DYNAMIC MECHANISM DESIGN FOR A GLOBAL COMMONS

• Published date: 01 August 2017
• Author: Rodrigo Harrison,Roger Lagunoff
• Date: 01 August 2017
• DOI: http://doi.org/10.1111/iere.12234

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 3, August 2017

DYNAMIC MECHANISM DESIGN FOR A GLOBAL COMMONS∗

BYRODRIGO HARRISON AND ROGER LAGUNOFF1

Instituto de Econom´

ıa Ponticia, Universidad Cat ´

olica de Chile, Chile; Georgetown University,

U.S.A

We model dynamic mechanisms for a global commons. Countries value both consumption and conservation

of an open access resource. A country’s relative value of consumption to conservation is privately observed and

evolves stochastically. An optimal quota maximizes world welfare subject to being implementable by Perfect

Bayesian equilibria. With complete information, the optimal quota is first best; it allocates more of the resource

each period to countries with high consumption value. Under incomplete information, the optimal quota is fully

compressed: Identical countries receive the same quota even as environmental costs and resource needs differ.

This is true even when private information is negligible.

1. INTRODUCTION

The global effects of environmental problems such as greenhouse gas (GHG) emissions,

deforestation, and species extinction present a significant challenge for policy makers. The

global scale of GHG emissions, for instance, requires that most countries be involved in any

climate negotiations. Moreover, the accumulation of atmospheric GHG is an inherently dynamic

process. Its effects are difficult to predict and are heterogeneous across countries. According to

the Intergovernmental Panel on Climate Change (IPCC):

Peer-reviewed estimates of the social cost of carbon in 2005 average US$12 per tonne of CO2, but

the range from 100 estimates is large (–$3 to $95/tCO2). This is due in large part to differences in

assumptions regarding climate sensitivity, response lags, the treatment of risk and equity, economic and

non-economic impacts, the inclusion of potentially catastrophic losses and discount rates. Aggregate

estimates of costs mask significant differences in impacts across sectors, regions and populations and

very likely underestimate damage costs because they cannot include many non-quantifiable impacts.

(IPCC 2007 Synthesis Report).

In light of this, any international agreement must be structured so that countries find it in

their self-interest to follow its prescriptions at each point in time, all the while accounting for

difficult-to-predict and asymmetrically observed changes in the benefits and costs of carbon

usage.

This article examines the nature of optimal self-enforcing agreements to regulate a global

commons. We posit an infinite horizon model of global resource consumption. The resource

is depletable, and its aggregate use imposes environmental costs on each country. Access to

the resource is not limited, and each country derives simultaneous benefit both from its own

resource consumption and from the aggregate conservation of the resource stock.

Conservation is intrinsically beneficial to each country because it allows the country to avoid

the environmental costs of global resource consumption. The conservation benefits are assumed

∗Manuscript received November 2014; revised March 2016.

1We thank seminar participants at Brown, NYU, CETC Montreal, the NBER Summer Political Economy and

Public Finance Workshop, USACH (Chile), University Carlo Alberto, and Masaki Aoyagi, Sandeep Baliga, Andy

Postlewaite, Debraj Ray, and three anonymous referees for valuable comments and suggestions.

Pleaseaddress correspondence to:Roger Lagunoff, Department of Economics, G eorgetown University, Washington,

DC 20057. E-mail: lagunofr@georgetown.edu.

751

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

752 HARRISON AND LAGUNOFF

to be heterogeneous across countries and are stochastically determined as countries are hit with

private, idiosyncratic “payoff” shocks. The shock process in our model captures a common

feature in many commons problems: Environmental costs are difficult to forecast and often

vary widely across countries.2

Our model adopts a parametric approach which, for a variety of technical reasons, has

proved useful in studies in dynamic resource allocation.3One of the first of these was the classic

common pool resource model of Levhari and Mirman (LM; 1980). LM posit a parameterized

“fish war” model of an open access resource problem. In their model identical users choose how

much to extract each period. The residual is left for future extraction. There are no extraction

costs or associated externalities. Conservation is therefore valued in the LM model only for

instrumental reasons: Preserving the stock allows one to smooth consumption. The LM model

and its many successors admit closed form solutions yielding a transparent view of the “tragedy

of the commons” problem.

A new generation of parametric models augment the LM model. Dutta and Radner (2006,

2009) examine energy consumption with emissions externalities. Antoniadou et al. (2013) ex-

amine resource extraction in a more general class of parametric models.

Our article works from these blueprints, adding some modifications along the way. We

consider a heterogeneous externality in resource consumption that makes conservation directly

beneficial. We add private shocks that alter each country’s relative value of conservation.

Despite the generalization, the parameterization is tractable enough to yield explicit, close

form solutions. From these explicit solutions, we examine how optimal commons mechanisms

respond to uncertainty, private information, and cross-sectional variation among countries.

In particular, we solve for an optimal quota system. An optimal quota system is an international

agreement specifying each country’s resource consumption (or emissions) at each date, given

any carbon stock and payoff realization, such that (a) the agreement jointly maximizes the

expected long-run payoffs of all countries, and (b) the agreement can be implemented by a

Perfect Bayesian equilibrium (PBE).

