DEA models with Russell measures

In real applications, data envelopment analysis (DEA) models with Russell measures are widely used although their theoretical studies are scattered over the literature. They often have seemingly similar structures but play very different roles in performance evaluation. In this work, we systematically examine some of the models from the viewpoint of preferences used in their Production Possibility Sets (PPS). We identify their key differences through the convexity and free-disposability of their PPS. We believe that this study will provide guidelines for the correct use of these models. Two empirical cases are used to compare their differences

Métodos para incorporar juicios de valor en las medidas de eficiencia técnica basadas en DEA

281 p.En la siguiente tesis se proponen metodologías basadas en modelos de Análisis Envolvente de Datos (Base de datos Envelopment Analysis – DEA), las cuales permiten realizar un cálculo de las preferencias de un agente decisor con respecto a los multiplicadores, con el fin de obtener mejores estimaciones de eficiencia en la evaluación de las unidades organizacionales. En estas metodologías se utilizan medidas de eficiencia no radiales, para la incorporación de todas las fuentes de ineficiencia. Este desarrollo de métodos para incorporar juicios de valor a las medidas de eficiencia se separan en tres metodologías. En primer lugar, tomando de base el trabajo realizado por Zhu (1996), que incorpora juicios de valor a través de asignación de pesos a las entradas y a las salidas, se proponen dos metodologías para el cálculo de estos pesos. Estas metodologías serán realizadas para la versión de rendimiento a escala constante (CRS-constant returns to scale) del modelo propuesto por Zhu (1996). Además serán comparadas entre sí, y con los resultados del modelo de Russell (Färe y Lovell., 1978) y DEA/CRS (Charnes et al., 1978). Este se realiza para demostrar las diferencias entre aplicar medidas de eficiencia no radiales y medida de eficiencia radial. En segundo lugar, basado de Thanassoulis y Allen (1998), se incorporan de juicios de valor a través de unidades no observadas. Para esto se crean dos métodos para la generación de unidades no observadas y se comparan estos métodos. Los resultados de estas metodologías son comparados de manera separada, tanto para sus orientaciones de entradas, como de salidas, en los cuales para el modelo propuesto por Zhu (1996)es comparado en sus dos métodos de cálculos de pesos y contrastadas con el modelo de Russell (Färe y Lovell., 1978) y DEA/CRS (Charnes et al., 1978), además de entre ellos, mientras que los métodos de unidades no observadas es analizado aparte, debido a que no es mediante la importancia de los factores. Concluyendo que la incorporación de pesos, al incorporar los juicios de valor permite tener un orden más realista de la eficiencia dado a que los decisores ya tienen juicio formado en relación a la importancia de las entradas y las salidas, y entregando en todos los casos diferencias entre los modelos no radiales de los radiales, siendo este último menos restrictivo. Mientras que para la integración de DMUs no observadas, se solicita una mayor cantidad de experimentación para tener diferencias significativas entre ambos métodos.Palabras Claves: DEA, medidas de eficiencia no radial, juicios de valor, unidades no observadas./ABSTRACR: In the following thesis methodologies based on models of Base de datos Envelopment Analysis (Base de datos Envelopment Analysis - DEA) are proposed, which allows a calculation of the preferences of a decision maker with respect to the multipliers, in order to obtain better estimates of efficiency in the evaluation of the organizational units. In these methods no radial efficiency measures are used for the incorporation of all sources of inefficiency. The development of methods for incorporating value judgments to the efficiency measures are separated into three methodologies. First, taking the basis work done by Zhu (1996), which incorporates value judgments by assigning weights to the inputs and outputs, two methodologies for calculating these weights are proposed. These methodologies will be made for the performance version constant scale (CRS-constant returns to scale) proposed by Zhu model (1996). Furthermore,both models will be compared with each other, and with the results of the model of Russell (Färe and Lovell., 1978) and DEA / CRS (Charnes et al., 1978). This is done to show differences between apply non- radial and radial efficiency measures.Second, based on Thanassoulis and Allen (1998), incorporate value judgments through unobserved units. For this, two methods of generating units not observed are created and compared.The results of these methodologies are compared separately for both orientations of inputs and outputs, in which for the proposed by Zhu model (1996) is compared in the two methods of calculations of weights and compared with the model Russell (FARE Lovell., 1978) and DEA / CRS (Charnes et al., 1978), besides between them, while methods units not observed is analyzed separately because it is not by the importance of the factors. Concluding that the incorporation of weights, incorporating value judgments allows a more realistic efficiency given by decision makers and to have judgment made in relation to the importance of inputs and outputs, and delivering in each case non-radial difference between the radial patterns, the latter being less restrictive. While the integration of unobserved DMUs, greater amount of experimentation is required to have significant differences between the two methods. Keywords: DEA, non-radial measures of efficiency, value judgments, unobserved units

Data Envelopment Analysis and Commercial Bank Performance: A Primer with Applications to Missouri Banks

This paper describes a particular methodology called Data Envelopment Analysis (DEA), that has been used previously to analyze the relative efficiencies of industrial firms, universities, hospitals, military operations, baseball players and, more recently, commercial banks. The use of DEA is demonstrated by evaluating the management of 60 Missouri commercial banks for the period from 1984 to 1990.IC2 Institut

