无可行解下Malmquist-Luenberger指数的改进与应用--以商业银行生产效率评价为例

Improvement and Application of Malmquist-Luenberger Index without Solution——A Case of Commercial Bank Productivity Evaluation

Malmquist-Luenberger(ML)指数无解的直接原因是方向距离函数(DDF)在测度混合时期效率值时会存在无可行解。已有研究中,Färe方法可以解决规模收益不变条件下DDF无解问题,但在规模收益可变条件下仍会存在无解现象。考虑将Lee解决超效率无解的两阶段方法与Färe方法相结合,探讨解决规模收益可变条件下ML指数无解问题的改进方法。并以商业银行生产效率评价为例,构建利润角度指标体系,将不良贷款作为非期望产出,运用改进的ML指数测度2013-2018年我国31家上市商业银行全要素生产效率的变化情况,并将其与传统的MI指数进行比较。结果表明:技术变化是影响我国上市商业银行全要素生产效率的主因,遗漏不良贷款往往会低估效率变化、高估技术变化。

The direct reason why there is no solution to the Malmquist-Luenberger(ML)index is that the direction distance function(DDF)has no solution when measuring the efficiency value in the mixing period.In previous studies,Fare method can solve the problem of no solution for DDF under the condition of constant return on scale,but there still exists no solution possibility under the condition of variable return on scale.Considering the combination of two-stage method for solving the super-efficient unsolvable problem from Lee with Fare method,an improved method to solve no solution of ML index under the condition of variable return on scale is discussed.Taking the evaluation of the productivity of commercial Banks for example,profit angle index system is constructed,the non-performing loans are taken as the non-expected output,the improved ML index is used to measure the change of total factor productivity of 31listed commercial Banks in China from 2013to 2018,and the measurement of improved ML index is compared with the measurement of traditional MI index.The results show that technological change is the main factor influencing the total factor productivity of listed commercial Banks in China,and the omission of non-performing loans tends to underestimate the efficiency change and overestimate the technical change.