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.     

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.     

中国农业生产率的变动与分解分析:1978～2004年--基于非参数的HMB生产率指数的实证研究

本文使用非参数的HMB生产率指数方法，考察了中国农村改革以来农业全要素生产率（TFP）的变动趋势，并把TFP的增长构成分解为技术进步、技术效率变化、规模效应和投入产出混合效应四个部分。结果表明，改革开放以来我国农业TFP的增长主要是由技术进步推动的，技术效率的下降对TFP的增长造成了不利影响，而规模效应和混合效应影响较弱。文章还指出中国农业的育种能力和生物技术的发展是农业技术进步的决定力量。     

A new decomposition and interpretation of Hicks-Moorsteen productivity index for analysis of Stock Exchange companies: Case study on pharmaceutical industry

This paper deals with the productivity index based on Hicks-Moorsteen (HM) productivity index for analysis of Stock Exchange firms. In this paper, a decomposition of Hicks-Moorsteen productivity index is provided that uses data envelopment analysis (DEA) models. On the other hand, it is offered a new interpretation and decomposition for components of HM productivity index that in previous studies were not performed any interpretation of it. These components have named the output production and the input consumption in terms of changing the efficiency frontier. In addition, by comparing the components of HM productivity index and productivity value, the optimal values of output production and input consumption are determined. Also, the analysis is determined how to identify the optimal value of a firm over a period of time. The proposed approach is applied to 26 pharmaceutical manufacturers that are from Tehran Stock Exchange. Data have been collected for six consecutive years (2009–2014) and have been considered financial ratios for evaluating companies. The results show that the Hicks-Moorsteen productivity index is more able to provide managerial aspects than other productivity indexes such as the Malmquist productivity index.     

Shadow Price Approach to Total Factor Productivity Measurement: With an Application to Finnish Grass-Silage Production

This paper explores an intermediate route between the Fisher and the Malmquist productivity indexes so as to minimize data requirements and assumptions about economic behavior of production units and their production technology. Assuming quantity data of inputs and outputs and the behavioral hypothesis of allocative efficiency, we calculate the exact value of the Fisher ideal productivity index using implicit shadow prices revealed by the choice of input–output mix. The approach is operationalized by means of a nonparametric data envelopment analysis (DEA) model. Empirical application to Finnish grass silage farms suggests that the Malmquist and the Fisher productivity indices yield similar results when averaged over firms, but there can be major differences in the results of the two approaches at the level of individual firms.     

A superlative index number formula for the Hicks-Moorsteen productivity index

The Malmquist and Hicks-Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth. Since these productivity indexes are defined by unknown distance functions, it is necessary to estimate the distance functions to compute them in principle. On the other hand, the Törnqvist productivity index is an empirical index number formula that is directly computable from the prices and quantities of the inputs and outputs alone. Caves et al. (1982) imply that the Malmquist index coincides with the Törnqvist index under profit maximizing behaviour and constant returns to scale technology. The purpose of the present paper is to point out that the Hicks-Moorsteen productivity index coincides with the Törnqvist productivity index under the same condition. We emphasize that the condition of constant returns to scale is indispensable for deriving the equivalence between the two indexes. Moreover, even when this condition is relaxed to the α returns to scale, the equivalence between the Hicks-Moorsteen and Törnqvist productivity indexes is shown to hold true.     

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.

     

Exact decomposition of the Fisher ideal total factor productivity index

Decompositions of total factor productivity (TFP) shed light on the driving factors behind productivity change. We develop the first exact decomposition of the Fisher ideal TFP index which contains no debatable mixed-period components or residuals. We systematically isolate five effects of (1) technical change, (2) technical efficiency, (3) scale efficiency, (4) allocative efficiency, and (5) price effect. The three efficiency components (2–4) represent the efficiency of achieving a given target point. Components (1) and (5) capture the changes of the target point. While the technical change component is well-established, changes in the relative input–output prices can have real effects on the scale and scope of the target. Such changes are captured by the new price effect component (5). The new decomposition is compared with existing decompositions both in theory and by means of an empirical application to a panel data of 459 Finnish farms in years 1992–2000.

