Estimation of cost functions in a data poor environment: the case of capacity estimation in fisheries

Abstract

Fisheries economic analysis is often handicapped by the lack of adequate data to undertake robust econometric analyses. In this study, a translog cost function was required to estimate the potential direction of adjustment in a UK fleet segment if a new regulatory regime was introduced. However, the available data were not appropriate for such estimation. Data envelopment analysis (DEA) was used to modify the data subsequently used in the estimation of the long-run cost function. The resulting model appears robust and is consistent with economic theory and the supporting evidence produced using DEA.

Acknowledgement

This project was undertaken as part of the EU funded project ‘Modelling fishermen behaviour under new regulatory regimes’ (QLRT-2000-01535). This work was undertaken whist working at the Centre for the Economics and Management of Aquatic Resources (CEMARE), University of Portsmouth UK.

Notes

¹ A fishery is generally considered to consist of a set of vessels targeting a similar set of species in a particular geographical area. Usually, the size of the geographical area is defined by the distribution of the stock. For some species, this can be expansive, while for other species it may be a relatively small area. As several different types of fishing gear are often used, the fishery is broken down into a number of fleet segments.

² Production functions and stochastic production frontiers have been employed to consider the implications of input controls in fisheries (e.g. Pascoe et al ., 2001; Del Valle et al ., 2003; Weninger and Strand, 2003; Kompas et al ., 2004). The assumption underlying these analyses is that capital is effectively fixed in the short term, and that incentives exist to maximize output or revenue (e.g. Kirkley and Strand, 1988). When considering the adoption of individual transferable quotas, this assumption is not valid, as fishers would be expected to adjust their capital in order to minimize the costs given the output constraint. Hence, a cost or profit function may be considered more appropriate (Lipton and Strand, 1992 and Alam et al. , 2002 for examples).

³ The delineation of the fleet into ‘over 10 m’ and ‘10 m and under’ length categories has implications for management regulations both within the UK and also at the European level. The under 10 m fleet segment dominate the industry in terms of vessel numbers (74% in 2002 (DEFRA, 2003)), but contribute less than 10% of the value of the catch. The under 10 m fleet are not subject to individual quota controls, but are generally subject to catch limits that vary month to month.

⁴ The cost function can also be developed for a multi-output industry. The single output case is presented for the sake of simplification.

⁵ Data on a small number of vessels under 10 m were also available. As these vessels are not subject to the same individual quota regulations as the larger vessels these data were not used. The data were collected through personal interview by the Seafish Industry Authority for the North Sea and Irish Sea, and by CEMARE for the English Channel.

⁶ In the UK, VCUs are defined by length * breadth + 0.45 * engine power. These were found to be highly correlated with fishing capacity in trawl fisheries (Pascoe et al ., 2001).

⁷ This essentially assumes constant returns to fishing effort. Previous studies of revenue functions for the North Sea and English Channel demersal whitefish trawl fleet have found the production elasticity associated with days fished is around 1 (Pascoe et al ., 2003), suggesting that such an assumption is realistic.