Extracting information or resource? The Hotelling rule revisited under asymmetric information

• DOI: http://doi.org/10.1111/1756-2171.12233
• Author: David Martimort,Francesco Ricci,Jérôme Pouyet
• Date: 01 June 2018
• Published date: 01 June 2018

RAND Journal of Economics

Vol.49, No. 2, Summer 2018

pp. 311–347

Extracting information or resource?

The Hotelling rule revisited under

asymmetric information

David Martimort∗

J´

erˆ

ome Pouyet∗∗

and

Francesco Ricci∗∗∗

A concessionaire has private information on the initial stock of resource. A “virtual Hotelling

rule” describes how the resourceprice evolves over time and how extractioncosts are compounded

with information costs along the optimal extraction path. Fieldswhich are heterogeneous in terms

of their initial stocks follow different extraction paths. Resource might be left unexploited in the

long run as a way to foster incentives. The optimal contract may sometimes be implemented

through royalties and license fees. With a market of concessionaires, asymmetric information

leads to a “virtual Herfindahl principle” and to another form of heterogeneity across active

concessionaires.

1. Introduction

Motivation. Resource extraction heavily relies on the division between ownership and

control. The oil and gas sectors are two prime examples. There, various kinds of contracts rule

the relationships between public authorities, which own the land where production takes place,

and specialized firms in charge of resource management.1Actually, these firms are most often

∗Paris School of Economics-EHESS; david.martimort@psemail.eu.

∗∗THEMA-CNRS, ESSEC Business School, Universit ´

e de Cergy-Pontoise; pouyet@essec.edu.

∗∗∗Universit´

e de Montpellier (ART-Dev); francesco.ricci@umontpellier.fr.

Wethank Fanny Henriet, Katheline Schubert, and participants to the “Shale Gas and Energy Transition” workshop held at

CEPREMAP (January 2016, Paris), as well as participants to SURED 2016 (Banyuls-sur-Mer), EAERE 2016 (Zurich),

and FAERE 2016 (Bordeaux), for their comments and suggestions. We also thank Julien Daubannes, Louis Daumas,

Corrado di Maria, Andr´

e Grimaud, Louise Guillouet, DavidHemous, Pier re Lasserre, Charles Mason, Michel Moreaux,

Aggey Semenov, Antony Millner,and Jean-Christophe Poudou for useful discussions. Finally, the insightful comments of

tworeferees have helped us improve this article. This research has benefited from the support of CEPREMAP (Paris) and of

ANR POLICRE (ANR 12-BSH1-0009). Ricci acknowledges financial support byANR REVE (ANR 14-CE05-0008-02).

All remaining errors are ours.

1To illustrate, three different sorts of contracts are most commonly observed in the oil sector. “Concessions

contracts” are such that the firm owns oil in the field. For “production-sharing agreements,” the firm owns only part of

the produced oil. Finally, “service contracts” are such that the firm receives a financial compensation for production.

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312 / THE RAND JOURNAL OF ECONOMICS

international ventures operating on a large scale. The first consequence of such specialization

is that these firms certainly have the capability to mobilize specific know-how, to finance risky

exploration, or to build all infrastructures needed for production and transportation. A second but

more perverse consequence of such specialization is that those firms enjoy also a comparative

advantage vis-`

a-vis public authorities when it comes to assess the amount of reserves in a

given geographical area.2In this article, we thus ask how public authorities and concessionaires

should design contracts for the management of resource in contexts plagued with asymmetric

information.

At a broad level, the delegated management of resource should share some of the general

features found with other forms of procurement.The existing literature has forcefully stressed that

the design of optimal procurement contracts under informational constraints results from a trade-

off between efficiency and rent extraction.3Operating at the efficient scale might also require

leaving excessive and socially costly information rents to the concessionaire. Reducing these

rents calls instead for a lower output, lower-poweredincentives, and, more generally,procurement

policies that are less sensitive to information.

Yet, and although our analysis below confirms that these insights still have some bite in

the context of resource management, resource extraction is inherently a dynamic phenomenon.

This dynamic perspective is probably best illustrated by the importance taken by the Hotelling

rule in resource economics.4The Hotelling rule shows how the resource price should evolve

along an efficient path of extraction. Although much has been said on its empirical validity,5this

rule provides an important benchmark to assess how the trade-off between efficiency and the

extraction of information rent must be revisited in a dynamic model of resource extraction. As

our analysis shall demonstrate, such dynamics requires a specific analysis, which unveilsnew and

important effects.6

Virtual cost of extraction and virtual Hotelling rule. Before unveiling the new insights

brought by asymmetric information, it is useful to briefly review the mechanism underlying the

Hotelling rule under complete information. Suppose thus that the stock of resource is common

knowledge and that, because of depletion, the marginal cost of extractionincreases over time. The

