Emerging Trends in The Social and Behavioral Sciences

Modeling Coal and Natural Gas Markets

Item

Title

Modeling Coal and Natural Gas Markets

Author

Holz, Franziska

Research Area

Social Institutions

Topic

Markets

Abstract

Coal and natural gas market modeling has seen an impressive upsurge in the last decade. After a long period with a focus on optimization models, complementarity models have been developed since the 1980s and seen a renaissance after 2000. Such models are also called equilibrium models as they allow representing a market game and its equilibrium solution. First versions of complementarity models of the coal and natural gas markets were used to analyze the market structure of the international commodity trade. While they confirmed an oligopolistic market structure in the European natural gas market, the global coal market has been found to be competitive. Moreover, infrastructure analyses are carried out with such models that allow detecting bottlenecks and, in multiperiod models, computing cost‐efficient capacity expansions. Other recent advances besides multiperiod modeling are the modeling of multilevel games and stochastic models. Emerging topics are related to computational methods and a better understanding of both energy sectors. Among the challenges to the modeling community are the ongoing shortcomings of publicly available data and an improved understanding of the mathematical modeling and solution approaches by economists. Finally, both sectors are subject to a climate policy constraint which may well lead to a considerable shift in the importance as well as in regional consumption patterns of coal and natural gas and, hence, require improved modeling analysis.

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extracted text

Modeling Coal and Natural
Gas Markets
FRANZISKA HOLZ

Abstract
Coal and natural gas market modeling has seen an impressive upsurge in the last
decade. After a long period with a focus on optimization models, complementarity models have been developed since the 1980s and seen a renaissance after 2000.
Such models are also called equilibrium models as they allow representing a market game and its equilibrium solution. First versions of complementarity models of
the coal and natural gas markets were used to analyze the market structure of the
international commodity trade. While they confirmed an oligopolistic market structure in the European natural gas market, the global coal market has been found to
be competitive. Moreover, infrastructure analyses are carried out with such models
that allow detecting bottlenecks and, in multiperiod models, computing cost-efficient
capacity expansions. Other recent advances besides multiperiod modeling are the
modeling of multilevel games and stochastic models. Emerging topics are related to
computational methods and a better understanding of both energy sectors. Among
the challenges to the modeling community are the ongoing shortcomings of publicly available data and an improved understanding of the mathematical modeling
and solution approaches by economists. Finally, both sectors are subject to a climate
policy constraint which may well lead to a considerable shift in the importance as
well as in regional consumption patterns of coal and natural gas and, hence, require
improved modeling analysis.

INTRODUCTION
The modeling of coal and natural gas markets has traditionally focused on
the international trade of these energy commodities. This relates to trade
of natural gas through high-pressure pipeline or in form of liquefied natural gas (LNG), and the trade of steam coal on the seaborne market. In the
standard modeling literature of coal and natural gas markets, each sector is
investigated on its own, that is with a supply and demand representation of
this sector only. These sector-specific models (sometimes also called “partial
equilibrium models”) have the advantage to represent more complex supply

Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

structures compared to energy system models where the substitution relation
with other energy commodities is included.
More particular, it will be explained in the following that sector-modeling
of coal and natural gas trade allows for the analysis of market power, in particular on the supply side. This is a highly relevant feature in markets with
very concentrated supply structures. Monopolies, cartels, and oligopolies can
be modeled in this framework, as well as perfectly competitive markets.
Other questions than the existence of market power that are being investigated with models of the coal or natural gas markets are supply security and
investment requirements in infrastructure, and more recently the interaction
with climate policies. A concentrated supply structure is often accompanied
by congested infrastructure and even more so in situations of increasing
demand (e.g., opening of new markets, increasing energy demand in
emerging economies). This leads both to supply security concerns because
of few suppliers/supply routes available to supply a certain market and to
the necessity to expand transport infrastructure (export ports, pipelines, or
import ports). It may be of commercial or public interest to build or expand
infrastructure, and the economic modeling provides indications where the
investment would be most needed.
The models usually represent the supply chains in a quite detailed manner,
although some approximation of the complex technical processes has to be
made to deal with solvable models. In the coal sector, the models include the
following players:
•

•
•
•

producers (combining the activities of exploring, extracting, and preparing/washing the coal in a single supply function)
exporters (or export ports)
shippers
final demand by an importing country, where the demands by various
consumers (in general, power producers) are aggregated.

Similarly for the natural gas sector, (a selection of) the following players are
represented in the models:
•

•
•
•
•
•

producers (here, too, combining the activities of exploration, extraction,
and processing the natural gas)
(dedicated) traders (which may be dedicated to a specific producer)
LNG players: liquefaction, shipment, regasification
pipeline operators
storage operators (for seasonal arbitrage over the course of a year)
final demand (aggregating the national demand from the three
sectors using natural gas, namely power generation, industry, and
residential/commercial).

Modeling Coal and Natural Gas Markets

3

This field of research is characterized by an interaction of economists with
applied mathematicians from operations research. With the level of detail
and the computational methods, the modeling of coal and natural gas markets is part of the same literature in energy economics and applied operations
research as electricity market modeling. It has only a lose relation to traditional resource economics which consists mostly in the modeling of a reserve
constraint that producers have to respect in the long run.
FOUNDATIONAL RESEARCH
OPTIMIZATION MODELING
Following the development and wide-spread application of (linear) optimization methods after World War II, this method has also been used in
energy economics since the 1960s. Sectoral modeling using linear programming/optimization (LP) solution techniques allows for a great number of
technical details to be included in the models, albeit with the simplifying
requirement of using linear functions. Such models have found large interest
in academia and even more so in the strategy and operational departments
of energy companies where they are still widely used today.
An optimization model consists of an objective function that is either maximized or minimized subject to constraints. Typically, the objective function
is a total cost function that shall be minimized. A variant with welfare maximization of the specific sector is equivalent to a cost minimization problem
given a certain demand level. The constraints are various technical details, for
example, maximum production capacity of a mine, maximum throughput
capacity of a pipeline. This makes optimization models attractive for companies where they are mostly used today because they are convenient for
engineers and helping in day-to-day operational decisions. Generally, these
models are static which means that they model one time period. The time
period depends on the level of investigation: it can be very short (e.g., 1 h)
for an operational analysis (e.g., of a natural gas network) or much longer for
strategic analysis (e.g., 1 year). Many models include an optimization of network flows based on graph theory to compute cost-minimal pipeline flows.
The economic assumptions in optimization models are rather simple: with
cost-minimization being the objective and the assumption that market prices
are equal to the sum of all marginal costs along the value chain (production
plus transportation, etc.), these models implicitly assume perfect competition
in the markets. In many regions, such as natural gas markets in Europe and
Asia, but also coal markets in the US and globally in the 1980s, this assumption has seemed too strong given the small number of suppliers and apparent
price levels above (marginal) costs.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

COMPLEMENTARITY MODELING
Hence, more advanced computational methods have increasingly been used
by economists since the 1980s. This was possible with the development of
advanced solution algorithms and solvers as well as easily accessible software for economists (namely, GAMS, the standard software used by energy
market modelers today). A different class of models than optimization problems is used nowadays: so-called complementarity (or equilibrium) models.
These models consist of the so-called Karush-Kuhn-Tucker (KKT) optimality conditions. The KKT conditions are obtained by deriving the first-order
(hence, optimality) conditions of the optimization problem (objective function and constraints) of the players. The Hence, a complementarity model
also calculates the optimal solution to an economic problem and follows a
similar understanding of the market in question as in optimization models.
However, in contrast to optimization models, in a complementarity model,
the optimization problems of several, interdependent players can be solved
simultaneously. This allows for a more adequate modeling of a market, with
an interaction of supply and demand (i.e., supply functions and demand
functions) and with strategic behavior of the suppliers. Hence, perfect competition is not a necessary assumption and one can model a situation with
market prices higher than (marginal) costs, for example due to oligopolistic
withholding.
This is a strong advantage of complementarity models for the economic
analysis of energy markets and has led to an increasing use after 2000. In the
1980s, such models were first developed, in particular for coal markets (US
and global markets, e.g., Kolstad & Abbey, 1984) and for natural gas markets (Europe, e.g., Mathiesen, Roland, & Thonstad, 1987). However, the solution algorithms (solvers) and the computer capacities were not yet advanced
enough to replace optimization models. Owing to the KKTs, complementarity models have more constraints than optimization models which leads to
higher mathematical complexity and computation time.
After some significant advances, in particular with the development of the
PATH solver for GAMS, applied complementarity modeling saw a “renaissance” in the late 1990s. While in the 1980s the coal and natural gas sectors
triggered the model innovations, it was the electricity sector that was precursor in the late 1990s. The coal and natural gas sectors this time were following
behind and modelers of these sectors used model setups and solution techniques that were first used for electricity market analyses.
The early natural gas complementarity models of the 2000s focused on the
European natural gas sector and analyzed imports and supply security. European natural gas markets were traditionally segmented with monopolistic
national wholesale traders that imported within long-term contracts from a

