# APPENDIX VII - PEAK-TO-PEAK METHOD

1. PEAK-TO-PEAK METHODOLOGY

Ballard and Roberts (1977) distinguish between two approaches to assess capacity output and capacity utilization.

Type 1: Peak-to-Peak

Following Ballard and Roberts (1977), a production function which is Cobb-Douglas or similar to the short-run Schaeffer model is specified:

 Yt = A Lta Ktb Tt , (A.1)

where Yt represents total catch or output which can be produced in the current time period t, Lt is the quantity of available labor in time t, Kt is the capital stock in time t, Tt is an adjusting technology trend, and A is a constant or aligning coefficient.

Labor and capital are adjusted in the equation by their marginal factor products, a and b. Under constant returns to scale (so that a proportionate increase in inputs increases output by the same proportionate amount), the factor output elasticities must sum to one:

 a + b = 1. (A.2)

To adapt the methodology to the available data, a second constraint is added:

 Yt = A Vt Tt , (A.3)

where

 Vt = Lta Ktb . (A.4)

In equation (A.3), the labor and capital inputs have been combined into a single production unit, Vt, which assumes that labor and capital are in fixed proportion over time (Leontief separability). The inputs would always be applied in the same proportions if a = b; alternatively, it is assumed that conditions for Hicksian aggregation characterize the relationship. The relationships in equations (A.3) and (A.4) allow circumvention of labor and capital data.

The specification used in the empirical analysis is a modified version of equation (A.3):

(A.5)

Equation (A.5) modifies the original relationship, equation (A.3), to deal with measurable phenomena. Output per producing unit is the dependent variable, and a technology trend is the main independent variable. Equation (A.5) is the final relationship used to determine the capacity potential.

To estimate the technology trend, the peak-to-peak methodology is applied. The level of technology in a particular time period t is determined by the average rate of change in productivity between peak years:

(A.6)

Relative to a particular year, t, the values of m and n correspond to the length of time from the previous and following peak years.

Equation (A.6) is a linear simplification of a 'pure' log-linear relationship. This formula, which includes compounding, is as follows:

(A.7)

The compounding error should not be large. Ballard and Roberts (1977) observe that to reduce computational requirements, the linear method was used for their empirical analysis.

Type 2: Base Year Comparison

Ballard and Roberts (1977) observe another method can be used if there are an insufficient number of peaks to use the Type 1 methodology, or if the fleet has not operated near full capacity during the study period.

The same specification as equation (A.5) is used, but the values of 'A' and 'Tt' are now constant.

(A.8)

where A = 1. Here, base is a predetermined year or set of years before the study period. During these year(s), the capacity utilization rate is assumed to be equal to 100 percent.

2. THE APPROACH

The peak-to-peak method is a direct and simple measurement of the institutionalized or observed response by the industry to changes in demand (Ballard and Roberts 1977). It is generally not considered as reliable as a survey, but is a practical technique when a survey is unavailable. It is extremely limited because it is assumed that the basic technology is the same between peaks. The further between peaks the less reliable the results will be.

There is an important caveat in the interpretation of the results from the peak-to-peak method (Ballard and Roberts, 1977). First, a capacity rate of say 50 percent in a given year does not necessarily imply that either there are 50 percent too many vessels or that the fleet would be more economically efficient if there were fewer. The only conclusion that can be drawn from these results is that the potential exists for a greater catch without the necessity of major expenditures of new capital or equipment. To draw conclusions about the efficiency or desirability of a high-capacity utilization rate requires examining the market structure of the industry, monetary and social costs involved, target levels for the resource stock and effort, stock rebuilding strategies, and other factors. In addition, an analysis of the industry's pricing and profitability structure must determine whether the fishers would use the excess capacity to catch more fish if given the opportunity.

The catch per ton of both peak and nonpeak years is compared and adjusted for productivity changes to obtain the historical capacity utilization rate (Ballard and Roberts 1977). That is, the approach compares the capacity output to actual output levels in different time periods to derive measures of capacity utilization.

3. EMPIRICAL APPLICATIONS OF PEAK-TO-PEAK

The next three subsections discuss three specific applications of the peak-to-peak method to measure fishing capacity in the United States, Canada, and world-wide.

3.1. Peak-to-peak: United States

Ballard and Roberts (1977) used the peak-to-peak method to calculate fishing capacity and rates of capacity utilization for ten Pacific coast fisheries in the USA.

