# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2021028

## Can the reform of green credit policy promote enterprise eco-innovation? A theoretical analysis

 a. College of Economic and Management, Nanjing University of Aeronautics, and Astronautics, Nanjing 211106, China b. College of Intelligent Manufacturing, TaiZhou Institute of Sci.& Tech., Njust, Taizhou 225300, China c. College of Management Engineering, Nanjing University of Information, Science & Technology, Nanjing, 210044, China

* Corresponding author: 1017379408@qq.com

Received  August 2020 Revised  November 2020 Published  February 2021

The weakness that China's traditional credit fails to effectively limit enterprise emissions has become increasingly evident. Although the industry-oriented green credit policy has achieved certain effects on environmental performance through the differentiated resource allocation of the industries, banking financial institutions have the ambiguity in the definition of the credit object and the characteristics of profit maximization, which cannot achieve the essential purpose of green credit sustainably. Hence, we propose a new eco-innovation-oriented green credit policy. We prove theoretically that the new green credit is feasible and can be used as an exogenous driver for improving enterprises' eco-innovation. Contrasting with traditional credit, the newly proposed credit policy is an expansionary monetary policy, which has the characteristics of expanding credit lines and differential interest rates. Utilizing evolutionary game theory, we calculate the evolution stability conditions of green credit and eco-innovation. The results show that the key to green credit to maintaining sustainable development is the return on investment due to eco-innovation. Our theoretical analysis also reveals that environmental benefit-cost ratios and adjustment cost parameters of different assets are the important factors for green credit.

