One of the most popular approaches in the theoretical measurement and empirical estimation of the efficiency of various economic systems is known as Data Envelopment Analysis, abbreviated as DEA. This approach is rooted in and cohesive with theoretical economic modeling via the so-called Activity Analysis Models and is estimated via the powerful linear programming approach.

In this chapter, we consider a variety of models that can be used to estimate particular types of technologies: constant, nonincreasing and variable returns to scale, convex and non-convex technologies. This chapter does not exhaust everything that has been suggested in the literature – fulfilling such a task would be practically impossible in one chapter. The goal is more modest, yet practically valuable: we focus on the most popular methods and consider their “step-by-step construction,” intuition, some of the most important properties, some interesting variations and modifications, etc. We pay attention to aspects that we consider very useful for a reader to advance in his/her own research and, possibly, advance the frontier of the research.

INTRODUCTION TO ACTIVITY ANALYSIS MODELING

An economist's approach to thinking about nonparametric efficiency measurement can be viewed through the so-called Activity Analysis Models – a way of mathematically modeling production relationships. An activity analysis model (AAM) can be defined as a set of mathematical formulations designed to mimic a technology set from the observed data of some real-world production process of interest. The best way to understand such modeling is to actually build a few AAMs.

There are two fundamental assumptions behind most AAMs. The first fundamental assumption we will always make for AAMs in this book is that all decision making units (DMUs) have access to the same technology (which can be characterized by the technology set T that satisfies the main regularity axioms; see Chapter 1). This assumption is important to justify the estimation of one frontier from the full sample – often called the (observed) best practice frontier for the population represented by that sample. Note that this assumption does not imply that all firms have the same access, nor does it imply that all firms use this technology to full capacity. On the contrary, it is allowed that, for various reasons, each particular firm may not be on the frontier. The reasons for “deviations” from the technology frontier are well-explained by asymmetric information and behavioral economics theories and are documented in many empirical studies.