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During the 1970s, oil market models offered a framework for understanding the growing market power being exercised by major oil producing countries. Few such models have been developed in recent years. Moreover, most large institutions do not use models directly for explaining recent oil price trends or projecting their future levels. Models of oil prices have become more computational, more data driven, less structural and increasingly short run since 2004. Quantitative analysis has shifted strongly towards identifying the role of financial instruments in shaping oil price movements. Although it is important to understand these short-run issues, a large vacuum exists between explanations that track short-run volatility within the context of long-run equilibrium conditions. The theories and models of oil demand and supply that are reviewed in this paper, although imperfect in many respects, offer a clear and well-defined perspective on the forces that are shaping the markets for crude oil and refined products.The complexity of the world oil market has increased dramatically in recent years and new approaches are needed to understand, model, and forecast oil prices today. There are several kinds of models have been proposed, including structural, computational and reduced form models. Recently, artificial intelligence was also introduced.This paper provides: (1) model taxonomy and the uses of models providing the motivation for its preparation, (2) a brief chronology explaining how oil market models have evolved over time, (3) three different model types: structural, computational, and reduced form models, and (4) artificial intelligence and data mining for oil market models.
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Oil Markets and Price Movements: A Survey of Models1
Hillard Huntingtona, Saud M. Al-Fattahb, Zhuo Huangc Michael Gucwaa, and Ali Nouria
aEnergy Modeling Forum, Huang Engineering Center, Stanford University, 475 Via Ortega,
Stanford, CA 94305-4121.
bKing Abdullah Petroleum Studies and Research Center, P.O. Box 88550, Riyadh 11672, Saudi
cPeking University, Beijing, 100871, China.
During the 1970s, oil market models offered a framework for understanding the growing market
power being exercised by major oil producing countries. Few such models have been developed in
recent years. Moreover, most large institutions do not use models directly for explaining recent oil
price trends or projecting their future levels. Models of oil prices have become more computational,
more data driven, less structural and increasingly short run since 2004. Quantitative analysis has
shifted strongly towards identifying the role of financial instruments in shaping oil price movements.
Although it is important to understand these short-run issues, a large vacuum exists between
explanations that track short-run volatility within the context of long-run equilibrium conditions.
The theories and models of oil demand and supply that are reviewed in this paper, although
imperfect in many respects, offer a clear and well-defined perspective on the forces that are shaping
the markets for crude oil and refined products.
The complexity of the world oil market has increased dramatically in recent years and new
approaches are needed to understand, model, and forecast oil prices today. There are several kinds
of models have been proposed, including structural, computational and reduced form models.
Recently, artificial intelligence was also introduced.
This paper provides: (1) model taxonomy and the uses of models providing the motivation for its
preparation, (2) a brief chronology explaining how oil market models have evolved over time, (3)
three different model types: structural, computational, and reduced form models, and (4) artificial
intelligence and data mining for oil market models.
Keywords: Oil models, oil prices, supply and demand analysis, financial markets.
1 Huntington, Hillard and Al-Fattah, Saud M. and Huang, Zhuo and Gucwa, Michael and Nouri, Ali, Oil
Markets and Price Movements: A Survey of Models (June 10, 2013). USAEE Working Paper No. 13-129.
Available at SSRN: or
This paper reviews models that have been applied to the world oil market since the early 1970s.
Discussion of the advantages and limitations of modeling approaches and recommendations for
promising future strategies on modeling will be the main topic of this paper. (Evaluations of a model
require that the purpose of the original model’s approach is very well articulated and understood.
Evaluating a model’s past forecasting capability, for example, may not be relevant if the model was
not developed for projecting oil prices). Additionally, reviews of model structure often fail to
identify how one model performs relative to others. Much more insightful are model-comparison
studies where all models that focus on a common objective are simulated using similar common
assumptions and the results are compared with each other, as has been done at the Energy Modeling
Forum (Energy Modeling Forum 1981; Huntington, Weyant et al. 1982).
This paper focuses on models that integrate the fundamental supply and demand factors in an
effort to explain or track the oil price path. It does not address modeling efforts focused on only
part of the world oil market, such as oil demand or supply in either the aggregate or in key regions
unless the framework tries to explain world oil prices as well.
An effort has been made to review representative papers across different economic and modeling
approaches without evaluating every paper on the topic. Our goal has been to review the main
approaches for modeling the oil market that would provide guidance for future research.
The organization of this paper is as follows. Section 2 discusses model taxonomy and the uses of
models providing the motivation for its preparation. Section 3 presents a brief chronology
explaining how oil market models have evolved over time. Sections 4 through 7 present detailed
discussions on different model types: structural, computational, reduced form models, and artificial
intelligence, respectively while section 8 concludes the paper.
