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Doctoral Thesis
Prices vs. quantities at the inter-country level
An economic analysis of instrument choice in environmental
policy
Author(s):
Rohling, Hannes Moritz
Publication Date:
2013
Permanent Link:
https://doi.org/10.3929/ethz-a-009913128
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DISS. ETH Nr. 21046
"Prices vs. Quantities at the Inter-Country Level"
An Economic Analysis of Instrument Choice in
Environmental Policy
ABHANDLUNG
zur Erlangung des Titels
DOKTOR DER WISSENSCHAFTEN
der
ETH ZÜRICH
vorgelegt von
HANNES MORITZ ROHLING
Dipl.-Volksw. Univ., Ludwig-Maximilians-Universität München
geboren am 04.03.1982
von Deutschland
Angenommen auf Antrag von
Prof. Dr. Renate Schubert, Referentin
Prof. Dr. Stefanie Engel, Korreferentin
Dr. Markus Ohndorf, Korreferent
2013
For
Eugen Bernhard Rohling-Bauer
Acknowledgements
This thesis was written during my time as a researcher at the Chair of Economics at
ETH Zurich. Writing this thesis has proven a challenging, but also a rewarding task.
Without the continuous support of my advisors, colleagues, family and friends, this
thesis would not have been possible.
First of all, I want to thank Professor Dr. Renate Schubert for giving me the
opportunity to write this thesis and for continuously supporting me throughout the
years. Her encouragement, experience, expertise, as well as patience made the success
of this thesis feasible. I would also like to thank her for approving generous travel
funds that gave me the possibility to share and discuss ideas with experts at numerous
conferences, workshops, and summer schools.
Furthermore, I would like to express my thankfulness to Professor Dr. Stefanie Engel
for being my co-supervisor for this thesis and for giving valuable comments in all stages
of my work. I am also very grateful to Dr. Markus Ohndorf, my third supervisor and
coauthor. He was not only extremely helpful and encouraging with the paper we wrote
together, which is part of this thesis, but also in continuously supporting me, giving
thoughtful and valuable comments and critique, having fruitful ideas and feedback,
and for always pushing me to think harder.
I also want to thank all my colleagues, Catharina Bening, Julia Blasch, Thomas
Epper, Helga Fehr-Duda, Joschka Gerigk, Katja Halbritter, Manuel Luethi, Johannes
Manser, David Pham, and Raoul Steiger for interesting discussions and comments on
my research. Beside their academic input, they helped me to get through bad days
I had during my research activities in whatever area. My thanks also go to Beatrix
Haag-Sturm for her everlasting help in administrative purposes.
Most of all, I’m deeply indebted to my family, Hans, Lisa, Julia Rohling, and Marie
Viennet for always believing in me, for keeping me grounded, and for continuously
motivating me throughout the years of research. I’m tremendously grateful to Kristin
i
Hoffmann and Luu Hong Ha Alzinger for being amazing friends in good times as in
bad, for helping me with words and deeds, for showing me the path when I lost my
track, and supporting me when I lost confidence in myself. I consider this as not being
self-evident. Finally, I would like to thank all my friends from Zurich, Munich, Kassel,
Bern, and New York for their never ending support, faith and trust in me.
Contents
List of Figures
v
List of Tables
v
Abstract
vii
Zusammenfassung
ix
1 Introduction
1.1 Internalization of Environmental Externalities . . . . . . . . . . . . .
1.2 Optimal Instrument Choice under Uncertainty . . . . . . . . . . . . .
1.3 Monitoring and Enforcement . . . . . . . . . . . . . . . . . . . . . . .
1.4 Research Questions and Structure of the Thesis . . . . . . . . . . . .
1.4.1 Optimal Enforcement under Fiscal Cushioning . . . . . . . . .
1.4.2 ’Prices vs. Quantities’ with different Enforcement Probabilities
1.4.3 To Tax or to Cap in Inter-Country Climate Agreements . . . .
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2 Fiscal Cushioning and the Optimal Enforcement of Inter-Country Environmental Taxes
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Model under Full Compliance . . . . . . . . . . . . . . . . . . .
2.2.2 Model under Noncompliance . . . . . . . . . . . . . . . . . . . .
2.3 The Regulator’s Perspective . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Optimal Audit Policies . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Heterogeneity in the Probability of Detection . . . . . . . . . .
2.4.2 Heterogeneity in the Potential for Fiscal Cushioning . . . . . . .
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Contents
2.5
2.6
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Prices vs. Quantities with Fiscal Cushioning
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
3.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Compliance strategy under incomplete enforcement .
3.4 Optimal policy design under incomplete enforcement
3.5 Instrument choice . . . . . . . . . . . . . . . . . . . .
3.6 Numerical Simulations . . . . . . . . . . . . . . . . .
3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .
4 To Cap or Not to Cap: An Assessment of Critiques
Cap-and-Trade Climate Policies
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
4.2 Participation in Inter-Country Climate Agreements .
4.3 Revenue-Raising Potential . . . . . . . . . . . . . . .
4.4 Treatment of Uncertainty . . . . . . . . . . . . . . .
4.5 Price Volatility . . . . . . . . . . . . . . . . . . . . .
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . .
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of Inter-Country
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5 Conclusion
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A Appendix to Chapter 2
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A.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 Proof of Proposition 3 and 4 . . . . . . . . . . . . . . . . . . . . . . . . 110
A.3 Proof of Proposition 6 and 7 . . . . . . . . . . . . . . . . . . . . . . . . 113
B Appendix to Chapter 3
B.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3 Proof of Proposition 3 . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Bibliography
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List of Figures
1.1
Prices vs. Quantities under uncertainty
2.1
2.2
Optimal compliance decision of a κ-type country . . .
Optimal monitoring policies with limited budget and
the probability of detection. . . . . . . . . . . . . . .
Optimal monitoring policies with limited budget and
the potential for fiscal cushioning. . . . . . . . . . .
2.3
3.1
3.2
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heterogeneity
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heterogeneity
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in
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∆pq dependent on β for b = 9$/t . . . . . . . . . . . . . . . . . . . . . .
∆pq dependent on β for b = 35$/t . . . . . . . . . . . . . . . . . . . . .
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List of Tables
3.1
Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
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vi
Abstract
The present dissertation discusses the question, which regulatory approach ought to be
chosen to internalize a global externality at the inter-country level, e.g. emissions that
contribute to climate change. For this purpose, we compare price (emission tax) and
quantity (tradable permits) regulations and place special emphasis on potential enforcement concerns of the two instruments. In particular, inter-country tax regulations
are associated with considerable difficulties in monitoring and enforcement. The reason
is that countries can offset the effect of an international emission tax via adjustments
in the domestic fiscal policies. Such measures reduce the incentive to abate emissions
at the domestic level and hence undermine the purpose of the inter-country regulation.
This problem, which is often referred to as fiscal cushioning, is a central element in our
comparison of price- and quantity-based regulations at the inter-country level.
In chapter 1 we provide an introduction to the theoretical principles of optimal
instrument choice to internalize a global externality and discuss potential enforcement
concerns of the instruments.
In chapter 2 of the present dissertation, we determine the characteristics of the
optimal monitoring strategy that enforces an inter-country price regulation with respect
to fiscal cushioning. To reflect the risk of fiscal cushioning, we assume that countries
differ along two dimensions. On the one hand, we expect that measures to offset the
international emission tax are more difficult to detect in some countries than in others.
On the other hand, we assume that countries differ with respect to their national
fiscal policies and hence in their potential to offset the international emission tax.
In the former case, we find that those countries ought to be audited first in which
noncompliance is easy-to-detect, even though this might seem counterintuitive at a
first sight. However, when countries differ along the potential to offset the emission
tax, those countries ought to be audited first that have a large potential for fiscal
cushioning.
viii
Abstract
Note that inter-country price regulations are affect by fiscal cushioning measures,
while quantity instruments are not. Thus, the feasibility of enforcement is often expected to be lower under an inter-country price than under a quantity regulation. In
chapter 3, we consider differences in the instruments’ enforceability in an extension
of the formal Prices vs. Quantities debate, in which the optimal choice of instrument
under uncertainty of costs and benefits is investigated. Our analysis indicates that
the level of the marginal benefit curve, institutional parameters, and the variance in
abatement costs crucially affect the optimal choice between a price and a quantity
instrument. Moreover, we can show that a quantity regulation is strictly preferable
when the variance of costs is sufficiently low. Remarkably, in this case, the slopes
of the marginal cost and benefit curve are, contrary to commonly accepted insights
from the Prices vs. Quantities literature, completely irrelevant for optimal instrument
choice. Numerical calculations, using data taken from the context of inter-country
climate policy, support our theoretical finding that a quantity instrument might be
strictly preferable.
In the context of mitigating anthropogenic climate change, the choice of instrument is controversially discussed. The currently implemented inter-country climate
agreement, the Kyoto Protocol, is based on a system of tradable permits. The same
approach is also most likely to be adopted in a post-2020 climate agreement. Yet, the
choice of instrument is heavily criticized. It is claimed that a price approach dominates
a quantity regulation. The most commonly cited reasons in favor of an inter-country
emission tax are the countries’ broader participation in the climate agreement, the
possibility to raise revenues, the treatment of uncertainty, and the incentives to invest
in climate-friendly technologies. Chapter 4 addresses these allegations in more detail. We show that neither of the allegations presents a valid argument to replace the
currently implemented quantity regulation by a system of emission taxes. In fact, our
analysis indicates that the countries’ participation in the climate agreement is more
likely when the regulation is based on a quantity rather than on a price approach. We
conclude that a quantity regulation might well be the better instrument to mitigate
global climate change at the inter-country level.
Chapter 5 summarizes the main findings of the present dissertation.
Zusammenfassung
Die vorliegende Doktorarbeit diskutiert die Frage, welches Regulierungsinstrument auf
internationaler Ebene idealerweise eingesetzt werden sollte, um eine globale Externalität, z.B. Emissionen die zum Klimawandel beitragen, zu internalisieren. Wir vergleichen hierzu Preis- (Emissionssteuern) und Mengenregulierungen (handelbare Zertifikate) und gehen vor allem auf mögliche Durchsetzungsprobleme der beiden Instrumente ein. Insbesondere scheint die Überwachung und Durchsetzung von internationalen Preisregulierungen mit erheblichen Schwierigkeiten behaftet zu sein. Dies
ist dadurch begründet, dass Länder die Wirkung einer internationalen Emissionssteuer durch Anpassungen in ihren nationalen Steuerpolitiken aufheben können. Solche
Massnahmen reduzieren auf nationaler Ebene den Anreiz Emissionen zu vermeiden und
untergraben somit den Zweck der internationalen Regulierung. Dieses Problem, das
vielfach Fiscal Cushioning genannt wird, ist zentraler Bestandteil in unserem Vergleich
von Preis- und Mengenregulierungen auf internationaler Ebene.
Im Kapitel 1 geben wir eine Einführung in die theoretischen Grundlagen zur optimalen Wahl eines Instrumentes zur Internalisierung globaler Externalitäten und diskutieren mögliche Durchsetzungsprobleme der Instrumente.
Im Kapitel 2 der vorliegenden Dissertation bestimmen wir Charakteristika einer
optimalen Monitoring-Strategie, um internationale Preisregulierungen im Hinblick auf
Fiscal Cushioning durchzusetzen. Um das Risiko von Fiscal Cushioning darzustellen,
nehmen wir an, dass sich die Länder in zwei Punkten unterscheiden. Zum einen erwarten wir, dass Massnahmen zum Aufheben der internationalen Emissionssteuer bei
einigen Ländern schwieriger zu entdecken sind als bei anderen. Zum anderen nehmen
wir an, dass sich Länder im Hinblick auf ihre nationalen Steuerpolitiken und somit auf
ihr Potential die internationale Emissionssteuer aufzuheben, unterscheiden. Im erstgenannten Fall zeigen wir, dass vor allem diejenigen Länder kontrolliert werden sollen
deren Missachtung der Regeln leicht zu entdecken ist, auch wenn dies auf den ersten
x
Zusammenfassung
Blick kontraintuitiv erscheint. Unterscheiden sich Länder hingegen in ihrem Potential die Emissionssteuer zu reduzieren, sollen vor allem diejenigen Länder kontrolliert
werden, die ein hohes Potential für Fiscal Cushioning aufweisen.
Es gilt zu beachten, dass Fiscal Cushioning internationale Steuerregulierungen
beeinträchtigen, nicht jedoch Mengenregulierungen. Daher wird häufig angenommen,
dass die Durchsetzbarkeit von internationalen Preisregulierungen niedriger ist als die
von Mengenregulierungen. Im Kapitel 3 berücksichtigen wir Unterschiede in der
Durchsetzbarkeit der Instrumente in einer Erweiterung der formalen Prices vs. Quantities Diskussion, in der die optimale Wahl des Instruments unter Unsicherheit von
Kosten und Nutzen untersucht wird. Unsere Analyse deutet darauf hin, dass die
Höhe der Grenznutzenkurve, institutionelle Parameter und die Varianz der Vermeidungskosten die optimale Wahl zwischen einem Preis- und Mengeninstrument massgeblich beeinflussen. Darüber hinaus können wir zeigen, dass eine Mengenregulierung
sogar grundsätzlich vorzugswürdig ist, wenn die Kostenvarianz ausreichend klein ist.
Bemerkenswert hierbei ist, dass die Steigungen der Grenzkosten- und Grenznutzenkurve,
entgegen allgemein anerkannter Erkenntnisse aus der Prices vs. Quantities Literatur,
für die optimale Wahl des Regulierungsinstrumentes vollkommen irrelevant sind.
Numerische Berechnungen mit Daten aus der internationalen Klimapolitik belegen
unser theoretisches Ergebnis, dass eine Mengenregulierung grundsätzlich vorzugswürdig
sein kann.
Mit Blick auf die Bekämpfung des anthropogenen Klimawandels wird die Wahl des
Regulierungsinstrumentes kontrovers diskutiert. Das derzeit implementierte internationale Klimaabkommen, das Kyoto Protokoll, basiert auf einem System von handelbaren Zertifikaten. Aller Voraussicht nach wird dieser Ansatz auch in einem post2020 Klimaabkommen verfolgt werden. Die Wahl des Instruments wird jedoch heftig
kritisiert. Es wird behauptet, dass ein Preisansatz einer Mengenregulierung überlegen sei. Häufig genannte Gründe für eine internationale Emissionssteuer sind die
breitere Teilnahme am Klimaabkommen, die Möglichkeit Einkommen zu generieren,
der Umgang mit Unsicherheit und die Anreize in klima-freundliche Technologien zu
investieren. Kapitel 4 geht auf diese Behauptungen näher ein. Wir zeigen, dass
keine dieser Behauptungen ein valides Argument darstellt, das derzeit implementierte
Mengeninstrument durch eine Emissionssteuer zu ersetzen. Unsere Analyse ergibt
sogar, dass die Teilnahme der Länder am Klimaabkommen wahrscheinlicher ist, wenn
die Regulierung auf einem Mengen- und nicht auf einem Preisinstrument basiert. Wir
Zusammenfassung
xi
schliessen daraus, dass eine Mengenregulierung tatsächlich das geeignetere Instrument
ist, den Klimawandel auf internationaler Ebene zu bekämpfen.
Kapitel 5 fasst die Hauptergebnisse der vorliegenden Dissertation zusammen.
xii
Zusammenfassung
Chapter 1
Introduction
To the economist, environmental degradation is a problem in which economic agents
impose external costs on society in the form of pollution discharges. Without appropriate regulations that incentivize a reduction in emissions, an excessive depletion of the
environment’s limited assimilative capacity occurs. The consequences are considerable
damages to the society. This is most obvious for global externalities such as the pressing issue of climate change. The excessive discharge of emissions with a greenhouse
potential increases the radiative forcing of the atmosphere regardless from where these
emissions arise. This inevitably results in an increase in the average surface temperature. The associated costs for the global economy, human health, or biodiversity are,
though highly uncertain, considered to be tremendous.
To internalize costs of a global externality, various regulatory instruments, from marketbased to command-and-control instruments, are available. Such a regulation is ideally
implemented globally at the inter-country level, as this would cover emissions from
all pollution sources around the globe. Yet, the optimal choice of instrument to internalize a global externality at the inter-country level is an ongoing debate among
environmental economists.
This dissertation contributes to the literature on the optimal choice of instrument
by considering a specific enforcement concern, i.e., the risk of fiscal cushioning, which
can be considered as a decisive factor for optimal instrument choice, at least at the
inter-country level. The remainder of the introduction briefly explains the economics
of internalizing global externalities, the optimal choice of instrument, the risk of fiscal
cushioning, addresses the three key questions that will be answered in the course of
the thesis, and summarizes the main results of this dissertation.
2
1.1
1.1. Internalization of Environmental Externalities
Internalization of Environmental Externalities
The economists’ straightforward answer to internalize environmental externalities is to
put a ’price’ on pollution discharges either via taxation or via tradable permits.
The idea of taxing emissions can be traced back to the early work of Pigou (1920).
A tax levied on the externality-producing commodity internalizes the social costs by
incentivizing lower production volumes of the harmful good. Applied to the context
of environmental degradation, the tax is simply a price levied on each discharged unit
of pollution. By imposing a tax on emissions, polluters face an opportunity cost for
producing emissions that creates an incentive for reducing pollution. Profit maximizing
agents will invest in abatement activities as long as the marginal costs for pollution
abatement are lower than the additional price which has to be paid when this emission
is produced, i.e. the emission tax. Ideally, the tax rate is at the level where marginal
benefits from pollution abatement equal marginal abatement costs. In this case, the
Pigouvian tax internalizes the external costs on society, i.e., maximizes social welfare
from emission reductions.
In the late 60’s, a second instrument emerged as a regulatory approach to internalize
externalities, i.e., a cap-and-trade system (see Dales (1968)). This policy instrument
controls the quantity of emissions directly rather than through the manipulation of
prices via taxation. The regulator issues or auctions a limited amount of pollution
allowances. Each of which entitles the certificate holder to discharge a predefined
amount of a specific pollutant. As the amount of pollution permits is limited, a market
emerges for certificates. The corresponding market-clearing price for permits creates
– similar to the tax – an opportunity cost for producing emissions. Profit maximizing
agents with abatement costs lower than the equilibrium permit price abate emissions.
Non-used permits are sold to actors with abatement costs higher than the permit
price. To maximize social welfare, the scarcity of pollution allowances ought to be
chosen such that emission reductions are at the level where marginal benefits equal
marginal costs from pollution abatement. In this case, the external costs on society
are fully internalized, i.e., social welfare from emission reductions is maximized, when
the market for pollution permits is perfectly competitive.
Note that a global externality, e.g. the discharge of emissions that contribute to
climate change, is ideally regulated globally at the inter-country level. Such a regulation
would cover emissions of all countries and pollution sources around the globe. In case
a price approach is chosen to regulate the environmental externality, each country
1. Introduction
3
would commit to levy a tax on the harmful emission. The tax rate, which would
be harmonized across the globe, would thus determine the global price per unit of
emission. In case a quantity control instrument is chosen, countries would receive
a limited amount of pollution allowances that cap global discharges of the regulated
pollutant. As these certificates would be tradable among countries, a global price for
allowances, i.e., emissions, emerges. Thus, irrespective of the choice of instrument, the
price per unit of pollution, i.e., the tax rate or the permit price, is in theory equalized
across all countries and pollution sources. Hence, a desired abatement level is achieved
at lowest possible costs under both so-called market-based instruments. This is a
remarkable difference to command-and-control regulations, e.g. non-tradable emission
permits. Such a regulation specifies the emission level of each country individually. In
this case, marginal abatement costs might differ across the globe, implying inefficiently
high aggregate abatement costs. Given this economic inefficiency of command-andcontrol instruments, we focus in the following on the optimal choice of instrument
between the two market-based policies.
1.2
Optimal Instrument Choice under Uncertainty
The two market-based policy alternatives, emission taxes and tradable pollution permits, perform identically under certainty of the marginal curves. External costs are
internalized under either instrument if the stringency of the policy is set to achieve
the welfare-maximizing abatement level, i.e., where marginal costs from emission reductions equal marginal benefits. In this case, the amount of permits issued is such
that the resulting permit price is identical to the chosen tax rate. Thus, the cost for
emitting one unit of pollution and hence the incentive to abate pollution discharges are
identical under both policy alternatives. Under these idealized conditions, a supranational regulatory authority is indifferent between choosing emission taxes and a system
of tradable permits to internalize a global externality.1 Both instruments achieve the
optimal amount of emission reductions and maximize global social welfare.
Yet, neither instrument achieves the first-best optimum when we realistically consider the marginal curves as uncertain. Benefits from pollution abatement are avoided
1
Specialized agencies under the United Nations system, e.g. the International Monetary Fund, or
an institution such as the United Nations Framework Convention on Climate Change could assume
the role of a supranational regulatory authority to internalize an international externality.
4
1.2. Optimal Instrument Choice under Uncertainty
damages from a changing environment and hence highly person-, group-, and sitespecific and, given ethical concerns, disputable. That is, marginal benefits from pollution abatement are difficult to estimate and uncertain. Furthermore, marginal abatement costs have to be expected to be uncertain. Day-to-day fluctuations in input
prices, extreme weather events, imperfect foresight of technological change, or other
information gaps can unexpectedly affect the abatement costs. That is, both marginal
curves realistically have to be expected to be uncertain.
Under uncertainty, the regulator implements an ex-ante optimal policy. That is, according to the expectations about the marginal benefit and marginal cost curve, the
regulator determines, dependent on the regime, the ex-ante optimal tax rate or the
ex-ante optimal amount of pollution allowances. The chosen stringency of the policy
intervention is, however, likely to differ from the ex-post optimal solution, i.e., after
the resolution of uncertainty in marginal costs and benefits. The corresponding loss
in social welfare can significantly differ between the two policy instruments. This, in
fact, may give insight into which policy alternative is more efficient and ought to be
preferred to internalize the externality.
Let us first consider only the marginal benefits from pollution abatement as uncertain, while the marginal abatement costs are assumed to be known with certainty. In
this case, the same welfare loss is to be expected under both instruments. The rationale is as follows: the amount of emissions under a tax approach and the equilibrium
permit price under a cap-and-trade system are determined by the known marginal cost
curve. That is, emission prices and abatement levels are not subject to uncertainty
and coincide under price and quantity control instruments. However, the abatement
level is likely to be inefficient ex-post, i.e., after the resolution of uncertainty in the
marginal benefits. Given that the sub-optimal abatement level is identical under both
policies, price and quantity control instruments result in the same expected welfare
loss. To conclude, uncertainty solely in the marginal benefits from pollution abatement has undesirable welfare effects. Yet, the loss in social welfare gives no indication
of which policy alternative is more efficient and ought to be preferred to internalize the
externality.
The equivalence of price and quantity instruments no longer holds when marginal
abatement costs are considered to be uncertain, while marginal benefits are assumed
to be known with certainty. Here, the basic functioning of the two policy alternatives
becomes important. A system of tradable pollution permits directly determines the
amount of emissions and hence emission reductions. The regulator, however, may
1. Introduction
5
be appalled by the corresponding costs for abatement. By contrast, emission taxes
directly control the price per unit of pollution. However, the regulator may fail to
achieve a desired level of environmental performance, i.e., abatement. The two policy
alternatives, therefore, yield different emission prices and different pollution levels when
marginal costs are uncertain. In general, when the marginal abatement cost curve is
higher than expected and when both policies are implemented ex-ante optimally, the
following holds: emission taxes generate a shortage in emission reductions, while a
system of tradable pollution permits creates excess abatement. The reverse holds true
when marginal abatement costs turn out to be lower than expected. To conclude, price
and quantity control instruments result in different distortions between the ex-ante and
ex-post optimal policy when marginal abatement costs are uncertain. This, in fact, can
give indication for the optimal choice of instrument.
The literature on Prices vs. Quantities analyzes the magnitude of the relative distortions between ex-ante and ex-post optimal regulations. This gives insights into which
policy alternative is more efficient and ought to be preferred as regulatory approach.
A simple criterion for optimal instrument choice has been established in Weitzman
(1974). The study assumes that marginal curves can be linearly approximated and
that uncertainty affects the level of the marginal curves. In this case, the relative
steepness of the marginal benefit and marginal cost curves determines the instrument
with a higher expected welfare when costs are uncertain. If the marginal curves have
the same slope in absolute values, both policy alternatives create the same distortions.
In case the marginal cost curve is, in relative terms, steeper than the marginal benefit
curve, the emission tax performs better than the system of tradable permits. The reverse is true when marginal benefits from pollution abatement are more steeply curved
than the marginal abatement costs.2
This result can be best explained using a graphical illustration of the underlying
problem. Consider the scenario visualized in figure 1.1. The figure depicts marginal
benefits M B and marginal costs M C dependent on the level of pollution abatement
q. Actual marginal abatement costs M Creal are higher than expected M Cexp . The
regulator implements the ex-ante optimal policy which, given the expectations about
the marginal abatement costs, maximizes social welfare. That is, the regulator chooses
2
Uncertainty in the marginal benefits from pollution abatement becomes relevant when the uncertainties in the cost and benefit functions are correlated. A positive correlation favors quantity-based
regulations and vice versa. See Stavins (1996) for a formal analysis and a graphical illustration.
6
1.2. Optimal Instrument Choice under Uncertainty
MC
MB
MC
MB
M Creal M Cexp
preal
M Creal
M Cexp
preal
t = p∗
∗
t =p
t = pexp
∗
∗
t = pexp
MB
qt q ∗
qq
MB
q
Fig. 1.1a: relatively steep marginal costs
qt
q ∗ qq
q
Fig. 1.1b: relatively flat marginal costs
Figure 1.1: Prices vs. Quantities under uncertainty
the tax rate t or issues allowances such that the amount of pollution abatement is qq .
The expected permit price is pexp . As already discussed above, a system of tradable
pollution permits fixes the amount of emission reductions at whatever costs. Hence,
when the abatement level is fixed at qq and actual marginal abatement costs are higher
than expected, the permit price turns out to be preal . The emission tax, in contrast,
directly controls the price per unit of pollution. However, the abatement quantity is
unknown as the tax rate always equates marginal costs. The actual abatement level,
given the emission tax t, is only qt . As already indicated above, when the marginal
costs are higher than expected, the tax results in inadequate, the quantity approach
in excess emission reductions relative to the ex-post optimal abatement level q ∗ . Note
that the linearity of the marginal curves implies that over-abatement creates exactly
the same loss in social welfare than under-abatement of the same amount. That is,
the policy with less distortion between actual and optimal abatement generates lower
expected welfare losses from uncertain costs. This instrument ought to be preferred as
regulatory approach.
Consider first figure 1.1a, which depicts the scenario with relatively flat marginal
benefits and steep marginal abatement costs. Under a quantity regulation, the error
1. Introduction
7
about the marginal cost function results in the distortion |q ∗ − qq | which is greater
than the distortion under an emission tax, which is |qt − q ∗ |. This implies a greater
welfare loss under a quantity instrument, indicated by the dotted triangle, than under
a price approach, indicated by the solid triangle. Emission taxes, therefore, ought to
be preferred as regulatory instrument. The rationale is as follows. When the marginal
benefit curve is relatively flat, the level of the emission tax, though based on an expected
value, is close to the optimal tax rate and hence creates only minor distortions. In other
words, adhering to the abatement level qq cannot be justified when marginal abatement
costs are higher than expected, as abatement costs would increase tremendously.
The reverse is true in figure 1.1b, which depicts the case of relatively steep marginal
benefits and flat marginal costs. As indicated by the triangles, the loss in social welfare
from uncertain abatement costs under emission taxes (solid triangle) is greater than
that under a system of tradable permits (dotted triangle). That is, a quantity control
approach ought to be preferred as regulatory instrument. The underlying rationale is
similar to the one above. When the marginal benefit function is relatively steep, the
chosen quantity of pollution permits, though based on expected values, is close to the
optimal level of emissions. In other words, a higher marginal cost curve does not justify
a reduction in pollution abatement, as the loss in benefits would be tremendous.
The criterion established in Weitzman (1974) provides a straightforward policy tool
for the optimal choice of instrument under uncertainty. This policy ranking can be easily applied to different environmental issues, when the characteristics of the underlying
externality provide reasonable information on the corresponding marginal costs and
benefits. Global climate change, for example, is particularly determined by the already
existing stock and not by the annual flow of pollution (Nordhaus (2007)). That is, the
benefits from avoided carbon emissions in the atmosphere are roughly the same for all
reduction units. Marginal benefits can, therefore, be considered to be almost constant.
In contrast, abatement costs can be expected to be highly sensitive to the actual level
of emission reductions. More and more expensive abatement opportunities are used to
meet increasingly ambitious emission targets. Marginal abatement costs can therefore
be expected to be rather steep. Hence, the conventional opinion from Weitzman (1974)
is that a carbon tax approach is more efficient and ought to be preferred to mitigate
global climate change.3
The current inter-country climate agreement, the Kyoto Protocol and its cap-and3
This has been formally supported, e.g. in Hoel and Karp (2002) or Newell and Pizer (2003).
8
1.3. Monitoring and Enforcement
trade-based mechanism to regulate Greenhouse Gas emissions, does not follow this
recommendation. It is hence not surprising that the Protocol is often criticized for
the choice of the underlying regulatory approach (see e.g. Nordhaus (2007) or Cooper
(2010)). Yet, it has to be noted that the treatment of uncertainty is not the sole issue that determines the optimal choice of instrument. For example, differences in the
enforceability of the two policy alternatives affect the relative efficiency and hence the
question of instrument choice. This will be discussed below in more detail.
1.3
Monitoring and Enforcement
An efficient regulation to internalize a global externality secures that all countries
around the globe participate in the regulation and reduce emissions until their marginal
abatement costs equal the price per unit of pollution, i.e., depending on the regime,
the harmonized emission tax rate or the equilibrium permit price. This requires the
countries’ full participation in and complete compliance with the inter-country environmental agreement. Yet, given the sovereignty of states, countries are free to choose
whether to join an international treaty or not. Ratification is likely when governments
expect positive net benefits from joining the agreement. If this is not the case, participation can be incentivized by financial transfers or issue linkage, such that all countries
can gain from joining the inter-country environmental agreement (see e.g. Barrett and
Stavins (2003)).4 Thus, when non-participation can be deterred and at least some countries join the agreement, enforcement within the regime can be addressed.5 Countries
may, though having ratified the environmental agreement, violate parts of their regulatory obligations, as, for example, costs of compliance turn out to be much higher than
expected at the time of ratification. Enforcement rules, e.g. sanctioning mechanisms,
should deter noncompliance of the participating countries. These rules, however, are
likely to be insufficient to promote the countries’ full compliance. The main reason here
is that the participating countries themselves negotiate the enforcement mechanisms.
Countries that expect their noncompliance negotiate for rather weak enforcement rules
or refuse to ratify the agreement at all (see e.g. Hovi and Holtsmark (2006)). This
4
Chapter 4 discusses the advantages of financial transfers to incentivize countries’ participation in
an international agreement to mitigate global climate change in more detail.
