# The External Performance Appraisal of China Energy Regulation: An Empirical Study Using a TOPSIS Method Based on Entropy Weight and Mahalanobis Distance

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Research on the Energy Regulation

#### 2.2. Research Related to TOPSIS Appraisal Method

## 3. The Method for Appraising the External Performance of Energy Regulation

#### 3.1. Traditional TOPSIS Method

#### 3.2. An Improved TOPSIS Method Based on Entropy Weight and Mahalanobis Distance

#### 3.2.1. Definition of Mahalanobis Distance

#### 3.2.2. E-M-TOPSIS Method

#### 3.2.3. Properties of the E-M-TOPSIS Method

**Property**

**1.**

**Proof of Property**

**1.**

**Property**

**2.**

**Proof of Property**

**2.**

## 4. Appraisal Indexes and Data Concerning External Performances of Energy Regulation

#### 4.1. The Appraisal Indexes Concerning External Performance of Energy Regulation

_{2}emission amount per GDP, dust emission amount per GDP, and wastewater discharge amount per GDP. These indexes reflect the influence of energy utilization on the environment. The energy safety performance mainly deals with the core problem of energy safety: whether the energy supply is sufficient and stable or not, and its specific indexes include external dependence, the proportion of primary energy yield in the total world yield, and the primary energy self-sufficient rate. Here, the external dependence reflects the correlation degree of a country on the foreign energies, while the proportion of the primary energy yield in the worldwide yield and the primary energy self-sufficient rate both show the supply capability of China’s energies.

_{2}emission amount per GDP $({X}_{5})$, dust emission amount per GDP $({X}_{6})$, wastewater discharge amount per GDP $({X}_{7})$, and external dependence $({X}_{8})$ are all cost indexes.

#### 4.2. Descriptive Statistical Analysis

_{2}and dust emission amounts, and wastewater discharge amount from 1999~2015 are taken from the CSMAR database. The data about the yields, import volumes, and consumptions of the primary energy during 1999~2015 are collected from the Wind database. The total world energy yields during 1999~2015 are taken from the yearly China Energy Statistical Yearbook. It is worth noting that the total world energy yield in 2015 was not recorded because the China Energy Statistical Yearbook of 2017 has not been published. The study acquired the total world energy yield in 2015 by measuring the average growth rate of the total world energy yields in the most recent five years from 2010 to 2014. Additionally, the GDP is calculated according to the GDP deflators by taking 1999 as the base period.). All index data have been subjected to a descriptive statistical analysis and the specific descriptive statistical results are shown in Table 3.

_{2}emission amount per GDP $({X}_{5})$, dust emission amount per GDP $({X}_{6})$, and wastewater discharge amount per GDP $({X}_{7})$ (environmental performance index) decreased year by year. This implied that China pays more attention to environmental protection while consuming plenty of energy. Moreover, in Figure 4, although the proportion of primary energy yield of China in the worldwide yield $({X}_{9})$ basically improved year by year, the primary energy self-sufficient rate $({X}_{10})$ declined overall and the external dependence $({X}_{8})$ significantly rose. This indicated that China’s energy consumption is still greatly increasing while the domestic energy supply capacity cannot satisfy the rapidly growing energy demand.

_{2}emission amount per GDP $({X}_{5})$ basically show a significant correlation relationship with all the other indexes. Therefore, during selecting the methods for performance appraisal, it is necessary to select a proper method for solving the correlation in order to avoid the information overlap problem.

## 5. Empirical Results of the External Performance Appraisal of China Energy Regulation

#### 5.1. The External Performance Appraisal of China Energy Regulation Based on the E-M-TOPSIS Method

#### 5.2. Discussion and Policy Implications

## 6. Conclusions

#### Future Work

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Fluctuation trends of relative closeness degrees of the equivalent-weight traditional TOPSIS, E-TOPSIS, and E-M-TOPSIS methods.

**Figure 6.**The fluctuation trends of the external economic and social responsibility performances using E-M-TOPSIS.

**Table 1.**The properties, advantages, and limitations of traditional TOPSIS, E-TOPSIS, and E-M-TOPSIS.

Methods | Properties | Advantages | Limitations |
---|---|---|---|

Traditional TOPSIS | The relative closeness degree is changed for non-singular linear transformation | 1.Rational and understandable logic 2. Limited subjective input 3.The ability to identify the best alternative quickly and incorporate relative weights of criterion importance | 1. Subjective weight-determining process 2. The correlation between indexes cannot be eliminated |

E-TOPSIS | The relative closeness degree is unchanged for non-singular linear transformation | 1. Objective weight-determining process 2. Other advantages are the same as traditional TOPSIS | The correlation between indexes cannot be eliminated |

E-M-TOPSIS | 1. The relative closeness degree is unchanged for non-singular linear transformation 2.When the appraisal indexes are independent of each other, the weighted Mahalanobis distance is equivalent to the weighted Euclidean distance | 1. Objective weight-determining process 2. Scale-invariant property 3. Elimination of the linear correlation among indicators 4. Other advantages are the same as traditional TOPSIS | The nonlinear correlation between indexes cannot be eliminated |

