地理加权的随机前沿效率——以中国寿险业为例

Geographically Weighted Stochastic Frontier Efficiency:A Study of the Life Insurance Industry in China

各类决策机构的经营成果普遍受到自然、经济和社会等方面环境因素的影响,所处环境更接近的机构也更会直接相互影响,所以在评价一家决策机构的经营业绩时,应当更多地将该机构与所处环境相似的机构进行比较。本文基于2001-2015年中国67家寿险企业的面板数据,根据两家企业在内地283个地级地区的收入分布情况计算二者所处地理环境的差异度,结合假设较为灵活的随机前沿分析（SFA）模型,为每家企业估计了以自身所处环境为＂权重＂计算基准的SFA模型。研究发现,采用地理加权估计与采用普通方法得到生产函数参数和效率值的估计结果有较大差异。具体而言：采用地理加权估计后,①内勤劳动和物料对营销劳动的替代弹性的估计值降低了28.8%;②单位投入对＂损失补偿＂产出的生产能力的估计值降低了44.4%;③寿险业的规模报酬系数从2.464降低到1.763（个体均值）和1.953（个体中位数）;④技术效率值的均值和中位数分别从0.598和0.632分别提高到0.716和0.698。

In various fields, the operating results of the decision-making unit（DMU） are widely affected by local natural, economic and social environmental factors, and the DMUs are more likely to influence each other directly when they have more similar environment. Therefore, when evaluating the performance of a DMU, it is appropriate to put more emphasis on those DMUs whose environmental factors are more similar to the DMU. Based on 2001-2015 panel data of China＇s 67 life insurance companies,this paper calculates the pairwise geographically environmental discrepancy of life insurance companies according to their income distribution among 283 prefecture-level regions in the mainland of China. Combined with the stochastic frontier approach（SFA） model which has relative high flexible assumptions,we estimates the SFA model for each life insurer using its environment as the benchmark for calculating the ＂weights＂. Significant differences lie between the results of geographically weighted estimation and the general estimation. When geographically weighted estimation is applied： 1） The estimates of the elasticity of substitution for back-office labor and material to marketing labor reduces by 28.8%; 2） The production capacity estimate of unit input for ＂loss compensation＂ output decreases by 44.4%; 3） The estimate of life insuracne industry＇s return of scale decreases from 2.464 to 1.763（mean of individual estimate） and 1.763（median of f individual estimate）; and 4） The mean and median of technical efficiency increases from 0.598 and 0.632 to 0.716 and 0.698, respectively.