Data envelopment analysis for scale elasticity measurement in the stochastic case:with an application to Indian banking

In the nonparametric data envelopment analysis literature,scale elasticity is evaluated in two alternative ways:using either the technical efficiency model or the cost efficiency model.This evaluation becomes problematic in several situations,for example(a)when input proportions change in the long run,(b)when inputs are heterogeneous,and(c)when firms face ex-ante price uncertainty in making their production decisions.To address these situations,a scale elasticity evaluation was performed using a value-based cost efficiency model.However,this alternative value-based scale elasticity evaluation is sensitive to the uncertainty and variability underlying input and output data.Therefore,in this study,we introduce a stochastic cost-efficiency model based on chance-constrained programming to develop a value-based measure of the scale elasticity of firms facing data uncertainty.An illustrative empirical application to the Indian banking industry comprising 71 banks for eight years(1998–2005)was made to compare inferences about their efficiency and scale properties.The key findings are as follows:First,both the deterministic model and our proposed stochastic model yield distinctly different results concerning the efficiency and scale elasticity scores at various tolerance levels of chance constraints.However,both models yield the same results at a tolerance level of 0.5,implying that the deterministic model is a special case of the stochastic model in that it reveals the same efficiency and returns to scale characterizations of banks.Second,the stochastic model generates higher efficiency scores for inefficient banks than its deterministic counterpart.Third,public banks exhibit higher efficiency than private and foreign banks.Finally,public and old private banks mostly exhibit either decreasing or constant returns to scale,whereas foreign and new private banks experience either increasing or decreasing returns to scale.Although the application of our proposed stochastic model is illustrative,it can be potentially applied to all firms in the information and distribution-intensive industry with high fixed costs,which have ample potential for reaping scale and scope benefits.

Literature Review of Agricultural Scale Management and Efficiency

Scale management remains the core position in entire development process of the economics and is a major issue of academic research and government concern. Focusing on related problems of agricultural scale management,this paper explored 4 aspects of past literature.( i) It defined the agricultural scale management based on economies of scale theory and changes in returns to scale.( ii) From the perspective of the returns to scale of grain production,there are changes in returns to scale of China's grain production,but the measured changes are not significant.( iii) Existing analysis on factors influencing agricultural scale management mainly includes factors influencing farmers' willingness of scale management and restrictive factors of implementation of scale management.( iv) In studies of the relationship between land management scale and production efficiency,many scholars made qualitative and quantitative analysis on land scale efficiency on the basis of economic indicators they defined,but they reached different conclusions. Finally,it summarized literature and pointed out several issues needing special attention in this field.

Special Relationship among Decision Making Units based on Partially Ordered Set and New Evaluation and Projection Methods

This paper provides data envelopment analysis methods based on partially ordered set theory.These methods reveal the special relationships between two decision making units from the perspective of mathematical theory and offer the classification,projection and improvement methods of decision making units.It is proved that an efficient decision making unit must be a maximal element of the related poset,and the maximal element may not be efficient.For this,we introduce the concepts of minimum envelope and efficiency envelope which further reveal the special relationship among efficient and inefficient decision making units.Compared with the previous methods,this method not only reveals theoretically the complex relationship among decision making units and the causes of the ineffectiveness,but also gives a new importance and competitiveness measurement method to each decision making unit.Finally,related algorithm and examples are given for the application of these methods to complex decision making problems.

Directional congestion in the framework of data envelopment analysis

This studyfirst proposes a definition for directional congestion in certain input and output directions within the framework of data envelopment analysis.Second,two methods from different viewpoints are proposed to estimate the directional congestion.Third,we address the relationship between directional congestion and classic(strong or weak)congestion.Finally,we present a case study investigating the analysis performed by the research institutes of the Chinese Academy of Sciences to demonstrate the applicability and usefulness of the methods developed in this study.