基于最小一乘准则的中国粮食产量与影响因素的相关性分析

Relative analysis of China’s grain yield and influence factors based on criterion of least absolute deviation

该文提出了中国粮食产量与影响粮食产量的一些主要因素之间,更多呈现的是指数关系,也少量呈现幂指数关系,为了获得较小的误差从而有较准确的描述定义了一种新的指数型生产函数;指出了最小一乘法是一种能找到在数据背后隐含的,对数据起支配控制作用的"隐函数"的最好方法。将二者捏合起来,用最小一乘法对指数型生产函数模型进行拟合,可以找到符合中国粮食变化的某些规律。该文介绍了最小一乘法和指数型生产函数,将影响粮食产量的5个主要因素(化肥施用量、粮食播种面积、成灾面积、农业机械总动力、第一产业就业人数)与中国粮食产量建立关联,用最小一乘法对生产函数模型进行拟合,并对中国1983-2011年的数据进行处理。在获得29a间中国粮食产量的Mae(平均绝对误差)不超过393万t,以及Mape(平均绝对百分误差)小于0.87%的数据处理结果的基础上,对数据给出的结论进行了解释和分析。1983-2011年的29a间,中国粮食产量的增长主要取决于化肥施用量和农业机械总动力,其中化肥施用量还继续在起"正"影响,而农业机械总动力趋于动态饱和,属于理论上的"负"影响,但不构成实际的"负"效应;粮食播种面积是最大的"正"影响,粮食产量在粮食播种面积在不增条件下,依然可以增长,但是增大粮食播种面积将能够迅速提高中国的粮食产量;成灾面积是粮食增长的"负"影响,影响的绝对量值在增加但相对量值在减小;由于受1984-1991年第一产业就业人数急剧增长的巨大冲击及滞后效应影响,第一产业就业人数的减少对粮食增长构成"负"影响,随着农业现代化与城镇化进程的发展,这种"负"影响在不断减小中。文中对上述这些定性结论给出了具体的定量值。该文并对2012年粮食产量进行了预测,其值为59133万t,预测的误差为0.3%;也对2013年粮食产量进行了预测,其值为61148万t。该文最后对最小一乘法、指数型生产函数等存在的问题进行了必要的讨论。最小一乘准则意义下的指数型生产函数,对中国粮食产量与主要影响因素之间关系的描述具有一定的准确性和指导意义。

The relations between China’s grain yield and some main factors influencing the grain yield, more present the exponential function and few exponent sign function relations. To describe with a new type of exponential production function can obtain a better result because of less error. The paper pointed out that the least absolute deviations （LAD） method, as its excellent properties, may be a best method to find the＂implicit function＂which is behind the data and control the data. To knead the two together, with the LAD method to fit the exponential production function, trying to find out some rules for China＇s grain change is a subject that is worth of exploring in theory and application. The paper introduces the LAD method and the exponential production function, establishes correlations between the China’s grain yield and its 5 major influencing factors （consumption of chemical fertilizer, total sown area, total area affected by natural disaster, total agricultural machinery power, and total employed persons of primary industry）. The production function model was fit with the LAD method, and the data of 1983-2011 were calculated. The results with Mae （mean absolute error） not over 3.93 million tons and Mape （mean absolute percentage error） not more than 0.87% for China’s grain yield during the 29 years were obtained, and the conclusions were explained and analyzed; The analysis showed that, in the 29 years of 1983-2011, the growth of China’s nation grain yield mainly depended on the consumption of chemical fertilizer and the total agricultural machinery power, of which the consumption of chemical fertilizer is still playing a positive roll up to now, while the total agricultural machinery power is dynamically in a saturated state. Theoretically it should have a ＂negative＂ effect now, but in reality it does not. The total sown area was the most influencing ＂positive＂ factor. The national grain yield may still grow further without increasing the total sown area, but increasing the sown area can rapidly boost the China’s nation grain yield. The total area affected by natural disaster imposed ＂negative＂ effect on the growth; However, the trend of its influence is increasing in terms of absolute values, but is decreasing in terms of relative values. By the huge impact and lagged effects of the rapid growing of the total employed population of primary industry in China during 1983-1993 period, the reduction of the total employed population of primary industry to grain growth constituted ＂negative＂ impact. With the modernization of agriculture and urbanization development, this ＂negative＂ impact continued to reduce. These conclusions give the specific quantitative values. The paper predictes that the grain yield for year 2012 is 8 5.9133×10^8t, the later result indicates the absolute error is 6 1.78×10^6t, and the relative error is 0.3%. For year 2013, the prediction is 8 6.1148×10^8t. In the last the paper gives some discussion about the LAD method, the exponential production functions and so on, and is concluded that the exponential production function under the meaning of LAD criterion to describe the relationships between China＇s grain yield and the main effect factors, has a certain accuracy and guiding sense.