1. BACKGROUND

Fishing power provides a measure of vessel efficiency. Garstang (1900) developed the notion of fishing power to measure relative efficiency between gear and vessel types and over time, based on total annual catch (Smith 1994). Garstang tried to account for the greater relative efficiency of one type of fishing gear compared to another. In the process, Garstang develop the procedure of standardization. Subsequently, Gulland (1956) and Beverton and Holt (1957) and others further developed the notion.

2. DEFINITION

Following Gulland (1956), fishing power can be defined as the
product of the area of influence of the gear during a unit operation and the
efficiency of the gear during that operation. Because absolute fishing power is
difficult to measure, the concept of relative fishing power is frequently used.
Relative fishing power as defined by Beverton and Holt (1957; pp. 172-173) is
the “ratio of the catch per unit fishing time of a vessel to that of
another taken as standard and fishing on the same density of fish on the same
type ground.”^{1} More operationally, fishing power of any vessel
can be defined by reference to a standard vessel, whose fishing power is
expected to be constant, by comparing the catches of these vessels when fishing
at the same time and place (Smith, 1994; Turvey, 1964). This standardization
attempts to account for heterogeneity in vessel characteristics, such as size,
age, engine horsepower, gear, and skipper skill.

3. STANDARDIZATION OF FISHING POWER

One commonly used approach to standardize fishing time is to divide the catch per unit of effort of a vessel (or class of vessels) by the catch per unit of effort of the reference vessel (or class of vessels), where the unit of effort is some period of time (Garstang, 1890; Gulland, 1956; Beverton and Holt, 1957). This approach provides what an economist terms a partial productivity measure, since it measures catch per vessel. Partial productivity measures, however, may provide misleading results, since output increases may arise from the increased or decreased use of other economic inputs with changes in market conditions, such as crew size, the state of technology (e.g. fish finders, other electronics), or changes in capacity utilization. This limitation to partial productivity has led economists to an emphasis upon what is called total factor productivity. The multidimensional nature of effort is recognized, so that effort is viewed as a collection of all inputs used in the production process.

When a vessel class is used to standardize catching power, the vessel must have a constant (relative) catching power or productivity (Smit, 1996). A group should be selected which has been stable over the considered period, in that there were no investments in new and more efficient vessels and no drain of skilled skippers to new vessels in other groups. Even standardized fishing capacity should be corrected by the potential number of days at sea for each group (Smit, 1996).

3.1. Index numbers

Fishing power can be standardized by one or more intermediate steps (Gulland, 1983; page 40). This raises issues from economic index numbers such as transitivity, circularity, type of index numbers (e.g. superlative, or essentially functional form issues), chain versus fixed based indexes, bilateral versus multilateral indices, and others.

Indexes can be formed by either the chain or fixed-based methods. The fixed-base procedure directly compares all changes in catch to a selected vessel category. This base group may remain constant or may be changed after some time period. Chain indexes directly compare adjacent groups in a sequence of comparisons. A fixed-based index may be obtained by multiplication of chain indices. Nonadjacent observations are compared indirectly by using the intervening observations as intermediaries. This practice results in transitive comparisons and makes use of all the available data, using intervening observations as intermediaries.

Bilateral comparisons provide intertemporal comparisons of groups. Because of the large number of possible binary combinations which are not necessarily transitive, bilateral comparisons are inappropriate for comparisons that are not binary. For example, suppose that vessel or gear group 1 serves as the basis of standardization for fishing power and there are two other groups, 2 and 3. Then fishing power is standardized for groups 2 and 3 vis-a-vis group 1 in binary comparisons. However, the fishing power of groups 2 and 3 cannot necessarily be accurately compared to one another, since these types of comparisons are not necessarily transitive.

Multilateral comparisons can be made that are transitive (Caves et al., 1982). Transitive comparisons are made by making all possible binary comparisons in terms of the geometric mean of all groups. Thus the fishing powers of groups 2 and 3 are compared with each other by comparing both with the geometric mean. Multilateral indexes directly compare adjacent and nonadjacent observations but only by destroying the fixity of historical comparisons. As additional observations are added over time, thereby expanding the set of comparisons, the multilateral index changes because the geometric mean of the observations changes. In contrast, bilateral indexes do not directly compare nonadjacent observations and the historical comparisons remain intact.

Kirkley and Strand (1981) and Kirkley and DuPaul (1995) considered the use of index numbers to characterize standardized measures of fishing power and effort for the U.S. Mid-Atlantic surf clam and ocean quahog fisheries, the New England groundfish fishery, and the Atlantic sea scallop fishery. Standardization was based on several factors: (1) LPUE, (2) costs, (3) revenues, and (4) technical efficiency. In all cases, fishing power measures were converted to multilateral indices.

3.2. Frontier functions

Fishing power can also be standardized using the stochastic production frontier approach to measuring technical efficiency (Kirkley and DuPaul, 1995). This approach incorporates input usage (days at sea, capital or vessel or size, crew size, etc.), possible environmental limitations (e.g. a vessel of some size may not be able to fish on certain grounds in some parts of the year) and random noise, such as storms, into the standardization. A stochastic production frontier is estimated and estimates of maximum output and technical efficiency obtained. The estimation could be over a year, month, or some other time interval, depending on the data availability. The most efficient vessel has the maximum output per bundle of inputs given resource conditions and so on. The most efficient vessel serves as the benchmark for standardization with other vessels efficiency or fishing power evaluated in terms of this most efficient vessel. Standardization can then be based on the number of days fished or total catch per unit effort.

Fishing power can also be standardized with the fixed effects panel data approach to measuring technical efficiency, discussed in Atkinson and Cornwell (1994). Either an output or input technical efficiency could be adopted, but consistency with the Garstang-Gulland-Beverton-and-Holt approach, which is focused on output or catch, would indicate that output technical efficiency is the desired approach. (Output technical efficiency evaluates technical efficiency in terms of maximum output given the input bundle while input technical efficiency evaluates technical efficiency in terms of the minimum input bundle required to produce a given output. The two measures coincide only under constant returns to scale.) In this approach, a production function is estimated with one firm chosen as the base case or intercept and the relative catch rates of other firms (the variation between firms) accounted for by the intercept dummy variables while the variation within firms accounted for by the economics inputs (capital, labor, fuel, etc.). The resource stock can be assumed constant for short time periods or estimates of biomass used or fixed effects extended to time effects (dummy variables for time periods).

4. ALTERNATIVE NOTION OF FISHING POWER: POTENTIAL ABILITY TO CATCH FISH

An alternative notion of fishing power underlies most notions of “fishing capacity” in the fisheries literature. This notion of fishing power is not that of Garstand-Berton and Holt-Gulland. Rather, this concept of fishing power measures, as observed by Taylor and Prochaska (1985), the potential ability of a vessel to catch fish, with this potential defined in terms of average vessel characteristics rather than the catch rates per unit of time of individual vessels.

Taylor and Prochaska (1985) observe that a vessel with a larger crew or larger size should have the potential to catch more fish than a vessel smaller in both dimensions, regardless of the type of fishing ground or density of the resource stock. Fishing power is defined in terms of the aggregate input composition of vessels in the fishery rather than the catch rates per unit of time of individual vessels. They further observe that the Garstang-Beverton and Holt-Gulland notion of fishing power is theoretically attractive, but of limited empirical tractability. Either differences in relative fishing power must be assumed away (as in composite effort measures such as vessel-ton-days), or an alternative notion of fishing power with less stringent data requirements must be developed.