Oil market modeling methods are categorized into three groups: structural, computational and
reduced form or financial models. Although sometimes a hybrid framework encompasses more than
one approach, most models usually emphasize only one methodology. The intention of these
categories is not to create a formal taxonomy of oil price models, but instead to build some
terminology that aids in their comparison.
Our model taxonomy is based upon those traits that will be most critical for an organization that
wants to hire the right experts with the appropriate skills to have impact on the policy decisions.
These traits include the required skills for implementing the model correctly as well as the ability to
communicate the important insights to the decision-makers. Other taxonomies may serve other
useful purposes. For example, one could separate the models by their treatment of OPEC behavior,
where models representing competition, dominant producer(s) or cartels are separated from each
other. An econometrician or a game theorist, however, could use the same techniques to derive a
model that would apply to any one of these types of OPEC behavior. Alternatively, one could view
“computational” models as simply large “structural” models. However, it is much more challenging
to explain why oil prices move in a computational model than it is in a simpler structural model that
represents fewer mechanisms. Another alternative but appropriate framework would be to consider
top-down versus bottom-up models. A top down model starts with a holistic market or system view
and adds details such as engineering constraints or market specifics as needed. A bottom-up
approach starts with relevant details and then simulates the interactions that unify the components
into a complete system. This categorization is complementary to the taxonomy proposed in this
One reason for this diversity in approaches originates from diversity of interests. A model
developed to forecast future oil prices may not be the best approach for understanding the
incentives for oil exporters who can influence prices with their production decisions. A framework
for tracking long-run oil price paths will be unsuitable for understanding near-term oil price volatility
and its interactions with the financial markets. A model focused on oil market supply and demand
factors alone will not provide appropriate guidance for the role of the oil market in supporting
broader development goals of an oil-producing nation. Each question requires a different approach,
as inferred from the common idiom, “horses for courses.”2 One should choose the methodology
that best fits the issue under investigation.
This diversity means that each model will represent different elements in the world oil market.
Some models explaining long-term supply and demand drivers may ignore the financial market and
the distinction between different crude types. Other models explaining short-term drivers may
ignore the oil resource base and the various vintages of the automobile fleet. No one model will
represent all real-world institutions and actors comprehensively, because a model is a simplifying
framework that helps to understand a more complicated real-world phenomenon. If a model
becomes too complicated, it loses its ability at some point to aid the decision-maker.
Oil market models are being asked to address different questions today than in the past. Many
previous quantitative assessments of energy markets during previous decades have emphasized
energy’s role in long-run economic growth (Putnam 1953; Resources for the Future 1960). The first
major energy modeling project within the U.S. government was conducted immediately after the
1973-74 oil price shock with a model called the Project Independence Evaluation System or PIES
(Hogan 2002). As its name implied, analysts used this system to explore strategies that limit U.S. oil
dependence over a decade or longer, perhaps with the effect of reducing oil prices. Since 2003,
however, new shorter-term issues have emerged with the increased oil price volatility and the
growing role of financial markets.
A second reason for the range of modeling approaches is the dramatic improvement in computer
technology over the last few decades, combined with fundamental advancements in the
mathematical and empirical sciences underlying modeling techniques. It is much easier to develop
large-scale systems with massive computational power today than it was during the 1970s and 1980s.
Additionally, energy modelers have much more accessible data representing different historical
experiences and regions than was available previously. As computing power and data sources
developed, analysts were also provided with much more advanced techniques for solving larger
models and drawing more reliable statistical inferences from the available data. For this reason, one
sees more econometric and computationally intensive oil market models today than in the past.
2 A horse that runs well over a dry, mile and a quarter race track of the Kentucky Derby may not be one that runs well
over a muddy, mile and a half race track of another major American horse race, the Belmont Stakes.
2.1 Structural Models
Structural models take at their core, fundamental microeconomic theories about the objectives,
constraints, and behaviors of market actors. These theories are distilled into a mathematical
structure, allowing for interaction between the actors and the market in the model. While structural
models can become quite complicated in aggregate, typically each component is easily understood
and motivated by some economic, political, or rule-of-thumb mechanism. Having utilized this
approach, the models serve to give insights into the driving forces of the market.
2.2 Computational Models
Computational models rely on heavy computing power, allowing modelers to characterize the
market in great detail. For comparison, a ‘structural model’ may have only three market agents
(OPEC, non-OPEC producers, and demand) and generally one product (generic crude) all
exchanged in a single node global market. Computational models on the other hand might model
refineries, individual producers, specific reserves, distinct refined product demands and prices, and a
fully specified variety of crude assays. These models typically seek either a partial or full general
equilibrium with other energy or other sectors in the economy.
