Structural Diffusion Model and Urban Green Innovation Efﬁciency—A Hybrid Study Based on DEA-SBM, NCA, and fsQCA

: This research is based on structural theory and innovation diffusion theory, exploring the theoretical foundations and inﬂuencing factors of urban green innovation to provide theoretical support for the realization of the world’s sustainable development goals (SDGs). By using the methods of Data Envelopment Analysis with Slacks-Based Measure (DEA) non-expected model, Necessary Condition Analysis of Research Methods (NCA), and Fuzzy Set Qualitative Comparative Analysis (fsQCA) in combination, the research analyzes the variables inﬂuencing the capability of urban green innovation. The study ﬁnds that the level of urban culture and absorptive capacity are necessary conditions for urban green innovation, with urban absorptive capacity having a high level of inﬂuence. The main paths for urban green innovation are a comprehensive cultural innovation path, an open cultural inclusion path, an open participation innovation integration path, and an outcome transformation to drive the innovation path. In addition, the research discovered patterns of cultural inﬂuence that go beyond institutional and resource-based structural factors, subject action processes, and transformation models guided by absorption and sustainable participation. The research results have important signiﬁcance for understanding the driving factors and promotion paths of urban green innovation, providing empirical evidence for the realization of the world’s SDGs.


Introduction
One of the Sustainable Development Goals of the world is to establish sustainable cities and communities [1].In this process, green innovation is not only a crucial driving force for building sustainable cities but is also gradually becoming a core element in urban planning and community design.This type of green innovation not only helps in gaining and maintaining competitive advantages but also serves as a significant pathway toward achieving sustainable development.The efficiency of green innovation is mainly measured by the output-input ratio.Some studies have discussed the construction of regional green innovation efficiency indicators from an input-output perspective [2][3][4], and others have explored the effects of patent applications and authorizations, innovation policies, cultural dimensions of innovation, R&D funding and expenditure, etc., on green innovation efficiency [5][6][7].However, many studies are based solely on a single linear path; some complex studies lack systematic thinking about the objective and subjective factors of green innovation behavior itself and fail to consider optimizing the process of green innovation development.There is a need for further research and discussion.
Cities, as relatively well-developed social and economic systems, gather various green innovation elements such as human resources, technology, and industries and have irreplaceable advantages in information exchange and resource allocation.However, because many cities still favor rapid growth at the expense of resources and the ecological environment, and with the agglomeration-style growth of city innovation activities, issues such as high energy and resource consumption, environmental pollution, and the greenhouse effect are restricting sustainable urban development.Against this backdrop, in October 2008, the United Nations Environment Program released the "Global Green New Deal and Green Economy Plan," advocating for governments worldwide to establish a highenergy resource efficiency, low ecological and environmental pollution, and sustainable "green economy" growth model to promote green economic development [8].In 2012, the United Nations made "Green Economy in the Context of Sustainable Development and Poverty Eradication" the theme of its Sustainable Development Conference, attempting to promote green innovative development as a path that balances sustainable development and poverty eradication.Promoting innovative green development and embracing the path of sustainable development is a profound lesson drawn from historical experience and the correct choice [9].Many developed countries view green innovation as a new engine for sustainable development.In the context of the 2030 Agenda for SDGs [1], the SDGs should be the focal point of attention for the years 2022-2023.
The concept of "urban green innovation" encapsulates a multidimensional paradigm situated at the intersection of urban development, environmental sustainability, and technological advancement.The work focus of the SDGs for 2022-2023 should be to reorganize the green innovation dimensions of urban sustainability, integrating both explicit and implicit dimensions through a theoretical and practical framework.Simultaneously, SDGrelated work should focus on the components of green innovation efficiency and the factors that influence it.The foundational essence of urban green innovation is aligned with the principles of sustainable development [10], integrating innovative strategies and technologies meticulously designed to mitigate environmental degradation, enhance resource efficiency, and fortify urban ecological resilience.By infusing cutting-edge technologies, design methodologies, and policy frameworks into the intricate fabric of urban infrastructure, resource management, and ecological preservation, the objectives of urban green innovation extend beyond mere environmental impact reduction.They harmoniously align with the overarching principles of sustainable development goals [11].Considering the objective and subjective factors influencing urban green innovation efficiency and its dynamic development process, this study intends to construct an initial model based on structural theory and diffusion theory.The structural theory posits that the formation process of the green innovation subject and structure are not two independent phenomena (dualism) but reflect a duality.To analyze the structural duality of innovative activities, one must understand how green innovation activities within a certain range are rooted in a broader time and space [12].The urban comprehension and development of green innovation, upon incorporating the concept of sustainable development goals, can opt for whether to execute and adopt it, integrating it into the temporal and spatial dimensions of green innovation [13].This facilitates external "economies of scale" to better promote the enhancement of their own green innovation capabilities.At the same time, the typical patterns of subject movement are routine activities repeated within a few days or longer.When all subjects interact with each other, the characteristics of these environments and the actors' abilities also interact [12], ultimately resulting in the output of green innovation efficiency.The early innovation diffusion theory was proposed by Bass, also known as innovation adoption, which refers to the evolution process when a new idea, thing, or technology is introduced into a social system [14].Rogers believed that whether innovation would be adopted depended on five main stages: knowledge, interest, evaluation, implementation, and adoption [15].Schulz believes that "without diffusion, innovation cannot have a substantial impact."More and more studies are beginning to use organizations as a unit of adoption for research, examining the diffusion of organizational, city, and regional innovation.
Combining structural theory and diffusion theory can comprehensively grasp the influence mechanism of urban green innovation efficiency.The development of urban green innovation is a complex process with dynamic, non-linear influencing factors.For instance, in elements such as culture, time and space, resources, and institutions, there might be necessary conditions that influence the efficiency of urban green innovation.Moreover, a single condition in urban development, such as resources, may not be a sufficient condition for green innovation but could become a sufficient condition affecting green innovation when combined with other conditions.Therefore, different cities have different configurations in natural resource distribution, socio-economic foundation, resource supply, and policy and regulatory formulation.There are also significant differences in the output-input ratio brought about by green innovation.Some city governments provide a lot of financial input for the development of green innovation; however, does it yield immediate benefits such as economic growth?The influences and mechanisms of these issues and factors on green innovation capability are still unknown, and some theoretical and practical issues remain unanswered.This study intends to use the urban green innovation performance measured by DEA as the result variable, using the NCA and QCA combined methods, based on the data of 101 typical prefecture-level cities in China and the analysis of factors affecting urban green innovation efficiency established on theoretical foundations.It aims to formulate a relatively complete index system of preconditions for urban green innovation, explore effective paths to enhance urban green innovation performance, and build a sustainable development system for urban green innovation.