Productivity change in a multisectoral economic system

We estimate productivity growth without recourse to data on factor input shares or prices. In the proposed model, the economy is represented by the Leontief input–output model, which is extended by the constraints of primary inputs. A Luenberger productivity indicator is proposed to estimate productivity change; this is then decomposed in a way that enables us to examine the contributions of individual production factors and individual commodities to productivity change. The results allow for the identification of inputs or outputs that are the drivers of the overall productivity change. Their contributions are then decomposed into efficiency change and technical change components. Using input–output tables of the US economy for the period 1977–2006, we show that technical progress has been the main source of productivity change. Technical progress was mostly driven by capital, whereas low-skilled labour contributed negatively.     

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.     

Productivity,efficiency and technical change: measuring the performance of China’s transforming agriculture

As China enters the twenty-first century the health of the agricultural economy will increasingly rely, not on the growth of inputs, but on the growth of total factor productivity (TFP). However, the tremendous changes in the sector—sometimes back and sometimes forwards—as well as evolving institutions make it difficult to gauge from casual observation if the sector is healthy or not. Research spending has waxed and waned. Policies to encourage the import of foreign technologies have been applied unevenly. Structural adjustment policies also triggered wrenching changes in the sector. Horticulture and livestock production has boomed; while the output of other crops, such as rice, wheat and soybeans, has stagnated or fallen. At a time when China’s millions of producers are faced with complex decisions, the extension system is crumbling and farmer professional associations remain in their infancy. In short, there are just as many reasons to be optimistic about the productivity trends in agriculture as to be pessimistic. In this paper, we pursue one overall goal: to better understand the productivity trends in China’s agricultural sector during the reform era—with an emphasis on the 1990–2004 period. To do so, we pursue three specific objectives. First, relying on the National Cost of Production Data Set—China’s most complete set of farm input and output data—we chart the input and output trends for 23 of China’s main farm commodities. Second, using a stochastic production frontier function approach we estimate the rate of change in TFP for each commodity. Finally, we decompose the changes in TFP into two components: changes in efficiency and changes in technical change. Our findings—especially after the early 1990s are remarkably consistent. China’s agricultural TFP has grown at a healthy rate for all 23 commodities. TFP growth for the staple commodities generally rose around 2% annually; TFP growth for most horticulture and livestock commodities was even higher (between 3 and 5%). Equally consistent, we find that most of the change is accounted for by technical change. The analysis is consistent with the conclusion that new technologies have pushed out the production functions, since technical change accounts for most of the rise in TFP. In the case of many of the commodities, however, the efficiency of producers—that is, the average distance of producers from the production frontier—has fallen. In other words, China’s TFP growth would have been even higher had the efficiency of production not eroded the gains of technical change. Although we do not pinpoint the source of rising inefficiency, the results are consistent with a story that there is considerable disequilibrium in the farm economy during this period of rapid structural change and farmers are getting little help in making these adjustments from the extension system.     

Fisher ideal output,input, and productivity indexes revisited

A productivity index for a firm is generally defined as an output index divided by an input index. The first part of the paper uses the test or axiomatic approach to index number theory in order to determine the appropriate functional form for the output and input indexes. It is found that the Fisher ideal index satisfies 21 reasonable tests and is uniquely characterized by a subset of these tests. In the remainder of the paper, the economic approach to productivity indexes introduced by Caves, Christensen, and Diewert is adopted and, again, a strong justification for the Fisher productivity index is provided.The editor of this paper was N.R. Adam.This research was supported by a Strategic Grant from the Social Science and Humanities Research Council of Canada. The author is indebted to Shelley Hey for typing assistance.     

Malmquist Indexes Using a Geometric Distance Function (GDF). Application to a Sample of Portuguese Bank Branches

Traditional approaches to calculate total factor productivity (TFP) change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate TFP change may introduce some bias in the analysis, and therefore we propose a procedure that calculates TFP change through observed values only. Our total TFP change is then decomposed into efficiency change, technological change, and a residual effect. This decomposition makes use of a non-oriented measure in order to avoid problems associated with the traditional use of radial oriented measures, especially when variable returns to scale technologies are to be compared. The proposed approach is applied in this paper to a sample of Portuguese bank branches.     

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.     