Modeling Coal and Natural Gas Markets

5

very limited number of suppliers. The import infrastructure (pipelines and
import terminal of LNG) was dedicated to sales under long-term contracts.
Hence, complementarity modeling was necessary to represent this market
appropriately and in order to analyze such questions as infrastructure adequacy.
The first modeling teams were based in countries with a strong interest in a
better understanding of international natural gas trade, namely Norway and
the Netherlands (producing countries) as well the United States (a prospective large importer at the time). In Norway, Lars Mathiesen et al. were at
the forefront of natural gas modeling; Rolf Golombek et al. developed a cost
function approach that is still widely used in the natural gas and oil modeling literature (Golombek, Gjelsvik, & Rosendahl, 1995). In the Netherlands,
Maroeska Boots and Wietze Lise developed and used the GASTALE model
to which Benjamin F. Hobbs contributed (Boots, Rijkers, & Hobbs, 2004; Lise
& Hobbs, 2008). Ruud Egging, together with Steven A. Gabriel, developed
the European Gas Model (Egging & Gabriel, 2006; Egging, Gabriel, Holz, &
Zhuang, 2008) which was later extended to the World Gas Model (Egging,
Holz, & Gabriel, 2010). More recently, the Institute of Energy Economics at
the University of Cologne in Germany moved from optimization modeling
to complementarity modeling of natural gas (Hecking & Panke, 2012).
In complementarity models, too, a flow optimization in a network can
be implemented. The modeling approach has the advantage, compared to
optimization models, to allow for the implementation of a simultaneous,
concurrent use of an (pipeline) arc by several players or even types of
players. Moreover, in a complementarity model, the dual variable of a
capacity constraint can directly be used in the equations of the model. The
dual (or shadow) variable gives an economic value to an additional unit
of the constrained capacity, for example, the implicit economic valuation
of a marginally higher pipeline capacity. The information on the value of a
constrained arc can, for example, directly be used in the pricing formulae of
the arc transportation.
The resurgence of coal modeling came some years after that for natural gas
and followed some few empirical analyses. The international steam coal market seems to be characterized by a less complex institutional structure, in particular because of lower asset specificity of the export/import infrastructure
(ports, ships), and a more diversified supply structure. However, increasing concentration of producing companies in the last decade has raised the
interest of economists, too. Hence, first modeling efforts were directed at
market structure analysis and market power detection, for instance with the
Coalmod-Trade model by Haftendorn and Holz (2010) and for more recent
years by Trüby and Paulus (2012). For both, coal and natural gas markets,

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

there is a strong limitation of data availability: because company information, for example on costs, is hardly available, most models use country data.
However, price and quantity results give an acceptable approximation and
allow to detect if there is exertion of market power.
CUTTING-EDGE RESEARCH
The first complementarity models of natural gas and coal markets that are
mentioned above were static one-period analyses with perfect competition
or Cournot competition (i.e., one-stage games). They served for market structure analysis or the identification of infrastructure bottlenecks. Cutting-edge
research today goes in three main directions:
•

•
•

multiperiod modeling with endogenous investment decisions (usually
in transport infrastructure),
stochastic modeling,
multilevel games with sequential decisions, for example, Stackelberg
games, and other games with joint constraints by several players
(Generalized Nash equilibrium problems).

MULTIPERIOD MODELS
Multiperiod models of coal and natural gas markets are usually based on
a net present value optimization by rational players with perfect foresight.
These models go beyond the identification of bottlenecks in infrastructure.
Their results also show which infrastructure will be economic to be built, as
a result of a complex interaction of minimization of investment costs and
variable costs of infrastructure utilization, for an endogenously computed
level of transportation and commodity demand in each period. Computing
such settings with several optimization problems and market equilibrium
while having a relatively large number of endogenous variable types is a
strength of the complementarity approach.
Several such much models of the European or global natural gas markets
and of global coal markets are currently in use. A state-of-the-art example
in natural gas market modeling is the World Gas Model (Egging, Gabriel,
& Holz, 2010); for coal markets, the COALMOD-World (Haftendorn, Holz
& Hirschhausen, 2012) was the first of its kind. The models usually cover
time periods until 2030 or 2050 in 5-year steps. An increase in the number of
time steps more than proportionally increases the computation time (often
exponentially); hence, the relatively small number of model periods.
In game-theoretic terms, the multiperiod models today are open-loop models based on a perfect foresight assumption. In the open-loop approach, the

Modeling Coal and Natural Gas Markets

7

decisions for all periods are taken at once in a single intertemporal optimization over the entire model horizon. All players are assumed to have perfect
and complete information on the outcomes of all (current and future) periods.
This is a strong assumption, which is necessary to remain in the framework
of (non-) linear complementarity modeling in which the KKT optimality conditions give the unique solutions. Open-loop models have the advantage of
a limited solution space that ensures unique equilibrium results (under some
conditions). Hence, they can be solved numerically in the mixed complementarity format (cf. Gabriel, Gabriel, Conejo, Fuller, Hobbs, & Ruiz, 2012).
After market structure analyses were in the focus of economic studies
with static market models, multiperiod models are used to study the
long-term perspectives of the resource markets, in particular under climate
policy constraints. Hence, scenario analyses are current contributions to the
literature with multiperiod natural gas or coal market models. Such climate
policies can be varying levels of CO2 prices, export taxes on fossil fuels, or
(mandatory) consumption reductions (see e.g., Haftendorn, Holz, Kemfert,
& Hirschhausen, 2013).
Not all functions of the models in use are well-founded, both in their functional form and the data input. This is a problem both on the demand and
the supply side. On the supply side, cost functions for production, transportation, and investment must be included in the model. They are often
assumed to be linear to ensure convexity of the optimization problem. More
complex functional forms than linear functions are possible and could potentially enrich the models. Only for production costs, an alternative curve has
become a standard assumption in the European literature: it is assumed that
(marginal) costs are increasing, with a strong rise close to the production
capacity constraint (the often called “Golombek cost function”, mentioned
above). However, this cost function still has to be introduced in multiperiod
models that allow for endogenous investment decisions in the production
capacity. Huppmann (2013) has paved the way for this model extension.
STOCHASTIC MODELING
Another stream of literature at the current research frontier is stochastic modeling. While this approach has not been applied for coal market models yet,
there have been a few applications to natural gas markets (e.g., Zhuang &
Gabriel, 2008). As for deterministic models, the availability of perfect and
complete information is assumed. The stochasticity consists in having multiple possible realizations of a variable. The realizations are predetermined
and are assigned a known probability of occurrence.
Computing the outcome of a stochastic model has the advantage to include
the reaction of the players to uncertainty. This can lead to a different outcome

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

than in a deterministic model and it is also different from the average of the
outcomes of the equivalent deterministic models of each stochastic scenario.
Similar to (deterministic) multiperiod models, the number of nodes in the
scenario tree cannot be extended at will due to the more than proportional
increase of computation time.
MULTILEVEL AND COUPLED CONSTRAINT MODELS
A third advance in the recent literature of coal and natural gas modeling
deals with the application of multilevel and coupled-constraint games. Even
in a relatively simple market setup with sequential decisions as a Stackelberg game with one leader and a few Cournot-playing followers, there
can be more than one solution. A Stackelberg game describes a sequential
“leader-follower” problem and can be used to describe market structures
with a high concentration in market power by just a few of players (e.g.,
OPEC in the oil market).
In general, if the feasible set of a player type depends on the decisions taken
by other players, multiple solutions are possible and numerical algorithms
face problems. Hence, there is a challenge to reduce the solution space to the
only reasonable solution(s). This challenge is even greater with more complex
models, for example with several leaders competing in addition to the game
between the followers. Multilevel complementarity models are either mathematical programs with equilibrium constraints (i.e., optimization problem
of one player in the first stage) or equilibrium problems (e.g., game of several players in the first stage) with equilibrium constraints (MPEC or EPEC,
respectively). Clearly, they are a generalization of static game complementarity models.
KEY ISSUES FOR FUTURE RESEARCH
Several topics have recently emerged in the coal and natural gas market
research. They would promote this field of research both in the complementarity modeling stream and with other modeling methods. In the following,
the emerging topics will be discussed first, before presenting some major
challenges for current and future research.
EMERGING TOPICS IN THE COAL AND NATURAL GAS MARKET MODELING
One major advance currently under research are new solution methods for
computationally large problems, that is, multiperiod models, stochastic models, or multilevel models. In these large models, it can often be helpful to
reduce the solution space in order to decrease the model running time to a

