# Spatiotemporal Evolution and Spatial Convergence Analysis of Total Factor Productivity of Citrus in China

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

#### 2.2.1. Measurement of TFP

^{t}and y

^{t}represent the input and output vectors of the citrus industry in the period t, respectively; ${D}_{i}^{t}$ is the distance function; M

_{i}(TFP) is the total factor productivity index; EFFCH is the technical efficiency change index; and TECH is the technological progress change index. The technical efficiency change index (EFFCH) can be further decomposed into pure technical efficiency index (PECH) and scale efficiency change index (SECH). A value of EFFCH greater than 1 represents an increase in technical efficiency, and a value of TECH greater than 1 represents a technological advancement or innovation; A value of PECH greater than 1 represents an increase in the level of technology, and vice versa; and a value of SECH greater than 1 represents a scale of production operation close to the optimal scale of production, and a scale deterioration if it is lower than 1.

#### 2.2.2. Spatial Correlation Index

_{n}and x

_{m}are the index values of variable x on the geographical unit of region n and region m, respectively; $\overline{x}$ is the average of the index values in each region; ω

_{nm}is the spatial weight matrix; ω

_{nm}= 1 when n and m provinces are contiguous, and 0 otherwise; S

^{2}is the sample variance; and N is the total number of measured areas. In general, the range of the Moran’s I index is −1 to 1. An index greater than 0 indicates positive spatial autocorrelation, and the closer the index value is to 1, the stronger the spatial correlation and clustering of similar attributes. An index less than 0 indicates negative spatial autocorrelation, and the closer the index value is to −1, the stronger the spatial correlation and agglomeration of different attributes. An index close to 0 indicates that the spatial distribution is random and there is no spatial autocorrelation [24].

#### 2.2.3. Convergence Model

_{n,t}is the citrus TFP of province n in year t; $\overline{TF{P}_{t}}$ is the average of the TFP for all provinces in year t; and N is the number of major citrus-producing provinces.

_{n,t}. γ is the spatial lag coefficient of the independent variable, representing the influence of the citrus TFP of neighboring provinces.

## 3. Spatial and Temporal Evolution of Citrus TFP

#### 3.1. Time Series Evolution of Citrus TFP

#### 3.2. Regional Differences in TFP for Citrus

#### 3.3. Spatial Correlation Analysis of Citrus TFP

## 4. Convergence Analysis of TFP of Citrus

#### 4.1. σ Convergence Test Result Analysis

#### 4.2. Absolute β Convergence Test Result Analysis

#### 4.3. Conditional β Convergence Test Result Analysis

## 5. Conclusions and Policy Implications

#### 5.1. Conclusions

#### 5.2. Policy Implications

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Changes in TFP and deconstruction of its components for China’s mandarin production from 2007 to 2020.

**Figure 2.**Changes in TFP and deconstruction of its components for China’s tangerine production from 2007 to 2020.

**Table 1.**Average TFP and its composition for the major mandarin- and tangerine-producing provinces in China from 2007 to 2020.

Classification | Provinces | EFFCH | TECH | PECH | SECH | TFP |
---|---|---|---|---|---|---|

