Safe Minimum Standards in Dynamic Resource Problems: Conditions for Living on the Edge of Risk

Safe Minimum Standards (SMSs) has been advocated as a policy rule for certain environmental problems where uncertainty about risks and consequences are thought to be profound. This paper explores the rationale for such a policy within both static and dynamic frameworks and derives conditions for when SMS can be summarily dismissed as a policy choice and for when SMS can be defended as an optimal policy based on standard economic criteria. It turns out that these conditions can be checked with quite limited information about damages and risks. In order to analyze the SMSs in a dynamic setting, we develop a method for solving optimal control problems when state space is divided into risky and non-risky sub-sets.      

On the dynamics of renewable resource harvesting and pollution control

The paper presents a dynamic partial equilibrium model which combines optimal renewable resource harvesting and optimal pollution control. Pollution accumulates as a slowly decaying stock and is assumed to affect the growth and the quality of the renewable resource stock. The aim is to maximize a social welfare functional which gives the present value of the difference between natural resource benefits and pollution control costs. The existence, uniqueness and the dynamic properties of the steady states are investigated. The analysis also gives a general result concerning the steady state of any two state variable optimal control problems.     

Policies for the management of weeds in natural ecosystems: the case of scotch broom (Cytisus scoparius,L.) in an Australian national park

Environmental weeds are plants that invade natural ecosystems and present a serious threat to conservation of nature. Environmental weeds have been implicated in the extinction of several indigenous plant species, and they also threaten ecosystem stability and functional complexity. Historically, emphasis in weed control in Australian national parks has been placed on chemicals, manual pulling of small plants, excluding tourists and feral animal control measures. Recently, biological control has been introduced to control weed infestations. These methods typically have been applied as funds have become available, with little opportunity to consider their long-term effectiveness. As the threat from environmental weeds is becoming more fully recognised, an integrated, strategic, ecological and economic approach to weed management is needed. A deterministic dynamic programming model is developed for this purpose in this paper. A case study for scotch broom is presented, to assess the ways in which this approach can address the policy issues that face the community in the management of an environmental weed in a national park. The model takes account of the weed population dynamics, the effectiveness and cost of control measures, and the value of the park outputs (biodiversity, recreation and grazing). The dynamic programming model includes weed density and seed bank as state variables and a budget constraint for the control variables. The model is used to derive optimal control rules for any given state of the weed population. An optimal decision rule provides a package of control measures that can be used to attack the problem each year, depending on the current weed density and seed bank. Optimal trajectories are developed for a planning horizon of 45 years, and the effect of the budget constraint is analysed. The marginal value of an extra dollar for weed control, in terms of discounted future benefits, is estimated. It is shown that a combination of controls that targets both weed density and the seed bank is important. It is also shown (given the assumed parameters) that biological control is worth undertaking, as it appears as part of most of the optimal strategies identified. The paper concludes with policy recommendations for managing weeds in natural ecosystems.     

How to Get There From Here: Ecological and Economic Dynamics of Ecosystem Service Provision

Using a bioeconomic model of a coral reef-mangrove-seagrass system, we analyze the dynamic path of incentives to achieve an efficient transition to the steady state levels of fish biomass and mangrove habitat conservation. Our model nests different types of species habitat dependency and allows for changes in the extent of habitat to affect the growth rate and the long-run fish level. We solve the two-control, two-state non-linear optimal control problem numerically and compute the input efficiency frontier characterizing the tradeoff between mangrove habitat and fish population. After identifying the optimal locus on the frontier, we determine the optimal transition path to the frontier from a set of initial conditions to illustrate the necessary investments. Finally, we demonstrate how dynamic conservation incentives (payments for ecosystem services) for a particular habitat with multiple services are interdependent, change over time, and can be greater than contemporaneous fishing profits when the ecosystem is degraded.     

A model for international capital markets closure in an economy with incomplete markets and short sales

Using a two-country dynamic optimization model, we investigate the impact of exchange risk, incomplete information and short sales constraints on international portfolio decisions around market closure. Using optimal control theory, we provide solutions and simulation results. Our model can be applied to solve several problems in financial economics in the presence of market closure, information asymmetry and short sales constraints.     

Comparative dynamics (sensitivity analysis) in optimal control theory

This paper considers an optimal control problem with a parameter and develops a systematic method for comparative dynamics. A sufficient condition for the optimum solution to be differentiable with respect to the parameter is provided. Formulas for computing the derivative are given in the form of initial-value problems of linear differential equations. The possibility of discontinuous optimal controls is fully taken care of. An example of the comparative dynamics is given in terms of a model of optimal capital accumulation.     