Modeling Coal and Natural Gas Markets

9

feasible duration (or in some cases to obtain a solution at all). Branch-and-cut
or decomposition methods have been experimented with in the natural gas
modeling literature so far. Other methods may emerge in the future.
Optimization and complementarity models depict market settings that are
well-founded in economic theory, namely perfect competition and Cournot
competition, sometimes also a bilevel Stackelberg market or monopoly.
However, the player’s optimization problems in real world are more complex than in the abstract economic theory and richer formulations may
reveal new insights in the players’ behavior and the market structure. For
example, many companies in the natural gas market are entirely state-owned
and are operated under different premises than standard profit maximizing,
such as an objective of revenue maximization or employment maximization.
Alternatively, a regulated player may also have to obey to rules that are not
covered by the standard perfect competition model, for example, certain
pricing rules. It is not straightforward to include such deviant objectives
in a standard optimization or complementarity model and other modeling
techniques can more easily accommodate them. In particular, agent-based
modeling is a promising approach to include complex objectives. This
method has, however, the drawback of a lack of theoretical foundation of its
economic relations.
For any modeling approach to be used, a considerable improvement of
the understanding and modeling of reserves is needed. This entails several
aspects: first, the mechanism how (uneconomic) resources become (economically exploitable) reserves needs better understanding in order to derive a
general relation that can be included a model. Second, the impact of reserve
depletion on the production cost function is hardly taken into account in the
models so far. One can assume that low-cost reserves are produced first and
that higher-cost ones remain in the ground for longer, but that at the same
time a variety of types of basins are in production. Hence, one can assume an
upward shift of the cost function over time. A seminal contribution by Haftendorn (2012) to long-term coal market modeling gives an example of an
integration of reserves in the cost function. Third, unconventional resources
need to be included in the models, for example shale gas. The models usually
only include information on the reserves, but not on the resources. Obtaining this information is hard for most types of resources, but for some such as
shale gas more and more information has become available.
CHALLENGES TO COAL AND NATURAL GAS MARKET MODELING
The availability of data is one of the major challenges for coal and natural
gas market modeling. In particular access to supply side data, such as production costs, is very limited for the scientific community. It is somewhat

10

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

better for companies of the energy industry (utilities, consultants). However,
statistical information by the International Energy Agency (OECD) and the
Energy Information Administration (U.S. Department of Energy), as well
as organizations close to the industry (e.g., IEA Clean Coal Centre for coal,
Observatoire Méditerranéen de l’Energie for natural gas) and recent research
efforts (e.g., the Global Energy Assessment) provide a satisfactory basis for
sound academic research.
Another major challenge for the further development of coal and natural
gas market models, in particular the complementarity models is the increasing mathematical complexity of the modeling and solution techniques. An
improved understanding by economists of the advanced mathematical modeling is needed and requires more and more involvement of mathematicians
in addition to economists and engineers in the modeling community.
If more complex and nonstandard objectives and constraints are to be
included in the models, a better understanding of the real-world players’
behavior and optimization problems is needed. Experimental economics
has started to investigate some aspects of energy markets (e.g., auctioning
of transportation capacities), but there remain plenty of topics to be examined. This will also be a valuable input for nonstandard models such as
agent-based models of the natural gas or coal markets.
Last but not least, the looming transformation of the energy systems under
climate change and climate policy pressure may well lead to a strong reduction of the consumption of coal and natural gas, hence to a disappearing
object of analysis of natural gas or coal market modeling. Owing to different
carbon intensities, fossil fuels are presumably differently affected by climate
policies due to differing carbon intensities. This calls for using models
of the entire energy system, ideally in the same modeling format as the
state-of-the-art coal and natural gas market models (i.e., complementarity
modeling) which allows for the representation of market power in order
to be able to investigate the effects of systemic changes on coal and natural
gas markets. A first such modeling step was suggested by Egging and
Huppmann (2012) in a multifuel complementarity model.
In conclusion, the modeling techniques and experience of coal and natural gas modeling are potentially relevant for modeling other (nonenergy)
resource markets, for example, metals and rare earths.

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FRANZISKA HOLZ SHORT BIOGRAPHY
Dr. Franziska Holz (*1979) is a Researcher at the German Institute for Economic Research (DIW Berlin), where she directs a research group on resource
markets (coal, natural gas, and oil). She studied economics at the Paris 1 University Panthéon-Sorbonne (1998–2003) where she graduated with a Master’s degree in International Economics. Between 2004 and 2008, she prepared her PhD thesis on modeling of the European natural gas market at
DIW Berlin, which she successfully defended at TU Berlin in 2009. Dr. Holz
has published extensively on modeling the global gas, coal, and oil markets.
She participated and coordinated a number of research projects, i.a. for the
European Commission, the German Ministry of Education and Research, and
the Stanford University’s Program on Energy and Sustainable Development.
She has participated in the Energy Modeling Forum (EMF 23 on global natural gas markets, EMF 28 on European technology options for climate policy)
and organized various academic events (e.g., European Doctoral Seminar on
Natural Gas 2005–2010, Infratrain workshops at TU Berlin and DIW Berlin
since 2004). Dr. Holz is married and has one child.
RELATED ESSAYS
The Role of Data in Research and Policy (Sociology), Barbara A. Anderson
Global Economic Networks (Sociology), Nina Bandelj et al.
The Public Nature of Private Property (Sociology), Debbie Becher
Can Public Policy Influence Private Innovation? (Economics), James Bessen
Sociological Theory After the End of Nature (Sociology), Robert J. Brulle
Neoliberalism (Sociology), Miguel Angel Centeno and Joseph N. Cohen
The State and Development (Sociology), Samuel Cohn
Trust and Economic Organization (Sociology), Karen S. Cook and Bogdan
State
Misinformation and How to Correct It (Psychology), John Cook et al.
Architecture of Markets (Sociology), Neil Fligstein and Ryan Calder
Organizational Populations and Fields (Sociology), Heather A. Haveman and
Daniel N. Kluttz
Behavioral Economics (Sociology), Guy Hochman and Dan Ariely
Technology Diffusion (Economics), Adam B. Jaffe

Modeling Coal and Natural Gas Markets

13

Search and Learning in Markets (Economics), Philipp Kircher
Natural Resources and Development (Political Science), Kevin M. Morrison
Economics of Renewable Energy Production (Economics), Gregory F. Nemet
Organizations and the Production of Systemic Risk (Sociology), Charles
Perrow
Economics and Culture (Economics), Gérard Roland
Sociology of Entrepreneurship (Sociology), Martin Ruef
Sustainability (Archaeology), Joseph A. Tainter et al.
The Social Science of Sustainability (Political Science), Johannes Urpelainen



Modeling Coal and Natural
Gas Markets
FRANZISKA HOLZ

Abstract
Coal and natural gas market modeling has seen an impressive upsurge in the last
decade. After a long period with a focus on optimization models, complementarity models have been developed since the 1980s and seen a renaissance after 2000.
Such models are also called equilibrium models as they allow representing a market game and its equilibrium solution. First versions of complementarity models of
the coal and natural gas markets were used to analyze the market structure of the
international commodity trade. While they confirmed an oligopolistic market structure in the European natural gas market, the global coal market has been found to
be competitive. Moreover, infrastructure analyses are carried out with such models
that allow detecting bottlenecks and, in multiperiod models, computing cost-efficient
capacity expansions. Other recent advances besides multiperiod modeling are the
modeling of multilevel games and stochastic models. Emerging topics are related to
computational methods and a better understanding of both energy sectors. Among
the challenges to the modeling community are the ongoing shortcomings of publicly available data and an improved understanding of the mathematical modeling
and solution approaches by economists. Finally, both sectors are subject to a climate
policy constraint which may well lead to a considerable shift in the importance as
well as in regional consumption patterns of coal and natural gas and, hence, require
improved modeling analysis.