Given the expense of running and maintaining these kinds of models, large scale computational
energy models are only built by a few organizations—most notably the U.S. Energy Information
Administration, the International Energy Agency, OPEC Secretariat and climate policy groups.
These models typically support detailed policy analysis, using a high level of detail to understand a
variety of impacts on different stakeholders.
2.3 Reduced Form/Financial Models
The structural models and computational models are appealing because they provide an explanation
for the different factors that can cause oil price movements in the longer run. Sometimes, however,
analysts want to track near-term price movements without necessarily explaining market behavior in
detail.. These models typically assume too many model parameters and are subject to model
misspecification. Unlike the structural models and computational models which explicitly specify the
economic behaviors of the oil market, reduced form models, including linear and nonlinear time
series models, focus on the time variation and the statistical relationships among the oil price and
other relevant variables. Reduced-form models, in general, provide predictive power in forecasting
future oil prices in the near term. Vector autoregression (VAR) is the most popular family of
reduced form models.
The recent development of econometric methods and improved availability of data have
encouraged the use of structural autoregression (SVAR) models for evaluating the oil market. The
structural equations specified in the SVAR models facilitate economic explanations of observed and
predicted fluctuations. In order to develop a mapping from parameters estimated from the reduced
form VAR models to the structural parameters in SVAR models, either parametric or sign
restrictions will be imposed. The SVAR models share the benefits of the conventional structural
models by providing economic explanations that potentially allow the estimates to be used for policy
analysis. At the same time, these frameworks have a similar advantage as the reduced-form VAR
models in terms of forecasting prices.
In this section we briefly describe how the oil models have evolved over time. Driven by advances in
the underlying disciplines, decreasing computation costs, greater access to data, and a changing
global oil market, the art of oil market modeling has changed over time. Understanding this history,
not only as an evolutionary process as methods were refined but also as an indication of the
changing nature of the underlying questions being addressed, puts the models in the correct context,
allowing for the appropriate elements to be abandoned or maintained in future modeling work.
3.1 1970-1982: Understanding the post-crises market
After decades of relatively stable prices, the oil crises of 1973 and 1979 provided significant
motivation for research into the behavior of the oil market and prices. With both price shocks ,
there was great interest in studying new structure of the oil market which led to the development of
numerous structural oil models in the 1970s and 1980s.
In these post-crises periods, the role played by OPEC had significant emphasis. Many questions
arose: Was OPEC a full profit-maximizing cartel? Was it a loose association with a cartel core? Was
it driven by Saudi Arabia? Did OPEC optimize in the formal sense, or did the organization follow
some other strategic production rule entirely? Did political factors trump (or mediate) their
economic behavior? That OPEC had significant market power was clear following the crises, but
models were required to explore the extent of that power and the impact it would have under the
different assumptions about the organization’s behavior and cohesion.
Models developed in this period were typically structural, resulting from the numerous
structural theories pertaining to OPEC that were proposed in response to the crises of the day.
Under the belief that the market structure had fundamentally changed following the rise of OPEC,
there was limited historical data necessary to develop an econometric analysis. Thus, in the absence
of well-defended data-based estimates, expert judgment was required to estimate many of the
parameters in early models. Finally, limited by computation power, demand was aggregated at a
global level and was typically either linear or exhibited constant elasticity.
With these limitations, it may seem that only minimal attention should be given to these first
efforts. Yet, these early efforts have redeeming qualities warranting significant attention. Perhaps
most importantly, with their simpler structures, the models are easier to understand, interpret, and
compare while still providing insights on the global market.
3.2 1982-2000: Econometric refinement
While the oil modeling literature from the 1990s is sparser than the surrounding decades, the studies
from this time frame contributed substantial understanding to the strategic behavior of supply,
refining, distribution and demand. In this time period, a series of econometric studies tested
assumptions and added depth to the understanding of oil market forces and agents. In particular, the
models enhanced our understanding of oil demand and OPEC behavior.
The consensus of hypothesis testing of OPEC behavior started by Griffin (1985) and extended
by other studies, is that none of the models from classical economic theory is an appropriate way to
describe OPEC’s behavior, leading to a number of new explanatory theories and hybrid models.
On the demand side, growth and industrialization are modeled more explicitly with measured
data. To incorporate the richness of many different regional differences in key factors, analysts more
frequently use panel data based upon time series for many different countries. They also explore
how demand responded differently to positive and negative price changes through equations that
allow for asymmetric effects in the demand response. Finally even greater nuance is given to demand
by allowing for variable elasticity as a function of demand and income, and by allowing for
technological progress.
