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.

Cambridge University Press has published a number of successful books that focus on topics related to ours: Chambers (1988), Färe et al. (1994b), Chambers and Quiggin (2000), Kumbhakar and Lovell (2000), Ray (2004), Balk (2008), and Grifell-Tatjé and Lovell (2015). These books – and an increasing number of articles related to production analysis, published in top international journals in economics, econometrics, and operations research – suggest a growing interest in the academic and business audience on the subject.

Our book is meant to complement and expand selected topics covered in the above-mentioned books, as well as the volume edited by Fried et al. (2008) and the edited volume by Grifell-Tatjé et al. (2018), and addresses issues germane to productivity analysis that would be of interest to a broad audience. Our book provides something genuinely unique to the literature: a comprehensive textbook on the measurement of productivity and efficiency, with deep coverage of both its theoretical underpinnings as well as its empirical implementation and a coverage of recent developments in the area. A distinctive feature of our book is that it presents a wide array of theoretical and empirical methods utilized by researchers and practitioners who study productivity issues. Our book is intended to be a relatively self-contained textbook that can be used in any graduate course devoted to econometrics and production analysis, of use also to upper-level undergraduate students in economics and in production analysis, and to analysts in government and in private business whose research or business decisions require reasoned analytical foundations and reliable and feasible empirical approaches to assessing the productivity and efficiency of their organizations and enterprises. We provide an integrated and synthesized treatment of the topics we cover. We have covered some topics in greater depth, some at a broader scope, but at all times with the same theme of motivating the material with an applied orientation.

Our book is structured in such a way that it can be used as a textbook for (instructed or self-oriented) academics and business consultants in the area of quantitative analysis of productivity of economic systems (firms, industries, regions, countries, etc.). In addition, some parts of this book can be used for short, intensive courses or supplements to longer courses on productivity and other topics, such as empirical industrial organization.