Comparing Malmquist and Hicks–Moorsteen productivity indices: Exploring the impact of unbalanced vs. balanced panel data

We explore the effect of balancing unbalanced panel data when estimating primal productivity indices using non-parametric frontier estimators. First, we list a series of pseudo-solutions aimed at making an unbalanced panel balanced. Then, we discuss some intermediate solutions (e.g., balancing 2-years by 2 years). Furthermore, we link this problem with a variety of literatures on infeasibilities, statistical inference of non-parametric frontier estimators, and the index theory literature focusing on the dynamics of entry and exit in industries. We then empirically illustrate these issues comparing both Malmquist and Hicks–Moorsteen productivity indices on two data sets. In particular, we test for the differences in distribution when comparing balanced and unbalanced results for a given index and when comparing Malmquist and Hicks–Moorsteen productivity indices for a given type of data set. The latter tests are crucial in answering the question to which extent the Malmquist index can approximate the Hicks–Moorsteen index that has a Total Factor Productivity (TFP) interpretation. Finally, we draw up a list of remaining issues that could benefit from further exploration.     

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.     

基于定向技术距离函数的投入产出型Malmquist指数

本在分析了基于产出距离函数的Malmquist指数的局限性后，定义了在t时期上的定向技术距离函数，提出了修正的Malmquist指数(简称ARD，AGL)，并用线性规划给出了求解方法。同时运用修正后的Malmquist指数对技术进步、技术效率变化和规模效率三方面进行了分解，并辅以经济解释。     

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).     

Aggregation of Malmquist productivity indexes allowing for reallocation of resources

In this paper we consider aggregate Malmquist productivity index measures which allow inputs to be reallocated within the group (when in output orientation). This merges the single period aggregation results allowing input reallocation of Nesterenko and Zelenyuk (2007) with the aggregate Malmquist productivity index results of Zelenyuk (2006) to determine aggregate Malmquist productivity indexes that are justified by economic theory, consistent with previous aggregation results, and which maintain analogous decompositions to the original measures. Such measures are of direct relevance to firms or countries who have merged (making input reallocation possible), allowing them to measure potential productivity gains and how these have been realised (or not) over time.     

α-Returns to scale and multi-output production technologies

This contribution proposes a specification of strictly increasing and decreasing returns to scale in multi-output technologies. Along this line a notion of α-returns to scale is derived from that of homogeneous multi-output technology. For a large class of technologies we establish necessary and sufficient conditions characterizing strictly increasing and strictly decreasing returns to scale to scale. Furthermore, a relationship between input, output and graph distance functions is established. These connections lead naturally to a link between the various Malmquist indexes and the Chavas–Cox productivity index. Finally, we show that these concepts can be implemented in a DEA context using a piecewise homogeneous constant elasticity substitution–transformation model due to [Färe, R., Grosskopf, S., Njinkeu, D., 1988b. On piecewise reference technologies. Management Science 34, 1507–1511].     

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。     

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.     

Measuring performance improvement of Taiwanese commercial banks under uncertainty

In order to enable domestic commercial banks to be more competitive globally, the Taiwanese government has twice attempted to financially restructure them, in 2001 and 2004. Different from other studies which use deterministic analyses to measure changes in performance between two periods, this paper adopts probabilistic analysis to take the uncertainty related to certain factors into account. Data from six years, from 2005 to 2010, are divided into two periods, 2005–2007 and 2008–2010, to calculate the global Malmquist productivity index (MPI) as a measure of the change in performance. By assuming beta distributions for the data, a Monte Carlo simulation is conducted to find the distribution of the MPI. The results show that, in general, the performance of the commercial banks has indeed improved. While conventional deterministic analyses may mislead top managers and make them overconfident about results that are actually uncertain, probabilistic analysis can produce more reliable information that can thus lead to better decisions.     

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.     

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.     

