The Management of High Seas Fisheries

FAIR CT96-1778

The Management of High seas Fisheries

Partner: Fisheries Research Institute, University of Iceland, Reykjavik, Iceland

Estimation of Cost Functions for

the Icelandic Purse Seine fleet [*]

by

Sveinn Agnarsson

Ragnar Arnason

and

Gylfi Magnusson

M-4.99

This document does not necessarily reflect the views of the

Commission of the European Communities and in no case

anticipates the Commission’s position in this domain.

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1. Introduction

In standard microeconomic theory, the costs associated with the production of a certain output are assumed to be a function of input prices and output,

(1)  C = f(W,Y )

where C is cost, W a vector of input prices and Y output. Equation (1) describes the case where all inputs are variable. Therefore, it is often referred to as the long run cost curve (Varian 1984). In the short run certain inputs, in particular physical capital variables, are restricted giving rise to the following short run cost function:

(1b) C = f(W,Y,K),

where K represents the restricted capital inputs.

However, as discussed in Arnason (1998, 1999), Haraldsson and Arnason (1998), Haraldson, Arnason and Agnarsson (1998) and Agnarsson, Arnason and Haraldsson (1999), fisheries are in certain respects different from the traditional production activity of economic theory. In particular, the use of inputs may take place without any production occurring. Consequently, the application of the standard cost function, (1), to fisheries may not be appropriate.

Therefore, instead of the conventional function, Arnason (1999) proposes the following fishing cost function applicable to a given vessel:

(2) C = f(W,Y,K,T),

where T represents the operating time of the vessel. Under this specification, costs may increase with T although Y remains constant.

A simple form for (2) is:

(3) , i = 1, …, I.

where Ci represents the real costs of the fishing operation, i.e. the nominal cost divided by the appropriate input price index for W.[1] The index i refers to vessel i. The variable I represents the size of the observation sample. b0, b1, b2, b3, d1, d2, d3 are parameters to be estimated, Ti is total operating time of vessel i, Ki vessel's i characteristics, Yi its harvest and ei a stochastic error term. Here, b0 represents fixed costs.

A more flexible version of (2) can be defined as

(4)

where special attention is now paid to the fact that the vessel in question may be engaged in the fishing of different species, ys, which entail different costs. As before, a0, a1, a2, bs, g1, g2 and ds are parameters to be estimated.

Icelandic purse seiners are primarily engaged in the fishing of pelagic species such as the domestic capelin and herring, as well as the Atlanto-Scandian herring, but many of these vessels also participate in demersal and shrimp fisheries during pelagic off-seasons. Since the specification in (4) decomposes total vessel costs into fixed costs, operating costs, and the costs of harvesting different species it may provide a suitable description of this type of a multipurpose fishing activity.

There are, however, reasons to suspect that the cost function in (4) may not be sufficiently flexible to fully represent the cost structure of Icelandic purse seiners. For these vessels, as in fact most fishing vessels, a considerable part of total costs are directly linked with the value of landings. Most importantly, in addition to a fixed salary the crew receives a fixed share (amounting to about 1/3) of the gross value of landings. Also harbour fees are generally calculated as a fraction of gross landings. As a result, a good part of total costs is determined by the value of landings. Since the value of a given volume of landings varies dramatically with the species in question as well as the quality of the catch, it is clear that the volume of landings does not really capture this component of total costs.

An improved specification is to include the total value of landings in the cost function as follows:

(5) ,

where all the variables are as defined above, except that the variable Vsi represents the real value of landings. e and h, of course, are the corresponding parameters. It should be noted that the V variable includes the real value of all landings, both pelagic and non-pelagic species. The cost function in (5) is similar to the standard multi-output cost functions found in the literature (Caves et. al (1980), Baumol et. al (1988) Toft and Björndal (1993)), except that output enters both as quantity and value.

2. Data

The data used consist of observations on nine Icelandic purse seiners during the period 1989-1994. However, since all the boats are not observed every year the number of observations is only 45. Summary statistics describing the data are presented in Table 1.

Table 1.

