Leif Kristoffer Sandal

How to Improve the Management of Renewable Resources: The Case of Canada's Northern Cod Fishery

The paper examines howan easy-to-apply optimal feedback rule can be used to solve for optimal levels of exploitation of a renewable resource. Using data from Canadas northern cod fishery, the optimal feedback rule is used to derive optimal levels of exploitation for the years 1962–91 under different discount rates, alternative model specifications, and parameter assumptions. The optimal feedback rule indicates that over much of the period the fishery was economically overexploited and, given the stock development that actually took place, a harvesting moratorium should have been instituted three years earlier than when it was introduced. The results show how the use of a simple and flexible optimal rule by managers of renewable resources can generate substantial gains. Copyright 2000, Oxford University Press.

Optimal Feedback Controls: Comparative Evaluation of the Cod Fisheries in Denmark, Iceland, and Norway

The economic efficiencies of the Danish, Icelandic, and Norwegian cod fisheries are examined. For this purpose, nonlinear aggregate models of these fisheries are constructed. Comparing the calculated optimal harvest and biomass quantities with the actual fisheries provides a measure of the degree of efficiency in these fisheries. The comparisons confirm that the cod harvesting policies of these countries have been hugely inefficient in the past. It appears that inefficiency has been increasing over the last three to four decades, even after TAC regulations replaced open access, indicating that the management policies adopted by all three countries have failed to cure overfishing. Copyright 2004, Oxford University Press.

A maximum entropy approach to the newsvendor problem with partial information

In this paper, we consider the newsvendor model under partial information, i.e., where the demand distribution D is partly unknown. We focus on the classical case where the retailer only knows the expectation and variance of D. The standard approach is then to determine the order quantity using conservative rules such as minimax regret or Scarfs rule. We compute instead the most likely demand distribution in the sense of maximum entropy. We then compare the performance of the maximum entropy approach with minimax regret and Scarfs rule on large samples of randomly drawn demand distributions. We show that the average performance of the maximum entropy approach is considerably better than either alternative, and more surprisingly, that it is in most cases a better hedge against bad results.

Implications of a nested stochastic/deterministic bio-economic model for a pelagic fishery

Abstract Use is made of an economically optimal feedback rule to determine optimal levels of exploitation of a pelagic fish species. Data from the southern bluefin tuna fishery for the years 1960–1996 are utilised to apply this rule to aggregated deterministic and stochastic models of population dynamics. Comparison of the rule-based results with historical records indicates that over much of the period the fishery was economically overexploited and a harvesting moratorium could have been imposed to improve economic returns from the fishery and to allow stock recovery.

Optimal Steady States and the Effects of Discounting

A simple expression for finding and characterizing the optimal steady state of a general dynamic optimization problem is derived. This expression is easy to interpret and easy to apply for various purposes as, for example, to analytically investigate the effect of the discount rate upon optimal steady state stock levels. It is shown that an increase in the discount rate may result in higher optimal stock levels even in the one-dimensional (single species) case in nonlinear models. An important result is that if demand is inelastic at the optimal steady state, a higher discount rate will unequivocally imply higher standing stock(s). Increasing marginal cost of harvest will further strengthen this result. In the multidimensional case it is demonstrated that an increased discount rate may result in higher optimal stock levels for all stocks included in the model.

Estimating the parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistic

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per realisation. We compare and contrast parameter estimation for linear and nonlinear first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic. put forward by Hurn and Lindsay (1997), and one based on the Kolmogorov-Smirnov statistic. The estimates generated reflect the true parameter values well for all models. examined, especially when using the Kolmogorov-smirnov criterion function.

Rescuing the Prey by Harvesting the Predator: Is It Possible?

A predator–prey model is used to analyse the case where the prey has been overexploited for a while and therefore is threatened by extinction even along the optimal harvesting path due to depensation in the biological model. It is assumed here, however, that extinction is unacceptable for non-economic reasons. Various sub-optimal rescue operations involving increased harvest of the predator and reduced, or zero, harvest of the prey are therefore considered. The question is how and when it is possible to rescue the prey from extinction by departing from the optimal path. Such sub-optimal policies are not always feasible. If they are feasible, they imply certainly reduced profits and may even produce negative profit. The objective of this chapter is to find the criteria for when a rescue operation is feasible and to explore the dynamics of this situation.

The Ensemble Kalman Filter in Bioeconomics

We demonstrate the power of the Ensemble Kalman Filter in specifying ecosystem models ideal for bioeconomic analysis. Bioeconomic analysis requires models to be relatively simple, but models must still capture the nature and dynamics of the system. With the Ensemble Kalman Filter, we are able to capture complex dynamics in multispecies models with models simple enough to allow further bioeconomic analysis. While bioeconomic analysis has had limited influence on management decisions, the advent of new methods and the need for high dimensional ecosystem based management models may make bioeconomic research more relevant in the future. The filter is applied to a ecosystem model of the commercially most important species in the Barents Sea. The simpler, aggregated stochastic biomass models capture the complex dynamics of the pelagic stocks on the level needed for making decisions on for example allowable catches.

Do Species Interactions and Stochasticity Matter to Optimal Management of Multispecies Fisheries

The multispecies fisheries management looks at a bigger picture in addressing the long-term consequences of present decisions. This implies an ecosystem management that includes a number of species and their physical, biological and economic interactions. These interactions make the growth of resources stochastic and increase complexity in understanding stock dynamics and optimal catch for such a stochastic and multiple stocks´ system. To address the issue of identifying optimal catch of stochastically growing multi stocks, we have formulated and applied a time-continuous stochastic model. The model contributes to multispecies bioeconomic management of marine ecosystems. An application of model in a predator-prey relationship in Barent Sea revealed that the optimal catch for stochastically growing stocks in a multispecies interaction model is different from the deterministic model.

Potential Collapse in Fisheries with Increasing Returns and Stock-dependent Costs

Abstract We develop a bioeconomic model to analyze a fishery with fixed costs as well as a within-season continuous cost function for the generalized Schaefer production function with increasing marginal returns to effort level. We analyze the consequences of the combined effects of increasing marginal returns and fixed costs. We find that regardless of the magnitude of the fixed costs, cyclical policies are optimal. We also demonstrate that the danger of potential collapse increases with increasing fixed costs. This result is quite counterintuitive, as higher costs are usually considered to have a conservative effect on resources. JEL Classification Codes: Q20, Q22, Q57