# Relationship between Green Financing and Investment Logic and Effectiveness Evaluation of Financing Decisions

Authors: Lei Kong; Yu Lei; Qian Zhang; Jing Zhang; Xingzhi Guo; Daoyuan Shi
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

Green financing diverts more funds to green industries such as environmental protection, and clean energy, enabling the industries to realize structural adjustment. On green financing, the existing studies at home and abroad mainly focus on the definition of concepts and service scope and system construction. There are few attempts to combined green financing efficacy with corporate investment from the angles of investment level, investment efficiency, and investment risks. This paper associates green financing policy with corporate investment, analyzes the logical connection between the two, and thereby evaluates the effectiveness of green financing decisions. Specifically, a decision model was established for the government participation in green financing via green product subsidy, and a solving algorithm was developed for the model. After that, the authors analyzed the correlations of green financing with the investment level and investment efficiency of green enterprises. Next, the effectiveness of green financing decisions was discussed under dynamic operation risks. Finally, the proposed approach was demonstrated through simulation and empirical analysis.


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## Body

## 1. Introduction

The sustainable development of all industries is severely bottlenecked by environmental pollution and resource depletion, which arise from the traditional high-pollution and high-consumption development model [1–6]. The long-term development of the green economy hinges on the optimization of industrial structure [7–9]. To achieve green industry restructuring, it is necessary to integrate green development philosophy into the financial system, which plays an important role in the allocation of social resources, and divert more funds to green industries such as environmental protection and clean energy [10–13]. Short supply, weak incentives, and period mismatch are the main problems with the green financing policy, the result of government-led policy guidelines, and system arrangements [14–16]. Green enterprises, as undertakers of green investment, often encounter inefficient investment issues, such as insufficient investment and excessive investment [17–22]. Therefore, exploring the logic relationship between green finance and green enterprise investment would provide an important reference for further optimization of green finance policy.Wu et al. [23] highlighted how critical the commercialization of emerging green technology is to the sustainability of the industrial process, put forward two mixed-integer linear programming models to optimize the innovation financing strategies, and demonstrated the optimization effect through a case study on a biorefinery. Tan et al. [24] researched nonsymmetric competitive supply chain models with financing risks and compared the optimal quantity, optimal price, and optimal profit under two scenarios. It was found that under complete information, the financing risks of capacity investment do not affect the selection of equilibrium price and quantity of the two supply chains. Criscuolo and Menon [25] detailed the risk capital investment of 29 countries in the green sector from 2005 to 2010 and explained the possible role of policy in the observed cross-country differences.Green bonds are becoming a major financial source of green infrastructure, including air and water projects. Ludvigsen [26] introduced the important factors for the issuance of green bonds and the latest technical standard for water affairs of Climate Bonds Standard 2.1. Yatim et al. [27] regarded the green economy as an important path towards sustainable development goals, as well as a promoter of economic growth, and the innovation of new low-carbon production technologies and products. They also elaborated extensively on the current financing policy and measures, such as Green Technology Financing Scheme (GTFS). Dong and Li [28] summarized the recent research results on green finance, defined the basic connotations of green finance, explained the action mechanism of green finance, and provided suggestions on green credit, green insurance, green securities, and green risk investment. Koester et al. [29] pointed out that millions of new capitals from risk fund, private equity fund, and hedge fund are being diverted to clean technology, creating a huge innovation opportunity for clean technology development. In addition, they discussed the optimal organizational form, intellectual property protection, stock options, risk investment locations, offshore finance, financing options, and so on.As green financing attracts more and more attention, many domestic and foreign scholars have defined the concept of green financing, delineated the service scope of green financing, and constructed green financing systems. However, few of them studied green financing efficiency and corporate investment from the angle of investment level, investment efficiency, and investment risk. Neither have many evaluated the effect of green financing policies from macroperspectives such as economic operation and institutional environment. There is no in-depth research into the niches. As a result, corporate managers lack a theoretical basis for implementing green financing.To evaluate the green financial decision, this paper links the macroconcept of green financing policy with the microconcept of corporate investment and analyzes the correlation between green financing and the green corporate investment logic. The research effectively solves the information loss in the traditional discretization process. The association rules of technical indices extracted in this research greatly reduce the computing load of further research.The main contents are organized as follows: (1) Section2 models the government decision to participate in green financing in the form of green product subsidy, and provides the solving algorithm; (3) Section 3 analyzes the correlations between green financing, green corporate investment level, and investment efficiency; (4) Section 4 discusses how to analyze the effectiveness of green financing decision under dynamic operating risks; and (4) Section 5 carries out simulations and presents the empirical results.


