A Quasi-Malmquist Productivity Index

The Malmquist productivity index is based on distance functions, which are reciprocals of radial Debreu-Farrell efficiency measures, and which have a number of desirable properties. Linear programming techniques are frequently employed to calculate the efficiency measures. However these techniques can leave slacks, which constitute a non-radial form of inefficiency which is not incorporated into the analysis. Thus a radial efficiency measure overstates true efficiency, the reciprocal distance function understates the distance to the relevant efficient subset, and the Malmquist productivity index is adversely affected, although in an analytically indeterminate direction. This has led us to consider a new definition of one-sided efficiency, and to develop a new nonradial efficiency measure which incorporates all slacks on the selected side. Replacing conventional radial efficiency measures with our new non-radial efficiency measures generates what we call a quasi-Malmquist productivity index. We illustrate our quasi-Malmquist productivity index with an application to productivity change in Spanish banking.     

Hicks-Moorsteen versus Malmquist: a connection by means of a radial productivity index

A primal index of productivity change is introduced which decomposes exactly into three components: technical change, technical efficiency change and average scale economies (radial scale change). The productivity index is defined using variations of the distance function along pre-assigned input–output rays and, for this reason, it is deemed a radial productivity index (RPI). It is proven that: first, the RPI index collapses to the Malmquist productivity index when the technology is constant returns to scale (CRS); second the RPI index equals the Hicks-Moorsteen productivity index under homotheticity of technology (and non-CRS). The key to these results is a new definition and measure of the contribution of scale economies to productivity change.     

A semiparametric stochastic input distance frontier model with application to the Indonesian banking industry

This paper proposes a semiparametric smooth-varying coefficient input distance frontier model with multiple outputs and multiple inputs, panel data, and determinants of technical inefficiency for the Indonesian banking industry during the period 2000 to 2015. The technology parameters are unknown functions of a set of environmental factors that shift the input distance frontier non-neutrally. The computationally simple constraint weighted bootstrapping method is employed to impose the regularity constraints on the distance function. As a by-product, total factor productivity (TFP) growth is estimated and decomposed into technical change, scale component, and efficiency change. The distance elasticities, marginal effects of the environmental factors on the distance elasticities, temporal behavior of technical efficiency, and also TFP growth and its components are investigated.

     

Undesirable outputs and a primal Divisia productivity index based on the directional output distance function

Despite their great popularity, all the conventional Divisia productivity indexes ignore undesirable outputs. The purpose of this study is to fill in this gap by proposing a primal Divisia-type productivity index that is valid in the presence of undesirable outputs. The new productivity index is derived by total differentiation of the directional output distance function with respect to a time trend and referred to as the Divisia–Luenberger productivity index. We also empirically compare the Divisia–Luenberger productivity index and a representative of the conventional Divisia productivity indexes–the radial-output-distance-function-based Feng and Serletis (2010) productivity index–using aggregate data on 15 OECD countries over the period 1981–2000. Our empirical results show that failure to take into account undesirable outputs not only leads to misleading rankings of countries both in terms of productivity growth and in terms of technological change, but also results in wrong conclusions concerning efficiency change.     

Measuring input-specific productivity change based on the principle of least action

In for-profit organizations, efficiency and productivity measurement with reference to the potential for input-specific reductions is particularly important and has been the focus of interest in the recent literature. Different approaches can be formulated to measure and decompose input-specific productivity change over time. In this paper, we highlight some problems within existing approaches and propose a new methodology based on the Principle of Least Action. In particular, this model is operationalized in the form of a non-radial Luenberger productivity indicator based on the determination of the least distance to the strongly efficient frontier of the considered production possibility sets, which are estimated by non-parametric techniques based upon Data Envelopment Analysis. In our approach, overall productivity change is the sum of input-specific productivity changes. Overall productivity change and input-specific changes are broken up into indicators of efficiency change and technical change. This decomposition enables the researcher to quantify the contributions of each production factor to productivity change and its components. In this way, the drivers of productivity development are revealed. For illustration purposes the new approach is applied to a recent dataset of Polish dairy processing firms.     

An econometric approach to estimating support prices and measures of productivity change in public hospitals

In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes, measures of environmental change, levels of efficiency, and support prices for a sample of Australian public hospitals.     

Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

Determining the contribution of technical change, efficiency change and scale change to productivity growth in the privatized English and Welsh water and sewerage industry: 1985–2000

The water and sewerage industry of England and Wales was privatized in 1989 and subjected to a new regime of environmental, water quality and RPI+K price cap regulation. This paper estimates a quality-adjusted input distance function, with stochastic frontier techniques in order to estimate productivity growth rates for the period 1985–2000. Productivity is decomposed so as to account for the impact of technical change, efficiency change, and scale change. Compared with earlier studies by Saal and Parker [(2000) Managerial Decision Econ 21(6):253–268, (2001) J Regul Econ 20(1): 61–90], these estimates allow a more careful consideration of how and whether privatization and the new regulatory regime affected productivity growth in the industry. Strikingly, they suggest that while technical change improved after privatization, productivity growth did not improve, and this was attributable to efficiency losses as firms appear to have struggled to keep up with technical advances after privatization. Moreover, the results also suggest that the excessive scale of the WaSCs contributed negatively to productivity growth.     