Optimal risk-sharing with effort and project choice

We consider first-best risk-sharing problems in which “the agent” can control both the drift (effort choice) and the volatility of the underlying process (project selection). In a model of delegated portfolio management, it is optimal to compensate the manager with an option-type payoff, where the functional form of the option is obtained as a solution to an ordinary differential equation. In the general case, the optimal contract is a fixed point of a functional that connects the agent's and the principal's maximization problems. We apply martingale/duality methods familiar from optimal consumption-investment problems.     

A model of the optimal allocation of government expenditures

Government expenditures can be used for various socioeconomic objectives, including public education, consumption of public goods and services, and social protection. This paper analyzes the optimal allocation of public expenditures among these competing functions. We establish an overlapping generations model with heterogeneous individuals in which the government optimally chooses income tax, transfer payment, educational spending, and public consumption. Our model characterizes the transitional dynamics and the steady state of each function with and without a pay‐as‐you‐go intergenerational contract. We also conduct a simulation illustrating that the presence of an intergenerational contract may raise public consumption and social welfare in the steady state.     

隐马尔可夫模型算法基础探析

隐马尔可夫模型是一个具有双重随机过程的统计模型,已被广泛应用于语音识别、生物序列分析和管理等领域。在隐马尔可夫模型中存在三个基本问题,即学习问题、解码问题和估值问题,一般分别使用Baum-Welch算法、Viterbi算法和向前-向后算法进行解决。其中,学习问题的Baum-Welch算法本质上是EM算法在隐马尔可夫模型中的一个应用,解码问题的Viterbi算法本质上是动态规划算法在隐马尔可夫过程中的一个应用。文章就EM算法和动态规划算法进行了一定的梳理和分析,以促进对隐马尔可夫模型算法的理解。     

Optimal Dynamic Control of Visitors and Endangered Species in a National Park

To enable visitors to enjoy nature while protecting endangered species is the key challenge for national parks around the world. In our optimal dynamic control model, a park management maximizes tourism revenues and conservation benefits net of control costs by choosing optimal dynamic levels of conservation and visitor management. The optimization is constrained by an extended food chain model representing species-habitat-visitor interactions. We illustrate for a game bird in an Alpine national park that ecotourism can indeed lead to ecosystem degradation when the park management is more concerned about increasing tourism revenues than about achieving the conservation target and if the endangered species is unknown to most visitors. If, however, the park management is well aware of the potentially negative consequences of ecotourism and hence cares for species conservation, limited ecotourism can provide funding for species conservation which ensures population levels above the uncontrolled steady state.     

Optimal bunching without optimal control

This paper presents simple sufficient conditions under which optimal bunches in adverse-selection principal-agent problems can be characterized without using optimal control theory.     

The industrial implications of an optimal reflationary mix for the British economy

This paper derives an optimal reflationary mix for the next decade and comments on the industrial implications of this policy. The discussion is based on simulations of the multisectoral dynamic model of the UK economy developed by members of the Cambridge Growth Project. The results suggest that the concentration on macroeconomic policy alone may be misguided and that instruments which attack the roots of Britain's industrial problems should receive more attention. The paper also demonstrates that the optimal control procedure is a reliable tool for steering an economy towards a desired target trajectory and that this is feasible for very large econometric models.     

Fixed Wages and Bonuses in Agency Contracts: The Case of a Continuous State Space

In this paper, we extend the state‐contingent production approach to principal–agent problems to the case where the state space is an atomless continuum. The approach is modelled on the treatment of optimal tax problems. The central observation is that, under reasonable conditions, the optimal contract may involve a fixed wage with a bonus for above‐normal performance. This is analogous to the phenomenon of “bunching” at the bottom in the optimal tax literature.     

Price and quality changes in metal working machine tools

A dynamic optimal control model is constructed to study US dairy policy alternatives under bovine somatotropin (bST). The results indicate that the adoption of bST might be slower than that indicated by the early surveys. Even if adoption is widespread, the government can have the potentially large milk surplus problems under control with a combination of price support, generic milk advertising, and a cow buy-out. With bST adoption, the government would set lower support prices and would increase assesment for milk advertising, compared with the no-bST case. The higher adoption rates, the lower the support prices and the higher the advertising assesments. It is found that bST adoption is socially beneficial; consumers gain at the expense of producers. The government can, however, help produces by giving a larger policy weight to producers in setting the optimal levels of policy variables. Finally, it is found that the current levels of generic advertising are too low, and the allocation of advertising between fluid milk and manufactured products is not optimal.     

