# Sustainable Evolution of China’s Regional Energy Efficiency Based on a Weighted SBM Model with Energy Substitutability

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Methodology

#### 3.1. The Weighted SBM Model

_{0}; ${\omega}_{i}^{I}$ and ${\omega}_{r}^{O}$ denote the weights of input $i$ and output $r$, respectively; ${s}^{I}=({s}_{1}^{I},{s}_{2}^{I},\cdots ,{s}_{m}^{I})$ and ${s}^{O}=({s}_{1}^{O},{s}_{2}^{O},\cdots ,{s}_{s}^{O})$ correspond to the input slack vectors and output slack vectors, respectively. Further, we transfer the above nonlinear programming problem into a linear programming problem using the Charnes–Cooper transformation. Specifically, set $1+\frac{1}{s}{\displaystyle \sum _{r=1}^{s}\frac{{\omega}_{r}^{O}{s}_{r}^{O}}{{y}_{r0}^{}}}=\frac{1}{t}$, and then we can acquire the following linear programming model (L-weighted SBM):

#### 3.2. Modeling the Sustainable Evolution Based on Efficiency Convergence Analysis

## 4. Empirical Analysis of Regional Energy Efficiency in China

#### 4.1. Modeling the Sustainable Evolution Based on Efficiency Convergence Analysis

#### 4.2. The Input–Output Data for Regional Energy Efficiency and Regional Divisions in Mainland China

#### 4.3. Provincial Energy Efficiency Results and Tendency Analysis

#### 4.4. Energy Efficiency Results and Tendency Analysis of the Three Areas

#### 4.5. Energy Efficiency Results and Tendency Analysis of the Seven Economic Zones

#### 4.6. Analysis of Regional Energy Efficiency over Different Five-Year Plans

## 5. Convergence Analysis of Chinese Regional Energy Efficiency

#### 5.1. Convergence Analysis of Energy Efficiency in the Whole Period

#### 5.2. Convergence Analysis of Energy Efficiency during Different Time Intervals

## 6. Conclusions and Policy Implications

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Li, Y.; Oberheitmann, A. Challenges of rapid economic growth in China: Reconciling sustainable energy use, environmental stewardship and social development. Energy Policy
**2009**, 37, 1412–1422. [Google Scholar] [CrossRef] - Rao, X.; Wu, J.; Zhang, Z.Y.; Liu, B. Energy efficiency and energy saving potential in China: An analysis based on slacks-based measure model. Comput. Ind. Eng.
**2012**, 63, 578–584. [Google Scholar] [CrossRef] - Noel, U.D. A reconsideration of effect of energy scarcity on economic growth. Energy
**1995**, 20, 1–12. [Google Scholar] - Boyd, G.A. Estimating plant level energy efficiency with a stochastic frontier. Energy
**2008**, 29, 23–43. [Google Scholar] [CrossRef] - Lin, B.Q.; Du, K.R. Technology gap and China’s regional energy efficiency: A parametric metafrontier approach. Energ. Econ.
**2013**, 40, 529–536. [Google Scholar] [CrossRef] - Wang, H.; Ang, B.W.; Wang, Q.Q.; Zhou, P. Measuring energy performance with sectoral heterogeneity: A non-parametric frontier approach. Energ. Econ.
**2017**, 62, 70–78. [Google Scholar] [CrossRef] - Filippini, M.; Zhang, L. Estimation of the energy efficiency in Chinese provinces. Energ. Effic.
**2016**, 9, 1315–1328. [Google Scholar] [CrossRef] - Colombi, R.; Kumbhakar, S.C.; Martini, G.; Vittadini, G. Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency. J. Prod. Anal.
**2014**, 42, 123–136. [Google Scholar] [CrossRef] - Belotti, F.; Ilardi, G. Consistent inference in fixed-effects stochastic frontier models. J. Econom.
**2018**, 202, 161–177. [Google Scholar] [CrossRef][Green Version] - Charnes, A.; Cooper, W.; Rhodes, E. Measuring the efficiency of decision making units. Eur. J. Oper. Res.
**1978**, 2, 429–444. [Google Scholar] [CrossRef] - Liu, J.S.; Lu, L.Y.; Lu, W.; Lin, B.J. A survey of DEA applications. Omega
**2013**, 41, 893–902. [Google Scholar] [CrossRef] - Meng, F.; Su, B.; Thomson, E.; Zhou, D.; Zhou, P. Measuring China’s regional energy and carbon emission efficiency with DEA models: A survey. Appl. Energ.
**2016**, 183, 1–21. [Google Scholar] [CrossRef] - Wu, F.; Fan, L.W.; Zhou, P.; Zhou, D.Q. Industrial energy efficiency with CO
_{2}emissions in China: A nonparametric analysis. Energy Policy**2012**, 49, 164–172. [Google Scholar] [CrossRef] - Feng, C.; Wang, M. Analysis of energy efficiency in China’s transportation sector. Renew. Sustain. Energ. Rev.
**2018**, 94, 565–575. [Google Scholar] [CrossRef] - Yang, W.; Shi, J.F.; Qiao, H.; Shao, Y.M.; Wang, S.Y. Regional technical efficiency of Chinese iron and steel industry based on bootstrap network data envelopment analysis. SocioEcon. Plan. Sci.
**2017**, 57, 14–24. [Google Scholar] [CrossRef] - Feng, C.; Wang, M. The economy-wide energy efficiency in China’s regional building industry. Energy
**2017**, 141, 1869–1879. [Google Scholar] [CrossRef] - Xu, S.; Li, Y.; Tao, Y.; Wang, Y.; Li, Y.-F. Regional Differences in the Spatial Characteristics and Dynamic Convergence of Environmental Efficiency in China. Sustainability
**2020**, 12, 7423. [Google Scholar] [CrossRef] - Wang, Q.; Zhou, P.; Zhao, Z.; Shen, N. Energy Efficiency and Energy Saving Potential in China: A Directional Meta-Frontier DEA Approach. Sustainability
**2014**, 6, 5476–5492. [Google Scholar] [CrossRef][Green Version] - Färe, F.; Grosskopf, S. Network DEA. SocioEcon. Plan. Sci.
