The optimal depletion of exhaustible resources: A complete characterization

We provide the closed form solution to the Dasgupta–Heal–Solow–Stiglitz (DHSS) model. The DHSS model is based on the seminal articles Dasgupta and Heal, 1974, Solow, 1974 and Stiglitz (1974) and describes an economy with two assets, man-made capital and a nonrenewable resource stock. We explicitly characterize, for such an economy, the dynamics along the optimal trajectory of all the variables in the model and from all possible initial values of the stocks. We use the analytical solution to prove several properties of the optimal consumption path. In particular, we show that the initial consumption under a utilitarian criterion starts below the maximin rate of consumption if and only the resource is abundant enough and that under a utilitarian criterion, it is not necessarily the present generation that benefits most from a windfall of resources.     

A step beside the maximin path: Can we sustain the economy by following Hartwick's investment rule?

If sustainability is interpreted as the requirement to sustain consumption or utility at an optimal level, a maximin objective appears to be relevant. The sustained economy is characterized by an optimal investment following Hartwick's investment rule. This paper examines how the sustainability of a production-consumption economy with a non-renewable resource is modified in the neighborhood of the maximin path, i.e. when the consumption and the resource price are not optimal. A Sustainable Consumption Indicator is introduced in order to characterize the sustainability of constant consumption paths, defined as deviations from the maximin path. We describe how an over-consumption jeopardizes future sustainability.     

Ordering the extraction of renewable resources: The case of multiple aquifers

Optimal sequencing of resource extraction is typically studied for nonrenewable resources. We provide conditions for optimal use of multiple sources of a renewable resource and characterize the resulting extraction sequence, resource scarcity values, and (single) efficiency price path for two groundwater aquifers and an abundant alternative resource. Even with one demand, the optimal sequence depends on the differential opportunity costs of the two renewables. A numerical simulation for the South O‘ahu aquifer system, which also allows for different distribution costs, illustrates the case of using the “leakier” aquifer first and then switching to simultaneous use of both resources. The welfare gain from specialization relative to independent management is $4.7 billion.     

Testing the Assumptions and Predictions of the Hotelling Model

In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Using panel data on fourteen nonrenewable natural resources to estimate this empirical Hotelling model, we get qualitatively different results as compared to the related literature. We find evidence of stock-dependent extraction costs for most resources. There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. These results depend on whether firms use different extractive technologies or whether the structural break observed on resource prices is taken into account.     

Optimal Extraction of a Polluting Nonrenewable Resource with R&D toward a Clean Backstop Technology

We study the optimal extraction of a polluting nonrenewable resource within the following framework: environmental regulation is imposed in the form of a ceiling on the stock of pollution and a clean unlimited backstop technology can be developed by research and development. More specifically, the time taken to develop a new technology depends on the amount spent on R&D. A surprising result is that the stringency of the ceiling and the size of the initial stock of the polluting nonrenewable resource have a bearing on whether environmental regulation speeds up the optimal arrival date of this new technology. Compared to a scenario with no environmental externalities, stringent environmental regulation drives up the optimal R&D investment and brings forward the optimal backstop arrival date only in the case of a large initial resource stock. Otherwise, if the initial resource stock is small, regulation reduces optimal R&D and postpones the optimal backstop arrival date. These results are explained by the two roles played by the backstop technology. First, the backstop serves to replace oil once it has been exhausted. As extraction is slowed down by regulation, the exhaustion of the nonrenewable resource is postponed and the long‐run gains of innovation are lowered. Second, environmental regulation raises the short‐run gains of innovation by increasing the cost of consuming just oil.     

Optimum Growth and Carbon Policies with Lags in the Climate System

We study the optimal carbon tax in an economy in which climate change, stemming from polluting non-renewable resource, affects the economy’s growth potential. Our main contribution is to introduce and explore the natural time lag of the climate system between emissions and damages to capital accumulation in an endogenous growth setting. This allows us to investigate how optimal climate policy, and its interplay with climate dynamics, affect long-run growth and the transition of the economy towards it. Without pollution decay, a higher speed of emissions diffusion steepens the growth profile of the economy. With pollution decay, this leads to lower short-run but higher long-run economic growth during transition. Poor understanding of the emissions diffusion process leads to suboptimal carbon taxes, resource extraction and growth.     

Jurisdictional Tax Competition and the Division of Nonrenewable Resource Rents

This paper presents a model of nonrenewable resource extraction across multiple jurisdictions which engage in strategic tax competition. The model incorporates rents due to both resource scarcity and capital scarcity as well as intra-region Ricardian rents. Regions set taxes on nonrenewable resource production strategically to balance tax revenues and local benefits from investment conditional on other regions’ tax rates. A representative extraction firm then allocates production capital across regions and time to maximize the present value of profits. Generally, we find that the division of resource rent between firms and regional governments ultimately depends on the relative scarcity of natural and production capital, relative costs across space, and the value regional governments place on economic activity. This theoretical result provides policymakers with information on the determinants of optimal tax rates and motivates future empirical research on the factors influencing the division of resource rent in practice.     