Considerably less empirical research has been applied to non-OPEC production, due most
likely to the difficulty of representing geologic and cost information for different producing areas.
Notable exceptions include: (Eckbo, Jacoby et al. 1978; Smith and Ward 1981; Smith and Paddock
1984; Watkins 2002).
During this period, some studies also began evaluating the time series properties of oil prices,
the properties of commodities returns, the estimation of risk premia for commodities, and the
measurement and estimation of convenience yields among other topics closely related to
understanding oil price developments. These topics were explored further after 2000 as well.
3.3 2000-2010: Computational and financial models emerge
With the rapid growth of computing power and increasing volumes of data, computational models
and a second wave of structural models began to emerge. At the core, these models are still driven
by structural theories, but support more detailed and complex agents and interactions.
The first wave of structural modeling in this period grew as a response to pronounced oil crises
largely took the perspective of oil-consuming nations seeking to understand international crude oil
price behavior. The second wave of models sought instead to tackle numerous, distinct challenges: If
it does not conform to one classical theory, how should we model OPEC? What are the welfare
impacts of price change from the producers’ perspective? What role does oil consumption play in
anthropogenic climate change? How will government policies impact production, refining, imports,
and consumption on a regional level? What role does the financial market have in influencing oil
price? To answer these questions institutions and researchers alike have turned increasingly to more
complicated, computationally intensive models.
With increasing trading volume in oil futures and options markets (and substantial advances in
finance and econometric theory), there has been a sharp rise in empirically-based financial models of
oil prices that will be reviewed in section 6. The primary focus of these models has been in
forecasting prices for purposes of hedging, risk management, and speculation. The models are
typically non-structural from a classic microeconomic theory standpoint, but are instead driven by
financial theories and statistical techniques. Underlying economic measures such as oil reserves may
be considered as variables in such a predictive analysis, but may not be limited to the interactions
implied by formal theory. A description of the methods used in these models will be covered in the
reduced form section.
A structural model takes at its core microeconomic theories about the objectives, constraints, and
behaviors of market actors. The framework often does not test the validity of various theories about
individual consumers and producers with econometric techniques applied to historical data series.
Instead it combines these theories into a unified system for explaining how oil producers and
consumers interact with each other through markets to determine oil prices.
4.1 Types of Structural Models
Structural oil models are placed into one of three categories: optimization, simulation, or game-
theoretic. In the optimization framework actors have specific, well-defined objective functions (such
as maximizing the net present value of profits). Optimizing agents usually have perfect foresight and
will choose the best strategy over the full time period. These systems are intertemporal because the
decision-maker evaluates his choices over all periods.
In contrast, the simulation approach assigns specific behavioral rules to agents that may or may
not result in optimal decisions. For instance, a consumer might have a single demand curve in each
time period, consuming according to this rule without accounting for how it may impact future
consumption or prices. With each agent in the model following their respective decision rules, the
models are solved recursively, adjusting prices to equate supply with demand sequentially in each
period. This technique contrasts with the intertemporal approach where the agent considers all time
periods when making his decision.
Game-theoretic equilibrium models consider two or more optimizing agents in the market.
These optimizing agents could be different members in OPEC, OPEC and major non-OPEC
producers, etc. Game theory or computable general equilibrium is used to find equilibrium solutions
to these problems. Game theoretic models typically need more computational power to find a
solution (compared to the previous two groups).
In practice the distinction between the three models is often hard to make. While there are
some pure simulation models, most ‘optimization’ models include at least some market actors that
are not fully optimizing. Indeed it may be more relevant to think through which agents are
optimizing and which are simulated on an actor-by-actor basis. A table summarizing the details of
the various structural models can be found in Appendix A.
4.2 Model Agents
Structural models have great flexibility on how to aggregate and treat different players in the market,
but three broad categories are typical in most of the models: global oil demand, OPEC production,
non-OPEC production.
4.2.1 Demand
In high-level structural models, demand is usually highly aggregated and modeled through price and
income elasticities. Only rarely are consumers assumed to be optimizing their consumption over
time, and instead respond rather myopically to current prices. However, if consumers are price-
takers with little or no market power, it may be presumed that their optimal intertemporal
consumption decisions would differ little from myopic demand. On the other hand, suppliers
(whether or not they wield market power) might adopt optimal long-run actions that differ from
myopic behavior. Additionally, with few exceptions, the models focus on a single representative
crude oil without much detail on the refining industry. Modeling different crude types and
petroleum products is generally reserved for the computational models.