**2000**, 34, 35–49. [Google Scholar] [CrossRef] - Tone, K. A slacks-based measure of efficiency in data envelopment analysis. Eur. J. Oper. Res.
**2001**, 130, 498–509. [Google Scholar] [CrossRef][Green Version] - Li, H.; Shi, J.F. Energy efficiency analysis on Chinese industrial sectors: An improved Super-SBM model with undesirable outputs. J. Clean. Prod.
**2014**, 65, 97–107. [Google Scholar] [CrossRef] - Du, H.B.; Matisoff, D.C.; Wang, Y.Y.; Liu, X. Understanding drivers of energy efficiency changes in China. Appl. Energ.
**2016**, 184, 1196–1206. [Google Scholar] [CrossRef] - Bian, Y.W.; Hu, M.; Wang, Y.S.; Xu, H. Energy efficiency analysis of the economic system in China during 1986–2012: A parallel slacks-based measure approach. Renew. Sustain. Energ. Rev.
**2016**, 55, 990–998. [Google Scholar] [CrossRef] - Shao, Y.; Han, S. The Synergy in the Economic Production System: An Empirical Study with Chinese Industry. Sustainability
**2019**, 11, 980. [Google Scholar] [CrossRef][Green Version] - Cai, H.; Fan, R. Regional Total Factor Energy Efficiency Evaluation of China: The Perspective of Social Welfare. Sustainability
**2019**, 11, 4093. [Google Scholar] [CrossRef][Green Version] - Du, J.; Zhao, M.; Zeng, M.; Han, K.; Sun, H.-P. Spatial Effects of Urban Agglomeration on Energy Efficiency: Evidence from China. Sustainability
**2020**, 12, 3338. [Google Scholar] [CrossRef][Green Version] - Lin, B.Q.; Zhang, G.L. Energy efficiency of Chinese service sector and its regional differences. J. Clean. Prod.
**2017**, 168, 614–625. [Google Scholar] [CrossRef] - Yang, T.; Chen, W.; Zhou, K.; Ren, M. Regional energy efficiency evaluation in China: A super efficiencyslack-based measure model with undesirable outputs. J. Clean. Prod.
**2018**, 198, 859–866. [Google Scholar] [CrossRef] - Zhu, L.; Wang, Y.; Shang, P.; Qi, L.; Yang, G.; Wang, Y. Improvement path, the improvement potential and the dynamic evolution of regional energy efficiency in China: Based on an improved nonradial multidirectional efficiency analysis. Energy Policy
**2019**, 133, 110883. [Google Scholar] [CrossRef] - Liu, H.; Zhang, Z.; Zhang, T.; Wang, L. Revisiting China’s provincial energy efficiency and its influencing factors. Energy
**2020**, 208, 118361. [Google Scholar] [CrossRef] - Cheng, Z.; Liu, J.; Li, L.; Gu, X. Research on meta-frontier total-factor energy efficiency and its spatial convergence in Chinese provinces. Energ. Econ.
**2020**, 86, 104702. [Google Scholar] [CrossRef] - Zhou, Y.; Liang, D.P.; Xing, X.P. Environmental efficiency of industrial sectors in China: An improved weighted SBM model. Math. Comput. Model.
**2013**, 58, 990–999. [Google Scholar] [CrossRef] - Zhou, Y.; Xing, X.P.; Fang, K.N.; Liang, D.P.; Xu, C.L. Environmental efficiency analysis of power industry in China based on an entropy SBM model. Energy Policy
**2013**, 57, 68–75. [Google Scholar] [CrossRef] - Xiong, S.; Tian, Y.; Ji, J.; Ma, X. Allocation of Energy Consumption among Provinces in China: A Weighted ZSG-DEA Model. Sustainability
**2017**, 9, 2115. [Google Scholar] [CrossRef][Green Version] - Baumol, W.J. Productivity growth, convergence, and welfare: What the long-run data show. Am. Econ. Rev.
**1986**, 76, 1072–1085. [Google Scholar] - Arcelus, F.J.; Arocena, P. Convergence and productive efficiency in fourteen OECD countries: A non-parametric frontier approach. Int. J. Prod. Econ.
**2000**, 66, 105–117. [Google Scholar] [CrossRef] - Li, K.; Lin, B.Q. Metafrontier energy efficiency with CO2 emissions and its convergence analysis for China. Energ. Econ.
**2015**, 48, 230–241. [Google Scholar] [CrossRef] - Zhang, W.; Pan, X.F.; Yan, Y.B.; Pan, X.Y. Convergence analysis of regional energy efficiency in China based on large-dimensional panel data model. J. Clean. Prod.
**2017**, 142, 801–808. [Google Scholar] [CrossRef] - Han, L.; Han, B.; Shi, X.; Su, B.; Lv, X.; Lei, X. Energy efficiency convergence across countries in the context of China’s Belt and Road initiative. Appl. Energ.
**2018**, 213, 112–122. [Google Scholar] [CrossRef][Green Version] - Pan, X.F.; Liu, Q.; Peng, X.X. Spatial club convergence of regional energy efficiency in China. Ecol. Indic.
**2015**, 51, 25–30. [Google Scholar] [CrossRef] - Smyth, R.; Narayan, P.K.; Shi, H.L. Substitution between energy and classical factor inputs in the Chinese steel sector. Appl. Energ.
**2011**, 88, 361–367. [Google Scholar] [CrossRef] - Barro, R.J.; Sala-i-Martin, X.X. Convergence. J. Polit. Econ.
**1992**, 100, 223–251. [Google Scholar] [CrossRef] - Flannery, M.J.; Ranga, K.P. Partial adjustment toward target capital structures. J. Financ. Econ.
**2006**, 79, 469–506. [Google Scholar] [CrossRef] - Hoerl, A.E.; Kennard, R.W. Ridge regression: Biased estimation for nonorthogonal problems. Technometrics
**1970**, 42, 80–86. [Google Scholar] [CrossRef] - China Statistical Yearbook; State Statistical Bureau (SSB), China Statistical Publishing House: Beijing, China, 1991–2015. (In Chinese)
- Yeh, T.; Chen, T.; Lai, P. A comparative study of energy utilization efficiency between Taiwan and China. Energy Policy
**2010**, 38, 2386–2394. [Google Scholar] [CrossRef]

