Productivity growth in electric energy retail in Colombia. A bootstrapped malmquist indices approach

This paper offers a productivity growth estimate for electric energy commercialization firms in Colombia, using a non-parametric Malmquist bootstrap methodology. The estimation and methodology serve two main purposes. First, in Colombia Commercialization firms are subject to a price-cap regulation scheme, a non-common arrangement in the international experience for this part of the industry. Therefore the paper’s result suggest an estimate of the productivity factor to be used by the regulator, not only in Colombia but in other countries where commercialization is a growing part of the industry (renewable energy, for instance). Second, because of poor data collection from regulators and firms themselves, regulation based on a single estimation of productivity seems inappropriate and error-prone. The nonparametric Malmquist bootstrap estimation allows an assessment of the result in contrast to a single one estimation. This would open an opportunity for the regulator to adopt a narrower and more accurate productivity estimation or override an implausible result and impose a productivity factor in the price-cap to foster the development of the industry.

Comparing public-private school management through a new educational Malmquist index approach. 'Comparación entre la gestión escolar pública y privada a través de un nuevo enfoque del índice educacional Malmquist'.

Resumen tomado de la publicación

The use of bootstrapped Malmquist indices to reassess productivity change findings: an application to a sample of Polish farms

This article assesses the extent to which sampling variation affects findings about Malmquist productivity change derived using data envelopment analysis (DEA), in the first stage by calculating productivity indices and in the second stage by investigating the farm-specific change in productivity. Confidence intervals for Malmquist indices are constructed using Simar and Wilson's (1999) bootstrapping procedure. The main contribution of this article is to account in the second stage for the information in the second stage provided by the first-stage bootstrap. The DEA SEs of the Malmquist indices given by bootstrapping are employed in an innovative heteroscedastic panel regression, using a maximum likelihood procedure. The application is to a sample of 250 Polish farms over the period 1996 to 2000. The confidence intervals' results suggest that the second half of 1990s for Polish farms was characterized not so much by productivity regress but rather by stagnation. As for the determinants of farm productivity change, we find that the integration of the DEA SEs in the second-stage regression is significant in explaining a proportion of the variance in the error term. Although our heteroscedastic regression results differ with those from the standard OLS, in terms of significance and sign, they are consistent with theory and previous research.

Productivity change in Polish agriculture: an illustration of a bootstrapping procedure applied to Malmquist indices

This article illustrates the usefulness of applying bootstrap procedures to total factor productivity Malmquist indices, derived with data envelopment analysis (DEA), for a sample of 250 Polish farms during 1996-2000. The confidence intervals constructed as in Simar and Wilson suggest that the common portrayal of productivity decline in Polish agriculture may be misleading. However, a cluster analysis based on bootstrap confidence intervals reveals that important policy conclusions can be drawn regarding productivity enhancement.

Avaliação da eficiência dos investimentos do programa Inova-RN em micro e pequenas empresas Uma integração da análise envoltória de dados e índice Malmquist

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Smoothed bootstrap Malmquist index based on DEA model to compute productivity of tax offices

This paper analyses the productivity growth of the SUMA tax offices located in Spain evolved between 2004 and 2006 by using Malmquist Index based on Data Envelopment Analysis (DEA) models. It goes a step forward by smoothed bootstrap procedure which improves the quality of the results by generalising the samples, so that the conclusions obtained from them can be applied in order to increase productivity levels. Additionally, the productivity effect is divided into two different components, efficiency and technological change, with the objective of helping to clarify the role played by either the managers or the level of technology in the final performance figures.

Malmquist indexes using a geometric distance function (GDF)

Traditional approaches to calculate total factor productivity change through Malmquist indexes rely on distance functions. In this paper we show that the use of distance functions as a means to calculate total factor productivity change may introduce some bias in the analysis, and therefore we propose a procedure that calculates total factor productivity change through observed values only. Our total factor productivity 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.

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.

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. © 2003 Elsevier B.V. All rights reserved.

