Corporate financial capability refers to the ability of an enterprise to have controllable financial resources (Zhang, 2003). Based on the narrow definition, corporate financial capability refers to the ability of corporate financial performance (Beaver, 1996; Liu, 2016), including an enterprise’s profitability, solvency, development capability, and operating capacity. According to the research purpose, enterprise financial capability in this study refers to enterprise financial capability in the narrow sense.

Based on the theory of redundant resources, whether an enterprise engages in social responsibility, including environmental protection, depends mainly on its ability to deploy sufficient redundant resources (Preston and Obannon, 1997; Campbell, 2007). The corporate financial capacity directly determines the number of redundant resources available to the enterprise to meet its social responsibilities, such as environmental protection responsibilities. (Waddock and Graves, 1997), and affects the effectiveness of enterprises’ implementation of various environmental protection measures. In other words, corporate financial capability is the economic condition for enterprises to take environmental responsibility. Enterprises are more likely to engage in social responsibility by using their resources only when their development needs are met (Preston and Obannon, 1997). Under the financial constraint, investment in environmental governance is bound to have a crowding-out effect on productive investment in the short run (Wang and Wang, 2021), while enterprises with financial advantages will have more flexibility to invest in CSR-related activities and thus better take environmental responsibility (Cheng et al., 2014; Zhang, 2020). Hasan and Habib (2015) believed that in the long run, organizations with better financial capability have more redundant resources and are better able to absorb CSR-related investments and make cost adjustments, thus facilitating the assumption of social responsibility. The green innovation project is characterized by long cycles, significant investments, high risks, and considerable uncertainties regarding the transformation of innovation results and the generation of economic benefits. Therefore, the enthusiasm of enterprises to make green investments is vulnerable to their inherent resources. The willingness of enterprises with a weak resource base to engage in innovation activities is low (Li and Xiao, 2020). In summary, corporate financial performance can impact corporate green innovation performance.

(1) Profitability. Lu et al. (2014) pointed out that the business capacity of enterprises has a positive impact on the assumption of corporate social responsibility, including environmental responsibility. Strong and sustainable profitability can bring a steady flow of material resources to enterprises, and based on meeting their development needs, they can also have sufficient redundant resources for environmental responsibility.

H_1-1: The profitability of enterprises positively affects corporate green innovation performance.

(2) Solvency. Enterprises with more robust solvency usually have more liquid assets and cash flow, more stable market shares, and a more vital ability to withstand risks (Hao, 2019). Enterprises with more robust solvency are more willing to assume social and environmental responsibilities (Ross, 1977). Due to the long payback period of environmental protection investment, as well as the high cost and investment risk, robust solvency can reduce the enterprise’s debt repayment pressure and the possibility of re-financing, with a solid ability to withstand risks, which helps to alleviate the risk-taking of environmental protection investors, so that the enterprise is more willing to participate in environmental protection, thus enhancing the corporate green innovation performance.

H_1-2: The solvency of enterprises positively affects corporate green innovation performance.

(3) Operating capacity. A more robust operating capacity means enterprises have more resources to deploy and allocate to fulfill environmental protection responsibilities. On the one hand, enterprises with more substantial operating capacities can fully use existing resources and transform them into available resources and cash flow faster (Hao, 2019). On the other hand, a more robust operating capacity can ensure the reasonable allocation of environmental protection and green innovation resources.

H_1-3: The enterprise’s operating capacity positively affects corporate green innovation performance.

(4) Development capacity. Compared with enterprises in the rapid growth stage, enterprises in the mature stage have a larger scale and higher profit margins and accumulate more redundant resources (Hasan et al., 2015). On the other hand, early-stage enterprises mainly use resources for production and sales, which will inevitably squeeze out a particular share of environmental protection investment. In addition, fast-growing enterprises tend to reduce their financial resources and willingness to invest in environmental protection due to their products or services’ good market prospects and rapidly increasing market competitiveness.

H_1-4:The enterprise’s development capacity has a negative effect on the corporate green innovation performance.

Command-based environmental regulation, characterized by solid deterrence and distinct signaling effects, refers to the government’s setting of environmental protection standards and objectives through enacting laws or administrative rules and regulations. Incentive-based environmental regulation refers to the government’s efforts to guide enterprises on green transformation through subsidies or financial, tax, and fee, forming a long-term mechanism of environmental protection incentives and constraints. The above two regulatory tools deliver policy orientation signals of different intensities to enterprises, affecting their perceptions of environmental pressures with different expected effects, thus influencing their green innovation decisions.

