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.     

Human capital and the time-profile of human fertility revisited

This paper examines a model of the intertemporal distribution of births recently proposed by Cigno that concludes 1) the optimal time profile will satisfy the Hotelling rule of natural resources depletion, and 2) women with high initial endowments of human capital will have all their children early in married life while those with low initial endowments will spread childbearing more evenly over the fertile period. This paper argues that Cigno's model is inconsistent with the empirical evidence. Specifically, it is claimed that: 1) the natural resource analogy has been misapplied; 2) the stated 1st order conditions are incorrect; 3) optimal birth profiles do not satsify the Hotelling rule; and 4) the optimal time profile is for all women, regardless of their human capital, to concentrate births at the end of the fertile period. Since the discounted opportunity cost of a birth declines over time, it always pays to postpone a birth as long as possible. However, again, the theoretical prediction of delayed childbirth is not consistent with available evidence, suggesting that important factors have been omitted from this model.     

NATIONAL ACCOUNTING FOR NON-RENEWABLE NATURAL RESOURCES IN THE MINING INDUSTRIES*

This paper discusses alternatives to current national accounting procedures for non-renewable natural resources in the mining industries. Three alternative approaches to valuing the discovery and use of these resources are compared and alternative estimates for U.S. oil and gas for the period 1948-79 are presented. The focus is on the conceptual and empirical difficulties associated with valuing non-renewable natural resources.     

中国不可再生能源消耗效率的关键影响因素研究

随着中国工业化和城市化进程的加快,不可再生能源消耗在急剧增长,经济发展对能源供给与环境约束的压力已经濒临可持续发展平衡底线。无论从国家能源安全还是能源、经济、环境系统的和谐发展角度出发,提高不可再生能源消耗效率都是必然选择。在此背景下,基于C2B-DEA、超效率DEA模型,测算出1 990-2009年间中国不可再生能源消耗效率值,选定产业结构、对外开放程度、城市化进程、技术进步以及不可再生能源消耗结构等五大影响因素与效率值进行影响因素回归模型的实证分析。研究结果表明:第三产业比重、对外贸易进出口总额比重、城市化率以及不可再生能源消耗构成中煤炭消耗比重与不可再生能源消耗效率呈负相关,科技研发经费投入比重与不可再生能源消耗效率呈显著正相关。现阶段内,技术改造及创新与煤炭消耗比重的降低是提高我国不可再生能源消耗效率的重要途径。     

Adverse selection,commitment and exhaustible resource taxation

This paper studies the contractual relationship between a government and a firm in charge of the extraction of an exhaustible resource. Governments design taxation scheme to capture resource rent and they usually propose contracts with limited duration and possess less information on resources than the extractive firms do. This article investigates how information asymmetry on costs and an inability to commit to long-term contracts affect tax revenue and the extraction path. This study gives several unconventional results. First, when information asymmetry exists, the inability to commit does not necessarily lower tax revenues. Second, under asymmetric information without commitment, an efficient firm may produce during the first period more or less than under symmetric information. Hence, the inability to commit has an ambiguous effect on the exhaustion date. Third, the modified Hotelling's rule is such that an increase in the discount factor does not necessarily reduce the first-period extraction.     

矿产开发中资源生态环境补偿的理论基础评述

矿产开发中伴随资源损耗、生态环境破坏与区域可持续发展能力下降。经济发展的现实要求对资源生态环境以及区域发展进行补偿。但补偿依据、原则、主体等如何确定？经济学理论为其提供了阐释。矿产资源耗竭性理论强调：矿产资源不可再生强化了其相对稀缺性,通过资源合理定价可以起到保护资源的目的;资源生态环境价值理论认为：资源、生态环境是稀缺的、有价值的,在使用过程中需要为之付费;外部性理论解释了资源开发区域的外部不经济现象与全国范围内的外部经济现象,指出生态环境补偿、区域补偿的责任主体;区域可持续发展能力理论要求企业规范开采行为以维持资源生态环境的基本功能,通过资本转化保持区域总财富不减少。     

Untested Hypotheses in Non-Renewable Resource Economics

The present paper reviews the literature on the empirical implications of the Hotelling rule and suggests directions for further research in this area.     

Strategic resource dependence

We consider a situation where an exhaustible-resource seller faces demand from a buyer who has a substitute but there is a time-to-build delay for the substitute. We find that in this simple framework the basic implications of the Hotelling model (1931) are reversed: over time the stock declines but supplies increase up to the point where the buyer decides to switch. Under such a threat of demand change, the supply does not reflect the current resource scarcity but it compensates the buyer for delaying the transition to the substitute. The analysis suggests a perspective on costs of oil dependence.     