Demand is usually assumed to be a log-linear function of GDP and oil price (constant elasticity)
adjusted for technical progress. In recent studies (e.g. Dées, Karadeloglou et al. 2007) exchange rates
and domestic prices are also considered in the demand model.
4.2.2 Non-OPEC producers
Non-OPEC producers are typically assumed to be price-taking competitive firms, with differential
ability to respond to price changes in the short and long run. Only rarely are these firms considered
to exercise any form of market power or to be optimizing their production over multiple time
periods. Technological progress and resource depletion are usually represented by a trend over time
in the cost of production, decreasing and increasing the cost of production respectively.
Some studies use rather complicated econometric models to describe non-OPEC behavior. An
example is Kaufmann et al (2004) who do not use a supply-demand framework. Most models
determining the world oil price, however, have represented non-OPEC production using one (or
more) of the following approaches:
1. A simple function of price:
Some models have represented non-OPEC production with a simple function of price. The
function can be a constant elasticity function of the price or an asymmetric function of price
where producers respond differently to price increases and decreases. Often these
relationships are first calibrated to a historical situation or base case projection, and the
elasticities then determine how projected consumption will deviate from the base case
projection. For example, see Blitzer et al. (1975), Daly et al. (1982), Gately (1983; 2004;
2. Geologically-estimated base case with/without elasticities:
Following Hubbert’s idea (Hubbert 1962), some models estimate future non-OPEC
production by extrapolating geological data. In most models price elasticities are also added
to those values to account for economic responses of non-OPEC countries. E.g. Baldwin
and Prosser (1988), Horn (2004), Dees et al. (2007).
3. Hotelling framework:
In a Hotelling framework a limited resource with known reserves is assumed for the non-
OPEC country and the optimal extraction path over time is determined. These models
require that the producers have an expectation on all prices in the future. e.g. Cremer and
Weitzman (1976), Salant (1982).
4. Resource Expansion and Discovery
Rather than take reserve availability as a given, some models attempt to explicitly include
exploration and resource expansion. These models attempt to determine the future potential
of a field or region by using historical exploration and production information. For
examples, see (Eckbo, Jacoby et al. 1978; Smith and Ward 1981; Smith and Paddock 1984;
Watkins 2002)
5. Non-Conventional Fuels
Some models allow for non-OPEC producers to produce non-conventional fuels to
compete with oil products. Typically this is done by exogenously specifying the production
capacity and costs, with capacity increasing over time and costs decreasing over time. Most
of the models discussed in the Energy Modeling Forum 6 study included such a non-
conventional option as specified in the study design (Beider 1981).
4.2.3 OPEC
Due to its critical role in the market, perhaps the greatest variety of treatment is given to how OPEC
behavior is modeled. OPEC is usually the price setter and market leader in the models and either
optimizes its profits or follows some other decision rule (Eckbo 1976, Gately 1984). A common
behavioral rule in the early literature is target capacity utilization (TCU). In TCU models OPEC first
sets a price and fills any gap between the resulting demand and non-OPEC supply. OPEC will
follow a price setting rule to try to keep its production at some target rate of capacity utilization.
The models can differ in the degree of cartel behavior—from full cooperation among members,
to only the cartel core exercising market power, to each member of the organization acting
competitively. In most cases, the entity assuming market power in the market, OPEC (or the cartel
core or the dominant firm) chooses the prices and provides the gap between demand and non-
OPEC supply.
4.3 Energy Modeling Forum 6 - “World Oil”
The Energy Modeling Forum, centered at Stanford, seeks to understand specific topics through the
use of multiple existing models. Their studies serve two purposes: to create deeper understanding of
the area of study and to compare different analytical techniques and modeling choices. One of the
forum’s early studies, EMF 6, compares models dealing with world oil.3
EMF 6 explores the behavior of different models of the world oil markets under a set of
standardized assumptions and scenarios (Energy Modeling Forum 1981). The study includes 10
unique independent structural oil models, and an additional explanatory model created by the EMF
staff. By comparing scenarios across the different models, the study is able to explore how different
model choices can influence the long-term trajectory of prices and their behavior over time. The
design and standardization of the project allows for clean comparisons of techniques and their
implications. Creating models necessarily means focusing on certain characteristics over others, and
3 A second EMF study on international oil supplies and demands was done on the early 1990s Energy Modeling Forum
(1992). International Oil Supplies and Demands, EMF 11 Summary Report. Stanford, Stanford Energy Modeling
Forum. Many of the models evaluated in this study are listed throughout this paper without specifically linking them to
this study.
it is important to know the implications of making certain assumptions and ascertaining if those
assumptions interfere with answering the question at hand.