(1) Incentive-based environmental regulation and corporate green innovation performance.

Based on organizational legitimacy and resource base, compliance with environmental regulations is the foundation of enterprises, and scarce innovation resources and government policy support tend to flow to enterprises with a solid sense of social responsibility and active response to policy guidance (Li et al., 2018; Deng et al., 2021). The resource effect theory clarifies that the heterogeneity of scarce innovation resources and government support policies enterprises possess creates differences in their green innovation capabilities. It has been illustrated that policy support such as government subsidies provides a resource base for corporate green innovation, alleviates the financing dilemma of corporate green innovation, and reduces the cost of corporate green transformation (Montmarin and Herrera, 2015). Resource constraints and insufficient incentives limit corporate green innovation (Manso, 2011). Incentive-based environmental regulatory tools, such as investment in pollution control projects, can effectively help to overcome these difficulties and promote corporate investment in green innovation.

However, the neoclassical school argues that environmental regulations, such as pollution charges fees (environmental taxes since the year 2018), increase compliance costs and exacerbate the financial constraints of enterprises, crowding out green innovation resources (Petroni et al., 2019). Whereas green innovation requires long-term and substantial resource investments, decision-makers will reduce their green innovation investments due to enterprises’ short-term business performance and cash flow pressure.

(2) Command-based environmental regulation and corporate green innovation performance

According to Porter’s hypothesis, appropriate environmental regulation has a push effect on corporate green innovation (Porter and Van der Linde, 1995). Confronting rigid command-based environmental regulation, firms tend to create more green innovations, thereby reducing environmental pollution, enhancing green competitiveness, and effectively circumventing environmental regulatory costs (Berrone et al., 2013).

However, suppose the cost of complying with government regulation is much lower than that of green innovation. In that case, enterprises may make environmental investments to meet government requirements rather than committing to green innovation. Namely, since the green innovation investment has a more extended payback period and more uncertainty, the incentive for enterprises to engage in green innovation will be suppressed if they can meet the government regulatory standards through environmental investment or direct environmental restoration (Li et al., 2019). For example, enterprises can obtain environmental impact assessment (EIA) document approvals for construction projects through other means, thus avoiding the pressure and cost of green innovation, which may crowd out some resources and incentives to engage in green innovation.

H₂: Environmental regulation tools have heterogeneous effects on corporate green innovation performance.

This paper selects all A-share listed companies in China during 2010–2020 (the data after 2020 has yet to be published by China Environmental Yearbook) as the research object, and the sample contains 25,579 data. The data sources are as follows: (1) Financial capacity data were obtained from the China Stock Market and Accounting Research Database (CSMAR), with reference to the provisions of the “Enterprise Economic Efficiency Evaluation Index System (Implementation)” and the “Rules for Evaluating the Performance of State-owned Capital Funds”. (2) The environmental regulation indicators are derived from China Statistical Yearbook, China Environmental Yearbook, China Environmental Statistical Yearbook, and China Taxation Yearbook and compiled by manual calculation. As the measure of corporate green innovation performance, data on corporate green patents, including green inventions independently obtained in the year, green utility models independently obtained in the year, green inventions jointly obtained in the year, and green utility models jointly obtained in the year, are obtained from the Chinese Research Data Service (CNRDS) database. The classification follows the standard of the World Intellectual Property Office, which classifies according to the patent classification number. The remaining indicators are obtained from the China Stock Market and Accounting Research (CSMAE) database. The above raw data were screened as follows: (1) The samples of listed companies in the ST, PT, and financial categories were excluded; (2) The sample data of the Tibetan region were excluded due to the deficiency of fundamental indicators of environmental regulation; (3) Dealing with outliers. Outliers may harm the modeling. We use the deletion of extreme values of 1% and consider the fixed effects of individual enterprises to avoid the influence of outliers on the model; (4) Scaling of features. The independent variables in this paper have different characteristics, and their values have different ranges of variation, so they must be processed in a certain way. We use normalization to process the ranges of variation and distributions of the different characteristics to ensure that the variables have the same scaling.

Tables 2–4 show the descriptive statistics of financial data, environmental regulation data, and the number of corporate green patents by industry.