Who Cares about Biodiversity? Optimal Conservation and Transboundary Biodiversity Externalities

The Convention on Biological Diversity’s (2010) target to reduce the rate of biodiversity loss was achieved by very few countries. Why? We use the theory of conservation implicit in the Hotelling model of non-renewable resource pricing to analyze the problem, distinguishing between the benefits to countries where conservation takes place, and to other countries. We estimate models for three taxonomic groups, and find that while individual countries value conservation within their borders, in poor countries this effect is dominated by the negative impact of income growth. International concessional financial contributions to conservation in poor countries are found to be statistically insignificant. We conclude that countries care about the biodiversity within their national borders, but only when development priorities permit, and only when it becomes scarce enough that its value grows more rapidly than the return on alternative assets. There is little evidence that high income countries yet care sufficiently about biodiversity in the places where it is most threatened to affect conservation outcomes there.     

Trends in the extraction of non-renewable resources: The case of fossil energy

This paper considers a strategy for the extraction and production of non-renewable resources that are finite in quantity. Specifically, we illustrate empirical data on reserves, production, consumption, and price evolution for fossil fuel. Our model is an intertemporal model of a short decision time horizon with a monopolistic resource producer extracting non-renewable resources. The model is solved numerically using a finite horizon solution method called Nonlinear Model Predictive Control (NMPC), which approximates well models with a longer decision time horizon. Consistent with the results of recent empirical studies, our numerical solution method shows a U-shaped path for the price and an inverted U-shaped path for the extraction rate, in the case of modest initial stock of proved reserves.     

An inquiry into the Ramsey-Hotelling connection

Ramsey’s 1928 Ramsey, F. P. 1928. “A Mathematical Theory of Saving.” Economic Journal 38 (152): 543–559. doi:10.2307/2224098[Crossref] , [Google Scholar] paper on saving and Hotelling’s 1931 article on exhaustible resources are considered to be two seminal contributions in economic dynamics. They have been associated because of their temporal proximity, use of the calculus of variations, and because of Hotelling’s citation of Ramsey. This connection however needs to be precisely investigated and characterized. On the basis of archival material, this paper shows that, on the interpersonal and theoretical ground, the connection is quite thin, but that significant parallels are found in Ramsey’s and Hotelling’s expectations with mathematical economics for the progress of science and for informing public decision.     

Modeling Nonrenewable Resources Use with Multiple Demands and Multiple Sources

The theoretical literature following Hotelling (J Polit Econ 39:137–175, 1931) assumed that all nonrenewable resource needs are satisfied by one type of resource (e.g. “oil”), extractible at different per-unit costs. This formulation implicitly assumes that all users are the same distance from each resource pool, that all users can switch costlessly from one type of resource to another (e.g. liquid fossil fuels to coal or vice-versa), and that all users are subject to the same regulations. These assumptions imply, as Herfindahl (Extractive resources and taxation. University of Wisconsin Press, Madison, pp 63–90, 1967) showed, that in competitive equilibrium all users will exhaust a lower-cost resource completely before beginning to extract a higher-cost resource: simultaneous extraction of different grades of oil or of oil and coal should never occur. In trying to apply the single-demand curve model during the last twenty years, several teams of authors have independently found a need to generalize it to account for users differing in their (1) location, (2) resource needs, or (3) regulatory environment. Each research team found that Herfindahl’s strong, unrealistic conclusion disappears in the generalized model; in its place, a weaker Herfindahl result emerges. Since each research team focussed on a different application, however, it has not always been clear that everyone has been describing the same generalized model. The goal in this paper is to integrate the findings of these teams and to present an easily accessible generalization of the nonrenewable resource model to multiple demand curves.     

Capital Gains and Income Arising from Nonrenewable Resources

Should capital gains be included in income arising from nonrenewable resources? In the present paper, I show that capital gains from a nonrenewable resource can be divided into two terms: real price change effects and real interest rate change effects. By application of sectoral income theory developed by Asheim and Wei (Environ Res Econ 42:65–87, 2009), only the former term is part of real income of the resource and the latter term should not be included. This result is significant in the sense that all change in real resource wealth can be included as part of real income only if future real interest rates are assumed to be constant. Hotelling rule always implies that capital gains from nonrenewable resources coincide with real interests on resource wealth; net investment generated from the resource cancels out current cash flow from the resource; and real income comes from price change effects.     

The Elephant In The Ground: Managing Oil And Sovereign Wealth

One of the most important developments in international finance and resource economics in the past twenty years is the rapid and widespread emergence of the $6 trillion sovereign wealth fund industry. Oil exporters typically ignore below-ground assets when allocating these funds, and ignore above-ground assets when extracting oil. We present a unified stylized framework for considering both. Subsoil oil should alter a fund’s portfolio through additional leverage and hedging. First-best spending should be a share of total wealth, and any unhedgeable volatility must be managed by precautionary savings. If oil prices are pro-cyclical, oil should be extracted faster than the Hotelling rule to generate a risk premium on oil wealth. Finally, we discuss how our analysis could improve the management of Norway’s fund in practice.     