5
Taking the environmental regime as given and analyzing participation and compliance issues
separately is a common in the literature on incomplete enforcement. For a simultaneous analysis of
both problems see Barrett (2005).
1. Introduction
9
might lead, for example, to a dilution of monitoring, reporting, and verification rules
of actual emissions and thus emission reductions. Weak enforcement rules might also
offer opportunities for second-order free-riding, i.e., when countries in the agreement
do not contribute to costly sanction of noncompliant countries.6 As a consequence, information that provides evidence for a country’s violation of the regulatory obligations
is incomplete and the threat of sanctions when noncompliance is detected is reduced.
That is, the underlying enforcement rules can be considered to be insufficient in deterring noncompliance. Therefore, countries might claim compliance without providing
an adequate amount of emission reductions. Such opportunistic behavior undermines
the environmental integrity of whatever regulation is in place, i.e., a price or a quantity
control regime.
Beside the misrepresentation of actual emissions, there is an additional enforcement
problem of inter-country price regulations that is often referred to as fiscal cushioning
(Wiener (1999)).7 Victor (2001) discusses this issue in the context of an international
carbon tax and states that:
Monitoring and enforcement [of an international carbon tax] are extremely
difficult. In principle, it might be easy to verify whether a country had
implemented the agreed tax by simply examining the country’s tax code.
In practice, it would be extremely difficult to estimate the practical effect
of the tax, which is what matters. For example, countries could offset a tax
on emissions with less visible compensatory policies that offer loopholes for
energy-intensive and export-oriented firms that would be most adversely
affected by the new carbon tax. [..] The resulting goulash of prior distortions, new taxes, and political patches [..] undermine the goal of making
countries internalize the full cost of their greenhouse gas emissions. (Victor
(2001), p. 86)
The risk of fiscal cushioning is closely related to the basic functioning of pollution
taxes. As discussed above in more detail, a tax on emissions establishes a price per
unit of pollution. The actual abatement incentive, however, is co-determined by a
country’s domestic fiscal policies that indirectly price emissions, e.g. other domestic
6
See Oliver (1980) for details on second-order free-riding.
Fiscal cushioning is a well-recognized enforcement concern of inter-country environmental taxes.
See among others Aldy et al. (2010), Cooper (1998, 2007), Eizenstat (1998), Hoel (1991), Nordhaus
(2008), Parry (2003), Stavins (1997), Wiener (2001) or Zhang and Baranzini (2004).
7
10
1.4. Research Questions and Structure of the Thesis
environmental taxes and subsidies. Hence, countries can abuse their fiscal sovereignty
to offset the international emission tax at the domestic level by adjusting national
fiscal policies. Applicable fiscal adjustments include energy tax breaks, subsidies for
pollution intensive products, or special tax provisions for export-oriented industries.
The abatement incentive effect would also be reduced when complements or substitutes
to the regulated pollutant would be subsidized or taxed (Hoel (1993)). A similar effect
arises when emission-related taxes and subsidies are not increased or reduced to the
same extent, as they would have been in the absence of the emission tax. All those fiscal
cushioning measures reduce the abatement incentive effect of the emission tax. This
undermines the environmental integrity and hence the purpose of the tax regulation,
i.e., pollution abatement. Thus, fiscal cushioning is considered as a special type of
noncompliance with an inter-country tax regulation.
Fiscal cushioning measures, e.g. a reduction in energy taxes, reduce the industries’ burden of emission reductions. Hence, such strategies can also be expected under
an inter-country cap-and-trade system. Yet, a remarkable difference to inter-country
price-based regulations is that fiscal policy adjustments do not reduce the environmental integrity of an inter-country quantity approach (Wiener (1999)). The reasons is
that – although fiscal cushioning measures might be applied – countries still have to
meet the emission target, which is determined by the scarcity of certificates. That
is, the aggregate abatement level remains unaffected by domestic policy adjustments.
Hence, fiscal cushioning is solely an issue under an inter-country price approach. This
often leads to the conclusion that the enforcement of inter-country tax regulations is
less feasible than that of cap-and-trade-based policies. This provides a strong argument in favor of a quantity-based approach to internalize a global externality at the
inter-country level. While this is well-recognized in the political debate on optimal
instrument choice, it has not been attended to in the formal economic literature. We
address this research gap, as will be discussed in the following section in more detail,
in the present dissertation.
1.4
Research Questions and Structure of the Thesis
The purpose of this dissertation is to contribute to a more sophisticated understanding
of optimal instrument choice to internalize a global externality, e.g. the discharge of
Greenhouse Gas emissions that contribute to climate change, at the inter-country level.
1. Introduction
11
In this endeavor, special emphasis is put on the choice between market-based instruments, i.e., between price (emission taxes) and quantity (tradable pollution permits)
control policies, and the risk of fiscal cushioning.
We already indicated above that the problem of fiscal cushioning is well-known and
is given careful consideration in the political debate on optimal instrument choice, especially in the context of regulating global climate change. However, a formal assessment
of the enforcement concerns associated with fiscal cushioning, its effect on the efficiency ranking of the two market-based policy alternatives and hence on the criterion
for optimal instrument choice established in Weitzman (1974), and the consequences
for the optimal choice of instrument to tackle anthropogenic climate change has not
yet been attempted. This thesis addresses these issues. Thus, we define the following
three research questions that will be answered in the course of this dissertation:
• Is fiscal cushioning a serious issue for enforcing inter-country environmental
taxes?
• What are the implications for the optimal choice of instrument when fiscal cushioning is taken into account in the classic analysis of ’Prices vs.
Quantities’?
• Is the cap-and-trade regulation under the current – and most likely also under the post-2020 – inter-country climate agreement an appropriate policy
instrument to control Greenhouse Gas emissions?
By addressing these questions, we provide meaningful insights that contribute to the
literature on optimal instrument choice to internalize a global externality at the intercountry level. Next, we describe each of these key questions in more detail, formulate
the research questions that are addressed in the process of answering the key questions,
and outline the main results of our analyses.
1.4.1
Optimal Enforcement under Fiscal Cushioning
As already indicated in section 1.3, fiscal cushioning is a well-recognized enforcement
concern of inter-country tax-based regulations, though solely in the political-economic
literature. The economic literature does not provide a formal assessment of the risk of
fiscal cushioning. In chapter 2 of the present dissertation, we address this issue and
thus the first of the above defined key questions:
12
1.4. Research Questions and Structure of the Thesis
Is fiscal cushioning a serious issue for enforcing inter-country environmental
taxes?
To answer this question, we formulate the following research questions:
• What is the countries’ optimal compliance decision when countries can offset the
pollution abatement incentive effect and misreport the corresponding emission
level?
• Which features characterize the regulator’s optimal monitoring policy? How does
the regulator’s budget endowment affect the effectiveness of the optimal auditing
strategies?
• What are the differences and similarities in the auditing strategies for enforcing
the level of the emission tax rate to enforcing compliance with a given tax rate?
To address these research questions, we extend the theoretical model presented in
Macho-Stadler and Pérez-Castrillo (2006), which analyze the optimal enforcement of
polluters’ compliance with a given tax rate. We assume an environmental protection
policy based on emission taxes at the inter-country level. An environmental authority
announces a tax rate, which countries commit to levy domestically. Yet, the actual tax
rate and the corresponding emission level are observable for the regulator only during
costly inspections. Hence, countries can apply fiscal cushioning strategies to reduce
the actual tax rate and to misrepresent the corresponding emission level.
To reflect the risk of fiscal cushioning, we assume that countries differ according to
their verifiability and according to their potential for fiscal cushioning. The first characteristic accounts for the fact that noncompliance is easier to verify for some countries
than for others. The second characteristic allows for differences in the potential to offset the pollution abatement incentive effect. Some countries are able to change policies
that are closely related to the regulated pollutant, e.g. other environmental levies.
Fiscal systems of other countries may rely more on traditional taxes, e.g. levies on
income or profits. The former countries can be expected to have a larger potential to
offset the emission tax than the latter countries.
We begin with the analysis of the compliance decision of a single country whose
verifiability and potential for fiscal cushioning are assumed to be common knowledge.
Our findings indicate that the country cannot be incentivized to (partially) comply with
the regulation when the audit pressure is very low. In this case, the country puts a
1. Introduction
13
maximum effort into the distortion of the effective tax rate. When the audit pressure is
strong enough, the country reduces the effort put into fiscal cushioning. Only when the
monitoring pressure is very high, the country practices no fiscal cushioning measures.
The main focus in this chapter is on the characteristics of the monitoring policies
that minimize aggregate pollution discharges. This is analyzed for two different scenarios. The first scenario considers a continuum of countries that differ along their
verifiability, while the potential to offset the emission tax is assumed to be constant
across countries. In this case, countries can, even when audited with certainty, be
incentivized to (partially) comply with the regulation only when the probability of detection is high enough. Hence, the optimal monitoring strategy features, irrespective
of the regulator’s budget endowment, a ’jump’ in the auditing pressure at the marginal
audited country. For a limited monitoring budget, the regulator discriminates among
countries according to their verifiability. Countries in which noncompliance is easy-todetect are audited first, while those with a low probability of detection are monitored
less regularly, if at all. Such a strategy might seem counterintuitive, as countries with
a great chance for noncompliance, i.e., with a low probability of detection, are audited less regularly than those with a limited chance for noncompliance. This strategy,
however, maximizes the deterrence of audits against fiscal cushioning and minimizes
aggregate emissions. Note that this monitoring policy is quite similar to the one established in Macho-Stadler and Pérez-Castrillo (2006). Hence, no significant differences
exist between enforcing a specific tax level to enforcing compliance with a given tax
rate when countries differ with respect to their verifiability.
The similarity to the optimal monitoring policy established in Macho-Stadler and
Pérez-Castrillo (2006) breaks down in the second scenario. In this scenario, we consider
the case in which countries are assumed to differ solely along the potential for fiscal
cushioning. The probability of detection is assumed to be constant. We find, even
when audited with certainty, countries can be incentivized to comply with the regulation only when the potential for fiscal cushioning is large enough. As a consequence, the
optimal monitoring policy features, irrespective of the regulator’s budget endowment,
a jump in the auditing pressure at the marginal audited country. With limited monitoring resources, the regulator discriminates between countries. Those countries that
have a large potential for fiscal cushioning are audited first, while those with a limited
offsetting potential are audited less regularly, if at all. That is, the counterintuitive
monitoring policy established in the first scenario and in Macho-Stadler and PérezCastrillo (2006) does not apply here. Notably, the regulator targets those countries
14
1.4. Research Questions and Structure of the Thesis
first that have larger opportunities for noncompliance, i.e., those with a larger potential for fiscal cushioning. This alteration of the regulator’s optimal auditing strategy
is of particular importance, as the countries’ offsetting potential represents, in fact, a
distinctive feature of fiscal cushioning.
In conclusion, the regulator can, even when endowed with unlimited monitoring
resources, never completely disincentivize fiscal cushioning. Some countries, i.e., those
for which noncompliance is hard-to-detect or which have a limited potential for fiscal
cushioning, always apply fiscal cushioning measures. This undermines the purpose of
the regulation and thus the environmental effectiveness of the emission tax. Hence,
referring to the first key question, fiscal cushioning can be expected to be a serious
enforcement issue of inter-country environmental tax regulations.
1.4.2
’Prices vs. Quantities’ with different Enforcement Probabilities
From our analysis presented in chapter 2, we know that fiscal cushioning can never be
completely deterred and can thus be expected to be a serious enforcement problem of
inter-country price-based regulations. Given the fact that quantity-based instruments
are unaffected by domestic fiscal policy adjustments, fiscal cushioning can be considered as an additional enforcement problem of inter-country environmental taxes. As a
consequence, both market-based instruments are likely to differ with respect to their
enforceability. More precisely, enforcement of inter-country cap-and-trade policies can
be expected to be stricter than that of inter-country price regulations. However, differences in the instruments’ enforceability may alter the efficiency ranking of the two
policy alternatives and hence the criterion for optimal instrument choice established in
Weitzman (1974). We analyze this issue and thus provide a contribution to the formal
’Prices vs. Quantities’ debate. In this endeavor, we determine the impact of the risk
of fiscal cushioning on the optimal choice of instrument when costs and benefits are
uncertain. The corresponding analysis, presented in chapter 3, allows us to address the
second key question of this dissertation:
What are the implications for the optimal choice of instrument when fiscal cushioning is taken into account in the classic analysis of ’Prices vs.
Quantities’?
1. Introduction
15
The research questions addressed in this endeavor are outlined below:
• How does a difference in the enforceability between price and quantity control
instruments affect the policy ranking established in Weitzman (1974)? Is the
instrument with higher expected social welfare determined by the relative steepness of the marginal curves? Do other parameters than the slopes of the marginal
curves affect the choice among the two policy alternatives?
• Can the risk of fiscal cushioning alter the recommended choice of instrument to
tackle anthropogenic climate change derived from Weitzman (1974)?
We already discussed in more detail in section 1.2 that a simple criterion for optimal
instrument choice has been established in Weitzman (1974). The analysis indicates
that the relative slopes of the marginal curves determine the instrument with a higher
expected social welfare when abatement costs are uncertain.
The only framework that simultaneously analyzes the choice of instrument under
uncertainty and incomplete enforcement is presented in Montero (2002). The result is
an altered version of the classic relative-slope criterion established in Weitzman (1974).
Under incomplete enforcement, emission taxes have a comparative disadvantage over
quantity control instruments. The rationale is simple. The sanction for noncompliance
acts just like a price ceiling in a hybrid scheme à la Roberts and Spence (1976).8 Hence,
when permit prices turn out to be high, as the marginal costs are higher than expected,
noncompliance may be more efficient than purchasing allowances. This reduces the
expected costs of being regulated under a quantity regime and creates the comparative
advantage over emission taxes. However, similar to Weitzman (1974), the relative
slopes of the marginal curves remain the sole determinants for the optimal choice of
instrument.
Chapter 3 extends the model presented in Montero (2002) by the risk of fiscal cushioning. As fiscal cushioning is not an issue under quantity regulations, we assume a
lower enforcement probability for a price regulation than for a quantity control instrument. Our result features two additively separable terms. The first term, referred to as
the uncertainty effect, reflects the impact of uncertain abatement costs on instrument
choice. The slopes of the marginal curves determine the relative performance of the
policy alternatives. The second term, the differentiated enforceability effect, measures
8
A hybrid scheme refers to a cap-and-trade policy combined with a price floor and ceiling.
16
1.4. Research Questions and Structure of the Thesis
the efficiency advantage of the policy that results from stricter enforcement. Hence,
this effect unambiguously favors a quantity approach and exists even under certainty
of abatement costs. The relative strength of these two potentially opposing effects
determines optimal instrument choice.
Our theoretical results challenge commonly accepted insights from the formal Prices
vs. Quantities literature. First, the relative slopes of the marginal curves are no longer
the sole determinants for optimal instrument choice. The level of the marginal benefit curve and the enforcement parameters mainly drive the level of the differentiated
enforceability effect. Hence, level effects and institutional parameters affect and can
ultimately determine the instrument with higher expected social welfare.
Second, the variance in abatement costs becomes a decisive factor for instrument choice.
When the cost uncertainty is low enough, the differentiated enforceability dominates
the uncertainty effect. In this case, a quantity control instrument outperforms a tax
approach, as the welfare advantage of improved enforceability always exceeds a potential welfare disadvantage from cost uncertainty. Remarkably, in such situations, the
relative slopes of the marginal curves are completely irrelevant for optimal instrument
choice.
As already indicated in section 1.2, the conventional opinion is that a price approach
ought to be preferred to regulate anthropogenic climate change (see e.g. Hoel and Karp
(2002), Newell and Pizer (2003)). Numerical calculations give insight whether this recommendation is still valid under the risk of fiscal cushioning. Using data presented
in Newell and Pizer (2003), our simulations indicate that a price approach still outperforms a quantity instrument. That is, the differentiated enforceability effect is not
strong enough to alter the recommended choice of instrument to tackle global climate
change.
Yet, the simulations reveal an important element of our result, i.e., the sensitivity of
instrument choice relating to the level of the marginal benefit curve. The actual value
of the social cost of carbon is subject to dispute in the literature. While a level of
the marginal benefit curve of 9$/t is assumed in Newell and Pizer (2003), more recent
studies estimate much higher values. Tol (2008), for example, includes 211 estimates of
the social cost of carbon in a meta-analysis to form a probability density function and
reports a mode of 35$/t. Using this level of the marginal benefit curve, our simulations
indicate that quantity control instruments outperform price regulations irrespective of
the slopes of the marginal curves. Hence, a cap-and-trade regulation might well be the
preferred instrument to tackle global climate change, at least at the inter-country level.
1. Introduction
17
In conclusion, the risk of fiscal cushioning changes commonly accepted insights
from the formal ’Prices vs. Quantities’ analysis significantly. Most notably, the relative
slopes of the marginal curves are no longer the sole determinants for optimal instrument
choice. Instead, the level of the marginal benefit curve and institutional parameters,
i.e., the enforcement parameters, affect and can ultimately determine the optimal choice
of instrument. In fact, numerical calculations in the context of global climate change
indicate that the risk of fiscal cushioning might well alter the recommended choice of
instrument derived from the classic ’Prices vs. Quantities’ literature. That is, a capand-trade regulation, at least on the inter-country level, might well be the best policy
instrument to control global Greenhouse Gas emissions.
1.4.3
To Tax or to Cap in Inter-Country Climate Agreements
The debate over the optimal choice of instrument under uncertainty is well-recognized
in the political discussion whether price or quantity regulations ought to be preferred
to mitigate anthropogenic climate change. The analysis in Weitzman (1974) provides
the basis for the commonly accepted opinion that a price approach, e.g. a Harmonized
Carbon Tax system, is more efficient than a cap-and-trade-based approach to regulate
the discharge of Greenhouse Gas emissions at the inter-country level. This argument
is often used to criticize the current quantity control approach that is implemented
under the Kyoto Protocol. However, our analyses in chapter 2 and 3 indicate that a
quantity instrument might well be more efficient and hence preferable to regulate global
Greenhouse Gas emissions when the risk of fiscal cushioning is taken into account.
Thus, the findings reported in this dissertation allow refusing one strong argument in
favor of inter-country price-based regulations to control global carbon emissions.
In chapter 4, we review the political discussion on optimal instrument choice to limit
global Greenhouse Gas emissions. The focus is on arguments that are repeatedly
brought forward to support a replacement of the currently implemented cap-and-tradebased climate change mitigation regime by a system of Harmonized Carbon Taxes. This
allows us to address the third and last key question of this dissertation:
Is the cap-and-trade regulation under the current – and most likely also under the post-2020 – inter-country climate agreement an appropriate policy
instrument to control Greenhouse Gas emissions?
18
1.4. Research Questions and Structure of the Thesis
In this endeavor, we address the following research questions:
• What are the main arguments to replace the currently running inter-country capand-trade-based regime by a system of Harmonized Carbon Taxes? What are the
points of criticism of the current climate change mitigation policy? Do arguments
that support the use of a carbon tax approach to mitigate global climate change
hold up to scrutiny?
• Is a system of Harmonized Carbon Taxes, given the criticism on the current capand-trade-based climate agreement, preferable to mitigate global climate change
at the inter-country level?
The currently implemented inter-country climate agreement, the Kyoto Protocol,
is based on a cap-and-trade system. The same instrument is likely to be adopted in
a post-2020 climate change mitigation policy. However, the choice of the underlying
regulatory approach is subject to criticism. It is often claimed that a price approach
is superior to a cap-and-trade system at the inter-country level. The most commonly
cited reasons for favoring a price approach are the countries’ broad participation in
the climate agreement, the revenue-raising potential, the treatment of uncertain costs
and benefits, and the incentives for investments in new abatement technologies (see
e.g. Nordhaus (2007), Cooper (2001)). We discuss whether these allegations hold to
scrutiny and whether a system of Harmonized Carbon Taxes ought to be preferred to
internalize the costs of anthropogenic climate change at the inter-country level.
We find, however, that neither point of criticism is a valid argument to replace the
currently implemented cap-and-trade regulation by a system of Harmonized Carbon
Taxes. In fact, a quantity control approach is likely to promote broad participation
in the climate agreement. The reason is that side-payments, which create incentives
to participate in the climate agreement, are, from a political economy perspective,
more likely under a quantity than under a price instrument. In the latter approach,
side-payments take the form of apparent monetary transfers from high- to low-income
countries or from beneficiaries to losers of the regulation. The visibility of such transfers
is, however, likely to encounter significant public resistance. By contrast, under capand-trade regulations, side-payments materialize indirectly. Losers of the regulation
or low-income countries are granted generous allowance allocations that can be sold
– thereby generating monetary transfers – to beneficiaries of the regulation or highincome countries. The actual level of transfer payments is less visible and therefore
1. Introduction
19
more likely to occur. As a consequence, side-payments that incentivize a country’s
participation in the climate agreement are more likely under a quantity- than under
a price-based regulation. Participation can therefore be expected to be higher in the
former than in the latter approach.
The revenue-raising potential of a tax regime is neither a valid argument to replace
the current cap-and-trade-based system. Generating public funds is a design issue
of domestic policies rather than a question of instrument choice at the inter-country
level. Under an inter-country cap-and-trade regulation, domestic policies can still be
designed to raise revenues, e.g. via a domestic carbon tax or a domestic cap-and-trade
regulation with auctioned certificates. The European Union Emission Trading System
(EU ETS) is probably the best example for the revenue-raising potential of domestic
policies under an inter-country climate agreement based on tradable permits, i.e., the
mechanisms under the Kyoto Protocol. In phase III of the EU ETS, at least 50% of
allowances are subject to auctions. This share is planned to be consistently increasing
until full auctioning is realized in 2027 (European Commission (2011)). The revenues
from auctioning are expected to be substantial (Cooper and Grubb (2011)).
A further often quoted drawback of inter-country cap-and-trade-based regulations is
the treatment of uncertain costs and benefits. We know from Weitzman (1974) that
the structure of benefits and costs in the climate context provide a strong argument for
a carbon tax approach (see section 1.2 for details). However, extensions to the Prices
vs. Quantities literature that are particularly relevant for inter-country regulations,
alter the recommended choice of instrument. For example, quantity regulations might
be preferable in the presence of tipping points, i.e., when the carbon concentration in
the atmosphere ought to stay below a critical climate threshold. Otherwise, emissions
might cause irreversible and catastrophic damages to the environment and to the global
economy. Moreover, as indicated by the analysis presented in chapter 3, the risk of
fiscal cushioning might well recommend the use of a quantity control regulation to
tackle global climate change at the inter-country level.
Finally, volatility in allowances price is expected to discourage the adoption of climatefriendly technologies. This issue does not arise under a price regulation, as the tax
directly determines the price of emissions. The problem of price volatility, however, is
likely to be overstated as a determining factor for instrument choice at the inter-country
level. For example, several cost-containment mechanisms exist that dampen the effect
of volatile permit prices without – when properly designed – affecting the environmental
integrity of the regulation. Moreover, Fischer and Newell (2008) and Hoel (2010)
20
1.4. Research Questions and Structure of the Thesis
argue that a single climate change mitigation policy, price- and quantity-based, is not
sufficient to optimize the adoption of new technologies. Climate regulations always
ought to be combined with additional instruments, e.g. subsidies for renewable energy,
to accelerate technological change and reduce abatement costs.
We conclude, that neither argument put forward to replace the currently implemented cap-and-trade-based regulation by a system of Harmonized Carbon Taxes holds
to scrutiny. In fact, contrary to the allegations, quantity instruments have a considerable advantage over price regulations. Side-payments that encourage the participation
in the climate agreement are, from a political economy perspective, more likely under
the former approach. The feasibility of side-payments, however, can be expected to be
a decisive factor in the negotiations for a post-2020 climate change mitigation policy.
This agreement should be completed until 2015, enter into effect in 2020, and should
include all countries (UNFCCC (2012b)). Hence, a cap-and-trade-based policy that
facilitates the use of side-payments to encourage participation might well be the better
regulatory choice to slow global climate change at the inter-country level.
Chapter 2
Fiscal Cushioning and the Optimal
Enforcement of Inter-Country
Environmental Taxes
2.1
Introduction
Emission taxes are primarily used for domestic policies to protect the environment.
Yet they are also frequently considered in inter-country approaches to address global
environmental issues, such as the climate change (Cooper (2010)). At the inter-country
level, however, emission taxes are particularly prone to incomplete enforcement. Noncompliance with environmental agreements occurs under specific information asymmetries. For example, the imperfect observability of actual emissions might create
incentives to over-pollute. In inter-country tax regulations, further information asymmetries hamper the policy enforcement. The ’actual emission tax’ is imperfectly observable because the price per unit of pollution is, beside the international emission
tax, co-determined by domestic policies that indirectly price the respective pollutant.
Hence, countries can offset the emission tax by adjusting domestic fiscal policies. Such
practices are often referred to as fiscal cushioning and are well-recognized in the political debate on inter-country tax regulations (see among others Wiener (1999) and
Nordhaus (2007)). A formal analysis of the countries’ compliance decisions with respect to fiscal cushioning and the regulator’s optimal monitoring strategy, however,
has not yet been attempted. This chapter addresses this issue.
22
2.1. Introduction
The enforcement problem analyzed in our approach differs from the compliance
questions discussed in the existing formal literature on incomplete enforcement.1 Earlier literature on noncompliance with environmental taxes focuses mainly on national
regulations, in which it is assumed that firms over-pollute and under-report their actual emissions. A bulk of literature exists on this compliance issue, e.g. Harford
(1978, 1987), Kaplow (1990), Kaplow and Shavell (1994), Schmutzler and Goulder
(1997), Innes (1999), Bontems and Bourgeon (2005), Macho-Stadler and Pérez-Castrillo
(2006).2
In contrast, the enforcement problem considered here refers to the manipulation of
the abatement incentive of environmental taxes. This issue arises in the context of an
inter-country tax regulation. In such a regime, countries commit to levy a uniform tax
on emissions. The emission tax increases the price of pollution and creates abatement
incentives at the firm level.
However, the emission levy also increases costs for the domestic industry. To enhance
international competitiveness, countries might cushion the firms’ emission tax burden
by diluting the inter-country regulation domestically. This can be achieved by adjusting
domestic environmental policies that indirectly price the taxed pollutant. For example,
complete exemptions or partial tax reliefs from levies on energy, fuel, or road use would
dilute the emission tax domestically. Subsidies for pollution intensive production processes, e.g. coal subsidies, would have a similar effect. Such fiscal cushioning strategies
foster the industries’ international competitiveness, but also undermine the purpose
of the emission tax, i.e. abatement (see e.g. Hoel (1993), Wiener (1999), Nordhaus
(2007)). Fiscal cushioning is, hence, considered a particular type of noncompliance.3
The risk of fiscal cushioning is well-recognized in the political debate on an intercountry tax regulation. Proponents of emission taxes often propose the International
1
The literature on noncompliance was initiated within Becker (1968) and found great attention in
environmental economics. Some milestones in the literature on incomplete enforcement in the context
of environmental regulation are for example Downing and Watson (1974), Harrington (1988), Malik
(1990), Livernois and McKenna (1999), Sandmo (2002).
2
The design of optimal audit policies for standards, cap-and-trade, and credit schemes are analyzed
e.g. in Harford (1978, 1987), Malik (1990), Stranlund (2007), Keeler (1991), Macho-Stadler (2008),
MacKenzie and Ohndorf (2012b).
3
Tirole (2008) and IMF (2011b), for example, report that a majority of countries could offset
the effect of a carbon tax on electricity and fuel prices by reducing other taxes on the respective
commodity. The general problem of fiscal cushioning is also discussed e.g. in Aldy et al. (2008, 2010),
Cooper (1998, 2007), Eizenstat (1998), Hoel (1991), Hovi and Holtsmark (2006), Nordhaus (2008),
Parry (2003), Stavins (1997), Victor (2001), Zhang and Baranzini (2004).
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
23
Monetary Fund (IMF) to enforce an inter-country tax regime (see e.g. Nordhaus (2007),
Cooper (2010)).4 Under Article IV of the Agreement of the International Monetary
Fund, the IMF is already entitled to monitor the domestic fiscal systems of almost all
countries (IMF (2011a)). During these surveillances, the IMF could specifically focus
on emission-related policies. Thereby gathered fiscal data might reveal a country’s
fiscal cushioning strategies, which would allow enforcing the level of the inter-country
emission tax. However, the IMF’s reviews are often claimed to be insufficient in deterring domestic fiscal cushioning strategies (see e.g. Victor (2001) or Aldy et al. (2008)).
Complex tax loopholes and subsidy programs are expected to remain undetected during the IMF’s surveillances. Moreover, reviews of the countries’ fiscal policies are
likely to be inaccurate when available monitoring resources are constrained. Hence, an
optimization of the monitoring policy under a constrained monitoring budget seems
necessary to maximize enforcement of inter-country tax regulations. We address this
issue in the present chapter.
The following analysis is based on the model presented in Macho-Stadler and PérezCastrillo (2006). In this study, the amount of pollution is imperfectly observable. This
allows firms to over-pollute and evade the emission tax. We now extend this model
by considering the risk of fiscal cushioning. Hence, when the actual emission price is
not perfectly observable, countries can apply fiscal cushioning strategies to offset the
emission tax at the domestic level, hereby diluting the pollution abatement incentive
effect.5 That is, the choice variable in our approach is the effort put into fiscal cushioning.
To reflect the risk of fiscal cushioning, we consider countries that differ along two characteristics that are exogenously given and assumed to be common knowledge. First,
countries differ along the probability with which actual noncompliance is detected.
That is, evidence for the existence of fiscal cushioning strategies can be gathered more
easily for some countries than for others. Second, countries differ along their potential
for fiscal cushioning, as the effectiveness of fiscal cushioning strategies can be expected
to depend on the design of the domestic tax scheme. Some countries have the ability
to cushion the emission tax by adjusting closely related fiscal policies. This would have
4
Alternatively, an institution such as the United Nations Framework Convention on Climate
Change could assume the role of the regulator.
5
We consider countries as payoff-maximizing agents and omit, for sake of simplicity, from analyzing
external influences such as political considerations or lobbying activities.
24
2.1. Introduction
a strong distortive effect on the emission tax rate. Fiscal systems of other countries,
however, may rely more on taxes that are less related to the regulated pollutant. In
this case, fiscal cushioning will have only moderate distortive effects.
Both characteristics crucially determine a country’s compliance decision, i.e., the effort
put into fiscal cushioning. We find for low monitoring pressures that a country puts
a maximum effort into the distortion of the actual tax rate. When the audit pressure is strong enough, the country reduces the effort put into fiscal cushioning. This
strengthens the abatement incentive effect of the emission tax and reduces pollution
discharges. Only when the audit pressure is very high, the country applies no fiscal
cushioning strategies.
Given the country’s optimal compliance strategy, we analyze the optimal enforcement
policy for a given (limited) monitoring budget. The regulator is assumed to aim at
the minimization of aggregate emissions. In a first scenario we consider a continuum
of countries that differ along their verifiability, i.e., their probability of detection. We
show that the regulator ought to target first those countries in which noncompliance
is ’easy-to-detect’. Countries in which noncompliance is ’hard-to-detect’ ought to be
audited less regularly, if at all. This discrimination maximizes the deterrence effect
of inspections against fiscal cushioning and minimizes the aggregate level of pollution.