## 2. Model Construction and Solution

### 2.1. Model Construction

Referring to the existing results on the interplay between green financing policy and green corporate investment, this paper defines the investment subject as a two-level supply chain involving a green product manufacturer and a green product service provider. Under the effect of the government’s environmental policy, green enterprises are forced to further invest in environmental protection. The resulting shortage of funds calls for financing by financial institutions. Thanks to the guidance of the government, the financing policy of financial institutions favors green enterprises. As a result, green financing helps lower the financing cost and increase the financing efficiency of green enterprises. In this paper, two green financing scenarios are considered, namely, government subsidy for green product manufacturing and green service provision. The specific mechanism of the subsidy is illustrated in Figure1.Figure 1
Financing flow of green enterprises with government participation.This paper mainly studies the government participation in green financing in the form of green product subsidy, in order to optimize the financing decisions of the relevant enterprises. Let MD be the potential market demand of the green products being invested; SE be the sensitivity coefficient of consumers to the price of green products/services; PR be the production cost per unit of green products; SQ be the amount of government subsidy per unit of green products; LR be the sales profit per unit of green products; TP be the unit price of green products;h be the green level of green products; l be the green sensitivity of consumers to green products/services; ω be the ratio of the investment cost of green products to that of the relevant green services; and FU (FU > 0) be the initial fund of the green manufacturer. Without any fund constraint, the green financing amount of a green product manufacturer needs to satisfy:(1)FU≥PR−SQMD−SELR+TP+lh+ω2h2.Formula (1) shows that when the initial fund is fewer than the required green financing amount, the green product manufacturer needs to obtain green financing from banks, venture capital, and other financial institutions. The fund size FI required by the green product manufacturer is defined as follows:(2)FI=PR−SQMD−SELR+TP+lh+ω2h2−FU.Considering the government participation in green financing in the form of green product subsidy, the overall objective of green financing decision was defined as the maximization of total social welfare ZF, composed of the profit of green product manufacturer and green service provider, the consumer surplus, and the environmental protection and governance cost. LetE be consumer demand; LV be the bank interest rate; GZ be consumer surplus; φZH be the profit of green product manufacturer; φSU be the profit of green service provider; and CZ = SQ. E be the government’s financial discount expenditure. Then, the functions of φSU, φZH, and ZF can be expressed as follows:(3)ϕSU=TP−PR+SQE−ω2h2−FI⋅LV,ϕZH=LR⋅E−12h2,ZF=ϕSU+ϕZH+GZ−CZ.SubstitutingE, FI, GZ, and CZ separately into (3), we get(4)ϕSU=TP−PR+SQMD−SELR+TP+lh−ω2h2−PR−SQMD−SELR+TP+lh+ω2h2−FULV,(5)ϕZH=LRMD−SELR+TP+lh−12h2,(6)ZF=TP−PRMD−SELR+TP+lh−ω2h2−PR−SQMD−SELR+TP+lh+ω2h2−FULV+LRMD−SELR+TP+lh−12h2+12MD−SELR+TP+lh2.The game between the government and the enterprises can be modeled as follows:(7)maxSQ≥0ZFSQ,s.t.LR andhare the optimal solution to the following programming:maxm≥0,g≥0ϕZHLR,h,s.tTP is the optimal solution to the following programming:maxTP≥0ϕSUTP.As shown in (7), the government leads the actions of enterprises. Therefore, the decision on green product subsidy SQ should be made first with ZF maximization as the top priority. Then, the green product manufacturer decides the greenness h of products, and the sales profit LR per unit of green products, with the aim to maximize the sales profit of its own products. Finally, the green service provider decides the unit price TP of green products, aiming to maximize the profit of service provision.


