Abstract
Large variation in stock dynamics affects the accuracy of stock estimates, which fisheries managers rely on when determining quotas and other regulations. The purpose of this paper is to investigate the implications of uncertainty on pulse fishing. We show that as the variance of the random natural fluctuations increases, the optimal pulse length decreases and converge toward a constant-escapement policy. Hence, in fisheries with large natural variability, a constant-escapement policy is a good approximation of the optimal policy.
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Notes
See e.g. Bjørndal and Conrad (1987).
See Beverton (1990) for an overview of stock collapse for small pelagics.
To be exact, we model the target quota directly rather than season length, as these are equivalent from the fishery manager’s perspective.
The Spence production function is: \(H_t = X_t (1-e^{-qK_t})\) where \(q\) is a catchability coefficient that indicates how efficient the fishing technology is. The Cobb-Douglas production function is: \(H_t = A K_t^b X_t^g\) , where \(A\) is a catchability coefficient. The main difference between the Spence and the Cobb-Douglas production functions for pelagic species is that the latter typically has stock-output elasticity \(0<g<1\), while the Spence production function implicitly assumes a stock-output elasticity of one.
This is a reduced form model. For a stochastic endogenous model based on individual behavior, see Rocha and Gutiérrez (2012).
Note that we implicitly restrict the abilities of individuals to form expectations about the stock. The production functions (both CD and SP) are aggregate functions, which prevents individuals from forming better expectations about aggregate sizes. Individuals therefore make their decisions based on the expected stock size.
All monetary values are expressed in 2001 Norwegian kroner (NOK).
This is in line with the results of Maroto and Moran (2008).
Where \(E[X]\) and \(ES\) denote the expected stock and escapement level in period \(t\), before the uncertainty regarding the stock estimate is resolved.
The code is written in MatLab and is available as supplementary material to this paper.
A fishing moratorium was imposed in 1977 to allow the stock to recover after it had been overexploited for several years. The moratorium was lifted in 1981 in the southern part of the North Sea and in 1983 in the northern part. See Nøstbakken (2008) for details on the fishery and regulations.
Note that evaluation of the actual harvest regime requires that we take into account the evolution in parameters such as costs and prices. Such analysis is beyond the scope of the current study.
If this was not the case, our calculations must have been wrong. Nonetheless, this supports the reliability of our numerical results.
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Financial aid from the European Commission (MYFISH, FP7-KBBE-2011-5, n 289257) and the Spanish Ministry of Economy and Competitiveness (ECO2012-39098-C06-00) is gratefully acknowledged. The first draft of the paper was written while Jose Maria Da Rocha was visiting Universitat Autònoma de Barcelona. He gratefully acknowledges its hospitality.
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Da-Rocha, JM., Nøstbakken, L. & Pérez, M. Pulse Fishing and Stock Uncertainty. Environ Resource Econ 59, 257–274 (2014). https://doi.org/10.1007/s10640-013-9727-y
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DOI: https://doi.org/10.1007/s10640-013-9727-y