Theoretical Analysis Framework and Literature Base
The study first establishes an analytical framework for the condition variables based on the five development stages of diffusion theory, with each dimension elaborated through structural theory, as shown in Figure 1.At the same time, the system describes the questionnaire measurement part in each dimension and the measurement of urban green innovation efficiency as a result variable.
Combining structural theory and diffusion theory can comprehensively grasp the influence mechanism of urban green innovation efficiency.The development of urban green innovation is a complex process with dynamic, non-linear influencing factors.For instance, in elements such as culture, time and space, resources, and institutions, there might be necessary conditions that influence the efficiency of urban green innovation.Moreover, a single condition in urban development, such as resources, may not be a sufficient condition for green innovation but could become a sufficient condition affecting green innovation when combined with other conditions.Therefore, different cities have different configurations in natural resource distribution, socio-economic foundation, resource supply, and policy and regulatory formulation.There are also significant differences in the output-input ratio brought about by green innovation.Some city governments provide a lot of financial input for the development of green innovation; however, does it yield immediate benefits such as economic growth?The influences and mechanisms of these issues and factors on green innovation capability are still unknown, and some theoretical and practical issues remain unanswered.This study intends to use the urban green innovation performance measured by DEA as the result variable, using the NCA and QCA combined methods, based on the data of 101 typical prefecture-level cities in China and the analysis of factors affecting urban green innovation efficiency established on theoretical foundations.It aims to formulate a relatively complete index system of preconditions for urban green innovation, explore effective paths to enhance urban green innovation performance, and build a sustainable development system for urban green innovation.

Theoretical Analysis Framework and Literature Base
The study first establishes an analytical framework for the condition variables based on the five development stages of diffusion theory, with each dimension elaborated through structural theory, as shown in Figure 1.At the same time, the system describes the questionnaire measurement part in each dimension and the measurement of urban green innovation efficiency as a result variable.

Awareness Dimension
Subjects in the dissemination process of urban green innovation need an open space to gain new knowledge.The subjects' cognition about innovation comes from their active search and selective contact with ideas that match their interests, needs, and existing attitudes.The city's communication services can provide the necessary means for the subjects

Awareness Dimension
Subjects in the dissemination process of urban green innovation need an open space to gain new knowledge.The subjects' cognition about innovation comes from their active search and selective contact with ideas that match their interests, needs, and existing attitudes.The city's communication services can provide the necessary means for the subjects to acquire new knowledge, facilitating the efficient circulation of innovative knowledge at specific times and spaces.Some scholars, based on the dimension of the transport network, correlation coefficient method, and Granger causality test, have found that the construction of transportation facilities significantly impacts innovation development [16].Others, through constructing a multi-attribute decision model of comprehensive transportation advantage and ArcGIS network analysis technology, have analyzed and found that the degree of comprehensive transportation advantage is highly correlated with the regional scientific and technological innovation development level, showing a positive correlation [17].
Different organizations within the city (such as universities, enterprises, research institutes, etc.) share knowledge through spatial dissemination, forming "temporary" innovation alliances, while the city's Internet development and communication services provide good conditions for the development of green innovation [18].Rogers, in his revision of the theoretical framework for the fifth edition of "The Diffusion of Innovation," introduced Internet communication channels, emphasizing the significant impact of network media in the diffusion process [19].Therefore, the indicator system for the Awareness dimension is constructed in this paper, as shown in Table 1.

Interest Dimension
The diffusion of government innovation relies primarily on societal mental support [20].If there is a mismatch in the thoughts and consciousness of the public, it can affect the transmission of information within the space and communication efficiency, consequently impacting the support for innovative ideas and possibly leading to their abandonment [21].If the cultural level of a city can create a trusting and fair environment, those aware of the innovation are more likely to feel government trust and support, thereby reducing the uncertainty of the consequences of green innovation.Furthermore, the level of education, as a latent rule, can effectively arouse the public's interest in innovation [22], and the knowledge capabilities possessed by the public can unconsciously shape the constraints and norms in the innovation process, granting greater subject initiative.Hence, this paper constructs the index system for the interest dimension, as shown in Table 2.

Measurement Dimension
If a city implements green innovation, there are inevitably differences in the environment, personnel, conditions, etc., compared to the city that first implemented green innovation.This determines the difficulty of imitation [23].A very complex, innovative achievement requires resource-based support to be emulated.Therefore, the resources and rules of the government itself are crucial for promoting the efficiency of green innovation.
In the initiation phase of green innovation, the most significant influencing factor is government policy.Environmental policy is a "regulatory" rule in Giddens's structuring context, which has rigid restraining characteristics.It allows for the technical carriers and general rules used by the subjects of green innovation implementation and any reproductive activities [12].Environmental policy has the characteristics of a practical methodology [24].It provides any green innovation subject with the ability and means to "measure" and solve problems when encountering favorable conditions or dilemmas, and to make optimal choices under various trade-offs.Therefore, the index system for the measurement dimension is constructed in this paper, as shown in Table 3.

Implementation Dimension
In the implementation phase of urban green innovation, the transformation of urban technological achievements can bring about agglomeration economic effects, which have a strong attraction for innovative enterprises and innovative elements [25].In this process, urban green innovation capability is also strengthened with the diffusion of talent and knowledge, which realizes sustainable economic development [26].How to effectively promote the transformation of technological achievements, maximize resource efficiency, protect and stimulate the innovation vitality of the subject, etc., are key to a city's implementation of a green innovation strategy and the construction of sustainable development.
Innovation implementation comes from the self-driving force of the subject.The importance of multiple subjects (such as research institutions, universities, enterprises, non-governmental organizations, etc.) in the diffusion process of urban green innovation is highlighted [27].The continuous participation of the public in emulating the achievements of green innovation in other regions will become the driving force for innovation implementation [28].When the government understands this desire of the public and other conditions are met, the implementation of green innovation will naturally fall into place.Therefore, this paper constructs the index system for the implementation dimension, as shown in Table 4.