INTRODUCTION
The modeling of coal and natural gas markets has traditionally focused on
the international trade of these energy commodities. This relates to trade
of natural gas through high-pressure pipeline or in form of liquefied natural gas (LNG), and the trade of steam coal on the seaborne market. In the
standard modeling literature of coal and natural gas markets, each sector is
investigated on its own, that is with a supply and demand representation of
this sector only. These sector-specific models (sometimes also called “partial
equilibrium models”) have the advantage to represent more complex supply

Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

1

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

structures compared to energy system models where the substitution relation
with other energy commodities is included.
More particular, it will be explained in the following that sector-modeling
of coal and natural gas trade allows for the analysis of market power, in particular on the supply side. This is a highly relevant feature in markets with
very concentrated supply structures. Monopolies, cartels, and oligopolies can
be modeled in this framework, as well as perfectly competitive markets.
Other questions than the existence of market power that are being investigated with models of the coal or natural gas markets are supply security and
investment requirements in infrastructure, and more recently the interaction
with climate policies. A concentrated supply structure is often accompanied
by congested infrastructure and even more so in situations of increasing
demand (e.g., opening of new markets, increasing energy demand in
emerging economies). This leads both to supply security concerns because
of few suppliers/supply routes available to supply a certain market and to
the necessity to expand transport infrastructure (export ports, pipelines, or
import ports). It may be of commercial or public interest to build or expand
infrastructure, and the economic modeling provides indications where the
investment would be most needed.
The models usually represent the supply chains in a quite detailed manner,
although some approximation of the complex technical processes has to be
made to deal with solvable models. In the coal sector, the models include the
following players:
•

•
•
•

producers (combining the activities of exploring, extracting, and preparing/washing the coal in a single supply function)
exporters (or export ports)
shippers
final demand by an importing country, where the demands by various
consumers (in general, power producers) are aggregated.

Similarly for the natural gas sector, (a selection of) the following players are
represented in the models:
•

•
•
•
•
•

producers (here, too, combining the activities of exploration, extraction,
and processing the natural gas)
(dedicated) traders (which may be dedicated to a specific producer)
LNG players: liquefaction, shipment, regasification
pipeline operators
storage operators (for seasonal arbitrage over the course of a year)
final demand (aggregating the national demand from the three
sectors using natural gas, namely power generation, industry, and
residential/commercial).

Modeling Coal and Natural Gas Markets

3

This field of research is characterized by an interaction of economists with
applied mathematicians from operations research. With the level of detail
and the computational methods, the modeling of coal and natural gas markets is part of the same literature in energy economics and applied operations
research as electricity market modeling. It has only a lose relation to traditional resource economics which consists mostly in the modeling of a reserve
constraint that producers have to respect in the long run.
FOUNDATIONAL RESEARCH
OPTIMIZATION MODELING
Following the development and wide-spread application of (linear) optimization methods after World War II, this method has also been used in
energy economics since the 1960s. Sectoral modeling using linear programming/optimization (LP) solution techniques allows for a great number of
technical details to be included in the models, albeit with the simplifying
requirement of using linear functions. Such models have found large interest
in academia and even more so in the strategy and operational departments
of energy companies where they are still widely used today.
An optimization model consists of an objective function that is either maximized or minimized subject to constraints. Typically, the objective function
is a total cost function that shall be minimized. A variant with welfare maximization of the specific sector is equivalent to a cost minimization problem
given a certain demand level. The constraints are various technical details, for
example, maximum production capacity of a mine, maximum throughput
capacity of a pipeline. This makes optimization models attractive for companies where they are mostly used today because they are convenient for
engineers and helping in day-to-day operational decisions. Generally, these
models are static which means that they model one time period. The time
period depends on the level of investigation: it can be very short (e.g., 1 h)
for an operational analysis (e.g., of a natural gas network) or much longer for
strategic analysis (e.g., 1 year). Many models include an optimization of network flows based on graph theory to compute cost-minimal pipeline flows.
The economic assumptions in optimization models are rather simple: with
cost-minimization being the objective and the assumption that market prices
are equal to the sum of all marginal costs along the value chain (production
plus transportation, etc.), these models implicitly assume perfect competition
in the markets. In many regions, such as natural gas markets in Europe and
Asia, but also coal markets in the US and globally in the 1980s, this assumption has seemed too strong given the small number of suppliers and apparent
price levels above (marginal) costs.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

COMPLEMENTARITY MODELING
Hence, more advanced computational methods have increasingly been used
by economists since the 1980s. This was possible with the development of
advanced solution algorithms and solvers as well as easily accessible software for economists (namely, GAMS, the standard software used by energy
market modelers today). A different class of models than optimization problems is used nowadays: so-called complementarity (or equilibrium) models.
These models consist of the so-called Karush-Kuhn-Tucker (KKT) optimality conditions. The KKT conditions are obtained by deriving the first-order
(hence, optimality) conditions of the optimization problem (objective function and constraints) of the players. The Hence, a complementarity model
also calculates the optimal solution to an economic problem and follows a
similar understanding of the market in question as in optimization models.
However, in contrast to optimization models, in a complementarity model,
the optimization problems of several, interdependent players can be solved
simultaneously. This allows for a more adequate modeling of a market, with
an interaction of supply and demand (i.e., supply functions and demand
functions) and with strategic behavior of the suppliers. Hence, perfect competition is not a necessary assumption and one can model a situation with
market prices higher than (marginal) costs, for example due to oligopolistic
withholding.
This is a strong advantage of complementarity models for the economic
analysis of energy markets and has led to an increasing use after 2000. In the
1980s, such models were first developed, in particular for coal markets (US
and global markets, e.g., Kolstad & Abbey, 1984) and for natural gas markets (Europe, e.g., Mathiesen, Roland, & Thonstad, 1987). However, the solution algorithms (solvers) and the computer capacities were not yet advanced
enough to replace optimization models. Owing to the KKTs, complementarity models have more constraints than optimization models which leads to
higher mathematical complexity and computation time.
After some significant advances, in particular with the development of the
PATH solver for GAMS, applied complementarity modeling saw a “renaissance” in the late 1990s. While in the 1980s the coal and natural gas sectors
triggered the model innovations, it was the electricity sector that was precursor in the late 1990s. The coal and natural gas sectors this time were following
behind and modelers of these sectors used model setups and solution techniques that were first used for electricity market analyses.
The early natural gas complementarity models of the 2000s focused on the
European natural gas sector and analyzed imports and supply security. European natural gas markets were traditionally segmented with monopolistic
national wholesale traders that imported within long-term contracts from a

Modeling Coal and Natural Gas Markets

5

very limited number of suppliers. The import infrastructure (pipelines and
import terminal of LNG) was dedicated to sales under long-term contracts.
Hence, complementarity modeling was necessary to represent this market
appropriately and in order to analyze such questions as infrastructure adequacy.
The first modeling teams were based in countries with a strong interest in a
better understanding of international natural gas trade, namely Norway and
the Netherlands (producing countries) as well the United States (a prospective large importer at the time). In Norway, Lars Mathiesen et al. were at
the forefront of natural gas modeling; Rolf Golombek et al. developed a cost
function approach that is still widely used in the natural gas and oil modeling literature (Golombek, Gjelsvik, & Rosendahl, 1995). In the Netherlands,
Maroeska Boots and Wietze Lise developed and used the GASTALE model
to which Benjamin F. Hobbs contributed (Boots, Rijkers, & Hobbs, 2004; Lise
& Hobbs, 2008). Ruud Egging, together with Steven A. Gabriel, developed
the European Gas Model (Egging & Gabriel, 2006; Egging, Gabriel, Holz, &
Zhuang, 2008) which was later extended to the World Gas Model (Egging,
Holz, & Gabriel, 2010). More recently, the Institute of Energy Economics at
the University of Cologne in Germany moved from optimization modeling
to complementarity modeling of natural gas (Hecking & Panke, 2012).
In complementarity models, too, a flow optimization in a network can
be implemented. The modeling approach has the advantage, compared to
optimization models, to allow for the implementation of a simultaneous,
concurrent use of an (pipeline) arc by several players or even types of
players. Moreover, in a complementarity model, the dual variable of a
capacity constraint can directly be used in the equations of the model. The
dual (or shadow) variable gives an economic value to an additional unit
of the constrained capacity, for example, the implicit economic valuation
of a marginally higher pipeline capacity. The information on the value of a
constrained arc can, for example, directly be used in the pricing formulae of
the arc transportation.
The resurgence of coal modeling came some years after that for natural gas
and followed some few empirical analyses. The international steam coal market seems to be characterized by a less complex institutional structure, in particular because of lower asset specificity of the export/import infrastructure
(ports, ships), and a more diversified supply structure. However, increasing concentration of producing companies in the last decade has raised the
interest of economists, too. Hence, first modeling efforts were directed at
market structure analysis and market power detection, for instance with the
Coalmod-Trade model by Haftendorn and Holz (2010) and for more recent
years by Trüby and Paulus (2012). For both, coal and natural gas markets,

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

there is a strong limitation of data availability: because company information, for example on costs, is hardly available, most models use country data.
However, price and quantity results give an acceptable approximation and
allow to detect if there is exertion of market power.
CUTTING-EDGE RESEARCH
The first complementarity models of natural gas and coal markets that are
mentioned above were static one-period analyses with perfect competition
or Cournot competition (i.e., one-stage games). They served for market structure analysis or the identification of infrastructure bottlenecks. Cutting-edge
research today goes in three main directions:
•

•
•

multiperiod modeling with endogenous investment decisions (usually
in transport infrastructure),
stochastic modeling,
multilevel games with sequential decisions, for example, Stackelberg
games, and other games with joint constraints by several players
(Generalized Nash equilibrium problems).