Consumption externalities, production externalities, and efficient capital accumulation under time non-separable preferences

The effects of consumption and production externalities on economic performance under time non-separable preferences are examined both theoretically and numerically. We show that a consumption externality alone has long-run distortionary effects if and only if labor is supplied elastically. With fixed labor supply, it has only transitional distortionary effects. Production externalities always generate long-run distortions, irrespective of labor supply. The optimal tax structure to correct for the distortions is characterized. We compare the implications of this model with those obtained when the consumption externality is contemporaneous. While some of the long-run effects are robust, there are also important qualitative and quantitative differences, particularly along transitional paths.     

The outcome of the Pasinetti process reconsidered: A note

Conclusion By introducing into the Pasinetti model the plausible assumption that workers and capitalists, respectively, maximize their consumption over time, it has been shown, that only with a well-behaved production function may the long-run outcome of the Pasinetti process be considered as an equilibrium position. In all other cases capitalists can increase their steadystate level of consumption without sacrificing any consumption today. As the maximal capitalists' consumption per head is determined by the technical conditions of production, the profit rate isnot independent of those conditions. We have not taken into account all problems of stability of the steady-state paths or the question of utility maximization over time, i. e. optimal saving; the former because the analysis of the transition processes are very difficult, the latter because of the dubious assumptions, which are necessary to get some convenient results.     

Sustainable management of renewable resources: an experimental investigation in continuous time

This study addresses one of the most basic questions in renewable resource management: the ability of economic agents to exploit a renewable resource in an efficient and sustainable manner. In a laboratory experiment, subjects are presented with renewable resource extraction problems, where optimal management will lead to a stable steady state. A test of sustainability of the extraction practices shows that extraction behaviour results in steady states only 56% of the time. The mode of the steady state distribution coincides with the optimal steady state extraction. The trade-off between accruing a higher payoff in the present and sustaining the resource for future exploitation leads to suboptimal behaviours such as initial overextraction of the resource compared to the optimal extraction policy, costly downward adjustment of the extraction later in time, and settling down for lower long-run resource and extraction. The suboptimal behaviours lead to 17% loss in efficiency on average in terms of the accumulated payoff. We further look at extraction behaviour in terms of the degree of impatience it projects and find, based on their extraction decisions, that most of our subjects seem more impatient in managing their resource than is justified by the decision-making problem presented to them.     

Constant-utility paths in a resource-based economy

This paper analyzes a social planner's solution in a resource-based economy under a constant-utility criterion. The utility function includes social progress in a multiplicative form. The resulting paths of consumption include the patterns of growth that are conventionally used in the literature. A closed form solution, derived for the Dasgupta-Heal-Solow (DHS) model, includes the Solow–Hartwick result as a special case. This paper extends the link between the utilitarian criterion and the maximin for the cases with finite elasticity of marginal utility. The result also implies that economic growth in a resource-based economy may be slower than exponential; therefore, the expression for utility with social progress may become a more appropriate measure of sustainable growth than the percentage of consumption growth.     

Optimal unemployment insurance: transitional dynamics vs. steady state

In this study, we ask whether the presence of precautionary savings substantially reduces the optimal replacement rate in an European economy type characterized by high unemployment benefits and moral hazard. We build a simple job search model calibrated on French data and, in line with previous studies, find that the optimality criterion based on comparisons of steady states leads to a low optimal ratio. Yet, this result ignores potential transitional costs due to the necessity for agents to increase their savings and reduce their consumption whenever the ratio is cut. We therefore build a dynamic model taking full account of the transition, and show that a reduction in benefits reduces welfare. Even though the long-run optimal replacement rate is lower than the current one, transitional costs dominate long-run gains.     

Optimal Time Interval Selection in Long-Run Correlation Estimation

This paper presents an asymptotically optimal time interval selection criterion for the long-run correlation block estimator (Bartlett kernel estimator) based on the Newey–West and Andrews–Monahan approaches. An alignment criterion that enhances finite-sample performance is also proposed. The procedure offers an optimal alternative to the customary practice in finance and economics of heuristically or arbitrarily choosing time intervals or lags in correlation studies. A Monte Carlo experiment using parameters derived from Dow Jones returns data confirms that the procedure can be MSE-superior to alternatives such as aggregation over arbitrary time intervals, parametric VAR, and Newey–West covariance matrix estimation with automatic lag selection.