Adoption Dimension
The introduction of foreign capital, as a constitutive rule, is a component dimension in the action and adoption of proposals by the subject.Moreover, the level of green innovation in a city is closely related to the optimized allocation of resources.The mutual matching of green inputs, infrastructure, and policy institutions can significantly improve the efficiency of green innovation [29].Some scholars have empirically found a positive impact between the city's resource allocation and the level of foreign direct investment [30].Specifically, the inflow of foreign capital promotes the effective allocation of economies between cities and the availability of scarce resources, products, or services by foreign enterprises in the city, thereby enhancing green innovation efficiency.
The construction of a smart city and green innovation share an inseparable, dynamic relationship.Smart city construction provides the spatial environment and resource elements for innovation, while green innovation reciprocally makes the city smarter [31].This is accomplished by reshaping the city's production space, living space, and ecological space through digital technology, enabling sustainable urban development, and making the city more informalized and intelligent [32].Therefore, the index system for the adoption dimension is constructed in this paper, as shown in Table 5.The measurements for "green culture awareness" and "sustained participation" in the interest dimension and implementation dimension are completed through a questionnaire.The questionnaire design involves eight variables, including green culture consciousness, green innovation willingness, green innovation communication, and continuous participation consciousness under green culture awareness.Continuous participation includes continuous participation behavior, the green innovation model, green innovation technology, and green innovation performance.All variables are measured on a Likert five-point scale, with 1-5 indicating strongly disagreeing to strongly agreeing.The variable measurements of the questionnaire are as follows: "Green cultural awareness" comprises four variables: (1) "Green culture consciousness" (GCC): "Green culture consciousness" refers to individuals' identification with environmental conservation values and their self-awareness of actively participating in environmental protection behaviors within an organization or institution.This study draws inspiration from the research of Deshpande and Webster [33], who posit that green values within organizational culture, environmental awareness, and support for environmental behaviors have profound effects on both internal and external environmental protection actions of the organization.They employed similar items to measure organizational green culture, such as recognition of the importance of environmental protection, promotion and encouragement of environmental protection behaviors, emphasis on the application and creation of environmental protection knowledge, and whether environmental protection is one of the core values of the organization.(2) Green innovation willingness (GIW): Urban green innovation willingness requires organizations to actively seek new green development approaches in the process of problem-solving and achieving sustainable development.This study draws upon Rogers' measurement of "willingness to adopt" in the context of innovation theory, which explores the dissemination and adoption of new ideas, products, or practices in society.Within this, "willingness to adopt" refers to an individual's or organization's inclination and readiness to embrace new ideas or innovations.They contend that intrinsic self-determination and autonomy are crucial for the continuity and quality of willingness and behavior when engaging in an activity or adopting a particular concept [34].
(3) Green innovation communication (GIC): Green innovation communication awareness involves the exchange of professional knowledge between urban organizations and key stakeholders.Effective communication of green innovation contributes to enhancing the organization's expertise in green product design, green process design, green procurement, forecasting green market demand trends, and major green product innovations.This study draws inspiration from the research of Nonaka and Takeuchi, who emphasize the importance of knowledge creation and sharing for organizational innovation and competitive advantage in their organizational learning theory.They categorize knowledge into explicit and tacit knowledge, highlighting the process of knowledge conversion through the stages of socialization, externalization, combination, and internalization to facilitate knowledge creation and sharing.Within these processes, knowledge communication and sharing play a pivotal role in organizational learning and innovation [35].(4) Continuous participation consciousness (CPC): Effective participation of diverse stakeholders can lead to broader resource sharing, knowledge dissemination, and collaborative synergy, thereby enhancing the sustainability and success rate of urban green innovation.This study draws upon Stern's research, which proposed the environmental behavior awareness model.This model emphasizes the impact of environmental issue recognition, knowledge, and attitudes on environmental behavior.Within his model, an individual's perception and level of knowledge about environmental issues, as well as their attitude and values towards the environment, all influence their environmental behavior [36].
Continuous participation also comprises four variables: (1) Continuous participation behavior (CPB): Designing the continuous participation behavior variables contributes to a comprehensive understanding of the actual engagement level and willingness to take action of urban organizations and individuals in the process of green innovation.This study draws inspiration from the research of Johan Schot, whose work revolves around sustainable development and environmental management, particularly focusing on organizational and individual behaviors related to reducing environmental pollution, complying with environmental regulations and policies, and adopting new energy-saving technologies.Their research underscores the diverse stakeholder participation in sustainable development, encompassing the proactive behaviors of both organizations and individuals in environmental management and green innovation [37].(2) Green innovation model (GIM): The green innovation model aims to comprehensively understand the specific patterns and strategies employed by urban organizations in green innovation, as well as the effects of this model on green innovation outcomes and sustainable development.This study draws upon the research of Joe Tidd and John Bessant, who focus on the implementation and promotion of innovation within organizations, particularly with a direction toward sustainable innovation.Their research underscores the significance of combining new products, new services, and new information within the innovation model, as well as the role of innovation in attracting new suppliers and partners [38].(3) Green innovation technology (GIT): Against the backdrop of rapid iteration and unpredictable development directions for green technologies, urban organizations must confront the challenges and opportunities arising from technological disruptions.This study draws inspiration from the research of Christensen, who delves into the impact of technology and innovation on industries and organizations, notably emphasizing the tumultuous nature of technological change and innovation.His theory incorporates the concept of "disruptive innovation," suggesting that in certain scenarios, new technologies and innovations may upheave existing industries and technological ecosystems, ushering in new opportunities and challenges [39].(4) Green innovation performance (GIP).As urban green innovation deepens, assessing its impact on environmental improvement and economic benefits allows for a comprehensive understanding of the specific environmental and economic outcomes achieved by urban organizations in green innovation practices.This study draws inspiration from the research of Robert D. Klassen and David Vachon, who focus on organizational performance and achievements in sustainable development and environmental protection.Their research underscores the significance of environmental practices adopted by organizations in their production and operational activities and how these practices influence aspects such as the environment, costs, and funding [40].

Sample Selection and Data Collection
This paper selects businesses, government institutions, and research institutions implementing green innovation and digital transformation in 101 cities as the survey subjects and collects data through online surveys.The respondents are managers, practitioners, and citizens in these institutions who understand green innovation and the development of green innovation activities in their cities.
The questionnaire distribution mainly follows the following forms: (1) distributing to related cities through the academic team, alumni association, friends and relatives, and cooperative institutions using an online questionnaire; (2) paying for distribution through questionnaire intermediary companies.To ensure the quality of the questionnaire, we repeatedly communicate the research content and objectives with the staff before distribution, highlight the keywords in the topic, and facilitate the respondents' quick grasp and understanding of the core content, thus ensuring data quality.During the official data collection period, we randomly revisited some middle-and high-level leaders and found no ambiguity in the respondents' understanding of the questions, and no significant differences were found in the return visit, indicating that the questionnaire quality is high.
After the data collection, this paper matches the corresponding IP addresses based on the questionnaire.A total of 5155 people filled out the questionnaire, and after excluding invalid questionnaires such as those completed too quickly or ended halfway, a total of 4772 valid questionnaires were obtained.The questionnaire's effective response rate is 92.6%, with about 50 questionnaires per case city.

Reliability and Validity Analysis
After the formal data collection concludes, it is necessary to conduct validation, and subsequent analysis only holds significance when reliability and validity are ensured.Data validation includes examining the reliability, convergent validity, and discriminant validity of each variable.Currently, the academic community widely employs Cronbach's Alpha coefficient to gauge the reliability of measurement tools, with a commonly accepted threshold of 0.7 deemed suitable by many scholars [41].As evident from Table 6, Cronbach's Alpha coefficients for each variable exceed 0.8, indicating the robust reliability of the data obtained in this study.Construct validity refers to the degree of consistency between the measured concepts and the theoretical intent.The measurement of construct validity can be examined primarily from the perspectives of convergent validity and discriminant validity.The Average Variance Extracted (AVE) is recommended to be above 0.5, indicating that the variable can explain more than 50% of the variance and thus exhibits good convergent validity.Common methods for assessing discriminant validity include the Fornell-Larcker criterion and Cross-Loadings.The Fornell-Larcker criterion requires that the square root of the AVE for each latent variable be greater than the correlation between latent variables [41].Cross-Loadings require that an indicator's loadings on its corresponding latent variable be greater than its loadings on other latent variables.
However, traditional methods for testing discriminant validity tend to overestimate factor loadings and underestimate relationships between variables and making it relatively easy to pass the test.To address this, Henseler introduced the Heterotrait-Monotrait Ratio (HTMT) method.It compares the average correlations between indicators of different variables to the average correlations between indicators of the same variable.It is generally recommended that the HTMT between two variables should be less than 0.85 [42].
As shown in Table 7, the AVE values for variables are all greater than the squared correlations between variables.As shown in Table 8, the factor loadings for variables are all greater than the cross-loadings.As shown in Table 9, the HTMT values between variables are all less than 0.85.Therefore, the measurement model exhibits good discriminant validity.

