Cost,revenue and profit efficiency measurement in DEA: A directional distance function approach

Estimation of efficiency of firms in a non-competitive market characterized by heterogeneous inputs and outputs along with their varying prices is questionable when factor-based technology sets are used in data envelopment analysis (DEA). In this scenario, a value-based technology becomes an appropriate reference technology against which efficiency can be assessed. In this contribution, the value-based models of Tone (2002) are extended in a directional DEA set up to develop new directional cost- and revenue-based measures of efficiency, which are then decomposed into their respective directional value-based technical and allocative efficiencies. These new directional value-based measures are more general, and include the existing value-based measures as special cases. These measures satisfy several desirable properties of an ideal efficiency measure. These new measures are advantageous over the existing ones in terms of (1) their ability to satisfy the most important property of translation invariance; (2) choices over the use of suitable direction vectors in handling negative data; and (3) flexibility in providing the decision makers with the option of specifying preferable direction vectors to incorporate their preferences. Finally, under the condition of no prior unit price information, a directional value-based measure of profit inefficiency is developed for firms whose underlying objectives are profit maximization. For an illustrative empirical application, our new measures are applied to a real-life data set of 50 US banks to draw inferences about the production correspondence of banking industry.     

Estimating the technical efficiency of health care systems: A cross-country comparison using the directional distance function

Economic activity produces not only desirable outputs but also undesirable outputs. Undesirable outputs are usually omitted from efficiency assessments (i.e., applications of Data Envelopment Analysis) which fail to express the true production process. The directional distance function model has been used for handling asymmetrically both desirable and undesirable outputs in the assessment process. In the present paper, we apply a generalized directional distance function to measure the efficiency of the health systems of 171 countries. We incorporate both desirable and undesirable outputs into the efficiency assessment without transforming the latter type of outputs into inputs or into their inverse form, as is done in most of the extant studies that deal with the measurement of health efficiency. The methodology that we apply introduces a modified definition of the efficiency score which yields results consistent with those obtained from radial DEA models. In addition, our results are independent of the length of the direction vector.     

A generalized multiplicative directional distance function for efficiency measurement in DEA

For measuring technical efficiency relative to a log-linear technology, a generalized multiplicative directional distance function (GMDDF) is developed using the framework of multiplicative directional distance function (MDDF). Furthermore, a computational procedure is suggested for its estimation. The GMDDF serves as a comprehensive measure of efficiency in revealing Pareto-efficient targets as it accounts for all possible input and output slacks. This measure satisfies several desirable properties of an ideal efficiency measure such as strong monotonicity, unit invariance, translation invariance, and positive affine transformation invariance. This measure can be easily implemented in any standard DEA software and provides the decision makers with the option of specifying preferable direction vectors for incorporating their decision-making preferences. Finally, to demonstrate the ready applicability of our proposed measure, an illustrative empirical analysis is conducted based on real-life data set of 20 hardware computer companies in India.     

A conditional directional distance function approach for measuring regional environmental efficiency: Evidence from UK regions

This paper, by using conditional directional distance functions as introduced by Simar and Vanhems [J. Econometrics 166 (2012) 342–354] modifies the model by Färe and Grosskopf [Eur. J. Operat. Res. 157 (2004) 242–245] and examines the link between regional environmental efficiency and economic growth. The proposed model using conditional directional distance functions incorporates the effect of regional economic growth on regions’ environmental efficiency levels. The results from UK regional data reveal a negative relationship between regions’ GDP per capita and environmental inefficiency up to a certain GDP per capita level. After that level it appears that the relationship becomes positive. As an overall result the regional environmental inefficiency-GDP per capita relationship appears to have a ‘U’ shape form.     