### 2.2. Model Solution

The proposed model was solved reversely. For simplicity, the following equation can be defined first:(8)g1=MD−SE⋅PR1+LV,g2=SESE−2,g3=l2−1+ω+ωLV,g4=l2−4SE,g5=SE21+LV+SE6LV−2,g6=l2−1+LV+ω+2LVω+LV2ω.By (4), the first-order derivative of φSU relative to the unit price TP of green products can be obtained as follows:(9)∂ϕSU∂TP=MD+hl+SE⋅LVPR−SQ−SELR+TP−SE−PR+SQ+TP.Then, the second-order derivative ofφSU relative to TP can be solved as follows:(10)∂ϕSU2∂2TP=−2SE<0.SinceφSU is a concave function about TP, there is a local maximum of the profit of green product/service enterprise. Suppose the second-order derivative of φSU relative to TP is zero. Then, TP can be described as a function of SQ, LR, and h as follows:(11)TP=MD+SE⋅PR+hl−SE⋅LR+SE⋅PR⋅LV−SE⋅SQ−SE⋅LV⋅SQ2SE.Combining (11) and (10), the derivatives relative to h and LR can be solved as follows:(12)∂ϕZH∂h=l⋅LR2−h,∂ϕZH∂h=12MD+hj−−2LR−PR−PR⋅LV+SQ+LV⋅SQ.Next, the second-order derivative ofφZH relative to h and LR can be solved as follows:(13)∂2ϕZH∂h2=−1,∂2ϕZH∂LR2=−SE,∂2ϕZH∂h∂LR=∂2ϕZH∂LR∂hl2.The Hessian matrix can be defined as follows:(14)Hessian=−SEl2l2−1.The Hessian matrix is negative definite when its absolute value is greater than 0, expressed as follows:(15)Hessian=SE−l24.In this case,φZH is the combined concave function of h and LR. The simultaneous solution can be solved by(16)LR=2MD+SE⋅PR−SE⋅PR⋅LV+SE⋅SQ+SE⋅LV⋅SQ4SE−l2,h=l−MD+SE⋅PR+SE⋅PR⋅LV−SE⋅SQ−SE⋅LV⋅SQl2−4SE.Substitutingh and LR into formula (11), TP can be updated as follows:(17)TP=MD+3SE−l21+LVPR−SQ4SE−l2.Substituting the updated SQ,h, and LR into (6), the first-order derivative of ZF relative to SQ can be obtained, and the second-order derivative of ZF relative to SQ can be solved as follows:(18)∂2ZF∂SQ2=SE21+LV−2SE1−3LV+SE21+LV+l21−LV−ω−2LVω−LV2ωl2−4SE2.If (18) is negative, ZF is a concave function of SQ and has a local maximum. Suppose the first-order derivative of ZF relative to SQ equals 0. Then(19)SQ∗=g5−g6−g4−g1SE1+LVg5+g6.When the government participates in green financing in the form of green product subsidy, the following condition must be satisfied:(20)SE>l24,SE21+LV+SE6LV−2<l2−1+LV+ω+2LVω+LV2ω.The optimal TP, LR,h, and SQ can be expressed as follows:(21)TP∗=g1g4+SESEg6−g5+MDSE,LR∗=2g1g6−g5,h∗=lg1g6−g5,SQ∗=g5−g6−g4−g1SE1+LVg5−g6.


## 2.1. Model Construction

Referring to the existing results on the interplay between green financing policy and green corporate investment, this paper defines the investment subject as a two-level supply chain involving a green product manufacturer and a green product service provider. Under the effect of the government’s environmental policy, green enterprises are forced to further invest in environmental protection. The resulting shortage of funds calls for financing by financial institutions. Thanks to the guidance of the government, the financing policy of financial institutions favors green enterprises. As a result, green financing helps lower the financing cost and increase the financing efficiency of green enterprises. In this paper, two green financing scenarios are considered, namely, government subsidy for green product manufacturing and green service provision. The specific mechanism of the subsidy is illustrated in Figure1.Figure 1
Financing flow of green enterprises with government participation.This paper mainly studies the government participation in green financing in the form of green product subsidy, in order to optimize the financing decisions of the relevant enterprises. Let MD be the potential market demand of the green products being invested; SE be the sensitivity coefficient of consumers to the price of green products/services; PR be the production cost per unit of green products; SQ be the amount of government subsidy per unit of green products; LR be the sales profit per unit of green products; TP be the unit price of green products;h be the green level of green products; l be the green sensitivity of consumers to green products/services; ω be the ratio of the investment cost of green products to that of the relevant green services; and FU (FU > 0) be the initial fund of the green manufacturer. Without any fund constraint, the green financing amount of a green product manufacturer needs to satisfy:(1)FU≥PR−SQMD−SELR+TP+lh+ω2h2.Formula (1) shows that when the initial fund is fewer than the required green financing amount, the green product manufacturer needs to obtain green financing from banks, venture capital, and other financial institutions. The fund size FI required by the green product manufacturer is defined as follows:(2)FI=PR−SQMD−SELR+TP+lh+ω2h2−FU.Considering the government participation in green financing in the form of green product subsidy, the overall objective of green financing decision was defined as the maximization of total social welfare ZF, composed of the profit of green product manufacturer and green service provider, the consumer surplus, and the environmental protection and governance cost. LetE be consumer demand; LV be the bank interest rate; GZ be consumer surplus; φZH be the profit of green product manufacturer; φSU be the profit of green service provider; and CZ = SQ. E be the government’s financial discount expenditure. Then, the functions of φSU, φZH, and ZF can be expressed as follows:(3)ϕSU=TP−PR+SQE−ω2h2−FI⋅LV,ϕZH=LR⋅E−12h2,ZF=ϕSU+ϕZH+GZ−CZ.SubstitutingE, FI, GZ, and CZ separately into (3), we get(4)ϕSU=TP−PR+SQMD−SELR+TP+lh−ω2h2−PR−SQMD−SELR+TP+lh+ω2h2−FULV,(5)ϕZH=LRMD−SELR+TP+lh−12h2,(6)ZF=TP−PRMD−SELR+TP+lh−ω2h2−PR−SQMD−SELR+TP+lh+ω2h2−FULV+LRMD−SELR+TP+lh−12h2+12MD−SELR+TP+lh2.The game between the government and the enterprises can be modeled as follows:(7)maxSQ≥0ZFSQ,s.t.LR andhare the optimal solution to the following programming:maxm≥0,g≥0ϕZHLR,h,s.tTP is the optimal solution to the following programming:maxTP≥0ϕSUTP.As shown in (7), the government leads the actions of enterprises. Therefore, the decision on green product subsidy SQ should be made first with ZF maximization as the top priority. Then, the green product manufacturer decides the greenness h of products, and the sales profit LR per unit of green products, with the aim to maximize the sales profit of its own products. Finally, the green service provider decides the unit price TP of green products, aiming to maximize the profit of service provision.


