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.