A second scenario analyzes the optimal monitoring policy when countries are heterogeneous along the potential for fiscal cushioning. Aggregate emissions are minimized
when the regulator focuses its monitoring on countries with a larger potential for fiscal
cushioning. In this case, some countries are never subject to audits, while others ought
to be audited with certainty.
Whether countries can be incentivized to comply with the regulation depends on the
countries’ characteristics, but also on the regulator’s access to monitoring resources. An
increase in the available monitoring budget is equivalent to an increase in inspections.
This can be associated with a decrease in fiscal cushioning, i.e., with lower emissions.
We find, however, that increasing the regulator’s monitoring budget above a certain
threshold does not improve compliance rates. By contrast, if the monitoring budget is
too low, there is no enforcement at all.
Furthermore, we compare our results with those obtained in Macho-Stadler and PérezCastrillo (2006). In the presence of heterogeneous verifiabilities, the main characteristics of the optimal monitoring policies remain the same. In either case, countries
with a greater chance for noncompliance, i.e., with a low probability of detection, are
imposed a low monitoring pressure. Countries with fewer chances for noncompliance,
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
25
i.e., a higher degree of verifiability, are audited more regularly. This counterintuitive
monitoring policy does not apply when countries are assumed to differ along the potential for fiscal cushioning. In this case, countries with the largest opportunities for
noncompliance are audited first. This is a remarkable difference to the auditing policy established in Macho-Stadler and Pérez-Castrillo (2006), as the offsetting potential
represents, in fact, a distinctive feature of fiscal cushioning.
The rest of the chapter is organized as follows. In the next section, we analyze a
country’s optimal compliance decision. Section 2.3 discusses the regulator’s objective
function when facing a continuum of heterogeneous countries. The optimal monitoring
policies, given different characteristics of the countries, are analyzed in section 2.4
before we discuss and compare our results to those obtained in Macho-Stadler and
Pérez-Castrillo (2006) in section 2.5. The last section concludes the analysis.
2.2
Model
In this section, we extend the model presented in Macho-Stadler and Pérez-Castrillo
(2006) by the risk of fiscal cushioning. We consider an inter-country environmental
regulation based on emission taxes that have been negotiated and accepted by the
signatory countries. The agreement determines the level of the uniform emission tax t
which countries commit to implement into their domestic fiscal systems. In response,
domestic firms choose an emission level e for which the tax has to be paid. Countries
transfer a share β ∈ [0, 1] of the corresponding tax revenues to the regulator, e.g. the
IMF.6 Tax revenues that are not transferred to the regulator are assumed to be redistributed lump-sum to the domestic industry.
As the actual level and the price of emissions are not perfectly observable for the regulator, countries can violate the regulation. Adjusting domestic fiscal policies that
indirectly price the regulated pollutant can dilute the emission tax. That is, the countries’ choice variable is the effort x put into the distortion of the tax rate.7 Fiscal
6
High β-values imply transferring a large fraction of the tax revenues to the regulator and vice
versa. Note, in inter-country regulations it can be plausibly expected that β = 0. That is, countries do
not transfer revenues to the regulator, respectively when tax revenues are transferred to the regulator,
other fiscal transfers are reduced to the same extent, such that the net effect of fiscal transfers is zero.
7
By contrast, the choice variable in Macho-Stadler and Pérez-Castrillo (2006) and in the existing
literature on noncompliance with environmental taxes is the emission level e.
26
2.2. Model
cushioning strategies reduce the actual emission tax τ < t, hereby undermining the
purpose of the regulation, i.e. pollution abatement.
However, the agreement entitles the regulator, e.g. the IMF, to enforce the level of
the inter-country emission tax. The regulator can audit countries for which a (limited)
monitoring budget B is available. In case a country’s noncompliance is detected, the
regulator imposes a sanctions F which is contingent on the degree of the violation.
In the following, we discuss the model more formally. We begin our analysis under
the assumption of full compliance, i.e. perfect enforcement, and consider this first-best
outcome as a benchmark for the model under (partial) noncompliance.
2.2.1
Model under Full Compliance
Consider a single country whose domestic industry emits a uniform pollutant e ≥ 0.
Both, the polluting firms and the country, benefit from emissions, denoted by the
function g(e). The function is common knowledge, increasing, and concave in e, i.e.,
g ′ (e) ≥ 0 and g ′′ (e) < 0.8
Countries within the inter-country environmental agreement commit to implement
the emission tax t > 0 into their fiscal system. Hence, given the emission tax t, the
profits Φ(e) of the domestic industry that produces emissions e are given by
Φ(e) = g(e) − te,
i.e., the difference between benefits from emissions and tax payments. Given the tax
rate t on emissions, firms choose the pollution level that maximizes Φ(e). The optimal
emission level e∗ is implicitly defined by the well-known result of marginal benefits
from pollution equal the tax rate, i.e.,
g ′ (e∗ ) = t.
(2.1)
Hereafter, we refer to e∗ as the intended emission level, which is the regulator’s intended
level of pollution when a tax rate t is announced.
Note that a country cannot directly choose an emission level, as the firms are the only
polluters. Yet, noncompliance with the actually implemented tax rate is, as we will
8
The benefit function can also be considered as a concave production function of domestic goods
in which emissions are generated by firms as by-product.
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
27
realistically assume in the following section, possible. Hence, the country might offset
the actual tax rate by domestic fiscal policy adjustments.
2.2.2
Model under Noncompliance
As already discussed in the introduction, information asymmetries regarding the actual
emission price and the actual level of pollution allow to cushion the environmental tax
at the domestic level. This section analyzes a country’s optimal compliance decision.
The analysis in Section 2.2.1 indicates that the international emission tax t creates
an incentive for pollution abatement at the firm level. The country can, however, dilute
the regulation at the domestic level. For example, changes in domestic fiscal policies
that co-determine the price of pollution would offset the emission tax. In practice, fiscal
cushioning refers to a reduction in levies, which indirectly put a price on pollution, e.g.
energy taxes, road charges, or fuel taxes. Subsidies for emission intensive production
processes, e.g. coal subsidies or special export provisions, have similar distortive effects.
The implementation of such strategies represents the attempt to cushion the pollution
abatement incentive effect of the emission tax at the domestic level. This reduces
the industry’s tax burden and enhances international competitiveness. We denote by
x ∈ [0, t] the effort a country puts into the distortion of the pollution tax. When
policies which indirectly price the respective emission remain unaltered in response to
the implementation of the tax, x is equal to zero. High x-values, in contrast, indicate
great efforts in fiscal adjustments that offset the emission tax.
Evidently, not all fiscal systems are equally suitable for fiscal cushioning. That is, the
effort invested in fiscal cushioning x can have different distortive effects. A country’s
potential for fiscal cushioning depends on the design of its domestic tax scheme, i.e.,
the type of existing taxes. For example, a fiscal system that heavily relies on taxes
closely related to the regulated emission, e.g. other environmental levies or energy
taxes, provides sufficient leeway for fiscal adjustments. In contrast, tax schemes might
also be designed to rely more on traditional sources, such as taxes on income, profits,
and sales. In this case, opportunities to dilute the emission tax are rather limited.
Differences in the country-specific offsetting potential are reflected in the parameter
κ ∈ [0, 1]. Low κ-values indicate a limited potential for fiscal cushioning, while high
κ-values imply a large potential to undermine the emission tax.
Given the effort x and the potential κ, we can calculate the actual tax rate levied on
emissions, which is denoted by τ (κx). The actual tax rate is the difference between the
28
2.2. Model
inter-country tax and the actual distortion level, i.e., τ (κx) = t − κx. If a country has
no potential for fiscal cushioning (κ = 0) or if no fiscal corrections are made (x = 0),
the actual emission price corresponds to the inter-country tax, i.e., τ (0) = t. The
minimum actual tax rate is given by τ (t) = 0, i.e., when a country with potential
κ = 1 puts a maximum effort into fiscal cushioning x = t. In this case, the country
perfectly offsets the emission tax domestically.
It is now straightforward that the country’s manipulation of the emission tax affects
the level of pollution. Under fiscal cushioning, i.e., when (x, κ) > 0, the country’s
emissions e∗∗ are implicitly defined by
g ′ (e∗∗ ) = t − κx,
(2.2)
the profit maximizing condition of the polluting industry.9 Obviously, emissions increase under fiscal cushioning. We denote by E(κ) the highest emission level, i.e.,
when a κ-type country puts a maximum effort into fiscal cushioning x = t. Note that
E(κ) is the higher, the larger the potential for fiscal cushioning. This is straightforward
because the distortion of the actual tax rate increases with κ. This reduces the incentives for pollution abatement and increases emissions. Hence, a country’s emissions are
E(κ) ≥ e∗∗ > e∗ when (x, κ) > 0.
The analysis above indicates that fiscal cushioning strategies undermine the purpose
of the regulation, i.e. abatement. The regulator, however, is entitled to enforce the
regulation by audits and sanctions. We denote the probability with which the regulator
monitors a country by α ∈ [0, 1]. As in Macho-Stadler and Pérez-Castrillo (2006),
auditing a country does not necessarily imply the actual detection of noncompliance.
We denote by γ ∈ [0, 1] the country-specific probability of detection when audited.
A country which is ’hard-to-detect’ can successfully hide its noncompliance, which is
associated with low γ-values. In contrast, high γ-values indicate an ’easy-to-detect’
country, in which evidence for noncompliance can be gathered more easily. Given the
monitoring probability α and the probability of detection γ, a country’s noncompliance
is discovered with probability γα ∈ [0, 1].
As the actual tax rate τ (κx) and the associated emission level e∗∗ are not perfectly
observable for the regulator, a country may submit a false emission report z ≤ e∗∗ .
9
Note, we assume that polluters comply with the domestic actual emission tax. This allows us
to highlight the country’s compliance decision with respect to fiscal cushioning in inter-country tax
regulations.
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
29
This reduces a country’s tax transfers to the regulator. However, when noncompliance
is detected, the country has to pay the evaded amount of tax money and an additional
sanction F . The regulator imposes the sanction contingent on the amount of underreporting, i.e., [e∗ − z], and excess pollution from fiscal cushioning, i.e., [e∗∗ − e∗ ].
The corresponding function F (e∗∗ − z) is increasing and convex in its arguments, i.e.,
F ′ (·) > 0, F ′′ (·) > 0, and F (0) = 0.10 We assume that the marginal sanction is always
high enough to create compliance incentives. That is, a report, which implies certain
sanctioning, can never be part of the country’s optimal compliance strategy. Note,
however, that any report that deviates from the intended emission level e∗ , which
is common knowledge, indicates a country’s noncompliance. Hence, the dominant
strategy is to report the intended emission level z = e∗ , whether this is true or not.
We are now able to establish the country’s maximization problem. The expected
pay-off Π(e(x, κ); α, γ) of a (γ, κ)-type country, facing an audit probability α and a tax
share β, can be written as11
Π(e(x, κ); α, γ) = g(e(x, κ)) − βte∗ − γαβt[e(x, κ) − e∗ ] − γαF (e(x, κ) − e∗ )
The country chooses the amount of fiscal cushioning x0 to maximize the expected
pay-off Π(e(x, κ); α, γ). Considering (2.2), the first-order condition for an interior solution is
∂Π
= e′ (x, κ) [t − κx − γα [βt + F ′ (e(x, κ) − e∗ )]] = 0.
∂x
(2.3)
Condition 2.3 determines the country’s optimal compliance behavior dependent
on the level of the perceived audit pressure. This allows us to establish different γα
probability ranges to specify the level of fiscal cushioning of a (γ, κ)-type country
(see the Appendix A.1). First, if γα takes very low values, the expected sanction is
insufficient to create compliance incentives. The country chooses the maximum effort
10
A convex sanction function is a common assumption in the literature on incomplete enforcement
(see e.g. Harford (1978), Keeler (1991), Sandmo (2002), Macho-Stadler and Pérez-Castrillo (2006),
MacKenzie and Ohndorf (2012b)).
11
For the sake of simplicity, we assume that the fraction (1 − β) of tax revenues which is not
transferred to the regulator is redistributed lump sum to the industry. Thus, no potential second
dividend from a revenue-recycling effect exists. See Goulder (1995) for further information on the
double dividend hypothesis.
30
2.2. Model
in fiscal cushioning x0 = t. Second, higher perceived audit pressures increase the
expected sanction for noncompliance. The country reduces the optimal effort level in
fiscal cushioning, which is implicitly defined by (2.3). Third, when the perceived audit
pressure is very high, the country’s optimal strategy is to not distort the international
emission tax, i.e., x0 = 0. The next proposition summarizes these findings more
formally.
Proposition 1. Given an international tax rate t, the tax share β, the sanction F (·),
and a monitoring probability α, the optimal effort in fiscal cushioning x0 of a (γ, κ)-type
country is
( a) x0 = t for γα ≤ βt+Ft[1−κ]
The amount of emissions is E(κ), implicitly
′ (E(κ)−e∗ ) .
defined by (2.2) for x = t.
t
∗∗
( b) x0 ∈ (0, t) for γα ∈ βt+Ft[1−κ]
′ (E(κ)−e∗ ) , βt+F ′ (0) . The amount of emissions is e ,
implicitly defined by (2.2).
( c) x0 = 0 for γα ≥
(2.1).
t
.
βt+F ′ (0)
The amount of emissions is e∗ , implicitly defined by
Proof: See the Appendix A.1
Figure 2.1 visualizes the country’s optimal compliance decision given different probability ranges of the perceived audit pressure γα. The actual tax rate is depicted by
the solid curve, the associated emission level by the dotted curve. Reported emissions
are represented by the dashed line, which is horizontal because the country’s dominant
strategy is to report z = e∗ . Figure 2.1 also depicts the existence of the probability
ranges (a) - (c) established in Proposition 1. Perceived audit pressures within region
(a) incentivize the country to put a maximum effort x = t into the distortion of the
actual tax rate. Note, however, that the country cannot perfectly offset the emission
tax when κ < 1. Hence, the actual tax rate τ (κt) remains positive. The corresponding amount of emissions is E(κ). In range (b) of the perceived audit pressures, the
country reduces the effort put into fiscal cushioning, x ∈ (0, t), as the probability of
being sanctioned increases. The corresponding emission level is e∗∗ . Perceived audit
pressures within range (c) deter the country from applying fiscal adjustments, x = 0,
which implies the intended discharge level e∗ .
Note that the thresholds separating regions (a) - (c) are decreasing in the fraction of
the tax rate a country transfers to the regulator β. Higher tax transfers are equivalent to
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
31
τ (κx)
e; z
E(κ)
e∗∗
t
z = e∗
τ (κx)
(a)
(b)
(c)
τ (κt)
0
γα
t[1−κ]
βt+F ′ (E(κ)−e∗ )
t
βt+F ′ (0)
Figure 2.1: Optimal compliance decision of a κ-type country
an increase in the expected costs of noncompliance. Ceteris paribus, when β increases,
a lower perceived audit pressure is sufficient to incentivize the country to (partially)
comply with the regulation.
So far, we have analyzed the optimal compliance decision of a single (γ, κ)-type
country, which adapts its compliance decision according to the level of the perceived
audit pressure γα. In the following section, we discuss the regulator’s objective function
before establishing the optimal monitoring policies.
2.3
The Regulator’s Perspective
The regulator faces a continuum of countries that can be heterogeneous along two dimensions. First, countries differ in their probability of detection γ ∈ [0, 1]. That is,
finding evidence for noncompliance is more difficult for some countries than for others.
The continuum of countries is distributed over the interval [0, 1] according to the distribution function v(γ), with v(γ) > 0 ∀ γ ∈ [0, 1], whose cumulative distribution function
is V (γ). Second, countries differ in their potential for fiscal cushioning κ ∈ [0, 1]. As
already discussed above in more detail, the parameter κ determines a country’s ability
to distort the abatement incentive effect of the emission tax. The continuum of coun-
32
2.4. Optimal Audit Policies
tries is distributed over the interval [0, 1] according to the distribution function r(γ),
with r(γ) > 0 ∀ κ ∈ [0, 1], whose cumulative distribution function is R(γ).
From proposition 1 it follows that the potential for fiscal cushioning and the probability of detection determine a country’s optimal compliance decision. Both parameters, κ and γ, are country-specific and assumed to be common knowledge. This allows
the regulator to choose audit pressures α according to the countries’ characteristics
(γ, κ). The optimal monitoring policy α(γ, κ) is chosen such that aggregate emissions
are minimized.
Without loss of generality, auditing costs are normalized to 1. That is, the monitoring budget B equals the number of inspections. For a given level of monitoring
resources, the regulator chooses the audit policy α(γ, κ) which minimizes the aggregate emission level. The optimal monitoring policy is, hence, characterized through
the following minimization program.
min
α
|γ,κ
Z
1
0
Z
1
0
e(x(γ, κ), κ)v(γ)r(κ)dγdκ
s.t.
Z
0
1
Z
0
1
α(γ, κ)v(γ)r(κ)dγdκ ≤ B
(2.4)
and
x ∈ argmax Π(e(x, κ); α, γ) ∀ (γ, κ)
(2.5)
Establishing the optimal auditing pressure for a (γ, κ)-type country, the regulator
needs to take into account the limited monitoring budget, i.e., constraint (2.4), and
the country’s optimal compliance decision expressed through constraint (2.5). The
regulator solves this game using backward induction.
2.4
Optimal Audit Policies
In this section, we analyze the characteristics of the regulator’s audit policy to meet
the objective of minimizing aggregate emissions. Note that the countries’ probability of
detection and the potential for fiscal cushioning are, for the sake of simplicity, assumed
to be common knowledge. Hence, the regulator can discriminate among (γ, κ)-type
countries and can accordingly adjust the monitoring pressure α to minimize aggregate
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
33
emissions. That is, the regulator distinguishes between countries that can be incentivized to fully comply, countries that are in partial compliance, and countries that
never comply. The separation is as follows:
First and similar to Macho-Stadler and Pérez-Castrillo (2006), we specify those countries that can be incentivized to fully comply with the regulation. This requires perceived audit pressures to be within region (c) of Figure 2.1. Hence, we can define
the minimum monitoring probability that induces countries to put no effort into fiscal
cushioning, i.e., x = 0. We know from Proposition 1 that this requires an auditing
pressure of α(γ) ≥ α̂(γ), where
α̂(γ) =
t
.
γ[βt + F ′ (0)]
As α; γ ∈ [0, 1], this audit pressure is only feasible when α̂ ≤ 1, i.e., if γ ≥ γ̂, where
γ̂ ≡
t
.
βt + F ′ (0)
Note that α̂(γ) and γ̂ are independent of κ. The rationale is straightforward, as the
potential for fiscal cushioning is irrelevant when full compliance is the countries’ optimal
strategy. In contrast, the potential for fiscal cushioning becomes crucial when we
separate the countries that never comply with the regulation from those that can be
incentivized to partially comply. The latter is the case for perceived audit pressures
within region (b) of Figure 2.1. Hence, we further define the minimum audit pressure
that incentivizes κ-type countries to partially comply with the regulation, i.e., to put
x < t effort in fiscal cushioning. This requires an audit pressure of α(γ, κ) > α̃(γ, κ),
where
t[1 − κ]
.
α̃(γ, κ) =
γ[βt + F ′ (E(κ) − e∗ )]
Again, this audit pressure is only feasible when α̃ ≤ 1, i.e., if γ(κ) ≥ γ̃(κ), where
γ̃(κ) ≡
t[1 − κ]
.
βt + F ′ (E(κ) − e∗ )
Note first that α̃(·) and γ̃(·) depend on the potential for fiscal cushioning and are both
decreasing in κ. The rationale is as follows. The potential for fiscal cushioning determines the marginal sanction via E(κ), which is increasing in κ. Given the convexity of
the sanction, a limited potential for fiscal cushioning implies a low marginal sanction
34
2.4. Optimal Audit Policies
for noncompliance. In this case, the perceived audit pressure must be high enough
to create compliance incentives. By contrast, a large potential for fiscal cushioning
implies a high marginal sanction. Hence, a lower perceived audit pressure is sufficient
to deter noncompliance.
Furthermore, both thresholds α̃(·) and γ̃(·) become zero for κ = 1. In this case, the
only country that can never be incentivized to comply with the regulation is the one
whose noncompliance can never be detected, i.e., for which γ = 0. This special case
corresponds to Macho-Stadler and Pérez-Castrillo (2006)’s analysis.
Taking into account the above-defined thresholds, we establish the regulator’s optimal monitoring policy for two different scenarios. In the first scenario, we assume that
countries are heterogeneous with respect to the probability of detection, yet homogeneous along the potential for fiscal cushioning. The reverse case is considered in the
second scenario. We begin each analysis by assuming that the regulator has unlimited
access to monitoring resources, i.e., when constraint (2.4) of the regulator’s minimization program is not binding. Thereby obtained results are used as a benchmark for the
more realistic case, in which the regulator is budget-constrained.
2.4.1
Heterogeneity in the Probability of Detection
In this section, we consider heterogeneity in the probability of detection. Yet, countries are homogeneous with respect to the potential for fiscal cushioning, i.e., κ = κ̄ is
constant across countries.12
Unlimited Monitoring Budget
Note that even when the regulator is endowed with an unlimited monitoring budget, the first-best outcome of full compliance can never be achieved. There will always
be countries for which complete or partial noncompliance is optimal. More precisely,
countries of type γ ∈ [0, γ̃(κ̄)] never comply and exert a maximum fiscal cushioning
effort x = t. The probability of detection is such that the perceived audit pressure is,
even when audited with certainty, insufficient to create compliance incentives. Countries with an intermediate probability of detection, i.e., those with γ ∈ (γ̃(κ̄), γ̂), can be
12
Parameters tagged with a bar are constant parameters.
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
35
incentivized to partially comply, which implies x ∈ (0, t). Without budget constraints,
the regulator imposes the highest audit pressure on those countries, i.e., α = 1. Only
countries whose probability of detection is very high, i.e., for which γ ≥ γ̂, can be
incentivized to fully comply with the regulation. These countries do not distort the
emission tax, i.e., x = 0. This requires a monitoring pressure of α̂(γ). Thus, the lowest
level of aggregate fiscal cushioning the regulator can achieve amounts to
κ̄xmin = κ̄tV (γ̃(κ̄)) +
Z
γ̂
κ̄x∗ (γ)v(γ)dγ.
γ̃(κ̄)
The first term sums up all countries within region (a) of Figure 2.1. Those countries
put a maximum effort into fiscal cushioning x = t. The second term measures the level
of fiscal cushioning of countries for which partial compliance is optimal (region (b)).
Those countries put x∗ (γ) effort into fiscal cushioning, which is implicitly defined by
[t − κ̄x∗ (γ)] − γ[βt + F ′ (e(x∗ (γ), κ̄) − e∗ )] = 0. Countries within region (c) comply with
the regulation and exert no fiscal cushioning effort, x = 0. From this we can calculate
the aggregate minimum emission level, which is given by13
eκ̄min
= E(κ̄)V (γ̃(κ̄)) +
Z
γ̂
γ̃(κ̄)
e (γ)v(γ)dγ +
∗∗
Z
γ̂
1
(2.6)
e∗ v(γ)dγ
The interpretation of (2.6) is analogous to the one of κ̄xmin . Countries within region (a)
emit E(κ̄), while those within field (b) discharge e∗∗ units of pollution. Only countries
in region (c) emit the regulator’s intended emission level e∗ .
κ̄
Subsequent to (2.6) we can calculate the lowest monitoring budget B which is
necessary to achieve the minimum emission level eκ̄min .
κ̄
B = V (γ̂) − V (γ̃(κ̄)) +
Z
γ̂
1
α̂(γ)v(γ)dγ.
The optimal audit policy when the regulator has unlimited access to monitoring resources is, given the above analysis, straightforward and is summarized in the following
proposition.
13
The superscript refers to the constant parameter.
36
2.4. Optimal Audit Policies
Proposition 2. When the regulator has unlimited access to monitoring resources, i.e.,
κ̄
when B ≥ B , the optimal monitoring policy is such that
I. α = 0 for all (γ, κ̄)-type countries with γ ∈ [0, γ̃(κ̄)].
II. α = 1 for all (γ, κ̄)-type countries with γ ∈ (γ̃(κ̄), γ̂).
III. α(γ) = M in{1, α̂(γ)} for all (γ, κ̄)-type countries with γ ∈ [γ̂, 1].
Most obvious, a significant share of countries, i.e., those within Region I of Proposition 2, can never be incentivized to comply with the regulation and are hence never
subject to audits. The underlying rationale is as follows. Countries’ emissions are
bounded from above by E(κ̄), which puts a cap on the marginal sanction for noncompliance. In case the probability of detection is very low, the expected sanction
is always insufficient in creating incentives for partial compliance. Hence, countries
within Region I of Proposition 2 are never audited in order to save expenses for monitoring. Note that the only agent which is never subject to audits in Macho-Stadler
and Pérez-Castrillo (2006) is the one whose noncompliance can never be detected, i.e.,
when γ = 0. Setting α = 0 in this case is straightforward. We are able to reproduce
this result by assuming κ̄ = 1.
Limited Monitoring Budget
Unrestricted access to monitoring resources is quite unrealistic in the real-world. Hence,
we extend our analysis by establishing the optimal monitoring policy when the regulator
κ̄
is budget-constrained, i.e., when B < B . In this case, the optimal audit policy from
Proposition 2 and the associated minimum emission level eκ̄min are no longer feasible.
The thresholds established in Section 2.4 provide the basis for the analysis of the
optimal monitoring policy with constrained monitoring resources. Note first that a
monitoring pressure α(γ) which yields γα ≤ γ̃ can never be part of an optimal monitoring policy. A country’s perceived audit pressure would always be insufficient to create compliance incentives. Second, the optimal monitoring policy is such that γα > γ̂
never holds. That is, the monitoring pressure should never exceed α̂(γ). An increase
in the monitoring intensity above α̂(γ) does not improve compliance rates, as these
countries already fully comply with the regulation. We summarize these findings in
the following lemma:
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
37
κ̄
Lemma 1. With limited budget B < B , the regulator never audits a (γ, κ̄)-type country with a probability α ∈ [0, 1]
i. lower than α̃(γ, κ̄) and
ii. higher than α̂(γ).
Considering Lemma 1, the budget-constrained regulator audits first those countries
in which the expected reduction in fiscal cushioning and, hence, in emissions per audit
is the highest. That is, for a monitoring policy being optimal, it must hold that a
marginal reallocation of budget δ between countries of type (γ1 , κ̄) and (γ2 , κ̄) does not
reduce the aggregate emission level. More formally,
−v(γ1 )δ
v(γ1 ) ∂e(α2 γ2 )
∂e(α1 γ1 )
+ v(γ2 )
δ
≥0
∂α(γ1 )
v(γ2 ) ∂α(γ2 )
(2.7)
with
∂e
βt + F ′ (e − e∗ )
= γ ′′
< 0 ∀ γα ∈
∂α
g (e) − γαF ′′ (e − e∗ )
t
t[1 − κ̄]
,
′
∗
βt + F (E(κ̄) − e ) βt + F ′ (0)
!
must hold, where ∂e/∂α can be obtained from applying the Implicit Function Theorem
on (2.3).14
This allows us to establish the characteristics of the optimal monitoring policy
κ̄
under limited budget B < B , which are summarized in the following proposition.
κ̄
Proposition 3. When the regulator is budget-constrained, i.e., when B < B , two
thresholds, γl (B, κ̄) and γh (B), exist with γ̃(κ̄) < γl (B, κ̄) ≤ γh (B) ≤ 1. The optimal
audit policy is such that
I. α = 0 for all (γ, κ̄)-type countries with γ ≤ γl (B, κ̄),
II. α(γ) ∈ (α̃(γ, κ̄), M in{1, α̂(γ)}) for all (γ, κ̄)-type countries with γl (B, κ̄) < γ <
γh (B), and
III. α(γ) = M in{1, α̂(γ)} for all (γ, κ̄)-type countries with γh (B) ≤ γ ≤ 1.
14
Note, in order to ensure that two identical countries are treated similarly, we assume e(αγ) being
decreasing and convex in αγ. This is, for example, the case when g ′′′ (e) > 0 and F ′′′ (·) < 0. See the
Appendix A.2 for more details.
38
2.4. Optimal Audit Policies
α; e; z
α; e; z
E(κ̄)
E(κ̄)
e∗∗
e∗∗
z = e∗
z = e∗
α(γ, κ̄)
I
γl (B1 , κ̄)
II
III
1
γh (B1 )
Figure 2.2a: B1 ∈ B κ̄ , B
I
κ̄
γ
α(γ, κ̄)
II
1
γl (B2 , κ̄)
κ̄ , B κ̄
Figure 2.2b: B2 ∈ Bcrit
γ
Figure 2.2: Optimal monitoring policies with limited budget and heterogeneity in the
probability of detection.
Given that the regulator implements a monitoring policy characterized by Proposition 3, we summarize the countries’ optimal compliance decisions in the following
corollary.
Corollary 1. When the regulator announces and commits to an audit policy characterized by proposition 3, a (γ, κ̄)-type country with
i. γ ≤ γl (B, κ̄) exerts a maximum effort in fiscal cushioning, x∗ =t. The associated
emission level is E(κ̄), implicitly defined by (2.2) for x = t.
ii. γ ∈ (γl (B, κ̄), γh (B)) exerts intermediate efforts in fiscal cushioning x∗ ∈ (0, t)
implicitly defined by (2.3). The associated emission level is e∗∗ , implicitly defined
by (2.2).
iii. γ ≥ γh (B) exerts no effort in fiscal cushioning x∗ =0. The associated emission
level is e∗ , implicitly defined by (2.1).
Proof: See the Appendix A.2
Figure 2.2 illustrates the optimal monitoring policy and the countries’ compliance
decisions that are summarized in Proposition 3 and Corollary 1. The optimal audit
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
39
policy α(γ, κ̄) is shown in the solid curve. The countries’ actual pollution level, incentivized by the actual tax rate, is represented in the dotted curve. The horizontal
dashed line depicts reported emissions.
In Figure 2.2a, the budget is limited, but still high enough, such that all three regions
established in Proposition 3 exist. In comparison to the case with unconstrained budget, the regulator reallocates the available resources and monitors first those countries
for which the expected reduction in emissions per audit is the highest. As expressed
within Proposition 3, this implies a discrimination towards easy-to-detect countries.
That is, countries with probabilities of detection within Region I of Figure 2.2a are not
audited. Creating compliance incentives for countries with γ ≤ γl (B1 , κ̄) is either not
possible or, given the constrained monitoring budget, not optimal. Note that Region
I is decreasing with higher κ̄-values, as γl (B1 , κ̄) is, for the same reasons identified for
γ̃(κ̄), decreasing in the potential for fiscal cushioning. For higher probabilities of detection, i.e., in Region II, countries are audited and incentivized to partially comply with
the regulation. This implies a reduction in fiscal cushioning measures and emissions
relative to non-audited countries. Monitoring resources are allocated as follows. We
know from Lemma 1 that auditing pressures must exceed α̃(γ, κ̄), which explains the
jump in the optimal monitoring policy at γl (B1 , κ̄). Furthermore, the regulator puts
a higher auditing pressure on countries with higher probabilities of detection. This
maximizes the deterrence effect of inspections against fiscal cushioning and minimizes
emissions. In Region III of Figure 2.2a, countries with γ ≥ γh (B1 ) can be incentivized
to perfectly comply with the regulation. This requires a monitoring probability of α̂(γ).