The illustrative model created by the EMF staff is particularly useful as a description of the
process and trade-offs involved in creating a structural model. This review of the EMF 6 models is
largely a summary of a working paper produced for the EMF study by Perry Beider (Beider 1981).
Most of the models in the study took a simulation approach, while three of the ten have some
optimization. The optimization models differed in which sectors optimized and had foresight:
consumers, OPEC, or non-OPEC producers. In general, in simulation models behavior was smooth
(with fluctuating prices), and in optimization models price paths were smooth (with strong behavior
fluctuations). In simulation models, without foresight and utility maximizing optimal choices, price is
left to absorb any shocks to the supply-demand equilibrium, where in optimization models the
foresight of agents allows for strong anticipatory behavior. Knowing what future conditions will be,
they adjust their current strategy, thereby smoothing out prices through arbitrage.
Most of the models in the study have similar treatment of OPEC behavior, with OPEC
capacity set exogenously and OPEC setting prices using some form of a “price determination
function.” After setting prices, OPEC observes non-OPEC production and produces enough to
meet any remaining demand. OPEC uses the price determination function to attempt to maintain a
constant, desired capacity utilization level. They set higher prices in the next period to reduce total
consumption and increase Non-OPEC production if the realized capacity utilization exceeds the
target in the current period. They lower prices if the capacity utilization falls short.
For the demand side of the market only one model has consumers optimizing, while in nine of
the models consumers respond through price elasticities. The latter models allowed the price
response to be considerably smaller in the short run than in the long run. The models also differed
in how they treated substitution across energy forms. A table summarizing the details of the various
models from EMF 6 can be found in Appendix B.
4.3.1 Evaluation of Energy Modeling Forum 6 Study:
The structured comparison of world oil models by the Energy Modeling Forum in the early 1980s
was the first to attempt explaining some of the major fundamental supply and demand factors
influencing oil prices, even if it was widely understood to be treacherous to project future oil price
levels under very uncertain conditions. The study tried to identify several issues related to model
Even as early as 1980, many modeling teams were replacing optimization models popularized
during the 1970s with simulation approaches. The strength of the optimization models lies in their
clear delineation of economic motives and their ability to incorporate expectations about future
conditions into current decisions. However, uncertainty about future conditions often calls the
optimization approach into question. Evaluating future income in each scenario is relatively
straightforward when market outcomes are deterministic. But surprises about future oil market
events as well as uncertainty about how producers and consumers actually respond to price make it
unlikely that decisions will be based upon these deterministic outcomes. In its place, modelers
shifted towards simulation approaches that provided more richness in representing capacity
utilization and other important factors.
Beider (1981) emphasized three major findings about oil market models included in the EMF
study: (1) both optimization and simulation have specific advantages and limitations, (2) the models
generally ignore the feedback effect of oil prices on aggregate economic output (GDP), and (3)
OPEC oil production capacity is often treated as exogenous.4
First, an optimization approach has very different objectives than a simulation framework.
Systems that optimize decisions focus upon what key decision makers should do to achieve a specified
goal, while a simulation approach emphasizes what producers and consumers might actually do.
Optimization often assumes that decision makers have perfect foresight about what conditions will
eventually transpire in future years. Thus, expectations based upon perfect foresight about future
conditions play a critical role in providing producers or consumers with flexibility in meeting future
In contrast, simulation often restricts producers and consumers to either myopic or adaptive-
expectation benchmark rules. Producers and consumers with myopic behavior do not expect oil
prices to change from current levels, more or less in line with the evidence provided by Hamilton
and Kilian on the relationship between current and next period’s prices. With adaptive expectations,
these agents expect future prices to move with a similar trend as in the recent past. These rules are
frequently considered as more realistic because they incorporate a number of factors or competing
priorities into the decisions of market participants. This emphasis on how to realistically represent
expectations will continue to be an important modeling issue and is extremely relevant today when
financial factors are reshaping market forces.
Second, economic activity often declines sharply for a few years and oil consumption falls when
oil prices spike. The oil market models in the EMF 6 study are essentially long-run systems for
evaluating no-surprise scenarios where oil price trends were gradual. As analysts begin to focus on
near-term developments, the depressing effects of GDP feedback effects will become more
important to include.
And third, these models for the most part assume that OPEC members’ decisions to build oil
production capacity are exogenous to the determination of oil prices. These decisions, however, are
strongly influenced by shifts in market conditions. OPEC is often considered as a single entity
focused on aggregate future income or aggregate excess capacity, when regional factors may be quite
important. Additionally, OPEC members will consider not only political factors in their decisions
but also their need for economic diversification and government revenues.