Measurement of City Green Innovation Efficiency
This paper measures the efficiency of urban green innovation from both input and output aspects while introducing unexpected outputs, taking environmental innovation efficiency comprehensively into account.The evaluation of green innovation efficiency differs from traditional innovation evaluation in that it considers both the "innovation" attribute that has technological output and the "green" attribute.The current main research approach is to incorporate environmental factors into the evaluation of innovation efficiency, thereby constructing a measurement model for green innovation efficiency.
Capital, human resources, and the environment are important production elements in urban green innovation, so the input indicators are divided into capital input, human resources input, and environmental input.Urban talent resources are the foundation of green innovation.This paper uses R&D staff input to represent human resources input [43].Funds are important resources for constructing green innovation cities, and R&D investment can well reflect the city's capital input intensity [44].The environment is extremely important for green innovation activities.The usual innovation environment indicators are related to information construction [45], so this paper selects electricity consumption and internet access volume in each city to represent environmental input elements.
"Green innovation" involves the development and application of environmentally friendly products, technologies, and solutions.During this process, innovators often pursue patent protection to ensure the recognition and safeguarding of their innovations [25].This paper uses the annual number of patents granted in the city to reflect urban innovation output.Sewage discharge and sulfur dioxide are important sources of urban environmental pollution, so this paper uses them as unexpected outputs of urban green innovation (see Table 10).Based on the aforementioned exploration of the formation mechanism of urban green innovation efficiency, this research builds a structured diffusion model of urban green innovation to describe the relationships therein (see Figure 2).

DEA
Given the goal of this paper to evaluate the impact of various factors on the efficiency

DEA
Given the goal of this paper to evaluate the impact of various factors on the efficiency of urban green innovation and use this to measure the overall level of urban green innovation, we use the SBM model proposed by Kaoru Tone (2001) in the DEA method to calculate the green innovation of the sample cities [46].Compared with traditional single-factor methods, the DEA-SBM method is a non-parametric method suitable for evaluating the efficiency of decision-making units with multiple input and output indicators.It regards the object to be evaluated as a decision-making unit and uses linear programming and convex analysis theory to determine the most efficient production frontier in the sample.The results of traditional DEA models are somewhat one-sided, and most efficiency measurements and analyses are based on angles and radii.Empirical analyses should consider the factors affecting efficiency as comprehensively as possible and not just analyze inputs and outputs separately [47].Therefore, this study uses the DEA-SBM method of "multiple inputsmultiple outputs," including unexpected outputs.The basic idea is shown as follows: Assume there are n decision-making units (DMU J , j = 1, 2, . . . . . ., n), each DMU contains input variables X, unexpected output Y b , and The expression of DEA-SBM is as follows: , where λ, S − , S g , S b ≥ 0 In the above formula, P represents the efficiency value of the target city's green innovation; this value is between 0 and 1, λ represents the weight of each variable, S − , S g , S b respectively represent too much input, insufficient expected output, and too much unexpected output.When S − = 0, S g = 0, S b = 0, and p = 1, it indicates that the production unit is efficient.If P < 1, it is believed that the production unit has an efficiency loss.

QCA and NCA
QCA is a method based on set theory to study the sufficiency and necessity of causal relationships.It is based on the Boolean algorithm and calibrates and calculates the index data corresponding to causal variables through cases, thus obtaining necessary conditions and sufficient configurations and providing diversified equivalent paths for theoretical and practical research of the problem [48].NCA is a new necessary condition analysis method based on complex causal relationships.Unlike QCA, it can not only identify the necessary conditions of the result variables but also quantitatively calculate the effective amount of the necessary conditions and the bottleneck level as the necessary conditions [49].Specifically, through NCA, the necessary conditions (insufficient) and their effect sizes for achieving high-level green innovation and non-high-level green innovation can be obtained, and the bottleneck levels that the corresponding condition variables must reach to achieve different degrees of results can be given.Through QCA qualitative comparative analysis, on the one hand, necessary conditions with consistency as the evaluation indicator can be obtained to further verify the NCA necessary condition results; on the other hand, various condition variables can be combined to find multiple differentiated equivalent paths and avoid paths for urban green innovation under each configuration and non-high urban green innovation.

Sample Selection
This study selects sample cities based on the "2021 China Population Census County Data" compiled by the Seventh National Population Census Leadership Group Office.China has a total of 105 large cities, including 7 mega-cities, 14 super-large cities, 14 type I large cities, and 70 type II large cities.These cities have strong comprehensive strengths and a strong demand for green innovation.They are the core competitors in urban quality development, and their practices have their own characteristics.The samples have certain comparability and typicality.Due to the severe data missing from Kunshan, Yiwu, Cixi, and Jinjiang, the final sample was determined to be 101 prefecture-level cities (see Table 11).
After importing the input and output indicator data into Matlab2023a software and running it, we obtained the green innovation efficiency of each city in 2022.As shown in Table 12, it can be seen that Beijing, Shenzhen, Nanjing, Ningbo, Quanzhou, and Harbin are DEA efficient, while the other cities are, to varying degrees, DEA inefficient.In the DEAinefficient cities, there are cities such as Shanghai, Guangzhou, Hangzhou, Wuhan, etc., which are national innovation pilot cities.However, in the DEA-efficient cities, including Ningbo and Quanzhou, their economic strength and reputation are far inferior to those of first-tier cities such as Shanghai.This paper uses a combination of Necessary Condition Analysis (NCA) and Qualitative Comparative Analysis (QCA) [50], first applying NCA based on the R language to examine the necessary level of individual factors for urban green innovation ability and to identify whether there are bottlenecks and the nature of these bottlenecks in combination with other factors.QCA is then used to combine various condition variables.
The aforementioned part provides support for the necessary condition analysis of green innovation and configurational path analysis through the measurement of the efficiency of urban green innovation.The variables are then converted to values between 0 and 1.The specific steps are as follows: First, the ranking of smart cities in the city's absorption capacity is processed using SPSSAU, so that higher numerical values represent higher rankings.The data is then normalized, and the evaluation variable's best-case scenario (D+) and worst-case scenario (D−) are calculated.The proximity procedure C value is calculated based on these distance values.Cities that are DEA-efficient have been used as factual cases in the NCA and QCA analysis, and the other cities are counterfactual cases.A comparison of the factual and counterfactual cases yields the pathway to high performance in urban green innovation.

