FAIR CT96-1778
The Management of High seas Fisheries
Partner: Fisheries Research Institute, University of Iceland, Reykjavik, Iceland
Estimation of Production Functions for
the Icelandic Purse Seine Fleet[*]
by
Sveinn Agnarsson
Ragnar Arnason
and
Gunnar Ó. Haraldsson
M-1.99
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
This paper describes discusses the general production theory for purse seine fisheries with an empirical application from the Icelandic purse seine fishery.
2.Fisheries catch functions
In standard production theory it is assumed that a certain flow of inputs, x, is needed to produce a flow of output, y, i.e. y = f(x). There is generally little uncertainty surrounding the production process as the producer can easily calculate the amount of output a certain input bundle will yield. It is also unlikely that the producer will wish to put the inputs to non-productive use, i.e. utilise the inputs without producing some output.
Fishing, the production of landings, is different. First, fishing really is combination of several different production processes, i.e. searching, fishing, sailing to harbour and landing. Second, due to the variable distance to the fishing grounds and the pervasive uncertainty of catches, the relationship between inputs and outputs is much weaker than in the classical case. Third, the use of certain inputs (e.g. fuel consumption) may easily occur without any output, and the use of some other inputs will only occur when there is output (e.g. landings).
Rather than model fishing as a function of inputs such as fuel, capital and labour, it might therefore be more reasonable to write the production function, or harvesting function as
(1)y = Y(e, z)
where e is fishing effort and z is biomass. It should be noted that (1) assumes landings of all catches. Effort is defined as
(2)e = tf. E(xk)
where tf is fishing time (including search) and xk are features of the fishing vessels (e.g. capital) that determine fishing power. Fishing time is further defined as
(3)tf = t0 - 2 d -
where t0 is total operating time (days at sea), d the distance to the fishing grounds, the reciprocal of the vessel speed and the time spent landing. Needless to say, (3) refers to a single fishing trip.
The harvesting function can then be written as
(4)y = Y(( t0 - 2 d - ).E(xk), z).
In this formulation, the only short run control is t0 while xk represents long run control variables.
The harvesting function in (4) differs from traditional production functions in two fundamental ways. On the one hand, it does not include standard inputs, such as fuel, labour or material. Instead, production is viewed as a function of days at sea and some vessel characteristics. On the other hand, total biomass is allowed to enter the function as a separate argument.
3.Data
The data consists of yearly observations of nine purse seiners during the period 1989-1994, and includes data on vessel characteristics, costs, sales and catches in tons, as well as the stocks of capelin and herring. According to the Fisheries Association (Fiskifélag Íslands) there were around 40 boats classified as purse seiners in those years so our sample represents approximately 25% of the population.
Descriptive statistics of the data used are presented in Table 1. The data on technical characteristics of individual vessels is obtained from the Fisheries Association and includes information on vessel size in GRT, length in meters, engine size in horsepowers (HP) and age of engine. As can be seen the purse seiners vary somewhat in size, with the largest boats almost three time bigger than the smallest.
Data on sales, catches and the use of various inputs are obtained from the National Economic Institute. These data are, not surprisingly, highly confidential and are not published except in aggregate form.
Table 1.
Descriptive statistics:
______
MeanStd. dev.Min.Max.
Vessel characteristics:
Size (GRT) 582.0217.6324.0 950.0
Length (meters) 50.1 8.4 36.9 67.6
Size of engine (HP)2073.9789.8900.03182.0
Age of engine (years) 10.4 7.0 1.0 27.0
Insurance value (mill. kr.) 246.3 136.1138.2 638.4
Effort variable:
Days at sea 205.0 79.2 0.0 338.0
Output variables:
Value of sales (mill. kr.) 143.5 66.9 48.0 317.8
Total catch of pelagic
species (tons) 23.9 15.5 1.5 112.3
Fish stocks:
Capelin (tons) 386.7134.1115.0 500.0
Herring(tons) 431.2111.0299.0 591.0
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4.Estimation procedure
The availability of panel data makes it possible for us to take advantage of estimation procedures specially developed for panels. In this study we apply the technique suggested by Kmenta (1986), which allows for autoregressive errors and groupwise heteroscedasticity, to estimate catch and cost functions for the purse seiners fleet.
The Kmenta method is as follows. Suppose we have N cross-sectional units (boats in our case) observed over T time periods. The regression can be written as
(5)
where is a vector of parameters to be estimated and is a random error term. An estimate of is obtained by a generalised least squares procedure (GLS) which makes the following assumptions on the error term.