公共投资对粮食主产区农业生产率增长的驱动效应分析——基于吉林省1989-2006年数据的实证检验

粮食主产区是我国农业发展的重心,而公共投资是推动粮食主产区农业生产率增长最主要的驱动力。因此,本文以吉林省为例运用Malmquist指数模型定量评估粮食主产区的农业生产率,并进一步应用向量误差修正(VEC)模型分析了公共投资与农业生产率之间的长期均衡关系,实证检验了公共投资对农业生产率的驱动效应。     

On the inconsistency of the Malmquist–Luenberger index

Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist–Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad outputs. In particular, we show that the usual interpretation of the technical change component in terms of production frontier shifts can be inconsistent with its numerical value, thereby resulting in an erroneous interpretation of this component that passes on to the index itself. We illustrate this issue with a simple numerical example. Finally, we propose a solution for this inconsistency issue based on incorporating a new postulate for the technology related to the production of bad outputs.     

The Delimitation of Local Government Electoral Areas in Scotland: A Semi-Automated Approach

After the reorganisation of local government in Scotland in 1975, all councils were asked to make a comprehensive review of electoral areas. Although parity of population was a prime concern, attention had to be given also to the compactness and contiguity of districts. The Act also recommended that local communities should be kept intact and that boundaries should accord with ground features. The allocative part of the Törnqvist location-allocation technique was used in the first stage of partitioning in certain Regions to provide a basic framework for an apportionment pattern. Although this algorithm maximises compactness, it can produce sub-optimal results with a high degree of parity. Final adjustment of boundaries depended on detailed local knowledge.     

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。     

Generalized Pólya–Szegö type inequalities for some non-commutative geometric means

In this paper, we shall show generalized Pólya–Szegö type inequalities of n positive invertible operators on a Hilbert space for any integer $n?3$ in terms of the following two typical non-commutative geometric means, that is, one is the higher order weighted geometric mean due to Lawson–Lim which is an extension of the Ando–Li–Mathias geometric mean, and the other is the weighted chaotic geometric mean. Among others, the Specht ratio plays an important role in our discussion, which is the upper bound of a ratio type reverse of the weighted arithmetic–geometric mean inequality.     

Productivity breakdown of the information and computing technology industries across countries

In this paper, we measure productivity growth of the information and computing technology (ICT) industries in 14 Organization for Economic Cooperation and Development countries over the 13-year period of 1978–1990. The ICT industries are the providers of essential information technology (IT) capital goods. This macro-level analysis seeks to find out how productively such IT capital goods are provided. The basic unit of analysis employed is the Malmquist Total Factor Productivity (TFP) index. The Malmquist TFP index is then decomposed into three constituent elements accounting for different sources of productivity growth: technological progress, efficiency change, and change in economies of scale. The approach of measurement is based on the concept of distance functions and employs the non-parametric frontier method of data envelopment analysis. Our results indicate that each country's ICT industry manifests its own particular patterns in various performance measures. Among the 14 countries examined, 10 had witnessed productivity growth in their ICT industries. Overall, these ICT industries are found more productive than other industries when compared with previous research. Further analyses reveal that (1) most of the productivity growth measured is due to technological progress; (2) efficiency change exerts a relatively small positive effect on productivity growth; and (3) the change in scale economies unfavourably affects productivity for most countries. Finally, practical implications for formulating IT policy are drawn from our results, and topics are identified for future research.     

Measuring sectoral productivity across time and across countries

This paper examines the problem of measuring the evolution of productivity changes over time and across the 14 countries included in the OECD's International Sectoral Data Base of two sectors considered essential to the economic growth of any nation, namely manufacturing and services. The basic units of analysis are generalized Malmquist productivity indices. These in turn can be decomposed into several components, associated to the various sources of productivity change. Included here are productivity fluctuations due to economies of scale, being constant or variable, to technical change and technical efficiency change. The computational procedure is based upon the concept of distance function, computed through the use of variations of data envelopment analysis.     

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.     

中国轻工业全要素生产率的空间溢出效应研究——基于空间计量与社会网络分析

基于Malmquist指数方法测算的中国轻工业全要素生产率的省域数据,运用空间计量方法和社会网络分析方法探讨轻工业全要素生产率的空间关联特征和空间溢出效应,从整体和区域的视角审视轻工业在区域间的协调发展。研究发现,区域轻工业全要素生产率的增长具有空间关联性,各地区轻工业联系紧密,其网络结构的整体性强,通透性高,稳定性好,且具有非对称可达性;轻工业的空间关联网络可划分为四个功能板块——主溢出板块、净溢出板块、经纪人板块和主受益板块,各个板块呈现明显的“阶梯型”溢出特征。