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.     

A circular global profit Malmquist productivity index in data envelopment analysis

To remove the difficulty caused by different profit frontiers in different periods of time for calculating profit efficiency changes and its components, this paper proposes a circular global profit Malmquist productivity index. This index is applicable when the input costs and output prices are known and when producers seek to maximize the total profit of their decision making units (DMUs). To this end, first, two methods are introduced to obtain the common costs and prices with or without the decision maker’s preferences, and then, a common profit efficient frontier is obtained. The proposed index can be decomposed into several circular components, viz., profit efficiency change, profit technical change, technical efficiency change, allocative efficiency change, technical change, and cost/price change. The proposed index is then generalised to compare the productivity of two different units at two different points in time. The global profit Malmquist productivity index developed here is unique and is computed using nonparametric linear programming model known as data envelopment analysis (DEA), and there is no need to resort to the geometric mean in the calculation. To illustrate the proposed index and its components, numerical examples at three successive periods of time are given.     

Costs and efficiency of higher education institutions in England: a DEA analysis

As student numbers in higher education in the UK have expanded during recent years, it has become increasingly important to understand its cost structure. This study applies Data Envelopment Analysis (DEA) to higher education institutions in England to assess their cost structure, efficiency and productivity. The paper complements an earlier study that used parametric methods to analyse the same panel data. Interestingly, DEA provides estimates of subject-specific unit costs that are in the same ballpark as those provided by the parametric methods. The paper then extends the previous analysis and finds that further student number increases of the order of 20–27% are feasible through exploiting operating and scale efficiency gains and also adjusting student mix. Finally the paper uses a Malmquist index approach to assess productivity change in the UK higher education. The results reveal that for a majority of institutions productivity has actually decreased during the study period.     

Nonparametric estimation of education productivity incorporating nondiscretionary inputs with an application to Dutch schools

In this paper we develop a Malmquist productivity index for public sector production characterized by the influence of environmental variables. We extend Johnson and Ruggiero (2011) to the more general case of variable returns to scale to further decompose the Malmquist productivity index into technical, efficiency, scale and environmental change. We apply our model to analyze productivity of Dutch schools using 2002–2007 data. The results indicate that the environment influences the productivity index as well as the technical, efficiency, scale and environmental change components. We see that schools with a moderate classification of environment have the highest productivity numbers. In line with expectations, schools with the worst environment also perform worse and would perform better with an improved environment.     

Efficiency and total quality management in health care organizations: A dynamic frontier approach

This paper analyses hospital performance using Data Envelopment Analysis (DEA) and the Malmquist productivity index. We follow two approaches to quantify movements in productivity: (1) the traditional approach that only considers output and input variables; and (2) a more comprehensive approach that incorporates movements in quality and restricts some achievements, if quality is reduced. On the premise that the indicator for quality (nosocomial infections) is equivalent to a bad output, we explore the characteristics of, and compare the results of, the different technological ways to incorporate quality (good or bad attributes, strong or weak disposability technological assumptions). After discussing the virtues and limitations of the existing possibilities, the paper presents a better formulation that allows the preservation of TQM postulates. The decomposition in the Malmquist productivity index shows an improvement in productivity and a positive technical change, especially when quality is introduced. This paper forms part of a more extensive research work, financed by the Spanish Science and Technology Ministry (ref. SEC2003-047707).     

Multi-period efficiency and Malmquist productivity index in two-stage production systems

Conventional two-stage data envelopment analysis (DEA) models measure the overall performance of a production system composed of two stages (processes) in a specified period of time, where variations in different periods are ignored. This paper takes the operations of individual periods into account to develop a multi-period two-stage DEA model, which is able to measure the overall and period efficiencies at the same time, with the former expressed as a weighted average of the latter. Since the efficiency of a two-stage system in a period is the product of the two process efficiencies, the overall efficiency of a decision making unit (DMU) in the specified period of time can be decomposed into the process efficiency of each period. Based on this decomposition, the sources of inefficiency in a DMU can be identified. The efficiencies measured from the model can also be used to calculate a common-weight global Malmquist productivity index (MPI) between two periods, in that the overall MPI is the product of the two process MPIs. The non-life insurance industry in Taiwan is used to verify the proposed model, and to explain why some companies performed unsatisfactorily in the specified period of time.     

A global cost Malmquist productivity index using data envelopment analysis

This paper proposes a global cost Malmquist productivity index, new cost Malmquist productivity index, that is circular and that gives a single measure of productivity change. The index is inspired by the global Malmquist productivity index as extended to productivity measurement. Decomposition of the proposed cost Malmquist productivity index is presented. Numerical results are presented for an example taken from the literature to illustrate the proposed algorithm.     