     

Repeated auctions of franchises for nonrenewable resources

In maximizing the net total government take from exploitation of nonrenewable natural resource endowments, the government faces the problem that extraction companies possess private information about extraction capacities (adverse selection). In a repeated auctions model, I show that it is optimal to deviate from bidding parity, even in the absence of moral hazard. The second period auction is biased to mitigate the externality problem that stems from intertemporal dynamics in extraction costs.This research has been financed by the Research Council of Norway. I would like to thank K»re P, Hagen, Geir B. Asheim, Diderik Lund, and two anonymous referees for helpful comments. I have also benefited from comments at a seminar at the Norwegian School of Economics and Business Administration, and at the International Institute of Public Finance (IIPF), 51st congress, Lisbon, August 1995. The paper is a refined version of Discussion paper 1/95, Institute of Economics, Norwegian School of Economics and Business Administration.     

Uncertainty in the public debt market and stochastic long-run growth

In a continuous time model, a representative household has to allocate its investment and consumption in an optimal manner under conditions of uncertainty. In the present study it is hypothesized that there are two types of assets: a risk-free and a risky asset. The risk-free asset is assumed to be the physical capital, while at the same time uncertainty is allowed to result from the exogenous random variations in the public debt market, rendering in this way government bonds to act as the risky asset. In the endogenous growth framework with productive public investment, the expected long-run growth rate, the dynamic path of consumption as well as the optimal allocation of investment between a risky and a riskless asset, are analytically derived. This kind of treatment allows us to create a locus for the long-run growth over the various levels of uncertainty. The outcome of the analysis is that a rise in uncertainty impacts negatively upon the long-run growth rate. In order to empirically assess the relationship between growth and uncertainty, we lay our emphasis on the US economy for the period 1957:1 to 2008:4. Within the framework of a bivariate BEKK–GARCH(1,1)-M model a significant negative relationship between uncertainty and economic growth has been established.     

Environment,Directed Technical Change and Economic Policy

We study the effects of an economic policy in an endogenous growth general equilibrium framework where production of consumption goods requires two resource inputs: a polluting non-renewable resource and a non-polluting labour resource. The use of the former contributes to the accumulation of pollution in the atmosphere, which affects welfare. There is a specific research sector associated with each of those resources. We provide a full welfare analysis, and we describe the equilibrium paths in a decentralized economy. We go on to study the effects of three associated economic policy tools: a tax on the polluting resource, and two research subsidies. We show that the optimal environmental policy has two main effects; it delays the extraction of the resource and with it the level of polluting emissions and it reallocates research efforts, decreasing the amount put into “grey” research to the benefit of “green” research. We also show that the environmental policy is grey-biased in the short-term, and green-biased in the long-term. Finally, we compute the optimal values for these tools.      

Maximin growth paths with recursive preferences: A complete characterization

This paper examines the growth paths that maximize the utility of the worst off generation for an economy where preferences are stationary and can be represented by a recursive utility function. The analysis focuses on the case where second period utility is an inferior good. It is shown that in such a case the maximin growth paths are time inconsistent. A possible solution to the time inconsistency problem is examined.     

Decentralization of Intertemporal Economies With Discounted Maximin Criterion

The intertemporal decentralization literature scrutinizes the ability of markets to achieve dynamically optimal allocation of resources. Put differently, it examines the possibility of designing a mechanism enabling short-lived agents to make independent decisions compatible with long-run optimum. The Hurwicz and Weinberger impossibility result states that the mechanisms that are both privacy preserving and optimal fail to exist when an infinite-horizon optimum is defined by Ramsey-type criteria with discounting. However, for a special case where the economy cannot sustain growth and agents do not discount future utilities, it is known that a decentralized mechanism using rolling plans is in a certain sense asymptotically optimal. To address the problem of possibility of decentralization mechanisms in a sustainable growth economy with discounting, I consider a 'discounted maximin' optimality criterion. It selects the programs that sustain growth of welfare at a given rate. The article argues that this criterion is consistent with the principles of intergenerational justice, which can be defined in terms of intergenerational Nash equilibrium. Furthermore, the article demonstrates that a decentralized mechanism designed on the basis of rolling plans generates decisions that are asymptotically optimal in terms of the discounted maximin.     

Aggressive oil extraction and precautionary saving: Coping with volatility

The effects of stochastic oil demand on optimal oil extraction paths and tax, spending and government debt policies are analyzed when the oil demand schedule is linear and preferences quadratic. Without prudence, optimal oil extraction is governed by the Hotelling rule and optimal budgetary policies by the tax and consumption smoothing principle. Volatile oil demand brings forward oil extraction and induces a bigger government surplus. With prudence, the government depletes oil reserves even more aggressively and engages in additional precautionary saving financed by postponing spending and bringing taxes forward, especially if it has substantial monopoly power on the oil market, gives high priority to the public spending target, is very prudent, and future oil demand has high variance. Uncertain economic prospects induce even higher precautionary saving and, if non-oil revenue shocks and oil revenue shocks are positively correlated, even more aggressive oil extraction. In contrast, prudent governments deliberately underestimate oil reserves which induce less aggressive oil depletion and less government saving, but less so if uncertainty about reserves and oil demand are positively correlated.     

Optimally eating a stochastic cake: a recursive utility approach

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion.