Construction of two-stage DEA models and economic applications

Abstract

This thesis focuses on the modeling of non-parametric production functions in two stages without assuming any specific functional form. Data Envelopment Analysis (DEA) is an approach based on linear programming and is used to assess the relative efficiency among a set of Decision Making Units (DMUs) while offering a number of advantages. However, conventional DEA models make no assumption regarding the procedures taking place inside the DMU. On the contrary, DEA treats a DMU as a “black box” which uses inputs to produce outputs without considering the internal procedures, a usually sufficient assumption. However in some cases, such as supply chain systems, DEA models consist of two or more stages and these internal procedures may be important for evaluating the efficiency. The stages are connected with intermediate variables which are considered as outputs in one stage and inputs in another stage. Network DEA models are used to accommodate such cases. This thesis classifies network DEA models into four categories which are independent, connected, relational and game theoretic models. Inside this framework this thesis constructs two-stage DEA models and use them create novel indices which evaluate the efficiency in various economic applications. Specifically, the most significant research contribution of this thesis is the incorporation of a priori information such as expert opinions and value judgements into the modeling process. This objective is achieved with the construction of the Weight Assurance Region (WAR) model which modifies the original additive model in order to incorporate a priori information using assurance region-based weights in the two-stages. Furthermore, WAR model solves the infeasibility problem of the original model. Another research contribution is the mathematical framework for the extension of the original additive model into a time-dependent window-based approach. This approach allows the handling of panel data in a two-stage network DEA framework and provides robust efficiency measures. A third research contribution is the incorporation of metafrontier framework into two-stage DEA analysis in order to treat the heterogeneity of DMUs in different groups (such as firms in different groups or regions in different countries) which experience different technologies. DMUs from different groups face different production opportunities; therefore feasible input-output combination in one group may not be feasible in another. These differences among groups may refer to physical, human and financial capital, infrastructures, economic environment, available resources etc; as a result every group has a different frontier. Therefore, the metafrontier is an overall frontier which envelopes the groups' specific frontiers so that no point of these frontiers can lie above points on the metafrontier. Finally, four economic applications are presented where the production processes are examined and novel indices are constructed using two-stage DEA formulations. The economic applications are in educational, banking and environmental sectors.