Variable Calibration
This paper uses Ragin's direct calibration method [51], first setting complete membership, crossover points, and non-membership points, and then setting three anchor points for each variable according to the minimum, average, and maximum values of the sample data.In addition, this paper will change the fuzzy membership to 0.49 or 0.51 when it is 0.5 during the calibration process to avoid a situation where the sample is difficult to categorize and is not included in the analysis.The final results of each variable's calibration are shown in Table 13.The results of the NCA analysis were obtained using R language.NCA distinguishes the observable and non-observable areas in the x-y scatter plot by constructing an upper limit line, and the necessity of condition x is judged by whether there is a blank area above the upper limit line.According to the category of variables, NCA mainly uses two upperlimit analysis techniques: Concave Envelope (CE) is used for binary or discrete variables with a few variable levels, and Concave Regression (CR) is used for discrete or continuous variables with multiple variable levels [49].Figures 3-9 reflect the relationship between seven major factors in different regions and the efficiency of urban green innovation.The results of the NCA necessary condition analysis are shown in Table 14.The NCA requires the necessary conditions to meet two standards: (1) Effect size d is greater than 0.1 (when d is between 0.1 and 0.3, it represents a low level of influence; when d is between 0.3 and 0.5, it represents a high level of influence) [52]; and (2) Results are significant in Monte Carlo simulation permutation tests [49].Based on these two standards, this paper identifies the necessary conditions for urban green innovation.As can be seen from Table 10, the cultural level of the city and its absorption capability are necessary (but not sufficient) conditions for urban green innovation.Moreover, the absorption capability of the city is a necessary condition with a higher level of influence (d > 0.3), and the cultural level of the city is a necessary condition with a medium level of effect (d > 0.1).
The degree of necessity of condition variables for the result variable is not fixed, and therefore further bottleneck-level analysis is required.Bottleneck level analysis can provide detailed descriptions of the necessary bottleneck levels for a given level of results [52].Table 15 shows the bottleneck levels of each variable, i.e., the certain percentile level of condition variables required to achieve a certain percentile level of green innovation efficiency.Here, "NN" indicates that the condition is not necessary.For example, to achieve 70% of the urban green innovation level, the city's absorption capability needs to reach at least 46.6%, and the degree of city openness only needs to reach 11%, etc.However, if you want to reach 10% of the city's green innovation level, you only need the city's cultural level to reach 3.2%, and other conditions are not necessary.

QCA Necessary Condition Analysis
Before using QCA for configurational analysis, this paper uses QCA to test the necessity of all condition variables.If a condition variable is a necessary condition leading to a result variable, then theoretically, this condition variable needs to be included in all condition configurations [51].In QCA, the way to judge whether a variable is a necessary condition is to analyze to what extent the condition is a superset of the result.If the consistency of the condition is greater than 0.9, it is considered a necessary condition.
The results of the QCA necessary condition analysis in this paper are shown in Table 16.The antecedent conditions leading to high urban green innovation capability do not all have a consistency greater than 0.9, i.e., not all conditions constitute necessary conditions for achieving high or non-high urban green innovation efficiency.As NCA and QCA have different standards for judging necessary conditions, QCA uses the diagonal of the scatter plot as a reference line, while NCA may move or rotate the upper limit line to form a reference line with an intercept to analyze the necessary conditions at different specified levels of the result variable.Therefore, the result set obtained from the QCA necessary condition analysis is a subset of the NCA; the two complement and verify each other, and the results do not conflict [53].This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.

Variables
Paths • denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.This study uses the fsQCA3.0software to obtain complex solutions, i lutions, and parsimonious solutions.Based on conventional practices in a alyzing condition configurations, intermediate solutions are used to deter ber of configurations leading to outcomes and the conditions included in t tions.Then, the parsimonious solution results are used to determine the important core conditions in each configuration [48].The study references urational approach, setting the original consistency threshold at 0.8, FR 0.75, and the case frequency threshold at 1.The results of the configuratio shown in Tables 17 and 18. Urban green innovation has four high config and three non-high configurational paths.The coverage of the solutions i indicating that these configurations can explain over 67% of the cases, s some extent the conditions required for urban green capacity.Note: ⊗ denotes the absence of a core condition, • denotes the presen denotes the absence of a marginal condition.

High Green Innovation Configurational Paths
(1) Comprehensive Cultural Innovation Path: In this path, t the city's cultural level, system foundation, and absorption ca conditions include results conversion and sustained participa citizens.The cultural level reflects the level of the city's social s nition [55].Cities with higher levels of literacy often encom knowledge and ways of thinking, which can help nurture inn velop the capacity for green innovation [56].The formulation an icies can offer resources, incentives, and standards.The effectiv cies can guide businesses and citizens within the city to activel tion activities, thereby enhancing the city's green innovation ca sorption capacity refers to the city's ability to absorb and appl technology.Cities with higher absorption capacity can quickly innovation results.While patent result conversion and sustain participation as peripheral conditions have a relatively weaker tion capability, they still provide support for the efficiency of ur certain extent.This configuration can explain 61.8% of cases, including Beijing, Guangzhou, Hangzhou, etc.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.
Table 18.Configurations for non-high urban green innovation efficiency.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Variables Paths
Table 18.Configurations for non-high urban green innovation efficiency.This study uses the fsQCA3.0software to obtain com lutions, and parsimonious solutions.Based on convention alyzing condition configurations, intermediate solutions ber of configurations leading to outcomes and the conditio tions.Then, the parsimonious solution results are used to important core conditions in each configuration [48].The urational approach, setting the original consistency thre 0.75, and the case frequency threshold at 1.The results of shown in Tables 17 and 18. Urban green innovation has and three non-high configurational paths.The coverage o indicating that these configurations can explain over 67% some extent the conditions required for urban green capa This study uses the fsQCA3.0software to obtain complex solutions, i lutions, and parsimonious solutions.Based on conventional practices in a alyzing condition configurations, intermediate solutions are used to deter ber of configurations leading to outcomes and the conditions included in t tions.Then, the parsimonious solution results are used to determine the important core conditions in each configuration [48].The study references urational approach, setting the original consistency threshold at 0.8, FR 0.75, and the case frequency threshold at 1.The results of the configuratio shown in Tables 17 and 18. Urban green innovation has four high config and three non-high configurational paths.The coverage of the solutions i indicating that these configurations can explain over 67% of the cases, s some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Variables Paths
Table 18.Configurations for non-high urban green innovation efficiency.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Variables Paths
Table 18.Configurations for non-high urban green innovation efficiency.This study uses the fsQCA3.0software to obtain complex solutions, i lutions, and parsimonious solutions.Based on conventional practices in a alyzing condition configurations, intermediate solutions are used to deter ber of configurations leading to outcomes and the conditions included in t tions.Then, the parsimonious solution results are used to determine the important core conditions in each configuration [48].The study references urational approach, setting the original consistency threshold at 0.8, FR 0.75, and the case frequency threshold at 1.The results of the configuratio shown in Tables 17 and 18. Urban green innovation has four high config and three non-high configurational paths.The coverage of the solutions i indicating that these configurations can explain over 67% of the cases, s some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Variables Paths
Table 18.Configurations for non-high urban green innovation efficiency.

Paths
denotes the presence of a core condition, • denotes the presence of a marginal condition, denotes the absence of a marginal condition.Note: ⊗ denotes the absence of a core condition, • denotes the presence of a marginal condition, denotes the absence of a marginal condition.