Mandarin | Chongqing | 0.998 | 1.176 | 1.000 | 0.998 | 1.173 |

Guangxi | 0.999 | 1.169 | 1.000 | 0.999 | 1.168 | |

Hunan | 0.999 | 1.147 | 1.000 | 0.999 | 1.146 | |

Hubei | 0.998 | 1.145 | 1.000 | 0.998 | 1.142 | |

Guangdong | 0.999 | 1.135 | 1.000 | 0.999 | 1.134 | |

Jiangxi | 1.000 | 1.123 | 1.000 | 1.000 | 1.123 | |

Fujian | 1.000 | 1.116 | 1.000 | 1.000 | 1.116 | |

Tangerine | Chongqing | 0.999 | 1.161 | 1.000 | 0.999 | 1.159 |

Hunan | 1.000 | 1.157 | 1.000 | 1.000 | 1.157 | |

Hubei | 0.998 | 1.148 | 1.000 | 0.998 | 1.147 | |

Jiangxi | 1.000 | 1.141 | 1.000 | 1.000 | 1.141 | |

Zhejiang | 1.001 | 1.131 | 1.000 | 1.001 | 1.133 | |

Guangdong | 0.999 | 1.134 | 1.000 | 0.999 | 1.133 | |

Fujian | 1.003 | 1.130 | 1.000 | 1.003 | 1.132 |

Year | Mandarin | Tangerine | ||||
---|---|---|---|---|---|---|

Moran’s I | z | p | Moran’s I | z | p | |

2007 | −0.069 | 0.565 | 0.286 | −0.299 | −0.836 | 0.202 |

2008 | −0.026 | 1.078 | 0.140 | −0.192 | −0.188 | 0.425 |

2009 | −0.041 | 1.051 | 0.147 | −0.053 | 1.049 | 0.147 |

2010 | 0.169 ** | 1.762 | 0.039 | 0.199 ** | 1.850 | 0.032 |

2011 | 0.109 * | 1.462 | 0.072 | 0.136 * | 1.595 | 0.055 |

2012 | 0.215 ** | 1.906 | 0.028 | 0.280 ** | 2.171 | 0.015 |

2013 | 0.208 ** | 1.880 | 0.030 | 0.075 | 1.187 | 0.118 |

2014 | 0.074 | 1.211 | 0.113 | 0.384 *** | 2.615 | 0.004 |

2015 | 0.046 | 1.049 | 0.147 | 0.237 ** | 2.238 | 0.013 |

2016 | −0.041 | 0.696 | 0.243 | 0.184 ** | 1.766 | 0.039 |

2017 | −0.184 | −0.088 | 0.465 | −0.084 | 0.420 | 0.337 |

2018 | −0.274 | −0.733 | 0.232 | 0.118 ** | 2.303 | 0.011 |

2019 | −0.356 | −0.991 | 0.161 | −0.185 | −0.103 | 0.459 |

2020 | −0.139 | 0.160 | 0.436 | 0.053 * | 1.310 | 0.095 |

Coefficient | Mandarin | Tangerine | ||||||
---|---|---|---|---|---|---|---|---|

OLS | SAR | SEM | SDM | OLS | SAR | SEM | SDM | |

β | −1.699 *** (0.0848) | −1.094 *** (0.105) | −1.540 *** (0.0885) | −1.571 *** (0.0899) | −1.697 *** (0.0900) | −1.301 *** (0.102) | −1.576 *** (0.0904) | −1.568 *** (0.0939) |

ρ or λ | — | 0.343 *** (0.0727) | 0.705 *** (0.0544) | 0.687 *** (0.0565) | — | 0.296 *** (0.0594) | 0.614 *** (0.0654) | 0.613 *** (0.0655) |

γ | — | — | — | 1.191 *** (0.126) | — | — | — | 0.939 *** (0.149) |

V | 0.026 | 0.169 | 0.044 | 0.040 | 0.026 | 0.086 | 0.039 | 0.040 |

Time effect | YES | YES | YES | YES | YES | YES | YES | YES |

Individual effect | YES | YES | YES | YES | YES | YES | YES | YES |

R^{2} | 0.919 | 0.605 | 0.675 | 0.697 | 0.928 | 0.760 | 0.781 | 0.781 |

Coefficient | Mandarin | Tangerine | ||||||
---|---|---|---|---|---|---|---|---|

OLS | SAR | SEM | SDM | OLS | SAR | SEM | SDM | |

β | −1.716 *** (0.0861) | −1.574 *** (0.0872) | −1.646 *** (0.0752) | −1.638 *** (0.0807) | −1.701 *** (0.0935) | −1.557 *** (0.0883) | −1.674 *** (0.0797) | −1.598 *** (0.0877) |

ρ or λ | — | 0.0997 * (0.0604) | 0.309 *** (0.117) | 0.198 * (0.122) | — | 0.151 *** (0.0534) | 0.349 *** (0.106) | 0.260 ** (0.107) |

γ | — | — | — | 0.342 * (0.212) | — | — | — | 0.308 (0.207) |

V | 0.024 | 0.040 | 0.031 | 0.032 | 0.025 | 0.042 | 0.028 | 0.037 |

Control variables | YES | YES | YES | YES | YES | YES | YES | YES |

Time effect | YES | YES | YES | YES | YES | YES | YES | YES |

Individual effect | YES | YES | YES | YES | YES | YES | YES | YES |

R^{2} | 0.925 | 0.725 | 0.663 | 0.535 | 0.930 | 0.869 | 0.841 | 0.541 |

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**MDPI and ACS Style**

Gu, Y.; Qi, C.; Liu, F.; Lei, Q.; Ding, Y.
Spatiotemporal Evolution and Spatial Convergence Analysis of Total Factor Productivity of Citrus in China. *Agriculture* **2023**, *13*, 1258.
https://doi.org/10.3390/agriculture13061258

**AMA Style**

Gu Y, Qi C, Liu F, Lei Q, Ding Y.
Spatiotemporal Evolution and Spatial Convergence Analysis of Total Factor Productivity of Citrus in China. *Agriculture*. 2023; 13(6):1258.
https://doi.org/10.3390/agriculture13061258

**Chicago/Turabian Style**

Gu, Yumeng, Chunjie Qi, Fuxing Liu, Quanyong Lei, and Yuchao Ding.
2023. "Spatiotemporal Evolution and Spatial Convergence Analysis of Total Factor Productivity of Citrus in China" *Agriculture* 13, no. 6: 1258.
https://doi.org/10.3390/agriculture13061258