Long horizon versus short horizon planning in dynamic optimization problems with incomplete information

Summary. This paper compares the implications of short and long horizon planning in dynamic optimization problems with the structure of a standard one-sector growth model if agents have incomplete knowledge about the production function. Agents know the output and rate of return at the current capital stock and use an estimation of the production function based on this knowledge to determine current consumption. For standard utility functions without wealth-effects both long and short planning horizons yield convergence to the steady state - however at a faster rate than optimal -, or fluctuations around the steady state, and in both cases, long horizon planning yields a policy which locally at the steady state is closer to the optimal one than short horizon planning. On the other hand, for preferences with wealth effects where the intertemporal optimal path exhibits fluctuations, long horizon planning destabilizes the path and short horizon planning can generate paths which are qualitatively closer to the optimal one and yield higher discounted utility.Received: 5 April 2001, Revised: 15 September 2003, JEL Classification Numbers: C61, D83, D90.Herbert Dawid: The author would like to thank Richard Day for numerous stimulating discussions which led to this article and an anonymous referee for helpful comments     

Computation of non-linear continuous optimal growth models: experiments with optimal control algorithms and computer programs

In this paper we discuss the use of optimal control methods for computing non-linear continuous optimal growth models. We have discussed various recently developed algorithms for computing optimal control, involving step-function approximations, Runge–Kutta solutions of differential equations, and we suggest that the discretization approach is preferable to methods which solve first-order optimality conditions. We have surveyed some powerful computer programs by : , and for computing such models numerically. These programs have no substantial optimal growth modelling applications yet, although they have numerous engineering and scientific applications. A computer program named by is developed in this study. Results are reported for computing the Kendrick–Taylor optimal growth model using and programs based on the discretization approach. References are made to the computational experiments with and . The results are used to compare and evaluate mathematical and economic properties, and computing criteria. While several computer packages are available for optimal control problems, they are not always suitable for particular classes of control problems, including some economic growth models. The -based and , however, offer good opportunities for computing continuous optimal growth models. It is argued in this paper, that optimal growth modellers may find that these recently developed algorithms and computer programs are relatively preferable for a large variety of optimal growth modelling studies.     

The hopf bifurcation and the existence and stability of closed orbits in multisector models of optimal economic growth

It is shown that under very general circumstances, the standard optimal growth model with two or more capital goods can give rise to optimal trajectories that are limit cycles. An example with a nonjoint production Cobb-Douglass technology giving rise to closed cycles around a unique steady state is constructed. The stability of orbits is also studied.     

Economic policy with bounded controls

When investigating optimal policies for macroeconomic models, it is common practice to modify the objective function so that the resulting optimal control trajectories become acceptable from a practical point of view. In this paper we argue that the sole purpose of the objective function should be to express the preference of the decision makers, and that explicit bounds on the controls should be used to ensure that the optimal controls will be practical. Using a piece-wise quadratic objective function involving only the unemployment and inflation rates, which are state (endogenous) variables, we first develop a discrete minimum principle, giving necessary and sufficient optimality conditions. Then we perform various bounded control experiments with the 35-equation quarterly CLEAR model of the Canadian economy, which is very briefly described. The empirical results which were obtained using a version of the GRG algorithm are discussed in view of the conclusions that might be drawn for a real-world practical policy analysis.     

On the optimality of limit cycles in dynamic economic systems

The purpose of this paper is to derive conditions for the optimality of a limit cycle in a dynamic economic system and to interpret them economically. A fairly general two-state continuous-time nonlinear optimal control problem is considered. It turns out that for this class of models three different economic mechanisms can be identified as the possible source of limit cycles. One relates to an intertemporal substitution effect expressed in terms of complementarity over time, the second one is a dominating cross effect between the state variables of the system (i.e., the capital stocks in our model), and the third one is positive growth at the equilibrium.We acknowledge the helpful comments by William A. Brock, Gerhard Sorger, Franz Wirl, and two anonymous referees. The research was partly supported by the Austrian Science Foundation under contract No. P6601.     

Optimal Disease Eradication in Sympatric Metapopulations

The paper analyses the management of an infectious disease in a sympatric metapopulation, under both Nash and cooperative behaviour, through the development of a differential game and an optimal control problem with connected local state variables. As pathogens are renewable resources with negative value, the problem may be non-convex. Since the disease can be transmitted across various connected populations, externalities may be involved. A numerical application is presented, with reference to a livestock disease that can be transmitted between herds on common pastures. The results suggest that optimal eradication in finite time should be pursued when possible. However, optimal eradication is not always feasible (sometimes eradication can be only achieved asymptotically), and the ecology of the disease is of paramount importance in this respect. Also, convergence to an internal steady-state does not minimise the present value of the disease damage and control cost (a result consistent with the existing literature). Ignoring these results may lead to inadequate policy design.