Class | Index | Calculation Method | Unit | |
---|---|---|---|---|

External economic performance | Energy consumption elasticity index $({X}_{1})$ | Average annual growth rate of energy consumptions/average annual growth rate of GDP | No | |

Power consumption elasticity index $({X}_{2})$ | Average annual growth rate of power consumptions/average annual growth rate of GDP | No | ||

Output of energy consumption per unit $({X}_{3})$ | GDP/total energy consumption | 10^{4} CNY/tons standard coal | ||

Output of power consumption per unit $({X}_{4})$ | GDP/total power consumptions | CNY/kW·h | ||

Social responsibility performance | Environmental performance | SO_{2} emission amount per GDP $({X}_{5})$ | SO_{2} emission amount/GDP | Tons/10^{4} CNY |

Dust emission amount per GDP $({X}_{6})$ | Dust emission amount/GDP | Tons/10^{4} CNY | ||

Wastewater discharge amount per GDP $({X}_{7})$ | Wastewater discharge amount/GDP | Tons/CNY | ||

Energy safety performance | External dependence $({X}_{8})$ | Energy import amount/total energy consumption | No | |

Proportion of primary energy yield in the worldwide yield $({X}_{9})$ | Primary energy yield/total world energy yield | No | ||

Primary energy self-sufficient rate $({X}_{10})$ | $1-\frac{\mathrm{Primary\; energy\; import}}{\mathrm{Primary\; energy\; consumption}}$ | No |

Index | Mean | Median | Mode | Standard Deviation | Minimum | Maximum | Skewness | Kurtosis |
---|---|---|---|---|---|---|---|---|

Energy consumption elasticity index $({X}_{1})$ | 0.714 | 0.610 | 0.130 ^{a} | 0.433 | 0.130 | 1.670 | 1.154 | 0.875 |

Power consumption elasticity index $({X}_{2})$ | 1.008 | 1.120 | 1.120 | 0.380 | 0.070 | 1.560 | −0.857 | 0.865 |

Output of energy consumption per unit $({X}_{3})$ | 0.756 | 0.729 | 0.644 ^{a} | 0.085 | 0.644 | 0.910 | 0.368 | −1.276 |

Output of power consumption per unit $({X}_{4})$ | 6.599 | 6.409 | 6.172 ^{a} | 0.400 | 6.172 | 7.360 | 0.925 | −0.547 |

SO_{2} emission amount per GDP $({X}_{5})$ | 0.012 | 0.012 | 0.005 | 0.005 | 0.005 | 0.021 | 0.051 | −1.535 |

Dust emission amount per GDP $({X}_{6})$ | 0.006 | 0.005 | 0.003 | 0.003 | 0.003 | 0.013 | 0.851 | −0.394 |

Wastewater discharge amount per GDP $({X}_{7})$ | 0.003 | 0.003 | 0.002 | 0.001 | 0.002 | 0.004 | 0.373 | −1.277 |

External dependence $({X}_{8})$ | 0.135 | 0.125 | 0.068 ^{a} | 0.038 | 0.068 | 0.184 | −0.035 | −1.314 |

Proportion of primary energy yield in the worldwide yield $({X}_{9})$ | 0.141 | 0.144 | 0.094 ^{a} | 0.032 | 0.094 | 0.185 | −0.169 | −1.387 |

Primary energy self-sufficient rate $({X}_{10})$ | 0.872 | 0.885 | 0.818 ^{a} | 0.036 | 0.818 | 0.932 | −0.218 | −1.276 |

^{a}refers to where the index shows several modes to present the minimum of the modes in this context.

${X}_{1}$ | ${X}_{2}$ | ${X}_{3}$ | ${X}_{4}$ | ${X}_{5}$ | ${X}_{6}$ | ${X}_{7}$ | ${X}_{8}$ | ${X}_{9}$ | ${X}_{10}$ | |

${X}_{1}$ | 1 | 0 .835 ** | − 0 .559 * | − 0 .094 | 0 .487 * | 0 .295 | 0 .423 | − 0 .350 | − 0 .440 | 0 .397 |

${X}_{2}$ | 0 .835 ** | 1 | − 0 .563 * | − 0 .060 | 0 .504 * | 0 .316 | 0 .455 | − 0 .356 | − 0 .458 | 0 .408 |

${X}_{3}$ | − 0 .559 * | − 0 .563 * | 1 | − 0 .334 | − 0 .932 ** | − 0 .768 ** | − 0 .873 ** | 0 .908 ** | 0 .859 ** | − 0 .916 ** |

${X}_{4}$ | − 0 .094 | − 0 .060 | − 0 .334 | 1 | 0 .609 ** | 0 .798 ** | 0 .718 ** | − 0 .625 ** | − 0 .708 ** | 0 .539 * |