**Figure 1.**Flowchart of the improved energy efficiency (EE) model and the whole empirical analysis steps.

${\mathit{K}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{t}}$ | ${\mathit{E}}_{\mathit{t}}$ | ${\mathit{K}}_{\mathit{t}}\cdot {\mathit{L}}_{\mathit{t}}$ | ${\mathit{K}}_{\mathit{t}}\cdot {\mathit{E}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{t}}\cdot {\mathit{E}}_{\mathit{t}}$ | ${\mathit{K}}_{\mathit{t}}\cdot {\mathit{K}}_{\mathit{t}}$ | ${\mathit{L}}_{\mathit{t}}\cdot {\mathit{L}}_{\mathit{t}}$ | ${\mathit{E}}_{\mathit{t}}\cdot {\mathit{E}}_{\mathit{t}}$ | |
---|---|---|---|---|---|---|---|---|---|

${K}_{t}$ | 1.0000 | ||||||||

${L}_{t}$ | 0.6097 | 1.0000 | |||||||

${E}_{t}$ | 0.9286 | 0.7775 | 1.0000 | ||||||

${K}_{t}\cdot {L}_{t}$ | 0.9999 | 0.6047 | 0.9262 | 1.0000 | |||||

${K}_{t}\cdot {E}_{t}$ | 0.9943 | 0.5338 | 0.8876 | 0.9949 | 1.0000 | ||||

${L}_{t}\cdot {E}_{t}$ | 0.9249 | 0.7957 | 0.9994 | 0.9224 | 0.8821 | 1.0000 | |||

${K}_{t}\cdot {K}_{t}$ | 0.9535 | 0.4364 | 0.7800 | 0.9553 | 0.9752 | 0.7749 | 1.0000 | ||

${L}_{t}\cdot {L}_{t}$ | 0.6440 | 0.9976 | 0.8089 | 0.6391 | 0.5684 | 0.8264 | 0.4676 | 1.0000 | |

${E}_{t}\cdot {E}_{t}$ | 0.9705 | 0.6672 | 0.9823 | 0.9692 | 0.9478 | 0.9778 | 0.8581 | 0.7031 | 1.0000 |