MULTIPERIOD MODELS
Multiperiod models of coal and natural gas markets are usually based on
a net present value optimization by rational players with perfect foresight.
These models go beyond the identification of bottlenecks in infrastructure.
Their results also show which infrastructure will be economic to be built, as
a result of a complex interaction of minimization of investment costs and
variable costs of infrastructure utilization, for an endogenously computed
level of transportation and commodity demand in each period. Computing
such settings with several optimization problems and market equilibrium
while having a relatively large number of endogenous variable types is a
strength of the complementarity approach.
Several such much models of the European or global natural gas markets
and of global coal markets are currently in use. A state-of-the-art example
in natural gas market modeling is the World Gas Model (Egging, Gabriel,
& Holz, 2010); for coal markets, the COALMOD-World (Haftendorn, Holz
& Hirschhausen, 2012) was the first of its kind. The models usually cover
time periods until 2030 or 2050 in 5-year steps. An increase in the number of
time steps more than proportionally increases the computation time (often
exponentially); hence, the relatively small number of model periods.
In game-theoretic terms, the multiperiod models today are open-loop models based on a perfect foresight assumption. In the open-loop approach, the

Modeling Coal and Natural Gas Markets

7

decisions for all periods are taken at once in a single intertemporal optimization over the entire model horizon. All players are assumed to have perfect
and complete information on the outcomes of all (current and future) periods.
This is a strong assumption, which is necessary to remain in the framework
of (non-) linear complementarity modeling in which the KKT optimality conditions give the unique solutions. Open-loop models have the advantage of
a limited solution space that ensures unique equilibrium results (under some
conditions). Hence, they can be solved numerically in the mixed complementarity format (cf. Gabriel, Gabriel, Conejo, Fuller, Hobbs, & Ruiz, 2012).
After market structure analyses were in the focus of economic studies
with static market models, multiperiod models are used to study the
long-term perspectives of the resource markets, in particular under climate
policy constraints. Hence, scenario analyses are current contributions to the
literature with multiperiod natural gas or coal market models. Such climate
policies can be varying levels of CO2 prices, export taxes on fossil fuels, or
(mandatory) consumption reductions (see e.g., Haftendorn, Holz, Kemfert,
& Hirschhausen, 2013).
Not all functions of the models in use are well-founded, both in their functional form and the data input. This is a problem both on the demand and
the supply side. On the supply side, cost functions for production, transportation, and investment must be included in the model. They are often
assumed to be linear to ensure convexity of the optimization problem. More
complex functional forms than linear functions are possible and could potentially enrich the models. Only for production costs, an alternative curve has
become a standard assumption in the European literature: it is assumed that
(marginal) costs are increasing, with a strong rise close to the production
capacity constraint (the often called “Golombek cost function”, mentioned
above). However, this cost function still has to be introduced in multiperiod
models that allow for endogenous investment decisions in the production
capacity. Huppmann (2013) has paved the way for this model extension.
STOCHASTIC MODELING
Another stream of literature at the current research frontier is stochastic modeling. While this approach has not been applied for coal market models yet,
there have been a few applications to natural gas markets (e.g., Zhuang &
Gabriel, 2008). As for deterministic models, the availability of perfect and
complete information is assumed. The stochasticity consists in having multiple possible realizations of a variable. The realizations are predetermined
and are assigned a known probability of occurrence.
Computing the outcome of a stochastic model has the advantage to include
the reaction of the players to uncertainty. This can lead to a different outcome

8

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

than in a deterministic model and it is also different from the average of the
outcomes of the equivalent deterministic models of each stochastic scenario.
Similar to (deterministic) multiperiod models, the number of nodes in the
scenario tree cannot be extended at will due to the more than proportional
increase of computation time.
MULTILEVEL AND COUPLED CONSTRAINT MODELS
A third advance in the recent literature of coal and natural gas modeling
deals with the application of multilevel and coupled-constraint games. Even
in a relatively simple market setup with sequential decisions as a Stackelberg game with one leader and a few Cournot-playing followers, there
can be more than one solution. A Stackelberg game describes a sequential
“leader-follower” problem and can be used to describe market structures
with a high concentration in market power by just a few of players (e.g.,
OPEC in the oil market).
In general, if the feasible set of a player type depends on the decisions taken
by other players, multiple solutions are possible and numerical algorithms
face problems. Hence, there is a challenge to reduce the solution space to the
only reasonable solution(s). This challenge is even greater with more complex
models, for example with several leaders competing in addition to the game
between the followers. Multilevel complementarity models are either mathematical programs with equilibrium constraints (i.e., optimization problem
of one player in the first stage) or equilibrium problems (e.g., game of several players in the first stage) with equilibrium constraints (MPEC or EPEC,
respectively). Clearly, they are a generalization of static game complementarity models.
KEY ISSUES FOR FUTURE RESEARCH
Several topics have recently emerged in the coal and natural gas market
research. They would promote this field of research both in the complementarity modeling stream and with other modeling methods. In the following,
the emerging topics will be discussed first, before presenting some major
challenges for current and future research.
EMERGING TOPICS IN THE COAL AND NATURAL GAS MARKET MODELING
One major advance currently under research are new solution methods for
computationally large problems, that is, multiperiod models, stochastic models, or multilevel models. In these large models, it can often be helpful to
reduce the solution space in order to decrease the model running time to a

Modeling Coal and Natural Gas Markets

9

feasible duration (or in some cases to obtain a solution at all). Branch-and-cut
or decomposition methods have been experimented with in the natural gas
modeling literature so far. Other methods may emerge in the future.
Optimization and complementarity models depict market settings that are
well-founded in economic theory, namely perfect competition and Cournot
competition, sometimes also a bilevel Stackelberg market or monopoly.
However, the player’s optimization problems in real world are more complex than in the abstract economic theory and richer formulations may
reveal new insights in the players’ behavior and the market structure. For
example, many companies in the natural gas market are entirely state-owned
and are operated under different premises than standard profit maximizing,
such as an objective of revenue maximization or employment maximization.
Alternatively, a regulated player may also have to obey to rules that are not
covered by the standard perfect competition model, for example, certain
pricing rules. It is not straightforward to include such deviant objectives
in a standard optimization or complementarity model and other modeling
techniques can more easily accommodate them. In particular, agent-based
modeling is a promising approach to include complex objectives. This
method has, however, the drawback of a lack of theoretical foundation of its
economic relations.
For any modeling approach to be used, a considerable improvement of
the understanding and modeling of reserves is needed. This entails several
aspects: first, the mechanism how (uneconomic) resources become (economically exploitable) reserves needs better understanding in order to derive a
general relation that can be included a model. Second, the impact of reserve
depletion on the production cost function is hardly taken into account in the
models so far. One can assume that low-cost reserves are produced first and
that higher-cost ones remain in the ground for longer, but that at the same
time a variety of types of basins are in production. Hence, one can assume an
upward shift of the cost function over time. A seminal contribution by Haftendorn (2012) to long-term coal market modeling gives an example of an
integration of reserves in the cost function. Third, unconventional resources
need to be included in the models, for example shale gas. The models usually
only include information on the reserves, but not on the resources. Obtaining this information is hard for most types of resources, but for some such as
shale gas more and more information has become available.
CHALLENGES TO COAL AND NATURAL GAS MARKET MODELING
The availability of data is one of the major challenges for coal and natural
gas market modeling. In particular access to supply side data, such as production costs, is very limited for the scientific community. It is somewhat