## 2.2. Model Solution

The proposed model was solved reversely. For simplicity, the following equation can be defined first:(8)g1=MD−SE⋅PR1+LV,g2=SESE−2,g3=l2−1+ω+ωLV,g4=l2−4SE,g5=SE21+LV+SE6LV−2,g6=l2−1+LV+ω+2LVω+LV2ω.By (4), the first-order derivative of φSU relative to the unit price TP of green products can be obtained as follows:(9)∂ϕSU∂TP=MD+hl+SE⋅LVPR−SQ−SELR+TP−SE−PR+SQ+TP.Then, the second-order derivative ofφSU relative to TP can be solved as follows:(10)∂ϕSU2∂2TP=−2SE<0.SinceφSU is a concave function about TP, there is a local maximum of the profit of green product/service enterprise. Suppose the second-order derivative of φSU relative to TP is zero. Then, TP can be described as a function of SQ, LR, and h as follows:(11)TP=MD+SE⋅PR+hl−SE⋅LR+SE⋅PR⋅LV−SE⋅SQ−SE⋅LV⋅SQ2SE.Combining (11) and (10), the derivatives relative to h and LR can be solved as follows:(12)∂ϕZH∂h=l⋅LR2−h,∂ϕZH∂h=12MD+hj−−2LR−PR−PR⋅LV+SQ+LV⋅SQ.Next, the second-order derivative ofφZH relative to h and LR can be solved as follows:(13)∂2ϕZH∂h2=−1,∂2ϕZH∂LR2=−SE,∂2ϕZH∂h∂LR=∂2ϕZH∂LR∂hl2.The Hessian matrix can be defined as follows:(14)Hessian=−SEl2l2−1.The Hessian matrix is negative definite when its absolute value is greater than 0, expressed as follows:(15)Hessian=SE−l24.In this case,φZH is the combined concave function of h and LR. The simultaneous solution can be solved by(16)LR=2MD+SE⋅PR−SE⋅PR⋅LV+SE⋅SQ+SE⋅LV⋅SQ4SE−l2,h=l−MD+SE⋅PR+SE⋅PR⋅LV−SE⋅SQ−SE⋅LV⋅SQl2−4SE.Substitutingh and LR into formula (11), TP can be updated as follows:(17)TP=MD+3SE−l21+LVPR−SQ4SE−l2.Substituting the updated SQ,h, and LR into (6), the first-order derivative of ZF relative to SQ can be obtained, and the second-order derivative of ZF relative to SQ can be solved as follows:(18)∂2ZF∂SQ2=SE21+LV−2SE1−3LV+SE21+LV+l21−LV−ω−2LVω−LV2ωl2−4SE2.If (18) is negative, ZF is a concave function of SQ and has a local maximum. Suppose the first-order derivative of ZF relative to SQ equals 0. Then(19)SQ∗=g5−g6−g4−g1SE1+LVg5+g6.When the government participates in green financing in the form of green product subsidy, the following condition must be satisfied:(20)SE>l24,SE21+LV+SE6LV−2<l2−1+LV+ω+2LVω+LV2ω.The optimal TP, LR,h, and SQ can be expressed as follows:(21)TP∗=g1g4+SESEg6−g5+MDSE,LR∗=2g1g6−g5,h∗=lg1g6−g5,SQ∗=g5−g6−g4−g1SE1+LVg5−g6.


## 3. Dynamic Risk-Based Analysis on Green Financing Decision

### 3.1. Correlation between Green Financing and Green Enterprise Investment

Figure2 presents the associations between green financing and green corporate investment level. To verify the hypothesis that green enterprises invest more than nongreen enterprises under green financing, this paper takes investment level ILiτ and the double differential cross-term (Gi × Tτ) as the explained variable and the explanatory variable, respectively, and denotes the control variable as CV, individual fixed effects as ξi, time fixed effects as βτ, and the random disturbance term as ρiτ. Then, the fixed-effects double differential model can be established as follows:(22)ILiτ=e0+e1Gi×Tτ+βCV+ξi+μt+ρiτ.Figure 2
Associations between green financing and green corporate investment level.The above model characterizes the associations between green financing and green corporate investment level. Our focus lies on the estimated value ofel, which represents the degree of impact of green financing on the green corporate investment level. If the estimated value is positive, then the hypothesis holds; if the estimated value is negative, then the hypothesis fails.