(6)heteroscedasticity
(7) for i j cross section independence
(8)first order autoregression
and E(vit) = 0, , E(vitvjt) = 0 for all i j, E(vitvjs) = 0 for t s and E(it-1vjt) = 0. These assumptions about the error structure imply the following: First, different purse seiners may have different error variance, i.e. different degrees or operational stability. Second, there is no tendency for common deviations from the efficiency mean for the purse seiners.[1] A relaxation to allow for cross-section correlation would involve: , and for t0. Third, the error terms of each purse seiner tend to correlated over time so that an efficient vessel in one year tends to remain so over time and vice versa.
The estimation of proceeds with the following steps. Step 1: Estimate in (13) by OLS and obtain the estimated residuals eit. Step 2: Compute the autocorrelation coefficients, i, as the sample correlation coefficient between eit and ei,t-1.[2] Step 3: Use the ’s to transform the observations, including the first observation, apply OLS to the transformed model and obtain the error covariance matrix, V. Step 4: Obtain the GLS estimator as where is the diagonal V matrix with zero’s on the off-diagonals.
5.Results
A harvest function, based on the specification outlined in (4), was estimated as
(9)
were, dropping subscripts, y is total catch of each boat of all pelagic species, d denotes days at sea, h is the size of the engine in HP, s the size of the boat in GRT, a the age of the engine, zc and zh the stocks of capelin and herring respectively and the ’s are parameters to be estimated. All variables are in natural logarithms. The parameter estimates are presented in Table 2.
Parameter estimates of a catch function and estimated elasticity. Dependent variable is catch of all pelagic species. All variables in natural logarithms. Standard errors in parenthesis.
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Parameter estimates
Constant / -2.600
(1.428)
Day / 0.421 / *
(0.024)
Engine size (HP) / -0.980 / *
(0.165)
Boat size (GRT) / 1.332 / *
(0.208)
Age of engine / -0.129 / *
(0.043)
Stock of capelin / 0.029
(0.056)
Stock of herring / 0.712 / *
(0.131)
Buse R2 / 0.932
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* denotes significance at the 1% level.
All the parameters except the constant and the zc-parameter are significant at the 1% level and given the high Buse R2 value the function appears to have good explanatory power.[3] However, the sign of the engine parameter is contrary to expectation, as one would, a priori, certainly expect a ship with a larger engine to fish more than a ship with a smaller engine. The age parameter is also negative, implying that having an old engine has a detrimental effect on the total catch. The sum of the effort and vessel characteristic parameters is 0.5, which could indicate the presence of economies of scale.
The herring stock parameter is significantly positive while the parameter associated with the capelin stock is insignificant. This could possibly be explained by the fact that during our period of observation the boats have usually managed to fish all their allocated quota of herring, while the capelin catch was sometimes less than the quota allocated. Since the total quota each year is closely correlated with estimates of the spawning stock of each species this could explain the results obtained.
References
Arnason, R. 1984. Efficient Harvesting of Fish Stocks: The Case of the Icelandic Demersal Fisheries. Ph.D. thesis. University of British Columbia.
Arnason, R. 1995. The Icelandic Fisheries – Evolution and Management of a Fishing Industry. Fishing News Books. Oxford.
Doll, J.P. 1988. Traditional Economic Models of Fishing Vessels: A Review with Discussion. Marine Resource Economics. Vol. 5. pp. 99-123.
Haraldsson, G.Ol. 1997. The Icelandic Fish Processing Industry. Unpublished M.Sc.-thesis. University of Iceland.
Judge, G.C., Hill, R.C., Griffiths, W.E., Lutkepohl, H., Lee, T. 1988. Introduction to the Theory and Practice of Econometrics. John Wiley & Sons.
Varian, H.R. 1978. Microeconomic Analysis. Norton, New York
White, K.J., Wong, S.D., Whistler, D. and Haun, S.A. 1990. Shazam User’s Reference Manual. McGraw-Hill.
Zarembka, P. 1974. Frontiers of Econometrics (ed.). Academic Press.
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[*]Acknowledgements: This document has been produced as a part of the European Commission research project: FAIR-CT-1778. Participants in this project are: The Foundation for Research in Economics and Business Administration and Centre for Fisheries Economics, Norwegian School of Economics, Bergen, Norway; Helsinki University of Technology, Helsinki, Finland; Fisheries Research Institute, University of Iceland, Reykjavik, Iceland; Universidade Nova de Lisboa, Lisbon, Portugal. The financial support of the European Commission FAIR programme is hereby gratefully acknowledged.
[1]This hypothesis is somewhat doubtful and may need a further check.
[2] is defined as , for i = 1,…,N
[3]The Buse R2 statistic is calculated as: where Y is an NTx1 vector of observations stacked by cross-section unit and . R is the NTxNT matrix that performs the autoregressive transformation. The matrix D is constructed as:
where W is a NTxN matrix such that column i has a vector of 1´s for cross-section i and 0´s elsewhere.Therefore Y-DY transforms the observations to deviations from a weighted mean.