One might also add another, fourth caveat. Model results will depend importantly upon
assumptions and parameters that influence fundamental supply and demand factors. Daly et al
(1982) provided results from a simulation model shortly after the EMF 6 results were reported.
Relative to the EMF 6 recommended scenario assumptions, their econometric demand relationships
revealed a higher long-run own-price elasticity (-0.73 rather than -0.6) and a lower long-run income
elasticity (0.75 rather than 1.0). Thus, as incomes increased over time, their oil demand curves did
not shift outward as rapidly. Additionally, as inflation-adjusted oil prices rose sharply in the early
4 See also Gately (1984).
1980, oil consumption would not rise as rapidly. Both adjustments would contribute to lower oil
price paths than in the EMF 6 study. Probably a more important factor for their lower prices,
however, was their much more optimistic assessment of future oil supplies that would eventually be
available at the relatively high prices prevailing in the early 1980s. Their resource evaluation
depended upon geological information obtained from both published data and informal interviews
with government and oil company experts.
It bears emphasis that Daly et al (1982) did not use their simulation model to project oil prices.
Instead, they use it very effectively for evaluating what would be the market conditions and output
shares for two different price paths equal to $32 and $15 per barrel (in 1980 US dollars). Many
energy agencies, international organizations and central banks follow this approach and do not
project future prices based upon mathematical models. Instead, they use the model to evaluate
whether certain world oil price paths will produce stable market conditions based essentially on
expert judgment.
In a retrospective view of the EMF 6 study, Huntington (1994) noted the wide gap between the
EMF 6 model results and the actual levels for world oil prices during the 1980s. He attributed these
differences to three main factors. During the first half of that decade, world economic recession and
technical progress in oil supply outside OPEC considerably weakened oil market conditions. Limited
Saudi oil production held prices at their early-1980s level. In the second half, oil consumption did
not respond strongly when oil prices collapsed, in contrast to what the EMF 6 models would have
expected. The lower response to oil price declines relative to the oil price increases that preceded
them is consistent with their being technical progress in oil consumption. Once the 1970 oil price
shocks transformed the vehicle stock, consumers during the 1980s were not allowed by automobile
manufacturers and government policy to return to purchasing less fuel-efficient vehicles that they
use to purchase in the previous decade. With oil consumption playing a critical role in these
developments, a later EMF study (1992) decomposed model projections of future oil consumption
into several different effects for the current price, income, technical progress and the delayed effect
of past oil price movements.
4.4 Simulation Models
In simulation models, all agents are described by a behavioral rule. Specifically OPEC countries,
despite their market power, do not optimize their actions but instead follow some behavioral rule.
There is great variety in the form of these rules and the justification for their use. Some researchers
have compared the result of simulating different behavioral rules in order to choose the one that
benefits OPEC the most. These models are discussed as ‘Strategy Selection’ models. An alternative
approach is to identify the behavior of each agent based on the available historical data and
determine key parameters through regression analysis, or an ‘Econometric Fit’. A third approach
uses rule-of-thumb relationships (such as a capacity utilization rule or a target price zone) to describe
producer behaviors.
4.4.1 Strategy Selection
In these models, the market is simulated using different possible strategies for OPEC, yielding
different market outcomes. The simulations’ results are compared (usually by a measure of net
present value of an income stream) and the best candidate is chosen to be either the preferred
strategy or the future prediction.
Blitzer et al. (1975) provide one of the first oil price models. They express total demand that
grows each year and is a function of price. Non-OPEC supply is determined as function of price and
a shift parameter that depends on previous investments in alternative energy resources. OPEC sets
either the price or its production level, with the other variable being determined in the market based
on the difference between resulting demand and non-OPEC supply. The market is simulated for six
different price/production policies by OPEC and results are compared for different assumptions on
demand and non-OPEC supply parameters. Similar to many models from the 1970s, the relations
describing demand and non-OPEC supply are rudimentary and use parameter values based upon
expert opinion.
Gately (2004; 2007) uses a demand model with parametric values developed by Gately and
Huntington (2002). He also assumes that the economic growth may be influenced by oil price. Non-
OPEC supply is modeled by two constant elasticity functions of price depending upon the price
level (and calibrated to EIA projections). Either the price path or OPEC production levels must be
specified in order to simulate the rest of the future market. Gately has compared different OPEC
strategies to increase/decrease its market share and has concluded that, out of the set of strategies,
OPEC should maintain its exports at a constant share of world consumption (excluding oil
consumption in OPEC countries).
