Calculation of agricultural production efficiency based on a three-stage Data Envelopment Analysis model and analysis of the spatial-temporal characteristics: An example from the Yangtze River Economic Belt
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摘要: 为响应长江经济带"大保护"的战略号召和完成国家赋予长江经济带各省市的重大历史任务，长江经济带正在推进农业产业结构调整、优化投入产出比例，保障稳定可持续的农业生产。本文基于三阶段DEA模型和聚类分析相结合的方法，以2008-2018年的长江经济带为例，测算其农业生产效率并分析时空特征。研究表明，外生环境因素对长江经济带农业生产效率的影响显著，存在明显的时空差异。其中：1）剔除环境因素后，长江经济带农业生产效率整体向好，四川省和江苏省处于效率前沿面，上海市的农业生产效率值出现明显下降；2）长江经济带农业生产效率逐年波动发展，长江中游地区相对上游和下游地区的农业生产效率更具优势，个别省份的农业生产效率水平与其经济社会发展程度不匹配；3）劳动力、土地、灌溉等投入要素的增加均会引起农业生产效率的增加，财政投入力度及人均GDP与农业生产效率之间不存在明显的正向相关关系，受灾面积对农业生产效率有显著负面影响。Abstract: In response to the strategic call for the "Great Protection" of the Yangtze River Economic Belt and to fulfill the important historical tasks assigned by the state to the provinces and cities of the area, the Yangtze River Economic Belt is adjusting the agricultural industry structure, optimizing the input-output ratio, and ensuring stable and sustainable agricultural production. Based on the combination of the three-stage Data Envelopment Analysis (DEA) model and cluster analysis, this study examined the Yangtze River Economic Belt from 2008 to 2018 to measure its agricultural production efficiency and to analyze its temporal and spatial characteristics. Studies shown that exogenous environmental factors significantly (P < 5%) impact agricultural production efficiency in the Yangtze River Economic Zone, and there were temporal and spatial differences. These include: 1) after excluding environmental factors, the overall agricultural production efficiency of the Yangtze River Economic Zone had improved. Sichuan and Jiangsu Provinces were at the forefront of efficiency, whereas the agricultural production efficiency of Shanghai had obviously declined. 2) The agricultural production efficiency of the Yangtze River Economic Belt varied year by year, with fluctuating development. The middle reaches of the Yangtze River had advanced agricultural production efficiency more than the upstream and downstream regions, and the agricultural production efficiency of the individual provinces did not match their economic and social development. 3) Increases in labor, land, irrigation, and other input factors increased agriculture production efficiency, there was no correlation between fiscal investment per capita gross domestic product (GDP) and agricultural production efficiency. The disaster-affected area had a significant negative impact on agricultural production efficiency.
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图 1 长江经济带农业生产总值及其占全国比重
Figure 1. Gross agricultural production value of the Yangtze River Economic Zone and its national proportion
图 2 长江经济带各省(市)调整前与调整后的农业生产效率
Figure 2. Agricultural production efficiencies of provinces (cities) of the Yangtze River Economic Belt before and after adjustment
图 3 2008 — 2 01 8年长江经济带上中下游省市农业生产效率均值趋势
Figure 3. Trends of average agricultural production efficiencies in the upper, middle and lower reaches of the Yangtze River Economic Belt from 2008 to 2018
表 1 长江经济带农业生产效率相关变量及其统计性描述
Table 1. Variables related to agricultural production efficiency in the Yangtze River Economic Belt and their statistical description
变量类型
Variable type名称
Name单位
Unit符号
Symbolic均值
Mean标准差
Standard deviation产出变量
Output variable农业总产值Total agricultural output value 108 ¥ OP 3181.44 1864.72 投入变量
Input variable农业机械总动力Total power of agricultural machinery 104 kW I1 3188.36 1728.36 农用化肥施用量Amount of agricultural fertilizer 104 t I2 192.14 107.74 第一产业劳动力Primary industry labor 104 peoples I3 1116.14 562.09 农作物播种面积Sown area of crops 103 hm2 I4 4954.79 2780.96 有效灌溉面积Effective irrigation area 103 hm2 I5 2127.21 1178.15 环境变量
Environment variable财政对农业的支持Financial support for agriculture 108 ¥ E1 474.32 251.24 人均GDP GDP per capita ¥ E2 46 181.66 20 614.85 受灾面积Disaster-affected area 103 hm2 E3 823.50 908.06 
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表 2 2008 —2018年长江经济带省市的农业产出与投入的Pearson相关系数检验
Table 2. Pearson correlation coefficient test of agricultural output and input in provinces and cities of the Yangtze River Economic Belt from 2008 to 2018
OP I1 I2 I3 I4 I5 OP 1.000 I1 0.754*** 1.000 I2 0.793** 0.832*** 1.000 I3 0.547*** 0.663*** 0.725*** 1.000 I4 0.296*** 0.692*** 0.639*** 0.518*** 1.000 I5 0.809*** 0.925*** 0.885*** 0.592*** 0.581*** 1.000 OP、I1-I5为表 1中的投入及产出变量。*和**表示P < 0.05和P < 0.01水平显著相关。OP and I1-I5 are the input and output variables shown in the table 1. * and ** represent significant correlations at P < 0.05 and P < 0.01 levels, respectively.