A global Malmquist-Luenberger productivity index

This paper introduces an alternative environmentally sensitive productivity growth index, which is circular and free from the infeasibility problem. In doing so, we integrated the concept of the global production possibility set and the directional distance function. Like the conventional Malmquist-Luenberger productivity index, it can also be decomposed into sources of productivity growth. The suggested index is employed in analyzing 26 OECD countries for the period 1990–2003. We also employed the conventional Malmquist-Luenberger productivity index, the global Malmquist productivity index and the conventional Malmquist productivity index for comparative purposes in this empirical investigation.     

Parametric decomposition of the input-oriented Malmquist productivity index: with an application to Greek aquaculture

Using a stochastic frontier approach and a translog input distance function, this paper implements the input-oriented Malmquist productivity index to a sample of Greek aquaculture farms. It is decomposed into the effects of technical efficiency change, scale efficiency change, input-mix and, technical change, which is further attributed to neutral, output- and input-induced shifts of the frontier. Implementable expressions for the aforementioned components are obtained using a discrete changes-approach that is consistent with the usual discrete-form data. Empirical findings indicate that the productivity of the farms in the sample increased during the period 1995–1999 and it was shaped up primarily by the input mix-effect and technical change.     

Indirect productivity measurement

Caves, Christensen and Diewert [1982a] showed that the Törnqvist productivity index is superlative in a considerably more general sense than had been previously believed. We examine the allocative and technical efficiency hypotheses on which their finding rests. We show that the allocative efficiency hypothesis can be modified, which makes the Törnqvist index superlative in a wider sense than even Caves, Christensen and Diewert showed, since it is consistent with a type of allocative efficiency other than the standard cost minimization and revenue maximization hypotheses considered by Caves, Christensen and Diewert. We also show that if the technical efficiency hypothesis is relaxed, the CCD result may no longer hold, and the distance functions that form the basis of the Malmquist productivity indexes, and hence of the Törnqvist productivity index, must be calculated. We then show how to calculate the underlying distance functions, and we argue that there are real advantages to doing so.The refereeing process of this paper was handled through N.R. Adam.     

Environmental regulation,total factor productivity,and enterprise duration: Evidence from China

Environmental regulation has been confirmed to have an important impact on enterprise productivity, which is regarded as a crucial factor of enterprise duration. However, existing studies have paid little attention to how environmental regulation affects enterprise duration. Using firm‐level data from the Chinese Industrial Enterprises Database (2003–2007) and the stochastic frontier analysis method, we estimate enterprise total factor productivity (TFP) and its four decomposed components (scale efficiency change, technological change, factor allocation efficiency change, and technical efficiency change). Meanwhile, we adopt a comprehensive index to measure the environmental regulation intensity. Furthermore, we use the linear probability model and the proportional hazards model to investigate the effect of environmental regulation on enterprise duration through the mediating role of enterprise TFP. The results show that although environmental regulation per se negatively impacts on enterprise duration, environmental regulation can present a synthetic positive effect on enterprise duration due to its positive effect on enterprise TFP. Specifically, environmental regulation significantly mitigates the scale efficiency and technical efficiency of regulated enterprises. It also stimulates regulated enterprises' technological innovation and improves their factor allocation efficiency. In addition, state‐owned and large‐scale enterprises are more malleable when facing environmental regulations. We propose that the government should encourage enterprises to innovate and improve the allocation efficiency of production factors, so as to achieve the purpose of controlling environmental pollution in stages while extending enterprise duration.     

Decomposing profit change: Konüs,Bennet and Luenberger indicators

We introduce complementary decompositions of profit change that, relying on the duality between the profit function and the directional distance function, shed light on the different sources of profit growth including measures of technical efficiency, allocative efficiency and technological change. Our decompositions extend the literature on Konüs and Bennet quantity and price indicators to profit change. The first decomposition is ‘exact’ in the sense of Diewert, by completely exhausting the sources of profit change into profit inefficiency change (including technical and allocative inefficiency change), technological change, and output and input price change. The second decomposition equates the Bennet quantity indicator to a productivity measure represented by the Luenberger indicator plus allocative inefficiency change. We deem it ‘complete’ because in contrast to the existing literature, it retains the information on allocative inefficiency change while preventing the existence of residual terms capturing price variations, whose meaningful interpretation has not been addressed until now. Our proposed solution takes advantage of the flexibility of the directional distance function when choosing a suitable directional vector. All decompositions have the same structural form and therefore their components can be compared to each other vis-à-vis, providing alternative measures of equivalent sources of profit growth.     

