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 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.     

Some Remarks on Productivity and its Decompositions

This paper provides a brief history of the Malmquist productivity index and its decomposition. Theoretical and empirical issues related to the index are discussed along with directions for future research.     

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.     

The biennial Malmquist productivity change index

In this paper we introduce a new Malmquist productivity index that has three attractive features: it avoids linear programming infeasibilities under variable returns to scale, it allows for technical regress, and it does not need to be recomputed when a new time period is added to the data set. The proposed index is compared to both the adjacent Malmquist index and the global Malmquist index in an empirical example, which highlights the drawbacks of the existing indexes compared to the proposed biennial Malmquist index.Our results show that 13% of the observations in the data set may have to be ignored due to infeasibilities when decomposing the adjacent Malmquist index. Using only this reduced data set does at times lead to quite different results than those generated by applying the proposed biennial Malmquist index to the entire data set. The empirical example also shows that productivity change estimated between two time periods using the global Malmquist index change substantially when a third time period is added to the data set, whereas the proposed biennial Malmquist index is immune to this problem.     

A new, transitive productivity index

The Malmquist productivity index is not transitive. This paper argues that, instead of trying to accommodate this two-period concept to a multi-period setting, it is preferable to look at the measurement of productivity, efficiency, and technical change in a multi-period setting from the outset. A new, transitive productivity index is developed with as by-product a measure of the non-neutrality of technical change. The various indices are illustrated on panel data of Swedish pharmacies.At the time of writing, R. Althin was employed by The Swedish Institute for Health Economics. The views expressed in this paper are those of the authors and do not necessarily reflect the policies of Statistics Netherlands or The Swedish Institute for Health Economics.     

Measurement of Productivity Changes: Two Malmquist Index Approaches

The adjacent Malmquist productivity index is compared to the more recently suggested base period Malmquist productivity index. The two index approaches are evaluated with respect to base period dependency, the circular test, and with respect to a set of additional classical index tests. In addition it is shown that the base period index is independent of base period if and only if the marginal rate of substitution of inputs is independent of time. Finally, the adjacent and the base period indexes are put through a Monte Carlo (bootstrap) test to see if they yield similar results when applied to a panel of Swedish pharmacy data.     

Parametric Decomposition of a Generalized Malmquist Productivity Index

This paper provides a parametric decomposition of a generalized Malmquist productivity index which takes into account scale economies. Unlike Balk (2001), the contribution of scale economies to productivity change is evaluated without recourse to scale efficiency measures, which are neither bounded for globally increasing, decreasing, or constant returns to scale technologies nor for ray-homogeneous technologies. An empirical application using panel data from Spanish savings banks is included. This application shows the advantages of the suggested method compared to Balk's approach. The results show an increase of total factor productivity which can be mainly attributed to technical progress and the positive effect of returns to scale.     

Measuring Scale Efficiency from a Translog Production Function

In parametric analysis based on a frontier production function, usually the scale elasticity rather than scale efficiency level is reported. In this paper we show how one can use an estimated translog production function to obtain output- and input-oriented measures of scale efficiency at an observed input bundle. We also show how the estimated model can be used to determine the optimal quantity of labor input for an exogenously fixed quantity of capital.     

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.     

Benchmarking and industry performance

In this paper I interrelate productivity analysis and the theory of industrial organization. A proposition proves that an industrial organization is efficient if and only if it is supportable in the entry-proofness sense. Industrial performance is decomposed in efficiency and technical change terms as well as an industrial organization component. The performance measure is shown to be consistent with the Solow residual and Malmquist productivity indices for its components are provided.     

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.     

Productivity changes in pre-crisis Western European banks: Does scale effect really matter?

Insofar as the completion of the Single Market for Financial Services, it has presented new challenges for European Banking industries. In this study, we use a recently developed generalized metafrontier Malmquist productivity index (gMMPI) to provide insights on productivity growth. We extend the gMMPI to broaden the index's capacity by decomposing various sources of productivity change in the metafrontier context. The sample contains commercial banks from 12 Western European countries prior to the recent financial crisis. A key advantage of our extension is that it introduces the role of scale effects. The empirical results show that an average bank's productivity growth arises mainly from technical changes and scale effects. Moreover, smaller and larger banks grow faster than medium ones. In addition, conservative banks tend to grow faster. These findings suggest that a more competitive and integrated financial market induced by financial deregulation is indeed able to improve banks’ productivity.     

