1. PROXY VARIABLES FOR PHYSICAL MEASURES OF CAPITAL STOCK OR EFFORT

One or more vessel attributes are frequently used as proxy variables to measure the physical capital stock. These attributes are proxy variables since the entire collection of inputs cannot be observed but it is believed that important vessel attributes, such as vessel size and engine power, provide observable and measurable surrogates for the variables of actual interest.

1.1. Vessel size

The most widely used proxy variable is vessel size. Vessel
size, measured in length or gross or net tonnage, and engine power are limited
measures of fishing power. There is no fixed relationship between them and
fishing mortality rates (Holden, 1994). Length and tonnage are closely related
but nonetheless differ and give different results (Cunningham and Whitmarsh,
1980).^{11}

Each measure has its own particular limitations. Vessel length
is limited in that vessels of the same length can vary dramatically in tonnage,
design, speed, hold capacity, gear type, weatherability, and so forth. Vessel
length can also be measured in a number of different ways, and great care must
be taken to insure a consistent measure.^{12} From a survey of marine
architects, the Southwest Region of the U.S. National Marine Fisheries Service
(1993) reported that a 50 foot vessel can be altered (width, depth, and hold
capacity) to act like a 70 foot vessel. Gross registered tonnage, a volumetric
measure, represents the enclosed volume of a vessel. It suffers from the
drawback that the rules which specify its measurement can lead to vessels with
identical external hull design but with different gross registered tonnages,
depending upon their internal construction (Hamlin ,1990; Holden, 1994). Pearce
and Wilen (1979; footnote 11) observe that the measurement of net tonnage is
complicated and not always consistent; that vessels can be redesigned to
increase catching power with a fixed tonnage; and that a large vessel may have
greater catching power than two or more smaller vessels of the same
tonnage.

When vessel size or number of vessels is used as a proxy variable for fishing power or effort, other problems arise in addition to the measurement error. Specifically, the stock of capital does not account for the different vintages (ages) of capital (which embody different levels of technology, such as hull design) or the amount which a stock of capital is actually used in a given time period (the services from the stock of capital).

A relationship does not necessarily exist between vessel size and the productivity of the gear and equipment on board the vessel (Travis, 1997). Large vessels may not carry the most technologically advanced equipment. Vessel size may not even dictate how much gear is kept on board. Vessel size also does not necessarily determine vessel design. Travis (1997; page 31) observes, “For example, two vessels of the same size could have very different hold and fuel capacities.” In addition, there may not be a relationship between vessel size and the amount of skills and knowledge possessed by the vessel's operator and crew.

Hamlin (1990) recommends measuring vessel size based on the cubic number found by multiplying length * beam * depth. According to Hamlin (1990), regression analysis has demonstrated that the building cost of a basic vessel of a given type can be quite accurately estimated knowing only this cubic measure and the total installed horsepower. To this could be added the estimated cost of such specialized equipment as fishing winches, etc.

In addition, vessel size at best provides a proxy variable for gross capital stock, but by excluding any notion of physical deterioration and investment not captured by a static vessel size, and hence economic depreciation, net capital stock is excluded. Over long enough time periods, a widening divergence between the inaccurately measured gross capital stock in one time period and the net capital stock is expected to increase.

2. MEASURES OF HETEROGENEOUS CAPITAL STOCK

Typically, the stock of capital in a fishery is heterogeneous (i.e., there are a multitude of capital goods employed in the harvesting process). The stock of capital includes the vessel hull, main and perhaps auxiliary engines, winches, booms, holds, chilling or cooling or freezing equipment, many types of vessel electronics, and still other types of fishing capital. The variety of capital assets in many cases leads to treating some types of capital as homogeneous even though they are not. For example, the different types of gear or electronics are typically lumped together, and for that matter, the entire capital stock is frequently lumped together and then measured by one or two proxy variables, such as length and main engine power.

The problem of aggregating heterogeneous capital into a consistent composite measure of capital is the same as creating a consistent composite measure of all inputs into fishing effort. This aggregation requires one of the three conditions: (1) (weak) homothetic separability of capital, so that the marginal rates of substitution of different pieces of capital remain constant in the face of changes in other inputs or outputs; (2) Leontief separability, where the quantities of the different pieces of capital remain in fixed proportions over time; or (3) Hicks separability, where the prices of different pieces of capital remain in fixed proportions over time.