Citation: Sheng Wu, Liangpeng Wu, Xianglian Zhao. Can the reform of green credit policy promote enterprise eco-innovation? A theoretical analysis. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021028
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Path of credits to provide benefits
Game matrix
Impacts of $\alpha$ and $\beta$ on $X_{2}$ when $\varepsilon = J$. Evolution stability constraint $X_{2}$ increases with the increase of the bank's environmental preference $\alpha$ and the enterprise's environmental preference $\beta$. The figure shows that some space remains where $X_{2}>0$ if $\varepsilon>J$ with the increase in $\alpha$ and $\beta$
Impacts of $\alpha$ and $\beta$ on $r.$ The green surface denotes the optimal interest rate of EOGC, and the red surface denotes the optimal interest rate of the traditional credit. The figure shows the change in the optimal interest rate of different credits with respect to environmental preferences
Impacts of $\alpha$ and $\beta$ on $\frac{I}{K} .$ The green surface denotes the ratio of the optimal credit line to the enterprise capital under EOGC, $\frac{I_{g}^{*}}{K},$ and the red surface denotes the ratio of the optimal credit line to the enterprise capital under the traditional credit, $\frac{I_{o}^{*}}{K} .$ The figure shows that the credit line of EOGC changes with the environmental preference, and the credit line of the traditional credit does not
Impacts of $\alpha$ and $\beta$ on $\frac{I_{ {ina}}^{*}}{I_{ {fia}}^{*}} .$ The green surface denotes the optimal eco-innovation investment ratio of intangible assets to fixed assets when $\eta_{i n a} = 0.1,$ the red surface is the optimal ratio when $\eta_{i n a} = 0.5,$ and the yellow surface is the optimal ratio when $\eta_{i n a} = 0.8,$ with the condition of $\eta_{fi a} = 0.3 .$ The figure shows that the impacts of $\alpha$ and $\beta$ on $\frac{I_{ {ina}}^{*}}{I_{ {fia}}^{*}}$ change with the environmental benefit-cost ratio of intangible assets
Impacts of $\eta_{ {ina}}$ and $\eta_{ {fia}}$ on $X_{2}$ when $\varepsilon = J$. The green surface denotes the evolution stability constraint $X_{2}$ when $\beta = 0.7,$ the red surface denotes $X_{2}$ when $\beta = 0.5,$ and the yellow surface denotes $X_{2}$ when $\beta = 0.2,$ with the condition of $\alpha = 0.3 .$ The figure shows that some space remains where $X_{2}>0$ if $\varepsilon>J$ with the increase in $\eta_{i n a}$ and $\eta_{f i a},$ and the impact of $\eta_{ {ina}}$ is greater than that of $\eta_{ {fia}}$
Impacts of $\eta_{i n a}$ and $\eta_{fi a}$ on $\frac{I_{i n a}^{*}}{I_{f i a}^{*}} .$ The green surface denotes the optimal eco-innovation investment ratio of intangible assets to fixed assets when $\beta = 0.7,$ the red surface denotes the optimal investment ratio when $\beta = 0.5,$ and the yellow surface denotes the optimal investment ratio when $\beta = 0.2,$ with the condition of $\alpha = 0.3 .$ The figure shows that the impacts of the environmental benefit-cost ratios on the optimal eco-innovation investment ratio of intangible assets to fixed assets change with the enterprise's environmental preference
Impacts of EOGC on the bank's economic benefits. The green surface denotes the bank's economic benefits under EOGC, and the red surface denotes the bank's economic benefits under the traditional credit. The values of the bank's environmental preference $\alpha$ and the enterprise's environmental preference $\beta$ in the figure are 0.1, 0.3, and 0.6, respectively. The figure shows that the bank's economic benefits under EOGC change with the environmental preferences and differ from that of traditional credit
Impacts of EOGC on the enterprise's economic benefits. The green surface denotes the enterprise's economic benefits growth caused by eco-innovation under EOGC, the red surface denotes the enterprise's economic benefits growth caused by the other activities under the traditional credit, and the yellow surface denotes the enterprise's economic benefits growth caused by eco-innovation under the traditional credit. The values of the bank's environmental preference $\alpha$ and the enterprise's environmental preference $\beta$ in the figure are 0.1, 0.3, and 0.6, respectively. The figure shows the change of the enterprise's economic benefits with the environmental preferences under EOGC
Comparison oftypes of credit
 types traditional credit EOGC characteristics ordinary credit IOGC credit object pollution industries √ × √ general industries √ × √ green industries √ √ √ guidance market means √ × √ administrative means × √ × credit standards maximum economic benefits √ √ × maximum comprehensive benefits × × √ loans usage activity with the greatest return on investment √ √ × eco-innovation × × √
 types traditional credit EOGC characteristics ordinary credit IOGC credit object pollution industries √ × √ general industries √ × √ green industries √ √ √ guidance market means √ × √ administrative means × √ × credit standards maximum economic benefits √ √ × maximum comprehensive benefits × × √ loans usage activity with the greatest return on investment √ √ × eco-innovation × × √
Variables and parameters