Obviously, the higher the probability of detection, the lower the monitoring pressure
required to force those countries into compliance. Hence, α̂(γ) is decreasing in γ. Recall that the potential for fiscal cushioning is irrelevant for compliant countries, i.e.,
γh (B1 ) is independent of κ̄.
Note that the regions established in Proposition 3 crucially depend on the level of the
limited monitoring budget. We, therefore, state the effects of a change in the regulator’s monitoring resources B on the thresholds γl (B, κ̄) and γh (B) in Proposition 4
and the implications for the optimal monitoring policy in the following Corollary 2.
Proposition 4. When the monitoring budget is limited, the thresholds γl (B, κ̄) and
γh (B) are non-increasing in B.
40
2.4. Optimal Audit Policies
Corollary 2. Given the properties of γl (B, κ̄) and γh (B) established in Proposition 4,
there exists a monitoring budget
κ̄
i. B ∈ [0, Bcrit
], for which γl (B, κ̄) = γh (B) = 1 and only Region I exists.
i
κ̄
ii. B ∈ Bcrit
, B κ̄ , for which γh (B) = 1 and γl (B, κ̄) ∈ (γ̃(κ̄), 1) that separates
Region I and II.
κ̄
iii. B ∈ B κ̄ , B , which separate Regions as specified in Proposition 3.
κ̄
iv. B ≥ B , for which γl (B, κ̄) = γ̃(κ̄) and γh (B) = γ̂.
Proof: See the Appendix A.2
Proposition 4 and Corollary 2 have important implications for the regulator’s monitoring budget, which determines feasible audit pressures and, hence, the existence of
the three probability ranges established in Proposition 3. Consider the case in which
κ̄
the monitoring budget is below Bcrit
, i.e., within Range i of Corollary 2. This implies
that feasible monitoring pressures would always be insufficient to create compliance
incentives. Both thresholds, γl (B, κ̄) and γh (B), are equal to 1 and only Region I of
Proposition 3 exists. That is, there is no enforcement at all. The regulator’s budget
κ̄
endowment therefore ought to exceed Bcrit
. Given a monitoring budget defined in
Corollary 2ii allows implementing a policy visualized in Figure 2.2b. In this case, the
monitoring budget is high enough to incentivize some countries to partially comply
with the regulation. Yet, creating incentives for full compliance is not possible or optimal given the limited enforcement budget. That is, γl (B, κ̄) < γh (B) = 1 and Regions
I and II exist. Corollary 2iii defines the budget range that allows implementing the
monitoring policy depicted in Figure 2.2a. In this case, all three Regions I - III exist
with cut-off points γ̃(κ̄) < γl (B, κ̄) < γh (B) < 1. Unlimited excess to monitoring resources, i.e., a budget endowment within the range of Corollary 2iv, allows realizing the
monitoring policy proposed in Proposition 2. Note that it is not optimal to endow the
κ̄
regulator with a monitoring budget larger than B . An increase in the monitoring budget above that level would allow an increase in the monitoring pressures. Yet, given the
audit policy specified in Proposition 2, compliance rates cannot be further improved,
as all partially complying countries are already audited with certainty. Hence, if the
regulator’s sole objective is to minimize emissions, the monitoring budget should never
κ̄
exceed B .
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
41
The above analysis indicates that countries with low probabilities of detection are
never subject to audits. This implies, depending on the level of the monitoring budget,
a significant share of countries putting a maximum effort into the distortion of the
emission tax. Hence, it might seem intuitive that the regulator refuses the participation of countries with γ ≤ γl (B, κ̄) in the inter-country agreement. Note, however,
that for every level of fiscal cushioning x ∈ [0, t], the actual tax rate τ (κ̄x) is positive
for all κ̄ < 1. That is, when the potential to offset the emission tax is limited, an incentive for pollution abatement exists irrespective of the countries’ compliance status.
The amount of emissions under complete noncompliance E(κ̄) is, hence, always lower
than the pre-regulation discharge level. Participation of noncompliant countries in the
inter-country environmental agreement is therefore strictly preferred. In fact, for κ̄ = 1,
countries can perfectly counterbalance the pollution abatement incentive effect of the
emission tax. As a consequence, pre-regulation pollution discharges coincide with the
emission level under complete noncompliance. In this case, the regulator is indifferent
between participation and non-participation of complete noncompliant countries.
Moreover, note that the compliance decision and the actual tax rates differ across countries in the environmental agreement. That is, fiscal cushioning not only undermines
the environmental integrity of the regulation, but also its economic efficiency. Marginal
benefits from emission are equalized across countries only within Region I, respectively
within Region III of Proposition 3. Similar conclusions can be drawn when countries
differ in the potential for fiscal cushioning, which is analyzed in the following section.
2.4.2
Heterogeneity in the Potential for Fiscal Cushioning
In this section, we consider the case in which countries solely differ in the potential
to offset the incentive effect set by the environmental tax. Hence, countries are heterogeneous in the parameter κ ∈ [0, 1], which was assumed constant in the previous
section. Yet, we assume that the probability of detection is constant, i.e., γ = γ̄, for all
countries. As before, a country’s (γ̄, κ)-type is assumed to be common knowledge. The
regulator hence adopts its monitoring intensity according to the country’s potential for
fiscal cushioning to meet the objective of minimizing aggregate emissions.
The assumption of the probability of detection being constant across countries can
be considered a realistic scenario if the enforcement proposal of the supporters of a
global environmental tax agreement is to be believed (see e.g. Cooper (1998)). It is
argued that the IMF Article IV Report reveals macroeconomic data that might disclose
42
2.4. Optimal Audit Policies
a country’s fiscal cushioning measures. Given the IMF’s reviews, it can plausibly be
expected that fiscal adjustments can be detected with equal probability.
Note that the constant probability of detection affects the monitoring effectiveness’, as
it determines feasible probability ranges for γ̄α. Whether γ̄ takes rather low or high
values depends on the stringency of the report. Consider, for example, the case in
which the report requirements are poorly drafted, such that no incriminating evidence
for noncompliance is found. In this case, γ̄ = 0 and no country can be incentivized
to comply with the regulation. By contrast, full compliance can be expected when
exceptionally strict report requirements reveal fiscal adjustment. This is the case when
the probability of detection takes very high values, i.e., when γ̄ ≥ γ̂. However, Aldy
et al. (2008) and others argue that, despite all the care taken by the IMF, deterrence
against fiscal cushioning will be incomplete. Even though report requirements are well
defined, countries may take advantage of complex tax-loopholes and subsidy programs,
i.e., fiscal policy adjustments that are likely to remain undetected by the IMF. We address this enforcement concern by assuming that the constant probability of detection
takes intermediate values, i.e., that γ̄ ∈ (0, γ̂).
Unlimited Monitoring Budget
We know from our analysis in Section 2.4 that full compliance is only feasible when
the probability of detection is high enough, i.e., when γ̄ ≥ γ̂. Thus, while complete
compliance is, by assumption, precluded when an γ̄ ∈ (0, γ̂) is assumed, countries can
still be incentivized to partially comply with the regulation. This requires a minimum
audit pressure of α(γ̄, κ) > α̃(γ̄, κ), which is only feasible when α̃(γ̄, κ) ≤ 1, i.e., if
γ̃(κ) < γ̄. As γ̃(κ) is decreasing in the potential for fiscal cushioning (see Section 2.4),
this holds true only when κ is large enough. The marginal country is denoted by κ̃,
which is implicitly defined by
γ̄ =
t[1 − κ̃]
.
βt + F ′ (E(κ̃) − e∗ )
As before, the limited potential for fiscal cushioning puts a cap on the marginal sanction for noncompliance. Hence, countries with κ ≤ κ̃ are never audited, as even an
audit pressure of 1 would be insufficient to create compliance incentives. As a consequence, these countries put a maximum effort into fiscal cushioning x = t. Countries
of type κ > κ̃ can be incentivized to partially comply with the regulation. With un-
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
43
limited monitoring resources, those countries are audited with certainty to maximize
the deterrence effect of monitoring against fiscal cushioning. Note that the perceived
audit pressure is identical for all countries that are subject to audits, as α = 1 and
γ = γ̄. Therefore, the optimal distortion κx of the international tax rate is identical
across those countries. In fact, countries that are audited with certainty maximize their
expected pay-off by adopting the actual tax rate of the marginal non-audited, i.e., the
κ̃-type country. Hence, for all countries with κ > κ̃, it is optimal to choose x∗ such
that κx∗ = κ̃t holds. This implies lower effort levels for a larger potential for fiscal
policy adjustments. Thus, the lowest aggregate level of fiscal cushioning the regulator
can achieve is
Z κ̃
κxγ̄min =
κtr(κ)dκ + [R(1) − R(κ̃)] κ̃t
0
The first term sums up all countries that are never subject to audits and that put a
maximum effort into fiscal cushioning. All other countries choose an effort level to
adopt the distortion of the marginal non-audited country, which is reflected in the
second term. The associated aggregate emission level is
eγ̄min =
Z
κ̃
0
E(κ)r(κ)dκ + [R(1) − R(κ̃)] E(κ̃)
γ̄
where E(κ) and E(κ̃) are implicitly defined by (2.2) for x = t. The budget B which
is necessary to achieve eγ̄min amounts to
γ̄
B =
Z
1
κ̃
r(κ)dκ.
The next proposition, which summarizes the optimal monitoring policy when the
regulator has unlimited access to monitoring resources, is immediate from the above
discussion.
γ̄
Proposition 5. When B ≥ B and γ̄ ∈ (0, γ̂), the optimal monitoring policy is
I. α = 0 for all (γ̄, κ)-type countries with κ ≤ κ̃.
II. α = 1 for all (γ̄, κ)-type countries with κ > κ̃.
Note that, contrary to the monitoring policy characterized in Proposition 2, no
country is incentivized to perfectly comply with the regulation. This is due to our assumption that the constant probability of detection takes intermediate values. In this
case, the perceived audit pressure is, even when countries are audited with certainty,
44
2.4. Optimal Audit Policies
always insufficient to disincentivize noncompliance. Thus, focusing on intermediate
probabilities of detection reflects, in fact, the enforcement concerns raised e.g. in Aldy
et al. (2008). It is claimed that, despite all attempts, a complete deterrence of fiscal
cushioning strategies can never be achieved.
Limited Monitoring Budget
We still assume that γ̄ takes an intermediate value. However, with limited moniγ̄
toring budget, i.e., when B < B , the audit policy summarized in Proposition 5 is no
longer feasible.
We proceed similarly to the analysis under limited monitoring budget in Section
2.4.1. Given the countries’ heterogeneity with respect to the potential for fiscal cushioning, the optimal monitoring policy has to meet the following requirements: no
(γ̄, κ)-type country is audited with a probability lower than α̃(γ̄, κ) and a marginal reallocation of monitoring budgets across countries does not reduce the aggregate emission
level.15
The next proposition summarizes the optimal monitoring policy, the following corollary the countries’ optimal compliance decisions.
γ̄
Proposition 6. When the regulator is budget-constrained, i.e., when B < B , and
when γ̄ ∈ (0, γ̂), two thresholds κl (B, γ̄) and κh (B, γ̄) exist with κ̃ < κl (B, γ̄) ≤
κh (B, γ̄) ≤ 1. The optimal monitoring policy is
I. α = 0 for all (γ̄, κ)-type countries with κ ≤ κl (B, γ̄).
II. α(κ) ∈ (α̃(γ̄, κ), 1) for all (γ̄, κ)-type countries with κl (B, γ̄) < κ < κh (B, γ̄).
III. α = 1 for all (γ̄, κ)-type countries with κ ≥ κh (B, γ̄).
15
Note, the upper limit of optimal monitoring pressure from Lemma 1 is irrelevant in this case. The
perceived audit pressure can never create incentives for full compliance, as the constant probability
of detection is assumed to take intermediate values, i.e., γ̄ ∈ (0, γ̂).
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
45
α; e; z
α; e; z
e∗∗
E(κ)
e∗∗
E(κ)
E(κ̃)
z = e∗
z = e∗
α(γ̄, κ)
α(γ̄, κ)
I
0
κl (B1 , γ̄)
II
III
1
κh (B1 , γ̄)
Figure 2.3a: B1 ∈ B γ̄ , B
γ̄
I
κ
0
II
1
κl (B2 , γ̄)
Figure 2.3b: B2 ∈ 0, B γ̄
κ
Figure 2.3: Optimal monitoring policies with limited budget and heterogeneity in the
potential for fiscal cushioning.
Corollary 3. When the regulator announces and commits to an audit policy characterized by Proposition 6, a (γ̄, κ)-type country with
i. κ ≤ κl (B, γ̄) exerts a maximum effort in fiscal cushioning x∗ = t. The associated
emission level is E(κ), implicitly defined by (2.2) for x = t.
ii. κ ∈ (κl (B, γ̄), κh (B, γ̄)) exerts intermediate effort in fiscal cushioning x∗ ∈ (0, t)
implicitly defined by (2.3). The associated emission level is e∗∗ , implicitly defined
by (2.2).
iii. κ ≥ κh (B, γ̄) exerts intermediate effort in fiscal cushioning x∗ ∈ (0, t) such that
κx∗ = κ̃t holds. The associated emission level is E(κ̃), implicitly defined by (2.2)
for x = t.
Proof: See the Appendix A.3
Corresponding to Proposition 6 and Corollary 3, Figure 2.3 depicts the course
of the optimal monitoring policy, the report and emission levels dependent on the
potential for fiscal cushioning κ. The optimal monitoring policy is represented in the
solid curve. The countries’ reported emissions are shown in the horizontal dashed line,
actual pollution discharges in the dotted curve.
46
2.4. Optimal Audit Policies
In Figure 2.3a, the budget is limited, yet still high enough, such that all three regions
established in Proposition 6 exist. The optimal monitoring policy indicates to focus
monitoring on countries with a larger potential for fiscal cushioning. Countries with
very low κ-values, i.e., those within Region I of Figure 2.3a, are never subject to audits.
Creating compliance incentives is either not possible or, given the limited monitoring
budget, not optimal. The countries’ compliance decision is to put a maximum effort into
fiscal cushioning. Emissions are increasing in this region, as the actual tax decreases
with κ for x∗ = t. Countries are audited only when the potential for fiscal cushioning
is large enough, i.e., when κ > κl (B1 , γ̄). Sufficient compliance incentives require an
auditing pressure of at least α̃(γ̄, κ). This explains the jump in the optimal monitoring
policy at κl (B1 , γ̄). In Region II of Figure 2.3, it is optimal to increase the auditing
pressure for countries with a larger potential for fiscal cushioning. Within this region,
the distortion of the tax rate κx∗ is decreasing in κ, implying a decreasing emission
level. The optimal monitoring pressure reaches α = 1 at κh (B1 , κ̄). That is, countries
with a large potential for fiscal cushioning, i.e., those in Region III of Figure 2.3,
are audited with certainty. Note that the perceived audit pressure is constant in this
region. As already discussed above, countries that are audited with probability α = 1
maximize their expected pay-off by adopting the actual tax rate of the κ̃-type country.
That is, the optimal effort put into fiscal cushioning x∗ is decreasing in κ, such that
τ (κx∗ ) = τ (κ̃t) holds. This implies the identical emission level E(κ̃) for all countries
of type κ ∈ [κh (B1 , γ̄), 1].
Indeed, the monitoring policy proposed in Proposition 6 and, therefore, the existence
of the Regions I - III crucially depend on the level of the monitoring budget B. We
therefore state the effects of a change in the monitoring budget on the thresholds
κl (B, γ̄) and κh (B, γ̄) in the following Proposition 7 and the implications for the optimal
monitoring policy in the following Corollary 4.
Proposition 7. When the monitoring budget is limited, the threshold κl (B, γ̄) is decreasing and κh (B, γ̄) is non-increasing in B.
Corollary 4. Given the properties of κl (B, γ̄) and κh (B, γ̄), there exists a monitoring
budget
i. B = 0, for which κl (B, γ̄) = κh (B, γ̄) = 1 and only Region I exists.
ii. B ∈ (0, B γ̄ ], for which κh = 1 and κl (B, γ̄) ∈ (κ̃, 1) that separates Regions I and
II.
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
47
γ̄
iii. B ∈ (B γ̄ , B ), which separates regions as specified in Proposition 6.
γ̄
iv. B ≥ B , for which κl (B, γ̄) = κh (B, γ̄) = κ̃. Regions are separated as specified
in Proposition 5.
Proof: See the Appendix A.3
Proposition 7 and Corollary 4 have important implications for the regulator’s budget
endowment. Note that the country with the largest potential for fiscal cushioning, i.e.,
κ = 1 can always be incentivized to partially comply with the regulation. Hence,
enforcement is feasible as long as the regulator is endowed with a positive monitoring
budget. Corollary 4ii expresses the range of the monitoring budget when the thresholds
are κl (B, γ̄) < κh (B, γ̄) = 1, i.e., when Region I and II exists. This implies that auditing
countries with certainty is either not possible or not optimal. Figure 2.3b illustrates
this situation. The monitoring policy shown in Figure 2.3a, in which countries with
an especially large potential for fiscal cushioning are audited with certainty, is feasible
only if the monitoring budget is within the range defined in Corollary 4iii. The cut-off
points are κl (B, γ̄) < κh (B, γ̄) < 1. Even higher monitoring budgets allow realizing
the auditing policy established for a budget-unconstrained regulator. That is, given
a monitoring budget defined in Corollary 4iv, auditing all countries of type κ > κ̃
with certainty is feasible. Note, however, that stricter monitoring relative to the policy
proposed in Proposition 5 does not improve compliance rates, as all partially complying
countries are already audited with certainty. Hence, when the regulator’s sole objective
γ̄
is to minimize aggregate emissions, the budget endowment should never exceed B .
Similar to the analysis done in Section 2.4.1, the regulator does not refuse the participation of countries that are never subject to audits. Countries with κ ∈ [0, κl (B, γ̄)]
have only a limited potential for fiscal cushioning. That is, whereas these countries
exert the maximum effort into fiscal cushioning, offsetting the pollution abatement
incentive effect of the emission tax is always imperfect. This implies a reduction in
pollution relative to the pre-regulation discharge level. That is, from the regulator’s
perspective, broad participation is desired even when noncompliance with the intercountry regulation can never be completely disincentivized.
Furthermore, the economic efficiency is, again, undermined by the use of fiscal cushioning strategies. The equivalence of marginal benefits from emissions across countries
holds only within Region III of Proposition 6. This field, however, exists only when
the regulator’s monitoring budget is large enough.
48
2.5
2.5. Discussion
Discussion
In this section, we compare our results to those obtained in Macho-Stadler and PérezCastrillo (2006). They have analyzed the optimal monitoring policy to enforce compliance with a given emission tax, i.e., when firms can over-pollute and evade the
environmental tax. By contrast, we analyze the optimal monitoring policy to enforce
the level of the tax rate itself, i.e., when countries can offset the emission tax and
misreport the corresponding emission level. We refer to this risk as fiscal cushioning.
Reducing levies which indirectly price the respective pollution, tax exemptions for exporting firms or subsidies for pollution intensive industries come into consideration for
fiscal policy adjustments. Such measures cause a decrease in the actual price per unit
of pollution. This inevitably leads, as indicated in the above analysis, to an increase in
emissions. In the following, we will discuss similarities and differences in the optimal
monitoring policy to enforce the level of the tax, respectively, to enforce compliance
with a given tax rate.
In a first scenario, we analyzed the regulator’s optimal auditing strategy when
countries solely differ along the probability of detection. We find that the regulator
discriminates among countries according to their verifiability. A higher monitoring
pressure is imposed on countries whose fiscal cushioning strategies are easy-to-detect.
This might appear counterintuitive at a first glance, as a higher monitoring priority
is given to countries with little chance for noncompliance, i.e., to those with a high
verifiability. By contrast, countries with a great chance for noncompliance are audited less regularly, if at all. This counterintuitive monitoring policy is similar to the
strategy pursued to enforce compliance with a given tax rate in Macho-Stadler and
Pérez-Castrillo (2006). In this setting, the regulator audits first those firms for which
over-pollution is easy-to-detect. Hence, the main characteristics of the monitoring
strategies do not significantly differ from enforcing a specific level of the emission tax
to enforcing compliance with a given tax rate.
However, the optimal monitoring policy in Macho-Stadler and Pérez-Castrillo (2006)
differs from the one characterized in our approach because the countries’ offsetting
potential is assumed to be limited. This assumption implies that emissions under fiscal
cushioning are bounded from above, which puts a cap on the sanction for noncompliance. Hence, even when audited with certainty, countries can be incentivized to
(partially) comply only when the probability of detection is high enough. That is, the
optimal monitoring policy features a ’jump’ at the level of the probability of detection
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
49
of the marginal audited country. This discontinuity in the optimal auditing strategy,
which does not exist in Macho-Stadler and Pérez-Castrillo (2006), has important implications for the enforcement of inter-country tax regulations. First, countries with a
low degree of verifiability are, irrespective of the regulator’s budget endowment, never
subject to audits. Second, when the monitoring budget is too low, feasible monitoring
pressures are insufficient to create compliance incentives for any country. In this case,
no country can be incentivized to at least partially comply with the regulation and
there is no enforcement at all.
The second scenario considered the case in which countries are assumed to differ
solely in the potential for fiscal cushioning. In this scenario, the optimal monitoring
policy features again a jump in the optimal monitoring policy. The rationale is as
follows. As explained above, a limited offsetting potential puts a cap on pollution
discharges and, hence, on the sanction for noncompliance. That is, a change in the
countries’ compliance behavior can only be incentivized if the potential for fiscal policy
adjustments, i.e., the corresponding sanction, is large enough. If the offsetting potential
is too low, countries can, even when audited with certainty, never be incentivized to
comply with the regulation. Hence, the optimal monitoring policy features a jump at
the level of the potential for fiscal cushioning that characterizes the marginal audited
country.
Interestingly, the counterintuitive monitoring policies, which have been established
in the first scenario and in Macho-Stadler and Pérez-Castrillo (2006), do not apply in
this case. Indeed, the optimal monitoring strategy is characterized by a discrimination
of countries according to the potential for offsetting the environmental tax. Yet, the
regulator’s strategy is to target first those countries that have a larger potential for
fiscal cushioning. Countries with a limited potential for noncompliance are audited less
regularly, if at all. Hence, a higher auditing pressure is imposed on countries that have
the largest opportunities for noncompliance. Countries with little opportunities for
noncompliance are monitored less regularly. This alteration of the regulator’s auditing
strategy is of particular importance, as the offsetting potential represents, in fact, a
distinctive feature of fiscal cushioning.
50
2.6
2.6. Conclusion
Conclusion
In the present chapter, we analyze the enforcement of inter-country environmental
taxes with respect to fiscal cushioning. As the actual level and the price of emissions
are imperfectly observable, countries can offset the pollution abatement incentive effect
of the inter-country emission tax and misrepresent the corresponding emission level.
Such strategies improve the international competitiveness of the domestic industry;
however, they also compromise the environmental integrity of the regulation.
In order to determine a country’s compliance decision and the regulator’s optimal monitoring policy, we extend the model presented in Macho-Stadler and Pérez-Castrillo
(2006). Countries are assumed to differ in the probability of detection and in the
potential to undermine the international emission tax. We show that the limited verifiability, respectively the limitation in the offsetting of the pollution abatement incentive
effect, puts an upper ceiling on the expected sanction for noncompliance. That is, deterrence against fiscal cushioning is always incomplete and the regulator cannot achieve
the first-best outcome of full compliance. This is the case even when the regulator has
unrestricted access to monitoring resources.
Of course, enforcement is more difficult when the regulator is budget-constrained. In
this case, the regulator audits first those countries for which the expected reduction in
emissions per audit is the highest. That is, similar to Macho-Stadler and Pérez-Castrillo
(2006), we can show that the regulator focuses its monitoring on countries with high
probabilities of detection. When countries differ in the potential to undermine the
actual tax rate, the regulator targets first those countries that have a large potential
for fiscal cushioning. Countries with low probabilities of detection, respectively a very
limited offsetting potential, are never subject to audits. Creating compliance incentives for these countries is either not possible or not optimal given the constraint on
the monitoring budget. That is, the deterrence against fiscal cushioning differs across
countries. This implies that countries levy different tax rates on the same pollutant.
Fiscal cushioning strategies therefore not only undermine the environmental integrity,
but also the economic efficiency of emission taxes.
Note that the regulator should not refuse the participation of countries, which are never
subject to audits. With a limited potential for fiscal cushioning, countries cannot perfectly offset the pollution abatement incentive effect. That is, the regulation creates
emission reductions irrespectively of the countries’ compliance decision. The regulator,
2. Fiscal Cushioning and the Optimal Enforcement of Inter-Country
Environmental Taxes
51
hence, desires broad participation, even though noncompliance with the regime can
never be completely disincentivized.
The analysis of the characteristics of the optimal monitoring policy under fiscal
cushioning can be extended in several desirable directions. For example, the information asymmetry problem is changed when the benefit function is assumed to be the
countries’ private information. In this case, countries can report emissions honestly and
claim compliance through a misrepresentation of the actual benefit function, which is
unknown for the regulator. Moreover, the probability of detection can be expected to
be endogenously determined. In this case, the regulator would face a two-stage enforcement problem. In the first stage, the regulator chooses the investments in enforcement
mechanisms that determine the degree of verifiability. Actual monitoring takes place
in the second stage. The regulator’s task would be to optimally allocate the limited
monitoring resources between the two stages. Furthermore, our analysis stresses the
importance of the monitoring budget on the effectiveness of the auditing policy. Monitoring, however, might be financed by the countries’ tax and sanction payments, which
would allow the regulator to influence the level of the monitoring budget. This would
imply an alteration of the regulator’s objective function, as environmental, as well as
financial targets would be pursued simultaneously.
52
2.6. Conclusion
Chapter 3
Prices vs. Quantities with Fiscal
Cushioning
with M. Ohndorf 1
Resource and Energy Economics, published
3.1
Introduction
Optimal choice of instrument for inter-country environmental policies is subject to
intensive debate. While price-based regulations (e.g. emission taxes) and quantity
controls (e.g. tradable permits) are equally efficient under full information, this result no longer holds if information is considered incomplete and asymmetric. Both
of these information problems often seem to engender two opposite effects. Under
uncertainty, for many global externalities, like climate change, the relative slopes of
expected marginal costs and benefits suggest that price instruments ought to be preferred (Pizer (2002), Weitzman (1974)). On the other hand, both instruments are often
assumed to engender different information structures for the regulator. The resulting
difference in enforcement probabilities suggests a comparative advantage for quantity
1
This chapter has been published together with Dr. M. Ohndorf as an article in the Journal of
Resource and Energy Economics (34), 2012, p. 169-187. The research question for this paper was
formulated by Mr. Ohndorf and was then further developed by Mr. Ohndorf and me. My contribution
to this work was the assembly of background information to the paper, the mathematical extension
of the model presented in Montero (2002), the mathematical proofs, the numerical calculations, and
writing large parts of the paper. Mr. Ohndorf particularly supported the finalization of the paper.
54
3.1. Introduction
regimes. The most often quoted reason for weaker enforceability of price instruments
is based on the fact that with their implementation, countries are likely to retain their
fiscal sovereignty, which enables them to (partially) offset the intended tax incentive
for emission reductions. This mechanism is often referred to as fiscal cushioning (Nordhaus (2007), Wiener (1999)). While both of the above arguments are often brought
forward in the policy debate, a formal analysis of both countervailing effects has not
been attempted yet. In this chapter, we extend the analysis on ’Prices vs. Quantities’
presented in Montero (2002) to analyze the relative strength of both effects.
We find that the difference in expected welfare for both instruments can be divided
into two additively separable terms, each of which reflecting one of the above-mentioned
information problems. The relative impacts of the two effects determine optimal instrument choice. The first term reflects the impact of uncertainty in marginal abatement
costs on instrument choice, where the relative performance of both instruments is determined by the slopes of the marginal curves. The difference in enforceability is reflected
in the second term. This effect is mainly driven by institutional variables and the level
of the marginal benefit curve. This leads to the insight that solely focusing on the relative slope criterion is insufficient to judge inter-country environmental policy choice.
In contrast to most previous contributions to the debate on Prices vs. Quantities, we
show that optimal instrument choice can be affected by level effects, the enforcement
parameters, and the level of uncertainty. Furthermore, for a large enough potential for
fiscal cushioning, the second will dominate the first effect, leading to an unambiguous
welfare advantage for quantity regimes. Numerical calculations in the context of intercountry climate policies support the potential dominance of quantity-based regulations,
at least at the inter-country level.
It is quite evident that inter-country regulations are particularly prone to enforcement issues, which, in turn, affect the performance of the policy instrument chosen.
Inter-country environmental policies are stipulated within treaties between countries.
As it is the signatories who decide unanimously on the stringency of the treaty’s compliance regime, it can be reasonably assumed that deterrence from noncompliance is
incomplete. Note that such issues are likely to exist within both, price and quantity
regulations. Obviously, under both types of policy, regulated actors can misrepresent
their actual emissions and claim compliance without a de facto reduction in emissions.
Yet, with the risk of fiscal cushioning, there exists an additional enforcement problem, which is exclusively specific to inter-country price regulations. This risk is closely
related to the basic functioning of a price regime. The introduction of a tax on emissions
3. Prices vs. Quantities with Fiscal Cushioning
55
creates an incentive for polluters to reduce their emissions to a level where—ideally—
marginal abatement cost equal the per-unit tax rate. However, in a more realistic setup,
the aggregate level of abatement within a country is determined by the ’effective’ price
on emissions. This effective domestic price not only depends on the international tax
rate, but also on the stringency of national fiscal instruments that indirectly price the
respective emission, like fuel taxes or energy subsidies. Hence, while the level of the
global emission tax rate is stipulated within an international treaty, opportunistic fiscal adjustments on the country level might lead to a lower effective price per unit of
emission. This problem arises because the parties to the treaty are, in fact, sovereign
states which typically retain their fiscal sovereignty. Thus, by adjusting its fiscal policies accordingly, a country is able to reduce the abatement incentive effect in order
to reduce the emission tax burden of its domestic polluters. The effective price on
emissions could for example be reduced by lowering levies that indirectly tax emissions
(e.g. energy taxes, road charges, etc.) or by an increase in subsidies on energy-intensive
production inputs (e.g. coal subsidies). A similar effect arises if countries do not raise
these domestic taxes—or reduce these subsidies—to the same extent as they would
have in the absence of a global emission tax (Hoel (1993)). Furthermore, taxing substitutes and subsidizing complements of the regulated good would have a similar effect
on pollution abatement incentives.2 All of these domestic fiscal adjustments aim at a
reduction in the emission tax burden, which directly translates into lower abatement
levels. These practices are classified in the literature as fiscal cushioning (Nordhaus
(2007), Wiener (1999)).