10

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

better for companies of the energy industry (utilities, consultants). However,
statistical information by the International Energy Agency (OECD) and the
Energy Information Administration (U.S. Department of Energy), as well
as organizations close to the industry (e.g., IEA Clean Coal Centre for coal,
Observatoire Méditerranéen de l’Energie for natural gas) and recent research
efforts (e.g., the Global Energy Assessment) provide a satisfactory basis for
sound academic research.
Another major challenge for the further development of coal and natural
gas market models, in particular the complementarity models is the increasing mathematical complexity of the modeling and solution techniques. An
improved understanding by economists of the advanced mathematical modeling is needed and requires more and more involvement of mathematicians
in addition to economists and engineers in the modeling community.
If more complex and nonstandard objectives and constraints are to be
included in the models, a better understanding of the real-world players’
behavior and optimization problems is needed. Experimental economics
has started to investigate some aspects of energy markets (e.g., auctioning
of transportation capacities), but there remain plenty of topics to be examined. This will also be a valuable input for nonstandard models such as
agent-based models of the natural gas or coal markets.
Last but not least, the looming transformation of the energy systems under
climate change and climate policy pressure may well lead to a strong reduction of the consumption of coal and natural gas, hence to a disappearing
object of analysis of natural gas or coal market modeling. Owing to different
carbon intensities, fossil fuels are presumably differently affected by climate
policies due to differing carbon intensities. This calls for using models
of the entire energy system, ideally in the same modeling format as the
state-of-the-art coal and natural gas market models (i.e., complementarity
modeling) which allows for the representation of market power in order
to be able to investigate the effects of systemic changes on coal and natural
gas markets. A first such modeling step was suggested by Egging and
Huppmann (2012) in a multifuel complementarity model.
In conclusion, the modeling techniques and experience of coal and natural gas modeling are potentially relevant for modeling other (nonenergy)
resource markets, for example, metals and rare earths.

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j.eneco.2006.09.004

FRANZISKA HOLZ SHORT BIOGRAPHY
Dr. Franziska Holz (*1979) is a Researcher at the German Institute for Economic Research (DIW Berlin), where she directs a research group on resource
markets (coal, natural gas, and oil). She studied economics at the Paris 1 University Panthéon-Sorbonne (1998–2003) where she graduated with a Master’s degree in International Economics. Between 2004 and 2008, she prepared her PhD thesis on modeling of the European natural gas market at
DIW Berlin, which she successfully defended at TU Berlin in 2009. Dr. Holz
has published extensively on modeling the global gas, coal, and oil markets.
She participated and coordinated a number of research projects, i.a. for the
European Commission, the German Ministry of Education and Research, and
the Stanford University’s Program on Energy and Sustainable Development.
She has participated in the Energy Modeling Forum (EMF 23 on global natural gas markets, EMF 28 on European technology options for climate policy)
and organized various academic events (e.g., European Doctoral Seminar on
Natural Gas 2005–2010, Infratrain workshops at TU Berlin and DIW Berlin
since 2004). Dr. Holz is married and has one child.
RELATED ESSAYS
The Role of Data in Research and Policy (Sociology), Barbara A. Anderson
Global Economic Networks (Sociology), Nina Bandelj et al.
The Public Nature of Private Property (Sociology), Debbie Becher
Can Public Policy Influence Private Innovation? (Economics), James Bessen
Sociological Theory After the End of Nature (Sociology), Robert J. Brulle
Neoliberalism (Sociology), Miguel Angel Centeno and Joseph N. Cohen
The State and Development (Sociology), Samuel Cohn
Trust and Economic Organization (Sociology), Karen S. Cook and Bogdan
State
Misinformation and How to Correct It (Psychology), John Cook et al.
Architecture of Markets (Sociology), Neil Fligstein and Ryan Calder
Organizational Populations and Fields (Sociology), Heather A. Haveman and
Daniel N. Kluttz
Behavioral Economics (Sociology), Guy Hochman and Dan Ariely
Technology Diffusion (Economics), Adam B. Jaffe

Modeling Coal and Natural Gas Markets

13

Search and Learning in Markets (Economics), Philipp Kircher
Natural Resources and Development (Political Science), Kevin M. Morrison
Economics of Renewable Energy Production (Economics), Gregory F. Nemet
Organizations and the Production of Systemic Risk (Sociology), Charles
Perrow
Economics and Culture (Economics), Gérard Roland
Sociology of Entrepreneurship (Sociology), Martin Ruef
Sustainability (Archaeology), Joseph A. Tainter et al.
The Social Science of Sustainability (Political Science), Johannes Urpelainen


Modeling Coal and Natural
Gas Markets
FRANZISKA HOLZ

Abstract
Coal and natural gas market modeling has seen an impressive upsurge in the last
decade. After a long period with a focus on optimization models, complementarity models have been developed since the 1980s and seen a renaissance after 2000.
Such models are also called equilibrium models as they allow representing a market game and its equilibrium solution. First versions of complementarity models of
the coal and natural gas markets were used to analyze the market structure of the
international commodity trade. While they confirmed an oligopolistic market structure in the European natural gas market, the global coal market has been found to
be competitive. Moreover, infrastructure analyses are carried out with such models
that allow detecting bottlenecks and, in multiperiod models, computing cost-efficient
capacity expansions. Other recent advances besides multiperiod modeling are the
modeling of multilevel games and stochastic models. Emerging topics are related to
computational methods and a better understanding of both energy sectors. Among
the challenges to the modeling community are the ongoing shortcomings of publicly available data and an improved understanding of the mathematical modeling
and solution approaches by economists. Finally, both sectors are subject to a climate
policy constraint which may well lead to a considerable shift in the importance as
well as in regional consumption patterns of coal and natural gas and, hence, require
improved modeling analysis.

INTRODUCTION
The modeling of coal and natural gas markets has traditionally focused on
the international trade of these energy commodities. This relates to trade
of natural gas through high-pressure pipeline or in form of liquefied natural gas (LNG), and the trade of steam coal on the seaborne market. In the
standard modeling literature of coal and natural gas markets, each sector is
investigated on its own, that is with a supply and demand representation of
this sector only. These sector-specific models (sometimes also called “partial
equilibrium models”) have the advantage to represent more complex supply

Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

1

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

structures compared to energy system models where the substitution relation
with other energy commodities is included.
More particular, it will be explained in the following that sector-modeling
of coal and natural gas trade allows for the analysis of market power, in particular on the supply side. This is a highly relevant feature in markets with
very concentrated supply structures. Monopolies, cartels, and oligopolies can
be modeled in this framework, as well as perfectly competitive markets.
Other questions than the existence of market power that are being investigated with models of the coal or natural gas markets are supply security and
investment requirements in infrastructure, and more recently the interaction
with climate policies. A concentrated supply structure is often accompanied
by congested infrastructure and even more so in situations of increasing
demand (e.g., opening of new markets, increasing energy demand in
emerging economies). This leads both to supply security concerns because
of few suppliers/supply routes available to supply a certain market and to
the necessity to expand transport infrastructure (export ports, pipelines, or
import ports). It may be of commercial or public interest to build or expand
infrastructure, and the economic modeling provides indications where the
investment would be most needed.
The models usually represent the supply chains in a quite detailed manner,
although some approximation of the complex technical processes has to be
made to deal with solvable models. In the coal sector, the models include the
following players:
•

•
•
•

producers (combining the activities of exploring, extracting, and preparing/washing the coal in a single supply function)
exporters (or export ports)
shippers
final demand by an importing country, where the demands by various
consumers (in general, power producers) are aggregated.

Similarly for the natural gas sector, (a selection of) the following players are
represented in the models:
•

•
•
•
•
•

producers (here, too, combining the activities of exploration, extraction,
and processing the natural gas)
(dedicated) traders (which may be dedicated to a specific producer)
LNG players: liquefaction, shipment, regasification
pipeline operators
storage operators (for seasonal arbitrage over the course of a year)
final demand (aggregating the national demand from the three
sectors using natural gas, namely power generation, industry, and
residential/commercial).

