Advances in Data Envelopment Analysis

The following sections are included:

• Acknowledgements
• Preface
• Contents

The purpose of our first chapter is to review the basic building blocks used as the foundation for the rest of this monograph. These will be familiar to the Data Envelopment Analysis (DEA) audience, although our notation and orientation toward axiomatic production theory may be less familiar…

This chapter focuses on what we can learn about technology directly from the data, before we introduce the structure imposed by the assumptions set out in the previous chapter. We also address issues of allowable transformations of the raw data. Allowable in the sense that the resulting efficiency scores are invariant to those transformations for two specific DEA models: the Charnes, Cooper and Rhodes (1978) or von Neumann (1938, 1945) models, and the variable returns to scale directional distance function model…

The intensity variables in DEA originally were restricted to be nonnegative, and the focus was on their role in constructing the technology and identifying peer DMUs. It was known that the resulting technology satisfied constant returns to scale. Interestingly, in much earlier work using linear programming models of technology, Sydney Afriat (1972) showed that by restricting the intensity variables to sum to one (as well as nonnegative), variable returns to scale (VRS) could be modeled. Similarly, technology could be restricted to exhibit nonincreasing returns to scale by restricting the sum of the intensity variables to be less than or equal to one. Färe, Grosskopf and Logan (1983) used the nested nature of these restrictions to analyze returns to scale in DEA. The more familiar Banker, Charnes and Cooper (1984) (BCC) model followed in 1984…

In Chapter 4 we undertake an in-depth study of directional distance functions and how they apply to DEA…

We begin the chapter with a discussion of the directional vectors and how they influence the DEA scores for inefficient DMUs. We next consider the role of the direction vectors when the goal is to aggregate across DMUs. Here we show that aggregation is facilitated when the DMUs are given the same direction vector, in particular the unit direction.

The concluding section addresses the choice of direction in general, and how to endogenize that choice in particular. This leads us to a discussion of directional distance functions and their indication properties, i.e., the subsets of the technology to which the DMUs under evaluation are projected. We also show how the endogenization of the directions are related to slackbased directional distance functions.

An appendix including an indication theorem concludes.

This chapter addresses a single DEA topic, time substitution. This topic is the study of how to allocate resources in time, with the two options (i) determine when to apply inputs and (ii) how long, i.e., in how many periods should inputs be used. These options allow the decision maker to determine when to start production and for how long to produce. The topic was initiated by Shephard and Färe (1980) in connection with ship building, refined by Färe and Grosskopf (1996), and finally given a DEA formulation by Färe, Grosskopf, and Margaritis (2010). Their results are presented and generalized here.

After an introductory theoretical presentation we devote the rest of the chapter to an empirical application examining the Pact for Stability and Growth adopted by the countries comprising the single currency Euro zone.

In this chapter we consider two DEA models, the first is the DEA specification with a non-Archimedean infinitesimal and the second is the ‘super-efficiency’ model. The first of these was introduced to address Charnes, Cooper and Rhodes' (1978) concern that the piecewise linear construction of technology in DEA may yield vertical and horizontal extensions, and the secondwas introduced byAndersen and Petersen (1993) to provide a means to ‘break ties’, i.e., to allow for ranking the DMU:s in a sample which are technically efficient.

For these two problems we provide an example which demonstrates the limitations of these 'fixes.' In the case of the non-Archimedian, we show that a slight change in the choice of the approximation for the non-Archimedean can result in changes in the rankings of DMUs. For the superefficiency model we provide an example showing that this approach may fail to break ties.

The following sections are included:

• References
• Index