Some of these fiscal adjustments only have a moderate impact on the incentive
for pollution abatement, while others could have a greater dilutive effect. In the case
of CO2 emissions, the Intergovernmental Panel on Climate Change (IPCC) estimates
that more than 25% of global emission reductions would come from the electricity and
transport sector (see Barker et al. (2007)). Hence, fiscal adjustments in these sectors
alone could reduce global abatement considerably. Combining these adjustments with
other opportunities for fiscal cushioning, e.g. in the industry sector, would evidently
further reduce the incentive for pollution abatement.
2
It is often argued that recycling revenues from an emission tax in order to reduce distortive taxes
(e.g. taxes on labor or capital) might create a double dividend (Goulder (1995)). However, such a
double dividend is unlikely to arise in the context of fiscal cushioning which refers to changes in fiscal
instruments that already price externalities. As the distortive character of such policies is rather low,
a double dividend is not to be expected in that context.
56
3.1. Introduction
Obviously, the strategies for fiscal cushioning laid out above would lead to a discrimination of effective tax rates for different classes of polluters within a country. Note
that this is quite common in national environmental regulations. There exists ample
evidence that legislative bodies discriminate environmental tax rates among polluters.
In an early analysis of OECD countries, Svendsen et al. (2001) find that industries
and especially energy-intensive sectors enjoy considerable reductions in CO2 taxes.
Lobbying activities of well-organized industry sectors successfully dilute the intended
environmental policy for the respective industry (see also Polk and Schmutzler (2005)).
Similar findings were reported in more recent studies analyzing the Green Tax Reform
in Germany and Sweden (Anger et al. (2006) and Sterner (2003)). These industry
specific tax exemptions are considered to be a crucial disadvantage of existing national
environmental tax regulations (see for example Stern (2006)).
The risk of such discriminatory fiscal adjustments seems even more imminent with
an international emission tax. Fiscal cushioning of an emission tax represents a strategy to formally comply with the treaty while de facto reducing the actual abatement
incentive—and hence cost—for selected sectors of a country. As this form of noncompliance to a treaty is difficult to detect, fiscal cushioning can be considered as an
additional problem to enforcement. Note that fiscal cushioning can only arise in the
context of price regulations, but not under quantity regulations.3 With quantity restrictions, global emissions are capped by the total amount of pollution allowances. As
this directly determines a country’s level of abatement, the required emission reduction
remains unaffected by domestic fiscal policy adjustments. Thus, fiscal cushioning occurs only with inter-country price regulations and persists irrespective of the tax being
nationally or internationally administered.
Cooper (1998) proposes the International Monetary Fund (IMF) to enforce international emission taxes and, thus, to reduce the risk of fiscal cushioning. The IMF
could gather necessary information on emission relevant domestic fiscal policies, as the
IMF already collects macroeconomic data from a majority of countries. Indeed, this
procedure is likely to lead to the detection of transparent changes in domestic fiscal
policies, e.g. in domestic fuel taxes. If this is anticipated by the countries, the negotiated environmental treaty could include directives which prohibit such forms of fiscal
3
In addition to the above-mentioned literature, Aldy et al. (2008), Cooper (1998, 2007), Eizenstat
(1998), Hoel (1991), Hovi and Holtsmark (2006), Parry (2003), Stavins (1997), Victor (2001), Wiener
(2001), Zhang and Baranzini (2004) discuss the enforcement problem of international emission taxes
due to the presence of fiscal cushioning.
3. Prices vs. Quantities with Fiscal Cushioning
57
cushioning. However, it would remain difficult to identify more sophisticated strategies of fiscal cushioning, involving for example "complex tax loopholes for expensing
of capital or technology investments" (Aldy et al. (2008), p. 27) or "less visible compensatory policies that offer loopholes for energy-intensive and export-oriented firms"
(Victor (2001), p. 86). Preventing the use of such strategies would require detailed
directives on the use of national fiscal policies. However, the setup of such directives
would imply a significant encroachment in the sovereignty of states, which is unlikely to
be acceptable to most parties of any environmental treaty (Hoel (1993)). Hence, despite
any attempts to protect inter-country price-based regulations against fiscal cushioning,
deterrence from the use of such strategies will be incomplete. Given that quantity
regulations do not suffer from the problem of fiscal cushioning, it can be reasonably
assumed that the probability of enforcement for these instruments is higher than for
price-based regimes.
The problem of fiscal cushioning establishes within the policy debate a well-founded
argument in favor of quantity regimes. Yet, the resulting difference in enforcement
probabilities has so far been neglected in formal comparisons of price and quantity
regulations. The latter often focus on the debate on Prices vs. Quantities under uncertainty, which was initiated within Weitzman (1974). In this paper, Weitzman demonstrates that the relative performance of price and quantity-based instruments may
differ in terms of welfare when marginal costs are uncertain. On this basis the relative
slope criterion can be derived, stating that price instruments ought to be preferred
over quantity regulations as long as the marginal abatement cost curve is relatively
steeper than the marginal benefit curve and vice versa. In most subsequent contributions to the debate on Prices vs. Quantities under uncertainty the relative slopes
remain the most important determinants of instrument choice (e.g. Adar and Griffin
(1976), Fishelson (1976), Hoel and Karp (2001, 2002), Newell and Pizer (2003), Quirion
(2004), Roberts and Spence (1976), Stavins (1996), Stranlund and Ben-Haim (2008),
Yohe (1977, 1978)).
Applied to the context of inter-country climate policies, the relative slope criterion
provides an argument in favor of a price instrument to regulate greenhouse gases. This
is explained by the fact that marginal benefits from pollution abatement depend on the
stock of emissions (i.e. atmospheric concentration), while marginal costs depend on the
flow of pollution. Hence, costs react much more sensitive to the level of abatement than
benefits, which renders price regulations preferable if the level of marginal abatement
cost is uncertain (Pizer (2002)). Based on the relative slope criterion it is often proposed
58
3.1. Introduction
to replace the current climate policy framework, which is mainly based on tradable
quantity restrictions, by a global emission tax on greenhouse gases (see e.g. Hepburn
(2006), McKibbin and Wilcoxen (2002), Nordhaus (2007)).
Most of the literature on Prices vs. Quantities abstracts from the fact that enforcement of policy instruments can plausibly be assumed to be imperfect. This assumption
is at the center of a different strand of literature dealing with instrument choice under incomplete enforcement (e.g. Chávez et al. (2009), Garvie and Keeler (1994),
Macho-Stadler (2008), Malik (1992), Montero (2002)).4 Yet, the only analysis introducing uncertainty and incomplete enforcement simultaneously is presented in Montero
(2002).
In order to derive a formal representation of the effects of fiscal cushioning, we extend the framework established in Montero (2002) by considering a lower enforcement
probability for price instruments than for quantity regulations. Interestingly, not only
the slopes of the marginal curves but also institutional variables, level effects and the
variance of costs affect instrument choice. In contrast to the commonly held view,
we find that the level of uncertainty in abatement cost can have a strong influence
on instrument choice. We show the existence of a threshold level of the variance of
cost below which a quantity approach is to be strictly preferred. Remarkably, in this
case, the relative slopes of the marginal curves are completely irrelevant for the choice
of instrument. In order to showcase the sensitivity of optimal instrument choice to
the above-mentioned variables, we present numerical calculations based on data taken
from the context of inter-country climate policy. Given early estimates of the level of
marginal benefits, price regulations dominate quantity controls in terms of welfare. Yet,
for more recent estimates, our results indicate that quantity-based instruments would
outperform price regulations. In this case, the estimated level of cost uncertainty is not
large enough to justify instrument choice based on the slopes of the marginal curves.
Hence, our simulations indicate that in the presence of fiscal cushioning quantity controls, at least at the inter-country level, could well be the dominant instrument for
global climate regulations.
4
The literature on incomplete enforcement is based on Becker (1968). The basic effects of incomplete enforcement and optimal policy designs under incomplete enforcement were subsequently
analyzed, e.g. Downing and Watson (1974), Harford (1978), Harrington (1988), Kaplow and Shavell
(1994), Keeler (1991), Livernois and McKenna (1999), Malik (1990), Macho-Stadler and PérezCastrillo (2006), Sandmo (2002).
3. Prices vs. Quantities with Fiscal Cushioning
59
The rest of the chapter is organized as follows: In the next section we introduce
the basic model setup. In section three, we determine the countries’ optimal compliance strategies under incomplete enforcement. The optimal policy design is derived
in section four for both instruments. The central question of instrument choice in the
presence of fiscal cushioning is discussed in section five before we present numerical calculations in the context of inter-country climate policy in section six. The last section
concludes.
3.2
Model
The model presented here extends the framework established in Montero (2002) to
include fiscal cushioning. We assume a continuum of countries of mass 1, participating
in an inter-country environmental treaty. A super-national Regulatory Authority (RA)
is mandated to implement a policy to induce a reduction in pollution discharges. The
regulation is in place over multiple periods with infinite horizon. Once implemented,
the environmental policy is irreversible due to high adjustment costs (see e.g. Roberts
and Spence (1976)). We focus on linear price (e.g. an emission tax) and quantity
instruments (e.g. tradable pollution permits). Depending on the regime, the RA levies
either a tax rate τ or distributes l tradable pollution allowances per period.5
Each single country j emits one unit of a uniform pollutant per period which can
be abated at costs cj . The countries’ individual abatement costs are assumed being
uniformly distributed over the interval cj ∈ [0, c]. The corresponding probability density function is g(c), the cumulative distribution function is G(c). Both functions are
common knowledge, while the actual abatement costs are unknown to the regulator.
The RA can hence calculate the annual expected abatement cost curve C(q). Costs
depend on the aggregated level of emission reductions q and are simply the sum of
individual abatement costs per period cj .6 The same applies for the aggregated benefit
function B(q). For the sake of comparability with the existing literature on Prices vs.
Quantities, we follow Weitzman (1974) and Montero (2002) and assume linear approx5
Note, banking/borrowing of permits over periods is not allowed in our approach. For a discussion
of prices vs. quantities vs. bankable permits, see Fell et al. (2008).
Rr
6
The abatement aggregated cost function is hence defined as C(q) = 0 cg(c)dc, with r = G−1 (q)
and C ′ (q) = r.
60
3.2. Model
imations for the marginal benefit and marginal cost curve with additive uncertainty.
The corresponding aggregated benefit and cost functions are
B(q, η) = (b + η)q +
C(q, θ) = (θ)q +
B ′′ 2
q ,
2
C ′′ 2
q ,
2
where C ′ (0) ≡ 0, C ′ (q) > 0, C ′′ > 0, B ′ (0) ≡ b, B ′ (q) > 0, B ′′ < 0, B ′ (0) > C ′ (0)
and C ′ (q) > B ′ (q) for a sufficiently large q.7 θ represents a random shock on marginal
costs, η on marginal benefits. The expected value of the stochastic terms are E[θ] = 0
and E[η] = 0, and the variance is E[θ2 ] = σθ2 and E[η 2 ] = ση2 . Cost and benefit
uncertainties are uncorrelated, i.e., E[θη] = 0.
The RA is also mandated to enforce the implemented instrument according to an
enforcement policy that is assumed to be stipulated by the participating countries
within the treaty. As emissions are not directly observable to the regulator, countries
are required to report in each period their compliance status, indicating whether the
country is in compliance or not. The RA verifies the correctness of the reports without
error via random inspections. Countries found to be in violation with the regulation
have to immediately return to compliance, pay a monetary sanction F and have to
remain compliant in the following period. Noncompliant countries return to compliance
by either reducing one unit of pollution domestically or, depending on the regime, by
paying taxes or buying permits. Note, countries agreed to the enforcement policy prior
to the RA’s choice of instrument. Hence, all countries face the same monetary sanction
F independent of the regime in place. As truthfully revealing noncompliance is not
rewarded with lower sanctions, the countries’ dominant strategy is to claim compliance,
whether this is true or not.8 Each country is hence monitored with the same constant
probability αi with i ∈ [t; q], where the subscript t refers to taxes, q to quantities.
Note, as countries either reduce exactly one unit of pollution or not, αi is independent
of the degree of noncompliance.9
Note, g(c) being a uniform distribution of cj , then g(c) = 1/c where c = C ′′ for cj ∈ [0, c]. Hence,
the linearity of the aggregated marginal cost curve simply results from the uniform distribution of cj .
8
In contrast, Livernois and McKenna (1999) impose lower fines on firms which truthfully reveal
noncompliance. Noncompliance and submission of a true report might be optimal in such a setting.
9
This assumption is solely made for the sake of simplicity. See also the comment in footnote 13.
7
3. Prices vs. Quantities with Fiscal Cushioning
61
Regulatory systems, price- and quantity-based, are prone to incomplete enforcement, reducing the effectiveness of the regulatory policy. Under the realistic assumption
of incomplete compliance, the enforcement parameters F and αi are insufficiently low
to guarantee full compliance.10 Hence, countries might have incentives to under-report
emissions and depending on the regime, to evade taxes or to hold an insufficient amount
of certificates. Moreover, potential fiscal cushioning provides additional leeway for noncompliance with inter-country price regulations. As laid out in the introduction, the
underlying information problem associated with fiscal cushioning is the unobservability
of uncooperative domestic fiscal adjustments. That is, actual discovery of noncompliance is more difficult under a price- than under a quantity-based system, as the latter
remains unaffected by domestic fiscal policy adjustments. It is hence reasonable to
reflect the risk of fiscal cushioning through a lower probability of detection of noncompliance for price instruments compared to quantity regimes. In our framework,
this is represented by assuming αt < αq , which holds throughout the remainder of this
chapter.11
3.3
Compliance strategy under incomplete enforcement
Given the above-made specifications, a price regime is characterized by the tuple
{τ, F, αt }, whereas a quantity regime is determined by {l, F, αq }. All elements of these
tuples are common knowledge. The enforcement policy, which is prenegotiated by the
parties and determined by the parameters αi and F , is exogenously given and not strict
enough to induce full compliance in either regime.12 Given the individual abatement
costs cj , countries choose compliance or noncompliance in order to minimize their expected costs of being regulated. Note, irrespective of the countries’ actual compliance
10
For simplicity, we assume that collecting penalties is costless and do not account for monitoring
costs.
11
For a more thorough discussion of the problem of fiscal cushioning as a problem of detection of
non-compliance, see for example Wiener (1999) and Victor (2001).
12
The assumption of F being exogenously given and hence beyond the regulators discretion is
quite intuitive. In international treaties, sanctioning mechanisms are negotiated by all participating
countries. Insufficiently large sanctions seem plausible, as some countries might anticipate their noncompliance and only agree on rather low sanctions. Even on the national level, monetary penalties
for noncompliance are reportedly often rather low (see Livernois and McKenna (1999)).
62
3.3. Compliance strategy under incomplete enforcement
decision, the dominant strategy is to report compliance, whether this is true or not.
Hence, countries either choose compliance and submission of a correct report or noncompliance and submission of a false report claiming compliance. As individual costs
are invariant over time, a country’s compliance decision will remain unaltered once the
regulation is in place. A date subscript can be therefore omitted.
Individual compliance behavior is determined by the marginal abatement costs cj
and the ’price’ per unit of emission x, which represents either the tax rate τ or the
permit price p(l). Countries with marginal abatement costs lower than x obviously
prefer reducing emissions rather than paying x. Given the regulation is in place over
infinite periods, individual compliance costs ZCj for a country with cj ≤ x consist of
the current and discounted abatement costs of all future periods and are hence given
by
ZCj = cj + δZCj ,
where δ is the discount factor. High cost countries with cj > x will prefer to pay the
’price’ per unit of emission. Hence, compliance cost for these countries are given by
ZC = x + δZC ,
For all countries individual discounted compliance costs are hence
ZCj =


cj
y
, with y =

1−δ

x
if cj ≤ x,
if cj > x.
(3.1)
For a country which chooses not to comply with the regulation, expected individual
costs of noncompliance ZNj are calculated as follows. If the country is not monitored,
which occurs with probability (1 − αi ), it incurs zero abatement costs and follows the
same strategy in the following periods. The associated costs are δZNj . Yet, noncompliance is revealed with probability αi . In this case, the above described enforcement
policy is applied. Countries are forced into immediate compliance which requires either
abatement of one unit of pollution at costs cj or payment of the emission ’price’ x, which
is, depending on the regime, either the tax rate or the permit price.13 These costs are
13
To keep the following analysis simple, we have assumed constant individual marginal abatement
costs. However, this is just for the sake of simplicity and comparability with Montero (2002). Our
63
3. Prices vs. Quantities with Fiscal Cushioning
reflected in the above-defined auxiliary variable y. Furthermore, countries have to pay
a monetary sanction F and are forced into compliance in the following period, which
engenders costs δy. Note, while we assume that a discovered noncompliant country will
be monitored with probability one in the next period, for all subsequent periods the
monitoring pressure returns to αi .14 The dominant strategy of a noncompliant country
is hence to return to noncompliance in the second period after being discovered. The
associated discounted costs are δ 2 ZNj . The costs for noncompliance can be generally
formulated as
ZNj = 0 + (1 − αi )δZNj + αi (y + F + δy + δ 2 ZNj )
Solving for ZNj yields the individual discounted costs for noncompliance
ZNj =


cj
αi (y + F + δy)
, with y = 
(1 − δ)(1 + αi δ)
x
if cj ≤ x,
if cj > x.
(3.2)
Given the individual expected costs of being regulated, a country’s optimal strategy
is to comply as long as the expected discounted costs for compliance are lower than for
noncompliance, i.e., ZCj ≤ ZNj . As we are interested in a certain level of noncompliance
in both regimes, we have to guarantee that ZCj > ZNj holds for at least some countries.
This requires the expected sanction for noncompliance to be lower than the ’price’ per
unit of pollution, which is the tax rate τ under a price regime or the permit price p
under the quantity instrument. More formally, we establish the following assumption
that holds throughout this analysis.
analysis could well be extended to reflect the case of non-constant individual marginal abatement
costs. Note that this would not change the qualitative results of our analysis, at least for the plausible
case of quadratic individual abatement costs.
14
Note, while αi is assumed constant in our approach, a country which was caught violating the
regulation in the previous period is monitored with probability 1 today. This, in fact, captures
the essence of state-dependent enforcement, in which the regulator clusters and monitors countries
according to their previous compliance behavior (see e.g. Harrington (1988)). As we will see in
the following sections, state-dependent enforcement improves compliance rates relative to perfectly
uniform enforcement probabilities.
64
3.3. Compliance strategy under incomplete enforcement
Assumption 1. The sanction F is lower than the sanction F which induces full compliance in either regime, i.e.,
(
(1 − αq )p (1 − αt )τ
;
F < F ≡ M in
αq
αt
)
Given assumption 1, the marginal compliant country is characterized through
c̃i =
αi
F.
1 − αi
(3.3)
Note, as assumption 1 guarantees c̃i < x, high cost countries that would prefer compliance by paying x will, in fact, never be in compliance except if detected by the regulator.
For price-based regulations, determining the set of noncompliant countries is easily
achieved by simply substituting x = τ and i = t in equations (3.1) to (3.3). Hence,
low cost countries, with 0 ≤ cj ≤ c̃t , comply through domestic pollution abatement
and submit a truthful compliance report. All other countries with higher marginal
abatement costs, i.e., c̃t < cj ≤ c, choose noncompliance and submit a false report.
For quantity-based regulations, however, it is to be taken into account that the
permit price p(l) is endogenously determined by supply and demand for pollution
allowances. Given the above-presented setup, the demand for permits is driven by the
fraction of countries whose noncompliance was detected in the previous and present
period. Note, only countries with marginal abatement costs higher than the permit
price p enter the market and purchase certificates. Following Livernois and McKenna
(1999) and Montero (2002), we determine the fraction of countries buying certificates to
return to compliance today as follows: K d countries were found violating the regulation
in period d − 1 and are forced into compliance today at date d. Hence, 1 − K d = N d
countries claim compliance at date d and are monitored with probability αq , such that
K d+1 = αq N d . Setting K d ≡ K d+1 for steady state, yields K = αq /(1 + αq ) = γq ,
the fraction of formerly noncompliant countries brought into compliance today. The
65
3. Prices vs. Quantities with Fiscal Cushioning
RA then auctions off l pollution allowances fulfilling the following market clearing
condition15
l = γq
c+θ
Z
g(c − θ)dc + αq (1 − γq )
p
c+θ
Z
g(c − θ)dc = 2γq
p
c+θ
Z
g(c − θ)dc.
(3.4)
p
Demand for allowances is hence determined by the formerly noncompliant countries
forced to comply today as well as the fraction of the remaining countries (1 − γq )
that are discovered with probability αq today and immediately forced into compliance.
Given that g(c) is assumed to reflect a uniform distribution of cj , the corresponding
market price is then16
p(l, θ) = c + θ −
l ′′
C = p(l) + θ
2γq
(3.5)
where p(l) ≡ E[p(l, θ)].
Given this market price, determining the set of noncompliant countries is analogous
to the price-based regime. We substitute x = p(l) and i = q in equations (3.1) to
(3.3). Hence, under a quantity instrument, low cost countries with 0 ≤ cj ≤ c̃q will
be in compliance with domestic pollution abatement and submit a truthful compliance
report. Countries with higher marginal abatement costs with c̃q < cj ≤ c always choose
noncompliance, and submit a false compliance report.
Obviously, with fiscal cushioning, the countries’ compliance behavior differs from
price- to quantity-based regulations. For αq > αt , more countries comply under a
quantity regime than under a price-based instrument, as this leads to c̃t < c̃q .
15
Note, grandfathering is identical to auctioning. Under grandfathering, the market clearing condition changes to
l
Z
p
g(c − θ)dc + (1 − 2γq )l
θ
Z
p
c+θ
g(c − θ)dc = 2γq (1 − l)
Z
c+θ
g(c − θ)dc,
p
which is identical to (3.4).
From (3.4), the expected permit price is given by p = G−1 1 − 2γl q , where G−1 (·) can be interpreted as the marginal abatement cost when (1 − l/(2γq )) emissions have been abated. Considering
footnote 7 yields equation (3.5).
16
66
3.4. Optimal policy design under incomplete enforcement
3.4
Optimal policy design under incomplete enforcement
In the following, we derive the ex-ante second-best policy design for both regimes.
Under the price-based regime {τ, F, αt } and the corresponding compliance behavior,
the RA levies a tax rate τ to maximize expected social welfare
E[W (τ, θ, η)] = E[B(qt (τ, θ), η) − C(qt (τ, θ), θ)].
(3.6)
Under a quantity-based regime {l, F, αq }, the RA fixes the amount of pollution
allowances l to maximize expected social welfare
E[W (l, θ, η)] = E[B(qq (l, θ), η) − C(qq (l, θ), θ)].
(3.7)
For the enforcement parameters F and αi and the respective countries’ compliance
strategies, the abatement level and the aggregated abatement costs are determined by
qi (·, θ) =
Z
c̃i
Ci (qi , θ) =
Z
c̃i
θ
θ
g(c − θ)dc + 2γi
x
Z
cg(c − θ)dc + 2γi
g(c − θ)dc,
c̃i
Z
(3.8)
x
c̃i
cg(c − θ)dc.
where 2γi = γi +αi (1−γi ) is the fraction of former and present noncompliant countries,
being forced to comply today.17 Note, in the presence of fiscal cushioning γq > γt , as
αq > αt is assumed.
For g(c) being a uniform distribution of cj equation (3.8) reduces, under a price
based regulation, to
2γt τ + γt F − θ
.
(3.9)
qt (τ, θ) =
C ′′
For a quantity instrument, (3.8) simplifies to
qq (l, θ) =
2γq p(l) + γq F − (1 − 2γq )θ
.
C ′′
(3.10)
With incomplete enforcement, pollution abatement is uncertain under a quantity
regime and adapts to possible cost shocks. The reason for this is the multiplicative
17
Deriving γt is analogous to that of γq (see section 3.3).
3. Prices vs. Quantities with Fiscal Cushioning
67
interaction of θ and γq in (3.10). As argued by Montero (2002), in the presence of
simple incomplete enforcement (i.e. αi = α), this reduces a potential comparative
disadvantage of quantity instruments, as countries can choose noncompliance in case
of a realization of high abatement costs. Note, however, that for identical enforcement
probabilities, the expected values of qt (τ ∗ ) and qq (l∗ ) are the same. Yet, with the hereassumed fiscal cushioning an additional effect arises. Because c̃t < c̃q and γt < γq , it is
immediate that the expected abatement level differs between the two regimes. For the
optimal values τ ∗ , p∗ and l∗ derived from maximizing (3.6) and (3.7), we can establish
the following proposition.
Proposition 1. qt (τ ∗ ) < qq (l∗ ) < qf (·)
With fiscal cushioning, the expected optimal abatement level under a quantity-based
regulation qq (l∗ ) is higher than under a price-based regulation qt (τ ∗ ). Both of these
abatement levels are lower than the optimal expected abatement level under full enforcement qf (·). Furthermore, ∂qq (p)/∂p > ∂qt (τ )/∂τ .
Proof: See the Appendix B.1
Proposition 1 highlights the effects of different enforcement issues in inter-country
regulations. Modifications of domestic tax policies only reduce the effectiveness of intercountry price regulations, while quantity-based regulations are unaffected by domestic
tax adjustments. As laid out in the introduction, the main argument with respect to
fiscal cushioning is that unobservable fiscal adjustments hamper policy enforcement.
This directly translates into higher aggregated emissions under a price- relative to
a quantity-based regulation. The above-made proposition reflects exactly this issue.
Hence, our assumption on different enforcement probabilities for price- and quantitybased instruments (αt < αq ) does indeed capture the essence of the problem of fiscal
cushioning. As we will see below, this allows us to discuss the effects of fiscal cushioning
within the standard framework used in the prominent debate on Prices vs. Quantities.
3.5
Instrument choice
With the above-established results we can now turn to the welfare comparison between
both instruments. Following Weitzman (1974) and Montero (2002), the expected difference in social welfare of prices over quantities can be expressed as
∆pq = E{[B(qt (τ, θ), η) − B(qq (l, θ), η)] − [C(qt (τ, θ), θ) − C(qq (l, θ), θ)]}
(3.11)
68
3.5. Instrument choice
Note that for stricter enforcement of the quantity regime it follows from proposition 1
that both square brackets are unambiguously negative, which is in line with Weitzman
(1974). Just as in the latter, price-based regulations are preferable if ∆pq > 0, while a
quantity regime should be chosen if ∆pq takes negative values.
In order to simplify notation of what follows, we define β ∈ R+ as the relative
slopes of the marginal benefit relative to the marginal cost curve, i.e., β = −B ′′ /C ′′ .
Both curves have the same slope in absolute value if β = 1. The marginal cost curve
is relatively steeper than the marginal benefit curve if β < 1, and vice versa. The
difference in social welfare of prices over quantities is then derived by substituting
qt (τ ∗ , θ), and qq (l∗ , θ) into (3.11). Taking expectations yields
∆pq =
2(1 − 2β(1 − γq ))γq σθ2
+
2C ′′
!
(2b + F )2
F2
(γq − γt )
−
4C ′′
(1 − 2γq )(1 − 2γt ) (1 + 2βγq )(1 + 2βγt )
(3.12)
The welfare difference is hence determined through two additively separable effects.
Note first, from equation (3.12) we can deduce Weitzman’s result by assuming perfect
policy enforcement. Choosing αi = α = 1, i.e., γi = 1/2, reproduces the classic relative
slope criterion established in Weitzman (1974). In this case, the relative slopes of
the marginal curves solely determine optimal instrument choice. Quantity regulations
ought to be preferred as long as β > 1.
Second, under incomplete enforcement, ∆pq reduces to a result which is similar
to what is presented in Montero (2002) if both policies are equally enforceable, i.e.,
αi = α < 1 and hence γi = γ.18 In this case, ∆pq is entirely determined by the
first additive term in (3.12), as the second term is zero. As Montero (2002) laid out,
the corresponding welfare difference diverges from the result presented in Weitzman
(1974), because incomplete enforcement entails a comparative advantage of quantity
regimes over price regulations. This advantage is due to the fact that noncompliance
might minimize expected costs from being regulated when permit prices, due to a
positive cost shock, are unexpectedly high. Quantity regulations hence resemble a
non-linear instrument as described in Roberts and Spence (1976). As a consequence,
18
Note, the difference to the result presented in Montero (2002) is a consequence of the here-assumed
stricter enforcement policy. Using the same enforcement policy in our approach would then reproduce
exactly Montero’s result.
3. Prices vs. Quantities with Fiscal Cushioning
69
incomplete enforcement reduces the disadvantages of a regime that fixes quantities at a
specific level without considering the corresponding costs. Formally, this is due to the
multiplicative interaction of γq and θ as specified in (3.10). The welfare consequences
are two-fold: The benefit advantage of a quantity compared to a price regime reduces
to 2(1−γq )γq . Yet, the cost advantage of prices reduces to γq , resulting in an advantage
of quantity- over price-based regulation because 2(1 − γq )γq > γq .
Obviously, under fiscal cushioning, where γq > γt , this comparative advantage of
quantity regulations persists and is reflected in the first additive effect in (3.12). From
the rationale presented above it is straightforward that this effect entirely depends on
the countries’ flexibility of choosing compliance or noncompliance under the quantity
regime. Hence, the first additive term is dependent on the enforcement probability
under the quantity regime reflected in γq , but is independent of γt . Obviously, the
1
. Note, the variance
effect is negative and in favor of a quantity approach if β > 2(1−γ
q)
of costs appears only in the first effect. Due to this reason we refer to the first term in
(3.12) as uncertainty effect.
The second term in equation (3.12) is characteristic for the here-assumed fiscal
cushioning. As this term is only different from zero if both policy instruments are not
equally enforceable, we will refer to it as the differentiated enforceability effect. This
effect reflects the net gain in social welfare from implementing the policy instrument
with stricter enforcement. The corresponding difference in welfare results from different abatement levels. Under fiscal cushioning, pollution abatement is higher under
quantity- than under price-based regulations. As follows from proposition 1, abatement under the quantity instrument is closer to the ex ante optimal abatement level,
which implies an advantage in terms of welfare for this instrument.19 The sign of this
differentiated enforceability effect is therefore unambiguously negative, as is shown in
the mathematical appendix. We summarize these insights in the following proposition.
Proposition 2. In the presence of incomplete enforcement with fiscal cushioning, i.e.,
αq > αt , the set of situations where a quantity instrument is to be preferred is strictly
larger than for full enforcement and for incomplete enforcement with equal enforcement
probabilities.
Proof: See the Appendix B.2
19
Note that all the potential disadvantages of quantity instruments under uncertainty are reflected
in the first term of equation (3.12).