Modeling Coal and Natural Gas Markets

3

This field of research is characterized by an interaction of economists with
applied mathematicians from operations research. With the level of detail
and the computational methods, the modeling of coal and natural gas markets is part of the same literature in energy economics and applied operations
research as electricity market modeling. It has only a lose relation to traditional resource economics which consists mostly in the modeling of a reserve
constraint that producers have to respect in the long run.
FOUNDATIONAL RESEARCH
OPTIMIZATION MODELING
Following the development and wide-spread application of (linear) optimization methods after World War II, this method has also been used in
energy economics since the 1960s. Sectoral modeling using linear programming/optimization (LP) solution techniques allows for a great number of
technical details to be included in the models, albeit with the simplifying
requirement of using linear functions. Such models have found large interest
in academia and even more so in the strategy and operational departments
of energy companies where they are still widely used today.
An optimization model consists of an objective function that is either maximized or minimized subject to constraints. Typically, the objective function
is a total cost function that shall be minimized. A variant with welfare maximization of the specific sector is equivalent to a cost minimization problem
given a certain demand level. The constraints are various technical details, for
example, maximum production capacity of a mine, maximum throughput
capacity of a pipeline. This makes optimization models attractive for companies where they are mostly used today because they are convenient for
engineers and helping in day-to-day operational decisions. Generally, these
models are static which means that they model one time period. The time
period depends on the level of investigation: it can be very short (e.g., 1 h)
for an operational analysis (e.g., of a natural gas network) or much longer for
strategic analysis (e.g., 1 year). Many models include an optimization of network flows based on graph theory to compute cost-minimal pipeline flows.
The economic assumptions in optimization models are rather simple: with
cost-minimization being the objective and the assumption that market prices
are equal to the sum of all marginal costs along the value chain (production
plus transportation, etc.), these models implicitly assume perfect competition
in the markets. In many regions, such as natural gas markets in Europe and
Asia, but also coal markets in the US and globally in the 1980s, this assumption has seemed too strong given the small number of suppliers and apparent
price levels above (marginal) costs.

4

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

COMPLEMENTARITY MODELING
Hence, more advanced computational methods have increasingly been used
by economists since the 1980s. This was possible with the development of
advanced solution algorithms and solvers as well as easily accessible software for economists (namely, GAMS, the standard software used by energy
market modelers today). A different class of models than optimization problems is used nowadays: so-called complementarity (or equilibrium) models.
These models consist of the so-called Karush-Kuhn-Tucker (KKT) optimality conditions. The KKT conditions are obtained by deriving the first-order
(hence, optimality) conditions of the optimization problem (objective function and constraints) of the players. The Hence, a complementarity model
also calculates the optimal solution to an economic problem and follows a
similar understanding of the market in question as in optimization models.
However, in contrast to optimization models, in a complementarity model,
the optimization problems of several, interdependent players can be solved
simultaneously. This allows for a more adequate modeling of a market, with
an interaction of supply and demand (i.e., supply functions and demand
functions) and with strategic behavior of the suppliers. Hence, perfect competition is not a necessary assumption and one can model a situation with
market prices higher than (marginal) costs, for example due to oligopolistic
withholding.
This is a strong advantage of complementarity models for the economic
analysis of energy markets and has led to an increasing use after 2000. In the
1980s, such models were first developed, in particular for coal markets (US
and global markets, e.g., Kolstad & Abbey, 1984) and for natural gas markets (Europe, e.g., Mathiesen, Roland, & Thonstad, 1987). However, the solution algorithms (solvers) and the computer capacities were not yet advanced
enough to replace optimization models. Owing to the KKTs, complementarity models have more constraints than optimization models which leads to
higher mathematical complexity and computation time.
After some significant advances, in particular with the development of the
PATH solver for GAMS, applied complementarity modeling saw a “renaissance” in the late 1990s. While in the 1980s the coal and natural gas sectors
triggered the model innovations, it was the electricity sector that was precursor in the late 1990s. The coal and natural gas sectors this time were following
behind and modelers of these sectors used model setups and solution techniques that were first used for electricity market analyses.
The early natural gas complementarity models of the 2000s focused on the
European natural gas sector and analyzed imports and supply security. European natural gas markets were traditionally segmented with monopolistic
national wholesale traders that imported within long-term contracts from a

Modeling Coal and Natural Gas Markets

5

very limited number of suppliers. The import infrastructure (pipelines and
import terminal of LNG) was dedicated to sales under long-term contracts.
Hence, complementarity modeling was necessary to represent this market
appropriately and in order to analyze such questions as infrastructure adequacy.
The first modeling teams were based in countries with a strong interest in a
better understanding of international natural gas trade, namely Norway and
the Netherlands (producing countries) as well the United States (a prospective large importer at the time). In Norway, Lars Mathiesen et al. were at
the forefront of natural gas modeling; Rolf Golombek et al. developed a cost
function approach that is still widely used in the natural gas and oil modeling literature (Golombek, Gjelsvik, & Rosendahl, 1995). In the Netherlands,
Maroeska Boots and Wietze Lise developed and used the GASTALE model
to which Benjamin F. Hobbs contributed (Boots, Rijkers, & Hobbs, 2004; Lise
& Hobbs, 2008). Ruud Egging, together with Steven A. Gabriel, developed
the European Gas Model (Egging & Gabriel, 2006; Egging, Gabriel, Holz, &
Zhuang, 2008) which was later extended to the World Gas Model (Egging,
Holz, & Gabriel, 2010). More recently, the Institute of Energy Economics at
the University of Cologne in Germany moved from optimization modeling
to complementarity modeling of natural gas (Hecking & Panke, 2012).
In complementarity models, too, a flow optimization in a network can
be implemented. The modeling approach has the advantage, compared to
optimization models, to allow for the implementation of a simultaneous,
concurrent use of an (pipeline) arc by several players or even types of
players. Moreover, in a complementarity model, the dual variable of a
capacity constraint can directly be used in the equations of the model. The
dual (or shadow) variable gives an economic value to an additional unit
of the constrained capacity, for example, the implicit economic valuation
of a marginally higher pipeline capacity. The information on the value of a
constrained arc can, for example, directly be used in the pricing formulae of
the arc transportation.
The resurgence of coal modeling came some years after that for natural gas
and followed some few empirical analyses. The international steam coal market seems to be characterized by a less complex institutional structure, in particular because of lower asset specificity of the export/import infrastructure
(ports, ships), and a more diversified supply structure. However, increasing concentration of producing companies in the last decade has raised the
interest of economists, too. Hence, first modeling efforts were directed at
market structure analysis and market power detection, for instance with the
Coalmod-Trade model by Haftendorn and Holz (2010) and for more recent
years by Trüby and Paulus (2012). For both, coal and natural gas markets,

6

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

there is a strong limitation of data availability: because company information, for example on costs, is hardly available, most models use country data.
However, price and quantity results give an acceptable approximation and
allow to detect if there is exertion of market power.
CUTTING-EDGE RESEARCH
The first complementarity models of natural gas and coal markets that are
mentioned above were static one-period analyses with perfect competition
or Cournot competition (i.e., one-stage games). They served for market structure analysis or the identification of infrastructure bottlenecks. Cutting-edge
research today goes in three main directions:
•

•
•

multiperiod modeling with endogenous investment decisions (usually
in transport infrastructure),
stochastic modeling,
multilevel games with sequential decisions, for example, Stackelberg
games, and other games with joint constraints by several players
(Generalized Nash equilibrium problems).

MULTIPERIOD MODELS
Multiperiod models of coal and natural gas markets are usually based on
a net present value optimization by rational players with perfect foresight.
These models go beyond the identification of bottlenecks in infrastructure.
Their results also show which infrastructure will be economic to be built, as
a result of a complex interaction of minimization of investment costs and
variable costs of infrastructure utilization, for an endogenously computed
level of transportation and commodity demand in each period. Computing
such settings with several optimization problems and market equilibrium
while having a relatively large number of endogenous variable types is a
strength of the complementarity approach.
Several such much models of the European or global natural gas markets
and of global coal markets are currently in use. A state-of-the-art example
in natural gas market modeling is the World Gas Model (Egging, Gabriel,
& Holz, 2010); for coal markets, the COALMOD-World (Haftendorn, Holz
& Hirschhausen, 2012) was the first of its kind. The models usually cover
time periods until 2030 or 2050 in 5-year steps. An increase in the number of
time steps more than proportionally increases the computation time (often
exponentially); hence, the relatively small number of model periods.
In game-theoretic terms, the multiperiod models today are open-loop models based on a perfect foresight assumption. In the open-loop approach, the

