Efficiency Analysis Of Two-stage Network Structures Based On DEA And StoNED

In conventional DEA (Data Envelopment Analysis) models, there are two potential pre-specified conditions:one is that DMUs (Decision Making Units) are treated as black-boxes while the internal structure of DMUs is ignored, the other is that DMUs are operating in a totally deterministic environment. The former means that efficiency evaluation is limited to the black-boxes, while we cannot find where the estimated inefficiency come from. The latter leader to DEA’s lack of statistical foundation and the disturbance come from random error is wrongly attributed to inefficiency part. Considering the first condition, Liang et al. (2008) opens the black-boxes and proposes DEA models based on game theory for strictly tandem two-stage network structures, in this paper, we extend Liang et al.’s model to general two-stage network structures in which there are final outputs produced by the first stage or external inputs used by the second stage. For the second condition, firstly, the current paper proposes two estimation methods for multiple outputs and multiple inputs frontier functions. Secondly, the proposed StoNED (Stochastic Non-parametric Envelopment of Data) with maximum likelihood estimation is applied to the frontier estimation and efficiency analysis of two-stage network structures. It is worth to note that the current paper is the first to consider both internal structures and random error of DMUs.There are five chapters in this paper, the main contents of each chapter are presented as follows.In the first chapter, we firstly introduce basic concepts and models of DEA, and basic steps and methods of StoNED. Then, the research meanings and research backgrounds of DEA models for extended two-stage network structures and estimation of two-stage network frontiers and efficiencies based on StoNED are presented.Liang et al. (2008) developed DEA models based upon game approach to decompose efficiency for two-stage network structures where all outputs of the first stage are the only inputs to the second stage. Chapter 2 extends Liang et al.’s models by assuming there are final outputs from the first stage or external inputs for the second stage. Two models are proposed to evaluate the performance of this type general two-stage network structures. One is a non-linear centralized model whose global optimal solutions can be estimated using a heuristic search procedure. The other is a non-cooperative model, in which one of the stages is regarded as the leader and the other is the follower. The newly developed models are applied to a case of regional R&D of China.Chapter 3 discusses the estimation of stochastic multiple inputs and multiple outputs frontier. We prove that the output oriented frontier is a concave function, which is monotonically non-decreasing at inputs and non-increasing at other outputs; while the input oriented frontier is a convex function, which is monotonically non-decreasing at outputs and non-increasing at other inputs. Two methods are developed to estimate the frontier functions, one is a maximum likelihood estimation model with constraints, the other is StoNED based on maximum likelihood estimation. We prove that the above estimators are equal to DEA when the variance of random error is zero. Two Monte Carlo trials are designed to test the estimation methods. Finally, the methods developed in this chapter are applied to estimate the frontier and efficiency of China commercial banks.Chapter 4 discusses the estimation of stochastic frontiers and efficiencies of two-stage network structures. With the assumptions of there are one intermediate measure and one final output contains normal random errors and half normal inefficiencies, we first use the StoNED based on maximum likelihood estimation to estimate sub-stage’s frontiers, and then use sub-stage’s frontiers to infer the DMU’s global frontier. Then, we propose models for transformation of estimated inefficiency to radial efficiency and rational models for estimating the DMU’s global efficiency, and discuss the relationship between global efficiency and sub-stage’s efficiencies. Finally, above estimators are used to estimate the frontier and efficiency of China commercial banks.In the chapter 5, we conclude the main works and innovations of this paper. Some problems and shortcomings are also presented, based on these, we provide some points for future research.The most important innovations of this paper are:(1) develops DEA models for extended two-stage network structures; (2) develops stochastic multiple inputs multiple outputs frontier estimation models; (3) develops stochastic frontier and efficiency estimation models for two-stage network structures; (4) new methods for efficiency analysis of R&D system and banking industry.