A circular Malmquist-type index for measuring productivity

This paper develops two new indices for measuring productivity in multi-input multi-output situations. One index enables the measure of productivity change of a unit over time while the second index makes it possible to compare two units on productivity at the same or different points in time. Productivity in a single input single output context is defined as the ratio of output to input. In multi-input multi-output contexts this ratio is not defined. Instead, one of the methods traditionally used is the Malmquist Index of productivity change over time. This is computed by reference to the distances of the input-output bundles of a production unit at two different points in time from the efficient boundaries corresponding to those two points in time. The indices developed in this paper depart form the use of two different reference boundaries and instead they use a single reference boundary which in a sense is the most efficient boundary observed over two or more successive time periods. We discuss the assumptions which make possible the definition of such a single reference boundary and proceed to develop the two Malmquist-type indices for measuring productivity. One key advantage of using a single reference boundary is that the resulting index values are circular. That is it is possible to use the index values of successive time periods to derive an index value of productivity change over a time period of any length covered by successive index values or vice versa. Further, the use of a single reference boundary makes it possible to construct an index for comparing the productivities of two units either at the same or at two different points in time. This was not possible with the traditional Malmquist Index. We decompose both new indices into components which isolate production unit from industry or comparator unit effects. The components themselves like the indices developed are also circular. The components of the indices drill down to reveal more clearly the performance of each unit over time relative either to itself or to other units. The indices developed and their components are aimed at managers of production units to enable them to diagnose the performance of their units with a view to guiding them to improved performance.

Malmquist-type indices in the presence of negative data:an application to bank branches

In this paper we develop an index and an indicator of productivity change that can be used with negative data. For that purpose the range directional model (RDM), a particular case of the directional distance function, is used for computing efficiency in the presence of negative data. We use RDM efficiency measures to arrive at a Malmquist-type index, which can reflect productivity change, and we use RDM inefficiency measures to arrive at a Luenberger productivity indicator, and relate the two. The productivity index and indicator are developed relative to a fixed meta-technology and so they are referred to as a meta-Malmquist index and meta-Luenberger indicator. We also address the fact that VRS technologies are used for computing the productivity index and indicator (a requirement under negative data), which raises issues relating to the interpretability of the index. We illustrate how the meta-Malmquist index can be used, not only for comparing the performance of a unit in two time periods, but also for comparing the performance of two different units at the same or different time periods. The proposed approach is then applied to a sample of bank branches where negative data were involved. The paper shows how the approach yields information from a variety of perspectives on performance which management can use.

Productivity change in the water industry in England and Wales:application of the meta-Malmquist Index

This paper uses a meta-Malmquist index for measuring productivity change of the water industry in England and Wales and compares this to the traditional Malmquist index. The meta-Malmquist index computes productivity change with reference to a meta-frontier, it is computationally simpler and it is circular. The analysis covers all 22 UK water companies in existence in 2007, using data over the period 1993–2007. We focus on operating expenditure in line with assessments in this field, which treat operating and capital expenditure as lacking substitutability. We find important improvements in productivity between 1993 and 2005, most of which were due to frontier shifts rather than catch up to the frontier by companies. After 2005, the productivity shows a declining trend. We further use the meta-Malmquist index to compare the productivities of companies at the same and at different points in time. This shows some interesting results relating to the productivity of each company relative to that of other companies over time, and also how the performance of each company relative to itself over 1993–2007 has evolved. The paper is grounded in the broad theory of methods for measuring productivity change, and more specifically on the use of circular Malmquist indices for that purpose. In this context, the contribution of the paper is methodological and applied. From the methodology perspective, the paper demonstrates the use of circular meta-Malmquist indices in a comparative context not only across companies but also within company across time. This type of within-company assessment using Malmquist indices has not been applied extensively and to the authors’ knowledge not to the UK water industry. From the application perspective, the paper throws light on the performance of UK water companies and assesses the potential impact of regulation on their performance. In this context, it updates the relevant literature using more recent data.