O.R. ApplicationsDifferent approaches to efficiency analysis. An application to the Spanish Trawl fleet operating in Moroccan waters
Introduction
Several approaches can be found in the literature for measuring technical efficiency of firms. The most traditional ones in the stochastic framework are the panel data (PD) approach and the stochastic production frontier (SPF) approach, whereas data envelopment analysis (DEA) is the most common among deterministic ones. Another more recent technique is the multi-output stochastic approach, known as stochastic distance functions (DF). The DF approach benefits from allowing both random error in the analysis and multiple outputs.
The use of panel data (PD) techniques is the most traditional approach. The most relevant difference from the stochastic production frontiers (SPF) approach is the estimation procedure. Whereas panel data techniques estimate the inefficiency component by the use of least squares, the stochastic production frontier approach assumes a certain distribution for the inefficiency term and the estimation procedure is based on maximum likelihood. The SPF and PD approaches can only be used in single-output production processes or in multi-output cases when the aggregation of all outputs into one is reasonable. On the contrary, the DEA methodology allows the inclusion of multiple outputs in the analysis but it presents the disadvantage of being deterministic.
The more recent multi-output stochastic approach, known as stochastic distance functions (DF), has the advantage of including random error and, at the same time, it possesses the desirable characteristic of including multiple outputs in the analysis. However, it requires restrictive assumptions (like the property of homogeneity of degree one for the outputs). Moreover, if there is evidence that a certain distribution can be assumed for the inefficiency term, then, the SPF approach provides better estimates.
The stochastic approaches present two important disadvantages when compared with DEA: (1) a functional form regarding the production process has to be imposed and (2) a distributional assumption has to be made for the error term. Furthermore, in the case of SPF and DF a distributional assumption has also to be made for the inefficiency term.
In general terms, it cannot be said that any of the above-mentioned methodologies is better than the rest. The most adequate methodology to be used in each study depends on the characteristics of the production process, the degree of stochasticity, number of outputs and possibility of aggregation.
In many recent papers, efficiency techniques are used and applied to different fields. Efficiency has been applied not just to measure efficiency itself but also for other purposes like capacity utilisation (Vestergaard et al., 2002; Pascoe et al., 2001a, Pascoe et al., 2001b), risk analysis (Herrero, 2004a, Herrero, 2004b), etc. The main goal of this work is to provide a summary of the main techniques for the estimation of technical efficiency and to make a comparison among them when applied to a Spanish fishery. The different efficiency estimation approaches have been applied to the Spanish trawl fishery that operated in Moroccan waters and some interesting conclusions has been drawn from the analysis.
Three different software packages have been used: NLOGIT8.0 (Greene, 2002) for panel data estimators, GAMS for DEA (Brooke et al., 1992) and FRONTIER (Coelli, 1996) for stochastic production functions and for distance functions.
The paper is structured as follows: in Section 2 a brief description of the fishery has been provided. Section 3 is dedicated to the analysis of the variables included in the study. Sections 4 Stochastic production frontiers models, 5 Panel data models, 6 Distance functions approach, 7 Data envelopment analysis approach summarised the SPF, PD, DF and DEA techniques (respectively) and presents the results when applied to the case study. The empirical results of the different approaches have been compared in Section 8. Finally the main conclusions of the study are discussed in the last section.
Section snippets
Brief description of the fishery
The study is based on a sample of 26 vessels from the Spanish Andalusian fleet that operated during 1993–1998. In the years under analysis, a close season was imposed during January and February, 1 so that the database is restricted to the period March–December each year. The fleet consists of deep-water trawl vessels that are based in the Port of Huelva and fish in Moroccan Waters. The target species are crustaceans (deep water
Variables included in the analysis
The dependent variables used in all approaches were the total value of the catch of the species over the month. Some aggregation had to be done due to the high number of different species in the catch. As a reasonable number of the most relevant ones could not be found (the number of the most valuable species was too high) they were aggregated into two, crustaceans and finfish, the former being of a much higher price than the latter. For the multi-output approaches, the value of these two types
Stochastic production frontiers models
In this section, the SPF approach was used to estimate the relationship between the level of inputs and outputs, and the distribution of technical efficiency in the fleet.
A translog production function was used in the analysis. This is a flexible functional form in which is nested the Cobb–Douglas and CES production functions. The translog production function is given bywhere Yit is the standardised output of unit i in time t,Xikt and Xijt are
Panel data models
What has been called the “panel data technique” (PD) is a parametric procedure that is commonly used when the number of firms involved in the analysis is bigger than the number of time periods (Hsiao, 1986). Consider a standard SPF of the form:where, the same notation as in the SPF model has been used. As before, Vit are the random errors, assumed to be independently and identically distributed (iid) N(0,σv2); and Uit are constant firm-specific variables, accounting for
Distance functions approach
The distance functions (DF) approach is a multi-output stochastic methodology for the estimation of efficiency. It is similar to the stochastic production function approach but it includes multiple outputs, one of which plays the role of the “dependent” output (Coelli et al., 1998; Kumbhakar and Lovell, 2000).
The output distance function is defined as (Coelli and Perelman, 2000):where P(x) is the output production possibility set:which is assumed
Data envelopment analysis approach
A standard DEA analysis was also carried out. For consistency and for comparative purposes, a model omitting each of the physical characteristics of the vessels was also carried out, similarly to the other approaches applied in this work.
A standard BBC (Banker et al., 1984) output oriented model was used. The BCC output (input) oriented model seeks to maximise (minimise) the proportion of the outputs (inputs) of the firm under evaluation, i0 based on a weighted convex combination of the inputs
Results and comparison of approaches
The results of the different approaches used in the analysis were compared. It can be observed (Table 8 (Panels A and B)) that the efficiency estimates are highly correlated when using all approaches.
In general terms, the SPF and DF models when omitting the power of the engines seem to perform better than the models where volume is omitted, in the sense that the former have more significant variables (volume and fishing) than the latter (which is only based on the fishing effort regardless the
Conclusions
In this paper some of the most relevant approaches that exist in literature for the estimation of technical efficiency have been compared and applied to analyse the efficiency of the vessels of the Spanish Trawl fleet that operated in Moroccan waters. While some of them allow the inclusion of multi-output measures, others are restricted to the case of single-outputs. Stochastic approaches have also been compared with deterministic ones.
As would be expected in most cases, it can be concluded
Acknowledgements
The study has been carried out with the financial support of the Commission of the European Communities Fifth Framework programme, QLK5-CT1999-01295, “Technical efficiency in EU fisheries: implications for monitoring and management through effort controls” and the support of the Centro de Estudios Andaluces, CentrA (research centre in Seville depending on the Andalusia Local Government). The author thanks the people in the register of the fish market of Huelva for their cooperation during the
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