The principal practical options for directly measuring capital stocks are to find a direct estimate of the capital stock; to adjust book values for inflation, mergers, and accounting procedures, or to use the perpetual inventory method (Hulten, 1990). As a direct estimate of the capital stock, Pearse (1972) suggested that the value of the harvesting capital stock provides a scalar measure of all the dimensions of harvesting capital (cited in DFO n.d.). Hannesson (1987; page 15) represented available fishing effort by the cost of capital invested in fishing equipment, measured at the time of investment. Valatin (n.d.) measured the stock of capital measured by the total market value of vessels in the fleet, where insurance values of the vessel (including gear and electronics) were observed to possibly be the best available approximation.

For Denmark, Frost, Lanters, Smit, and Sparre (1995) used the insurance value of Danish vessels to measure capacity conceived as fishing power (capital stock). They noted that vessel size measured in GRT and/or horsepower is considered a better capacity measure than the number of vessels, but that the development of electronic and hydraulic equipment made this capacity measure inappropriate, leading to the use of insurance value. They further observed that use of an economic term may also reflect expectations. Hence, fishers probably will not adjust the insurance value of each single vessel downwards due to poor expectations, so that decreases in insured value must come from a reduction in fleet size. Moreover, insurance value is not changed every year but rather mostly once new equipment has been installed or a major repair has occurred. To reflect the development in real fishing power, the insurance value has been deflated by a deflator-GNP (current prices)/GNP (fixed prices).

When the current dollar values of each component of the capital stock are added up, the values should be deflated to the price level prevailing in some base year (Hulten, 1990). Finding a plausible price index for the deflation process can pose challenges. When the individual asset prices move together, so that they are proportional, the price levels differ only by a constant. The units of quantity can then, at least in principle, be redefined to make asset prices identical. As Hulten (1990; page 132) observes, “This is the case in which the Hicks aggregation theorem applies and a capital stock can be calculated provided that the aggregate efficiency sequence is the same for each component of the aggregate.”

The theory of hedonic prices provides another approach to directly measuring the capital stock. It offers one solution to the problem of accounting for a wide variety and number of capital goods, such as the vessel hull, engine, gear, equipment, and even varying characteristics such as hold capacity (Hulten, 1990). In this framework, the individual capital goods are viewed as bundles of characteristics rather than as discrete physical entities. The “inputs” to the production or fishing power function are the amount of each characteristic rather than the amount of each physical good. The hedonic approach is especially useful when there are many varieties of capital embodying a few characteristics.

Kirkley and Squires (1988) used hedonic analysis to estimate the fleet capital stock and investment in New England. They also found that the number of vessels was an inadequate indicator of the level of capital stock and investment in a fleet comprised of vessels with heterogeneous characteristics. This approach could be used to establish a benchmark of capital for different gear types and vessel size classes and combined with the perpetual inventory method of measuring a capital stock. By measuring both the capital stock and investment, measures of net (as opposed to gross) capital stock are obtained.

Still another approach to measuring the capital stock is to apply the perpetual inventory method. This approach requires an estimate of the value of investment spending, a quality-adjusted investment deflator, possibly a retirement distribution, and an efficiency sequence. While there are numerous and various practical issues to applying the perpetual inventory method, there are three central problem areas: (1) the estimation of investment in current dollars by industry and asset; (2) the development of suitable investment-good deflators; and (3), the estimation of efficiency sequences and retirement distributions, due to different vintages, giving reductions in the capital stock (Hulten, 1990). The perpetual inventory method, which measures the growth rate of the capital stock, can estimate the growth rate of the service flow under the assumption that the flow of capital services is proportional to the stock of capital assets (Hulten, 1986).

The capital stock can be measured in efficiency units to
account for embodied technical progress (Mairesse, 1978). Though the measurement
of the capital stock in efficiency units, denoted K^{*}, theoretically
depends on the full age distribution of capital, a very good approximation to
K^{*} is given by Mairesse. The approach depends on the level K and the
average age of capital A (both conventionally measured) and is computed in the
following way:

Log K^{*}_{t} = LogK_{t} + e (t - A_{t}),

where A_{t}^{ =} S _{v = V to t }(t -
v)(K_{t}^{v}/K_{t}), t denotes the year or time period,
A_{t} denotes average age of capital at time t, e is the rate of embodied progress, and
K_{t}^{v} denotes the stock of capital at vintage v still in
operation in year t (the year V being remote enough in time as to mean that all
earlier investments have effectively been retired). Mairesse gives details on
the estimation of e.

