# Rating Regulatory Mechanism Effect Promotion under the Environmental Issuance Effects: Based on the Incentive Difference Hotelling Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Review of the Literature

## 3. The Incentive Difference Hotelling Model

#### 3.1. Model Assumptions

#### 3.2. Construction of the Incentive Difference Hotelling Model

## 4. Analysis of the Factors in the Incentive Difference Hotelling Model

#### 4.1. The First Stage of Game Model

**Situation**

**1.**

**Situation**

**2.**

#### 4.2. The Second Stage of Game Model

**Situation**

**3.**

**Situation**

**4.**

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

## 5. Numerical Analysis and Simulations

#### 5.1. Data Assignment

#### 5.2. Simulation of Rating Regulatory Mechanism Effect under Proposition 1

#### 5.3. Simulation of Rating Regulatory Mechanism Effect under Proposition 2

#### 5.4. Numerical Analysis of Rating Regulatory Mechanism Effect under Proposition 3

## 6. Discussion

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Indicators | Values |
---|---|

Market share of rating agencies ${b}_{1}$ | 0.5 |

Market share of certified green authorities ${b}_{2}$ | 0.3 |

Rating accuracy in the dual rating mechanism ${\delta}_{1}$ | 0.3 |

Rating accuracy in the integrated rating mechanism ${\delta}_{2}$ | 0.5 |

Green rating accuracy in the dual rating mechanism ${\sigma}_{1}$ | 0.5 |

Green rating accuracy in the integrated rating mechanism ${\sigma}_{2}$ | 0.4 |

Rating costs of rating agencies ${c}_{1}$ | 0.3 |

Rating costs of certified green authorities ${c}_{2}$ | 0.6 |

The total reputation of rating agencies and certified green authorities in the dual rating mechanism ${\rho}_{1}$ | 0.5 |

The total reputation of rating agencies and certified green authorities in the integrated rating mechanism ${\rho}_{2}$ | 0.2 |

Regulatory punishments ${c}_{s}$ | 0.5 |

Indicators | The First Stage | The Second Stage |
---|---|---|

The direct effect in the dual rating mechanism ${\mu}_{1}$ | [0.1, 1.6] | [0.1, 1.6] |

The direct effect in the integrated rating mechanism ${\mu}_{2}$ | [−1.025, −0.125] | [−0.82, −0.07] |

The indirect effect in the dual rating mechanism ${\theta}_{1}$ | 1 | [1.4286, 4.4286] |

The indirect effect in the integrated rating mechanism ${\theta}_{2}$ | 1 | [1.25, 2.75] |

Indicators | The First Stage | The Second Stage |
---|---|---|

The direct effect in the dual rating mechanism ${\mu}_{1}$ | [0, 0.75] | [0, 0.75] |

The direct effect in the integrated rating mechanism ${\mu}_{2}$ | [0, 1] | [0, 1] |

The indirect effect in the dual rating mechanism ${\theta}_{1}$ | 1 | (1, 1.35] |

The indirect effect in the integrated rating mechanism ${\theta}_{2}$ | 1 | (1, 6.25] |

Indicators | The First Stage | The Second Stage |
---|---|---|

The direct effect in the dual rating mechanism ${\mu}_{1}$ | 7.82 | 7.82 |

The direct effect in the integrated rating mechanism ${\mu}_{2}$ | 1.5 | 1.5 |

The indirect effect in the dual rating mechanism ${\theta}_{1}$ | 1 | 1.1188 |

The indirect effect in the integrated rating mechanism ${\theta}_{2}$ | 1 | 3.1319 |

Rating accuracy in the dual rating mechanism ${\epsilon}_{1}^{*}$ | 4.21 | 4.7100 |

Rating accuracy in the integrated rating mechanism ${\epsilon}_{2}^{*}$ | 1.10 | 1.3596 |

Profit in the dual mechanism ${\pi}_{1}^{*}$ | 0.9392 | 1.0503 |

Profit in the integrated mechanism ${\pi}_{2}^{*}$ | 0.0670 | 0.1846 |

Indicators | The First Stage | The Second Stage |
---|---|---|

The direct effect in the dual rating mechanism ${\mu}_{1}$ | 3.5870 | 3.5870 |

The direct effect in the integrated rating mechanism ${\mu}_{2}$ | 8.7250 | 8.7250 |

The indirect effect in the dual rating mechanism ${\theta}_{1}$ | 1 | 1.1200 |

The indirect effect in the integrated rating mechanism ${\theta}_{2}$ | 1 | 1.1319 |

Rating accuracy in the dual rating mechanism ${\epsilon}_{1}^{*}$ | 2.0935 | 2.3447 |

Rating accuracy in the integrated rating mechanism ${\epsilon}_{2}^{*}$ | 3.9900 | 4.5164 |