${X}_{5}$ | 0 .487 * | 0 .504 * | − 0 .932 ** | 0 .609 ** | 1 | 0 .917 ** | 0 .986 ** | − 0 .961 ** | − 0 .979 ** | 0 .954 ** |

${X}_{6}$ | 0 .295 | 0 .316 | − 0 .768 ** | 0 .798 ** | 0 .917 ** | 1 | 0 .955 ** | − 0 .873 ** | − 0 .914 ** | 0 .819 ** |

${X}_{7}$ | 0 .423 | 0 .455 | − 0 .873 ** | 0 .718 ** | 0 .986 ** | 0 .955 ** | 1 | − 0 .954 ** | − 0 .988 ** | 0 .933 ** |

${X}_{8}$ | − 0 .350 | − 0 .356 | 0 .908 ** | − 0 .625 ** | − 0 .961 ** | − 0 .873 ** | − 0 .954 ** | 1 | 0 .956 ** | − 0 .986 ** |

${X}_{9}$ | − 0 .440 | − 0 .458 | 0 .859 ** | − 0 .708 ** | − 0 .979 ** | − 0 .914 ** | − 0 .988 ** | 0 .956 ** | 1 | − 0 .946 ** |

${X}_{10}$ | 0 .397 | 0 .408 | − 0 .916 ** | 0 .539 * | 0 .954 ** | 0 .819 ** | 0 .933 ** | − 0 .986 ** | − 0 .946 ** | 1 |

**Table 5.**A comparison between the appraisal results separately obtained based on E-M-TOPSIS and E-TOPSIS methods.

Year | Mahal+ | Mahal− | E-M-TOPSIS | E-TOPSIS | Traditional TOPSIS | |||
---|---|---|---|---|---|---|---|---|

Closeness | Order | Closeness | Order | Closeness | Order | |||

1999 | 10.307 | 13.397 | 0.565 | 1 | 0.461 | 10 | 0.456 | 11 |

2000 | 11.416 | 12.644 | 0.526 | 4 | 0.387 | 13 | 0.408 | 13 |

2001 | 11.044 | 12.544 | 0.532 | 2 | 0.414 | 12 | 0.417 | 12 |

2002 | 11.482 | 12.202 | 0.515 | 5 | 0.383 | 14 | 0.371 | 15 |

2003 | 11.198 | 12.420 | 0.526 | 3 | 0.304 | 16 | 0.260 | 17 |

2004 | 13.080 | 10.555 | 0.447 | 17 | 0.291 | 17 | 0.267 | 16 |

2005 | 12.302 | 11.128 | 0.475 | 9 | 0.380 | 15 | 0.374 | 14 |

2006 | 12.530 | 10.987 | 0.467 | 13 | 0.454 | 11 | 0.504 | 10 |

2007 | 12.753 | 10.783 | 0.458 | 15 | 0.532 | 7 | 0.596 | 7 |

2008 | 12.198 | 11.329 | 0.482 | 8 | 0.655 | 2 | 0.735 | 2 |

2009 | 12.016 | 11.607 | 0.491 | 6 | 0.594 | 4 | 0.680 | 4 |

2010 | 12.398 | 11.204 | 0.475 | 10 | 0.511 | 8 | 0.592 | 8 |

2011 | 12.587 | 11.057 | 0.468 | 12 | 0.497 | 9 | 0.565 | 9 |

2012 | 12.860 | 10.713 | 0.454 | 16 | 0.583 | 5 | 0.680 | 5 |

2013 | 12.631 | 10.854 | 0.462 | 14 | 0.558 | 6 | 0.646 | 6 |

2014 | 12.442 | 11.015 | 0.470 | 11 | 0.628 | 3 | 0.731 | 3 |

2015 | 11.999 | 11.433 | 0.488 | 7 | 0.681 | 1 | 0.788 | 1 |

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**MDPI and ACS Style**

Wang, Z.-X.; Li, D.-D.; Zheng, H.-H.
The External Performance Appraisal of China Energy Regulation: An Empirical Study Using a TOPSIS Method Based on Entropy Weight and Mahalanobis Distance. *Int. J. Environ. Res. Public Health* **2018**, *15*, 236.
https://doi.org/10.3390/ijerph15020236

**AMA Style**

Wang Z-X, Li D-D, Zheng H-H.
The External Performance Appraisal of China Energy Regulation: An Empirical Study Using a TOPSIS Method Based on Entropy Weight and Mahalanobis Distance. *International Journal of Environmental Research and Public Health*. 2018; 15(2):236.
https://doi.org/10.3390/ijerph15020236

**Chicago/Turabian Style**

Wang, Zheng-Xin, Dan-Dan Li, and Hong-Hao Zheng.
2018. "The External Performance Appraisal of China Energy Regulation: An Empirical Study Using a TOPSIS Method Based on Entropy Weight and Mahalanobis Distance" *International Journal of Environmental Research and Public Health* 15, no. 2: 236.
https://doi.org/10.3390/ijerph15020236