The measurement of profit, profitability, cost and revenue efficiency through data envelopment analysis: A comparison of models using BenchmarkingEconomicEfficiency.jl

We undertake a systematic comparison of existing models measuring and decomposing the economic efficiency of organizations. For this purpose we introduce the package BenchmarkingEconomicEfficiency.jl for the open-source Julia language including a set of functions to be used by scholars and professionals working in the fields of economics, management science, engineering, and operations research. Using mathematical programming methods known as Data Envelopment Analysis, the software develops code to decompose economic efficiency considering alternative definitions: profit, profitability, cost and revenue. Economic efficiency can be decomposed, multiplicative or additively, into a technical (productive) efficiency term and a residual term representing allocative (or price) efficiency. We include traditional decompositions like the radial efficiency measures associated with the input (cost) and output (revenue) approaches, as well as new ones corresponding to the Russell measures, the directional distance function, DDF (including novel extensions like the reverse DDF, modified DDF, or generalizations based on Hölder norms), the generalized distance function, and additive measures like the slack based measure, their weighted variants, etc. Moreover, regardless the underlying economic efficiency model, many of these technical inefficiency measures are available for calculation in a computer software for the first time. This article details the theoretical methods and the empirical implementation of the functions, comparing the obtained results using a common dataset on Taiwanese BanksJosé L. Zofío thanks the grant PID2019-105952 GB-I00 funded by Ministerìo de Ciencia e Innovación/ Agencia Estatal de Investigación /10.13039/50110001103

How to properly decompose economic efficiency using technical and allocative criteria with non-homothetic DEA technologies

We discuss how to properly decompose economic efficiency when the underlying technology is non-homothetic using alternative allocative and technical efficiency criteria. We first show that only under the production of one output and assuming the particular case of constant returns to scale homotheticity, we may claim that the standard radial models correctly measure pure technical efficiency. Otherwise, when non-homotheticity is assumed, we then show that these traditional estimations would measure an undetermined mix of technical and allocative efficiency. To restore a consistent measure of technical efficiency in the non-homothetic case we introduce a new methodology that takes as reference for the economic efficiency decomposition the preservation of the allocative efficiency of firms producing in the interior of the technology. This builds upon the so-called reversed approach recently introduced by Bogetoft et al. (2006) that allows estimating allocative efficiency without presuming that technical efficiency has been already accomplished. We illustrate our methodology within the Data Envelopment Analysis framework adopting the most simple nonhomothetic BCC model and a numerical example. We show that there are significant differences in the allocative and technical efficiency scores depending on the approac

Pay for performance in health care: a new best practice tariff-based tool using a log-linear piecewise frontier function and a dual–primal approach for unique solutions

Health care systems worldwide have faced a problem of resources scarcity that, in turn, should be allocated to the health care providers according to the corresponding population needs. Such an allocation should be as much as effective and efficient as possible to guarantee the sustainability of those systems. One alternative to reach that goal is through (prospective) payments due to the providers for their clinical procedures. The way that such payments are computed is frequently unknown and arguably far from being optimal. For instance, in Portugal, public hospitals are clustered based on criteria related to size, consumed resources, and volume of medical acts, and payments associated with the inpatient services are equal to the smallest unitary cost within each cluster. First, there is no reason to impose a single benchmark for each inefficient hospital. Second, this approach disregards dimen sions like quality (and access) and the environment, which are paramount for fair comparisons and benchmarking exercises. This paper proposes an innovative tool to achieve best-practices tariff. This tool merges both quality and financial sustain ability concepts, attributing a hospital-specific tariff that can be different from hospital to hospital. That payment results from the combination of costs related to a set of potential benchmarks, keeping quality as high as possible and higher than a user-predefined threshold, and being able to generate considerable cost savings. To obtain those coefficients we propose and detail a log-linear piecewise frontier function as well as a dual–primal approach for unique solutions.info:eu-repo/semantics/publishedVersio