基于环境负产出的能效动态Malmquist模型研究

本文旨在研究环境效率—能源效率—经济效率的"三位一体动态全要素生产率"。首先基于数据包络分析建立了环境约束下的能效动态Malmquist模型,定义了能效效率改变指数、污效效率改变指数和动态进步指数。通过对中国18个行业2000～2007年的数据分析,指出未考虑环境效应、动态效应的Malmquist模型会带来误判,进而揭示出在中国能效全要素生产率改变过程中,能源环境效应起到了不可忽略的作用,而动态效应则是最大的瓶颈,却没得到应有的重视。     

Data envelopment analysis and Malmquist indices for measuring group performance

This paper develops measures, based on the Malmquist index, that enable the decision making units’ internal inefficiencies to be distinguished from those associated with their group (or program) characteristics. The applicability of these measures is illustrated with the assessment of bank branches’ performance. The analysis involves the construction of an index reflecting the relative performance of branches in four different regions, which can be decomposed into an index for the comparison of within-group efficiency spread, evaluating internal managerial efficiencies, and an index for the comparison of frontier productivity, reflecting the impact of environmental factors and regional managerial policies on branches’ productivity.     

The role of environmental factors in growth accounting

This paper explores a relatively new methodology, the directional distance function method, to analyse productivity growth. The method allows us to explicitly evaluate the role that undesirable outputs of the economy, such as carbon dioxide and other greenhouse gases, have on the frontier production process which we specify as a piecewise linear and convex boundary function. We decompose productivity growth into efficiency change (catching up) and technology change (innovation). We test the statistical significance of the estimates using recently developed bootstrap methods. We also explore implications for growth of total factor productivity in the OECD and Asian economies. Copyright © 2004 John Wiley & Sons, Ltd.     

Combining common-weights DEA window with the Malmquist index: A case of China’s iron and steel industry

In the conventional data envelopment analysis (DEA) window analysis, a decision-making unit (DMU) in each window is treated as different units in each period so that the evaluation for one unit is performed on different scales over time. This paper proposes a novel window analysis based on common weight across time (CWAT), which evaluates each unit in each window by its common scale independent of time. The model for obtaining common weights is described as linear programming. And the paper suggests the Malmquist productivity index (MPI) on CWAT, CWAT MPI, to analyze productivity change by inheriting the result of window analysis. The numerical experiments are illustrated to examine the validity of CWAT and MPI, and the result shows that the proposed method provides a new evaluation scale compared to previous studies. The proposed model is applied to evaluate the performance of China 45 iron and steel enterprises during 2009–2017. The energy and environmental efficiency are calculated using CWAT, and CWAT MPI analyzes the productivity change.     

Sustainability matters

This document aims at bridging productivity measurement and weak sustainability in a specific data envelopment analysis framework that allows for negative output. In this framework countries use two inputs: capital and labour and seeks to maximize output and adjusted net saving. Adjustment net saving is seen as a sustainability indicator and then the productivity indicator computed can be understood as a sustainability productivity index. The higher the indicator is the higher productivity is and the probability of targeting sustainability.     

Productivity Measurement from a Reference Technology: A Distance Function Approach

An approach to productivity measurement based on distance function measurement is developed in this paper. A series of reference technologies are constructed by augmenting observed inputs and outputs such that the resulting effective netputs are consistent with the weak axiom of profit maximization. Geometric means of year-ahead and year-back distance function values serve as measures of multifactor productivity changes. Both primal measures from the inner bound and dual measures from the outer bound of the reference technologies are calculated. Resulting productivity measures are similar to those derived using index number approaches, but potentially provide greater information regarding the reference technologies.     

中国经济增长的动力转换与政策选择

研究目标：探究经济增长动因结构及转换趋势。研究方法：基于中国1980～2014年三次产业的时间序列数据,构造结构指数生产函数,采取指数分析与对数分析相结合的方法进行实证研究。研究发现：2008年以来全要素生产率贡献缩减是经济增长大幅减速的最主要因素;要素规模增长率下降与产出弹性缩减的双重挤压导致资本和劳动力规模贡献下滑;资本和劳动生产率增长双减速是造成全要素生产率大幅下降的主导因素;全要素生产率增长动力从以产业要素生产率的提升为主转向以产业之间要素配置结构的优化为主。研究创新：从三次产业的要素规模和效率进行考察,三个层次层层推进,为经济增长动力及其变迁轨迹分析创造更加广阔的拓展空间。研究价值：揭示了中国经济增长变迁的动因结构以及最新转换趋势,为旨在推动国民经济又快又好发展的政策设计提供了新的科学决策参考。