Interval and fuzzy optimization. Applications to data envelopment analysis

Enhancing concern in the efficiency assessment of a set of peer entities termed Decision Making Units (DMUs) in many fields from industry to healthcare has led to the development of efficiency assessment models and tools. Data Envelopment Analysis (DEA) is one of the most important methodologies to measure efficiency assessment through the comparison of a group of DMUs. It permits the use of multiple inputs/outputs without any functional form. It is vastly applied to production theory in Economics and benchmarking in Operations Research. In conventional DEA models, the observed inputs and outputs possess precise and realvalued data. However, in the real world, some problems consider imprecise and integer data. For example, the number of defect-free lamps, the fleet size, the number of hospital beds or the number of staff can be represented in some cases as imprecise and integer data. This thesis considers several novel approaches for measuring the efficiency assessment of DMUs where the inputs and outputs are interval and fuzzy data. First, an axiomatic derivation of the fuzzy production possibility set is presented and a fuzzy enhanced Russell graph measure is formulated using a fuzzy arithmetic approach. The proposed approach uses polygonal fuzzy sets and LU-fuzzy partial orders and provides crisp efficiency measures (and associated efficiency ranking) as well as fuzzy efficient targets. The second approach is a new integer interval DEA, with the extension of the corresponding arithmetic and LU-partial orders to integer intervals. Also, a new fuzzy integer DEA approach for efficiency assessment is presented. The proposed approach considers a hybrid scenario involving trapezoidal fuzzy integer numbers and trapezoidal fuzzy numbers. Fuzzy integer arithmetic and partial orders are introduced. Then, using appropriate axioms, a fuzzy integer DEA technology can be derived. Finally, an inverse DEA based on the non-radial slacks-based model in the presence of uncertainty, employing both integer and continuous interval data is presented

Families of Linear Efficiency Programs based on Debreu's Loss Function

Gerard Debreu introduced a well known radial efficiency measure which he called a “coefficient of resource utilization.†He derived this scalar from a much less well known “dead loss†function that characterizes the monetary value sacrificed to inefficiency, and which is to be minimized subject to a normalization condition. We use Debreu’s loss function, together with a variety of normalization conditions, to generate several popular families of linear efficiency programs. Our methodology also can be employed to generate entirely new families of linear efficiency programs.

Data Envelopment Analysis Models of Investment Funds

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Productivity drivers in European banking: Country effects, legal tradition and market dynamics

This paper analyses efficiency drivers of a representative sample of European banks by means of the two-stage procedure proposed by Simar and Wilson (2007). In the first stage, the technical efficiency of banks is estimated using DEA (data envelopment analysis) in order to establish which of them are most efficient. Their ranking is based on total productivity in the period 1993-2003. In the second stage, the Simar and Wilson (2007) procedure is used to bootstrap the DEA scores with a truncated bootstrapped regression. The policy implications of our findings are considered

The shape of aggregate production functions: evidence from estimates of the World Technology Frontier

The article provides multifaceted evidence on the shape of the aggregate country-level production function, derived from the World Technology Frontier, estimated on the basis of annual data on inputs and output in 19 highly developed OECD countries in the period 1970–2004. A comparison of its estimates based on Data Envelopment Analysis and Bayesian Stochastic Frontier Analysis uncovers a number of significant discrepancies between the nonparametric estimates of the frontier and the Cobb–Douglas and translog production functions in terms of implied efficiency levels, partial elasticities, and returns-to-scale properties. Furthermore, the two latter characteristics as well as elasticities of substitution are found to differ markedly across countries and time, providing strong evidence against the constant-returns-to-scale (CRS) Cobb–Douglas specification, frequently used in related literature. We also find notable departures from perfect substitutability between unskilled and skilled labor, consistent with the hypotheses of skill-biased technical change and capital–skill complementarity. In the Appendix, as a corollary from our results, we have also conducted a series of development accounting and growth accounting exercises.world technology frontier, aggregate production function, Data Envelopment Analysis, Stochastic Frontier Analysis, partial elasticity, returns to scale, substitutability

On the measurement of technological progress across countries

We construct 14 alternative measures of technological progress for 19 OECD countries over the period 1970–2000, distinguishing between measures of productivity gains actually obtained in a given country (TFP growth, Malmquist index) and technological progress at the world technology frontier (potential TFP growth, the “frontier shift” index). We then compare these measures according to a range of characteristics, shedding light on some of their relative weaknesses and strengths. We find that these characteristics are sensitive to the precision of estimates of the world technology frontier, and then we demonstrate that this precision can be increased substantially by allowing for imperfect substitutability between unskilled and skilled labor and using US state-level data apart from cross-country data for estimating the world technology frontier. Because none of the 14 measures dominates all others on all dimensions, we conclude that the choice of appropriate measurement method should be suited to the question addressed in each particular study.technological progress, world technology frontier, countrylevel data, US state-level data, production function, DEA

Estimating Vessel Efficiency Using a Bootstrapped Data Envelopment Analysis Model

Technical efficiency, which measures how well a firm transforms inputs into outputs, gives fishery managers important information concerning the economic status of the fishing fleet and how regulations may be impacting vessel profitability. Data envelopment analysis (DEA), and the stochastic production frontier (SPF) have emerged as preferred methods to estimate efficiency in fisheries. Although each of the approaches has strengths and weaknesses, DEA has often been criticized because it is "deterministic" and fails to account for noise in the data. This paper presents a method for examining the underlying statistical structure of DEA models using bootstrap methods and readily available software. The approach is then applied to a case study of the U.S. mid-Atlantic sea scallop dredge fleet. Results show that the 95% confidence interval for technically efficient output is well above the maximum sustained yield (MSY) level of output.Bootstrap methods, data envelopment analysis, technical efficiency., Research Methods/ Statistical Methods, C44, Q22,