Descriptive statistics

______

Mean Std.dev. Min Max

Real total costs (m. ISK) 106 25 46 147

Real sales (m. ISK) 124 32 61 201

Pelagic catch (metric tonnes) 22371 9230 6215 43674

Other catch (metric tonnes) 312 307 0 1347

Days at sea (days) 218 69 82 338

Engine size (hp) 1974 779 900 3182

Vessel size (grt) 737 263 408 1170

Costs and sales were deflated using the consumer price index. Catch of pelagic species includes only capelin and herring, while catch of non-pelagic species includes demersal and flatfish as well as shrimp. It should be noted that the date covers considerable variability in harvest levels and somewhat less in costs and vessel characteristics.

3.  Estimation results

Although the data at hand are close to being a perfect panel, it was decided to pool the observations and estimate the cost functions defined above using standard non-linear techniques. There are two main reasons for this. The vessel characteristics (size in GRT, engine size in HP) were constant throughout the data period for each purse seiner. Therefore, combining this vessel specific variable with a fixed effect panel model would be problematic e.g. due to collinearity problems. Secondly, the cost functions specified are highly non-linear and imposing a complex error structure on these functions would drastically increase the numerical requirements of the estimation procedure and possibly lead to problems of non-convergence. This is especially important since the data set used was rather small.

We started off estimating the following cost function that corresponds to equation (5):

(5a) .

Here, as before, Ti is vessel's i number of days at sea during one year, Ki represents its characteristics, defined as the product of engine size measured in horsepower (HP) and vessel size measured in gross registered tons (GRT), Y1i represents vessel's i catch of pelagic species during the year, Y2 its catch of non-pelagic species and Vi vessel's i total catch value.

As the statistical precision in the resulting parameter estimates turned, not surprisingly, out to be unsatisfactorily low ¾ 11 parameters were estimated on the basis of 45 observations employing highly correlated regressors ¾ the number of estimation parameters was gradually reduced by successively restricting or dropping the least significant ones.[2] The eventual model, containing four estimated parameters, is presented in Table 2. Note that likelihood ratio tests on all of the restrictions employed are presented in Table A1 in the appendix.

Table 2. Regression results. The
dependent variable is real total costs.
Standard errors in parenthesis.
______
a0 / 0.0
a1 / 1.0
a2 / 1.0
b2 / 1.0
e / 1.0
g1 / 1.6556 / **
(0.0930)
g2 / 0.6557 / **
(0.0287)
d2 / 1.3585 / **
(0.0531)
h / 0.9671 / **
(0.0054)
log likelihood / -489.605
R2 / 0.726
Jarque-Bera test / 1.165
Parameter Wald tests:
g1=g21=d2=h=1 / 631.551 / **
d2=h / 52.642 / **
______
** indicates significance at the 1% level.

The statistical properties of this estimation appear satisfactory. The explanatory power of the equation, as measured by the R2, is quite high. The hypothesis that the residuals are normally distributed cannot be rejected. All the estimated parameters appear highly significant. On the basis of a Wald test the hypothesis that all the power parameters equal unity is firmly rejected, as is the hypothesis that the two output parameters are equal. The likelihood ration tests on the parameter restrictions employed provide support for the restrictions both individually and jointly (See table A1 in the appendix).

4. Discussion

The estimated cost function according to the above estimates is:

(6)

This function is clearly convex in days at sea, T, and the catch of non-pelagic species, Y2, but concave in vessel characteristics, K, and the real value of sales, V. The interpretation of the days at sea and vessel characteristic variables is quite straightforward; the costs associated with keeping the vessel at sea rise at an increasing rate, while the fixed costs associated with the vessel as a unit of physical capital decline with the size of the boat. The reason for the increasing marginal cost of the days at sea, may be the upper bound imposed by the limited number of days in the year. As the number of operating days approaches this upper limit, it becomes more and more difficult to keep the vessel at sea, due to maintenance and other requirements. Therefore the marginal costs are bound to rise.

Ideally, we would like to be able to decompose the value variable into the value of the catch of pelagic and non-pelagic species respectively. Then, the sum of the value and catch parameters could be regarded as an approximation of the returns to fishing the species in question. Although this option is not open to us here, the parameter estimates indicate that purse seiners engaged in the fishing of non-pelagic species suffer some increasing, additional costs. The catch parameter is 1.36 and since the value parameter is close to unity, it follows that costs are convex in the fishing of non-pelagic species. This can be attributed to various set up costs associated with refurbishing the seiners with new fishing gear and equipment, new crewmembers may have to be hired, and costs associated with the fishing itself and processing the catch onboard the boat may be higher. In addition, harbour fees may rise since they are calculated as a fraction of the value of gross landings. Costs associated with catching pelagic species are, on the other hand, decreasing with the value of sales, indicating some increasing returns to those fisheries.