From Table 4, the mean value of green patents is 1.85, the minimum is 0, and the maximum is 991, manifesting that the overall corporate green innovation performance is deficient and highly differentiated. The first quartile (Q1), the median (Q2), and the third quartile (Q3) are all 0, indicating that the dataset is unbalanced. The number of green patents in the ecological protection and environmental management industry and public facilities management industry is relatively evenly distributed, with the highest average of 3.34. The green innovation ability of the secondary industry, comprised of the extractive, manufacturing, energy, and construction industries, is remarkable, and the number of green patents obtained by a single firm in the extractive industry has reached as high as 991. The reason is that resource-intensive industries, confronted with burdensome social responsibilities and environmental pressures, have a greater sense of responsibility, technical support, and preferential policies for green transformation and industrial restructuring. Nevertheless, the development of green innovation performance in this industry is also uneven, as there are still enterprises with no patents obtained. The number of green patents in tertiary industries, such as the information technology industry, cultural communication, and social service industry, is relatively scarce, indicating that measures should be taken to optimize the industrial structure, provide green financial support, incubate green projects, improve the technical capacity of enterprises, and introduce high-precision enterprises into the tertiary industry to push forward the green transformation.

Due to the apparent long-tailed distribution of the target variable in the data set, we use the category quantile loss function to balance the weights of different categories in the data set to effectively alleviate the sample imbalance problem and improve the prediction performance for minority categories. The loss function is defined as: L y i , y ^ i = q ∗ y i − y ^ i 2 ∗ I y i − y ^ i ≤ 0 + 1 − q ∗ y i − y ^ i 2 ∗ I y i − y ^ i > 0

Based on the data distribution, this paper shows that the top 20% with less green innovation performance possesses 80% of the total sample, hence the q value is 0.2. y i represents the actual value, and y ^ i is the predictive value. I ∙ is the indicative function: I ∙ = 1 , indicated conditions are met 0 , indicated conditions are not met

We use MAE, MSE, RMSE, and R-squared metrics to measure the accuracy and reliability of the prediction results. MAE (Mean Absolute Error) is the average of the absolute values of the differences between the predicted and actual values. It measures the average error size of the model, and a smaller MAE indicates that the model’s prediction result is more accurate. 1 N ∑ i N y i − y ^ i where y i denotes the actual value, and y ^ i represents the predictive value.

MSE (Mean Squared Error) is the average of the squares of the differences between the predicted and actual values. It also measures the magnitude of the model error but is more concerned with the effect of significant errors than the MAE. Therefore, the MSE is more sensitive than the MAE, and a smaller MSE indicates a more accurate prediction result from the model. 1 N ∑ i N y i − y ^ i 2

RMSE (Root Mean Squared Error) is the square root of the MSE. It retains the magnitude of the error and has the same units as the target variable, making it easier to understand. A smaller RMSE indicates a more accurate prediction by the model. 1 N ∑ i N y i − y ^ i 2

R-squared is used to measure the ability of a model to explain the variation in the data. Its value ranges from 0 to 1, and the closer it is to 1, the better the model fits the data. R-squared can help us determine whether the model is over- or under-fitted, as well as the reliability and stability of the model. 1 − ∑ i N y i − y ^ i 2 ∑ i N y i − y ¯ i 2

We conduct repeated experiments within the range of specific parameter values and compare experimental results to select the optimal results to obtain the model’s parameter values. The adjusted model parameters mainly include the following:

(1) Learning rate: The learning rate controls how much each weak learner (base learner) contributes to the overall model. A lower learning rate makes the model more stable but may require more weak learners to perform better. Typically, the learning rate takes values between 0 and 1. For example, in a gradient boosting model, a new regression tree g t x i , yielding:

Parameter selection is crucial. Taking the random forest and gradient boosting model as examples, we exhaustively search all possible parameter combinations within a given range and use cross-validation to evaluate the model’s performance to select the best parameter combination that performs well on the test set. These parameters include the “number of decision trees” and the “maximum depth of decision trees”, ranging from 1 to 100. By analyzing the experimental results, we find that different numbers of decision trees and maximum depths significantly affect the model’s performance. The results of the experimental images indicate that the performance of the gradient boosting model is optimal and stable when the number of decision trees and the maximum depth of decision trees reach about 20 (as shown in Figures 1C, D). In the random forest model, the number of decision trees and the maximum depth of the decision trees reach approximately 30 before reaching the optimal performance and starting to stabilize (Figures 1A, B).

