# Time-Spatial Convergence of Air Pollution and Regional Economic Growth in China

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Model of Pollution Convergence

- (1)
- Construct the cross-sectional variance ratio $\raisebox{1ex}{${\mathrm{H}}_{1}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_{\mathrm{t}}$}\right.$
- (2)
- Run the regression of the following formula:$$\mathrm{log}\left(\raisebox{1ex}{${\mathrm{H}}_{1}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{H}}_{\mathrm{t}}$}\right.\right)\text{}-\text{}2\mathrm{logL}\left(\mathrm{t}\right)\text{}=\text{}\mathrm{a}\text{}+\text{}\mathrm{b}\text{}\mathrm{log}\left(\mathrm{t}\right)+{\text{}\mathsf{\epsilon}}_{\mathrm{t}}$$
- (3)
- b conditionally converges to $2\mathsf{\alpha}$. Let $\mathsf{\alpha}\text{}=\text{}0.5\mathrm{b}$, and calculate the t statistic of b using the heteroskedasticity and autocorrelation consistent (HAC )standard. If $\mathsf{\alpha}\text{}\ge 0$, and the one-sided t test satisfies t < −1.65, it is considered that at the 5% significant level, the null hypothesis of convergence is rejected. Otherwise, we accept the null hypothesis that there is convergence.

## 3. Time-Space Test of Air Pollution Convergence in China

#### 3.1. Data Description

#### 3.2. Convergence Identification Process

- (1)
- The model was used to reconstruct Equation (8) across the whole sample selected in the study. If the result satisfies the acceptance criteria of the original hypothesis as described in the preceding sections, it is assumed that there is absolute convergence in time dimension for the whole sample.
- (2)
- If the original hypothesis is rejected, it is assumed that there is no absolute convergence in the time dimension of the original sample. Furthermore, the time convergence club recognition algorithm rule constructed by Phillips and Sul [15] can be used to segment the sample population and distinguish the convergence club in the time dimension. If the recognition result is not significant, then the selected sample has no convergence in the time dimension.
- (3)
- If step (1) is satisfied or step (2) is completed, it is necessary to further examine whether there is convergence in the spatial dimension. First, the global Moran index is used to investigate whether there is a spatial correlation in the whole sample. If the index shows that correlation does not exist, it is considered that there is no need for a further spatial convergence test. If the index indicates that there is a high spatial correlation, then the local Moran index is further used to investigate the convergence of the spatial correlation in the sample, and the appropriate spatial regions are divided.
- (4)
- For the partitioned spatial region, the regression test of the non-linear time-varying factor model is carried out again for samples in each region. If the test result shows that there is a convergence trend, it is determined that there is a convergence of fine particulate matter emission concentration in the designated area. If the results are reversed, then step (2) is repeated to check whether there is an independent club convergence in the domain.

#### 3.3. Time Convergence of Fine Particulate Matter

#### 3.4. Spatial Correlation Index Analysis of Fine Particles

#### 3.5. Spatial Convergence of PM 2.5

## 4. Relationship between Regional Air Pollution and Economic Development

#### 4.1. Test Model Construction of Environment Kuznets Curve

- (1)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}=\text{}0$, ${\mathsf{\beta}}_{3}\text{}=\text{}0$, it indicates that environmental pollution becomes more serious with economic growth, as shown in straight line a in the following graph;
- (2)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}=\text{}0$, ${\mathsf{\beta}}_{3}\text{}=\text{}0$, it indicates that environmental pollution is improved with economic growth, as shown by straight line b;
- (3)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}\text{}0$, ${\mathsf{\beta}}_{3}\text{}=\text{}0$, it indicates that the quality of the environment in the process of economic growth improves after deterioration, and there is a positive U-shaped relationship, as shown in curve c;
- (4)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}\text{}0$, ${\mathsf{\beta}}_{3}\text{}=\text{}0$, it indicates that the quality of the environment in the process of economic growth deteriorates after improvement, there is an inverted U-shaped relationship, which conforms to the typical EKC hypothesis, as shown in curve d;
- (5)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}\text{}0$, ${\mathsf{\beta}}_{3}\text{}\text{}0$, it shows that environmental pollution has a positive N-type curve with the level of economic growth, that is, with economic growth, environmental pollution increases first and then decreases, and then increases again, as shown by curve e;
- (6)
- when ${\mathsf{\beta}}_{1}\text{}\text{}0$, and ${\mathsf{\beta}}_{2}\text{}\text{}0$, ${\mathsf{\beta}}_{3}\text{}\text{}0$, it shows that there is an inverted N-type curve between environmental pollution and the level of economic growth, as shown by curve f;
- (7)
- when ${\mathsf{\beta}}_{1}\text{}=\text{}0$, and ${\mathsf{\beta}}_{2}\text{}=\text{}0$, ${\mathsf{\beta}}_{3}\text{}=\text{}0$, it suggests that there is no environmental EKC curve.

#### 4.2. Test Results

## 5. Policy Recommendations

## 6. Research Conclusions

## Acknowledgments

## Conflicts of Interest

## References

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Province | City | Province | City | Province | City | Province | City |
---|---|---|---|---|---|---|---|

Beijing | Beijing | Zhejiang | Hangzhou | Guangdong | Guangzhou | Hubei | Wuhan |

Tianjin | Tianjin | Ningbo | Shenzhen | Yichang | |||

Hebei | Shijiazhuang | Wenzhou | Zhuhai | Xiangyang | |||

Tangshan | Jiaxing | Shantou | Hunan | Changsha | |||

Qinghuangdao | Huzhou | Foshan | Zhuzhou | ||||

Handan | Shaoxing | Jiangmen | Changde | ||||

Baoding | Jinhua | Kanjiang | Inner Mongolia | Hohhot | |||

Cangzhou | Quzhou | Huizhou | Baotou | ||||

Langfang | Zhoushan | Dongguan | Guangxi | Nanning | |||

Liaoning | Shenyang | Fujian | Fuzhou | Zhongshan | Liuzhou | ||

Dalian | Xiamen | Hainan | Haikou | Guilin | |||

Anshan | Putian | Sanya | Sichuan | Chengdu | |||

Shanghai | Shanghai | Quanzhou | Shanxi | Taiyuan | Mianyang | ||

Jiangsu | Nanjing | Zhangzhou | Jilin | Changchun | Yunnan | Kunming | |

Wuxi | Longyan | Jilin | Shannxi | Xi’an | |||

Xuzhou | Shandong | Jinan | Heilongjiang | Harbin | Baoji | ||

Changzhou | Qingdao | Daqing | Gansu | Lanzhou | |||

Suzhou | Zibo | Anhui | Hefei | Qinghai | Xining | ||

Nantong | Dongying | Wuhu | Ningxia | Yinchuan | |||

Lianyungang | Yantai | Maanshan | Xinjiang | Urumqi | |||

Huai’an | Weifang | Jiangxi | Nanchang | ||||

Yanchen | Jining | Henan | Zhenzhou | ||||

Yanzhou | Weihai | Luoyang | |||||

Zhenjiang | Linyi | Anyang | |||||

Chongqing | Chongqing | Guizhou | Guiyang | Nanyang |

L(t) = log(t + 1) | L(t) = log(t) | L(t) = log(t − 1) | |
---|---|---|---|

b | 18.41003 | 18.40986 | 18.40966 |

2.83 | 2.83 | 2.83 | |

a | −52.02939 | −52.02884 | −52.02823 |

−2.88 | −2.88 | −2.88 |

Year | Moran Index | E(I) | sd(I) | p-Value |
---|---|---|---|---|

2000 | 0.768 | −0.011 | 0.102 | 0.000 |

2001 | 0.749 | −0.011 | 0.102 | 0.000 |

2002 | 0.786 | −0.011 | 0.102 | 0.000 |

2003 | 0.806 | −0.011 | 0.102 | 0.000 |

2004 | 0.786 | −0.011 | 0.102 | 0.000 |

2005 | 0.764 | −0.011 | 0.102 | 0.000 |

2006 | 0.769 | −0.011 | 0.102 | 0.000 |

2007 | 0.761 | −0.011 | 0.102 | 0.000 |

2008 | 0.777 | −0.011 | 0.102 | 0.000 |

2009 | 0.817 | −0.011 | 0.102 | 0.000 |

2010 | 0.840 | −0.011 | 0.102 | 0.000 |

2011 | 0.820 | −0.011 | 0.102 | 0.000 |

2012 | 0.764 | −0.011 | 0.102 | 0.000 |

Region | Parameter | L(t) = log(t + 1) | L(t) = log(t) | L(t) = log(t − 1) |
---|---|---|---|---|

East | b | 1.434791 | 1.434617 | 1.434422 |

0.22 | 0.22 | 0.22 | ||

a | −4.860393 | −4.859842 | −4.859232 | |

−0.26 | −0.26 | −0.26 | ||

Middle | b | 79.61884 | 79.61868 | 79.61949 |

4.78 | 4.78 | 4.78 | ||

a | −222.0877 | −222.0872 | −222.0866 | |

−4.79 | −4.79 | −4.79 | ||

West | b | 71.89226 | 71.89209 | 71.8919 |

12.09 | 12.09 | 12.09 | ||

a | −200.5981 | −200.5975 | −200.5969 | |

−12.13 | −12.13 | −12.13 |

95 Cities | East | |||||
---|---|---|---|---|---|---|

GLS | Random | Fixed | GLS | Random | Fixed | |

C | 37.95818 *** | 37.95818 *** | 42.02255 *** | 42.80357 *** | 42.80357 *** | 60.3849 *** |

2.393372 | 1.314376 | 1.60851 | 4.629631 | 2.752783 | 3.326338 | |

GDP | 0.0003144 *** | 0.0003144 *** | 0.0001439 | 0.0002078 | 0.0002078 | −0.000649 *** |

0.0000671 | 0.0000548 | 0.0000662 | 0.0001927 | 0.0001743 | 0.0001933 | |

GDP^{2} | −1.26 × 10^{−9} *** | −1.26 × 10^{−9} * | −1.75 × 10^{−}^{10} | −9.70 × 10^{−}^{10} | −9.70 × 10^{−}^{10} | 7.96 × 10^{−9} *** |

4.16 × 10^{−}^{10} | 4.70 × 10^{−}^{10} | 5.15 × 10^{−}^{10} | 2.42 × 10^{−9} | 2.81 × 10^{−9} | 2.89 × 10^{−9} | |

GDP^{3} | 1.64 × 10^{−}^{15} ** | 1.64 × 10^{−}^{15} * | −9.55 × 10^{−}^{17} | 1.06 × 10^{−}^{15} | 1.06 × 10^{−}^{15} | −2.76 × 10^{−}^{14} ** |

6.58 × 10^{−}^{16} | 9.04 × 10^{−}^{16} | 9.57 × 10^{−}^{16} | 8.87 × 10^{−}^{15} | 1.23 × 10^{−}^{14} | 1.23 × 10^{−}^{14} | |

R^{2} | 0.0268 | 0.0268 | 0.0289 | 0.0062 | 0.0062 | 0.0174 |

Hausman | 19.39 *** | 71.17 *** | ||||

Middle | West | |||||

GLS | Random | Fixed | GLS | Random | Fixed | |

C | 35.87851 *** | 35.87851 *** | 36.41891 *** | 30.89278 *** | 30.89278 *** | 45.63498 *** |

1.381159 | 2.349397 | 2.601868 | 2.132795 | 5.16157 | 6.787467 | |

GDP | 0.0005855 *** | 0.0005855 *** | 0.0005685 *** | 0.0001557 | 0.0001557 | −0.0010218 |

0.0000509 | 0.0000883 | 0.0000974 | 0.0003291 | 0.0006236 | 0.0007374 | |

GDP^{2} | −2.90 × 10^{−9} *** | −2.90 × 10^{−9} *** | −2.85 × 10^{−9} *** | 1.89 × 10^{−9} | 1.89 × 10^{−9} | 2.37 × 10^{−}^{8} |