 Notation Definition Variables $B$ comprehensive benefits of the bank $R$ economic benefits of the bank $F$ comprehensive benefits of the enterprise $V$ economic benefits of the enterprise $M$ environmental benefits $I$ credit line $r$ interest rate Parameters $\alpha$ environmental preferences of the bank $\beta$ environmental preferences of the enterprise $\eta$ environmental benefit-cost ratio $q$ Tobin's Q $d$ credit risk $\rho$ adjustment cost parameter $J$ return on capital of eco-innovation $\varepsilon$ return on capital of the other activities $K$ enterprise capital $\tau$ discount rate Indexes $fna$ intangible assets of the enterprise $fia$ fixed assets of the enterprise $o$ traditional credits $g$ EOGC $t$ time
 Notation Definition Variables $B$ comprehensive benefits of the bank $R$ economic benefits of the bank $F$ comprehensive benefits of the enterprise $V$ economic benefits of the enterprise $M$ environmental benefits $I$ credit line $r$ interest rate Parameters $\alpha$ environmental preferences of the bank $\beta$ environmental preferences of the enterprise $\eta$ environmental benefit-cost ratio $q$ Tobin's Q $d$ credit risk $\rho$ adjustment cost parameter $J$ return on capital of eco-innovation $\varepsilon$ return on capital of the other activities $K$ enterprise capital $\tau$ discount rate Indexes $fna$ intangible assets of the enterprise $fia$ fixed assets of the enterprise $o$ traditional credits $g$ EOGC $t$ time
Evolutionary stability conditions
 Scenarios Points $\operatorname{det} T$ $\operatorname{tr} T$ Equilibrium results Stability conditions I (0, 0) $+$ $+$ instability point (0, 1) $-$ $\pm$ saddle point $B_{1}>B_{2}$ (1, 0) $-$ $\pm$ saddle point $F_{1}>F_{3}$ (1, 1) $+$ $-$ ESS II (0, 0) $-$ $\pm$ saddle point (0, 1) $+$ $-$ ESS $B_{2}>B_{1}$ (1, 0) $+$ $+$ instability point $F_{2}>F_{4}$ (1, 1) $-$ $\pm$ saddle point III (0, 0) $-$ $\pm$ saddle point (0, 1) $+$ $+$ instability point $B_{3}>B_{4}$ (1, 0) $+$ $-$ ESS $F_{3}>F_{1}$ (1, 1) $-$ $\pm$ saddle point IV (0, 0) $+$ $-$ ESS (0, 1) $-$ $\pm$ saddle point $B_{4}>B_{3}$ (1, 0) $-$ $\pm$ saddle point $F_{4}>F_{2}$ (1, 1) $+$ $+$ instability point
 Scenarios Points $\operatorname{det} T$ $\operatorname{tr} T$ Equilibrium results Stability conditions I (0, 0) $+$ $+$ instability point (0, 1) $-$ $\pm$ saddle point $B_{1}>B_{2}$ (1, 0) $-$ $\pm$ saddle point $F_{1}>F_{3}$ (1, 1) $+$ $-$ ESS II (0, 0) $-$ $\pm$ saddle point (0, 1) $+$ $-$ ESS $B_{2}>B_{1}$ (1, 0) $+$ $+$ instability point $F_{2}>F_{4}$ (1, 1) $-$ $\pm$ saddle point III (0, 0) $-$ $\pm$ saddle point (0, 1) $+$ $+$ instability point $B_{3}>B_{4}$ (1, 0) $+$ $-$ ESS $F_{3}>F_{1}$ (1, 1) $-$ $\pm$ saddle point IV (0, 0) $+$ $-$ ESS (0, 1) $-$ $\pm$ saddle point $B_{4}>B_{3}$ (1, 0) $-$ $\pm$ saddle point $F_{4}>F_{2}$ (1, 1) $+$ $+$ instability point
Optimal interest rates and credit lines
 Scenarios Optimal interest rates Optimal credit lines I $\frac{1}{2}(q+d)+\frac{\tau\left(\eta_{{ina}} \rho_{\text {fia}}+\eta_{{fia}} \rho_{{ina}}\right)}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)}\left(\frac{\beta}{1-\beta}-\frac{\alpha}{1-\alpha}\right)$ $\frac{K\left(\rho_{{ina}}+\rho_{{fia}}\right)}{2 \rho_{{ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{{fia}}+\eta_{ {fia}} \rho_{ {ina}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}\left(\frac{\alpha}{1-\alpha}+\frac{\beta}{1-\beta}\right)$ II $\frac{1}{2}(q+d)+\frac{\tau\left(\eta_{{ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{{ina}}\right) \beta}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)(1-\beta)}$ $\frac{K\left(\rho_{{ina}}+\rho_{{fia}}\right)}{2 \rho_{{ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{ {ina}}\right) \beta}{2 \rho_{{ina}} \rho_{{fia}}(1-\beta)}$ III $\frac{1}{2}(q+d)-\frac{\tau\left(\eta_{{ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{{ina}}\right) \alpha}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)(1-\alpha)}$ $\frac{K\left(\rho_{{ina}}+\rho_{ {fia}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{ {fia}}+\eta_{ {fia}} \rho_{ {ina}}\right) \alpha}{2 \rho_{ {ina}} \rho_{ {fia}}(1-\alpha)}$ IV $\frac{1}{2}(q+d)$ $\frac{K\left(\rho_{ {ina}}+\rho_{ {fia}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}(q-d)$
 Scenarios Optimal interest rates Optimal credit lines I $\frac{1}{2}(q+d)+\frac{\tau\left(\eta_{{ina}} \rho_{\text {fia}}+\eta_{{fia}} \rho_{{ina}}\right)}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)}\left(\frac{\beta}{1-\beta}-\frac{\alpha}{1-\alpha}\right)$ $\frac{K\left(\rho_{{ina}}+\rho_{{fia}}\right)}{2 \rho_{{ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{{fia}}+\eta_{ {fia}} \rho_{ {ina}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}\left(\frac{\alpha}{1-\alpha}+\frac{\beta}{1-\beta}\right)$ II $\frac{1}{2}(q+d)+\frac{\tau\left(\eta_{{ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{{ina}}\right) \beta}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)(1-\beta)}$ $\frac{K\left(\rho_{{ina}}+\rho_{{fia}}\right)}{2 \rho_{{ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{ {ina}}\right) \beta}{2 \rho_{{ina}} \rho_{{fia}}(1-\beta)}$ III $\frac{1}{2}(q+d)-\frac{\tau\left(\eta_{{ina}} \rho_{{fia}}+\eta_{{fia}} \rho_{{ina}}\right) \alpha}{2\left(\rho_{{ina}}+\rho_{{fia}}\right)(1-\alpha)}$ $\frac{K\left(\rho_{{ina}}+\rho_{ {fia}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}(q-d)+\frac{\tau K\left(\eta_{ {ina}} \rho_{ {fia}}+\eta_{ {fia}} \rho_{ {ina}}\right) \alpha}{2 \rho_{ {ina}} \rho_{ {fia}}(1-\alpha)}$ IV $\frac{1}{2}(q+d)$ $\frac{K\left(\rho_{ {ina}}+\rho_{ {fia}}\right)}{2 \rho_{ {ina}} \rho_{ {fia}}}(q-d)$
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