2.1. Weighting the components of capital

In some instances, an aggregate or composite measure of the capital stock is desired. The issue then arises of how to best weight the individual components to derive an overall aggregate. For example, Vessel Capacity Units (VCUs) used in the United Kingdom, are defined as Vessel Capacity Units = length * breadth + 0.45*power, where length is the overall length of the vessel in meters, breath is the breadth of the vessel in meters, and power is engine power of the vessel in kilowatts (Valatin 1992, Smith 1997). The weight attached to length*breadth is 1 and that attached to engine power is 0.45.

Value (dollar, ecu, etc.) measures of heterogeneous capital stock allow weighting of the heterogeneous capital goods. Two widely applied indices in this case are arithmetic and geometric means using the value shares as weights. Still other indices are available, such as the Tornqvist, Vartia, and Fisher Ideal.

2.2. Vessel numbers and fleet sizes

Statistics on fleet sizes or vessel numbers may also be limited. In the European Union, most Member States do not keep records of the number of small vessels (Holden, 1994). In no Member States are there records of which registered fishing vessels are actually engaged in fishing (Holden, 1994). However, all fishing vessels will be licensed under the provisions of Regulation No. 3760/92 and it is also foreseen in the proposals of the European Commission that their activities will be monitored by satellite (Holden, 1994).

The fleet's harvest capacity is not necessarily the sum of the vessels' harvest capacities because of interdependencies between the vessels' abilities to catch fish (Valatin, 1992; Travis, 1997). Thus there are external effects.

2.3. Engine power

When engine power (HP or kw) is used as either a complete or partial measure of fishing power or available fishing effort, problems of measurement error can arise. In the U.S., the Coast Guard collects horsepower information but it is not routinely updated. Thus, for example, an engine may be replaced and upgraded with a higher engine power, but the original engine power is retained in the records. Engine power is difficult to monitor and is easy to manipulate. However, despite its disadvantage, engine power is internationally defined with standardized rules for measurement (Holden, 1994). This limits disputes among vessel owners and even nations. Another issue is whether to include power of any auxiliary engines.

2.4. Gear

Length of trawl net has been proposed as the unit to measure and manage available fishing effort. Two limitations of this approach have been voiced: (1) that the opening of the net (which determines the swept area) has more to do with available fishing effort than the length of the trawl net and (2) trawl nets are fairly easy to change (Csirke, 1996). In addition, mesh size and design affects catch rates and compositions. When longline gear are used, the number, spacing, and type of hook is important. For example, Ginter (1993) observes, ...“the harvesting capacity of the Pacific halibut fishery practically doubled with the substitution of the circle hook for the “J” hook regardless of the number of vessels in the fishery or their dimensions.” In the case of dredges, the width of dredges may be considered to be an indicator of available fishing effort.

3. CAPITAL VINTAGE AND EMBODIED TECHNICAL CHANGE

The stock of capital entails substantial heterogeneity in terms of its effectiveness (marginal productivity) and embodiment of different states of technical progress. Physical measures of vessel size not only fail to fully capture the entire stock of capital but they overlook differences in design embodied in investment that reflect different states of technical progress. Physical measures of vessel size also overlook physical deterioration. The concept of vintage of the capital stock deals with these types of issues.

To some extent, technical progress can occur in the absence of gross investment, called disembodied technical progress. Other innovations may require only slight modifications of the existing capital equipment and hence only small capital expenditures. Many vessel electronics probably fall into this group. Other innovations, however, can only be introduced by scrapping the old capital stock and replacing it by new capital that embodies the new technology. These changes are introduced by gross investment. These embodied innovations also alter the effectiveness or marginal productivity of the other factors of production, such as labor.

The age or vintage of the capital stock is sometimes used to capture the effects of technical change that has been embodied in the capital stock. For example, differences in basic hull designs might be captured by the age of the vessel in a production or fishing power function. Estimates of the years of remaining vessel or engine life have also been used to account for vintage effects (Alam et al., 1997).

Vessel age is also sometimes used to capture physical deterioration and hence economic depreciation of the capital stock. Regular maintenance of a vessel, engine, and gear both prolong their lifetimes and also their effectiveness. Nonetheless, some physical deterioration typically occurs, limiting the capital stock's effectiveness, unless there has been a substantial rebuilding or overhauling.

Capital vintage may not capture the changes that have occurred when a vessel or engine was rebuilt or overhauled. Taken to an extreme, some vessels were built at a very early date, but due to extensive rebuilding and overhauling over the years, are scarcely the same vessels as when they were originally constructed.

