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This book provides a detailed introduction to the theoretical and methodological foundations of production efficiency analysis using benchmarking. Two of the more popular methods of efficiency evaluation are Stochastic Frontier Analysis (SFA) and Data Envelopment Analysis (DEA), both of which are based on the concept of a production possibility set and its frontier. Depending on the assumed objectives of the decision-making unit, a Production, Cost, or Profit Frontier is constructed from observed data on input and output quantities and prices. While SFA uses different maximum likelihood estimation techniques to estimate a parametric frontier, DEA relies on mathematical programming to create a nonparametric frontier. Yet another alternative is the Convex Nonparametric Frontier, which is based on the assumed convexity of the production possibility set and creates a piecewise linear frontier consisting of a number of tangent hyper planes.

Three of the papers in this volume provide a detailed and relatively easy to follow exposition of the underlying theory from neoclassical production economics and offer step-by-step instructions on the appropriate model to apply in different contexts and how to implement them. Of particular appeal are the instructions on (i) how to write the codes for different SFA models on STATA, (ii) how to write a VBA Macro for repetitive solution of the DEA problem for each production unit on Excel Solver, and (iii) how to write the codes for the Nonparametric Convex Frontier estimation. The three other papers in the volume are primarily theoretical and will be of interest to PhD students and researchers hoping to make methodological and conceptual contributions to the field of nonparametric efficiency analysis.



Chapter 1. Estimation of Technical Inefficiency in Production Frontier Models Using Cross-Sectional Data

In this paper, we discuss the specification and estimation of technical efficiency in a variety of stochastic frontier production models. The focus is on cross-sectional models. We start from the basic neoclassical production theory and introduce technical inefficiency in there. Various model specifications with several distributional assumptions on the inefficiency component are explored in detail. Theoretical and empirical issues are illustrated with empirical examples using STATA.
Subal C. Kumbhakar, Hung-Jen Wang

Chapter 2. Data Envelopment Analysis for Performance Evaluation: A Child’s Guide

In this paper we offer a simple exposition of the neoclassical production theoretic foundations of Data Envelopment Analysis (DEA). The concepts of technical efficiency (both input and output oriented), scale efficiency, and cost efficiency are explained, and the corresponding DEA models are described in detail. We offer step-by-step instruction on how to write the codes for solving various DEA models using the Solver option in the widely accessible MS Excel software. An important feature of this paper is a detailed exposition of how to write various Visual Basic Macro programs for solving DEA problems. We also describe the non-convex free disposal hull (FDH) procedure and the second-stage regression analysis that seeks to account for variation in measured efficiency scores due to external factors.
Subhash C. Ray, Lei Chen

Chapter 3. An Introduction to CNLS and StoNED Methods for Efficiency Analysis: Economic Insights and Computational Aspects

This chapter describes the economic insights of the unifying framework known as Stochastic semi-Nonparametric Envelopment of Data (StoNED), which combines the virtues of the widely used neoclassic production models, Data Envelopment Analysis (DEA), and Stochastic Frontier Analysis (SFA). Like DEA, StoNED is able to estimate an axiomatic production function relaxing the functional form specification required in most implementations of SFA. However, StoNED is also consistent with the econometric models of noise, providing a distinct advantage over standard DEA models. Further, StoNED allows for the possibility that systematic inefficiency is negligible consistent with neoclassical theory, thus providing a unifying framework. StoNED is implemented by estimating a conditional mean using convex nonparametric least squares (CNLS) followed by using standard SFA techniques to estimate the average efficiency and decompose the residual. Detailed descriptions of General Algebraic Modeling System (GAMS) and matrix laboratory (MATLAB) code will aid readers in implementing the StoNED estimator.
Andrew L. Johnson, Timo Kuosmanen

Chapter 4. Dynamic Efficiency Measurement

A philosophical problem for studies of inefficiency of firms is how to rationalise inefficiency. Since economics do not have any theory for inefficiency, explaining the results of efficiency analyses is notoriously more difficult than carrying out the estimations. The literature points to measures of inputs and management as not including quality dimensions as a reason for measured efficiency differences, indicating that more work needs to be done on data collection. Strategic behaviour in game situations between owners and management and between management and labour may also show up as inefficiencies. Another reason is technology differences. The frontier production function is the key to information on best practice technology. Estimation of efficiency is usually done for units observed during the same time period; thus, in this respect, the measures are static. Interpretations of dynamic efficiency measurement are offered. The vintage model of substitutability between inputs including capital before investment, but no substitution possibilities after investment, and ex post production possibilities characterised by fixed input coefficients, can rationalise inefficiency due to technology differences. Key elements in understanding structural change are the entering of capacity embodying new technology and exiting of capacity no longer able to yield positive quasi-rent. Three crucial production function concepts are identified as follows: the ex ante micro-unit production function as relevant when investing in new capacity, the ex post micro-production function, and the short-run industry production function giving the production possibilities at the industry level. Productivity measurement, taking these types of production functions into consideration, leads to different interpretations of productivity change than traditional approaches not being clear about which production function concept is used.
Finn R. Førsund

Chapter 5. Efficiency Measures for Industrial Organization

The aim of the paper was to measure the efficiency of an industry and to decompose it in firm efficiencies—which indicate how close firms approximate best practices—and an organization efficiency—which indicates the degree of optimality of the number of firms and their distribution. The latter component provides an efficiency measure for the industrial organization. Economies or diseconomies of scale and of scope play a big role in the determination of the optimal industrial organization and the consequent measurement of the efficiency of an observed industry. Different approaches to the modeling of scale economies will be reviewed. This paper shows in detail how the efficiency of an industrial organization can be measured as a gap between mean firm efficiency and overall industry efficiency. The analysis is extended to dynamic models to measure the role of entry and exit in the efficiency of the industrial organization.
Thijs ten Raa

Chapter 6. Multiplicative and Additive Distance Functions: Efficiency Measures and Duality

In this survey, we present, for the first time, a classification scheme for distance functions, considering two broad groups: the multiplicative and the additive distance functions. Guiding empirical work is one of the objectives of this paper; for this reason, we consider only linear distance functions within a data envelopment analysis (DEA) framework. This also constitutes an easy way of connecting distance functions and efficiency measures. Further, we analyze two classes of distance functions: the ratio-directional distance function and the loss distance function. The former opens the possibility of evaluating productivity change combining directional distance functions, additive in nature, with Malmquist indexes, multiplicative in nature. The latter unifies all the known linear distance functions under a common structure, allowing the numerical evaluation of any linear distance function, as shown by a numerical example. We end up with a revision of duality results so as to highlight the economic relevance of distance functions.
Jesus T. Pastor, Juan Aparicio
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