Statistics Canada uses a variation of the peak-to-peak method to determine the maximum potential output (DFO n.d.). Capacity is defined as the product of the highest historical output/capital output ratio and the current capital stock, which gives the maximum production that could be produced with the current year's capital stock. That is, the highest average product of capital is used to reflect the maximum output that a unit of capital can produce, which when multiplied by the capital stock for every year, gives an estimate of potential or capacity output.

Actual output minus maximum potential output then provides a measure of excess capacity (DFO n.d.). The Statistics Canada approach assumes zero excess capacity in a base period, and to the extent this assumption does not hold, excess capacity is underestimated. To allow for this possibility, survey estimates of capacity and utilization rates can be used to calibrate the capacity estimates.

3.3. Peak-to-peak: Garcia and Newton's world-wide estimates

In an important paper, Garcia and Newton (1997) employed the peak-to-peak method. Garcia and Newton (1997) used gross registered tons (GRT) of vessels from the world fleet (from the Lloyd's of London data base) as a measure of world fleet capacity. They then multiplied this measure by what they termed “the relative coefficient of technological efficiency,” to give a corrected index of world fishing fleet capacity in “standard” GRT. The relative coefficient of technological efficiency is used to reflect the changes in technological efficiency or “fishing power” of different vessel types due to technological progress. In a bioeconomic analysis, costs were assigned to fleet capacity to derive a measure of optimum or profit-maximizing total world fleet capacity and the corresponding amount of excess capacity.

4. LIMITATIONS OF PEAK-TO-PEAK

Several limitations exist for the peak-to-peak methodology (Ballard and Roberts, 1977). First, tonnage or operating units provide only a rough, general measure of the capital stock used as a base in measuring effective capacity. Second, there may have been several types of gear used over time or significant changes in the state of technology (e.g. vessel design, adoption of vessel electronics). The peak-to-peak method requires treating tonnage and operating units equally among gear types, a situation often not valid. Because the catch rate will vary substantially using several gears it would require a separate study for each gear type to solve this problem. Third, there may be double counting or under counting in the tonnage and operating unit series.

Fourth, the approach implicitly implies stable weather and biological (resource) conditions. Major or cyclical fluctuations in either of these two factors can lead to the exaggeration of the potential catch capabilities of the fleet since during the best or peak years the resource might be easier to harvest than normally expected. When resource stocks are in decline, the capacity can also trend downwards due to declining catches. Periods of stock rebuilding can also color the measure of capacity if catches are sufficiently contained to allow the resource stock to grow. Resource limitations and regulations, and changes in these regulations, can in general affect the capacity measure. An abnormally high peak alternatively dictates that nonpeak years will seem overly depressed.

Fifth, the potential catch capabilities of the fleet will be underestimated if there are embedded or “hidden” technological or regulatory constraints on the fishery. The measured peak will then lie below the potential peak if the resource were more available and the regulations or constraints relaxed. Sixth, the technology or productivity trend is in practice a catchall that accounts for all phenomena except capital use because no other variables are explicitly considered. Changes in regulatory policy, biological availability, or the application of skilled labor would, for example, affect the estimation of the trend. Seventh, capital and labor and other inputs are assumed to remain in fixed proportions or the time period (Leontief separability), implying there is no substitution among inputs. Also, by ignoring prices and costs, the measure is devoid of much economic content.

Eight, along similar lines, the output-capital ratio is an average productivity measure, which can be misleading since output growth may arise from the increased use of other inputs or changes in the utilization rate of an input (Squires, 1994b). Nine, the approach assumes zero excess capacity in a base period, and to the extent this assumption does not hold, excess capacity is underestimated. To allow for this possibility, survey estimates of capacity and utilization rates can be used to calibrate the capacity estimates.

Ten, aggregating total catch by simply summing up all the catches can also introduce errors into the analysis (Squires, 1994b). Eleven, the approach does not allow looking at complex problems such as stock rebuilding with nonmalleable capital. If there is a target biomass in any given period, the optimum capacity in any given time period may be difficult to determine. That is, the approach gives an indication of the industry's status but is less effective in providing a road map on how to get to the optimum. Twelve, the peak-to-peak method fails to directly link back to input utilization, which is the meaningful point of harvesting capacity.