Modeling Coal and Natural Gas Markets

7

decisions for all periods are taken at once in a single intertemporal optimization over the entire model horizon. All players are assumed to have perfect
and complete information on the outcomes of all (current and future) periods.
This is a strong assumption, which is necessary to remain in the framework
of (non-) linear complementarity modeling in which the KKT optimality conditions give the unique solutions. Open-loop models have the advantage of
a limited solution space that ensures unique equilibrium results (under some
conditions). Hence, they can be solved numerically in the mixed complementarity format (cf. Gabriel, Gabriel, Conejo, Fuller, Hobbs, & Ruiz, 2012).
After market structure analyses were in the focus of economic studies
with static market models, multiperiod models are used to study the
long-term perspectives of the resource markets, in particular under climate
policy constraints. Hence, scenario analyses are current contributions to the
literature with multiperiod natural gas or coal market models. Such climate
policies can be varying levels of CO2 prices, export taxes on fossil fuels, or
(mandatory) consumption reductions (see e.g., Haftendorn, Holz, Kemfert,
& Hirschhausen, 2013).
Not all functions of the models in use are well-founded, both in their functional form and the data input. This is a problem both on the demand and
the supply side. On the supply side, cost functions for production, transportation, and investment must be included in the model. They are often
assumed to be linear to ensure convexity of the optimization problem. More
complex functional forms than linear functions are possible and could potentially enrich the models. Only for production costs, an alternative curve has
become a standard assumption in the European literature: it is assumed that
(marginal) costs are increasing, with a strong rise close to the production
capacity constraint (the often called “Golombek cost function”, mentioned
above). However, this cost function still has to be introduced in multiperiod
models that allow for endogenous investment decisions in the production
capacity. Huppmann (2013) has paved the way for this model extension.
STOCHASTIC MODELING
Another stream of literature at the current research frontier is stochastic modeling. While this approach has not been applied for coal market models yet,
there have been a few applications to natural gas markets (e.g., Zhuang &
Gabriel, 2008). As for deterministic models, the availability of perfect and
complete information is assumed. The stochasticity consists in having multiple possible realizations of a variable. The realizations are predetermined
and are assigned a known probability of occurrence.
Computing the outcome of a stochastic model has the advantage to include
the reaction of the players to uncertainty. This can lead to a different outcome

8

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

than in a deterministic model and it is also different from the average of the
outcomes of the equivalent deterministic models of each stochastic scenario.
Similar to (deterministic) multiperiod models, the number of nodes in the
scenario tree cannot be extended at will due to the more than proportional
increase of computation time.
MULTILEVEL AND COUPLED CONSTRAINT MODELS
A third advance in the recent literature of coal and natural gas modeling
deals with the application of multilevel and coupled-constraint games. Even
in a relatively simple market setup with sequential decisions as a Stackelberg game with one leader and a few Cournot-playing followers, there
can be more than one solution. A Stackelberg game describes a sequential
“leader-follower” problem and can be used to describe market structures
with a high concentration in market power by just a few of players (e.g.,
OPEC in the oil market).
In general, if the feasible set of a player type depends on the decisions taken
by other players, multiple solutions are possible and numerical algorithms
face problems. Hence, there is a challenge to reduce the solution space to the
only reasonable solution(s). This challenge is even greater with more complex
models, for example with several leaders competing in addition to the game
between the followers. Multilevel complementarity models are either mathematical programs with equilibrium constraints (i.e., optimization problem
of one player in the first stage) or equilibrium problems (e.g., game of several players in the first stage) with equilibrium constraints (MPEC or EPEC,
respectively). Clearly, they are a generalization of static game complementarity models.
KEY ISSUES FOR FUTURE RESEARCH
Several topics have recently emerged in the coal and natural gas market
research. They would promote this field of research both in the complementarity modeling stream and with other modeling methods. In the following,
the emerging topics will be discussed first, before presenting some major
challenges for current and future research.
EMERGING TOPICS IN THE COAL AND NATURAL GAS MARKET MODELING
One major advance currently under research are new solution methods for
computationally large problems, that is, multiperiod models, stochastic models, or multilevel models. In these large models, it can often be helpful to
reduce the solution space in order to decrease the model running time to a

Modeling Coal and Natural Gas Markets

9

feasible duration (or in some cases to obtain a solution at all). Branch-and-cut
or decomposition methods have been experimented with in the natural gas
modeling literature so far. Other methods may emerge in the future.
Optimization and complementarity models depict market settings that are
well-founded in economic theory, namely perfect competition and Cournot
competition, sometimes also a bilevel Stackelberg market or monopoly.
However, the player’s optimization problems in real world are more complex than in the abstract economic theory and richer formulations may
reveal new insights in the players’ behavior and the market structure. For
example, many companies in the natural gas market are entirely state-owned
and are operated under different premises than standard profit maximizing,
such as an objective of revenue maximization or employment maximization.
Alternatively, a regulated player may also have to obey to rules that are not
covered by the standard perfect competition model, for example, certain
pricing rules. It is not straightforward to include such deviant objectives
in a standard optimization or complementarity model and other modeling
techniques can more easily accommodate them. In particular, agent-based
modeling is a promising approach to include complex objectives. This
method has, however, the drawback of a lack of theoretical foundation of its
economic relations.
For any modeling approach to be used, a considerable improvement of
the understanding and modeling of reserves is needed. This entails several
aspects: first, the mechanism how (uneconomic) resources become (economically exploitable) reserves needs better understanding in order to derive a
general relation that can be included a model. Second, the impact of reserve
depletion on the production cost function is hardly taken into account in the
models so far. One can assume that low-cost reserves are produced first and
that higher-cost ones remain in the ground for longer, but that at the same
time a variety of types of basins are in production. Hence, one can assume an
upward shift of the cost function over time. A seminal contribution by Haftendorn (2012) to long-term coal market modeling gives an example of an
integration of reserves in the cost function. Third, unconventional resources
need to be included in the models, for example shale gas. The models usually
only include information on the reserves, but not on the resources. Obtaining this information is hard for most types of resources, but for some such as
shale gas more and more information has become available.
CHALLENGES TO COAL AND NATURAL GAS MARKET MODELING
The availability of data is one of the major challenges for coal and natural
gas market modeling. In particular access to supply side data, such as production costs, is very limited for the scientific community. It is somewhat

10

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

better for companies of the energy industry (utilities, consultants). However,
statistical information by the International Energy Agency (OECD) and the
Energy Information Administration (U.S. Department of Energy), as well
as organizations close to the industry (e.g., IEA Clean Coal Centre for coal,
Observatoire Méditerranéen de l’Energie for natural gas) and recent research
efforts (e.g., the Global Energy Assessment) provide a satisfactory basis for
sound academic research.
Another major challenge for the further development of coal and natural
gas market models, in particular the complementarity models is the increasing mathematical complexity of the modeling and solution techniques. An
improved understanding by economists of the advanced mathematical modeling is needed and requires more and more involvement of mathematicians
in addition to economists and engineers in the modeling community.
If more complex and nonstandard objectives and constraints are to be
included in the models, a better understanding of the real-world players’
behavior and optimization problems is needed. Experimental economics
has started to investigate some aspects of energy markets (e.g., auctioning
of transportation capacities), but there remain plenty of topics to be examined. This will also be a valuable input for nonstandard models such as
agent-based models of the natural gas or coal markets.
Last but not least, the looming transformation of the energy systems under
climate change and climate policy pressure may well lead to a strong reduction of the consumption of coal and natural gas, hence to a disappearing
object of analysis of natural gas or coal market modeling. Owing to different
carbon intensities, fossil fuels are presumably differently affected by climate
policies due to differing carbon intensities. This calls for using models
of the entire energy system, ideally in the same modeling format as the
state-of-the-art coal and natural gas market models (i.e., complementarity
modeling) which allows for the representation of market power in order
to be able to investigate the effects of systemic changes on coal and natural
gas markets. A first such modeling step was suggested by Egging and
Huppmann (2012) in a multifuel complementarity model.
In conclusion, the modeling techniques and experience of coal and natural gas modeling are potentially relevant for modeling other (nonenergy)
resource markets, for example, metals and rare earths.

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j.eneco.2006.09.004

FRANZISKA HOLZ SHORT BIOGRAPHY
Dr. Franziska Holz (*1979) is a Researcher at the German Institute for Economic Research (DIW Berlin), where she directs a research group on resource
markets (coal, natural gas, and oil). She studied economics at the Paris 1 University Panthéon-Sorbonne (1998–2003) where she graduated with a Master’s degree in International Economics. Between 2004 and 2008, she prepared her PhD thesis on modeling of the European natural gas market at
DIW Berlin, which she successfully defended at TU Berlin in 2009. Dr. Holz
has published extensively on modeling the global gas, coal, and oil markets.
She participated and coordinated a number of research projects, i.a. for the
European Commission, the German Ministry of Education and Research, and
the Stanford University’s Program on Energy and Sustainable Development.
She has participated in the Energy Modeling Forum (EMF 23 on global natural gas markets, EMF 28 on European technology options for climate policy)
and organized various academic events (e.g., European Doctoral Seminar on
Natural Gas 2005–2010, Infratrain workshops at TU Berlin and DIW Berlin
since 2004). Dr. Holz is married and has one child.
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The Social Science of Sustainability (Political Science), Johannes Urpelainen



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Modeling Coal and Natural Gas Markets