# Analysis on Regional Differences and Spatial Convergence of Digital Village Development Level: Theory and Evidence from China

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Source

#### 2.2. Methods

#### 2.2.1. Construction and Evaluation Method of DVI

#### The Evaluation Index System of DVI

#### The Value of the DVI Evaluation Method

#### 2.2.2. Decomposition of Dagum Gini Coefficient

#### 2.2.3. Spatial Autocorrelation Analysis

#### 2.2.4. Spatial Convergence Model

#### $\sigma $-Convergence Model

_{i}represents the number of provinces in each region; ${\overline{Y}}_{ij}$ is the average DVI of region j.

#### $\beta $-Convergent Spatial Autoregressive Model (SAR)

#### Spatial Error Model with $\beta $-Convergence (SEM)

## 3. Results

#### 3.1. General Description of DVI in China and Four Major Regions

#### 3.2. Regional Difference Decomposition of DVI

#### 3.3. Convergence Analysis of DVI

#### 3.3.1. $\sigma $-Convergence Analysis of DVI in China

#### 3.3.2. $\beta $-Convergence analysis of DVI in China

#### Spatial Correlation Test

#### Absolute $\beta $-Convergence Analysis

#### Conditional $\beta $-Convergence Analysis

## 4. Discussion

## 5. Conclusions and Policy Recommendations

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Primary Indicators | Secondary Indicators | Unit | Weight (%) |
---|---|---|---|

Main development ability (31.9591%) | Per capita disposable income of rural residents | Yuan/person | 9.7124 |

Consumption level of rural residents | Yuan/person | 6.9659 | |

Average education level of rural residents | Year | 7.5285 | |

Per capita expenditure on transportation and communication of rural residents | Yuan/person | 7.7523 | |

Infrastructure construction (40.9690%) | Length of long-distance optical cable line | Km | 6.1673 |

Length of rural delivery route of long-distance optical cable line (one way) | Km | 10.0915 | |

Proportion of administrative villages with Internet broadband services | % | 2.5326 | |

Proportion of postal administrative villages | % | 2.8889 | |

Total power of agricultural machinery | Ten thousand kw | 8.4360 | |

Rural power consumption | Ten thousand kw/h | 7.5282 | |

Average weekly delivery times in rural areas | Times | 3.3245 | |

Information environment (27.0719%) | Internet penetration rate | % | 8.0714 |

Number of color TV sets per 100 rural households | Set | 2.9976 | |

Mobile phone ownership per 100 rural households | Department | 7.0624 | |

Computer ownership per 100 rural households | Set | 8.9405 |

Year | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Moran’s I | 0.306 | 0.313 | 0.315 | 0.303 | 0.318 | 0.374 | 0.336 | 0.360 | 0.352 | 0.350 | 0.326 | 0.309 | 0.291 | 0.253 |

Z-value | 2.839 | 2.900 | 2.918 | 2.812 | 2.931 | 3.397 | 3.094 | 3.308 | 3.240 | 3.221 | 3.031 | 2.904 | 2.756 | 2.421 |

p-value | 0.002 | 0.002 | 0.002 | 0.002 | 0.002 | 0.000 | 0.001 | 0.000 | 0.001 | 0.001 | 0.001 | 0.002 | 0.003 | 0.008 |

Test Method | Statistic | p-Value | Test Method | Statistic | p-Value |
---|---|---|---|---|---|

Lagrange multiplier (error) | 69.781 | 0.000 | Robust Lagrange multiplier (error) | 28.816 | 0.000 |

Lagrange multiplier (lag) | 42.207 | 0.000 | Robust Lagrange multiplier (lag) | 1.241 | 0.265 |

Model | SAR | SEM | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Regions | National | Eastern | Central | Western | Northeastern | National | Eastern | Central | Western | Northeastern |

$\beta $ | −0.0166 *** (0.0055) | −0.0347 *** (0.0076) | −0.0046 (0.0139) | −0.0039 (0.0064) | −0.0488 *** (0.0136) | −0.0351 *** (0.0086) | −0.0466 *** (0.0091) | −0.0063 (0.0164) | −0.0157 (0.0119) | −0.0542 *** (0.0143) |

$\rho $ | 0.3911 *** (0.0431) | 0.2212 *** (0.0447) | 0.1171 *** (0.0362) | 0.4742 *** (0.0421) | 0.0624 * (0.0353) | |||||

$\lambda $ | 0.4161 *** (0.0418) | 0.2378 *** (0.0423) | 0.1209 *** (0.0428) | 0.4848 *** (0.0417) | 0.0872 *** (0.0230) | |||||

LogL | 1343.4135 | 433.8977 | 269.2690 | 530.4190 | 117.4042 | 1345.4145 | 434.3711 | 269.2926 | 530.7026 | 117.4802 |

${R}^{2}$ | 0.0033 | 0.0983 | 0.0008 | 0.0002 | 0.0701 | 0.0223 | 0.1032 | 0.0011 | 0.0001 | 0.0728 |

Test Method | Statistic | p-Value | Test Method | Statistic | p-Value |
---|---|---|---|---|---|