**Table 2.**Multicollinearity diagnostics results of the variables in the translog production function.

Variables | Tolerance | VIF | Variables | Tolerance | VIF | Variables | Tolerance | VIF |
---|---|---|---|---|---|---|---|---|

LnK | 0.002 | >100 | LnK×LnL | <0.001 | >100 | LnK×LnK | 0.001 | >100 |

LnL | 0.064 | 16 | LnK×LnE | <0.001 | >100 | LnL×LnL | <0.002 | >100 |

LnE | <0.001 | >100 | LnL×LnE | <0.001 | >100 | LnE×LnE | 0.015 | 67 |

Variable | Standardized Coeff. | Coeff. | t-Statistic | p-Value | VIF |
---|---|---|---|---|---|

$ln{K}_{t}$ | 0.0890 | 0.0539 * | 1.8323 | 0.0776 | 0.0149 |

$ln{L}_{t}$ | 0.0241 | 0.1119 | 0.5628 | 0.5781 | 0.0216 |

$ln{E}_{t}$ | 0.1727 | 0.2667 *** | 3.6613 | 0.0010 | 0.0148 |

$ln{K}_{t}\cdot ln{L}_{t}$ | 0.0921 | 0.0046 * | 1.8666 | 0.0725 | 0.0093 |

$ln{K}_{t}\cdot ln{E}_{t}$ | 0.1271 | 0.0049 ** | 2.5613 | 0.0161 | 0.0051 |

$ln{L}_{t}\cdot ln{E}_{t}$ | 0.1421 | 0.0150 *** | 2.8777 | 0.0076 | 0.0080 |

$ln{K}_{t}\cdot ln{K}_{t}$ | 0.1367 | 0.0041 *** | 2.7923 | 0.0093 | 0.0102 |

$ln{L}_{t}\cdot ln{L}_{t}$ | 0.0286 | 0.0061 | 0.6669 | 0.5103 | 0.0215 |

$ln{E}_{t}\cdot ln{E}_{t}$ | 0.1792 | 0.0116 *** | 3.8533 | 0.0006 | 0.0165 |

Region Name (Notation) | The Provinces in the Corresponding Division Region | |
---|---|---|

Eastern area (E) | Liaoning, Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong, Hainan | |

Three Areas | Central area (C) | Jilin, Heilongjiang, Shanxi, Anhui, Jiangxi, Henan, Hubei, Hunan |

Western area (W) | Inner Mongolia, Guangxi, Guizhou, Yunnan, Shaanxi, Gansu, Xinjiang, Sichuan, Qinghai, Ningxia | |

Central Bohai (CB) | Beijing, Tianjin, Hebei, Shandong | |

Yangtze River Delta (CD) | Shanghai, Jiangsu, Zhejiang | |

Pearl River Delta (PD) | Fujian, Guangdong, Hainan | |

Seven Economic Zones | Northeast (N) | Liaoning, Jilin, Heilongjiang |

Central Provinces (CP) | Anhui, Jiangxi, Henan, Hubei, Hunan, Shanxi | |

Great Southwest (GS) | Guangxi, Guizhou, Yunnan, Sichuan | |

Great Northwest (GN) | Shaanxi, Gansu, Xinjiang, Inner Mongolia, Qinghai, Ningxia |

Panel A: Energy Efficiency Across Years | ||||||||

Year | Mean | Std. dev. | Year | Mean | Std. dev. | Year | Mean | Std. dev. |

1991 | 0.4776 | 0.2144 | 2000 | 0.3807 | 0.0758 | 2009 | 0.3675 | 0.1305 |

1992 | 0.3602 | 0.0915 | 2001 | 0.3817 | 0.0857 | 2010 | 0.3982 | 0.1433 |

1993 | 0.3020 | 0.0491 | 2002 | 0.3739 | 0.0895 | 2011 | 0.4257 | 0.1561 |

1994 | 0.3194 | 0.0512 | 2003 | 0.3547 | 0.0874 | 2012 | 0.4340 | 0.1719 |

1995 | 0.3488 | 0.0598 | 2004 | 0.3581 | 0.0925 | 2013 | 0.4475 | 0.1784 |

1996 | 0.3804 | 0.1003 | 2005 | 0.3578 | 0.0985 | 2014 | 0.4534 | 0.1817 |

1997 | 0.4191 | 0.1394 | 2006 | 0.3589 | 0.1085 | 2015 | 0.4628 | 0.1902 |

1998 | 0.3805 | 0.0934 | 2007 | 0.3707 | 0.1159 | - | - | - |

1999 | 0.3832 | 0.0807 | 2008 | 0.4273 | 0.1941 | Average | 0.3890 | 0.0843 |

Panel B: Energy Efficiency Across Provinces | ||||||||

Provinces | Mean | Std. dev. | Provinces | Mean | Std. dev. | Provinces | Mean | Std. dev. |