70
3.5. Instrument choice
The separability of the two effects in equation (3.12) provides a basis for further
interesting insights. As stated in proposition 2, under fiscal cushioning quantity instruments could be preferable even if β < 1/(2(1 − γq )), i.e., for values of the relative
slopes where the uncertainty effect is favorable to price regulations. It is hence useful
to identify the conditions under which the differentiated enforceability effect dominates
the altered relative slope criterion reflected in the first term of equation (3.12). This
is particularly interesting, as the differentiated enforceability effect is co-determined
by institutional variables: the enforcement probabilities and the sanction for noncompliance. This establishes a case for extending the debate on Prices vs. Quantities by
taking the institutional context into account.
As suggested by its name, the size of the uncertainty effect is co-determined by
the variance of the marginal abatement costs σθ2 .20 Note that the initial argument
developed by Weitzman (1974) builds upon the existence of such cost uncertainty. Yet,
as this uncertainty does not enter into the differentiated enforceability effect, the latter
might well outweigh the forces that are underlying to the relative slope criterion. Given
these considerations, we can establish the following proposition.
Proposition 3. For αq > αt , quantity-based regulation ought to be strictly preferred
as regulatory instrument if
σθ2 < σ 2θ ,
where
σ 2θ
(γq − γt )
=
4γq
(2b + F )2 (1 − γq )2
F2
.
−
1 − γq + γt
1 − 2γq − 2γt + 4γq γt
!
(3.13)
Proof: See the Appendix B.3
This proposition states a condition under which the differentiated enforceability
effect entirely outweighs the uncertainty effect, for any given level of the relative slopes
β. This result has important implications for the debate on Prices vs. Quantities.
First and most obviously, note that proposition 3 significantly qualifies the general
insight from the literature that the variance of costs is irrelevant for instrument choice.
Under fiscal cushioning, the level of uncertainty can be decisive for instrument choice.
20
An additional negative term enters into (3.12) if uncertainties are positively correlated, i.e., if
E[θη] > 0. For an analysis of Prices vs. Quantities under correlated uncertainties, see Stavins (1996).
Furthermore, if every country had its own cost schedule, the advantage of quantity-based instrument
would further increase if actual abatement costs are negatively correlated across countries. See Yohe
(1977) on this issue.
3. Prices vs. Quantities with Fiscal Cushioning
71
A second important qualification is to be made with respect to the relative slope
criterion itself. To see this, note that proposition 3 is valid for all possible levels of the
relative slopes β. Hence, our results suggest that at the inter-country level where fiscal
cushioning can be plausibly assumed, an a priori choice of policy instrument based on
a relative slope criterion alone might well yield inefficient results.21 Instead, further
variables need to be considered.
Most obviously from (3.13), it is the level of the marginal benefit curve b that can
become an important determinant of policy choice. The reason for this is that an
increase in b strengthens the differentiated enforceability effect. A higher level of the
marginal benefit curve increases both, the optimal tax rate and the optimal permit
price. This leads to an increase in pollution abatement, defined by (3.9) and (3.10).
Yet, as proposition 1 states, the increase in pollution abatement under a quantity-based
regulation is greater than under a price approach. Obviously, this decreases the relative
performance of price-based instruments relative to quantity regulations. Hence, again
deviating from the general insights of the literature, our results suggest that the level
of the marginal benefit curve b can be, at least at the inter-country level, an important
determinant of rational instrument choice.
One of the most important general insights from proposition 3 is related to the
role of the institutionally determined variables αi and F . First, the threshold level σ 2θ
unambiguously decreases with αt . A decline in the enforcement probability of prices
relative to quantities, increases the difference between the optimal emission prices x,
as well as between the corresponding abatement levels (see mathematical Appendix).
This strengthens the differentiated enforceability effect and decreases the performance
of price compared to quantity regulations. This reflects the often-made assertion that
weaker enforcement may render such instruments inappropriate for pollution control
at the inter-country level.
Second, the effect of the enforcement probability for quantity controls αq on σ 2θ is
ambiguous as two countervailing effects exist. The reason for this is that a variation of
αq affects the differentiated enforceability and the uncertainty effect. First and analogous to a decrease in αt , the differentiated enforceability effect is strengthened with a
rise in the enforcement probability for quantity-based instruments. This improves the
21
In a different setup, Wu and Babcock (2001) show that the variance of costs might also affect
optimal instrument choice. Yet, in contrast to our findings, the slopes of the marginal curves remain
crucial parameters for instrument choice in their approach.
72
3.6. Numerical Simulations
relative performance of quantities over prices. On the other hand, stricter enforcement
of quantity-based instruments increases the uncertainty effect. As already discussed
above, an increase in αq reduces the flexibility under quantity-based regulations. Less
countries choose noncompliance if the probability of detection increases. Obviously,
this reduces the comparative advantage of quantities over prices. The first effect dominates the latter for low levels of αq , which leads to an increase in σ 2θ . Yet, the opposite
is true for high αq -values. Hence, the loss of flexibility under a quantity regime, due to
stricter enforcement, may reduce the comparative advantage of such instruments.
Interestingly, the effect of F on the differentiated enforceability effect and, hence
on the threshold level σ 2θ is ambiguous. The underlying rationale is as follows. An
increase in the sanction for noncompliance leads to a larger increase in compliance
under a quantity regime, which by itself increases benefits from pollution abatement.
However, an increase in F also increases abatement costs, as less countries choose
noncompliance in case of a positive cost shock. For low levels of the sanction, the
benefits from improved compliance outweigh the disadvantage of increased abatement
costs. Hence, the threshold value of the variance of costs below which a quantity
regime ought to be always preferred increases. Yet, for high F -values, the latter effect
dominates the former, which leads to a reduction in σ 2θ .
3.6
Numerical Simulations
In order to provide further insights into the effects of fiscal cushioning, it is useful to
discuss the above-established results in the context of an actual global policy problem. In the following, we present the results of some numerical simulations based on
data provided in the context of inter-country climate policy. For this specific policy
area, the conventional opinion is that price-based regulations dominate quantity-based
instruments to control greenhouse gas emissions (see e.g. Hoel and Karp (2002) and
Newell and Pizer (2003)). It is surely an insightful exercise whether this stance is still
valid when fiscal cushioning is taken into account. Quite evidently, our model is meant
to only conceptually identify the effects of fiscal cushioning in the context of policy
choice. The results presented below would have to be interpreted with care when it
comes to derive actual implications for real-world policies. Nevertheless, our results
are suitable to provide a notion of the strength of the countervailing effects discussed
above.
3. Prices vs. Quantities with Fiscal Cushioning
73
For our simulation we use data presented in Newell and Pizer (2003), to determine
levels of C ′′ , B ′′ , σθ2 , and b (see table 3.1). Note, in the case of regulating CO2 emissions,
our assumption C ′ (0) = 0 is quite realistic. The intercept of the marginal abatement
cost curve for greenhouse gases presented by Enkvist et al. (2007) lies even below 0. For
the enforcement probability of the quantity regime, we choose somewhat optimistically
αq = 0.8. Yet, given this fixed level of the enforcement probability, we need to make
sure that our plausible assumption of incomplete enforcement is satisfied. Hence, in
order to mark out parameter F , we proceed as follows. The parameter F is expressed
as a share κ ∈]0, 1[ of the sanction F , the latter being defined as the lowest sanction
which induces full compliance in at least one regime. This is to ensure that assumption
q)
, is fulfilled. Note that F is dependent on the relative slopes β.
1, i.e., F < F = b(1−2γ
γq (1+β)
As laid out above, the range of β for which fiscal cushioning might influence instrument
1
. In order to determine the smallest possible level of the
choice lies between 0 and 2(1−γ
q)
full enforcement sanction F , we only have to take the upper boundary of this interval
into account. Given b = 9$/t and αq = 0.8, this approach yields a full enforcement
sanction of F ≈ 1.18$/t. The sanction F to be applied is then equal to κF . For our
purposes we choose, again quite optimistically, κ = 0.8, which yields F ≈ 0.95$/t.
Our choice of the level of the sanction F deserves some further motivation. As mentioned previously, penalty schemes are determined through political negotiations. Our
parameter κ can hence be interpreted as an indicator for the countries’ ex ante determination to comply with the regulation. High values of κ indicate a high commitment
to compliance and vice versa. In order to get a notion of the level of sanctions that
seems to be acceptable to countries in the real world, we revert to the Kyoto Protocol,
which is the only inter-country regime on greenhouse gases currently in place. If the
provisions of the Kyoto Compliance Regime are taken as a general proxy for an acceptable sanction for noncompliance, then parameter F would be the expected amount of
0.3 times the expected per unit price of an allowance in the second commitment period
of the Protocol (UNFCCC (2006)). The here assumed sanction amounts to roughly
20% of the permit price, which seems hence quite realistic. Table 3.1 gives an overview
of the parameter values used for our numerical calculations.
Figure 3.1 depicts the levels of ∆pq according to different specifications in relation
to the relative slopes β for the parameter values defined above. Just as before, pricebased regulations ought to be preferred for positive values of ∆pq , while quantity-based
instruments should be chosen for negative values. The two lower curves illustrate ∆pq
in the presence of fiscal cushioning, as specified in (3.12). The two functions differ
74
3.6. Numerical Simulations
Table 3.1: Parameter values
Parameter
Slope of marginal costs (C ′′ )
Slope of marginal benefits (B ′′ )
Cost uncertainty (σθ )
b
Sanction (F)
Enforcement probability of Quantities(αq )
Value
1.6 ∗ 10−7 $/t2
−8.7 ∗ 10−13 $/t2
13$/t
9$/t
0.95$/t
0.8
$/t refers to 1998 US $ per tonne of carbon
in their assumptions on the enforcement probability of price-based regulations, where
αt = 0.6 is assumed in the upper black curve and αt = 0.3 in the lower light gray curve.
The two upper lines serve as a benchmark for the effects of incomplete enforcement
with fiscal cushioning. We depict the results for equal enforcement probabilities, i.e.,
αi = α = 0.8, in the dashed curve. The dotted line depicts the specification of ∆pq
under full compliance (i.e. αi = 1), which corresponds to the standard relative slope
criterion derived in Weitzman (1974).
Obviously, fiscal cushioning can have a significant effect on optimal instrument
choice as both curves are located below the dashed curve, which implies a larger set
of situations where quantities are preferable. A comparison of both curves based on
(3.12) highlights the above-discussed increase in the differentiated enforceability effect
if the difference between both enforcement probabilities increases.
These results indicate that incomplete enforcement in general and in the presence
of fiscal cushioning in particular can potentially alter optimal instrument choice significantly. To see this, note that the curve corresponding to the result derived by
Weitzman (1974) crosses the axis of abscissae at exactly 1, where the marginal benefit
and cost functions have the same relative slopes. However, in the special case of regulating greenhouse gas emissions, the expected slopes of the marginal curves derived
by Newell and Pizer (2003) correspond to β ≈ 5.4 ∗ 10−6 , for which the depicted levels
of ∆pq would remain positive. Hence, for the data listed in Table 3.1, fiscal cushioning
would not alter the often-expressed policy recommendation of using a price instrument
to control greenhouse gases.
Yet, the example of climate change lends itself to highlight another interesting
feature of our model results. As discussed above, the size of the differentiated enforceability effect is dependent on the level of the marginal benefit curve b. In the context
3. Prices vs. Quantities with Fiscal Cushioning
75
Figure 3.1: ∆pq dependent on β for b = 9$/t
of climate change, the value of this parameter is subject to dispute in the literature.
In the simulation presented above we used the estimate by Newell and Pizer (2003) of
b = 9$/t. More recent studies, however, report much higher estimates for the marginal
benefits. Downing et al. (2005) states that it is very likely that marginal benefits exceed
50$/t. Choosing a higher level of the marginal benefits is also consistent with Tol (2005)
evaluating 103 estimates from 28 publications to form a probability density function.
Taking estimates only from peer-reviewed studies yielded a mean of 50$/t. However,
Tol concludes that marginal benefits might be considerably smaller than 50$/t. More
recently, Tol (2008) reported an estimated mode of 35$/t for marginal benefits.22
In order to showcase the importance of such higher estimates for optimal instrument
choice under fiscal cushioning, we calculate ∆pq for b = 35$/t.23 Figure 3.2 illustrates
the results of ∆pq for this value. All other parameter values are left unchanged. As
before, we assume αt = 0.6 in the black and αt = 0.3 in the light gray curve. The simple
22
Yohe et al. (2007) give a good overview on recent estimates on the marginal benefits from reducing
greenhouse gas emissions.
23
Estimates of marginal benefits mentioned above refer to near future marginal benefits. The initial
marginal benefits, i.e., the intercept of the marginal benefit curve, can hence be expected to be even
higher.
76
3.7. Conclusion
Figure 3.2: ∆pq dependent on β for b = 35$/t
incomplete enforcement result is again depicted as the dashed curve, the complete
compliance case in the dotted curve. The latter two remain obviously unaltered, as b
does not enter into the corresponding specification of ∆pq . However, the curves which
represent fiscal cushioning now always remain in the negative domain, even for β → 0.
This implies that for these situations quantity-based regulation are always preferable,
irrespective of the relative slopes of the marginal curves. Hence, a comparison of figures
3.1 and 3.2 showcases the sensitivity of the differentiated enforceability effect to the
level of marginal benefits b. Obviously, in the case depicted in Figure 3.2, this effect
is large enough to completely outweigh the uncertainty effect. In this specific case the
assumed level of uncertainty is lower than the threshold value σ 2θ , such that the relative
slopes become completely irrelevant for optimal instrument choice.
3.7
Conclusion
This chapter aims at comparing linear price- and quantity-based regulations, implemented to internalize international externalities, such as climate change. Policy instruments can be either ranked according to the relative slopes of the marginal curves
associated with the specific externality (Weitzman (1974)) and/or according to the
3. Prices vs. Quantities with Fiscal Cushioning
77
degree of enforceability (Wiener (1999)). Following Montero (2002), we calculate the
expected difference in social welfare of prices over quantities under uncertain marginal
costs and benefits with fiscal cushioning, i.e., lower enforceability of price-based instruments. Our result features two additively separable effects. The first effect, to which
we refer as uncertainty effect, results from the uncertainty in abatement costs. In line
with Montero (2002), we find a comparative advantage of quantity- over price-based
instruments under incomplete enforcement. In this first effect the relative slopes of
the marginal curves co-determine whether price or quantity regulations perform relatively better. However, the second differentiated enforceability effect unambiguously
favors quantity-based instruments. This term measures the gain in net social welfare
from implementing the policy instrument associated with stricter enforcement, i.e.,
quantity-based regulations. In the presence of fiscal cushioning, instrument choice is
determined by the relative impacts of these two effects. In contradiction to most previous contributions to the Prices vs. Quantities debate, enforcement policies, the level
of the marginal benefit curve, and the variance of costs affect instrument choice. We
show the existence of a threshold level of the variance of costs, below which a quantitybased instrument is to be strictly preferred. Hence, the relative slope criterion, which
is commonly brought forward in the discussion on Prices vs. Quantities so far, might
become completely irrelevant for the choice of instrument.
In order to give a better notion of the impacts of the two effects, we present numerical calculations based on data in the context of inter-country climate change policy.
A commonly held view is that price regulations are to be preferred for controlling
greenhouse gas emissions. We show, in the presence of fiscal cushioning, this cannot
be generally confirmed. Our calculations reveal a high sensitivity of instrument choice
with respect to the level of the marginal benefit curve, which is subject to dispute in
the literature. For low marginal benefits, price-based instruments still ought to be preferred to control climate change. Yet, for more recent estimates of marginal benefits,
the case might arise where the relative slopes become irrelevant for instrument choice.
Hence, our simulations reveal that quantities, at least on the inter-country level, might
well be the best policy instrument to control for global greenhouse gas emissions.
78
3.7. Conclusion
Chapter 4
To Cap or Not to Cap: An
Assessment of Critiques of
Inter-Country Cap-and-Trade
Climate Policies
4.1
Introduction
The optimal choice of instrument to tackle anthropogenic climate change at the intercountry level has been thoroughly discussed. Given that costs for abating carbon
dioxide emissions differ widely across the globe, market-based instruments have a considerable cost-advantage over command-and-control policies. Market-based regulations
are divided into price (carbon tax) and quantity (cap-and-trade) instruments. The latter approach is in effect under the Kyoto Protocol, the current inter-country climate
change mitigation policy. The post-2020 climate policy will also most likely be based
on a quantity approach. Yet, considering its underlying regulatory approach, the Kyoto Protocol is heavily criticized as being a flawed concept. In lieu thereof, several
economists propose the use of a system of Harmonized Carbon Taxes. The most often
quoted reasons in favor of a price approach are the broad country participation under
the tax regime, the revenue-raising potential, the treatment of uncertainty, and the
incentives to invest in climate-friendly technologies (see e.g. Nordhaus (2007), Aldy
et al. (2008), Cooper (2010)). These issues are addressed in the present chapter. We
80
4.1. Introduction
analyze whether these assertions hold to scrutiny, and hence whether an inter-country
price regulation ought to be preferred for tackling anthropogenic climate change.
This chapter focuses on the choice of instrument to mitigate global climate change
at the inter-country level, in which the regulated parties are sovereign countries.1 Ideally, a climate agreement should include all countries, since climate change is a global
negative externality. Carbon emissions cause an increase in average surface temperature irrespective of where greenhouse gas (GHG) emissions occur. Thus, a climate
change mitigation policy should be implemented globally, so that all pollution sources
around the globe are covered (see e.g. Wiener (2007)). Moreover, to achieve a desired
emission level at minimum costs, marginal abatement costs have to be equalized across
the globe. In theory, both a system of globally Harmonized Carbon Taxes and a global
cap-and-trade instrument meet this requirement.
Under a global cap-and-trade regulation, the countries’ emissions are capped by the
amount of pollution permits. Carbon allowances are tradable among countries, which
establishes a uniform carbon price across the globe. In a competitive market, countries
aim to reduce emissions domestically, as long as carbon abatement is less expensive
than purchasing certificates from other countries. Thus, abatement activities are efficiently allocated across the globe, that is, a desired emission level is achieved at the
lowest possible costs. It is worth noting that countries are free to choose the domestic
policy to meet their national emission targets.2 In this work, however, we omit from
discussing which regulatory approach ought to be preferred at the domestic level and
concentrate solely on the optimal choice of instrument at the inter-country level.
Under a system of Harmonized Carbon Taxes, countries would commit to domestically penalizing carbon emissions. In theory, profit-maximizing polluters within the
countries chose an abatement level such that their marginal abatement costs equal the
tax rate. If the carbon tax were harmonized across countries, the price of emissions
would be equalized among all pollution sources. Thus, abatement activities would be
efficiently allocated across the globe, and emission reductions would be achieved at
1
Note that we do not consider the choice of instrument to directly regulate the emitters of GHGs.
Among those regulations are domestic climate policies or the European Union Emissions Trading
System.
2
Cap-and-trade instruments are the prevalent domestic climate regulations (see OECD (2012) for
a list of currently running and planned domestic emission trading systems). Aldy et al. (2008) argue,
however, that many developing countries can be expected to lack institutional capacities to implement
and enforce a domestic cap-and-trade regulation. Carbon taxes could be administered by existing tax
institutions, which might promote the use of a domestic price approach in these countries.
4. To Cap or Not to Cap: An Assessment of Critiques of
Inter-Country Cap-and-Trade Climate Policies
81
minimum costs.3 The fact that all pollution sources would automatically face the same
price per unit of carbon emissions is, as indicated by Nordhaus (2007), a compelling
argument for the use of a system of Harmonized Carbon Taxes.
Depending on the regime, countries negotiate the level of the carbon tax under a price
approach, or national emission targets under a quantity regulation. In a first-best regulation, the stringency of the policy is chosen such that the global carbon price, i.e.,
the tax rate or the permit price, equals the social costs of carbon, a measure for the
economic costs imposed on the society when an additional ton of carbon is emitted. In
this case, either instrument internalizes the costs of anthropogenic climate change and
maximizes global social welfare, i.e., net benefits from carbon abatement.
While theory provides a straightforward way of restraining global carbon emissions, reality is far more complex. The Kyoto Protocol and its underlying cap-andtrade-based mechanism to limit GHG emissions is the result of more than ten years
of negotiations under the United Nations Framework Convention on Climate Change
(UNFCCC). The regulatory framework, however, is far from being comparable to the
above-described first-best quantity approach.
Under the Kyoto Protocol, Annex B countries were committed to reducing emissions
by at least 5% below 1990 levels during the first commitment period, from 2008 to
2012 (Kyoto Protocol (1997)). Carbon emissions of several countries are, however, not
covered by the agreement. This includes the U.S., which did not ratify the agreement,
and non-Annex B countries, mainly developing nations, which are a priori excluded
from mitigation actions. As a consequence, countries with legally binding abatement
commitments accounted for only one-third of the global carbon dioxide emissions.
Recently, a second commitment period of the Kyoto Protocol has been signed. The
European Union, Switzerland, Norway, Iceland, Croatia, Ukraine, Belarus, Kazakhstan
and Australia have committed to reducing emissions by around 18% below 1990 levels
until 2020 (UNFCCC (2012a)). Developing countries and several developed countries,
such as the U.S., Russia, and Canada, refused to take binding emission targets. Thus,
the agreement covers only about 14% of the global GHG emissions (European Commission (2012c)). Given that several countries did or do not participate in the first or
3
Indeed, a regime in which a carbon tax was levied on countries would grant these countries the
same flexibility in choosing the domestic climate policy (Hoel (1993)). Here, we focus on a regime
in which countries commit to implementing a carbon tax domestically, as taxing countries can be
considered politically and socially unacceptable.
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4.2. Participation in Inter-Country Climate Agreements
in the second commitment periods, the impact of the Kyoto Protocol on slowing global
climate change is considered to be only very limited.
Based on these somewhat pessimistic conclusions, the Kyoto Protocol has been
criticized for its underlying regulatory approach (see e.g. Nordhaus (2007), Aldy et al.
(2008), Cooper (2010)). A major point of criticism is the limited country participation. As indicated above, developing countries are a priori excluded from binding
commitments and several industrialized countries have refused to accept emission reduction obligations. However, an inter-country, but not globally-implemented climate
policy reduces the environmental performance and the cost efficiency of the regulation.
Moreover, the cap-and-trade approach is criticized for not raising revenues, as carbon
allowances would be grandfathered. This is claimed to increase the costs of the regulation because no revenues can be recycled to society. The cap-and-trade approach is
also expected to be disadvantageous with respect to the treatment of uncertain abatement costs, which would have undesirable welfare consequences. A final, often quoted
drawback of quantity-based regulations is the volatility of allowance prices, which is
expected to discourage investments in climate-friendly technologies.
These severe allegations raise doubts on whether the cap-and-trade approach under the
Kyoto Protocol is a viable solution for curbing carbon emissions at the inter-country
level. A system of Harmonized Carbon Taxes is claimed to be able to outperform a
quantity instrument with respect to the above-mentioned points of criticism. We discuss these assertions below. Our findings indicate, however, that none of the points
of criticism represents a valid argument to replace the currently implemented cap-andtrade-based regulation with a system of Harmonized Carbon Taxes.
In the following sections we discuss in more detail the allegations that an intercountry cap-and-trade regulation is inferior to a price approach, with respect to broad
country participation, revenue-raising measures, treatment of uncertainty, and incentives to invest in climate-friendly technologies. The last section summarizes our main
findings.
4.2
Participation in Inter-Country Climate Agreements
In the introduction, we already indicated that efficient control of carbon emissions
requires a regulation that is implemented globally. Yet, there are many reasons why
4. To Cap or Not to Cap: An Assessment of Critiques of
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83
country participation in the climate agreement is incomplete. A major problem is that
no supranational authority exists that can force countries to accept legally binding
commitments. Thus, participation can be rather expected if a country’s net benefits
from joining the agreement are positive. Moreover, the public good character of carbon
abatement allows countries to benefit from the climate agreement without incurring
the costs of participating in it. Such free riding and the potential inability to bear the
costs of carbon abatement reduce a country’s incentives to participate in the climate
agreement (see e.g. Barrett and Stavins (2003)). Thus, a globally implemented climate
policy is unlikely.
The reluctance of countries to participate in an inter-country climate agreement is
most obvious in the current climate change mitigation policy. Under the Kyoto Protocol, the world is divided into Annex B, comprising mainly developed countries, and
non-Annex B, with mainly developing ones. Annex B countries, with the exception
of the U.S., have agreed to reduce emissions by at least 5% below 1990 levels during
the first commitment period, from 2008-2012. For the second commitment period of
the Kyoto Protocol, from 2013-2020, European countries and Australia have accepted
binding commitments to reduce emissions by around 18% below 1990 levels. Several
industrialized countries that participated in the first commitment period, e.g. New
Zealand, Japan, and Russia, have not adopted binding emission targets. The same applies for the U.S., which have never ratified the Protocol, and Canada, which withdrew
from the agreement effectively in 2012 (United Nations (2011)). Moreover, developing
countries were excluded a priori from binding commitments in the first as well as in the
second commitment period of the Protocol. Thus, carbon emissions of the three largest
emitters – China, the U.S., and India – and other major emitting developing countries
are not covered by the Protocol. This reduces the impact of the climate agreement
on mitigating global climate change, and increases costs to meet the desired emission
reductions. The reason for this is that vast low-cost abatement potentials – located
mainly in developing countries – are not covered by the agreement.4
Given the limited participation in the climate agreement, the Kyoto Protocol is
far from being a first-best solution to mitigate global climate change. This politically driven and de facto implemented inter-country cap-and-trade instrument is often
4
The credit-based Clean Development Mechanism (CDM) under the Kyoto Protocol is meant
to mend these shortcomings. The CDM allows countries with emission reduction targets to cover
domestic emissions by abatement activities in unregulated countries. This should improve the cost
efficiency of the Kyoto Protocol.
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4.2. Participation in Inter-Country Climate Agreements
contrasted with the globally implemented system of Harmonized Carbon Taxes (e.g.
Nordhaus (2007) or Nordhaus (2008)). The conclusion that, in this case, a tax approach
outperforms a quantity approach is straightforward, but clearly undue.
Nevertheless, it seems worthwhile to discuss whether a system of Harmonized Carbon Taxes might in fact facilitate the implementation of a (close to) first-best climate
policy. Thus, the question arises of whether developing countries are more willing to
accept binding commitments under a price approach than under a quantity regulation,
or whether mechanisms that encourage the participation in the climate agreement are
more feasible under a tax than under a cap-and-trade instrument. Next, we discuss
these questions in more detail.
Developing Countries’ Participation
Under the Kyoto Protocol, developing countries are a priori excluded from binding
commitments, and no mechanisms exist that gradually ’forces’ countries to accept
emission reduction obligations in the future. This is subject to severe criticism, as a
solution to the climate change problem only seems feasible when developing countries
take mitigation actions. However, a regime based on Harmonized Carbon Taxes is
likely to share the same weakness.
The differentiated treatment of developed and developing countries in the current
climate agreement is based on the UNFCCC principle of ’common but differentiated
responsibilities’. The principle is justified on grounds of differences in the countries’
historical responsibility as well as capacity to address global climate change. Considerations of fairness are addressed by the concept of historical responsibility. Those
countries that have benefited most from building up GHGs in the atmosphere, and
hence account more for the current climate change, should bear most responsibility for
emission reductions. Fairness is considered a decisive factor in an inter-country climate
agreement, as countries will accept binding commitments only if they perceive to be
treated fairly (Rajamani (2000)).
The concept of differing capacities of countries to abate carbon emissions addresses
considerations of economic wealth. While industrialized countries have the technical
and economic capacity to deal with the global climate change, developing countries
first need to build up these capacities. However, economic growth – the top priority
of developing countries – is expected to slow down when mitigation actions are taken.
4. To Cap or Not to Cap: An Assessment of Critiques of
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85
Hence, according to the principle of ’common but differentiated responsibilities’, developing countries are excluded from binding emission targets.
Yet, differences in historical responsibility and capacity to address global climate change
exist, irrespective of the choice of instrument. That is to say, the effective participation of developing countries in global efforts to slow climate change will be delayed in
general. Under a system of Harmonized Carbon Taxes, as under the cap-and-tradebased regime implemented under the Kyoto Protocol, developing countries are likely
to be excluded from binding commitments. Thus, both policy alternatives, price- and
quantity-based, are likely to share the same weakness, i.e., an a priori exclusion of
developing countries from legally binding climate obligations. As a result, a first-best
price regulation, in which all countries levy a Harmonized Carbon Tax, as proposed by
Nordhaus (2007), seems unfeasible.
Unfortunately, no mechanisms exist under the Kyoto Protocol that gradually introduces binding emission targets in developing countries. This, however, is not a problem
of the principle of ’common but differentiated responsibilities’ itself, but rather of its
implementation under the UNFCCC. Industrialized countries have searched for an alternative interpretation of the principle, which would allow generous but real emission
targets for developing countries – so far with limited success. The reason here is that developing countries vehemently oppose any agreement that expects them to take legally
binding emission targets. Hence, China, India, South Africa, Brazil, and other major
emitting developing countries do not face emission reduction obligations in the second
commitment period of the Kyoto Protocol. Nevertheless, a change can be expected
for a post-2020 climate change mitigation policy. In the Durban Platform, countries
concurred to establish, until 2015, a legally binding climate agreement that shall come
into effect in 2020 and be applicable for all countries (UNFCCC (2012b)). This might
imply low, but real emission reduction obligations for developing countries, or mechanisms according to which developing countries shall gradually enter the agreement.
However, there are no reasons why an inter-country cap-and-trade system should be
inferior to a price approach in establishing mechanisms that encourage developing countries to accept binding commitments in the future.5 In fact, quantity control regulations
5
Nordhaus (2006) proposes that countries be obliged to take binding commitments when a predefined level of economic wealth, e.g. a per capita income of US$ 10,000, is reached. While such a
directive is possible under both price- and quantity-based instruments, its actual implementation is
likely to encounter considerable political resistance.
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4.2. Participation in Inter-Country Climate Agreements
can be expected to be superior to price regulations in creating participation incentives.
This argument is based on political economy considerations. Side-payments that promote broad participation in the climate agreement are more likely to occur under a
quantity- than under a price-based regime. Next, we discuss this matter in more detail.
Side-Payments to Encourage Broad Participation
The allocation of abatement costs across countries crucially affects the incentives to
participate in the climate agreement. Under the Kyoto Protocol, the burden of carbon
abatement is, according to the principle of ’common but differentiated responsibilities’,
put on industrialized countries. Yet, the allocation of abatement costs among Annex B
countries is often criticized for being arbitrary (see e.g. Nordhaus (2007)). In the first
commitment period of the Kyoto Protocol, Russia, for instance, only had to bear a
small burden of carbon abatement. The Russian Federation was granted generous carbon allowances, which could be sold to countries with stricter emission targets. Among
them is the U.S., which was expected to bear a large burden of carbon abatement. As
a consequence, however, the U.S. did not ratify the Protocol. The costs from joining
the agreement were claimed to exceed the perceived environmental benefits. Hence,
the allocation of the burden of emission reductions under the Kyoto Protocol did not
incentivize the U.S. to participate in the climate agreement. Nevertheless, we argue
that a cap-and-trade regulation is superior to a price approach for encouraging participation. The reason for this is, as discussed next, that a reallocation of the burden of
carbon abatement is more feasible in the former than in the latter approach.