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表 3 一阶段DEA-BCC模型下的2008 —2018年长江经济带的农业生产效率
Table 3. Agricultural production efficiencies of provinces (cities) of the Yangtze River Economic Belt Region from 2008 to 2018 based on the one-stage DEA-BCC model
省(市) Province (city) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 均值Mean 安徽Anhui 0.557 0.519 0.560 0.552 0.561 0.468 0.503 0.508 0.509 0.502 0.474 0.512 贵州Guizhou 0.620 0.563 0.554 0.518 0.572 0.526 0.514 0.494 0.494 0.518 0.535 0.537 江西Jiangxi 0.723 0.664 0.676 0.665 0.644 0.646 0.702 0.741 0.804 0.820 0.752 0.712 湖南Hunan 0.759 0.819 0.896 0.892 0.821 0.787 0.813 0.440 0.482 0.533 0.638 0.716 云南Yunnan 0.706 0.747 0.703 0.620 0.754 0.829 0.822 0.792 0.723 0.717 0.914 0.757 湖北Hubei 0.933 0.935 0.981 0.994 0.969 0.995 1.000 0.868 0.906 0.920 0.898 0.945 重庆Chongqing 0.899 0.929 0.932 0.963 0.942 1.000 1.000 1.000 1.000 1.000 1.000 0.970 江苏Jiangsu 0.869 0.869 0.964 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.973 浙江Zhejiang 1.000 0.960 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 0.996 四川Sichuan 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 上海Shanghai 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
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表 4 长江经济带的农业生产效率二阶段似SFA前沿回归调整结果
Table 4. SFA forward regression adjustment results in two-stage of agricultural production efficiency in the Yangtze River Economic Belt
环境变量Environment variable 松弛变量Slack
variableI1 I2 I3 I4 I5 E1 –0.171 –0.001 0.034** –0.133 –0.013 E2 0.001** 0.001* 0.000 0.214* 0.000 E3 0.0561 0.008 –0.0084** –0.0046** 0.0474 C –163.570* –8.870*** 25.910** –195.410** –92.770* LR test 72.45 45.45 42.89 85.35 83.96 Prob > chi 0.00 0.00 0.00 0.00 0.00 log likelihood –998.98 –611.87 –851.67 –1088.88 –929.67 E1-E3、I1-I5见表 1中的环境变量和投入变量。*、**和***表示P < 0.1、P < 0.05和P < 0.01水平显著相关。E1-E3 and I1-I5 are the environmental and output variables shown in the table 1. *, ** and *** represent significant correlations at P < 0.1, P < 0.05 and P < 0.01 levels, respectively.
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表 5 2008 —2018年三阶段DEA-BCC调整后长江经济带各省市的农业生产效率值
Table 5. Agricultural production efficiencies of provinces (cities) of the Yangtze River Economic Belt from 2008 to 2018 based on the three-stage DEA-BCC model
地区Area 省(市) Province (city) 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 均值Mean 上游
Upstream云南Yunnan 0.734 0.802 0.759 0.632 0.826 0.858 0.926 0.908 0.876 0.830 0.965 0.829 四川Sichuan 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 贵州Guizhou 0.646 0.535 0.724 0.679 0.571 0.643 0.634 0.444 0.502 0.527 0.583 0.590 重庆Chongqing 0.805 0.856 0.824 0.814 0.804 0.896 0.864 0.878 0.905 1.000 1.000 0.877 中游
Midstream湖北Hubei 0.989 0.988 0.979 0.949 0.981 1.000 1.000 0.972 1.000 1.000 1.000 0.987 湖南Hunan 0.961 0.997 1.000 0.999 1.000 0.996 0.970 0.572 0.650 0.797 0.766 0.883 江西Jiangxi 0.982 0.872 0.856 0.807 0.836 0.943 0.962 0.796 0.951 0.843 0.910 0.887 下游
Downstream江苏Jiangsu 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 安徽Anhui 0.814 0.894 0.755 0.767 0.731 0.750 0.741 0.704 0.752 0.752 0.691 0.759 浙江Zhejiang 1.000 0.983 1.000 1.000 0.956 1.000 1.000 0.927 0.832 0.864 0.956 0.956 上海Shanghai 0.480 0.240 1.000 1.000 0.660 1.000 0.460 0.515 0.680 0.130 0.230 0.581
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表 6 剔除环境变量后长江经济带农业生产效率聚类分析结果比较
Table 6. Comparison of cluster analysis results of agricultural production efficiencies in the Yangtze River Economic Belt after excluding environmental variables
地区分类Area class 第1阶段The first stage 第3阶段The third stage Ⅰ 四川、上海Sichuan, Shanghai 四川、江苏Sichuan, Jiangsu Ⅱ 湖北、重庆、江苏、浙江Hubei, Chongqing, Jiangsu, Zhejiang 重庆、湖南、江西、浙江、湖北Chongqing, Hunan, Jiangxi, Zhejiang, Hubei Ⅲ 云南、江西、湖南Yunnan, Jiangxi, Hunan 云南、安徽Yunnan, Anhui Ⅳ 安徽、贵州Anhui, Guizhou 贵州、上海Guizhou, Shanghai
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