In this study, multiple linear regression, decision tree, random forest, and gradient boosting models are used to predict the changes in corporate green innovation performance, and the prediction results are compared. Figures 2A–H shows the fitting effectiveness of the actual and predicted corporate green innovation performance values under four modeling algorithms. Compared with the previous three methods, the gradient ascent algorithm further improves the prediction accuracy of enterprise green innovation performance, and the trend of the predicted value coincides with that of the actual value. Table 5 lists the relevant evaluation indexes of each prediction model’s fitting effectiveness to the test set, including the R-squared and three error evaluation indexes of MAE, MSE, and RMSE. The smaller the value of the error evaluation indexes, the closer the R-squared is to 1, indicating that the smaller the deviation of the predicted value of the model from the actual value, the higher the accuracy of the prediction model. The comparison of the evaluation indexes of the fitting effect reveals that the values of all the error evaluation indexes of the gradient ascent model are significantly lower than those of the previous three models, and the R-squared value is closer to 1. Taking the MSE (Mean Squared Error) as an example, the value of the index of the test set of the gradient ascent model is 10.51, which is much lower than that of the multivariate linear regression (48.28), decision tree (59.67) and random forest (12.13).

As shown in Figures 2C–F, the prediction performance of the random forest algorithm is superior to that of the decision tree algorithm. A decision tree divides and predicts the data by constructing a tree structure as a primary classification and regression method. However, the decision tree model tends to focus excessively on noise and outliers in the training data, resulting in deficiencies in model generalization and, thus, inevitable overfitting problems. Random forest, as an integrated learning method, randomly selects a portion of features and samples for training when constructing each decision tree, thus avoiding overfitting and improving the accuracy and stability of the model. Therefore, compared to the individual decision tree, the random forest model has better generalization performance and stability to deal with complex classification and regression problems (Hastie et al., 2009; Kotsiantis, 2013).

The gradient boosting algorithm outperforms the former three algorithms. The reasons for this can be categorized into two aspects: 1. In statistical data applications, random forests are usually over-fitted for noisy data in classification or regression studies. The method may result in multiple similar decision trees for data sets with different characteristics, which may bias the research results. The gradient ascent model, based on gradient optimization, has high prediction accuracy and strong generalization ability, which can better adapt to the characteristics of the data and flexibly deal with both continuous and discrete data, especially when dealing with data sets with non-linear relationships. In addition, the gradient ascent model is more suitable for solving the non-linear regression problem, while the random forest is more suitable for solving the classification problem (Chen, 2021). 2. Unlike random forests, which generate decision trees in parallel, the gradient boosting model is an iterative integration algorithm where each tree is formed sequentially and trained on the residuals of the previous tree. In addition, while random forests take an undifferentiated approach to the training set, the gradient boosting model assigns weights to different decision trees according to their importance (Jerome, 2001). This iterative approach makes gradient-boosting trees usually outperform random forests regarding predictive performance.

The relative importance analysis of the predictor variables (Table 6) indicates that the relative importance of financial indicators, operational capacity, command-based environmental regulation, incentive-based environmental regulation, and industry attributes is 40.76%, 24.61%, 14.69%, 12.72%, 7.23%, respectively. Specifically, operating income growth rate, paid-in capital or equity, total profit, industry attributes, and completed investment in pollution control projects in the current year occupy the top five positions. Overall, first, the relative importance of financial indicators and operational capacity for corporate green innovation performance is remarkable. Second, the relative importance of command-based environmental regulation on corporate green innovation performance is more pronounced than that of incentive-based environmental regulation. Third, there is heterogeneity in the impact of the secondary indicators of each influencing factor. Fourth, there is industry heterogeneity in corporate green innovation performance.

Based on the gradient boosting prediction model, we derive the partial dependency diagrams (Figure 3), which reflect the non-linear relationship between each influencing factor and corporate green innovation performance.

(1) corporate green innovation performance is enhanced with the rise of enterprises’ financial indicator variables, whose secondary indicators, especially paid-in capital or equity and total profit, are at the top of the relative importance ranking. On the one hand, sound and sustainable profitability is the material basis and fundamental guarantee for enterprises to increase capital accumulation, expand cash flow, and increase enterprise value. Companies with higher profits tend to have more financial reserves that can be converted into high-quality innovation resources and can better invest human, material, and financial resources. On the other hand, solvency adequacy helps companies alleviate the pressure of debt repayment and refinancing caused by environmental investments. As environmental investments are enormous and have a long payback period, companies with adequate solvency are more resilient to risk and uncertainty and, therefore, more willing to fulfill their social responsibilities. In addition, according to the financial accelerator theory, companies with solid balance sheets can avoid financing constraints, expand financing channels, and thus obtain more financial support to promote green innovation.