### 3.2. Correlation Analysis between Green Financing and Green Corporate Investment Level

Figure3 presents the association mechanism between green financing and green corporate investment level. The following parameters were defined to test the interaction between green financing, the sufficiency of green corporate investment, and investment efficiency: the actual new capital investment CAi of the green enterprise in year τ; the Tobin’s Q TB-Qit–1 representing the growth opportunity of the green enterprise in year τ−1; the working fund ZYiτ−1 of the green enterprise in year τ−1; the asset-liability ratio DRiτ–1 of the green enterprise at the end of year τ−1; the scale growth rate SCiτ–1 of the green enterprise; the listing time MAiτ–1 of the green enterprise; the profitability YLiτ–1 of the green enterprise; the actual new capital investment CAiττ–1 of the green enterprise in year τ−1; and the dummy variables ND and HY of year and industry, respectively. Then, the investment efficiency of the green enterprise can be measured by(23)CAiτ=r0+r1TB_Qiτ−1+r2ZYiτ−1+r3DRiτ−1+r4SCiτ−1+r5MAiτ−1+r6YLiτ−1+r7CAiτ−1+∑ND+∑HY+ρiτ.Figure 3
Association mechanism between green financing and green corporate investment level.Based on the regression residual of (23), the underinvestment CA_Viτ, overinvestment CA_ZGiτ, and investment efficiency CA_Aiτ of the green enterprise were calculated separately. Then, CA_Viτ, CA_ZGiτ, and CA_Aiτ were treated as explained variables, and (Gi × Tτ) as the explanatory variable to build the double differential fixed-effects models (26–28), which test the interaction between green financing, the sufficiency of green corporate investment, and investment efficiency. Let us denote the control variable as CV, individual fixed effects as ξi, time fixed effects as βτ, and the random disturbance term as ρiτ. Then, we have(24)CA_Viτ=d0+d1Gi×Tτ+βCV+ξi+μτ+ρiτ,CA_ZGiτ=d2+d3Gi×Tτ+βCV+ξi+μτ+ρiτ,CA_Aiτ=d4+d5Gi×Tτ+βCV+ξi+μτ+ρiτ.The above models focus on the estimation of parametersd1, d3, and d5, which characterize how much green financing affects the sufficiency of green corporate investment and investment efficiency. If d1 is estimated to be positive, then the green financing policy worsens the insufficiency of corporate investment; if d1 is estimated to be negative, then the policy alleviates the insufficiency of corporate investment; if d3 is estimated to be positive, then the green financing policy intensifies the excessiveness of corporate investment; if d3 is estimated to be negative, then the policy alleviates the excessiveness of corporate investment; if d5 is estimated to be positive, then the green financing policy increases corporate investment efficiency; and if d5 is estimated to be negative, then the policy drags down that efficiency.


### 3.3. Dynamic Operation Risks and Green Financing Decision

This paper takes the net occupation of green credit and short-term financial debt ratio as the explained variables. Let GCD and GCS be the corporate demand and supply of green credit, respectively; GFAT, GFBP, GFP, GFACR, GFNR, and GFADR be the accounts payable, notes payable, prepayment, accounts receivable, notes receivable, and deposit received of green financing, respectively; and GPOI be the operation income of green products of the green enterprise. Then, the net occupation of green credit NO can be calculated by(25)NO=GCD−GCS=GFAT+GFBP−GFP−GFACR+GFNR−GFADRGPOI.Let STB be the short-term borrowing of green financing; IP be the interest payment of green financing; NCL be the noncurrent liabilities expired within the year; TFL be the trading financial liabilities; CA be the current assets; and OCL be the operating current assets. Then, the short-term financial debt ratio STF can be calculated by(26)STF=STB+IP+NCL+TFLCA−OCL.In this paper, the dynamic operation risks of the green enterprise are evaluated under the assumption that the enterprise’s profitability changes dynamically with the operation risks. Letητ be the operation risks in year τ; QPτ be the profit before interest, taxes, depreciation, and amortization in year τ; and ZCτ−1 be the total capital in year τ−1. Then, we have(27)ητ=1ψ−1∑τψPτ−1ψ∑τ=1ψPτ^2,Pτ=QPτZCτ−1.Because the green financing decision of the green enterprise is affected by many factors, several other control variables were chosen in addition to dynamic operation costs. Let B represent NO and STF;α0, α1, α2, α3, α4, α5, and α6 denote regression coefficients; IL denotes green product inventory level; NCF be the net cash flow of the operation activities of the green enterprise; CS be the scale of the green enterprise; CG be the growth of the green enterprise; PRO be the profitability of the green enterprise; and OR be the operating risks of the green enterprise. Then, the regression analysis model can be established as follows:(28)B=α0+α1IL+α2NCF+α3CS+α4CG+α5PRO+α6OR+ρ.Model (28) mainly measures how much the operation risks of the green enterprise influence NO and STF.