Another issue arises with capital vintage. Under what
conditions can different vintages of capital and technology be collapsed into an
aggregate production or fishing power function defined with respect to an
aggregate measure of capital? For example, the vessel hull may have been
constructed in one time period, the engine another, electronics in still
another; each item of capital embodying a different state of technology. How can
they be aggregated accounting for these different vintages of capital and
technology, forming the aggregate capital stock of a fishing vessel? In essence,
old capital enters the production process as if it were the equivalent to a
smaller amount of new capital (Hulten, 1990).^{13}

The capital stock can be measured in efficiency units to account for embodied technical progress and capital vintage (Mairesse, 1978). This approach was reviewed above.

4. PRODUCTIVITY GROWTH AND TECHNICAL PROGRESS

Vessel attributes such as hull size, engine power, and gear do not fully account for catch. Continued growth in productivity of fishing vessels also contributes to catch. This increase in “effective” rather than “nominal” effort, i.e. the growth of “fishing power”, arises from improvements in design, use of more efficient gear, adoption of vessel electronics, improvements in fishing practices, and other factors (Garcia and Newton, 1997; Kirkley, 1984; Holden, 1994; Squires, 1992 and 1994b; Travis, 1997). Exclusion of productivity growth can bias estimates of capacity and capacity utilization. For this reason, Garcia and Newton (1997), for example, accounted for productivity growth when they applied the peak-to-peak method of capacity measurement.

There is no easy approach to measuring productivity growth. Estimating a Solow (1957) residual from growth accounting, Kirkley (1977), Kirkley and Strand (1981), and Squires (1992; 1994b) applied the approach of economic index numbers.

5. FISHING SKILL

Vessel attributes such as age, length, tonnage, horsepower, and even productivity may not fully account for catch. Instead unobserved managerial ability - “skipper skill” - may be an important component explaining catch rates (Carlson, 1973; Cunningham and Whitmarsh, 1980; Hilborn and Ledbetter, 1985; Campbell, 1991; Travis, 1997; Kirkley et al., 1998). Gates, Holland, and Gudmundsson (1996) and Christy (1996) observed that the single most important component of the capacity of a vessel, aside from its size and gear, is the skill of the captain.

There are several ways to account for skipper skill in a fishery production function or “fishing power” function. First, skipper skill could be readily included by the proper pooling of cross-sectional and time series data (panel data), where a fixed effects model (separate dummy variables for vessels) accounts for fishing skill related to handling the different inputs and a variance components model (the intercept is a random variable) accounts for fishing skill related to differences between vessels such as finding and catching fish, handling inclement weather, vessel breakdowns, etc. (Squires and Kirkley, 1997). The fixed effect approach implies that skipper skill is closely related to how the skipper handles vessel attributes and other inputs. The random effects approach implies that skipper skill is more closely related to unobserved inter-vessel differences such as find and catching fish proper. The Hausman-Taylor test of exogeneity (Hausman and Taylor, 1981) can be used to statistically test which approach is appropriate. One limitation to this approach is that accounting for inter-vessel differences can also pick up factors other than managerial ability affecting differences in catch rates between vessels. This approach also assumes that managerial ability neutrally shifts the fishing power function.

A second approach to account for skipper skill includes indexes of managerial ability based on the performance of vessel captains, such as average, good, or excellent (Comitini and Huang, 1967; Campbell, 1991). One difficulty with this latter approach is that simultaneous equation bias may be introduced into any statistical estimates since the managerial measures are based on output.

Another approach is to consider the characteristics of the captain such as age, education, years experience, and the flexibility to make changes. Kirkley et al. (1998) found that years experience and education were important determinants of the catch rate. They also found that better captains or those with higher catch rates tended to make more frequent changes in trip length and crew size.

6. FISHING TIME (ACTIVITY)

Measures of fishing time (activity), giving service flows from the stock of heterogeneous capital, can be complex. This issue is conceptually similar to the measurement of capital services. The stock of capital is in some sense a repository for the services that are available for production (Hulten, 1986). Some of the heterogeneous capital stock may be used for only a limited portion of the time, while others pieces of capital may be used more. Which of these measures of activity should be used or even combined, and if combined, how?

Fishing time may be measured by days absent from port, days fished, number of fishing trips, or number of weeks fished. Hilborn and Walters (1992, page 122) distinguish among travel, search, setting/shooting, and handling time. The question is, which measure of fishing time to use? Even these measures do not capture the varying use of different pieces of capital equipment. Instead, these measures are more based on the different aspects of the harvesting process. The widespread collection of landings records, and sometimes logbooks, by governments provides some measure(s) of fishing time.

