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.

Evaluating returns to scale and congestion by production possibility set in intersection form

This research proposes a new method to estimate returns to scale(RTS) of decision making units(DM Us) with multiple inputs and outputs.The state of return to scale includes increasing RTS,constant RTS,decreasing RTS and evidence of congestion.The method is based on the production possibility set in the intersection form given by a set of linear inequalities.We propose and prove the necessary and sufficient conditions for the RTS estimation.With the new procedure,to estimate the RTS of a DM U is simply to check the position of the DM U on the production frontiers.We point out that the procedure is particularly important for dealing with a large number of DM U s.Therefore,it can be regarded as a complementary to the data mining.

A Comprehensive Method for Evaluating Precision of Transfer Alignment on a Moving Base

In this study, we propose the use of the Degree of Alignment(DOA) in engineering applications for evaluating the precision of and identifying the transfer alignment on a moving base. First, we derive the statistical formula on the basis of estimations. Next, we design a scheme for evaluating the transfer alignment on a moving base, for which the attitude error cannot be directly measured. Then, we build a mathematic estimation model and discuss Fixed Point Smoothing(FPS), Returns to Scale(RTS), Inverted Sequence Recursive Estimation(ISRE), and Kalman filter estimation methods, which can be used when evaluating alignment accuracy. Our theoretical calculations and simulated analyses show that the DOA reflects not only the alignment time and accuracy but also differences in the maneuver schemes, and is suitable for use as an integrated evaluation index. Furthermore, all four of these algorithms can be used to identify the transfer alignment and evaluate its accuracy. We recommend RTS in particular for engineering applications. Generalized DOAs should be calculated according to the tactical requirements.

Dynamic Concept of Returns to Scales and Its Characteristics on Production Frontier in Intersection Form

This paper gives a dynamic concept and a new non-parametric method for evaluating returns to scale（RTS） of economic units with multiple inputs and outputs.It is frequently noticed that when we increase the input of a decision making unit（DMU） with a certain status of RTS,different status of RTS is observed.For example,when we increase the input of a DMU with constant RTS under the traditional method,a decreasing RTS is often observed instead of the expected constant RTS.We thus define the RTS of each DMU in both input expansion and contraction regions respectively.The research starts from transferring the production possibility set into the intersection form,by giving the explicit linear inequality representation of production frontiers.The RTS structural characteristics of DMUs＇ on the production frontier are described.Status of RTS of those DMUs on the production frontier include increasing RTS,constant RTS,decreasing RTS,saturated RTS and evidence of congestion.Necessary and suficient conditions for RTS evaluation are provided.The definition and evaluation method given here provide more detailed economic characteristics of DMU for policy makers.

An Econometric Analysis of Cotton Production Technologies in Harran Plain, Turkey： Translog versus Cobb-Douglas Functions

This research explores the question of how the three production factors, capital, labor, and land may impact the current level of cotton output on the Harran Plain, a major cotton production area in Turkey. The objective of this paper is to estimate a Translog production function and compare the results to those from a Cobb-Douglas specification. Nested tests we performed resulted in the conclusion that the constant returns to scale, weak separability and Cobb-Douglas hypotheses are all satisfied. Thus the Cobb-Douglas specification is a superior functional form yielding results more robust than those from the translog model. Dwelling on Cobb-Douglas estimation results, farm size is found the most influential variable determining cotton output, followed by the variable representing capital as the second influential. Results also demonstrate that the returns-to-scale parameter calculated for this sample is not statistically different from unity, suggesting that cotton production technology in this region exhibits constant returns to scale. This result is consistent with current literature findings that render support to an inverse relationship between farm size and productivity in developing countries.

Economic Impact of Mutant Cassava （Manihot Species） for Agricultural Improvement in Ghana

The importance of agricultural innovations for raising the living standards of farmers has received substantial attention from the economic and political communities. In Ghana, cassava serves as an important source of calorie and cash crop. Production constraints such as the cassava mosaic disease caused by virus have limit farmers access to productivity potentials and marketing. Breeding efforts attempting to address this constraints have had some success such as the mutant Tech Bankye virus resistant variety. This research, therefore, analysed the impact of some production input on mutant cassava productivity growth in Ghana with the use of Cobb-Douglas production function. Results show that farmers cultivate the mutant variety in addition to other traditional varieties to averse risking in marketing and income. The average cost of production of the mutant variety is higher compared to that of the traditional variety. Eighty percent of the farmers complained difficulty in accessing market for the mutant variety because it could not replace the traditional variety in terms of its texture for the local native ＂fufu＂ production and ＂ampesi＂ and also deteriorate quickly in storage. However, for industrial production of ＂gari＂ and starch, the mutant is the best. Both the mutant cassava and the traditional varieties showed increasing returns to scale, however, the returns to scale of the mutant variety were lower compared to that of the traditional variety. Also, the opportunity cost of forgoing the traditional varieties to cultivating the mutant variety was very high making adopted farmers hesitant to continue it cultivation.

