Modelling Technical Efficiency

Focusing on technical efficiency excludes analyses of allocative and economic efficiency, which abound in the general economics literature. However, allocative- and economic-efficiency studies require price data and require that the principal objective of boat captains consists of maximising profits or minimising costs. Here we restrict attention to the purely technical relationships between inputs and outputs. One branch of early empirical work comparing catch per unit of effort of the operating boats has been criticized (Wilen, 1979) because it takes into account neither the multi-dimensional nature of effort nor the randomness of the fisheries production process. Hence, recent studies rely on multi-dimensional frameworks and accommodate random shocks in the production process. These studies are attractive for reasons other than the fact that they can be implemented with only input and output quantities, but this remains one compelling reason for their prevalence in applied econometric work.

Methods of efficiency measurement (reviewed in Coelli et al., 1998 and in Fried et al., 1993) are divisible into two categories, namely parametric and non-parametric approaches. Data envelopment analysis (DEA) (Charnes et al., 1978) is the predominant non-parametric approach. The method has been used extensively in agriculture and in banking but has been used only rarely in fisheries (Walden et al. (2003) is one recent exception). The relative unpopularity of non-parametric approaches stems from their inability to accommodate randomness, which, because of the biological processes impacting marine resources (weather, resource availability and environmental influences), is fundamental to fisheries-efficiency analysis (Bjorndal et al., 2002; Kirkley et al., 1995). In addition, non-parametric methods generate little information about the nature of the harvesting technology, such as its returns to scale or the degree of substitutability among inputs and outputs, both of which have important implications for fisheries management.

First generation, parametric methods (Aigner and Chu, 1968; Afriat, 1972) rely on deterministic frontiers and do not accommodate randomness. Although now largely obsolete, these methods are noteworthy because they include the first recorded fisheries efficiency study (Hannesson, 1983). Nowadays, parametric studies are derived from stochastic (composed-error) production frameworks (first proposed by Aigner et al., 1977). Unlike its precursor, composed-error models allow technical inefficiency to be distinguished from random shocks. A generic formulation has structure yi = f (xi; ¡3) + Ui - Zi, (2.1)

where yi denotes output of boat i and f (xi; f3) is the production function that depends on a vector of parameters f3 and a vector of inputs xi. The stochastic component of the model includes a random shock ui, which is usually assumed to be identically, independently and symmetrically distributed with variance a2; whereas the inefficiency term, zi, follows a one-sided, nonnegative distribution. The likelihood function can be expressed algebraically and maximized numerically to produce estimates of the unknown parameters. Typically, the inefficiency components take half-normal, truncated-normal or gamma distributed forms and predicted inefficiencies can be computed for each boat (Jondrow et al., 1982). One major limitation of this approach is that the efficiency scores cannot be estimated consistently (Khumbhakar and Lovell, 2000). Fisheries applications are numerous (see, for example, Kirkley et al., 1995; Grafton et al.,2000).

A somewhat deeper issue absorbing considerable econometric attention is locating the determinants of inter-vessel differences in efficiency; but the task, it seems, is beset with difficulty. Because, during estimation, it is usually necessary to invoke the assumption that the zi are iid across firms, it is inconsistent, in a second step, to explain efficiency levels by firm-specific characteristics (see Coelli et al., 1998; for discussion). A one-step procedure is developed by Battese and Coelli (1995) whereby the distribution of the zi > 0 is truncated normal with mean ji determined according to where wi = (wii, w2i,■ ■■, WKi)' denotes the variables conjectured to influence efficiency and 5 = (5i,52, ■ ■■, 5K)' denotes their impact on the conditional mean, A statistically significant coefficient associated with any wj indicates that the variable in question affects boat efficiency. This model has been applied extensively in fisheries research and remains popular currently. Recent examples include Pascoe and Coglan (2002); Squires et al. (1999); Andersen (2002); and Pascoe et al. (2003). The model's popularity is almost surely due to its ease of estimation as facilitated by FRONTIER, the freely-available software developed by Coelli.

Panel data remain mostly unexploited in fisheries efficiency analyses. In fact, with the exception of Squires et al. (2003) each of the aforementioned studies have panel structures with repeated (time series) observations on each boat. Yet, the potential richness of the panel structure remains untapped (Alvarez, 2001). In an effort to address this issue two recent approaches are noteworthy. One approach consists of modifying the previous framework to allow inefficiencies to vary parametrically over time. The most popular model here is the one advocated by Battese and Coelli (1992). They suggest that the inefficiency terms zii,zi2, ■■■, ziT evolve according to where the zi are iid normal with mean j, truncated at zero; t denotes the present time period; T denotes the terminal period; and n denotes a parameter to be estimated. In this model, technical inefficiencies are a monotonic function of time, which is increasing for n < 0 and decreasing for n > 0 and, thus, the estimation of n is paramount. The underlying idea, they claim, is that managers should learn from previous experience and technical inefficiency should evolve in some consistent pattern (Coelli et al., 1998). Applications include Herrero and Pascoe (2003), Pascoe et al. (2003) and Bjorndal et al. (2002).

A second approach to time-varying efficiency adjusts standard panel estimation techniques. The advantages are that panel-data models do not require the strong distributional and independence assumptions made in maximum-likelihood estimation and that panel models permit the consistent estimation

of efficiency scores (Schmidt and Sickles, 1984). One common reformulation of equation (2.1) assumes the existence of a firm-specific, non-stochastic effect. Under the assumption that zt is itself dependent on a vector of covari-ates the model is estimated using ordinary least squares (OLS) and produces consistent estimates of the efficiency scores (Kumbakhar and Lovell, 2000). Unfortunately, the approach has additional limitations. Most notably, the fixed effects provide reliable estimates of firm-level technical efficiency if (and only if) each of the frontier covariates is time-variant. Time-invariant covariates create major problems, which is a point worth emphasizing in the current context. In fisheries investigations boat characteristics remain largely invariant over the sample period and many of the frontier covariates will be time-invariant (see Alvarez, 2001 for a detailed discussion). Consequently, the fixed-effects model has rarely been applied to fisheries efficiency investigations (although Alvarez et al. (2003) lists Squires and Kirkley (1999) and Kirkley et al. (1995) as exceptions).

The introduction of random-effects into fisheries efficiency studies is important for two reasons. First, their introduction enables the time-invariance issue to be circumvented. Second, the (classical) random-effects methodology provides an important link to the hierarchical methodology that we exploit. As noted by McCulloch and Rossi (1994), in the Bayesian context there is no distinction between fixed and random-effects (because the parameters themselves are random), there is only a distinction between hierarchical and non-hierarchical analyses. However, Koop et al. (1997) suggest that it is useful, for pedagogic purposes, to retain this (frequentist) terminology. Applications of the random-effects methodology in fisheries include Squires and Kirkley (1999) and Alvarez and Perez (2000).

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