Improvement of the method for calculating agricultural energy efficiency based on the three-stage Data Envelopment Analysis

Energy is the basis for the development of modern society and an important guarantee for comfortable rural living and successful agricultural production. With industrialization and urbanization occurring rapidly in China, the demand for efficient energy in agricultural modernization will inevitably increase. In the face of increasingly severe global issues such as limited resources, environmental calamities, and food insecurity, accurate measurement is key to improving agricultural energy efficiency, facilitating users in identifying bottlenecks and potential in energy usage, optimizing the agricultural energy structure, and breaking through the dual constraints of energy and the environment, which in turn will effectively promote comprehensive rural revitalization. Previous concept exploration has revealed the existence of a conceptual intersection between conventional agricultural energy efficiency and agricultural production efficiency, where the calculation output of the former is in fact the latter including energy. To scientifically and logically calculate agricultural energy efficiency, we proposed an improved algorithm based on a three-stage Data Envelopment Analysis (DEA) model. Based on the conventional one-stage calculation method, this algorithm applied a second-stage Stochastic Frontier Approach (SFA) and third-stage DEA analysis. Panel data from 30 provinces (municipalities and autonomous regions, not including Hong Kong, Macao, Taiwan and Xizang of China) in China were used as a sample to test the updated algorithm. The reliability of the model was tested by comparing its calculated results with those obtained using the conventional method. The following observations were made: 1) Outputs from the second-stage SFA showed that the likelihood-ratio (LR) values of all input slack variables were greater than 10.501 (P<1%). The impacts of environmental variables and random factors on energy efficiency were significant, indicating that the SFA analysis is necessary and effective and can eliminate the effect of production factors on agricultural energy efficiency, thereby avoiding the problem of some calculated results being higher than the observed values. 2) Compared with the gap of approximately 0.1 derived from the conventional method of calculating agricultural energy efficiency in the past 20 years, the final (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 for the trend in China’s agricultural economy development. The fluctuation node was more consistent with the periods when the corresponding policies were introduced, such as the severe agricultural blow resulting from natural disasters at the end of the 20th century, the first China’s No. 1 central document with the theme of “Agriculture, Rural Areas, and Farmers” issued in 2004, the international economic and financial crisis in 2008, and other important nodes. 3) The estimates from the conventional method were greatly biased from actual values owing to price and cost influences, especially in Beijing, Qinghai, and Shanghai, where the differences between the traditional and improved models were 0.95, 0.87, and 0.77, respectively. In summary, the improved three-stage DEA method for calculating agricultural energy efficiency is superior to the conventional method, and can provide a more accurate decision-making basis for enterprises and governments in the fields of agricultural energy conservation and emissions reduction.