An aggregate quantity framework for measuring and decomposing productivity change

Total factor productivity (TFP) can be defined as the ratio of an aggregate output to an aggregate input. This definition naturally leads to TFP indexes that can be expressed as the ratio of an output quantity index to an input quantity index. If the aggregator functions satisfy certain regularity properties then these TFP indexes are said to be multiplicatively complete. This paper formally defines what is meant by completeness and reveals that (1) the class of multiplicatively complete TFP indexes includes Laspeyres, Paasche, Fisher, T?rnqvist and Hicks-Moorsteen indexes, (2) the popular Malmquist TFP index of Caves et al. (Econometrica 50(6):1393?C1414, 1982a) is incomplete, implying it cannot always be interpreted as a measure of productivity change, (3) all multiplicatively complete TFP indexes can be exhaustively decomposed into measures of technical change and efficiency change, and (4) the efficiency change component can be further decomposed into measures of technical, mix and scale efficiency change. Artificial data are used to illustrate the decomposition of Hicks-Moorsteen and Fisher TFP indexes.     

DEA of financial statements data: The U.S. computer industry

DEA (data envelopment analysis) is a technique for determining the efficiencyfrontier (the envelope) to the inputs and outputs of a collection of individual corporations or other productive units. DEA is here employed to estimate the intertemporal productive efficiency of U.S. computer manufactures, using financial data brought from earnings statements and balance sheets. The results indicate that a few corporations, including Apple Computer Inc., Compaq Computer Corp., and Seagate Technology were able to stay at the productivity efficiency frontier throughout the time period investigated. But not all successful corporations did; sometimes subefficiency (=disequilibrium) actually goes together with very rapid growth. A new Malmquist type productivity index is calculated for each corporation, measuring shifts of the estimated intertemporal efficiency frontier.     

Incorporating ancillary measures of process and quality change into a superlative productivity index

One of the persistent problems plaguing the measurement of productivity and output is accounting for changes in product quality. A similar problem arises in attempting to explain shifts in a production function using information on changes in the characteristics of the production process itself. We consider these problems under a behavioral model in which the firm chooses a profit-maximizing bundle of input/output/process characteristics as well as the profit maximizing levels of input and output. This view of quality change is similar to the endogenous design index advocated by Triplett [1983] for industrial prices and the endogenous quality indexes analyzed by Pollak [1983] for consumer prices. We show how a price-characteristics locus can be used to adjust the Tornqvist output- and input-oriented multifactor productivity indexes of Caves, Christensen and Diewert [1982] for changes in input, output and process characteristics. To show the applicability of the methodology to services, we apply the results in the framework of the commercial banking measurement of Fixler [1988] to measure the impact of bank branching on multifactor productivity.The refereeing process of this paper was handled through R. Färe.     

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.     

Forecasting the Malmquist productivity index

The Malmquist Productivity Index (MPI) suggests a convenient way of measuring the productivity change of a given unit between two consequent time periods. Until now, only a static approach for analyzing the MPI was available in the literature. However, this hides a potentially valuable information given by the evolution of productivity over time. In this paper, we introduce a dynamic procedure for forecasting the MPI. We compare several approaches and give credit to a method based on the assumption of circularity. Because the MPI is not circular, we present a new decomposition of the MPI, in which the time-varying indices are circular. Based on that decomposition, a new working dynamic forecasting procedure is proposed and illustrated. To construct prediction intervals of the MPI, we extend the bootstrap method in order to take into account potential serial correlation in the data. We illustrate all the new techniques described above by forecasting the productivity index of 17 OECD countries, constructed from their GDP, labor and capital stock.     

Malmquist productivity index for multi-output producers: An application to electricity generation plants

Different types of plants are used to generate electricity in the US: single-, multi-, and mixed-electricity plants. In this paper, we question the best type/design of plants for both renewable and non-renewable electricity. To do so, we suggest a new index that takes the form of a Malmquist productivity index. The specificity of our new index is that it offers the option to investigate the performances and the causes of the performance changes for each type of electricity separately; this is not possible when relying on more standard indexes. Moreover, our new index takes the links between the inputs and the outputs into account, and is nonparametric in nature. Using our index, we study the performances of more than 5000 plants for the period 2000–2012. Our findings reveal that single-electricity plants perform better for renewable electricity, while multi-electricity plants perform better for non-renewable electricity. This is coherent with the decreasing importance of multi-electricity plants in the US, and the increasing importance of single-electricity plants producing renewable electricity. Furthermore, our results do not suggest that combining renewable and non-renewable electricity generations within a plant improves the performance of the plants. Finally, we demonstrate that the reasons for the changes in performance are different for each type of electricity and plant.     

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.