ABSTRACT
CONTENTS 16.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 958 16.2 Production Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 959
16.2.1 Technical Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 16.2.2 Constant Returns to Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 962 16.2.3 Multipliers as Shadow Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 965 16.2.4 Slacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 966
16.3 Scale Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 968 16.3.1 Ray-Average Productivity and Returns to Scale . . . . . . . . . . . . . . . . . . . . . . 971 16.3.2 Most-Productive Scale Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 971 16.3.3 Identifying the Nature of the Local Returns to Scale . . . . . . . . . . . . . . . . . . . 972
16.3.3.1 Banker’s Primal Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 972 16.3.3.2 A Dual Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975 16.3.3.3 A Nesting Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975
16.3.4 Identifying the Returns to Scale for an Inefficient Unit . . . . . . . . . . . . . . . . . 976 16.3.5 The Case of Multiple MPSS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 977 16.3.6 Output-or Input-Oriented? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979
16.4 Nonradial Measures of Technical Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 980 16.4.1 Graph-Efficiency Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 981 16.4.2 Pareto-Koopmans Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 983 16.4.3 A Slack-Based Measure of Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984 16.4.4 Linearization of the Pareto-Koopmans DEA Problem . . . . . . . . . . . . . . . . . 985
16.5 Distance Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 986 16.5.1 Directional Distance Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 987 16.5.2 Geometric Distance Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988 16.5.3 Data Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 988
16.6 Weak Disposability and Bad Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 990 16.7 DEA with Market Prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 993
16.7.1 DEA for Cost Minimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994 16.7.2 Profit Maximization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 995
16.8 Summing Up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 996 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997
ABSTRACT Over the past few decades, data envelopment analysis (DEA) has emerged as an important nonparametric method of evaluating the performance of decision-making units through benchmarking. Although developed primarily for measuring the technical efficiency, DEA is now applied extensively for measuring the scale efficiency, cost efficiency, and profit efficiency as well.
This chapter integrates the different DEA models commonly applied in empirical research with their underlying theoretical foundations in neoclassical production economics. Under the assumptions of the free disposability of inputs and outputs and convexity of the production possibility set, the freedisposal convex hull of the observed input-output bundles provides an empirical “estimate” of the technology set. The graph of the technology provides an appropriate benchmark for the efficiency evaluation under alternative orientations. The radial models consider either a proportional upward scaling of all the outputs or a downward scaling of all the inputs and the efficiency measure does not reflect the presence of slacks. Nonradial models allow different inputs to decrease or individual outputs to increase at different rates, thereby ruling out input or output slacks at the optimal solution. Unless constant returns to scale are explicitly assumed, (locally) increasing, constant, or diminishing returns will hold at different points on the graph of the technology. A point where locally the constant returns to scale hold is the most-productive scale size. One can characterize a firm as too small, if it is located at a point on the frontier where increasing returns to scale holds or if both input-and output-oriented projections onto the frontier (when the firm is inefficient) are points in the region of the increasing returns. The firm is too large, when both projections are in the region of the diminishing returns to scale. A simple DEA model has to be solved to determine the scale efficiency of a firm as well as its appropriate scale characterization. Oriented models (both radial and nonradial) prioritize either the input conservation or the output expansion. As the models are based on the graph-hyperbolic distance function, directional distance function, geometric distance function, or Pareto-Koopmans efficiency, one looks for the output increase and input decrease simultaneously. The directional distance function, in particular, has emerged as the most popular analytical framework for measuring the efficiency when the objective is to expand the desirable or “good” output and reduce the undesirable of a “bad” output simultaneously. Finally, the chapter deals with the measurement of cost or profit efficiency in a market economy where the input and output prices are available.