Beijing | 0.5195 | 0.2358 | Zhejiang | 0.4513 | 0.0883 | Hainan | 0.3866 | 0.0459 |

Tianjin | 0.4609 | 0.1417 | Anhui | 0.3544 | 0.0540 | Sichuan | 0.3442 | 0.0653 |

Hebei | 0.3358 | 0.0355 | Fujian | 0.4662 | 0.0438 | Guizhou | 0.2899 | 0.0724 |

Shanxi | 0.3196 | 0.0470 | Jiangxi | 0.4621 | 0.1720 | Yunnan | 0.3363 | 0.0956 |

Inner Mongolia | 0.3620 | 0.0789 | Shandong | 0.4141 | 0.0491 | Shaanxi | 0.3482 | 0.0486 |

Liaoning | 0.3743 | 0.0554 | Henan | 0.3660 | 0.0313 | Gansu | 0.2901 | 0.0371 |

Jilin | 0.3709 | 0.0542 | Hubei | 0.3851 | 0.1382 | Qinghai | 0.2509 | 0.0325 |

Heilongjiang | 0.4157 | 0.0558 | Hunan | 0.4468 | 0.1593 | Ningxia | 0.2372 | 0.0402 |

Shanghai | 0.5865 | 0.2535 | Guangdong | 0.5470 | 0.1542 | Xinjiang | 0.2931 | 0.0408 |

Jiangsu | 0.4554 | 0.0920 | Guangxi | 0.4101 | 0.1339 | Average | 0.3890 | 0.0442 |

Three Areas | Years | ||||||||

1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | |

Eastern Area | 0.4180 | 0.3344 | 0.3002 | 0.3152 | 0.3362 | 0.3668 | 0.3915 | 0.4014 | 0.4150 |

Central Area | 0.5856 | 0.4059 | 0.3308 | 0.3485 | 0.3960 | 0.4582 | 0.5084 | 0.4228 | 0.4154 |

Western Area | 0.4566 | 0.3519 | 0.2811 | 0.3007 | 0.3251 | 0.3331 | 0.3779 | 0.3238 | 0.3226 |

Overall Area | 0.4868 | 0.3641 | 0.3040 | 0.3215 | 0.3524 | 0.3860 | 0.4259 | 0.3827 | 0.3843 |

Three Areas | Years | ||||||||

2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | |

Eastern Area | 0.4274 | 0.4451 | 0.4476 | 0.4265 | 0.4363 | 0.4445 | 0.4582 | 0.4772 | 0.5333 |

Central Area | 0.3985 | 0.3901 | 0.3758 | 0.3548 | 0.3521 | 0.3424 | 0.3334 | 0.3361 | 0.4224 |

Western Area | 0.3151 | 0.3053 | 0.2911 | 0.2757 | 0.2769 | 0.2748 | 0.2702 | 0.2812 | 0.3145 |

Overall Area | 0.3803 | 0.3802 | 0.3715 | 0.3523 | 0.3551 | 0.3539 | 0.3539 | 0.3649 | 0.4234 |

Three Areas | Years | ||||||||

2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | Total Average | ||

Eastern Area | 0.4871 | 0.5280 | 0.5610 | 0.5783 | 0.5980 | 0.6072 | 0.6234 | 0.4543 | |

Central Area | 0.3159 | 0.3417 | 0.3727 | 0.3720 | 0.3850 | 0.3928 | 0.3947 | 0.3901 | |

Western Area | 0.2773 | 0.3006 | 0.3192 | 0.3249 | 0.3321 | 0.3326 | 0.3406 | 0.3162 | |

Overall Area | 0.3601 | 0.3901 | 0.4176 | 0.4250 | 0.4384 | 0.4442 | 0.4529 | 0.3869 |

Economic Zones | Years | ||||||||

1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 | |

Central Bohai | 0.3990 | 0.3129 | 0.2890 | 0.3033 | 0.3184 | 0.3426 | 0.3511 | 0.3591 | 0.3701 |

Yangtze River Delta | 0.4446 | 0.3490 | 0.3107 | 0.3217 | 0.3235 | 0.3540 | 0.3879 | 0.4044 | 0.4293 |

Pearl River Delta | 0.4396 | 0.3518 | 0.3093 | 0.3322 | 0.3726 | 0.4086 | 0.4491 | 0.4523 | 0.4579 |

Northeast | 0.4102 | 0.3429 | 0.3041 | 0.3371 | 0.3603 | 0.4634 | 0.4537 | 0.3977 | 0.4034 |

Central Provinces | 0.6340 | 0.4238 | 0.3367 | 0.3449 | 0.4038 | 0.4420 | 0.5163 | 0.4331 | 0.4227 |

