Measurement of productivity index with dynamic DEA

Fare, Grosskopf, Norris and Zhang developed a non-parametric productivity index, Malmquist index, using data envelopment analysis (DEA). The Malmquist index is a measure of productivity progress (regress) and it can be decomposed to different components such as 'efficiency catch-up' and 'technology change'. However, Malmquist index and its components are based on two period of time which can capture only a part of the impact of investment in long-lived assets. The effects of lags in the investment process on the capital stock have been ignored in the current model of Malmquist index. This paper extends the recent dynamic DEA model introduced by Emrouznejad and Thanassoulis and Emrouznejad for dynamic Malmquist index. This paper shows that the dynamic productivity results for Organisation for Economic Cooperation and Development countries should reflect reality better than those based on conventional model.

A cost Malmquist productivity index

This paper develops a productivity index applicable when producers are cost minimisers and input prices are known. The index is inspired by the Malmquist index as extended to productivity measurement. The index developed here is defined in terms of input cost rather than input quantity distance functions. Hence, productivity change is decomposed into overall efficiency and cost technical change. Furthermore, overall efficiency change is decomposed into technical and allocative efficiency change and cost technical change into a part capturing shifts of input quantities and shifts of relative input prices. These decompositions provide a clearer picture of the root sources of productivity change. They are illustrated here in a sample of hospitals; results are computed using non-parametric mathematical programming. © 2003 Elsevier B.V. All rights reserved.

An overall profit Malmquist productivity index with fuzzy and interval data

Although crisp data are fundamentally indispensable for determining the profit Malmquist productivity index (MPI), the observed values in real-world problems are often imprecise or vague. These imprecise or vague data can be suitably characterized with fuzzy and interval methods. In this paper, we reformulate the conventional profit MPI problem as an imprecise data envelopment analysis (DEA) problem, and propose two novel methods for measuring the overall profit MPI when the inputs, outputs, and price vectors are fuzzy or vary in intervals. We develop a fuzzy version of the conventional MPI model by using a ranking method, and solve the model with a commercial off-the-shelf DEA software package. In addition, we define an interval for the overall profit MPI of each decision-making unit (DMU) and divide the DMUs into six groups according to the intervals obtained for their overall profit efficiency and MPIs. We also present two numerical examples to demonstrate the applicability of the two proposed models and exhibit the efficacy of the procedures and algorithms. © 2011 Elsevier Ltd.

A cost Malmquist productivity index capturing group performance

This paper develops an index for comparing the productivity of groups of operating units in cost terms when input prices are available. In that sense it represents an extension of a similar index available in the literature for comparing groups of units in terms of technical productivity in the absence of input prices. The index is decomposed to reveal the origins of differences in performance of the groups of units both in terms of technical and cost productivity. The index and its decomposition are of value in contexts where the need arises to compare units which perform the same function but they can be grouped by virtue of the fact that they operate in different contexts as might for example arise in comparisons of water or gas transmission companies operating in different countries.

CO2 emissions reduction of Chinese light manufacturing industries:a novel RAM-based global Malmquist-Luenberger productivity index

Climate change has become one of the most challenging issues facing the world. Chinese government has realized the importance of energy conservation and prevention of the climate changes for sustainable development of China's economy and set targets for CO2 emissions reduction in China. In China industry contributes 84.2% of the total CO2 emissions, especially manufacturing industries. Data envelopment analysis (DEA) and Malmquist productivity (MP) index are the widely used mathematical techniques to address the relative efficiency and productivity of a group of homogenous decision making units, e.g. industries or countries. However, in many real applications, especially those related to energy efficiency, there are often undesirable outputs, e.g. the pollutions, waste and CO2 emissions, which are produced inevitably with desirable outputs in the production. This paper introduces a novel Malmquist-Luenberger productivity (MLP) index based on directional distance function (DDF) to address the issue of productivity evolution of DMUs in the presence of undesirable outputs. The new RAM (Range-adjusted measure)-based global MLP index has been applied to evaluate CO2 emissions reduction in Chinese light manufacturing industries. Recommendations for policy makers have been discussed.

