Abstract: Input congestion analysis provides another perspective for input-output analysis, that is, increasing output by reducing redundant input, which is considered to be a new state after the decreasing returns to scale, and it means the increase of input can not bring the increase of output, but lead to the decrease of output, so it is urgent to optimize the production structure. The world economy has entered the stage of decreasing returns to scale. Some developed economies have even experienced input congestion. The means of economic stimulus are almost exhausted, but the economic burden is becoming more and more serious. Under this new normal, China has also put forward the supply side structural reform and the goal of “carbon peaking and carbon neutralization”, which is intended to stimulate green economic growth by optimizing the production structure of the internal driving force of economic development. In this context, using suitable input congestion analysis methods will help optimize the input-output structure of production units, thereby promoting healthy economic development.
At present, the main methods for input congestion analysis of production units are BCSW model and FGL model based on Data Envelopment Analysis (DEA) model. The basic idea of the two models is to compare the evaluated unit with the relative efficiency unit on the DEA frontier to obtain the input congestion. However, this method ignores the data sensitivity problem of DEA frontier, that is, the minimal change of units on the frontier will lead to a huge change in the evaluation results, resulting in the lack of robustness of the analysis results. The main impact of data sensitivity lies in the relatively effective units in DEA analysis results. Being relatively effective refers to the optimization space with technical inefficiency. The relatively effective unit is not located at the vertex position on the front surface constructed by DEA, so there is an optimization space. And since it is located at the edge of the frontier, it can be represented by linear combinations of other effective units. However, in practical situations, the probability that a certain production unit can be represented by a linear combination of other production units is very small, and there is always a greater or lesser gap, which leads to the instability of DEA analysis results.
Input congestion always occurs in the inefficient unit, and this inefficiency includes technical inefficiency and input congestion. When using the DEA model for input congestion analysis, it is necessary to distinguish the inefficiency to determine the specific value of the technical inefficiency and input congestion. Due to the data sensitivity issue of the DEA frontier, there are very few relatively effective units, which makes it difficult for input congestion analysis to distinguish between technical inefficiency and input congestion. The typical result is that all inefficiencies are attributed to input congestion, and that means the input congestion analysis results ars meaningless.
In order to avoid such situation, this paper proposes a heuristic method that starts from the perspective of improving DEA frontier, and improves the data sensitivity problem by adjusting the frontier within the error range, so as to make more relatively effective units and find the best frontier, finally makes the model analysis results more reasonable. In order to find the method, this paper starts from the data sensitivity of DEA frontier, and uses the basic idea of least square method to determine the property of DEA best frontier. Based on the property, the heuristic method is determined by using the idea and method of super-efficiency DEA model to solve the data sensitivity problems.
To verify the effectiveness of this method, this paper uses the dataset when the BCSW model was first proposed. In the analysis results of the original BCSW model, due to data sensitivity issues, the input congestion analysis results attribute all inefficiencies to input congestion, and the analysis results have little significance. On the basis of the optimal frontier determined by the method proposed, this paper also uses the BCSW model for input congestion analysis, and obtains more reasonable and explanatory results on instance data compared to using only the BCSW model. And this confirms the data sensitivity problem that does exist in DEA frontier when using input congestion analysis and the improvement effect of solving this problem on input congestion analysis methods.

Key words: input congestion analysis, BCSW model, DEA frontier, least squares method, super-efficient DEA model

摘要： 输入拥塞分析为投入产出分析提供了另一种视角,即通过减少冗余输入以增加输出。当前,对生产单位进行输入拥塞分析的主要方法是基于数据包络分析(DEA)模型的BCSW模型。BCSW模型的基本思想是将被评价单位与DEA前沿面上的有效率单位进行比较从而得出输入拥塞的值。但该方法忽略了DEA前沿面的数据敏感性问题,即前沿面上单位发生极小变动会导致评价结果的巨大改变,导致分析结果缺乏稳健性。本文提出了一种启发式方法,从改进DEA前沿面的角度出发,通过在误差范围内找到最佳前沿面,使输入拥塞分析结果更加合理。方法的提出从DEA前沿面的数据敏感性问题的原因出发,利用最小二乘法基本思想确定DEA最佳前沿面所需具备的性质。之后在该性质下,利用超效率DEA模型的思想和方法,解决DEA前沿面存在的问题,确定了该启发式方法。最后,本文在该方法所确定的最佳前沿面的基础上,利用BCSW模型进行输入拥塞分析,在实例数据上取得了相对于原始BCSW模型更合理也更具解释性的结果,证实了利用输入拥塞分析时,DEA前沿面确实存在的问题以及解决该问题对输入拥塞分析方法的改进作用。

关键词: 输入拥塞分析, BCSW模型, DEA前沿面, 最小二乘法, 超效率DEA模型