Implementability in a PBE captures the fact that there is no explicit mechanism designer

in global commons problems. There is no global government that can impose its will on the

countries. Instead, the PBE concept requires the quota system to be dynamically self-enforcing

in compliance and in public disclosure of information.

In the benchmark case of full information, each country’s payoff for consumption and con-

servation is known and there are no shocks. In this case, the first-best quota is shown to be

implementable and is characterized by stationary extraction rates that vary across countries.

Those countries that place, high value on consumption (or low value on conservation) are

permitted to extract more. Because the effects of full depletion are catastrophic, cheating is

deterred by graduated punishments that further deplete the stock each time a country violates

its prescribed resource use. For this reason, implementability does not depend on discounting.4

A second set of results pertain to the case of incomplete information—the case where persis-

tent, private payoffs shocks hit each of the countries. Under private information, all countries

have incentives to choose extraction policies that overstate their values for extraction. Hence,

the first-best quota system is not incentive compatible.

Unlike the full information benchmark, we show that with private shocks the optimal quota

is completely insensitive to a country’s realized type. We refer to this as the property of full

quota compression.

To illustrate what full compression means, consider two ex ante identical countries. Sup-

pose the realized shocks are such that one country ends up with high resource needs and/or

2Burke et al. (2011) find, for example, widely varying estimates of the effect of climate change on U.S. agriculture

when climate model uncertainty is taken into account. Desmet and Rossi-Hansberg (2013) quantify cross-country

variation in a calibrated model of spatial differences in welfare losses across countries due to global warming. These

differences come primarily from geography but may be amplified by trade frictions, migration, and energy policy.

3See Long (2011) for a survey of the vast literature since 1980.

4The punishment scheme can, in principle, implement any feasible payoff.

DESIGN FOR A GLOBAL COMMONS 753

low environmental damage, whereas the other ends up with low resource needs and/or high

environmental damage. Full compression then implies that the same quota is assigned to each

country at every point in time, regardless of the initial realization of the shocks.

Full compression also holds for arbitrarily small amounts of private information. Specifically,

as long as the support remains fixed, the distribution can place arbitrarily large mass on a single

resource type. The result suggests that arbitrarily small amounts of private information can

have first-order implications for international agreements.

The basic intuition for the compression results is straightforward. Global commons prob-

lems entail free-riding. Under the optimal quota, all countries have individual incentives to

overextract. Free-riding incentives are, of course, higher for higher types. Nevertheless, there

is a threshold extraction rate such that optimal extraction rates for all types will lie below this

cutoff. Meanwhile, free-riding incentives, if left unchecked, will push countries to extract above

the cutoff level. Hence, a quota that is not compressed will allow some types to indirectly free

ride by mimicking other types that are allocated higher extraction quotas.

It is worth noting that this intuition applies to commons problems but not necessarily to

markets. Optimal dynamic mechanisms for firms, for instance, will typically not be compressed

because allocation of market share inherently requires hard trade-offs between market shares

of different types of firms. A higher production quota assigned to one type of seller must be

offset with a lower one to another.5

By contrast, in the global commons problem there are no such trade-offs. A country’s “market

share” is its expected net present value of “stored resource,” which behaves like a public good.

Thus, a planner increases each country’s value of stored carbon simultaneously by reducing

everyone’s quota. This is not a good thing for the planner, however, since a reduction of

the quota increases all countries’ incentives to free ride via manipulation of information. The

planner is hamstrung by having no additional instrument beyond the quota to dampen these

incentives.

For more clarity on this point, we consider an extension of the model in which utility of the

representative agents of each country is transferable. The presence of transferable utility (TU)

is shown to eliminate the inefficiency because the transfers comprise a common unit of account

from which high type countries can be compensated by low types for truthful disclosure. This

additional “degree of freedom” admits an equilibrium that implements the first-best quota.

We argue, however, that transfers in a nontransferable utility (NTU) framework is a more

natural benchmark in our setting. With NTU transfers a welfare improving scheme may exist

in the context of the model but requires that countries that end up with low usage value be

subsidized by those with high usage value. This will sometimes require that developing countries

subsidize developed ones.

Up next, Section 2 summarizes the literature on dynamic mechanisms design as it applies to

global commons. Section 3 describes the benchmark model of full information. In that model

there are no shocks and each country’s resource type is common knowledge. Section 4 introduces

private persistent shocks. Section 5 explains the logic and implications of the full compression

result. We examine differences in implications if the model were to admit TU, imperfectly

persistent shocks, or a more general parametrization. Section 6 concludes with a discussion of

potential implications for policy. The Appendix contains proofs of the main results. The Online

Appendix examines some extensions and provides technical details underlying the proofs.

2. RELATED LITERATURE

There is, by now, a large literature analyzing mechanisms to address global commons prob-

lems. Understandably much of the literature focuses on a fairly narrow range of practical

5There are exceptions. For instance, Athey and Bagwell (2008) show that in certain types of markets with persistent

private shocks, the optimal collusive mechanism assigns a market share to each firm that is independent of the firm’s

realized cost type. We discuss differences and similarities between market mechanisms and the commons mechanisms

in the upcoming literature section and in Section 5.3.