A framework for measuring global Malmquist–Luenberger productivity index with CO2 emissions on Chinese manufacturing industries

China has achieved significant progress in terms of economic and social developments since implementation of reform and open policy in 1978. However, the rapid speed of economic growth in China has also resulted in high energy consumption and serious environmental problems, which hindering the sustainability of China's economic growth. This paper provides a framework for measuring eco-efficiency with CO2 emissions in Chinese manufacturing industries. We introduce a global Malmquist-Luenberger productivity index (GMLPI) that can handle undesirable factors within Data Envelopment Analysis (DEA). This study suggested after regulations imposed by the Chinese government, in the last stage of the analysis, i.e. during 2011–2012, the contemporaneous frontier shifts towards the global technology frontier in the direction of more desirable outputs and less undesirable outputs, i.e. producing less CO2 emissions, but the GMLPI drops slightly. This is an indication that the Chinese government needs to implement more policy regulations in order to maintain productivity index while reducing CO2 emissions.

The impact of Islamic banking on the cost efficiency and productivity change of Malaysian commercial banks

This study employs stochastic frontier analysis to analyze Malaysian commercial banks during 1996-2002, and particularly focuses on determining the impact of Islamic banking on performance. We derive both net and gross efficiency estimates, thereby demonstrating that differences in operating characteristics explain much of the difference in costs between Malaysian banks. We also decompose productivity change into efficiency, technical, and scale change using a generalised Malmquist productivity index. On average, Malaysian banks experience moderate scale economies and annual productivity change of 2.68 percent, with the latter driven primarily by technical change, which has declined over time. Our gross efficiency estimates suggest that Islamic banking is associated with higher input requirements. However, our productivity estimates indicate that full-fledged Islamic banks have overcome some of these cost disadvantages with rapid technical change, although this is not the case for conventional banks operating Islamic windows. Merged banks are found to have higher input usage and lower productivity change, suggesting that bank mergers have not contributed positively to bank performance. Finally, our results suggest that while the East Asian financial crisis had a short-term cost-reducing effect in 1998, the crisis triggered a more lasting negative impact by increasing the volume of non-performing loans.

The impact of Islamic banking on the cost efficiency and productivity change of Malaysian commercial banks

This study employs Stochastic Frontier Analysis (SFA) to analyse Malaysian commercial banks during 1996–2002, and particularly focuses on determining the impact of Islamic banking on performance. We derive both net and gross efficiency estimates, thereby demonstrating that differences in operating characteristics explain much of the difference in costs between Malaysian banks. We also decompose productivity change into efficiency, technical, and scale change using a generalized Malmquist productivity index. On average, Malaysian banks experience moderate scale economies and annual productivity change of 2.68%, with the latter driven primarily by Technical Change (TC), which has declined over time. Our gross efficiency estimates suggest that Islamic banking is associated with higher input requirements. However, our productivity estimates indicate that full-fledged Islamic banks have overcome some of these cost disadvantages with rapid TC, although this is not the case for conventional banks operating Islamic windows. Merged banks are found to have higher input usage and lower productivity change, suggesting that bank mergers have not contributed positively to bank performance. Finally, our results suggest that while the East Asian financial crisis had a short-term costreducing effect in 1998, the crisis triggered a long-lasting negative impact by increasing the volume of nonperforming loans.

The efficiency and productivity of Malaysian banks:an output distance function approach

This study employs stochastic frontier analysis to analyze Malaysian commercial banks during 1996-2002, and particularly focuses on determining the impact of Islamic banking on performance. We derive both net and gross efficiency estimates, thereby demonstrating that differences in operating characteristics explain much of the difference in outputs between Malaysian banks. We also decompose productivity change into efficiency, technical, and scale change using a generalised Malmquist productivity index. On average, Malaysian banks experience mild decreasing return to scale and annual productivity change of 2.37 percent, with the latter driven primarily by technical change, which has declined over time. Our gross efficiency estimates suggest that Islamic banking is associated with higher input requirements. In addition, our productivity estimates indicate that the potential for full-fledged Islamic banks and conventional banks with Islamic banking operations to overcome the output disadvantages associated with Islamic banking are relatively limited. Merged banks are found to have higher input usage and lower productivity change, suggesting that bank mergers have not contributed positively to bank performance. Finally, our results suggest that while the East Asian financial crisis had an interim output-increasing effect in 1998, the crisis prompted a continuing negative impact on the output performance by increasing the volume of non-performing loans.

