A COMMERCIAL FISHERY

A Commercial Fishery

A Commercial Fishery

Question A

In the standard model of open-access fisheries, the "catchability coefficient" q which links the catch per unit effort to the size of the fish stock is assumed to remain constant. This constraint gives rise to several difficulties: (i) in a fishery where the relative use of gear types and vessel tonnage classes is frequently changing, to assume a constant level of q has little a priori likelihood; (ii) even for a specific class of vessel and type of gear, to fix q ignores the existence of technical change that q may be dependent upon stock levels; and (iv) by fixing q over time, an complex error term is created that makes difficult the choice of a suitable estimator. This paper describes an estimation procedure which obviates the need to assume an unchanging q, and yet remains econometrically tractable (Gould, 2002, 56). The results of applying this algorithm to the case of a specific fishery are also reported. The second section describes the model itself.

An Algorithm for Estimating Dynamic Open-Access Models

The following harvest function is widely used at the fleet level:

Yt = qtXtEt

where: q = "catchability coefficient," here left unconstrained over time,

I X = stock offish, and'

E = "fishing effort" (in this paper captured by the number of days spent fishing).

This functional form has a number of recognised limitations. For example, it takes account neither of gear saturation nor of congestion among fishing vessels. Moreover, that q—the catchability coefficient—may be dependent upon the stock level X. The concept of effort—an "intermediate output"—this functional form is unsuitable for the exploration of such issues as the optimal employment of primary inputs, capital and labour (Aoki, 1996, 52). There is reason to suspect, then, that the true elasticities of effort and stock levels may differ from one. On the other hand, one of the explanatory variables in the harvest function— the stock level—is not only unobservable but also exhibits dynamic behaviour (based on the biological growth rate of the fish and on the rate of harvesting, as discussed below).

The parameters of this natural growth rate also need to be estimated. As a result of these complexities, elasticities other than one in the harvest function render estimation of the model intractable. To avoid such difficulties by using ICES data for stock levels but, in the present study, the emphasis is on estimation of stock levels and this approach cannot be used.

This study therefore uses the harvest function Y, = qiXiE^, recognising its limitations. Suppose that the growth rate of a particular fish stock, X, is assumed in the absence of harvesting to be given by the logistic growth function:

F(X) = rX[l - X/K]

where: r = biological growth rate of the species being modelled, and

K = environmental carrying capacity of the fishing ground.

With fishing yields being represented by Y, changes in the stock level are expressed as follows:

X,^, - X , = F(X,) - Y, + e,^,

= rXj - rX,2/K - Y, + e,, (1)

where ...