A Cost Indirect Evaluation of Productivity Change in UK Universities

The study provides an empirical analysis of productivity change in publicly-funded UK universities, against a background of government policy specifically designed to enhance the productive efficiency of universities in the provision of teaching and research. The nonparametric analysis employs a cost indirect approach to measuring productivity change, taking explicit account of the quality of research output and decomposing productivity change into technical change and efficiency change. The latter is also decomposed into changes in pure technical efficiency, scale efficiency and output congestion. Changes in size efficiency are also computed. On average, productivity declined by 4% over 1989–92, mainly as a result of regressive technical change. Evidence of biased technological change was found, with the frontier shifting out in favour of the teaching outputs and in relative to the research output.     

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.     

Productivity and efficiency dynamics in Indian banking: An input distance function approach incorporating quality of inputs and outputs

Banking technology is typically characterized by multiple inputs and multiple outputs that are associated with various attributes, such as different types of deposits, loans, number of accounts, classes of employees and location of branches. These quality differentials in inputs and outputs are mostly ignored in empirical studies. These omissions make the practical value of productivity studies in organizations like banks questionable because quality is a key component of performance. This paper proposes using hedonic aggregator functions (as a tool of aggregating inputs and outputs with quality attributes) within an input distance function framework and analyzes the impact of banking deregulation on efficiency and total factor productivity (TFP) change in the Indian banking industry using panel data for the period 1996–2005. Empirical results indicate that banks have improved their efficiency (from 61% in 1996 to 72% in 2005) during the post‐deregulation period, and the gain in efficiency of state‐owned banks has surpassed that of private banks. Improvement in capital base, as indicated by increased capital adequacy ratio, played an important role in ushering efficiency gain. The return to scale estimate suggests that state‐owned banks are operating far above their efficient scale and cost savings can be obtained by reducing their size of operations. Overall, TFP growth was above 3.5% annually. Both technical progress and technical efficiency change consistently played an important role in shaping TFP growth. Copyright © 2010 John Wiley & Sons, Ltd.     

Creation of climate-smart and energy-efficient agriculture in the European Union: Pathways based on the frontier analysis

Creation of the climate-smart agriculture requires efficient resource use and mitigation of the environmental pressures among other objectives. Therefore, it is important to assess the energy efficiency and productivity growth in the European Union's agriculture. This paper analyses the sample of the selected European Union member states. The productive technology including the energy consumption and the resulting greenhouse gas (GHG) emission is constructed. The measurement of the energy efficiency and productivity change relies on the slacks-based measure and Luenberger productivity indicator. The productivity growth was decomposed with respect to the input/output variables and the sources of growth (i.e., efficiency change and technical progress). The average annual productivity growth of 0.79% was obtained for the selected countries during 1995–2016. The highest productivity gains were observed in Lithuania, Denmark, Belgium and Romania (1.27%–1.94% per year). The productivity growth related to GHG emission dominated the contributions by the input/output variables in Lithuania, Denmark, Belgium, Romania, Poland, Austria, France, the Netherlands, Hungary and Estonia.     

Comparisons of agricultural productivity growth in China and India

We measure and compare agricultural total factor productivity (TFP) growth and its components (efficiency and technical change) in China and India and test the TFP series for the existence of structural breaks relating the evolution of TFP to policy milestones. Our results show that agricultural TFP growth accelerates in China after 1979 and in India after 1974, although China’s agricultural sector clearly outperforms India’s. The main explanation of these differentials is that agricultural growth in China benefited from more fundamental institutional and policy reforms in agriculture than India. There is some evidence that the transformation of industry in China was also important for agricultural TFP growth. Manufacture growth absorbed labor and reduced employment in agriculture, creating incentives for capital investment and technical change that kept output per worker in agriculture growing at high rates. Fewer changes in agricultural policies and in the dynamics of manufacturing in India resulted in slower growth in agricultural productivity, despite policy changes that accelerated economic growth in recent years.     

Cost Malmquist productivity index: an output-specific approach for group comparison

The cost Malmquist productivity index (CMPI) has been proposed to capture the performance change of cost minimizing Decision Making Units (DMUs). Recently, two alternative uses of the CMPI have been suggested: (1) using the CMPI to compare groups of DMUs, and (2) using the CMPI to compare DMUs for each output separately. In this paper, we propose a new CMPI that combines both procedures. The resulting methodology provides group-specific indexes for each output separately, and therefore offers the option to identify the sources of cost performance change. We also define our index when input prices are not observed and establish, in that case, a duality with a new technical productivity index, which takes the form of a Malmquist productivity index. We illustrate our new methodology with a numerical example and an application to the US electricity plant districts.