Available measures of fishing time (activity) can be limited. An inaccurate measure, giving measurement errors, may arise when the number of trips is used. Small vessels may make frequent but short trips whereas large vessels tend to make more infrequent but longer trips. Simply counting the number of fishing trips gives the appearance that small vessels fish more. Different vessels fish for different amounts of time in the complex mix of fishing modes and strategies encountered in many multispecies fisheries. Vessels may also make “split trips”, landing more than once on a fishing trip, adding complexity to accurate measures of fishing time. Allowance can be made for repairs, breakdowns, and bad weather (Sandberg, 1997). Transshipment time or unloading time can be important in some fisheries, such as the western Pacific United States purse seine tuna fishery.

When fisheries are regulated, at least in part, by fishing time or seasons, this provides an upper bound on fishing time (Northeast Region, United States National Marine Fisheries Service). Examples of fishing time limits include the New England groundfish trawl fishery, the Mid-Atlantic surf clam and ocean quahog fishery, the Northwest Atlantic sea scallop fishery, and formerly, the Pacific halibut fisheries (which led to “derbies” of short and intense fishing over just a few days). Maximum potential time can be calculated selecting time intervals for which utilization is fully realized; this is essentially the “peak-to-peak” method.

7. QUANTITATIVE METHODS AND STATISTICAL ISSUES

When fishing power based on vessel length or tonnage is used as a proxy variable for available fishing effort, several additional problems arise.

7.1. Functional form

The relationship between catch and vessel size may be nonlinear rather than linear (Squires and Huppert, 1988; Northwest Region, 1993). In addition, other forms of nonlinearity in the relationship between catch and vessel size may be characterized as discrete “shifts” in the relationships, leading to the use of binary or dummy variables for vessel size classes, seasons, areas, gear types employed, and even years (Squires and Huppert, 1988). Alternatively, the catch-effort responses may vary by vessel size resulting in a need for different specifications of the catch-effort model for different vessel size classes (Kirkley and Strand, 1988).

The functional form selected implicitly imposes restrictions on the possibility to technically substitute one input for another (Cunningham and Whitmarsh, 1980). A functional form which is simply linear imposes perfect substitutability among the inputs while a functional form with logarithms of all variables and no interaction terms (a Cobb-Douglas form) imposes a unitary elasticity of substitution. Measurement biases can result if the functional form and the underlying assumptions are incorrect.

7.2. Proxy variables

To capture the effects from the entire suite of inputs in the harvesting process (“nominal fishing effort”), a limited number of selected vessel attributes, such as vessel size and engine power, is used. These attributes, however, are proxy variables. As with all proxy variables, used to capture something with no observable counterpart, measurement error and bias can follow, although the asymptotic bias from inclusion is generally expected smaller than from exclusion.

7.3. Serial correlation

When time series of variables are used to estimate parameters by regression analysis, serial correlation can arise. Serial correlation leads to inefficient estimates (variances larger than without serial correlation).

7.4. Measurement error

When vessel attributes are inaccurately measured, estimates of
capacity and capacity utilization can suffer. When regression analysis is used,
the problem of errors in variables arises, giving biased estimates. Limiting
available fishing effort by focusing on only a limited number of key parameters,
such as vessel size or engine power, overlooks that fishing effort is comprised
of many components, such as seaworthiness, crew size, captain's fishing skill,
gear employed, vintage, etc., and may not even exist as a concept (Wilen, 1979;
Pearse and Wilen, 1979; Squires, 1987 and 1994a; Hannesson, 1983; Kirkley and
Strand, 1988; Dupont, 1991; Anderson, 1985; Campbell and Lindner, 1990; Squires
and Huppert, 1988). This can give omitted variable bias to any estimated
parameters.^{14}

7.5. Stocks versus flows

Another issue is that both capacity and capacity utilization are short-run concepts. Capital is both separate and is fixed, but effort is an aggregate of all primary inputs and is typically long-term and variable. Another way of looking at this is that effort is specified as a flow variable which is applied to the stock of fish giving a flow of the resource as output, the catch. But the concepts of capacity and capacity utilization are inherently short-run, which in turn requires effort to be a stock variable, and a stock variable, effort, cannot be applied to another stock variable, the resource, to produce a resource flow, the catch.

7.6. Predicted values of log of catch

When analyzing by regression analysis the relationship between
catch and perceived determinants of available or actual fishing effort, the log
of catch if often the dependent variable.^{15} The same issue arises
with standardizing effort. Care must be taken if predictions are made from the
estimated equation. The log of catch is predicted and its confidence interval
established and the anti-log of the predicted value of the log of catch and the
extreme points of the confidence interval are determined. This procedure results
in a biased prediction and an asymmetric confidence interval (Dadkhah,
1984).