However, as one of the manifestations of the development capacity of enterprises, the total asset turnover ratio has a negative driving effect. Enterprises with a high total asset turnover ratio have a pronounced growth capacity. They are in a period of rapid growth, focus more on their growth and expansion, and cannot devote sufficient resources to social responsibilities, including environmental protection (Cambell, 2007). Conversely, enterprises with a relatively low total asset turnover ratio may be mature and have greater flexibility to engage in environmental protection; Furthermore, due to their limited development capacity and the profit motive, they are more inclined to engage in green innovation reforms to reduce their dependence on the environment, improve the efficiency of resource use, and thus enhance their competitiveness.

(3) There is either an increase or a decrease in the corporate green innovation performance with the constraints of the command-based environmental regulation. The positive driving effect of environmental penalty decisions is the most pronounced. The reason is that, on the one hand, external stakeholders’ negative expectations and evaluations of the penalized enterprises lead to corporate financial losses, prompting managers to adopt green innovation strategies and rebuild their social image; on the other hand, the corporate economic losses resulting from the penalties force enterprises to compensate for their deficiencies, to improve the defects of corporate governance mechanisms and to produce more competitive green differentiated products.

The number of EIA document approvals for construction projects in the current year shows the opposite. To some extent, substitutability exists between the approval of EIA documents and the green patents obtained: By relying on the approval of environmental compliance by authorities, enterprises are bound to lose part of their innovation initiative. First, the cost of obtaining approvals may crowd out the green innovation inputs. Second, when the cost and the payback period of green investment are much higher than those of the EIA document approvals, the enterprise will need more incentive to improve its green innovation performance.

(4) The completed investment in pollution control projects in the current year and investment in industrial pollution control positively regulate corporate green innovation performance. On the one hand, pollution control investment stimulates enterprises to accelerate structural adjustment and promotes technological innovation and industrial upgrading; on the other hand, it guides the optimistic expectations of the market, attracts financial and private capital to flow into the green field, increases the accessibility of green financing for enterprises, and invigorates the development of green innovation.

The impact of the environmental tax shows an “inverted U″ shape, which implies that rational intensity is the key to effectively carrying out the environmental tax. If the cost of environmental protection is much higher than that of the environmental tax, the tax will be ineffective in preventing the enterprises from environmental vandalism; on the other hand, overly stringent taxation may cause a deterioration in the enterprise’s financial situation, resulting in a crowding-out effect on environmental investment behavior. In addition, it may trigger numerous enterprises’ relocation to avoid environmental pressures, thereby hindering regional economic development.

In this study, the above empirical results are significant for predicting and managing corporate green innovation performance in research and practice. Consistent with previous studies (Guo, 2019; Li and Xiao, 2020; Zhang, 2020), we found that the key to promoting corporate green innovation performance lies in effectively regulating the enterprises’ internal driving mechanism and rationally selecting external policy tools. Furthermore, this study not only offers a practical and effective corporate green innovation performance prediction model but also relies on a more diverse set of corporate financial indicators and environmental regulation tools to provide innovative empirical evidence for the debate on whether corporate financial capability and environmental regulation have a “conflict” or “coordination” effect on corporate green innovation performance and clarifies effective ways to incentivize corporate green innovation. Concretely, 1. Predict corporate green innovation performance. The gradient boosting model can help stakeholders accurately predict corporate green innovation performance through output indicators that reflect the green innovation performance of different enterprises. 2. Identify best practices. By comparing the green innovation performance of different enterprises and examining the relative importance and non-linear relationship of various influencing factors on corporate green innovation performance, decision makers such as governments and micro-entities can identify the best practices to optimize the top-level policy design and the resource base of enterprises and enhance the corporate green innovation performance. 3. Guide policy formulation. Accurate corporate green innovation performance prediction can provide an essential reference for policymakers to formulate targeted policies and interventions, thus realizing a “win-win” situation for environmental protection and enterprises’ competitiveness enhancement.4. Simulate the effect. The prediction model can simulate the effects of various influencing factors on corporate green innovation performance. By simulating the impact of different policies and strategies, we can better understand the results of each influencing factor on the green innovation performance of enterprises and provide a reference for decision-making by all parties.

We have attempted to introduce deep learning models, such as neural network models, for prediction and comparison in this study; however, as deep learning models are prone to overfitting problems, their predictions are not as effective as gradient boosting models and random forest models, and we initially speculate the reason is that the parameters have not been set optimally. In future studies, we will continue to refine our research on this issue and introduce deep learning models and other models into related research areas.