Great Southwest | 0.6935 | 0.4624 | 0.3368 | 0.3463 | 0.3570 | 0.3625 | 0.3878 | 0.3545 | 0.3598 |

Great Northwest | 0.2986 | 0.2782 | 0.2440 | 0.2702 | 0.3038 | 0.3135 | 0.3712 | 0.3033 | 0.2978 |

Economic Zones | Years | ||||||||

2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | |

Central Bohai | 0.3883 | 0.4118 | 0.4121 | 0.3939 | 0.4137 | 0.4321 | 0.4411 | 0.4642 | 0.4933 |

Yangtze River Delta | 0.4459 | 0.4591 | 0.4580 | 0.4437 | 0.4587 | 0.4738 | 0.5042 | 0.5330 | 0.5651 |

Pearl River Delta | 0.4639 | 0.4854 | 0.4958 | 0.4682 | 0.4806 | 0.4721 | 0.4818 | 0.4902 | 0.6200 |

Northeast | 0.4077 | 0.3995 | 0.3958 | 0.3856 | 0.3691 | 0.3624 | 0.3488 | 0.3478 | 0.3559 |

Central Provinces | 0.3974 | 0.3898 | 0.3723 | 0.3436 | 0.3393 | 0.3293 | 0.3231 | 0.3281 | 0.4417 |

Great Southwest | 0.3547 | 0.3459 | 0.3362 | 0.3151 | 0.3108 | 0.2982 | 0.2689 | 0.2757 | 0.3235 |

Great Northwest | 0.2886 | 0.2782 | 0.2611 | 0.2494 | 0.2543 | 0.2592 | 0.2710 | 0.2849 | 0.3086 |

Economic Zones | Years | ||||||||

2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | Total Average | ||

Central Bohai | 0.4741 | 0.5143 | 0.5430 | 0.5607 | 0.5929 | 0.6121 | 0.6209 | 0.4326 | |

Yangtze River Delta | 0.5678 | 0.6261 | 0.6787 | 0.7121 | 0.7240 | 0.7228 | 0.7459 | 0.4978 | |

Pearl River Delta | 0.4745 | 0.5040 | 0.5210 | 0.5239 | 0.5336 | 0.5363 | 0.5402 | 0.4666 | |

Northeast | 0.3374 | 0.3593 | 0.4024 | 0.4022 | 0.4225 | 0.4425 | 0.4620 | 0.3869 | |

Central Provinces | 0.3084 | 0.3360 | 0.3623 | 0.3633 | 0.3743 | 0.3781 | 0.3812 | 0.3890 | |

Great Southwest | 0.2593 | 0.2720 | 0.3007 | 0.3060 | 0.3219 | 0.3279 | 0.3505 | 0.3451 | |

Great Northwest | 0.2893 | 0.3196 | 0.3315 | 0.3375 | 0.3389 | 0.3358 | 0.3340 | 0.2969 |

Areas | 1991–1995Eighth-Five | 1996–2000Ninth-Five | 2001–2005Tenth-Five | 2006–2010 Eleventh-Five | 2011–2015 Twelfth-Five |

Eastern Area | 0.3408 | 0.4004 | 0.4400 | 0.4968 | 0.5936 |

Central Area | 0.4133 | 0.4407 | 0.3631 | 0.3499 | 0.3834 |

Western Area | 0.3431 | 0.3345 | 0.2848 | 0.2888 | 0.3299 |

Overall Area | 0.3657 | 0.3919 | 0.3626 | 0.3785 | 0.4356 |

Economic zones | 1991–1995Eighth-Five | 1996–2000Ninth-Five | 2001–2005Tenth-Five | 2006–2010Eleventh-Five | 2011–2015Twelfth-Five |

Central Bohai | 0.3245 | 0.3622 | 0.4127 | 0.4774 | 0.5859 |

Yangtze River Delta | 0.3499 | 0.4043 | 0.4587 | 0.5592 | 0.7167 |

Pearl River Delta | 0.3611 | 0.4464 | 0.4804 | 0.5141 | 0.5310 |

Northeast | 0.3509 | 0.4252 | 0.3825 | 0.3499 | 0.4263 |

Central Provinces | 0.4286 | 0.4423 | 0.3548 | 0.3475 | 0.3718 |

Great Southwest | 0.4392 | 0.3639 | 0.3212 | 0.2799 | 0.3214 |

Great Northwest | 0.2790 | 0.3149 | 0.2605 | 0.2947 | 0.3355 |

**Table 9.**Estimation results of convergence analysis of energy efficiency for the full sample in the whole period 1991–2015.

Parameter | $\mathit{\beta}\text{-}\mathbf{Convergence}$ | $\mathit{\sigma}\text{-}\mathbf{Convergence}$ | $\mathit{\lambda}\text{-}\mathbf{Convergence}$ | ||
---|---|---|---|---|---|

Pooled OLS | SYS-GMM Two Step | Pooled OLS | SYS-GMM Two Step | SYS-GMM Two Step | |

$\alpha $ | −0.0615 *** (−3.55) | - | −0.0037 (−0.91) | ||

$\beta $ | −0.0705 *** (−4.24) | −0.0697 *** (−15.56) | - | - | - |

$\sigma $ | - | - | −0.0554 *** (−3.74) | −0.4834 *** (−12.55) | - |

$\rho $ | −0.2275 *** (−48.34) | - | −0.1215 *** (−22.10) | - | |

$\lambda $ | - | - | - | - | 0.9440 *** (94.80) |

R^{2} | 0.0263 | - | 0.0206 | - | - |

Sargan test | - | 1.0000 | - | 1.0000 | 1.000 |

**Table 10.**Estimation results of convergence analysis of energy efficiency for the regional sample in the whole period 1991–2015.

$\mathit{\beta}\text{-}\mathbf{Convergence}$ | $\mathit{\sigma}\text{-}\mathbf{Convergence}$ | $\mathit{\lambda}\text{-}\mathbf{Convergence}$ | |||||||
---|---|---|---|---|---|---|---|---|---|

$\mathit{\beta}$ | Sargan Test | Pooled OLS-R^{2} | $\mathit{\sigma}$ | Sargan Test | Pooled OLS-R^{2} | $\mathit{\lambda}$ | Sargan Test | ||

Three Areas | Eastern | −0.0456 *** (−3.97) | 1.00 | - | −0.4541 ** (−2.41) | 1.00 | - | 0.9376 *** (26.72) | 1.00 |

Central | −0.0325 (−1.20) | 1.00 | - | −0.4904 *** (−5.35) | 1.00 | - | 0.8858 *** (10.33) | 1.00 | |

Western | −0.0390 ** (−2.47) | 1.00 | - | −0.3944 *** (−5.49) | 1.00 | - | 0.8981 *** (7.70) | 1.00 | |

Seven Economic Zones | Central Bohai | −0.0950 (−1.04) | 1.00 | - | −0.8983 * (−1.87) | 1.00 | 0.5817 (0.84) | 1.00 | |

Yangtze River Delta | 0.0180 (0.02) | 1.00 | - | 1.6322 (0.48) | 1.00 | - | 0.9402 ** (2014) | 1.00 | |

Pearl River Delta | −0.1203 ** (−2.21) | - | 0.07 | −0.0993 ** (−2.01) | - | 0.06 | 0.7648 ** (2.33) | 1.00 | |

Northeast | −0.2710 *** (−3.03) | - | 0.12 | −0.3141 *** (−3.49) | - | 0.15 | −0.1130 (−0.16) | 1.00 | |

Central Provinces | −0.3734 *** (−5.79) | 0.20 | −0.7471 *** (−3.37) | 1.00 | - | 0.8842 *** (6.16) | 1.00 | ||

Great Southwest | −0.3028 *** (−4.71) | - | 0.20 | −0.1758 *** (−3.95) | - | 0.15 | 1.1225 *** (3.20) | 1.00 | |

Great Northwest | −0.7528 ** (−2.13) | 1.00 | - | −0.4538 ** (−2.45) | 1.00 | - | 0.8328 *** (5.15) | 1.00 |

**Table 11.**Estimation results of convergence analysis of energy efficiency for the full sample in different time intervals.

$\mathit{\beta}\text{-}\mathbf{Convergence}$ | $\mathit{\sigma}\text{-}\mathbf{Convergence}$ | $\mathit{\lambda}\text{-}\mathbf{Convergence}$ | ||||
---|---|---|---|---|---|---|

$\mathit{\beta}$ | Sargan Test | $\mathit{\sigma}$ | Sargan Test | $\mathit{\lambda}$ | Sargan Test | |

1991–2005 | −0.0579 *** (−26.45) | 1.00 | −0.5424 *** (−28.23) | 1.00 | 0.9610 *** (523.41) | 1.00 |

2006–2015 | −0.0732 *** (−67.49) | 0.9704 | −0.7908 *** (−43.64) | 0.9742 | 0.9254 *** (4528.73) | 0.9627 |

**Table 12.**Estimation results of convergence analysis of energy efficiency for the three areas in different time intervals.