## 3.1. Correlation between Green Financing and Green Enterprise Investment

Figure2 presents the associations between green financing and green corporate investment level. To verify the hypothesis that green enterprises invest more than nongreen enterprises under green financing, this paper takes investment level ILiτ and the double differential cross-term (Gi × Tτ) as the explained variable and the explanatory variable, respectively, and denotes the control variable as CV, individual fixed effects as ξi, time fixed effects as βτ, and the random disturbance term as ρiτ. Then, the fixed-effects double differential model can be established as follows:(22)ILiτ=e0+e1Gi×Tτ+βCV+ξi+μt+ρiτ.Figure 2
Associations between green financing and green corporate investment level.The above model characterizes the associations between green financing and green corporate investment level. Our focus lies on the estimated value ofel, which represents the degree of impact of green financing on the green corporate investment level. If the estimated value is positive, then the hypothesis holds; if the estimated value is negative, then the hypothesis fails.


## 3.2. Correlation Analysis between Green Financing and Green Corporate Investment Level

Figure3 presents the association mechanism between green financing and green corporate investment level. The following parameters were defined to test the interaction between green financing, the sufficiency of green corporate investment, and investment efficiency: the actual new capital investment CAi of the green enterprise in year τ; the Tobin’s Q TB-Qit–1 representing the growth opportunity of the green enterprise in year τ−1; the working fund ZYiτ−1 of the green enterprise in year τ−1; the asset-liability ratio DRiτ–1 of the green enterprise at the end of year τ−1; the scale growth rate SCiτ–1 of the green enterprise; the listing time MAiτ–1 of the green enterprise; the profitability YLiτ–1 of the green enterprise; the actual new capital investment CAiττ–1 of the green enterprise in year τ−1; and the dummy variables ND and HY of year and industry, respectively. Then, the investment efficiency of the green enterprise can be measured by(23)CAiτ=r0+r1TB_Qiτ−1+r2ZYiτ−1+r3DRiτ−1+r4SCiτ−1+r5MAiτ−1+r6YLiτ−1+r7CAiτ−1+∑ND+∑HY+ρiτ.Figure 3
Association mechanism between green financing and green corporate investment level.Based on the regression residual of (23), the underinvestment CA_Viτ, overinvestment CA_ZGiτ, and investment efficiency CA_Aiτ of the green enterprise were calculated separately. Then, CA_Viτ, CA_ZGiτ, and CA_Aiτ were treated as explained variables, and (Gi × Tτ) as the explanatory variable to build the double differential fixed-effects models (26–28), which test the interaction between green financing, the sufficiency of green corporate investment, and investment efficiency. Let us denote the control variable as CV, individual fixed effects as ξi, time fixed effects as βτ, and the random disturbance term as ρiτ. Then, we have(24)CA_Viτ=d0+d1Gi×Tτ+βCV+ξi+μτ+ρiτ,CA_ZGiτ=d2+d3Gi×Tτ+βCV+ξi+μτ+ρiτ,CA_Aiτ=d4+d5Gi×Tτ+βCV+ξi+μτ+ρiτ.The above models focus on the estimation of parametersd1, d3, and d5, which characterize how much green financing affects the sufficiency of green corporate investment and investment efficiency. If d1 is estimated to be positive, then the green financing policy worsens the insufficiency of corporate investment; if d1 is estimated to be negative, then the policy alleviates the insufficiency of corporate investment; if d3 is estimated to be positive, then the green financing policy intensifies the excessiveness of corporate investment; if d3 is estimated to be negative, then the policy alleviates the excessiveness of corporate investment; if d5 is estimated to be positive, then the green financing policy increases corporate investment efficiency; and if d5 is estimated to be negative, then the policy drags down that efficiency.