Robustness Test
To ensure the robustness of the research conclusions, this study uses a theory-specific method for robustness testing [54].This study conducted robustness testing by replacing outcome variable indicators.In complex research domains, study outcomes might be influenced by a variety of factors.The measurement of urban green innovation capability can take various forms.Urban sustainability rankings encompass multiple dimensions such as economic, social, and environmental aspects, providing a comprehensive reflection of a city's sustainability performance.On the other hand, urban innovation rankings focus on a city's actual innovation domain, objectively measuring its innovative strength.Hence, for this study, the 2022 Urban Sustainability Ranking and Innovation Capability Ranking were chosen as substitute indicators for the outcome variables.These two indicators were calculated with equal weights of 50%.By utilizing these indicators as substitute outcome variables, it becomes possible to examine the variations in green innovation capabilities from multiple perspectives.This approach facilitates the observation of whether configuration paths remain stable under the condition of constant antecedent variable indicators.This ensures the reliability and generalizability of research outcomes while keeping the premise of unchanged antecedent variables, thereby enhancing the robustness and applicability of the study findings.
In this study, the Urban Sustainability Competitiveness Ranking indicator was transformed using the reverse-engineering formula.Ultimately, the TOPSIS method was applied to convert each variable into values ranging from 0 to 1, while the anchor points for the outcome variables were set at 0.86, 0.596, and 0.335.As evident from Tables 19 and 20, following the robustness testing involving the replacement of outcome variable indicators, the conclusions of this study remained relatively stable.This indicates that the findings of this study are reliable and not overly reliant on changes in a single condition.It demonstrates that the research results possess a certain degree of universality.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.This study uses the fsQCA3.0software to obtain complex soluti lutions, and parsimonious solutions.Based on conventional practice alyzing condition configurations, intermediate solutions are used to ber of configurations leading to outcomes and the conditions include tions.Then, the parsimonious solution results are used to determin important core conditions in each configuration [48].The study refer urational approach, setting the original consistency threshold at 0. 0.75, and the case frequency threshold at 1.The results of the configu shown in Tables 17 and 18. Urban green innovation has four high c and three non-high configurational paths.The coverage of the solut indicating that these configurations can explain over 67% of the ca some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.• denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, interme lutions, and parsimonious solutions.Based on conventional practices in academ alyzing condition configurations, intermediate solutions are used to determine t ber of configurations leading to outcomes and the conditions included in these co tions.Then, the parsimonious solution results are used to determine the relativ important core conditions in each configuration [48].The study references Ragin urational approach, setting the original consistency threshold at 0.8, FRI consi 0.75, and the case frequency threshold at 1.The results of the configurational ana shown in Tables 17 and 18. Urban green innovation has four high configuration and three non-high configurational paths.The coverage of the solutions is all ab indicating that these configurations can explain over 67% of the cases, summa some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex soluti lutions, and parsimonious solutions.Based on conventional practice alyzing condition configurations, intermediate solutions are used to ber of configurations leading to outcomes and the conditions include tions.Then, the parsimonious solution results are used to determin important core conditions in each configuration [48].The study refer urational approach, setting the original consistency threshold at 0. 0.75, and the case frequency threshold at 1.The results of the configu shown in Tables 17 and 18. Urban green innovation has four high c and three non-high configurational paths.The coverage of the solut indicating that these configurations can explain over 67% of the ca some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain complex solutions, interme lutions, and parsimonious solutions.Based on conventional practices in academ alyzing condition configurations, intermediate solutions are used to determine t ber of configurations leading to outcomes and the conditions included in these co tions.Then, the parsimonious solution results are used to determine the relativ important core conditions in each configuration [48].The study references Ragin urational approach, setting the original consistency threshold at 0.8, FRI consi 0.75, and the case frequency threshold at 1.The results of the configurational ana shown in Tables 17 and 18. Urban green innovation has four high configuration and three non-high configurational paths.The coverage of the solutions is all ab indicating that these configurations can explain over 67% of the cases, summa some extent the conditions required for urban green capacity.This study uses the fsQCA3.0software to obtain co lutions, and parsimonious solutions.Based on conventi alyzing condition configurations, intermediate solution ber of configurations leading to outcomes and the condi tions.Then, the parsimonious solution results are used important core conditions in each configuration [48].Th urational approach, setting the original consistency th 0.75, and the case frequency threshold at 1.The results o shown in Tables 17 and 18. Urban green innovation ha and three non-high configurational paths.The coverage indicating that these configurations can explain over 6 some extent the conditions required for urban green cap This study uses the fsQCA3.0software to obtain complex solutions, intermediate solutions, and parsimonious solutions.Based on conventional practices in academia for analyzing condition configurations, intermediate solutions are used to determine the number of configurations leading to outcomes and the conditions included in these configurations.Then, the parsimonious solution results are used to determine the relatively more important core conditions in each configuration [48].The study references Ragin's configurational approach, setting the original consistency threshold at 0.8, FRI consistency at 0.75, and the case frequency threshold at 1.The results of the configurational analysis are shown in Tables 17 and 18. Urban green innovation has four high configurational paths and three non-high configurational paths.The coverage of the solutions is all above 0.67, indicating that these configurations can explain over 67% of the cases, summarizing to some extent the conditions required for urban green capacity.Note: ⊗ denotes the absence of a core condition, • denotes the presence of a marginal condition, denotes the absence of a marginal condition.