Logic,rationality and knowledge in Ramsey's thought: reassessing ‘human logic’

This paper reconsiders Frank Ramsey's essay on subjective probability (1926) as a consistent way to articulate logic, rationality and knowledge. The first part of the essay builds an axiomatic theory of subjective probability based on ‘formal logic’, defining rationality as choice-consistency. The second part seems to open up different horizons: the evaluation of degrees of belief by ‘human logic’. Because of the interest Keynes (1931) had taken in ‘human logic’, it was considered to be a possible alternative to the formal logic underlying the neoclassical theory of individual behaviour. The analysis of Ramsey's method in the entire paper, the relation between logic and rationality it constructs and the conception of uncertainty it reveals, lead me to note on the contrary that Ramsey's human logic was a complementary logic rather than an alternative to formal logic. Defining a standard to evaluate beliefs formation according to a frequentist criterion, it completes a normative representation of rationality which supports an original theory of knowledge that appears more in line with further developments of neoclassical methodology than with Keynesian economics.     

Hotelling and recycling

We study the exploitation of recyclable exhaustible resources such as metals that are crucial for the energy transition or phosphorus that is crucial for agricultural production. We use a standard Hotelling model of resource exploitation that includes a primary sector and a recycling sector. We study two polar cases: competitive and monopolistic extraction. We show that, when the primary sector is competitive, the Hotelling’s rule holds and the price of the recyclable resource increases over time. We then show a new reason why the price of an exhaustible resource may decrease: when the primary sector is monopolistic, the primary producer has incentives to delay its production activities in order to delay recycling. As a consequence, the price path of the recyclable resource may be U-shaped. Numerical simulations reveal that the monopolist has an incentive to delay extraction when the recoverability rate is high (because more recycled goods are produced) or when the recoverability rate is low (when fewer recycled goods are expected to be produced in the future). As a consequence, the date of exhaustion of the virgin resource is further away in time for high and low levels of recoverability than for intermediate levels.     

The Role of Keynesian Policies in Semi-industrialized Countries: theory and evidence from India

This paper examines the relevance of Keynesian policies—interpreted as those policies implied by Keynes's theoretical analysis of unemployment developed in The General Theory—for a subset of developing economies, which are called semi-industrialized countries. It draws on recent contributions in development economics to argue on theoretical grounds that Keynesian policies are relevant for semi-industrialized countries even when they are constrained by capital shortages, stagnant agricultural sectors, and foreign exchange availability. It then discusses the recent development experience of India to illustrate the empirical relevance of some of these theoretical issues.     

Do Natural Resources Depress Income Per Capita?

Most evidence for the resource curse comes from cross‐country growth regressions suffers from bias originating from the high and ever‐evolving volatility in commodity prices. These issues are addressed by providing new cross‐country empirical evidence for the effect of resources in income per capita. Natural resource dependence (resource exports) has a significant negative effect on income per capita, especially in countries with bad rule of law or bad policies, but these results weaken substantially once we allow for endogeneity. However, the more exogenous measure of resource abundance (stock of natural capital) has a significant negative effect on income per capita even after controlling for geography, rule of law and de facto or de jure trade openness. Furthermore, this effect is more severe for countries that have little de jure trade openness. These results are robust to using alternative measures of institutional quality (expropriation and corruption instead of rule of law).     

The cost controversy: Pigouvian economics in disequilibrium

The standard treatment traces the relation between a firm's costs and output to Jacob Viner's seminal article in 1931. This glosses over the importance of the cost controversy a by-product of which is the development of the basic elements of the theory of the firm in the long-run perfectly competitive framework. This article focuses on the contributions to this area of Arthur Cecil Pigou who-while defending specifying and changing the Marashallian treatment of the laws of returns during the 1922–1932 period - separated external and internal economics of the equilibrium firm drew (perhaps for the first time) U-shaped cost curves and spelled out stability conditions for competitive equilibrum. These provided the building blocks of modern theory of the firm as presented in undergraduate economic textbooks.     

Canada’s dependence on natural capital wealth: Was Innis wrong?

Canada has abundant natural resources—its stock of natural capital wealth. A recurring debate in the literature is whether resource rich countries benefit in the form of higher sustained growth rates or not from the export of their natural resources. Canada's Harold Innis wrote extensively on this subject over 80 years ago and argued for the “no” side in the debate. Was he was right or wrong? I begin with the foundations of natural resource theory then turn to empirical work in recent decades. I agree with the literature that Canada overall has benefited from the export of its natural resources, but question whether that can continue given the focus on short term growth and the failure to account for the social costs of resource extraction and use—the environmental externalities that degrade and reduce stocks of natural capital. These externalities increasingly threaten our water and land resources and without more effective policy, the ability of resources to sustain growth and well‐being is questionable. Was Innis wrong? Yes in that the evidence supports the counter argument—resources have helped Canada become a developed economy with relatively high incomes and sustained growth rates. Innis was right that the uneven distribution of resources causes different impacts regionally especially during booms and busts and recognized the need to find substitutes for declining and degrading resource stocks. But Innis, like many after him, focused more on the intrinsic features of natural resources than policy to address the social costs of their development, a legacy that leaves us in a precarious position today.