3.72 × 10^{−}^{10} | 6.27 × 10^{−}^{10} | 6.67 × 10^{−}^{10} | 1.10 × 10^{−}^{8} | 2.05 × 10^{−}^{8} | 2.30 × 10^{−}^{8} | |

GDP^{3} | 4.05 × 10^{−}^{15} *** | 4.05 × 10^{−}^{15} *** | 4.01 × 10^{−}^{15} *** | −4.79 × 10^{−}^{14} | −4.79 × 10^{−}^{14} | −1.82 × 10^{−}^{13} |

6.58 × 10^{−}^{16} | 1.09 × 10^{−}^{15} | 1.15 × 10^{−}^{15} | 9.77 × 10^{−}^{14} | 1.90 × 10^{−}^{13} | 2.07 × 10^{−}^{13} | |

R^{2} | 0.1932 | 0.1932 | 0.1933 | 0.0077 | 0.0077 | 0.0164 |

Hausman | 0.19 | 8.99 *** |

East | Middle | West | ||||
---|---|---|---|---|---|---|

Result | p-Value | Result | p-Value | Result | p-Value | |

LM Test for Spatial Lag | 342.16 | 0.0000 | 21.1906 | 0.0000 | 20.393 | 0.0000 |

Robust | 8.7567 | 0.0031 | 12.3319 | 0.0004 | 4.3701 | 0.0366 |

LM Test for Spatial Error | 335.5374 | 0.0000 | 17.9619 | 0.0000 | 17.8563 | 0.0000 |

Robust | 2.1337 | 0.1441 | 9.1032 | 0.0026 | 1.8334 | 0.1757 |

East | Middle | West | ||||
---|---|---|---|---|---|---|

SLM | SEM | SLM | SEM | SLM | SEM | |

GDP | 1.251658 *** | 0.921818 *** | 0.00049175 *** | 0.000430432 *** | 0.001485549 *** | 0.001329185 *** |

22.55061 | 25.39407 | 12.232792 | 13.861633 | 8.427643 | 8.507777 | |

GDP^{2} | −1.28 × 10^{−}^{2} *** | −9.36 × 10^{−}^{3} *** | −1.90 × 10^{−9} *** | −1.78 × 10^{−9} *** | −3.54 × 10^{−}^{8} *** | −3.13 × 10^{−}^{8} *** |

−14.1 | −16.2 | −6.86 | −8.75 | −6.04 | −6.07 | |

GDP^{3} | 4.10 × 10^{−}^{5} *** | 3.10 × 10^{−}^{5} *** | 2.45 × 10^{−}^{15} *** | 2.35 × 10^{−}^{15} *** | 2.60 × 10^{−}^{13} *** | 2.30 × 10^{−}^{13} *** |

10.154337 | 12.4 | 5.34 | 7.06 | −3.65 | 4.73 | |

R^{2} | 0.8983 | 0.9552 | 0.896 | 0.9344 | 0.9119 | 0.9346 |

w | −0.236068 *** | −0.236068 *** | −0.236068 *** | |||

e | 0.55599 *** | 0.334969 *** | 0.332994 *** |

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## Share and Cite

**MDPI and ACS Style**

Pu, Z.
Time-Spatial Convergence of Air Pollution and Regional Economic Growth in China. *Sustainability* **2017**, *9*, 1284.
https://doi.org/10.3390/su9071284

**AMA Style**

Pu Z.
Time-Spatial Convergence of Air Pollution and Regional Economic Growth in China. *Sustainability*. 2017; 9(7):1284.
https://doi.org/10.3390/su9071284

**Chicago/Turabian Style**

Pu, Zhengning.
2017. "Time-Spatial Convergence of Air Pollution and Regional Economic Growth in China" *Sustainability* 9, no. 7: 1284.
https://doi.org/10.3390/su9071284