How Efficient Is China＂s Industrial Relocation from East to West？ - Evidence from 20 Manufacturing Industries

With the acceleration of the rise of central China and the western development drive, industrial relocation from China＇s eastern region to the central and western regions is in full swing. However, does the relocation demonstrate industrial clustering effect？ Empirical studies based on twenty two-digit manufacturing industries in 27provinces from 2000 to 2009 demonstrate that industrial clustering effect appeared in central and western regions which had undertaken industrial relocation from eastern region; however, the studies do not show excessive administrative interference as evidenced by the significantly improved productivity of the relocated industries. Compared with non-labor- intensive manufacturing industries, labor-intensive manufacturing industries are easier to form cyclic accumulative effects. Studies also revealed that improvement in supporting infrastructure, industrial chain and higher labor quality in non-agriculture employment during urbanization are significant for central and western regions to undertake industrial relocation.

Data Envelopment Analysis in Estimation of Technical Efficiency Change of Regional Agriculture Production EU, 1989-2007

Assessment of production efficiency in economic activity is a major issue focused on by economists since the middle of the 20th century. One of the methods suitable in this respect is data envelopment analysis （DEA） facilitating the estimation of technical efficiency based on results obtained by a specified set of producers. Dynamics of changes in efficiency in agricultural production may be assessed on the basis of time series of several years. In the study, one of the variants of DEA was applied to economic results recorded in the years 1989-2007 by average farms representing selected regions of the European Union. The resulting individual dynamics of technical efficiency changes were divided into four homogeneous groups to facilitate identification of differences in production technology. These differences were then explained by classical analysis of basic factors use in agricultural production.

Allocating Fixed Costs with Considering the Return to Scale: A DEA Approach

When the allocated fixed cost is treated as the complement of other costs, conventional data envelopment analysis （DEA） researches have ignored the effect of the return to scale （RTS） in fixed cost Mlocation problems. This paper first demonstrates why the RTS should be considered in fixed cost allocation problems. Then treating the fixed cost as a complementary input, the authors investigate the relationship between the allocated cost and the variable return to scale （VRS） efficiency based on the super BCC DEA model. However, the infeasibility problem may exist in this situation. To deal with it, the authors propose an algorithm. The authors find that the super BCC efficiency is a monotone non-increasing function of the allocated cost. Based on the relationship, the authors finMly propose a fixed cost allocation approach in terms of principles as： （i） The fixed cost proportion allocated to inelastic DMUs should be consistent with their consumed cost proportion, and （ii） the same efficiency satisfaction degree to the rest DMUs. The optimal allocation scheme is unique. A numerical example and a real example of allocating fixed costs among 13 subsidiaries are employed to illustrate the proposed approach.

A COMPREHENSIVE DEA APPROACH FOR THE RESOURCE ALLOCATION PROBLEM BASED ON SCALE ECONOMIES CLASSIFICATION

This paper is concerned with the resource allocation problem based on data envelopment analysis （DEA） which is generally found in practice such as in public services and in production process. In management context, the resource allocation has to achieve the effective-efficient-equality aim and tries to balance the different desires of two management layers： central manager and each sector. In mathematical programming context, to solve the resource allocation asks for introducing many optimization techniques such as multiple-objective programming and goal programming. We construct an algorithm framework by using comprehensive DEA tools including CCR, BCC models, inverse DEA model, the most compromising common weights analysis model, and extra resource allocation algorithm. Returns to scale characteristic is put major place for analyzing DMUs＇ scale economies and used to select DMU candidates before resource allocation. By combining extra resource allocation algorithm with scale economies target, we propose a resource allocation solution, which can achieve the effective-efficient-equality target and also provide information for future resource allocation. Many numerical examples are discussed in this paper, which also verify our work.

AN EXTENDED AGGREGATED RATIO ANALYSIS IN DEA

Data Envelopment Analysis（DEA） and Ratio Analysis（RA） are two widely used methods for measuring units＇ productivity and any other criteria that could be assessed based on the available input and output variables.A number of researchers have studied DEA and RA and noted the positive and negative differences between them.Aggregated ratio analysis（ARA） model,which provide an important linkage between DEA and RA theory,is equivalent to the CCR DEA model,and this equivalence property offers a great deal of opportunities for DEA to be interpreted and applied in different ways.This paper extends the results of ARA model and proposes an extended aggregated ratio analysis（EARA） model,similar as the development from CCR model to BCC model in DEA context.The proposed model can offer an insight into the characteristic of returns to scale,playing the corresponding role as BCC model does.The numerical example is revisited in the paper and the results are compared.

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.

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.