Profit in the dual rating mechanism ${\pi}_{1}^{*}$ | 0.2499 | 0.2713 |

Profit in the integrated rating mechanism ${\pi}_{2}^{*}$ | 0.3667 | 0.2786 |

Situation | The Direct Issuance Effect | The Indirect Issuance Effect | The Choice of Mechanisms |
---|---|---|---|

Non-equilibrium state | ${\mu}_{1}\in [\frac{1-2{\delta}_{1}}{2{\sigma}_{1}},\frac{2+2{\rho}_{2}-2{b}_{1}\cdot (1+{\rho}_{1}+{\rho}_{2})-{c}_{1}+{c}_{2}-2{\delta}_{1}}{2{\sigma}_{1}})$ ${\mu}_{2}\in (\frac{2+2{\rho}_{1}-2{b}_{2}\cdot (1+{\rho}_{1}+{\rho}_{2})+{c}_{1}-{c}_{2}-2{\delta}_{2}}{2{\sigma}_{2}},\frac{1-2{\delta}_{2}}{2{\sigma}_{2}}]$ | ${\theta}_{1}\in (1,\frac{2+2{\rho}_{2}-2{b}_{1}\cdot (1+{\rho}_{1}+{\rho}_{2})-{c}_{1}+{c}_{2}+{c}_{s}}{2{\delta}_{1}})$ ${\theta}_{2}\in (\frac{2+2{\rho}_{1}-2{b}_{2}\cdot (1+{\rho}_{1}+{\rho}_{2})+{c}_{1}-{c}_{2}+{c}_{s}}{2\cdot ({\delta}_{2}+{\sigma}_{2})},+\infty )$ | The dual rating mechanism |

${\mu}_{1}\in [0,\frac{1-2{\delta}_{1}}{2{\sigma}_{1}})$ ${\mu}_{2}\in (\frac{1-2{\delta}_{2}}{{\sigma}_{2}},1]$ | ${\theta}_{1}\in (1+\frac{2{c}_{s}}{2+2{\rho}_{2}-2{b}_{1}\cdot (1+{\rho}_{1}+{\rho}_{2})-{c}_{1}+{c}_{2}},+\infty )$ ${\theta}_{2}\in (1,1+\frac{2{c}_{s}}{2+2{\rho}_{1}-2{b}_{2}\cdot (1+{\rho}_{1}+{\rho}_{2})+{c}_{1}-{c}_{2}})$ | The integrated rating mechanism | |

Equilibrium state | ${\mu}_{1}^{*}=\frac{4-{b}_{1}\cdot (1+{\rho}_{1})+{b}_{2}\cdot {\rho}_{2}+2{c}_{2}-{c}_{1}-{\delta}_{1}}{{\sigma}_{1}}$ | ${\overline{\theta}}_{1}^{*}=1+\frac{{c}_{s}}{4-{b}_{1}\cdot (1+{\rho}_{1})+{b}_{2}\cdot {\rho}_{2}+2{c}_{2}-{c}_{1}}$ | The dual rating mechanism |

${\mu}_{2}^{*}=\frac{4+{b}_{1}\cdot (1+{\rho}_{1})-{b}_{2}\cdot {\rho}_{2}-2{c}_{2}+{c}_{1}-{\delta}_{1}}{{\sigma}_{2}}$ | ${\overline{\theta}}_{2}^{*}=1+\frac{{c}_{s}}{4+{b}_{1}\cdot (1+{\rho}_{1})-{b}_{2}\cdot {\rho}_{2}-2{c}_{2}+{c}_{1}}$ | The integrated rating mechanism |

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## Share and Cite

**MDPI and ACS Style**

Zhao, H.; Tian, Y.; Zhou, X.; Zhang, L.; Meng, W.
Rating Regulatory Mechanism Effect Promotion under the Environmental Issuance Effects: Based on the Incentive Difference Hotelling Model. *Sustainability* **2021**, *13*, 5368.
https://doi.org/10.3390/su13105368

**AMA Style**

Zhao H, Tian Y, Zhou X, Zhang L, Meng W.
Rating Regulatory Mechanism Effect Promotion under the Environmental Issuance Effects: Based on the Incentive Difference Hotelling Model. *Sustainability*. 2021; 13(10):5368.
https://doi.org/10.3390/su13105368

**Chicago/Turabian Style**

Zhao, Hanyi, Yixiang Tian, Xiangyun Zhou, Luping Zhang, and Wei Meng.
2021. "Rating Regulatory Mechanism Effect Promotion under the Environmental Issuance Effects: Based on the Incentive Difference Hotelling Model" *Sustainability* 13, no. 10: 5368.
https://doi.org/10.3390/su13105368