Hotelling rule stipulates that the resource price must reflect the scarcity rent. Efficiency requires

that, at any point in time, the marginal value of the last unit extracted covers not only the current

marginal cost (function of current reserves) but also the shadow cost of increasing the extraction

cost from that date on by depleting reserves. Those reserves decrease up to the point where the

marginal cost of extraction is equal to the choke price, and extraction ceases at that point. At the

same time, the resource price continuously increases over time to reflect the dynamic arbitrage

between consuming resource today or leaving more resource in the ground so as to facilitate

extraction tomorrow. Under complete information, the public authority can simply capture all

the concessionaire’s intertemporal profit along this optimal path by imposing a license fee whose

value is perfectly known.7

Historically,concession contracts prevailed at the inception of the industry in the United States because, there, ownership

of an estate includes subsurface mineral rights. They became used throughout the world afterward. Followingthe wave

of nationalizations in the 1970s, the dominant types of contracts are now production-sharing agreements, when the host

country contracts with a firm for exploration and management of production. Similar patterns are observed in the gas

sector.

2Osmundsen (2010) provides a detailed account of the various waysin which a firm in charge of the assessment of

the stock and the management of the resource strategically uses such information.

3See Laffont and Tirole (1993) and Armstrong and Sappington (2007) for accounts of the New Regulatory

Economics.

4Hotelling (1931).

5See Gaudet (2007) for a critical overview.

6These specificities of models of resource extraction from the perspective of the Theory of Incentives have also

been stressed by Gaudet and Lasserre (2015).

7An alternative would be to hold an auction for the franchise among potential concessionaires.

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The picture is strikingly different when the firm has private information on its initial stock.

Contracts must now induce firms with different stocks to select different extraction paths as a

means to reveal information. A firm with a large initial stock and thus a low cost of extraction

may just adopt the same extraction pattern as one with lower reserves and a higher extraction

cost. By doing so, the high-stock firm produces the same quantity as the low-stock one at any

point in time. It also pays a lower license fee and pockets the corresponding cost saving over the

whole extraction path. Slowing down extraction is thus a way to capture part of the information

rent left to firms with large initial stocks. Underestimating stocks is akin to keeping resource in

the ground.

An optimal contract must render such strategy less attractive so as to induce information

revelation at the inception of the relationship. This is achieved by the public authority through

the commitment to reduce extraction from firms which claim lower levels of reserve to start

with. By reducing the production of these firms, the public authority makes less valuable for

firms endowed with higher initial stocks to strategicallybehave as having lower reserves. In other

words, everything happens as if the marginal cost of extraction is replaced by a greater “virtual

cost of extraction” that accounts for the cost of extracting information.8Dynamic inefficiencies

in resource extraction arise when information has also to be extracted. This points to an important

dilemma in designing concession contracts: the cost of inducing information revelation is to leave

resource in the ground, stopping extraction before what efficiency would command.

We characterize the extraction path under asymmetric information by means of a “virtual

Hotelling rule” that governs how the resource price optimally evolves over time. This virtual

Hotelling rule has again a simple interpretation. The last unit extracted from a given field must

be such that the marginal benefit of consumption covers not only the current cost of extraction

and the shadow cost of increasing future extraction as under complete information, but also the

cost of the information rents captured by firms with supramarginal reserves.

Comparative statics. Altogether, scarcity and information rents shape the dynamics of

resource extraction. Although under complete information, all firms, whatever their initial stock,

evolvealong the same extraction path and extract up to a point where the marginal cost of extraction

equals the choke price, asymmetric information introduces heterogeneity across trajectories. A

firm with a smaller (larger) stock extracts less (more) and leaves thus more (less) resource in the

ground in the long run. The limit level of unexploited stock is now obtained when the virtual

marginal cost of extraction is equal to the choke price. That limit varies negatively with the initial

stock.

Interestingly,we provide closed-form expressions for the optimal paths and show that asym-

metric information does not necessarily slow down resource extraction, at least in the case of a

single concessionaire. In the case of linear demand and extraction cost, both the level of resource

and the quantity extracted converge toward their long-run limits at the same exponential rates as

under complete information. Yet, the overall amount extracted is always lower under asymmetric

information.

Implementation. We then ask whether the optimal contract can be implemented with

simple instruments that might echo real-world practices. Still, in the case of linear demand and

extraction cost, we first demonstrate that the choice of a dynamic extraction path can be reduced

to the choice of the quantity extracted at the start. The whole analysis of a dynamic extraction

problem then boils down to a static problem. We then show that a simple nonlinear paymentlinks

the firm’s compensation to that initial quantity extracted. Under a weak technical condition that

guarantees the convexity of this schedule, the optimal contract can be implemented by a menu

of linear schemes that specify royalties and license fees. Firms with greater initial stocks choose

more attractive royalties but also pay higher fees.

8To use the parlance of Myersonin numerous contributions.

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