## 3.3. Dynamic Operation Risks and Green Financing Decision

This paper takes the net occupation of green credit and short-term financial debt ratio as the explained variables. Let GCD and GCS be the corporate demand and supply of green credit, respectively; GFAT, GFBP, GFP, GFACR, GFNR, and GFADR be the accounts payable, notes payable, prepayment, accounts receivable, notes receivable, and deposit received of green financing, respectively; and GPOI be the operation income of green products of the green enterprise. Then, the net occupation of green credit NO can be calculated by(25)NO=GCD−GCS=GFAT+GFBP−GFP−GFACR+GFNR−GFADRGPOI.Let STB be the short-term borrowing of green financing; IP be the interest payment of green financing; NCL be the noncurrent liabilities expired within the year; TFL be the trading financial liabilities; CA be the current assets; and OCL be the operating current assets. Then, the short-term financial debt ratio STF can be calculated by(26)STF=STB+IP+NCL+TFLCA−OCL.In this paper, the dynamic operation risks of the green enterprise are evaluated under the assumption that the enterprise’s profitability changes dynamically with the operation risks. Letητ be the operation risks in year τ; QPτ be the profit before interest, taxes, depreciation, and amortization in year τ; and ZCτ−1 be the total capital in year τ−1. Then, we have(27)ητ=1ψ−1∑τψPτ−1ψ∑τ=1ψPτ^2,Pτ=QPτZCτ−1.Because the green financing decision of the green enterprise is affected by many factors, several other control variables were chosen in addition to dynamic operation costs. Let B represent NO and STF;α0, α1, α2, α3, α4, α5, and α6 denote regression coefficients; IL denotes green product inventory level; NCF be the net cash flow of the operation activities of the green enterprise; CS be the scale of the green enterprise; CG be the growth of the green enterprise; PRO be the profitability of the green enterprise; and OR be the operating risks of the green enterprise. Then, the regression analysis model can be established as follows:(28)B=α0+α1IL+α2NCF+α3CS+α4CG+α5PRO+α6OR+ρ.Model (28) mainly measures how much the operation risks of the green enterprise influence NO and STF.


## 4. Simulation and Empirical Analysis

The dynamic operation risks of the green enterprise are immensely impacted by market status and industry cyclicity. To ensure the reliability of experimental results, our data samples are Chinese enterprises of the same grade in the noncyclic industry of environmentally friendly electric vehicle manufacturing. After removing the enterprises lacking operation and economic data, a balanced panel data of 28 environmentally friendly electric vehicle manufacturers were established for 2010–2020, which include a total of 540 observations.The associations between green financing and green enterprise investment change with the time series. However, the changes in the associations do not impede the time series from helping the decision-maker of green financing. The decision-maker can still acquire valuable association rules from the panel data time series. Our sample data were obtained from enterprise annual reports and bank credit disclosures and were clustered by an improved fuzzy c-means (FCE) algorithm, producing the membership matrix of the attributes of the financing time series. These attributes were then applied to association rule analysis. Figure4 depicts the flow of our association rule analysis algorithm. A total of 30 experiments was carried out with the following parameters: the population size of the genetic algorithm (GA) was set to 25, the fuzzy weighting index to 2, the maximum number of iterations to 500, and the number of classes to 3. Table 1 compares the clustering results of different algorithms.Figure 4
Flow of our association rule analysis algorithm.Table 1
Clustering results of different algorithms.
AlgorithmStandard FCMGA-based fuzzy clusteringOur algorithmNumber of correctly clustered samples472485503Accuracy89.691.792.8Runtime262.7335.1343.6As shown in Table1, our algorithm achieved the best clustering effect, although it was a bit slower than standard FCM and GA-based fuzzy clustering. This means our algorithm is very unlikely to fall into local optimum and strong in global search. Figure 5 presents the curve of the mean optimal solution to the fitness of each algorithm. It is evident that our algorithm could easily jump out of local convergence, while the other two algorithms often fell into the local optimum, during the clustering of the panel data time series. The main reason is that our algorithm adaptively optimizes crossover and mutation.Figure 5
Curve of the mean optimal solution to the fitness of each algorithm.The membership matrix of the sample data could be obtained through cluster analysis. Several data were selected from the membership matrix of each kind of panel data time series, forming the financing decision form under the operation risks of green enterprises (Table2).Table 2
Financing decision form under the operation risks of green enterprises.
α0α1α2α3α4α5IL0.001677520.00516724−0.0102350.063412920.012162350.03623194NCF0.423759−0.016830.0057240.0053620.0175230.033574CS0.006521−0.009750.0053650.035219−0.00060.043245CG−0.00759−0.00120.0053620.035709−0.003620.025162PRO0.45529−0.014930.0122240.0077620.0183230.052174OR0.014261−0.010850.0089650.041219−0.00160.031145Decision attributes(1,0,0)(1,0,0)(0,1,0)(0,1,0)(0,0,1)(0,0,1)Next is to demonstrate the effectiveness of our model in characterizing the influence of green financing over green enterprise investment level and investment efficiency. For this purpose, the main variables of our model were subjected to descriptive statistics. Table3 shows the statistics on the model of the relationship between green financing and green enterprise investment level. The mean of ILiτ stood at 0.045, that is, the investment level of the surveyed green enterprises averaged at 0.045; the maximum and minimum of the investment level were −0.033, and 0.235, respectively, which represent the difference between green enterprises in investment level. Meanwhile, the mean, maximum, minimum, and standard deviation of TB-Qit−1 were 2.627, 11.125, 0.912, and 1.865, respectively, suggesting that different green enterprises vary in growth opportunity. Likewise, the other variables also differed across green enterprises.Table 3