Productivity growth and efficiency measurements in fuzzy environments with an application to health care

Health care organizations must continuously improve their productivity to sustain long-term growth and profitability. Sustainable productivity performance is mostly assumed to be a natural outcome of successful health care management. Data envelopment analysis (DEA) is a popular mathematical programming method for comparing the inputs and outputs of a set of homogenous decision making units (DMUs) by evaluating their relative efficiency. The Malmquist productivity index (MPI) is widely used for productivity analysis by relying on constructing a best practice frontier and calculating the relative performance of a DMU for different time periods. The conventional DEA requires accurate and crisp data to calculate the MPI. However, the real-world data are often imprecise and vague. In this study, the authors propose a novel productivity measurement approach in fuzzy environments with MPI. An application of the proposed approach in health care is presented to demonstrate the simplicity and efficacy of the procedures and algorithms in a hospital efficiency study conducted for a State Office of Inspector General in the United States. © 2012, IGI Global.

Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

Productivity change in the water industry in England and Wales:application of the meta-Malmquist Index

This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the meta-Malmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data.

Technical efficiency:efficiency, change, technical progress and productivity growth in the national health systems of continental African countries

In May 2006, the Ministers of Health of all the countries on the African continent, at a special session of the African Union, undertook to institutionalise efficiency monitoring within their respective national health information management systems. The specific objectives of this study were: (i) to assess the technical efficiency of National Health Systems (NHSs) of African countries for measuring male and female life expectancies, and (ii) to assess changes in health productivity over time with a view to analysing changes in efficiency and changes in technology. The analysis was based on a five-year panel data (1999-2003) from all the 53 countries of continental Africa. Data Envelopment Analysis (DEA) - a non-parametric linear programming approach - was employed to assess the technical efficiency. Malmquist Total Factor Productivity (MTFP) was used to analyse efficiency and productivity change over time among the 53 countries' national health systems. The data consisted of two outputs (male and female life expectancies) and two inputs (per capital total health expenditure and adult literacy). The DEA revealed that 49 (92.5%) countries' NHSs were run inefficiently in 1999 and 2000; 50 (94.3%), 48 (90.6%) and 47 (88.7%) operated inefficiently in 2001, 2002, and 2003 respectively. All the 53 countries' national health systems registered improvements in total factor productivity attributable mainly to technical progress. Fifty-two countries did not experience any change in scale efficiency, while thirty (56.6%) countries' national health systems had a Pure Efficiency Change (PEFFCH) index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. All the 53 countries' national health systems registered improvements in total factor productivity, attributable mainly to technical progress. Over half of the countries' national health systems had a pure efficiency index of less than one, signifying that those countries' NHSs pure efficiency contributed negatively to productivity change. African countries may need to critically evaluate the utility of institutionalising Malmquist TFP type of analyses to monitor changes in health systems economic efficiency and productivity over time. African national health systems, per capita total health expenditure, technical efficiency, scale efficiency, Malmquist indices of productivity change, DEA

Measurement efficiency and productivity in SAS/OR

This paper explores the use of the optimisation procedures in SAS/OR software with application to the measurement of efficiency and productivity of decision-making units (DMUs) using data envelopment analysis (DEA) techniques. DEA was originally introduced by Charnes et al. [J. Oper. Res. 2 (1978) 429] is a linear programming method for assessing the efficiency and productivity of DMUs. Over the last two decades, DEA has gained considerable attention as a managerial tool for measuring performance of organisations and it has widely been used for assessing the efficiency of public and private sectors such as banks, airlines, hospitals, universities and manufactures. As a result, new applications with more variables and more complicated models are being introduced. Further to successive development of DEA a non-parametric productivity measure, Malmquist index, has been introduced by Fare et al. [J. Prod. Anal. 3 (1992) 85]. Employing Malmquist index, productivity growth can be decomposed into technical change and efficiency change. On the other hand, the SAS is a powerful software and it is capable of running various optimisation problems such as linear programming with all types of constraints. To facilitate the use of DEA and Malmquist index by SAS users, a SAS/MALM code was implemented in the SAS programming language. The SAS macro developed in this paper selects the chosen variables from a SAS data file and constructs sets of linear-programming models based on the selected DEA. An example is given to illustrate how one could use the code to measure the efficiency and productivity of organisations.