High Green Innovation Configurational Paths
(1) Comprehensive Cultural Innovation Path: In this path, the core conditions include the city's cultural level, system foundation, and absorption capacity, and the peripheral conditions include results conversion and sustained participation in green behavior by citizens.The cultural level reflects the level of the city's social structure and cultural cognition [55].Cities with higher levels of literacy often encompass a broader body of knowledge and ways of thinking, which can help nurture innovative thinking and develop the capacity for green innovation [56].The formulation and implementation of policies can offer resources, incentives, and standards.The effective implementation of policies can guide businesses and citizens within the city to actively engage in green innovation activities, thereby enhancing the city's green innovation capacity [57].The city's absorption capacity refers to the city's ability to absorb and apply external knowledge and technology.
with higher absorption capacity can quickly and apply external innovation results.While result conversion and sustained citizen green behavior participation as peripheral conditions have a relatively weaker impact on green innovation capability, they still provide support for the efficiency of urban green innovation to a certain extent.This configuration can explain 61.8% of cases, with representative cities including Beijing, Guangzhou, Hangzhou, etc.
(2) Open Cultural Inclusion Path: The core conditions are the degree of city openness, city cultural level, and city absorption capacity, and the peripheral conditions are institutional basis, sustained participation, and non-high city resource foundation.The degree of city openness reflects the level of connection and communication with the external environment.Open cities are more likely to absorb external innovation resources and experiences, promoting knowledge and technology flows [58].The city's cultural level and absorption capacity remain core conditions.Simultaneously, the support and incentives from the government and sustained participation in green behaviors by citizens also impact the efficiency of urban green innovation to a certain extent.This configuration can explain 23.2% of cases, with representative cities including Shanghai, Nanjing, Suzhou, etc.
(3) Open Participation Innovation Integration Path: In this path, the city's openness degree and absorption capacity remain core conditions, but with a difference: citizen sustainable participation also emerges as a core condition, playing a critical role in green innovation capabilities.Citizens' active participation not only provides practical support but also contributes to fostering a favorable atmosphere and culture for urban green innovation [59].The city's cultural level and patent result conversion, which act as peripheral conditions, also have certain impacts on the development of green innovation capabilities.This configuration can explain 21.9% of cases, with representative cities including Qingdao, Jinan, Dalian, etc.
(4) Innovation Path Driven by Results Conversion: conversion refers to the process of transforming patents generated from research and development and innovation activities into practical applications and commercial value.Through patent transformation, cities can convert innovation results into actual green products, technologies, and services, promoting the application and promotion of green innovation at the economic, social, and environmental levels [60].The remaining conditions are all peripheral conditions, playing auxiliary and promotional roles in urban green innovation.This configuration can explain 53.1% of cases, with representative cities including Zhongshan, Foshan, Xi'an, etc.This study constructs the equivalent model of multiple configurational paths for urban green innovation efficiency based on the core conditions in the configurational paths, as shown in Figure 10.
sorption capacity remain core conditions.Simultaneously, the support and incentives from the government and sustained participation in green behaviors by citizens also impact the efficiency of urban green innovation to a certain extent.This configuration can explain 23.2% of cases, with representative cities including Shanghai, Nanjing, Suzhou, etc.
(3) Open Participation Innovation Integration Path: In this path, the city's openness degree and absorption capacity remain core conditions, but with a difference: citizen sustainable participation also emerges as a core condition, playing a critical role in green innovation capabilities.Citizens' active participation not only provides practical support but also contributes to fostering a favorable atmosphere and culture for urban green innovation [59].The city's cultural level and patent result conversion, which act as peripheral conditions, also have certain impacts on the development of green innovation capabilities.This configuration can explain 21.9% of cases, with representative cities including Qingdao, Jinan, Dalian, etc.
(4) Innovation Path Driven by Results Conversion: Result conversion refers to the process of transforming patents generated from research and development and innovation activities into practical applications and commercial value.Through patent transformation, cities can convert innovation results into actual green products, technologies, and services, promoting the application and promotion of green innovation at the economic, social, and environmental levels [60].The remaining conditions are all peripheral conditions, playing auxiliary and promotional roles in urban green innovation.This configuration can explain 53.1% of cases, with representative cities including Zhongshan, Foshan, Xi'an, etc.This study constructs the equivalent model of multiple configurational paths for urban green innovation efficiency based on the core conditions in the configurational paths, as shown in Figure 10.

Non-High Green Innovation Configurational Paths
The characteristics of the first non-high path is that in situations where urban openness and absorption capacity are low, urban green innovation ability is relatively low as well.This might be due to limitations and barriers faced by cities, such as constraints on technological exchange and knowledge acquisition, as well as limited innovation resources and external innovation sources.It is also challenging for them to effectively absorb external green innovation resources and experiences [61].The characteristics of the second non-high path reflect that these cities have relatively closed and traditional social structures, leading to lower acceptance of new ideas and innovations by their members.This, in turn, affects the city's green innovation capabilities.These cities are not only relatively closed in terms of connections and exchanges with the external environment but also weaker in terms of innovation culture and knowledge accumulation.It is also difficult for them to effectively absorb external green innovation resources [62].The characteristics of the third non-high path indicate that when citizens' participation in green behaviors is consistently low and the city's absorption capacity is also low, the city's green innovation ability is relatively low.At the same time, the city also struggles to effectively absorb external innovation resources.In this situation, the city's green innovation ability is constrained, and the lack of active citizen participation and utilization of external innovation resources may lead to a decline in green innovation ability [63].

Research Conclusion
(1) The results of the Necessary Condition Analysis (NCA) show that the degree of urban culture and absorption capacity are necessary conditions for promoting urban green innovation.Among them, when the urban absorption capacity satisfies a certain level of impact (d > 0.3), it can more effectively promote green innovation, and the degree of urban culture, under the necessary conditions of medium-effect impact (d > 0.1), can also promote the development of urban green innovation.The importance of these two variables is that they reflect the city's ability to absorb external innovation resources as well as the city's knowledge reserves and innovation atmosphere.
(2) The fsQCA results show that there are four high-configuration paths and three non-high-configuration paths, representing different urban green innovation strategies.Among them, the city's degree of openness, cultural level, and absorption capacity play a core role in multiple ways.Innovation diffusion theory points out that the diffusion process of innovation requires an open environment and sufficient acceptors [64].In this study, the degree of openness and absorption capacity of the city play such a role.In addition, this diversified innovation path also shows that urban green innovation does not only depend on a single factor or condition but is achieved through the interaction and coordination of multiple factors.
(3) The role of urban resources in this study is relatively weak, which is different from previous perceptions.Structuration theory shows that social behavior is not only the product of material conditions [65]; however, that social structure and the ideology and values of the behavior subject also play an important role in it.This to a certain extent shows that green innovation is a concept with a cultural view and an inclusive mindset, not just relying on the input of material resources but also relying on social cultural resources, including knowledge, skills, values, and non-material resources such as the social institutional environment.These non-material resources, especially the cultural level of the city and its absorption capacity, play a more critical role.
(4) At the same outcome level, urban absorption capacity and the level of urban culture exhibit higher necessary levels, signifying these two variables as key factors for urban green innovation and sustainable development.Urban absorption capacity reflects the sustained acceptance capability of societal practitioners such as businesses and citizens towards external knowledge and technology.Similarly, the level of urban culture also embodies the continuous innovative awareness and behavioral patterns of societal members.Both of these variables play significant driving roles in urban sustainable development, thereby ensuring the advancement of green innovation.
(5) Our research findings establish a strong connection with a specific Sustainable Development Goal, namely SDG 9: Industry, Innovation, and Infrastructure.This alignment directly contributes to the city's entrepreneurial innovations, institutional systems, and infrastructural arrangements in an important way.Moreover, our study's outcomes are intrinsically tied to Sustainable Development Goal 11: Sustainable Cities and Communities.The examination of various innovative strategies underscores the complex dynamics inherent in urban green innovation, emphasizing its significance in propelling sustainable urban progress while safeguarding economic, social, and environmental welfare.