The allocation of abatement costs is a determining factor for broad participation in
any inter-country climate change mitigation policy. A country with particularly high
abatement costs might refuse to take binding commitments, as net benefits from joining the agreement would be negative. In addition, some countries – mainly developing
ones – might not be able to bear the costs of emission reductions. In this sense, reallocating the burden of abatement costs via side-payments can promote broad country
participation. Financial transfers among countries may create net benefits from joining the agreement or enable countries to bear the costs of carbon abatement. Thus,
side-payments may incentivize reluctant industrialized as well as developing countries
to accept binding commitments.
Under a price approach, side-payments take the form of direct monetary transfers. Revenues of the carbon tax are directly transferred from high- to low-income countries, or
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87
from beneficiaries to losers of the regulation. In a cap-and-trade system, in contrast,
side-payments materialize indirectly. Low-income countries or losers from the regulation are granted excess emission allowances. Side-payments effectively occur, by selling
these extra permits to high-income countries or to beneficiaries of the agreement.6
The important difference here is that side-payments are, from a political economy
perspective, more feasible under a cap-and-trade regulation than under a tax agreement. The rationale is as follows: The initial allocation of carbon allowances is complex,
which limits the visibility of actual transfers and softens public resistance against this
kind of side-payment.7 In contrast, direct monetary transfers under a price regulation
are apparent. The visibility of side-payments is thus likely to encounter considerable
public resistance, which reduces the feasibility of fiscal transfers under a tax regulation
(Tirole (2008)). Consequently, broad participation incentivized by a reallocation of the
burden of emission reductions, via side-payments, is more likely under a quantity- than
under a price-based climate agreement.
The reluctance of countries to commit to inter-country tax transfers is most apparent in the context of Official Development Assistance (ODA). Here, donor countries
agreed to spend 0.7% of their aggregate gross national product, i.e., around US$ 300
billion, for the ODA (United Nations (2002)). The current volume of the ODA, however, falls far shorter than agreed, for economically- and politically-driven reasons (see
e.g. United Nations (2012)). In the context of climate change mitigation, transfer
payments necessary to incentivize the acceptance of binding commitments by the developing world would need to be even higher. According to the estimates of Jacoby
et al. (2008), developed countries would need to pay more than US$ 500 billion by 2020,
rising to more than US$ 3 trillion by 2050. Visibly transferring such a huge amount of
money, as it would be the case under a tax approach, is likely to encounter significant
6
Helm (2003) showed that social welfare is improved when losers from the regulation are incentivized to join the agreement by granting excess emission allowances. In response to the generous
permit allocation, beneficiaries from the agreement would accept stricter emission targets. The overall effect on aggregate emissions is ambiguous.
7
Note that actual side-payments might not materialize when excess certificates are not traded. For
example, countries might prohibit ex-post the use of such allowances to achieve national emissions
targets. If this could be anticipated during the negotiation process of the climate policy, side-payments
in the form of excess allowance allocations would not create participation incentives. Hence, the
agreement must include directives that prohibit discrimination between certificates depending on the
country of origin, in such way that side-payments can actually occur.
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4.3. Revenue-Raising Potential
public resistance. By contrast, from a political economy perspective, such payments
are more feasible when veiled by the allocation of carbon allowances across countries.
In conclusion, considering their reduced historical responsibility and lack of economic capacities, developing countries delay effective participation in attempts to slow
global climate change. Thus, participation in a climate agreement can realistically be
expected to be incomplete under either policy alternative, price- and quantity-based.
Yet, mechanisms that encourage developing as well as industrialized countries to accept
legally binding climate obligations are more promising under a cap-and-trade regulation than under a tax approach. The reason for this is that a quantity regulation
facilitates the reallocation of the burden of emission reductions across countries. This
can be expected to be a decisive factor for successful negotiations of a post-2020 climate
agreement, in which all countries are expected to take binding commitments. Thus,
from the point of view of broad participation in the climate change mitigation policy,
a replacement of the currently implemented cap-and-trade-based policy with a system
of Harmonized Carbon Taxes seems not recommendable.
4.3
Revenue-Raising Potential
The revenue-raising potential of a price regulation is often brought forward as an argument in favor of carbon taxes, against cap-and-trade regulations (see e.g. Cooper
(2000), Nordhaus (2007)). Here we show, however, that raising public funds is possible,
irrespective of the choice of instrument at the inter-country level.
Any climate regulation implies, apart from the costs and benefits of carbon abatement, also costs for the economy. The cost of carbon emissions, tax- or permit-pricedriven, raises the price for goods and services above efficient levels. This increases the
efficiency loss of the existing fiscal system, implying costs, i.e., a reduction in social
welfare from the climate regulation. The theory of the ’double dividend hypothesis’
refers to this effect as the tax-interaction effect (Goulder (1995)).
A price-based climate policy can counteract this welfare loss if the carbon tax is designed to be revenue-neutral. In this case, revenues from the tax are used to reduce
pre-existing distortionary taxes, levied e.g. on income, profits, and sales. Such measures reduce the inefficiency of countries’ existing fiscal systems, and can create a
so-called revenue-recycling effect. This implies that the climate policy can create social
welfare gains.
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89
A cap-and-trade regulation, by contrast, is claimed to preclude a revenue-recycling effect, as no revenues can be recycled to the society when countries receive allowances free
of charge. In fact, whether the cap-and-trade regime generates revenues depends on
the underlying allocation mechanism, i.e., auctioning vs. grandfathering of certificates.8
While auctioning carbon allowances to countries is – in theory – possible, present practices under the Kyoto Protocol and political feasibility considerations indicate that
grandfathering is the prevalent allocation mechanism under an inter-country cap-andtrade regime. Thus, no revenues would be raised that could be redistributed to society.
This would be an important drawback of a quantity regime, as the revenue-recycling
effect is expected to be substantial (Pearce (1991), Zhang and Baranzini (2004), Parry
and Williams III (2012)).9
Nevertheless, raising public funds is a design issue of domestic regulations, and not
a question of instrument choice at the inter-country level. Note that revenues, in a
system of Harmonized Carbon Taxes, are generated at the domestic level. This is also
feasible under an inter-country cap-and-trade regime. Domestic policies that assist the
country to meet the national emission target can be designed to be revenue-raising.
For example, countries could implement domestic carbon taxes or a domestic capand-trade regulation with auctioned certificates to generate public funds. Revenues
generated thereby could be used to create a revenue-recycling effect.
The revenue-raising potential of domestic policies under an inter-country cap-andtrade regulation is most apparent in the EU. The EU ETS is one of the main pillars of
the EU for achieving the emission reduction target under the Kyoto Protocol. In phase
III of the EU ETS, from 2013 onwards, at least 50% of allowances are to be auctioned.
This share is planned to consistently increase until full auctioning is carried out in
2027 (Ellerman (2007), Hood (2010), European Commission (2011)). The expected
dimension of revenues is substantial (Cooper and Grubb (2011)).
8
The economic efficiency of cap-and-trade systems remains unaffected of whether certificates are
auctioned of or grandfathered for free. Yet, either allocation mechanisms has specific merits as well
as drawbacks that have received considerable attention in the economic literature (see e.g. Goulder
and Parry (2008)).
9
The double dividend theory has been developed by Pearce (1991). An analytical model by Bovenberg and de Mooij (1994) shows that environmental regulations always come with a gross cost, i.e., the
tax interaction effect always exceeds the revenue-recycling effect. See Fullerton (1997) for a critique
on the model, and Bovenberg and de Mooij (1997)’s reply.
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4.4. Treatment of Uncertainty
Hence, independently of the choice of instrument at the inter-country level, revenues can be raised at the domestic level.10 The assertion of Cooper (2000) or Nordhaus (2007) that inter-country cap-and-trade regulations are inferior to a system of
Harmonized Carbon Taxes with respect to the revenue-raising potential can thus not
be supported.
4.4
Treatment of Uncertainty
The treatment of uncertainty is frequently mentioned as being a merit of price over
quantity regulations. When costs from pollution abatement are uncertain, remarkable
differences exist between the two policy alternatives with respect to the level and costs
of emission reductions. The reason for this is that a tax approach fixes the price per unit
of emission and lets the market decide about the produced quantity, while a quantity
approach fixes the amount of emissions and lets the market provide the corresponding
price of emissions. In the context of climate change, a tax that provides carbon price
certainty is expected to be superior to a system of tradable permits in terms of welfare
(see e.g. Nordhaus (2007), Aldy et al. (2008)). Next, this issue will be discussed in
more detail.
The assertion that a price approach achieves a higher social welfare than a quantitycontrol approach is based on the ’Prices vs. Quantities’ analysis in Weitzman (1974).
This study demonstrates that, when abatement costs are uncertain, a tax approach is
more efficient than a quantity regime, as long as the slope of the marginal abatement
cost curve is, in relative terms, steeper than the marginal benefit curve.11 A quantity
regulation is more efficient and ought to be preferred when the reverse is true.12
The structure of benefits and costs in the context of climate change militates in favor
10
Note that domestic non-revenue-raising policies are not necessarily inferior to revenue-raising
instruments. For example, newly generated public funds in the latter regime create room for polluters
as well as non-polluters to lobby for a share of these revenues. By contrast, in a non-revenue-raising
regime, only polluters engage in lobbying activities, e.g. for the share of grandfathered allowances.
This implies lower economic distortions from rent-seeking. MacKenzie and Ohndorf (2012a) show the
existence of a trade-off between the potential for a second dividend and the level of socially wasteful
rent-seeking activities. In case the benefits from a revenue-recycling effect are too low, non-revenueraising instruments might be more efficient than revenue-raising ones.
11
Uncertainty in the marginal benefits is relevant when correlated with the uncertainty in marginal
abatement costs. Quantity-based regulations are relatively more efficient when uncertainties are positively correlated and vice versa (Stavins (1996)).
12
An excellent graphical illustration of this result is given in Adar and Griffin (1976).
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of a price-based regulation. Climate change is particularly determined by the already
existing stock of GHGs in the atmosphere, and not by the flow of emissions. Hence,
the benefits from restraining emissions are roughly the same for each reduction unit.
In other words, marginal benefits from carbon abatement can be expected to be almost
constant. Abatement costs, in contrast, are likely to increase sharply when more and
more complex reduction measures are needed to achieve a higher abatement level. That
is to say, the marginal abatement cost curve can be expected to be rather steep (Nordhaus (2007)). Hence, from the initial discussion on Prices vs. Quantities in Weitzman
(1974), abatement cost uncertainty militates in favor of a tax approach to mitigate
climate change. This result has been formally supported by Hoel and Karp (2002) and
Newell and Pizer (2003).
However, the optimal choice of instrument derived from the Prices vs. Quantities
analysis may change, if problems are taken into account which seem particularly relevant in inter-country climate regulations. Difficulties in monitoring and enforcement
of tax agreements or the presence of tipping points might well recommend the use of a
quantity approach to control GHG emissions. We discuss these issues in the following
sections.13
Monitoring and Enforcement
Difficulties in monitoring and enforcement are commonly accepted downsides of a system of Harmonized Carbon Taxes (Eizenstat (1998), Wiener (1999), Victor (2001),
Nordhaus (2007), Aldy et al. (2008)). While countries may not provide actual emission
reductions under either policy alternative, enforcement of inter-country tax regulations is additionally hampered by potential fiscal cushioning. This risk refers to the
countries’ ability to (partially) offset the abatement incentive effect of the Harmonized
Carbon Tax by adjusting domestic fiscal policies that indirectly tax carbon emissions.
In this section, we argue that fiscal cushioning crucially affects the efficiency of a price
13
There is a long list of literature, which extends the seminal comparison of price and quantity controls in Weitzman (1974). Some contributions to the discussion of optimal instrument choice involve,
for instance, the simultaneous regulation of multiple goods (Yohe (1977)), endogenous technological
choice (Krysiak (2008)), risk-averse regulated actors (Baldursson and von der Fehr (2004)), imperfect competition in the product market (Mansur (2007)), strategic firms (Moledina et al. (2003)),
pre-existing fiscal distortions (Quirion (2004)), or polluter’s individual choice of instrument (Krysiak
and Oberauner (2010)). We refrain from discussing these analyses, as they seem more relevant for
domestic instrument choice.
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4.4. Treatment of Uncertainty
regulation, and hence the recommended choice of instrument derived from Weitzman
(1974).
Monitoring and enforcing a system of Harmonized Carbon Taxes is particularly
complicated, as the tax is difficult to administer effectively. In practice, countries can
offset the impact of the tax at the domestic level by adjusting fiscal policies, which
indirectly price carbon emissions. This risk is often referred to as fiscal cushioning
(Wiener (1999)).14 Most obviously, the abatement incentive effect of the international
carbon tax is reduced when countries cut domestic taxes that co-determine the price
of carbon emissions, e.g. taxes on energy and fuel, or road charges.15 IMF (2011b) and
Tirole (2008), for example, show that most countries could neutralize the impact of a
US$ 25 carbon tax on energy and gasoline prices by such measures. Moreover, countries
can cushion the impact of the tax by increasing subsidies for carbon-intensive inputs,
such as for coal or oil. All these fiscal policy adjustments offset the impact of the carbon
tax and undermine the purpose of the climate agreement, i.e., carbon abatement.16
Proponents of carbon taxes often propose the concept of an ’effective’ carbon tax
to enforce the inter-country price regulation with respect to fiscal cushioning (see e.g.
Cooper (1998) and Nordhaus (2007)).17 In such an approach, all pre-existing carbonrelated policies would be converted to a single carbon price. The difference between the
already existing carbon price and the Harmonized Carbon Tax would then represent
the level of carbon tax that the countries would be forced to levy domestically. Any
variation in carbon-related policies would require the adjustment of the domestic tax, in
such a way that the effective carbon price would remain harmonized across countries.
Such an approach would require complete information regarding countries’ carbon14
The risk of fiscal cushioning in a system of Harmonized Carbon Taxes has also been discussed
in Aldy et al. (2010), Nordhaus (2008), Wiener (2001), Hoel (1991, 1993), Cooper (1998, 2007), Hovi
and Holtsmark (2006), Parry (2003), Stavins (1997), and Zhang and Baranzini (2004).
15
Analyses indicate that countries that levy a carbon tax, provide tax concessions for the polluting
industry (Speck and Jilkova (2010)). Sweden, for example, exempts some industries from the carbon
tax. Other sectors are granted a tax break of 79% plus an additional rebate of 76% when a specific
level of tax payments is reached (OECD (2006)).
16
It is rather unlikely that fiscal cushioning, which refers to the manipulation of policies that already
price externalities, creates a second dividend as discussed in section 4.3. In contrast, the costs of
regulation can be expected to increase. The reason is that the revenue-recycling potential decreases
when revenues are used for fiscal cushioning measures rather than for reducing existing distortionary
taxes.
17
Furthermore, Hoel (1991), Aldy et al. (2008, 2010), Nordhaus (2008) and Cooper (2007) discuss
the advantage of an effective tax rate in the presence of fiscal cushioning.
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related policies and methodologies to convert the value of the policies into a single
carbon price. Both requirements are, as discussed next, difficult to achieve.
First, information on carbon-related policies would be required. Cooper (1998) asserts that the International Monetary Fund (IMF) could gather the relevant data during
the annual Article IV reports (IMF (2011a)). Yet, complete information on carbonrelated policies seems highly unlikely. This is primarily due to the reluctance of countries to provide detailed information on their domestic fiscal policies. Hence, during the
IMF’s review, countries might manipulate fiscal data by overstating emission-pricing
policies, or by understating subsidizing policies. Moreover, gathering information on
the countries’ carbon-related fiscal policies would be additionally hampered by the complexity of the countries’ fiscal systems. Thus, sophisticated policy adjustments such as
modifications of existing complex subsidy programs as well as the development of new
ones, would likely remain undetected by the IMF (Aldy et al. (2008)). Even if fiscal
cushioning strategies were detected, countries could still argue that such measures are
meant to foster economic activity, rather than to alleviate the burden of the carbon
tax (OECD (2006)).18 As a consequence, information on the countries’ carbon-related
policies would likely be incomplete.
Second, the value of carbon-related policies would have to be converted into a single
carbon price. In some cases, simple conversion rules would suffice, e.g. when calculating
the carbon equivalent price from a tax/subsidy on coal or gas. Yet, several environmental policies are implemented in the form of standards, e.g. energy efficiency standards.
In such cases, conversion factors cannot be applied, rendering the carbon equivalent
price of the domestic policies controversial. Nevertheless, the calculation of the pre-tax
carbon price is considered practicable as long as ”indirect or embodied emissions” are
not involved (Nordhaus (2007), p.41). Taking into account substitution effects would
require controversial assumptions about supply, demand, and cross-elasticities. Hence,
beside incomplete information on carbon-related policies, the conversion of their value
into a single carbon price would be prone to errors.
Considerable difficulties can be expected when calculating the pre-tax domestic carbon
price. To cope with these difficulties, detailed directives on the design of domestic fiscal
policies would be required in order to follow the approach of an effective carbon tax
18
This encounters a second-order emission effect from fiscal cushioning. Carbon emissions not only
increase due to the deterioration of the abatement incentive effect, but also due to a higher degree of
economic growth.
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4.4. Treatment of Uncertainty
rate. This would imply serious infringements in state sovereignty, which is likely to
be unacceptable for potential signatories of the climate agreement. The proposal of
an EU-wide carbon tax, for example, has been refused by member states opposing an
increase in the EU Commission’s fiscal power (Zhang and Baranzini (2004)). These
somewhat pessimistic conclusions indicate that the concept of an effective tax rate is
impracticable. As a consequence, fiscal cushioning can never be completely avoided
(Aldy et al. (2008)).
Note that inter-country cap-and-trade regulations are unaffected by fiscal cushioning strategies. The reason is that – although fiscal cushioning measures might be
applied – the countries still need to meet the national emission target. For instance,
consider a country under the cap-and-trade agreement that increases its coal subsidies,
thereby stimulating an increase in carbon emissions in sector A. To achieve the national emission target, the country would have to abate more in sector B, or purchase
allowances from other countries. The aggregate emission level, however, would not
change in response to the increase in coal subsidy, as the scarcity of carbon allowances
still puts a cap on emissions. Hence, fiscal cushioning strategies are problematic solely
under an inter-country price approach. This often leads to the conclusion that the
feasibility of enforcement is lower under a price than under a quantity regulation (e.g.
Victor (2001)).
Rohling and Ohndorf (2012) consider the risk of fiscal cushioning in an extension of
Weitzman (1974) by assuming a lower enforceability for a price- than for a quantitybased regulation. It is shown that the welfare advantage of a price approach from
uncertain costs can be counterbalanced by the welfare advantage of quantity regulations from stricter enforcement. Numerical calculations in the context of global climate
change indicate that an inter-country quantity control system might well dominate a
tax approach in terms of welfare. Thus, differences in the feasibility of enforcement
might well alter the recommended choice of instrument derived from Weitzman (1974).
Tipping Points
In addition, the existence of tipping points, i.e., climate change thresholds, might also
alter the recommended choice of instrument (Pizer (2002), Keohane (2009)). The rationale is as follows.
Tipping points refer to the existence of critical GHG concentration levels in the atmosphere. Carbon emissions beyond such threshold levels may cause rapid, irreversible,
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and catastrophic damages to the environment, and thus to the global economy.
There is convincing scientific evidence for the existence of such climate change thresholds, even though it has long been questioned. For example, scientists agree that an
increase in average surface temperature of 3 − 5 ◦ C above preindustrial levels would imply the deglaciation of Greenland and West Antarctic ice sheets (see e.g. EEA (2010),
OECD (2012)). The associated costs for the global economy are – although highly
uncertain – considered to be tremendous. In order to avoid such tipping points, countries have agreed in the Copenhagen Accord to restrain GHG emissions so that the
increase in average surface temperature would be below 2 degrees Celsius. This should
’prevent dangerous anthropogenic interference with the climate system’ (UNFCCC
(2010), p. 5).
When tipping points exist, it is important to restrain carbon emissions to below the
climate change thresholds. This would be problematic under a system of Harmonized
Carbon Taxes, as a price regulation may fail to achieve the desired environmental performance. A shortage in emission reductions poses the risk of overshooting a critical
climate change threshold, thereby causing large-scale damages to the society. In contrast, a cap-and-trade approach directly controls the amount of emissions, restraining
these in such a way that the GHG concentration levels in the atmosphere do not cross
critical thresholds. Thus, a quantity regulation that fixes the amount of emissions to
(slightly) below the climate change threshold at any costs might well be preferable over
a system of Harmonized Carbon Taxes.
This policy recommendation can also be obtained by applying the criterion for
optimal instrument choice established in Weitzman (1974). Recall that a tax approach
ought to be preferred as long as the marginal abatement cost curve is, in relative terms,
steeper than the marginal benefit curve. Following the argumentation of Nordhaus
(2007), a tax approach ought to be preferred, as the marginal benefits from carbon
abatement can be expected to be almost constant. The reason for this is that climate
change is particularly determined by the already existing stock of pollution in the
atmosphere, rather than by the flow of new emissions.
Yet, in the presence of tipping points, the rationale of the slopes of the marginal curves
no longer holds true. GHG emissions to the atmosphere beyond a critical threshold can
cause irreversible and large-scale damage to the environment. This way, as damages
from carbon emissions would rapidly increase beyond the climate change threshold,
marginal benefits from carbon abatement can be expected to be rather steep. In this
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4.5. Price Volatility
case, the policy ranking established in Weitzman (1974) might recommend the use of
a quantity rather than a price approach to mitigate global climate change.
In conclusion, the initial Prices vs. Quantities analysis provides strong indication
for price-based climate regulations when abatement costs are uncertain. However,
the recommended choice of instrument derived from Weitzman (1974) might change
if issues specific to inter-country climate change regulations are taken into account.
For example, quantity-based regulations ought to be preferred when difficulties in the
monitoring and enforcement of price regulations are considered, or when critical climate
change thresholds exist. Hence, the treatment of uncertainty might well recommend the
use of a quantity approach to tackle anthropogenic climate change at the inter-country
level.
4.5
Price Volatility
A further argument against the use of cap-and-trade-based regulations is the volatility
in allowance prices (Nordhaus (2007)). Changes in the demand for energy, in the
relative prices for clean and dirty fuels or technological improvements induce a shift
in the demand for allowances. This might trigger significant price movements, as the
supply of permits is perfectly inelastic. Price volatility increases the complexity of
investment decisions and thus creates incentives to postpone the adoption of climatefriendly technologies to the future. This is considered a crucial disadvantage of capand-trade regulations, given that price volatility is not an issue under a price approach.
A tax directly fixes the price of emissions and is adjusted only periodically and then
marginally, if at all.19 However, we discuss next that price volatility is unlikely to be
a determining factor for the choice of instrument at the inter-country level.
Note first that an inter-country cap-and-trade regulation, according to the magnitude of the market, is likely to be less affected by price volatility than a domestic
cap-and-trade policy. Yet, the latter is often brought forward as evidence for considerable price volatility. A frequently-used example is the U.S. Acid Rain Program. In this
program, SO2 allowance prices rose drastically, from US$ 200 to US$ 1600 in Decem19
Most domestic environmental tax programs do not include specific tax ramp ups. Although several
European countries increase their environmental taxes according to the inflation rate, no domestic
carbon tax is adjusted when a specific level of pollution abatement is not met (see Speck (2008) and
Sumner et al. (2011)).
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ber 2005, and normalized quickly in the beginning of 2006. The reason for this price
fluctuation was that the supply of coal-fired electricity generation increased after the
hurricanes Katrina and Rita caused disruptions in natural gas supply. This led to an
increase in the demand for SO2 allowances, and consequently in the price of permits
(see e.g. Schmalensee and Stavins (2012)). However, considering the magnitude of the
market, such local shocks can be absorbed in an inter-country cap-and-trade policy,
or even be counterbalanced by shocks somewhere else. Hence, highly volatile permit
prices seem unlikely at the inter-country level.20
Allowance price movements in cap-and-trade regulations can be attributed to specific market influences. The price drop of carbon allowance in the EU ETS in 2006
and 2008 was due to an oversupply of permits and the economic downturn (Chevallier
(2010), Mansanet-Bataller et al. (2011)). The rapidly increasing allowance prices in
the SO2 market by the end of 2005 can be attributed primarily to environmental and
political impacts (see e.g. Burtraw and Szambelan (2009), Schmalensee and Stavins
(2012)). Permit prices, therefore, do not follow irrational patterns, but reflect the polluters’ expectations about the future stringency of the emissions cap. This can also
be considered as valuable and directly observable information, e.g. for negotiating
emission caps for future commitment periods.
Furthermore, different cost containment mechanisms have been suggested to reduce
the effects of volatile allowance prices. Such mechanisms – when properly designed –
stabilize the price of permits without compromising the environmental performance of
the cap-and-trade regulation.
The first suggestion is to combine the cap-and-trade regulation with a price floor and
ceiling (see Roberts and Spence (1976), Weitzman (1978), Pizer (2002)). This would
prevent permit prices from rising too high or falling too low, and further reduce the
width of price fluctuations (see e.g. Grüll and Taschini (2011)). Sharply falling permit
prices, for example, may render the adoption of climate-friendly technologies unprofitable. A minimum return on investments is guaranteed, however, when the regulator
is obliged to purchase certificates at floor price (Hepburn (2006)). Rapidly increasing
allowance prices are unproblematic from the point of view of investment profitability,
20
Note that domestic permit prices, which seem particularly relevant for industries’ investment
decisions, do not necessarily experience the same volatility as inter-country allowances. For instance,
countries can implement a domestic carbon tax or decouple the domestic emission cap from the
international allowance allocation.
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4.5. Price Volatility
but are undesirable from a political perspective.21 The price increase raises compliance
costs, which might reduce public support for the climate agreement (Tirole (2008),
Kettner et al. (2011)). In this case, the regulator’s commitment to sell additional
allowances at the price ceiling, often referred to as ’safety valve’, limits compliance
costs.22 Note that a sanction for noncompliance can act just like a price cap. In case
permit prices rise dramatically, it might be profitable to choose noncompliance and
pay the sanction instead of purchasing certificates (Jacoby and Ellerman (2004)).23
The second suggestion is to use banking and borrowing provisions. Banking unused
allowances for later use or borrowing future allowances for today’s use allows reacting
to unexpected shifts in the demand for permits (Rubin (1996)).24 This increases the
elasticity of supply of permits and reduces the volatility of allowance prices.25
Note that the environmental performance becomes uncertain when a cap-and-trade
regulation is combined with cost-containment mechanisms. This concern is less problematic when the price floor kicks in, which tightens the cap, or when permits are
banked to postpone emissions into the future. Yet, the environmental integrity of the
regulation is reduced when additional allowances are sold at the price ceiling. Moreover, unlimited banking provisions allow compensating current emissions entirely by
future permits without providing emission reductions. These risks can be addressed
by applying an ’allowance reserve’ (see Murray et al. (2009)). Such an approach limits the amount of permits that can be borrowed from future commitment periods or
bought at the price ceiling. This maintains the environmental integrity of a cap-and21
It has to be noted that a cap on allowance prices might render technologies unprofitable that
would have been adopted only when permit prices could increase above the price ceiling.
22
Starting in 2015, Australia planned to apply a price collar in its domestic cap-and-trade system.
The floor price of AU$ 15, however, has been rejected in the course of linking with the EU ETS. The
ceiling is now set at AU$ 20 above the expected 2015-16 price for EU ETS allowances (European
Commission (2012a)). Furthermore, although no official floor price is defined in the EU ETS, the EU
Commission plans to increase allowance prices by ’back-loading’ 900 million certificates in the first
three years of EU ETS phase III (European Commission (2012b)).
23
Stranlund and Moffitt (2011) show that, by reason of variable sanction costs, a program with
full compliance and a well-designed safety valve is superior to a regime which relies on non-compliant
actors and a sanction as price ceiling.
24
The Australian emission trading system, for example, allows borrowing 5% of the polluter’s liability from the following commitment period. See http://www.cleanenergyfuture.gov.au.
25
Fell et al. (2008) show that banking and borrowing provisions reduce compliance costs in comparison to price regulations and cap-and-trade systems without these provisions.
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trade regulation that is combined with cost-containment mechanisms to dampen price
volatility.
It has to be noted that, although cost containment mechanisms reduce price volatility, it can never be completely avoided. Uncertainty about future allowance prices
discourages the adoption of climate friendly technologies, as the return on investments
becomes uncertain. Thus, an option value exists that provides incentives to put investment decisions off into the future (Dixit and Pindyck (1994)). This is expected to
slow technological change.
Yet, the literature is ambiguous on which policy alternative provides stronger incentives
to invest in new abatement technologies. Whether price or quantity regulations perform
better depends on various issues, such as the costs of the technology, the possibility of
licensing, knowledge spillovers, the level of innovation in new abatement technologies,
or whether or not the regulation adapts to technological change.26 Potential stronger
incentives to invest in new abatement technologies under a quantity regulation counteract the disadvantage of uncertain allowance prices. Yet, more research is required
to assess the relative strength of these two effects. This would contribute to a more sophisticated understanding of which policy alternative may provide stronger incentives
to invest in climate-friendly technologies.
Note that it is disputable whether a climate agreement ought to be the main driver
for technological change (Zhao (2003)). The purpose of the regulation is to internalize
the costs of emissions that contribute to climate change. If the policy achieves this,
there is no need for the climate agreement to promote the adoption of new abatement
technologies. Findings reported in Fischer and Newell (2008) and Hoel (2010) point in
a similar direction: Policies, price- or quantity-based, that are meant to incentivize a
26
Downing and White (1986), Jung et al. (1996), Milliman and Prince (1989) and Requate and Unold
(2003), for example, focus on the diffusion of an exogenously given climate-friendly technology when
the regulator acts myopically. A tax-based approach tends to dominate cap-and-trade regulations in
this case. At international level, however, a quantity control instrument might be welfare-superior
compared to price-based regulations (Endres and Rundshagen (2013)). A forward-looking regulator
which either implements the ex-post optimal regulation before actual technological change takes place
or revises the policy once the new technology has been adopted, has been analyzed e.g. in Coria (2009),
Weber and Neuhoff (2010) and Montero (2011). A quantity control instrument, in combination with
a price collar or a subsidy for technology adoption, ought to be preferred in this case. With respect
to technological innovation, Fischer et al. (2003) found no dominant policy that creates stronger
incentives to invest in R&D. Which instrument actually performs better depends on various issues,
such as the costs of the technology, the slope and level of the marginal benefit curve, the ability to
imitate new technologies, and the number of emitters. See e.g. Jaffe et al. (2003), Requate (2005) or
Popp et al. (2010) for an overview.
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4.6. Conclusion
reduction in carbon emissions should be combined with other regulatory instruments,
for instance R&D or renewable energy subsidies, in order to reduce abatement costs
and accelerate technological change.
To summarize, price volatility is an inherent risk of cap-and-trade-based policies.