Combining the assumptions of variable and constant returns to scale in the efficiency evaluation of secondary schools

Our paper reports on the use of data envelopment analysis (DEA) for the assessment of performance of secondary schools in Malaysia during the implementation of the policy of teaching and learning mathematics and science subjects in the English language (PPSMI). The novelty of our application is that it makes use of the hybrid returns-to-scale (HRS) DEA model. This combines the assumption of constant returns to scale with respect to quantity inputs and outputs (teaching provision and students) and variable returns to scale (VRS) with respect to quality factors (attainment levels on entry and exit) and socio-economic status of student families. We argue that the HRS model is a better-informed model than the conventional VRS model in the described application. Because the HRS technology is larger than the VRS technology, the new model provides a tangibly better discrimination on efficiency than could be obtained by the VRS model. To assess the productivity change of secondary schools over the years surrounding the introduction of the PPSMI policy, we adapt the Malmquist productivity index and its decomposition to the case of HRS model.     

Do mergers improve hospital productivity?

This paper complements the existing literature on hospital mergers by using data envelopment analysis (DEA) to generate both efficiency and productivity measures to ascertain whether hospital mergers, at least in the short run, result in performance gains. Using data over the period 1996–1998, we apply DEA, both pre-merger and post-merger, to set of hospitals that merged in 1997 as well as to a matching control group of non-merging hospitals over the same timeframe. A comparison of DEA efficiency scores and the Malmquist index values across the case and control hospitals allow us to assess whether any increase in productivity is the result of a merger rather than simply and randomly adding two hospitals' inputs and outputs together.     

Malmquist生产率指数评析结果——技术变动的新诠释

为了判断创新活动是否有利于技术进步,预测技术变动的发展趋势,将Malmquist生产率指数评价结果进一步分解,挖掘技术变动的深层次知识,并将之应用于我国电子行业的技术创新活动分析。研究表明,运用经济学中的等产量曲线的分析原理,能够获取Malmquist生产率测算结果中技术变动指数各个构成部分所包含的管理信息,并可以判断决策单元的技术变动方向是否有利,最后对我国电子行业技术创新活动的实证研究发现我国电子行业创新活动总体上朝着有利于技术进步的方向发展。     

A non-radial DEA approach to measuring environmental performance

Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. Past studies about the application of DEA to environmental performance measurement often follow the concept of radial efficiency measures. In this paper, we present a non-radial DEA approach to measuring environmental performance, which consists of a non-radial DEA-based model for multilateral environmental performance comparisons and a non-radial Malmquist environmental performance index for modeling the change of environmental performance over time. A case study of OECD countries using the proposed non-radial DEA approach is also presented. It is found that the environmental performance of OECD countries as a whole has been improved from 1995 to 1997.     

A generalized Malmquist productivity index

In 1953 Sten Malmquist, a Swedish economist and statistician, published inTrabajos de Estadística the foundations of a productivity index which now bears his name. In this paper we generalize the Malmquist productivity index. We show that (i) the generalized Malmquist productivity index can be expressed as the product of a Malmquist productivity index and a Malmquist scale index; (ii) the generalized Malmquist productivity index can also be expressed as the ratio of a Malmquist output quantity index to a Malmquist input quantity index; (iii) the geometric mean of a pair of Malmquist scale indexes is equal to the reciprocal of the Törnqvist scale index, which implies that (iv) the geometric mean of a pair of generalized Malmquist productivity indexes is equal to a Törnqvist productivity index.     

Productivity development of Norwegian institutions of higher education 2004–2013

Productivity growth of institutions of higher education is of interest for two main reasons: education is an important factor for productivity growth of the economy, and in countries where higher education is funded by the public sector, accountability of resource use is of key interest. Educational services consist of teaching, research and the “third mission” of dissemination of knowledge to the society at large. A bootstrapped Malmquist productivity change index is used to calculate productivity development for Norwegian institutions of higher education over the 10-year period 2004–2013. The confidence intervals from bootstrapping allow part of the uncertainty of point estimates stemming from sample variation to be revealed. The main result is that the majority of institutions have had a positive productivity growth over the total period. However, when comparing with growth in labour input, the impact on productivity varies a lot.     