The cost estimates obtained using the above cost function rhyme quite well with observed costs, as revealed in Figure 1.

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Appendix

Table A1.
Results from estimating the unrestricted cost function in (5a) and several restricted versions of that function (columns I-VII).
The dependent variable is real total costs. Standard errors in parenthesis.
______
Unrestricted / I / II / III / IV / V / VI / VII
a0 / -162.09 / -162.09 / -161.97 / -55.651 / 0 / 0 / 0 / 0
(140.40) / (1.0167) / ** / (1.0698) / ** / (174.85)
a1 / 14.972 / 1 / 1 / 1 / 1 / 1 / 1 / 1
(11.325)
a2 / 0.0000 / 0.0000 / 0.0000 / 1 / 1 / 1 / 1 / 1
(0.0001) / (0.0001) / (0.0001)
b1 / 3534.0 / * / 3534.0 / ** / 3534.0 / ** / 105.68 / 63.378 / 440960 / 1 / 1
(1587.5) / (1.0000) / (1.0000) / (170.89) / (115.60) / (2794100)
b2 / 921.75 / 921.75 / ** / 922.37 / ** / 1358.8 / 1356.5 / 1 / 1 / 1
(630.22) / (1.0019) / (2.2228) / (2183.9) / (2398.4)
e / 2.3697 / ** / 2.9460 / 1 / 1 / 1 / 1 / 1 / 1
(0.5857) / (3.9228)
g1 / 1.1357 / ** / 1.5704 / ** / 1.5569 / ** / 1.5712 / ** / 1.5712 / ** / 1.6490 / ** / 1.6555 / ** / 1.6556 / **
(0.1865) / (0.1293) / (0.1020) / (0.1386) / (0.1426) / (0.0938) / (0.0873) / (0.0804)
g2 / 1.4009 / 1.4120 / ** / 1.4434 / ** / 0.6562 / ** / 0.6562 / ** / 0.6536 / ** / 0.6557 / ** / 0.6557 / **
(0.8182) / (0.3191) / (0.2427) / (0.0260) / (0.0256) / (0.0269) / (0.0272) / (0.0268)
d1 / -437.09 / * / -437.09 / ** / -437.09 / ** / -0.0871 / -19.282 / -0.4039 / 0.4123 / * / 1
(193.92) / (1.0000) / (1.0000) / (5.4088) / (40.647) / (0.7153) / (2.2598)
d2 / 0.4352 / ** / 0.4331 / ** / 0.4571 / ** / 0.3879 / * / 0.3881 / * / 1.3175 / ** / 1.3585 / ** / 1.3585 / **
(0.1058) / (0.0657) / (0.0348) / (0.2247) / (0.2482) / (0.0621) / (0.0492) / (0.0457)
h / 0.8930 / ** / 0.8767 / ** / 0.9670 / ** / 0.9623 / ** / 0.9622 / ** / 0.9610 / ** / 0.9671 / ** / 0.9671 / **
(0.0205) / (0.1069) / (0.0039) / (0.0063) / (0.0062) / (0.0085) / (0.0053) / (0.0050)

Log likelihood

/ -486.1424 / -486.1771 / -486.5857 / -487.0597 / -487.0600 / -488.4614 / -489.6026 / -489.6045
R2 / 0.7662 / 0.7655 / 0.7609 / 0.7552 / 0.7552 / 0.7395 / 0.7352 / 0.7352

Runs test for normality

/ -2.8632 / ** / -2.8632 / ** / -2.8479 / ** / -2.8632 / ** / -2.8632 / ** / -1.6562 / -1.6360 / -1.6360
Likelihood ratio tests:
d1=1 / 0.0694
a1=e=1 / 0.8866
a1=a2=e=1 / 1.8346
a1=a2=e=1
a0=0 / 1.8352
a1=a2=d2=e=1
a0=0 / 4.638
a1=a2=d1=b2=e=1
a0=0 / 6.9204
a1=a2=d1=b2=e=1
b1=a0=0 / 6.9242
Testing each
restriction separately / 0.0694 / 0.8172 / 0.948 / 0.0006 / 2.8028 / 2.2824 / 0.0038
______
* and ** indicate significance at the 5% and 1% level respectively. The R2 reported is the R2 between observed and predicted values.

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