$\mathit{\beta}\text{-}\mathbf{Convergence}$ | $\mathit{\sigma}\text{-}\mathbf{Convergence}$ | $\mathit{\lambda}\text{-}\mathbf{Convergence}$ | |||||
---|---|---|---|---|---|---|---|

$\mathit{\beta}$ | Sargan Test | $\mathit{\sigma}$ | Sargan Test | $\mathit{\lambda}$ | Sargan Test | ||

1991–2005 | Eastern | −0.0366 *** (−4.68) | 1.00 | −0.1271 ** (−2.28) | 1.00 | 0.9340 *** (98.04) | 1.00 |

Central | −0.0407 ** (−2.11) | 1.00 | −0.4872 ** (−8.94) | 1.00 | 0.9944 *** (14.84) | 1.00 | |

Western | −0.0039 (−0.230) | 1.00 | −0.4227 *** (−4.84) | 1.00 | 0.9892 *** (15.82) | 1.00 | |

2006–2015 | Eastern | −0.0931 *** (−29.36) | 1.00 | −0.4098 *** (−4.73) | 1.00 | 0.8917 *** (37.76) | 1.00 |

Central | −0.0640 *** (−61.40) | 1.00 | −0.8678 *** (−18.67) | 1.00 | 0.9012 *** (39.65) | 1.00 | |

Western | −0.0580 *** (−67.85) | 1.00 | −0.5782 *** (−12.33) | 1.00 | 0.9690 *** (56.41) | 1.00 |

**Table 13.**Estimation results of convergence analysis of energy efficiency for the seven economic zones in different time intervals.

$\mathit{\beta}\text{-}\mathbf{Convergence}$ | $\mathit{\sigma}\text{-}\mathbf{Convergence}$ | $\mathit{\lambda}\text{-}\mathbf{Convergence}$ | |||||
---|---|---|---|---|---|---|---|

$\mathit{\beta}$ | Sargan Test | $\mathit{\sigma}$ | Sargan Test | $\mathit{\lambda}$ | Sargan Test | ||

1991–2005 | Central Bohai | −0.4724 (−1.48) | 1.00 | −1.3168 (−1.19) | 1.00 | 1.1067 *** (2.78) | 1.00 |

Yangtze River Delta | −0.2243 (−1.15) | 1.00 | −0.3208 (−0.60) | 1.00 | 0.6585 (0.99) | 1.00 | |

Pearl River Delta | −0.5165 * (−1.94) | 1.00 | −4.9890 (−1.15) | 1.00 | 0.5969 * (1.85) | 1.00 | |

Northeast | −0.2602 (−1.24) | 1.00 | −1.9425 (−1.32) | 1.00 | −0.1133 (−0.16) | 1.00 | |

Central Provinces | −0.0299 (−1.00) | 1.00 | −0.5219 *** (−3.67) | 1.00 | 1.0233 *** (10.78) | 1.00 | |

Great Southwest | −0.0250 (−0.47) | 1.00 | 1.0528 (1.38) | 1.00 | 0.6773 * (1.65) | 1.00 | |

Great Northwest | −0.0489 ** (−2.29) | 1.00 | −0.4949 *** (−2.79) | 1.00 | 0.8001 *** (4.77) | 1.00 | |

2006–2015 | Central Bohai | −0.0546 *** (−3.00) | 1.00 | 0.0627 (0.45) | 1.00 | 0.9741 *** (8.62) | 1.00 |

Yangtze River Delta | −0.3679 ** (−2.00) | 1.00 | 0.4717 (0.22) | 1.00 | 0.9419 *** (10.79) | 1.00 | |

Pearl River Delta | −0.0691 (−0.28) | 1.00 | −0.2203 *** (−5.82) | 1.00 | 0.9711 *** (2.57) | 1.00 | |

Northeast | −0.0690 (−0.13) | 1.00 | −0.0313 (−0.02) | 1.00 | 0.6240 (1.56) | 1.00 | |

Central Provinces | −0.0651 *** (−5.90) | 1.00 | −0.7551 *** (−9.60) | 1.00 | 0.8689 *** (22.25) | 1.00 | |

Great Southwest | −0.0627 *** (−20.31) | 1.00 | −0.2481 *** (−8.37) | 1.00 | 0.9575 *** (−41.02) | 1.00 | |

Great Northwest | −0.0451 *** (−3.34) | 1.00 | 0.0836 (0.82) | 1.00 | 0.9747 *** (10.37) | 1.00 |

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## Share and Cite

**MDPI and ACS Style**

Yang, W.; Lu, Z.; Wang, D.; Shao, Y.; Shi, J. Sustainable Evolution of China’s Regional Energy Efficiency Based on a Weighted SBM Model with Energy Substitutability. *Sustainability* **2020**, *12*, 10073.
https://doi.org/10.3390/su122310073

**AMA Style**

Yang W, Lu Z, Wang D, Shao Y, Shi J. Sustainable Evolution of China’s Regional Energy Efficiency Based on a Weighted SBM Model with Energy Substitutability. *Sustainability*. 2020; 12(23):10073.
https://doi.org/10.3390/su122310073

**Chicago/Turabian Style**

Yang, Wei, Zudi Lu, Di Wang, Yanmin Shao, and Jinfeng Shi. 2020. "Sustainable Evolution of China’s Regional Energy Efficiency Based on a Weighted SBM Model with Energy Substitutability" *Sustainability* 12, no. 23: 10073.
https://doi.org/10.3390/su122310073