Theoretical Contributions
(1) A cultural influence model that transcends institutions and resources was found.Social behavior is the joint product of structure and behavior [66].It is important to note that the findings of this study emphasize the pivotal role of cultural aspects in shaping urban green innovation, surpassing the mere constraints imposed by social structures such as institutions and resources.This study found that the cultural level of the city is a necessary condition for influencing urban green innovation and plays a core role in the comprehensive cultural innovation path, the open cultural inclusiveness path, and the open participation innovation integration path.This phenomenon might be attributed to the fact that cities endowed with a heightened cultural profile possess a broader spectrum of knowledge and cognitive approaches.This enhanced cultural milieu fosters the cultivation of innovative thinking and the refinement of capabilities to promote green innovation.This perspective, rooted in cultural influence, accentuates the paramount significance of culture in the innovation process.Functioning as both a recipient and source of innovation, a robust cultural foundation allows the tenets of green innovation to take root and flourish within urban landscapes.The traditional innovation diffusion theory overemphasizes the external environment and internal resource conditions [67] while considering cultural factors.This study, to a certain extent, further enriches and advances the theories of structuration and innovation diffusion.It contends that the level of culture is even more crucial for driving innovation than resources and institutions, as the true driving force behind green innovation and sustainable development originates from the profound cultural aspects.
(2) The process of subject action is oriented toward absorption (result) and continuous participation.In the theory of innovation, diffusion, absorption, and adoption are considered key stages of the innovation process [68].Building upon this foundation, the current study augments our understanding by unearthing the profound impact of a city's absorption capacity on the realm of urban green innovation.Meanwhile, the continuous participation of citizens also plays a central role in the path of open participation in innovation integration.As the guarantor of sustainable development, social behavior is not only a product of structure but also the outcome of the sustainable participation and actions of behavioral subjects [69].Furthermore, it introduces a novel layer by spotlighting the entities involved, i.e., cities and citizens, as pivotal agents in the realm of innovation promotion.The research findings not only underscore the foundational tenets of structuration theory but also shed light on the intricate interplay between these two theories, offering an enriched conceptual framework that affirms the instrumental role of subjects-both urban entities and citizens-in fostering and steering the course of innovation.In doing so, the study contributes novel theoretical insights and empirical validations that reinvigorate the realms of both structuration and innovation diffusion theories.
(3) Structural (resource system, etc.) control also has an impact on the efficiency of urban green innovation to a certain extent.However, its significance reverberates more profoundly in the art of orchestrating the metamorphosis of institutional and resource inputs into tangible outcomes of innovation.This dynamic is exemplified through patent transformation, wherein cities deftly transmute innovation outputs into tangible manifestations such as green products, technologies, and services.In effect, this catalyzes the propagation and advancement of green innovation across economic, social, and environmental strata.This provides new empirical support for Giddens' structuration theory, that is, the function of structural factors is not in themselves but in how they produce actual social effects through the action processes of the subjects [69].Moreover, the sustainable development of a city is also a continuous process of accumulating and re-creating green innovation outcomes, which in turn requires the renewal and iteration of resources and institutions.

Research Limitations and Future Directions
This study has certain limitations: (1) The study sample only includes 101 large cities in China, which may limit the universality of the research results.Considering the diversity and regional differences of urban green innovation, future studies will expand the sam-ple range and include city data from other countries or regions to increase the external validity of the research; (2) Although this study used a variety of methods, such as the DEA-SBM model, NCA, and fsQCA, each method has its limitations.Future research can consider combining more methods or introducing other analysis frameworks to understand the complexity and multi-dimensionality of urban green innovation in depth.At the same time, this study collected data on variables through questionnaires; however, the reliability and consistency of the data may pose certain challenges.Future research can consider conducting surveys in other regions, forming diversified data sources to increase the credibility and accuracy of the data; (3) The conditional variables chosen in this study cover different aspects of urban green innovation; however, whether all key factors are included still needs evaluation.Future research can further explore other potential conditional variables to improve the explanatory power and predictive ability of the model; (4) While our approach has certain advantages in evaluating the efficiency of urban green innovation, "green patents" could be a better indicator to measure green urban innovation than "patents."Due to the incomplete data sources, we retreated to using patents as the main indicator for measuring the output of urban green innovation.Future research will delve into the exploration of a multidimensional metric framework, integrating qualitative and quantitative methods, including surveys and in-depth interviews, to comprehensively assess the output of urban green innovation.

Figure 1 .
Figure 1.The five stages of the innovation diffusion process.

Figure 1 .
Figure 1.The five stages of the innovation diffusion process.

Sustainability 2023 , 30 Figure 2 .
Figure 2. Initial Construction of the Urban Green Innovation Structured Diffusion Model.

Figure 2 .
Figure 2. Initial Construction of the Urban Green Innovation Structured Diffusion Model.

Figure 3 .
Figure 3. CO and green innovation.Figure 3. CO and green innovation.

Figure 3 .
Figure 3. CO and green innovation.Figure 3. CO and green innovation.

Figure 5 .
Figure 5. RB and green innovation.Figure 5. RB and green innovation.

Figure 6 .
Figure 6.SF and green innovation.Figure 6. SF and green innovation.

Figure 8 .
Figure 8. SP and green innovation.Figure 8. SP and green innovation.

Figure 10 .
Figure 10.Equivalent model of multiple configurational paths for urban green innovation efficiency (the solid line represents core conditions, the dotted line represents substitutable variables, and the gradient color of the solid line represents the percentage setting of the condition's NCA results).

Figure 10 .
Figure 10.Equivalent model of multiple configurational paths for urban green innovation efficiency (the solid line represents core conditions, the dotted line represents substitutable variables, and the gradient color of the solid line represents the percentage setting of the condition's NCA results).

Table 1 .
Condition Variables and Measurement Indicators for the Awareness Dimension of Urban Green Innovation.

Table 2 .
Condition Variables and Measurement Indicators for the Interest Dimension in Urban Green Innovation.

Table 3 .
Condition Variables and Measurement Indicators for the Measurement Dimension of Urban Green Innovation.

Table 4 .
Condition Variables and Measurement Indicators for the Implementation Dimension of Urban Green Innovation.

Table 7 .
The Fornell-Larcker Criterion for the questionnaire.

Table 8 .
Cross-loadings of the questionnaire.

Table 9 .
HTMT of the questionnaire.

Table 10 .
Evaluation Index System of Green Innovation Efficiency.

Table 11 .
List of Selected Cities.

Table 13 .
Calibration and Descriptive Statistics of Fuzzy Set.

Table 14 .
Necessary condition analysis of urban green innovation.

Table 14 .
Necessary condition analysis of urban green innovation.

Table 15 .
Bottleneck-level analysis of necessary conditions for urban green innovation.
Note: NN = not necessary.

Table 16 .
QCA necessary condition analysis results for urban green innovation.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a ma ⊗ denotes the absence of a marginal condition.Note: • denotes the presence of a core condition, • denotes the prese ⊗ denotes the absence of a marginal condition.

Table 20 .
Configurations for non-high urban green innovation efficien

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficie Note: • denotes the presence of a core condition, • denotes th ⊗ denotes the absence of a marginal condition.

Table 18 .
Configurations for non-high urban green innovation e

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a ma ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a ma ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 19 .
Configurations for high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a marginal c ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence o ⊗ denotes the absence of a marginal condition.

Table 18 .
Configurations for non-high urban green innovation efficiency.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a marginal condition, ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation efficiency.

Table 18 .
Configurations for non-high urban green innovation efficiency.
Note: • denotes the presence of a core condition, • denotes the presence of a marginal c ⊗ denotes the absence of a marginal condition.

Table 17 .
Configurations for high urban green innovation effic Note: • denotes the presence of a core condition, • denotes ⊗ denotes the absence of a marginal condition.

Table 18 .
Configurations for non-high urban green innovation

Table 17 .
Configurations for high urban green innovation efficiency.

Table 20 .
Configurations for non-high urban green innovation efficiency.