Descriptive statistics for the model of the relationship between green financing and green enterprise investment level.
VariableILiτGi × TτZYiτ–1TB-Qit–1SCiτ−1YLiτ−1MAiτ−1Mean0.0450.0560.4322.6270.1790.0524.762Median0.0320.0010.4621.9650.0950.0564.981Standard deviation0.0420.2230.2621.8650.3670.0520.695Minimum−0.0320.0010.0450.912−0.256−0.1262.753Maximum0.2351.0020.88511.1252.1530.2765.799Quantity11867118671186711867118671186711867The double differential model must satisfy the null hypothesis of parallel trend. This paper tests the effect of our model on green financing. Figure6 presents the time trends of green enterprise investment level in 2010–2020. One of the curves is about the test group, and the other is about the control group. It can be observed that before 2015, the investment levels of the two groups declined similarly. This is because the investment expenditure grows slower than the total assets, due to the cluster analysis and normalization of total assets of green enterprises and relevant economic panels. After 2015, the investment level of the test group dropped at a slower pace and even slightly rebounded, while that of the control group continued to fall. After 2017, the gap between the two groups widened. The results confirm the hypothesis that green enterprises invest more than nongreen enterprises under green financing.Figure 6
Time trends of green enterprise investment level.Table4 gives the descriptive statistics for the model of the relationship between green financing and green enterprise investment efficiency. In 2010–2020, the annual mean of the new investment of green enterprises took up 4.5% of the total assets; the maximum, minimum, and standard deviation were 18.5%, −3.4%, and 4.2%, respectively. This means green enterprises make only a few new investments, and the enterprises differ in the investment scale. It could be similarly deduced that different enterprises varied significantly in profitability, scale growth rate, cash holding level, leverage ratio, working funds, and so on. That is, the new investment scale differs between enterprises, owing to the disparity between them in terms of the influencing factors on the new capital investment.Table 4
Descriptive statistics for the model of the relationship between green financing and green enterprise investment efficiency.
VariableCAiττCAiττ−1DRiτ−1ZYiτ−1TB-Qit−1SCiτ−1MAiτ−1YLiτ−1Observations11,95411,95411,95411,95411,95411,95411,95411,954Mean0.0450.0520.4360.17602.5360.1854.6170.053Standard deviation0.0420.0430.2180.1451.7320.3570.8750.056Minimum−0.034−0.0250.0470.0120.915−0.2350.672−0.129Maximum0.1850.2360.8950.67710.7652.1625.7350.278Table5 summarizes the investment efficiency of green enterprises. The mean of CA_Aiτ was 0.032, a sign of the heavy presence of inefficient investment among Chinese green enterprises, which drags down investment efficiency. The mean and quantity ratio of CA_Viτ were 0.025 and 63.26%, respectively; the mean and quantity ratio of CA_ZGiτ were 0.041 and 36.74%, respectively. Hence, underinvestment is more common among green enterprises than overinvestment. The main causes include internal factors of these enterprises, such as the long lifecycle of projects, and low environmental risk evaluation, as well as the defects of green financing and relevant financial services, namely, unreasonable financing policy, credit discrimination, and imperfect guarantee system. The underinvestment becomes a prominent problem for the following reasons: the green financing market in China started later than that in developed countries. The financing mechanism needs to be optimized; the financing channels are not diverse; and the financing instruments are outdated. Most green enterprises face different degrees of financing obstacles and constraints. As for green credit, the approval cycle is rather long, and the qualification review is too strict. To solve the problem, more favorable policies should be rolled out to support green financing.Table 5
Statistics on green enterprise investment efficiency.
VariableCA_AiτCA_ViτCA_ZGiτMean0.0320.0250.041Median0.0230.0190.025Standard deviation0.0270.0120.036Minimum0.0010.0010.001Maximum0.1390.0630.138Quantity1235720584Quantity ratio (%)98.0563.2636.74


## 5. Conclusions

From the angle of dynamic risks, this paper tries to clarify the relationship between green financing and the investment logic and evaluates the effectiveness of financing decisions. Firstly, a decision model was established for the government participation in green financing via green product subsidy, and the solving algorithm was designed for the model. Next, the authors analyzed the correlations of green financing with the investment level and investment efficiency of green enterprises and then proposed a method to analyze the effectiveness of green financing decisions under dynamic operation risks. Through experiments, the associations between green financing and green enterprise investment were analyzed, followed by the cluster analysis and association rule analysis on the collected panels. In this way, the analysis results were obtained, and the operation risk-based financing decisions of green enterprises were summarized in a form. In the end, the main variables of our model were subjected to descriptive statistical analysis, which confirm that our model can effectively represent the influence of green financing on green enterprise investment level and investment efficiency.The proposed association analysis model for green financing and green corporate investment mainly targets investment level and investment efficiency. Many other issues are yet to be analyzed from the perspective of dynamic risks. For example, one state or phenomenon under dynamic risks could be described by multiple variables. Hence, future research will deal with the prediction based on multivariate time series.



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*Source: 4051379-2022-04-19.xml*