Parametric Decomposition of the Input-Oriented Malmquist Productivity Index: With an Application to Greek Aquaculture

Parametric Decomposition of the Input-Oriented Malmquist Productivity Index: With an Application to Greek Aquaculture

Using a stochastic frontier approach and a tranlog input distance function, this paper implements the input-oriented Malmquist productivity index to a sample of Greek aquaculture farms.

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The Malmquist productivity index, introduced by Caves, Christensen and Diewert (1982), started gaining popularity only after the influential work of Fare et al. (1992), who developed a tractable way to estimate it by non-parametric techniques (i.e., Data Envelopment Analysis, DEA) and provided an intuitive decomposition of it into two mutually exclusive sources (i.e., technical change and technical efficiency changes). Since then a considerable amount of effort (e.g., Ray and Desli, 1997; Balk, 2001, 2004; Lovell, 2003; Grosskopf, 2003) has been devoted to extend this decomposition and to develop a more detailed analysis of its sources of growth. Even though there is a general cohesion on measuring the effect of technical efficiency changes, several alternatives (more or less intuitive) exist for measuring the effects of technical change and of scale economies. However, as clearly noted by Balk (2004) there is no unique way of decomposing any measure of productivity change.

Concerning the implementation of the Malmquist productivity index, on the other hand, it is evident from the survey of Fare, Grosskopf and Roos (1998) that the majority of empirical studies have used DEA. In a non-parametric context, estimates of the Malmquist productivity index as well as its sources of growth are obtained by computing appropriate ratios of distance function values corresponding to constant- and variable-returns-to-scale technologies. The advantages of the non-parametric approach stem from its ability first, to function in cases with insufficient degrees of freedom; second, to overcome extreme invariability in the data and third, to model production technology without imposing a particular functional form. Nevertheless, it lacks statistical hypotheses testing regarding the significance of the assembling parts of the Malmquist productivity index as sources of change.

Several more recent studies (i.e., Coelli, Rao and Battese, 1998; Rossi, 2001; Balk, 2001; Fuentes, Grifell-Tatje and Perelman, 2001; Orea, 2002) have used the parametric (i.e., econometric). Unlike DEA, the parametric approach does not require the estimation of constant-returns-to-scale production technology. Instead estimates of various components, and consequently of the Malmquist productivity index, are obtained from a fitted distance function with variable returns to scale.1 In fact, two distinct routes have been used within the parametric approach. First, Coelli, Rao and Battese (1998, p. 234) and Rossi (2001), following Nishimizu and Page (1982), estimated the Malmquist productivity index by using geometrical means of time derivatives for any two adjacent periods. Second, Balk (2001), Fuentes, Grifell-Tatje and Perelman (2001) and Orea (2002) used discrete differences of the fitted distance function values evaluated at adjacent periods’ input and output quantity data. Since economic data do not come in the form of continuous records, the use of time derivatives to estimate discrete changes may be misleading.

The advantages of the parametric approach stem for the fact that first, it allows for an appropriate treatment of measurement errors and random noise and second, it permits formal statistical hypotheses testing. The latter is particularly important as it can be tested whether (i) technical efficiency is time varying; (ii) there is technical change; and (iii) production technology exhibits (local) constant returns to scale.3 In each case, one (or more) of the components constituting the Malmquist productivity index will remain unchanged and thus, it will not contribute to growth. For example, if technical efficiency is found to be time invariant, then the contribution of the technical efficiency change effect on productivity would be zero. Similarly, if the rate of technical change is statistically not different than zero, then the technical change effect vanishes. Finally, if production exhibits (local) constant returns to scale, then there is no scale effect. Even though these features have not explored in previous parametric studies, it is clear that have important implications in obtaining appropriate empirical results and in dealing with policy measures design to enhance productivity.

The aim of this paper is to extend the methodology of Fuentes, Grifell-Tatjé and Perelman (2001) to accomplish the remaining assembling parts of the Malmquist productivity index, namely scale efficiency change and input-mix effects. We also develop the necessary hypotheses testing regarding the statistical significance of the various sources of growth. For these purposes, parametric restrictions are derived for testing the hypotheses of constant returns to scale, ray homogeneous technology, no technical change, and implicit Hicks input- and output-neutral technical change. It is expected that these hypotheses testing strengthen further the parametric approach.

The proposed procedure is applied to a sample of Greek seabass and seabream farms for the period 1995-1999. During the last two decades, seabass and seabream industry has been one of the faster growing industries in Greece and since the first half of the 1990s it has dominated the aquaculture sector. Output grew dramatically and the number of seabass and seabream farms almost doubled in the first half of the 1990s. Eventually Greece became the largest producer of seabass and seabream in Europe accounting for around 50% of total European production and also the largest exporter. Identifying the sources of growth in such a fast expanding industry is of considerable importance for gaining insights on its development process and also for designing future policies. 

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