold test are presented in Table 7. The threshold variable l n G I only passed the single threshold test at a significance level of 1%, not passing the double and triple threshold tests. The estimated single threshold value and its 95% confidence interval for the threshold variable l n G I are shown in Table 8. The estimated value for the single threshold is 2.196. Therefore, GI has a significant impact on EQ, and there is a single threshold effect. The results of the threshold regression model are shown in Table 9.

The results indicate that the threshold variable l n G I passes the statistical test at a 1% significance level, whether it is less than 2.196 or greater than 2.196. When l n G I is less than 2.196, the impact coefficient is 0.685, indicating a significant promoting effect of GI on EQ. With the increase of GI, EQ also improves. When l n G I is greater than 2.169, the impact coefficient is −0.227, indicating a significant inhibitory effect of GI on EQ. With the increase of GI, EQ decreases. The conclusion of the threshold regression model is consistent with the fixed-effects regression model, both indicating an inverted “U”-shaped impact of GI on EQ.