基于超效率DEA模型的中国各地区钢铁行业能源效率及节能减排潜力分析

DEA方法对具有多投入和多产出指标的各个DMU之间的相对效率评价具有独特优势.首先应用超效率DEA模型对2005-2007年间中国各地区钢铁行业的全要素能源效率作出评价,并计算了此间中国各地区钢铁行业的节能减排潜力;然后利用Malmquist效率指数对钢铁行业能源利用效率的变动进行动态分析;最后应用Tobit回归模型对影响钢铁行业节能减排的因素进行了多元分析.     

基于DEA-Tobit方法的人工智能行业上市公司融资效率研究

人工智能产业发展对实现我国总体产业升级和供给侧结构性改革具有重要意义。该领域投资态势向好,但融资渠道较为混乱。本文结合我国37家人工智能产业上市公司2013~2016年的融资数据,首先采用了DEA方法对我国人工智能产业上市公司融资效率进行测度,同时采用Malmquist指数法从动态角度来反映人工智能产业上市公司融资变化,然后通过Tobit方法构建融资效率影响因素模型。从实证结果可以看出,人工智能产业融资效率不高,大多数企业并未达到DEA有效,综合技术效率的不高主要是由于规模效率较低引起的;资本结构、企业的营业能力和成长性与融资效率具有显著的相关性,是影响融资效率的重要因素。最后从提高融资资金利用率、优化融资结构两个方面提出了相关建议。     

基于复合DEA和Malmquist指数的科技投入产出效率评价

本文利用非参数方法DEA对2004~2008年福建省9个地市的科技投入产出效率进行评价,并应用复合DEA方法和Malmquist指数来分析科技投入产出效率非DEA有效地区的形成原因及其生产力的动态变化。实证结果显示,福建省各市的科技效率总体呈上升趋势,但各地区科技的投入产出规模以及效率还存在着较大的差距,而其生产力的提高主要是技术效率所带来的贡献,技术进步则呈现大起大落的状态,技术进步对生产力的拉动仍需得到进一步加强与巩固,应加大科技研发投入和强化科技的引进创新,并注重消化吸收创新。     

Technical change and the von Neumann coefficient of uniform expansion

We study technical change for multi-product technologies to examine its effect on economic growth for 27 OECD (Organization for Economic Cooperation and Development) countries during 1951–2014. We review the Malmquist index and reexamine von Neumann’s model of an expanding economy. We estimate the coefficient of uniform expansion via DEA (Data Envelopment Analysis) and use it to measure technical change via a Solow residual and an alternative von Neumann technical change index which equals the difference between the growth rates of the slowest growing output and the fastest growing input. We also exploit a property of constant returns to scale in order to examine technical change of the average technology. During 2005–2014 the Solow residual shows relatively fast technical change. In contrast, the Malmquist, average technology and alternative von Neumann technical change indexes show negative or stagnant technical change.     

基于DEA-Malmquist和Tobit regression的物联网上市公司效率评价

物联网的发展已经成为我国实现经济转型的有力支撑,但其发展过程中呈现的波动性问题仍亟需深入研究.从效率的角度,对我国19家物联网公司的发展状况进行了研究.首先,运用DEA模型测算了19家公司2013-2015年的技术效率、纯技术效率、规模效率以及各公司的规模收益状况.计算结果表明物联网上市公司的效率在整体上呈现上升趋势,只有同方股份在三年内规模收益状况为递减.其次,运用DEA-Malmquist测算了19家公司的技术效率变化指数、技术进步指数、纯技术效率变化指数、规模效率变化指数和全要素生产率变化指数.结果表明,技术进步指数低是制约这19家公司生产力发展的关键问题.最后,运用Tobit regression分析了11项财务指标对技术效率、纯技术效率以及规模效率影响的显著性,得出财务指标对规模效率存在显著影响.基于效率和影响因素分析的实际,为物联网上市公司的发展提供合理的建议,推动我国物联网产业实现良性有序发展.     

中国电力生产业的效率:一个基于政府管制的研究视角

通过使用数据包络分析(DEA)和Malmquist指数分析方法对中国电力生产业从1998年到2007年的技术效率和全要素生产率(TFP)进行了估算,并从效率比较以及生产率变化的角度分析了中国电力管制政策的效果。实证分析表明,中国电力产业的技术效率经历了一个先下降后上升的U型过程,地理区位、企业类型、企业性质、电力管制改革等因素对效率有着显著的影响。TFP在10年间经历了缓慢的增长,技术效率的提高解释了TFP的所有变化。从管制政策的效果来看,从1997年开始的电力管制改革对电力生产企业的技术效率产生了实质性的影响,促进了企业技术效率的提高。但是,电力管制改革对TFP的影响并不明显,特别是在促进企业的技术进步方面并没有取得明显效果。