Improvement of agricultural energy efficiency calculation method based on three-stage DEA

Energy is the basis for the development of modern society, it is also an important guarantee for rural life and agricultural production. With the rapid development of industrialization and urbanization in China, the demand for efficient energy in agricultural modernization will inevitably increase. In the face of increasingly severe global issues, such as resources, environment and food security etc., accurate measurement is the basis for improving agricultural energy efficiency. It will facilitate identifying the bottlenecks and potential in energy usage, optimizing the agricultural energy structure, breaking through the dual constraints of energy and the environment, which in turn, will effectively promote rural comprehensive revitalization. The concept exploration revealed that there is a conceptual intersection between the conventional agricultural energy efficiency and agricultural production efficiency, the calculation output of conventional agricultural energy efficiency is actually the agricultural production efficiency including energy. In order to calculate agricultural energy efficiency scientifically and logically, this paper proposes an improved algorithm with referencing to three-stage data envelopment analysis (DEA) model. On the basis of the conventional one-stage calculation method, this algorithm also applies the second-stage stochastic frontier approach (SFA) and the third-stage DEA analysis. Panel data of thirty provinces (municipalities, autonomous regions) in China were taken as the sample to test the updated algorithm. The analysis results were compared to that of the conventional method to test the model reliability. The results showed that: 1) Outputs from the second-stage SFA analysis showed that the LR values of all input slack variables were greater than 10.501, passing the significance test of 1% LR. The impact of environmental variables and random factors on energy efficiency was significant. This indicated that SFA analysis was necessary and effective, can eliminate the impact of production factors on agricultural energy efficiency, which avoided the problem that some of the calculated results were higher than the observed values. 2) Compared with the gap of about 0.1 derived from the conventional method of agricultural energy efficiency in the past 20 years, the final (the third stage) efficiency value from the improved model increased from 0.240 in 2003 to 0.541 in 2018, demonstrating that the estimated result was more appropriate to the development trend of China's agricultural economy. And the fluctuation node was more consistent with the time when the corresponding policies were introduced: such as the severe agriculture blow resulted from natural disasters at the end of the 20th century, the first central document on “agriculture, rural areas and farmers” issued in 2004, and the international economic and financial crisis in 2008 and other important nodes. 3) The estimates of the conventional method were greatly biased from the real agricultural energy efficiency because to the influence of prices and costs, especially in Beijing, Qinghai, Tianjin, and Shanghai, which differences between the traditional and improved models were 0.88, 0.86, 0.72, and 0.67, respectively. In summary, the improved three-stage DEA agricultural energy efficiency method was obviously superior to the conventional method, which can provide more accurate decision-making basis for enterprises and governments in the fields of agricultural energy conservation and emission reduction.