Yet, cost-containment mechanisms, such as a price collar or banking and borrowing
provisions, can dampen undesirable effects of volatile permit prices. Moreover, the
economic literature offers no unambiguous answer to which policy alternative provides
stronger incentives to invest in new technologies. Some economists suggest that either
instrument, price- or quantity-based, ought to be combined with additional mechanisms
in order to accelerate technological change and reduce abatement costs. We therefore
conclude that price volatility and its effects on technological change are likely to be
overstated as determining factors in favor of a tax regulation at the inter-country level.
4.6
Conclusion
This chapter aims to discuss the most frequently mentioned arguments supporting the
use of a Harmonized Carbon Taxes system rather than an inter-country cap-and-trade
regime to mitigate global climate change. It can be noted at this point that common
assertions about a price-based climate regulation being advantageous with respect to
broad country participation, revenue-raising potential, treatment of uncertainty, or
technological change are not convincing.
We observe, in fact, that participation is more likely under an inter-country capand-trade regulation than under a price approach. The reason for this is that, from
a political economy perspective, side-payments to encourage participation are more
feasible in the former than in the latter regime. Moreover, the revenue-raising potential
is not a valid argument in favor of a price approach. Under an inter-country cap-andtrade regulation, domestic policies can still be designed to generate public funds. The
EU ETS is probably the best example for the possibility of raising revenues under an
inter-country cap-and-trade regulation. Furthermore, the treatment of uncertainty is
not a decisive factor for favoring a price approach. The existence of tipping points and
difficulties in monitoring and enforcement of emission taxes provide strong arguments
for a quantity-based regulation. Finally, the effect of volatile permit prices on delaying
investments in climate-friendly technologies is likely to be overstated. In order to
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accelerate technological change and reduce abatement costs, additional instruments
are required under both price- and quantity-based regulations. We therefore conclude
that the arguments recommending the use of a price rather than a quantity approach
to internalize the costs of anthropogenic climate change at the inter-country level do
not hold to scrutiny. Thus, a replacement of the currently implemented cap-and-trade
approach by a system of Harmonized Carbon Taxes cannot be endorsed.
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4.6. Conclusion
Chapter 5
Conclusion
Internalizing costs from a global externality at the inter-country level is a challenging
task for various economic, political, and technical reasons. Remarkably, already the
question of the optimal choice of instrument is controversially discussed among politicians and economists. A generally accepted opinion is that market-based instruments
ought to be preferred over command-and-control solutions, as the latter imply inefficiently high aggregate control costs. Which market-based instrument, i.e., a price
(emission tax) or a quantity (tradable pollution permits) control approach, is more
efficient and effective to internalize external costs is, however, an ongoing dispute.
The present dissertation addressed the choice between the two market-based instruments to internalize a global externality at the inter-country level. We contribute
to the literature on optimal instrument choice by considering the risk of fiscal cushioning, an enforcement concern that is inherent to inter-country tax regulations. In
such a regime, countries commit to levy a tax on emissions domestically. This creates
incentives for pollution abatement at the firm level. The tax, however, always implies
additional costs for the domestic industries. As a consequence, countries might have
incentives to render the emission tax domestically as ineffective as possible. Countries can achieve this by adjusting other national fiscal policies that indirectly price
the regulated pollutant. These adjustments include, for example, a reduction of taxes
on energy, road use, and gasoline, or an increase in subsidies for pollution intensive
production processes. Such measures curb the industries’ costs of the regulation but
also offset the pollution abatement incentive effect of the inter-country emission tax.
This undermines the purpose of the tax regulation, i.e., abatement.
Indeed, fiscal policy adjustments that reduce the domestic industries’ costs from the
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Conclusion
regulation can also be expected under an inter-country quantity regime. In this case,
however, fiscal cushioning measures do not undermine the environmental integrity of
the regulation. The reason is that – although fiscal cushioning measures are applied
– countries still need to meet the emission target. Thus, in contrast to price-based
policies, the aggregate abatement level remains unaffected by domestic fiscal policy
adjustments under a cap-and-trade regime. Fiscal cushioning is therefore an enforcement problem specific to inter-country tax regulations.
Notably, the risk of fiscal cushioning is well-known and is given careful consideration
in the political debate on the optimal choice of instrument to internalize a global externality, such as the discharge of Greenhouse Gas emissions that contribute to climate
change. However, a formal assessment of the enforcement concerns associated with
fiscal cushioning, its effect on the efficiency ranking of the two policy alternatives and
hence on the criterion for optimal instrument choice established in Weitzman (1974),
and the consequences for the optimal choice of instrument to tackle anthropogenic climate change has not yet been attempted. We addressed these issues in the present
dissertation by answering the following three key questions that have been defined in
the introduction to this thesis:
• Is fiscal cushioning a serious issue for enforcing inter-country environmental taxes?
• What are the implications for the optimal choice of instrument when fiscal cushioning is taken into account in the classic analysis of ’Prices vs. Quantities’?
• Is the cap-and-trade regulation under the current – and most likely also under the
post-2020 – inter-country climate agreement an appropriate policy instrument to
control Greenhouse Gas emissions?
Proponents of international emission taxes often downplay the risk of fiscal cushioning.
The reason is that – in theory – an institution such as the International Monetary
Fund (IMF) can monitor and enforce compliance with an inter-country tax approach.
The IMF gathers macroeconomic data from almost all countries during its Article IV
reviews. These surveillances could reveal a country’s fiscal adjustments that offset the
international emission tax. Note also that the G20 countries committed in September
2009 to ’rationalize and phase out over the medium term inefficient fossil fuel subsidies
that encourage wasteful consumption’ (G20 Leaders (2009)). This commitment implies
that detailed information on a country’s domestic environmental subsidy programs will
Conclusion
105
be published. Such data could, in addition to the IMF’s reviews, provide valuable
information to enforce an inter-country tax regulation. However, such reviews are
likely to be insufficient in deterring the use of fiscal cushioning measures. One reason
is that limited monitoring resources hamper verification of national fiscal reports and
detailed surveillances of the countries’ domestic tax code. Therefore, complex tax
loopholes or sophisticated subsidy programs are likely to remain undetected during the
IMF’s Article IV or other fiscal policy reviews (see e.g. Aldy et al. (2008)). Given
constraints in the monitoring budget, the allocation of the monitoring resources to
maximize the enforcement of the inter-country tax regulation ought to be optimized.
Chapter 2 provided the formal analysis of this issue, which gives important insights
into answering the first key question of the dissertation:
Is fiscal cushioning a serious issue for enforcing inter-country environmental
taxes?
Our formal analysis of the optimal enforcement of inter-country environmental taxes
shows that emissions are minimized when countries in which fiscal adjustments are easyto-detect are given the highest monitoring priority. A low auditing priority should be
given to countries in which evidence for noncompliance is hard-to-detect. This approach
might seem counterintuitive at a first glance, because countries with the lowest chance
for noncompliance are audited more regularly than those with the highest chances for
noncompliance.
A distinctive feature of fiscal cushioning is the countries’ potential to undermine the
emission tax rate. This depends on the countries’ domestically implemented fiscal policies. Fiscal systems of some countries might include several environmental policies, e.g.
levies on energy and road use, or subsidies for coal and gas. Other countries might
focus more on traditional fiscal policies, e.g. taxes on income, profits, and sales. The
former fiscal system is likely to provide a larger potential to offset the international
emission tax than the latter. We find that enforcement is maximized when the highest
monitoring priority is given to countries with the largest offsetting potential. By contrast, a low monitoring priority should be given to countries with a limited potential
for fiscal cushioning. Hence, this monitoring policy does not follow the counterintuitive
approach described above.
A common result, however, is that fiscal cushioning can never be completely disincentivized. Deterrence against domestic fiscal policy adjustments is always incomplete,
even when the regulator is endowed with unlimited monitoring resources. As a con-
106
Conclusion
sequence, there will always be some countries that distort the pollution abatement
incentive effect of the emission tax that undermines the regulation. Thus, referring
to the first key question of this dissertation, fiscal cushioning might well be a serious
enforcement issue of inter-country environmental taxes.
To answer the second key question,
What are the implications for the optimal choice of instrument when fiscal cushioning is taken into account in the classic analysis of ’Prices vs.
Quantities’?
we considered the results presented in chapter 2, i.e., that deterrence against the use
of fiscal cushioning measures is always incomplete. This, in combination with the fact
that fiscal cushioning is an enforcement problem specific to inter-country tax regulations, leads to the conclusion that the feasibility of enforcement is higher under an
inter-country quantity than under a price approach. In chapter 3, we account for
differences in the instrument’s enforceability in a formal extension of the ’Prices vs.
Quantities’ analysis, in which the optimal choice of instrument under uncertain costs
and benefits is investigated.
The findings of our theoretical model challenge important insights from the formal
’Prices vs. Quantities’ debate. A commonly held opinion is that institutional parameters and the benefits from an additional abatement unit are irrelevant for optimal
instrument choice. This no longer holds true when the risk of fiscal cushioning is
taken into account. In this case, the sanction for noncompliance, the feasibility of enforcement, and the level of the benefits from an additional emission reduction become
decisive factors for which policy alternative ought to be preferred. Moreover, we can
show that these parameters ultimately determine the choice of instrument when the
variance in abatement costs is low enough. In this case, a quantity approach ought to
be strictly preferred over a price approach.
In order to gain better insights from our theoretical findings into the optimal choice
of instrument at the inter-country level, we ran numerical calculations in the context
of global climate change. The conventional opinion, as indicated in Hoel and Karp
(2002) or Newell and Pizer (2003), is that a price regulation ought to be preferred over
a quantity approach. Using data taken from Newell and Pizer (2003), we show that
differences in the feasibility of enforcement do not alter the ranking of the two policy
alternatives. That is, in line with previous calculations in the climate context, a price
approach ought to be preferred to mitigate anthropogenic climate change. Hence, the
Conclusion
107
risk of fiscal cushioning is not strong enough to justify the choice of an inter-country
cap-and-trade approach. Our simulations, however, are remarkably sensitive to the
level of the benefits from carbon abatement, which is controversially discussed in the
literature. Using more recent estimations of the social costs of carbon of 35$/t, rather
than 9$/t as estimated in Newell and Pizer (2003), changes our results. In this case, a
quantity-control instrument dominates a tax regime to curb Greenhouse Gas emissions
in terms of welfare. Hence, a cap-and-trade-based approach might well be the best
policy instrument to tackle anthropogenic climate change, at least at the inter-country
level.
The formal extension of the ’Prices vs. Quantities’ debate in chapter 3 indicates
that – contrary to the commonly accepted opinion – the cap-and-trade-based policy
under the current inter-country climate agreement, the Kyoto Protocol, might well
be the correct choice of instrument. Thus, our theoretical findings provided a strong
argument for answering the third and last key question of this dissertation:
Is the cap-and-trade regulation under the current – and most likely also under the post-2020 – inter-country climate agreement an appropriate policy
instrument to control Greenhouse Gas emissions?
The negotiations for the current inter-country climate change mitigation policy have
started more than 20 years ago. At that time, the European Union promoted the use
of a carbon tax approach to reduce global Greenhouse Gas emissions. By contrast,
the U.S. proposed, given their experience with domestic cap-and-trade regulations, a
quantity-based regime. This approach has then been adopted under the first and second commitment period of the Kyoto Protocol. Ironically, the U.S. never ratified the
agreement and is now one of the leading critics of the Kyoto Protocol and its underlying regulatory approach.
In the political debate on optimal instrument choice, it is often claimed that a system
of Harmonized Carbon Taxes ought to be preferred over a cap-and-trade regulation to
mitigate global climate change at the inter-country level. The most often cited reasons
in favor of a price approach are the broader participation of countries in the climate
agreement, the revenue raising potential, the treatment of uncertainty, or the incentives to invest in climate friendly technologies. These allegations have been discussed
in chapter 4. We found, however, that neither allegation is a valid argument to replace
the currently implemented cap-and-trade-based climate change mitigation policy by a
system of carbon taxes.
108
Conclusion
In fact, our analysis reveals an important advantage of a cap-and-trade-based regime.
A quantity regulation is, contrary to the often stated view, likely to promote the countries’ broad participation in the agreement. The reason is that side-payments are more
feasible to occur under a quantity than under a price approach. Side-payments create
incentives to participate in the climate agreement by reallocating the burden of carbon
abatement from losers to beneficiaries of the regulation or from low- to high-income
countries. Under a tax approach, such side-payments take the form of apparent monetary transfers. The visibility of transfer payments is, however, likely to encounter
considerable public resistance. This reduces the feasibility of creating incentives for
participation via a reallocation of the burden of emission reductions. By contrast,
side-payments materialize indirectly under a quantity approach. Losers of the regulation or low-income countries are granted excess allowances that can be sold – thereby
creating financial transfers – to beneficiaries of the regulation or high-income countries.
Yet, the initial allocation of allowances across countries is complex, which reduces the
visibility of actual transfers. This is likely to soften public resistance against that form
of side-payments. Thus, a reallocation of the burden of emission reductions is more
feasible under a quantity than under a price approach. The former instrument might,
therefore, well encourage broader participation in the climate agreement than the latter.
The feasibility of side-payments is likely to be a decisive factor for successful negotiations of a post-2020 climate change mitigation policy. Countries agreed in Durban,
South Africa, in December 2011 to establish a treaty until 2015 that enters into effect
in 2020 and covers all countries, including the U.S., China, and India. Reaching an
agreement is likely to require a radical reallocation of the burden of carbon abatement
across countries. This, as indicated in our analysis, is more feasible under an intercountry cap-and-trade than under a system of Harmonized Carbon Taxes.
To sum up, this dissertation contributes to a more sophisticated understanding
of optimal instrument choice to internalize a global externality at the inter-country
level. Special emphasis is placed on an enforcement issue inherent to price regulations,
i.e., fiscal cushioning. The risk of domestic fiscal policy adjustments that offset the
pollution abatement incentive effect of the emission tax is considered a decisive factor
for optimal instrument choice. Thus, an inter-country cap-and-trade-based regulation
might well be preferable over a tax approach to internalize a global externality, e.g.
carbon dioxide emissions that contribute to climate change.
Chapter A
Appendix to Chapter 2
A.1
Proof of Proposition 1
In order to proof Proposition 1, we solve the following constrained maximization:
max
Π(e(x, κ); α, γ)
x
subject to
x ≥ 0,
(A.1)
t−x≥0
(A.2)
The Lagrangian is
L = g(e(x, κ)) − βte∗ − γαβt[e(x, κ) − e∗ ] − γαF (e(x, κ) − e∗ ) + λx + θ[t − x]
where λ and θ denote the non-negative Lagrange-multipliers. The Kuhn-Tucker conditions are
Lx =e′ (x, κ) [g ′ (e(x, κ)) − γαβt − γαF ′ (e(x, κ) − e∗ )] + λ − θ = 0
(A.3)
Lλ =x ≥ 0
Lθ =t − x ≥ 0
where e′ (x, κ) = −κ/g′′ (e(x,κ)) > 0 can be obtained from applying the Implicit Function
Theorem on (2.2). Furthermore, a sufficient condition for ∂ 2 Π/∂x2 < 0 is g ′′′ (e(x, κ)) > 0,
which is also assumed for the proof of Proposition 3.
110
A.2. Proof of Proposition 3 and 4
Proof of Proposition 1.I.
In this case, condition (A.3) is fulfilled iff the
Suppose that γα ≤ βt+Ft[1−κ]
′ (E(κ)−e∗ ) .
Lagrange-multipliers are λ = 0 and θ > 0. That is, constraint (A.2) is binding and
x = t maximizes Π(e(x, κ); α, γ).
Proof of Proposition 1.II.
t
Suppose that γα ∈ βt+Ft[1−κ]
′ (E(κ)−e∗ ) , βt+F ′ (0) . In this case, condition (A.3) is fulfilled iff
the Lagrange-multipliers are λ = 0 and θ = 0. That is, we are in an interior solution,
constraints (A.1) and (A.2) are not binding, and x ∈ (0, t) maximizes Π(e(x, κ); α, γ).
Proof of Proposition 1.III.
Suppose that γα ≥ βt+Ft ′ (0) . In this case, condition (A.3) is fulfilled iff the Lagrangemultipliers are λ > 0 and θ = 0. That is, constraint (A.1) is binding and x = 0
maximizes Π(e(x, κ); α, γ).
A.2
Proof of Proposition 3 and 4
In order to proof Proposition 3 and 4 we first state and proof the following lemmas.
Lemma B1. When two (γ, κ̄)-type countries 1 and 2 are identical, α1 = α2 minimizes
emissions.
Proof of Lemma B1
For the proof of Lemma B1, consider two identical (γ, κ̄)-type Countries 1 and 2,
which are audited with probability α1 and α2 . If M in{α1 , α2 } ≥ M in{α̂(γ), 1} or if
M ax{α1 , α2 } ≤ α̃(γ, κ̄), both countries choose the same effort in fiscal cushioning and
no reallocation of budget among countries would reduce aggregate emissions. For a
budget-constrained regulator, it follows from Lemma 1 that α1 = α2 = M in{α̂(γ), 1},
respectively α1 = α2 = 0 is optimal. For α(γ) ∈ (α̃(γ, κ̄), M in{1, α̂(γ)}), i.e., in
region (b), we assume that e is decreasing and convex in α. A sufficient condition is
(∂ 2 e(·))/(∂α2 ) > 0, which is e.g. fulfilled for g ′′′ (e(·)) > 0 and
F ′′′ (e(·)−e∗ ) < 0. Under
t
this assumptions, e(α) is decreasing and convex in α for α ∈ γ[βt+Ft[1−κ̄]
′ (E(κ̄)−e∗ )] , γ[βt+F ′ (0)] .
Hence, emissions are minimized when both countries are audited with the same probability α(γ).
A. Appendix to Chapter 2
111
Lemma B2. An optimal monitoring
policy requires that for two countries of type
t[1−κ̄]
(γ1 , κ̄) and (γ2 , κ̄), with γi αi ∈ βt+F ′ (E(κ̄)−e∗ ) , βt+Ft ′ (0) , i ∈ {1, 2}
∂e(x(α2 γ2 ), κ̄)
∂e(x(α1 γ1 ), κ̄)
=
∂α1
∂α2
must hold.
Proof of Lemma B2
The proof of Lemma B2 is immediate from Lemma B1.
Lemma B3. When γ1 < γ2 , then x2 ≤ x1 ≤ t and e1 ≤ e2 ≤ e∗ iff γ1 α(γ1 ) ≤ γ2 α(γ2 ).
Respectively, x2 < x1 < t and e1 < e2 < e∗ iff α̃ < γ1 α(γ1 ) < γ2 α(γ2 ).
Proof of Lemma B3
Consider two countries of type γ1 < γ2 which are audited with probability α(γi ) with
i ∈ {1, 2} such that γ1 α(γ1 ) ≤ γ2 α(γ2 ). Then the following holds:
• if α(γ1 ) ≥ α̂(γ1 ), then also γ̂ ≤ γ1 α(γ1 ) ≤ γ2 α(γ2 ) and x1 = x2 = 0, i.e.,
e1 = e2 = e∗ .
• if α(γ2 ) ≤ α̃(γ2 ), then also γ1 α(γ1 ) ≤ γ2 α(γ2 ) ≤ γ̃ and x1 = x2 = t, i.e.,
e1 = e2 = E(κ̄).
• if α(γ2 ) > α̃(γ2 ) and α(γ1 ) ≤ α̃(γ1 ), then also γ1 α(γ1 ) ≤ γ̃ < γ2 α(γ2 ) and
x2 < x1 = t, i.e., e2 < e1 = E(κ̄).
• if α(γ2 ) ≥ α̂(γ2 ) and α(γ1 ) < α̂(γ1 ), then also γ1 α(γ1 ) < γ̂ ≤ γ2 α(γ2 ) and
x1 > x2 = 0, i.e., e1 > e2 = e∗ .
The rest of the proof of Lemma B3 is part of the proof of Proposition 3.II.
Proof of Proposition 3.II.
Note, in region (b) of Figure 2.1, where γ̃ < γ1 α(γ1 ) ≤ γ2 α(γ2 ) < γ̂, ∂e/∂(γα(γ)) postulates a negative relation between emissions e and γα(γ). To prove γ1 α(γ1 ) ≤ γ2 α(γ2 ) in
this region, suppose for a contradiction that γ1 α(γ1 ) > γ2 α(γ2 ) which requires α1 > α2
for γ1 < γ2 . Given (2.7), the monitoring policy is optimal iff a marginal reallocation
112
A.2. Proof of Proposition 3 and 4
of budget δ > 0 from Country 1 to Country 2 does not reduce the aggregate emission
level. Considering Lemma B2, this implies
#
"
∂e2
∂e1
+ γ2
=0
v(γ1 )δ −γ1
∂(γ1 α1 )
∂(γ2 α2 )
Yet, for γ1 α(γ1 ) > γ2 α(γ2 ), and considering lemma B1
"
#
∂e1
∂e2
−γ1
< 0.
+ γ2
∂(γ1 α1 )
∂(γ2 α2 )
The reallocation of monitoring pressure from Country 1 to Country 2 reduces the aggregate emission level. Hence, a monitoring policy in which α(γ1 ) > α(γ2 ) for countries
of type γ1 < γ2 can never be optimal.
Proof of Proposition 3.I. and Proposition 4
In order to prove γ̃(κ̄) < γl (B, κ̄), suppose for a contradiction that γ̃(κ̄) = γl (B, κ̄).
Consider an arbitrary country γ ∈ (γ̃(κ̄), γh (B)) which is audited with its optimal
probability α(γ). Recall from Lemma 1 that α(γ) > α̃(γ) is required to disincentivize
x = t. When γ → γ̃(κ̄), then α(γ) → 1. This requires, considering the proof of
κ̄
κ̄
Proposition 3.II., a monitoring budget of B . Hence, γ̃(κ̄) < γl (B, κ̄) for B < B .
Note that for an increase in the monitoring budget, the condition in Lemma B2 must
still hold. Hence, countries within Region II of Proposition 3 are audited more intensely.
Considering Lemma 1 and the argument above, it follows that γl (B, κ̄) is non-increasing
in the monitoring budget B.
Proof of Proposition 3.III. and Proposition 4
To show that γh (B) < 1, suppose for a contradiction that γh (B) = 1 and take an
arbitrary country of type γ ∈ (γl (B, κ̄), 1]. That is, we are in Region II of Figure
2.2b and α(γ) < M in{1, α̂(γ)}. From equation (2.7) and Lemma B1, e′ (α(1)) =
γe′ (γα(γ)) ≤ e′ (α̂(1)) must hold, as α(1) ≤ α̂(1). Then, from Lemma B2 it follows
that α(γ) < α̂(γ) ∀ γ ∈ (γ̂, 1). We denote the maximum monitoring costs for auditing
κ̄
countries of type γ ∈ (γ̂, 1) with probability α by B κ̄ . This is strictly lower than B ,
where countries are monitored with probability α̂(γ). If B ≤ B κ̄ , then γh (B) = 1, while
κ̄
γh (B) < 1 for B ∈ (B κ̄ , B ). It is hence straightforward that γh (B) is non-increasing
in B.
A. Appendix to Chapter 2
A.3
113
Proof of Proposition 6 and 7
Note first, under the current assumptions, emissions e are still decreasing and convex
in α for α(κ) ∈ [α̃(γ̄, κ), 1). Hence, in order to minimize emissions, two identical κ-type
countries ought to be audit with the same probabilities. The next two lemmas follow
immediately.
Lemma C1. An optimal monitoring
policy requires that for two countries of type
t[1−κ̃]
(γ̄, κ1 ) and (γ̄, κ2 ), with γ̄αi ∈ βt+F ′ (E(κ̃)−e∗ ) , βt+Ft ′ (0) and αi < 1, i ∈ {1, 2},
∂e(x(α1 γ̄), κ1 )
∂e(x(α2 γ̄), κ2 )
=
∂α1
∂α2
must hold.
Lemma C2. Under the current assumptions, the following holds for all αγ̄ ∈ [α̃(γ̄, κ), 1)
and κ ∈ [0, 1].
∂ 2 e(x(αγ̄), κ)
<0
∂α∂κ
The rest of the proof of Proposition 6 is similar to the proof of Proposition 3.
Proof of Proposition 6.II.
Consider two countries 1 and 2 with κ1 < κ2 and κi ∈ (κl (B, γ̄), κh (B, γ̄)) that are
audited with probability αi < 1 with i ∈ [1, 2]. To proof α1 < α2 suppose for a
contradiction that the countries are audited with probabilities, such that α1 ≥ α2 . The
monitoring policy is optimal if a marginal reallocation of budget δ > 0 from Country
1 to Country 2 does not reduce the aggregate emission level. Considering lemma C1,
this implies
#
"
∂e(x(α2 γ̄), κ2 )
∂e(x(α1 γ̄), κ1 )
+ γ̄
= 0.
(A.4)
r(κ1 )δ −γ̄
∂α1 γ̄
∂α2 γ̄
Given Lemma C2, condition (A.4) is always negative for α1 ≥ α2 . Hence, auditing
countries of type κ1 < κ2 with κi ∈ (κl (B, γ̄), κh (B, γ̄)) such that α1 ≥ α2 holds, can
never be part of an optimal monitoring policy.
114
A.3. Proof of Proposition 6 and 7
In order to show that ∂e/∂κ < 0 for α(κ) ∈ [α̃(γ̄, κ), 1) we apply the Implicit
Function Theorem on (2.3), which yields
α′ (κ)γ̄β [F ′ (e(·) − e∗ ) + t]
∂e(x(αγ̄, κ), κ)
= ′′
< 0.
∂κ
g (·) − α(κ)γ̄F ′′ (e(·) − e∗ )
Furthermore,
∂ 2 e/∂κ2
(A.5)
> 0 for α′′ < 0.
Proof of Proposition 6.I. and Proposition 7
The proof for κ̃ < κl (B, γ̄) is similar to the proof of Proposition 3.I. and therefore
omitted. Considering Lemma C1 and the argument above, it follows that κl (B, γ̄) is
decreasing in the monitoring budget B.
To show that emissions are increasing in κ for κ ∈ [0, κl (B, γ̄)] note that for α = 0
the constraint on x is binding, resulting in the corner solution x = t (see the proof of
proposition 1.I.). Now, ∂e/∂κ > 0 for x = t is straightforward from (2.2).
Proof of Proposition 6.III. and Proposition 7
The proof for κh (B, γ̄) < 1 is similar to the proof of Proposition 3.III. and therefore
omitted. From this, it follows that κh (B, γ̄) is non-increasing in the monitoring budget
B.
To show that emissions are constant for κ ≥ κh (B, γ̄) replace α′ (κ) = 0 in (A.5) as
α(κ) = 1 is bounded from above. Hence, ∂e/∂κ = 0 and emissions remain constant over
κ. That is, the effort in fiscal cushioning x∗ (κ) is decreasing in κ such that e∗∗ = E(κ̃)
holds for all countries with κ ≥ κh (B, γ̄).
Chapter B
Appendix to Chapter 3
B.1
Proof of Proposition 1
The optimal tax rate can be deduced from the First Order Condition of (3.6) with
respect to τ , i.e.
γt
γt
τ γt
′′
E (b + η) ′′ + B qt (τ, θ) ′′ − ′′ = 0
C
C
C
The First Order Condition of (3.7) with respect to p(l), i.e.
"
#
γq
γq
(p(l) + θ)γq
E (b + η) ′′ + B ′′ qq (l, θ) ′′ −
= 0.
C
C
C ′′
yields the optimal permit price p∗ . Replacing p(l) by p∗ in (3.5), solving for l and
taking expectations, yields the optimal amount of pollution allowances l∗ .
Substituting τ ∗ and p∗ in (3.9) and (3.10) respectively, yields the expected abatement level
(2b + F )γt
(2b + F )γq
qt (τ ∗ ) = ′′
and qq (p∗ ) = ′′
.
′′
C − 2B γt
C − 2B ′′ γq
Given αq > αt by assumption, it follows that qt (τ ∗ ) < qq (p∗ ). Considering Assumption
1 it is straightforward that qq (p∗ ) < qf (·), where qf is the abatement level with complete
enforcement, i.e., if αi = 1 and F = 0. Furthermore, ∂qq (p)/∂p > ∂qt (τ )/∂τ is obvious
from comparing (3.9) and (3.10). Q.e.d.
116
B.2
B.2. Proof of Proposition 2
Proof of Proposition 2
By construction, incomplete enforcement requires
F <
b(1 − 2γq )
(1 − αi )
p=
αi
γq (1 + β)
Substituting F by d(b(1 − 2γq ))/(γq (1 + β)), with d ∈]0, 1[, in (3.12), the differentiated enforceability effect rewrites
b2 (γq − γt )
4C ′′ γq2 (1 + β)2
(
d2 (1 − 2γq ) (d(1 − 2γq ) + 2γq (1 + β))2
−
(1 − 2γt )
(1 + 2βγq )(1 + 2βγt )
)
Since (1 − 2γq )/(1 − 2γt ) < 1 for αq > αt ,this term is strictly negative if
(d(1 − 2γq ) + 2γq (1 + β))2
≥1
d2 (1 + 2βγq )(1 + 2βγt )
which is always the case for αq > αt , d ∈]0, 1[ and β ∈ R+ .
The differentiated enforceability effect is thus always negative. Q.e.d.
B.3
Proof of Proposition 3
Proposition 3 requires
Ψ(β) + Ω(β) < 0,
(B.1)
where
Ψ(β) =
2(1 − 2β(1 − γq ))γq σθ2
2C ′′
(B.2)
and
(γq − γt )
Ω(β) =
4C ′′
(
F2
(2b + F )2
−
(1 − 2γq )(1 − 2γt ) (1 + 2βγq )(1 + 2βγt )
)
(B.3)
117
B. Appendix to Chapter 3
A sufficient condition for ∆pq < 0 would obviously be
"
1
max Ψ(β) < min |Ω(β)| ∀ β ∈ 0,
β
β
2(1 − γq )
#
Note,
argmax
i Ψ(β) = 0
h
1
β∈ 0, 2(1−γ
q)
which is obvious from (B.2). In order to derive
argmax
h
i Ω(β),
1
β∈ 0, 2(1−γ
q)
consider the constrained maximization program
max Ω(β) s.t.
β
1
− β ≥ 0.
2(1 − γq )
Solving the Lagrangian program while denoting the Lagrange multiplier with λ, the
Kuhn-Tucker conditions are
∂L
∂Ω(β)
=
−λ=0
∂β
∂β
1
1
∂L
=
− β ≥ 0; λ ≥ 0; λ
=0
∂λ
2(1 − γq )
2(1 − γq )
∂Ω(β)/∂β is strictly positive for αq > αt . Hence, λ is positive and the constraint is
binding, which implies
1
argmax
h
i Ω(β) = 2(1 − γ ) .
q
1
β∈ 0, 2(1−γ
q)
1
into (B.3) and solving (B.1) for σθ2 ,
Substituting β = 0 into (B.2) and β = 2(1−γ
q)
yields a sufficient condition for the threshold level
σ 2θ
(γq − γt )
=
4γq
(
(2b + F )2 (1 − γq )2
F2
−
1 − γq + γt
1 − 2γq − 2γt + 4γq γt
below which ∆pq is always negative. Q.e.d.
)
118
B.3. Proof of Proposition 3
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