Lagrange multiplier (error) | 51.579 | 0.000 | Robust Lagrange multiplier (error) | 8.707 | 0.003 |

Lagrange multiplier (lag) | 48.259 | 0.000 | Robust Lagrange multiplier (lag) | 5.387 | 0.020 |

Model | SAR | SEM | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Regions | National | Eastern | Central | Western | Northeastern | National | Eastern | Central | Western | Northeastern |

$\beta $ | −0.2332 *** (0.0419) | −0.2460 *** (0.0773) | −0.4911 *** (0.0802) | −0.2145 *** (0.0623) | −0.6787 *** (0.1696) | −0.2529 *** (0.0438) | −0.2450 *** (0.0749) | −0.4714 *** (0.0741) | −0.2098 *** (0.0582) | −0.6944 *** (0.1709) |

$\rho $ | 0.3238 *** (0.0462) | 0.1873 *** (0.0425) | 0.1108 *** (0.0409) | 0.4274 *** (0.0486) | −0.0524 (0.0966) | |||||

$\lambda $ | 0.3440 *** (0.0451) | 0.1829 *** (0.0442) | 0.1461 ** (0.0695) | 0.4413 *** (0.0467) | −0.1103 * (0.0668) | |||||

Ln DEN | 0.0288 ** (0.0115) | 0.0107 (0.0294) | 0.1102 *** (0.0321) | 0.0499 ** (0.0227) | −0.2178 ** (0.0917) | 0.0252 ** (0.0100) | 0.0048 (0.0300) | 0.1230 *** (0.0278) | 0.0517 ** (0.0245) | −0.2321 ** (0.1019) |

Ln STR | 0.0207 ** (0.0083) | 0.0258 (0.0214) | 0.0146 (0.0101) | 0.0146 (0.0164) | 0.1143 *** (0.0379) | 0.0169 ** (0.0081) | 0.0231 (0.0214) | 0.0105 (0.0122) | 0.0114 (0.0141) | 0.1222 *** (0.0428) |

Ln URB | 0.0118 (0.0108) | −0.0099 (0.0403) | 0.1656 *** (0.0362) | 0.0651 *** (0.00232) | −0.3658 ** (0.1616) | 0.0140 (0.0121) | −0.0222 (0.0435) | 0.1696 *** (0.0416) | 0.0556 *** (0.0217) | −0.4087 ** (0.1931) |

Ln ECO | 0.0321 *** (0.0067) | 0.0368*** (0.0132) | 0.0538 *** (0.0101) | 0.0162 ** (0.0075) | 0.0959 *** (0.0276) | 0.0330 *** (0.0070) | 0.0369 *** (0.0136) | 0.0538 *** (0.0094) | 0.0176 ** (0.0086) | 0.1012 *** (0.0315) |

Ln OPE | −0.0025 (0.0027) | 0.0006 (0.0072) | −0.0222 ** (0.0095) | 0.0014 (0.0030) | 0.0481 *** (0.0169) | −0.0035 (0.0027) | −0.0014 (0.0083) | −0.0223 ** (0.0098) | 0.0016 (0.0025) | 0.0487 *** (0.0136) |

Ln GOV | −0.0036 * (0.0021) | −0.0038 (0.0049) | −0.0252 *** (0.0029) | −0.0001 (0.0030) | −0.0068 (0.0068) | −0.0022 (0.0025) | −0.0031 (0.0055) | −0.0267 *** (0.0044) | 0.0022 (0.0036) | −0.0097 (0.0093) |

LogL | 1380.1760 | 443.7616 | 286.5129 | 542.8184 | 129.2942 | 1380.0814 | 443.1522 | 286.6016 | 541.2971 | 129.4549 |

${R}^{2}$ | 0.2141 | 0.2466 | 0.3568 | 0.2146 | 0.4940 | 0.2083 | 0.2352 | 0.3541 | 0.1643 | 0.4958 |

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**MDPI and ACS Style**

Li, X.; Singh Chandel, R.B.; Xia, X.
Analysis on Regional Differences and Spatial Convergence of Digital Village Development Level: Theory and Evidence from China. *Agriculture* **2022**, *12*, 164.
https://doi.org/10.3390/agriculture12020164

**AMA Style**

Li X, Singh Chandel RB, Xia X.
Analysis on Regional Differences and Spatial Convergence of Digital Village Development Level: Theory and Evidence from China. *Agriculture*. 2022; 12(2):164.
https://doi.org/10.3390/agriculture12020164

**Chicago/Turabian Style**

Li, Xiaojing, Raj Bahadur Singh Chandel, and Xianli Xia.
2022. "Analysis on Regional Differences and Spatial Convergence of Digital Village Development Level: Theory and Evidence from China" *Agriculture* 12, no. 2: 164.
https://doi.org/10.3390/agriculture12020164