CO2 emissions trading planning in combined heat and power production via multi-period stochastic optimization

The EU emissions trading scheme (ETS) taking effect in 2005 covers CO₂ emissions from specific large-scale industrial activities and combustion installations. A large number of existing and potential future combined heat and power (CHP) installations are subject to ETS and targeted for emissions reduction. CHP production is an important technology for efficient and clean provision of energy because of its superior carbon efficiency. The proper planning of emissions trading can help its potential into full play, making it become a true “winning technology” under ETS. Fuel mix or fuel switch will be the reasonable choices for fossil fuel based CHP producers to achieve their emissions targets at the lowest possible cost. In this paper we formulate CO₂ emissions trading planning of a CHP producer as a multi-period stochastic optimization problem and propose a stochastic simulation and coordination approach for considering the risk attitude of the producer, penalty for excessive emissions, and the confidence interval for emission estimates. In test runs with a realistic CHP production model, the proposed solution approach demonstrates good trading efficiency in terms of profit-to-turnover ratio. Considering the confidence interval for emission estimates can help the producer to reduce the transaction costs in emissions trading. Comparisons between fuel switch and fuel mix strategies show that fuel mix can provide good tradeoff between profit-making and emissions reduction.     

Industry structural inefficiency and potential gains from mergers and break-ups: A comprehensive approach

An efficiency indicator of industry configuration (allowing for entry/exit of firms) is presented which accounts for four sources components: (1) size inefficiencies arising from firms which can be conveniently split into smaller units; (2) efficiency gains realized through merger of firms; (3) re-allocation of inputs and outputs among firms; (4) technical inefficiencies. The indicator and its components are computed using linear and mixed-integer programming (data envelopment analysis models). A method to monitor the evolution of these components in time is introduced. Data on hospitals in Australia show that technical inefficiency of hospitals accounts for less than 15% of total industry inefficiency, with 40% attributable to size inefficiencies and the rest to potential mergers and re-allocation effects.     

Simulation with system dynamics and fuzzy reasoning of a tax policy to reduce CO2 emissions in the residential sector

This methodological paper presents a planning and control methodology illustrated by a simplified case study on the carbon-tax design in the residential sector. The first objective is to show how to simulate with system dynamics the consumers’ behaviour and the continuous tax-control mechanism depending on few important feedbacks, often ignored in static macroeconomic modelling. A second objective is to show how to aggregate external data driving this model and stemming from different sources with various credibility levels. This is realised by means of fuzzy-reasoning techniques incorporated into the system-dynamics model.     

Local air pollutant emission reduction and ancillary carbon benefits of SO2 control policies: Application of AIM/CGE model to China

While a great deal of literature has been published in recent years on the ancillary benefits of greenhouse gas mitigation (e.g., reductions in local air pollution), less attention has been focused on the climate benefits of local air pollution strategies themselves. Local air pollution is, however, a more immediate issue now faced by developing countries. This study assesses the impacts on local air pollutant emission reduction and ancillary CO₂ emission reduction of SO₂ control policies in China, such as a sulphur tax, SO₂ total emissions control (TEC), and improvement of energy efficiency, based on the Asia-Pacific Integrated Model (AIM)/Computable General Equilibrium (CGE) country model. The simulation period is from 1997 to 2020. Major conclusions include the following: an SO₂ emission cap will help to control SO₂ emissions, but will result in a large GDP loss; the role of a SO₂ emission tax at the present level is very limited; and an ancillary carbon reduction benefit can be achieved through the introduction of SO₂ control policies in China.     

A conjecture on a class of elements of finite order in K2Fp

For a local field F the finite subgroups of K₂ F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.     

Preparation and optical properties of GaSb nanoparticles embedded in SiO2 composite films

The composite films of GaSb nanoparticles embedded in SiO₂ matrices were fabricated by radio-frequency magnetron co-sputtering. Transmission electron microscope and X-ray diffraction pattern indicate that the GaSb nanoparticles were uniformly dispersed in SiO₂ matrices. Room temperature transmission spectra exhibit a blue shift of about 2.73 eV. The blue shift increases with decreasing size of GaSb nanoparticles, suggesting the existence of quantum size effects. Room temperature Raman spectra show that there is a larger Raman peak red shift and broadening of the composite films than that of bulk GaSb. This phenomenon is explained by photon confinement effect and tensile stress effect     

Bifurcation set and number of limit cycles in Z2-equivariant planar vector fields of degree 5

An Z₂-equivariant polynomial Hamiltonian system of degree 5 with two perturbation terms is considered in this paper. The phase plane (a, b) is divided into 15 different regions which give the bifurcation set of the system. Using the bifurcation theory of planar dynamical system and the method of detection function, we obtain the bifurcation set and the configurations of compound eyes of the system with 21 or 23 limit cycles.