New Definitions of Economic Cross-Efficiency

Overall efficiency measures were introduced in the literature for evaluating the economic performance of firms when reference prices are available. These references are usually observed market prices. Recently, Aparicio and Zofío (2019) have shown that the result of applying cross-efficiency methods (Sexton et al., 1986), yielding an aggregate multilateral index that compares the technical performance of firms using the shadow prices of competitors, can be precisely reinterpreted as a measure of economic efficiency. They termed the new approach ‘economic cross-efficiency’. However, these authors restrict their analysis to the basic definitions corresponding to the Farrell (1957) and Nerlove (1965) approaches, i.e., based on the duality between the cost function and the input distance function and between the profit function and the directional distance function, respectively. Here we complete their proposal by introducing new economic cross-efficiency measures related to other popular approaches for measuring economic performance. Specifically those based on the duality between the profitability (maximum revenue to cost) and the generalized (hyperbolic) distance function, and between the profit function and either the weighted additive or the Hölder distance function. Additionally, we introduce panel data extensions related to the so-called cost Malmquist index and the profit Luenberger indicator. Finally, we illustrate the models resorting to Data Envelopment Analysis techniques--from which shadow prices are obtained, and considering a banking industry dataset previously used in the cross-efficiency literature

Transit Costs and Cost Efficiency: Bootstrapping Nonparametric Frontiers.

This paper explores a selection of recently proposed bootstrapping techniques to estimate non-parametric convex (DEA) cost frontiers and efficiency scores for transit firms. Using a sample of Norwegian bus operators, the key results can be summarised as follows: (i) the bias implied by uncorrected cost efficiency measures is numerically important (close to 25%), (ii) the bootstrapped-based test rejects the constant returns to scale hypothesis (iii) explaining patterns of efficiency scores using a two-stage bootstrapping approach detects only one significant covariate, in contrast to earlier results highlighting, e.g., the positive impact of high-powered contract types. Finally, comparing the average inefficiency obtained for the Norwegian data set with an analogous estimate for a smaller French sample illustrates how the estimated differences in average efficiency almost disappear once sample size differences are accounted for.

Return to Dollar, Generalized Distance Function and the Fisher Productivity Index

Exploring the duality between a return to dollar definition of profit and the generalized distance function we establish the relationship between the Laspeyres, Paasche and Fisher productivity indexes and their alternative Malmquist indexes counterparts. By proceeding this way, we propose a consistent decomposition of these productivity indexes into two mutually exclusive components. A technical component represented by the Malmquist index and an economical component which can be identified with the contribution that allocative criteria make to productivity change. With regard to the Fisher index, we indicate how researchers can further decompose the Malmquist technical component rendering explicit the sources of productivity change. We also show how the proposed model can be implemented by means of Data Envelopment Analysis techniques, and illustrate the empirical process with an example data set.Generalized Distance Function; Return to Dollar; Fisher and Malmquist Productivity Indexes

Estimation of semiparametric stochastic frontiers under shape constraints with application to pollution generating technologies

A number of studies have explored the semi- and nonparametric estimation of stochastic frontier models by using kernel regression or other nonparametric smoothing techniques. In contrast to popular deterministic nonparametric estimators, these approaches do not allow one to impose any shape constraints (or regularity conditions) on the frontier function. On the other hand, as many of the previous techniques are based on the nonparametric estimation of the frontier function, the convergence rate of frontier estimators can be sensitive to the number of inputs, which is generally known as “the curse of dimensionality” problem. This paper proposes a new semiparametric approach for stochastic frontier estimation that avoids the curse of dimensionality and allows one to impose shape constraints on the frontier function. Our approach is based on the singleindex model and applies both single-index estimation techniques and shape-constrained nonparametric least squares. In addition to production frontier and technical efficiency estimation, we show how the technique can be used to estimate pollution generating technologies. The new approach is illustrated by an empirical application to the environmental adjusted performance evaluation of U.S. coal-fired electric power plants.stochastic frontier analysis (SFA), nonparametric least squares, single-index model, sliced inverse regression, monotone rank correlation estimator, environmental efficiency