4.4.2 Econometric Fit
Many models seek an econometric fit to identify behavioral rules that match historical behavior,
which are then used to describe OPEC countries’ behaviors. These models can be used either to
provide projection of future prices or to perform counter-factual analysis.
MacAvoy (1982) provides one of the first models completely based on econometric
representation of the agents. He divides OPEC members into three groups based on their
production/reserve ratio. In addition, he considers the United States as a fourth group and all other
oil producers in a fifth group. For each of the five groups, he models supply by log-linear function
of oil prices, reserves and lagged productions. The demand side is studied in three groups: United
States, Developed World and LDCs. Each groups' demand is estimated with a log-linear function of
prices, income and lagged demand. For each year, an equilibrium price is determined such that the
market clears.
MacAvoy also estimates how reserves grow over time. Using various assumptions on demand
and supply due to the large uncertainty created by the Iran-Iraq war at the time the study was
published, he has provided a range of results drawn from the model for a time horizon of 7 years.
Amano (1987) builds an annual small-scale econometric fit model for the oil market forecasting
through the years 1986-1991. Consisting of only 32 equations, the paper is a tractable example of the
methods behind an econometric fit model. The model splits demand into two regions: OECD and
non-OECD regions. Consumption is driven by level of economic activity and the price of oil. Non-
OPEC production is modeled to exhibit a distributed lag in response to prices. Finally OPEC is split
into three categories: (1) revenue seekers, (2) reserve preservers, (3) swing producers, with the latter
actively seeking to stabilize short-term prices.
In a series of works, Kaufmann et al. (2004), Dees et al. (2007) and Kaufmann et al (2008) have
model different aspects of the world oil market econometrically. A particular feature of their model
is explaining the world price with econometrically fitted equations whereas, in the common
approaches, price is either exogenous or set by OPEC such that it clears the market. Their price
functions are relatively short run because they do not explain OPEC’s decision to invest in new oil
production capacity.
Dees et al. (2007) have put the econometric results in a supply-demand framework. In their
model, demand for each region is estimated as a function of the income, domestic prices, exchange
rates and technological progress. Non-OPEC production is expressed as function of geological
forecast (based on a logistic curve Hubbert approach), regional and asymmetric oil price effects.
OPEC production fills the gap between total demand (considering changes in OECD oil stocks) and
total non-OPEC supply (including natural gas liquids). Price is determined by the rule from
Kaufmann et al. (2004).
An out-of-sample forecast by the model is not presented but it is stated that the model can
estimate the quarterly prices during 2000 to 2005 with a high precision. However, as they have also
mentioned, this means that the model can describe previous changes very well, not forecast the
future accurately.
The model could also be used to study policy and supply/demand shocks. By changing any of
the exogenous variables (e.g. OECD stocks, OPEC capacity) their effect could be observed. Also by
treating price as an exogenous variable, effects of price shocks could be studied.
Kaufmann et al. (2008) have upgraded their price rule from Kauffman et al. (2004) to be able to
describe the price rise during 2004-2006. They show that there exists a non-linear relationship
between oil prices and capacity utilization levels. Interestingly, the results suggest that the
relationship between prices and refinery utilization is negative. They associate this result with the
increase in less expensive heavy oil production in the times of high refinery capacity utilization rates.
The model has not been used to provide a forecast about future conditions.
4.4.3 Capacity Utilization
A price increase is usually expected when the spare crude oil capacity of the major producers
decreases. This fact has been used to describe producers’ behaviors in the oil market.
Lorentsen and Roland (1986) describe (not at a detailed level) their World Oil Market (WOM),
with which they simulate the market by modeling OPEC’s behavior with a capacity utilization price
rule. For non-OPEC producers they use a different criterion: that a constant fraction of known
reserves is produced each year. The new discoveries depend on the price of oil. The optimal
recovery factor depends on the oil price as well but it is adjusted slowly from its previous value.
They have presented a forecast for 15 years based on different assumptions on economic growth.
Gately’s model (1983) is based on capacity utilization pricing rule in which OPEC sets the price
based on the percent of capacity used in the previous time step. (i.e., prices increase if the market
was tight or tightening in the last time step). Demand is estimated as a log-linear function of income
and oil price. Gately models non-OPEC producers by two linear functions of price with different
slopes depending upon the price level. Therefore, price is determined for each period based on the
previous period’s capacity utilization. Total consumption and non-OPEC production are determined
based on the price. OPEC production is simply the difference between total consumption and non-
OPEC production. Hence, the model can do long-term forecasts by simulating next year’s price
recursively based upon this year’s demand and supply conditions.
Baldwin and Prosser (1988) have introduced the World Oil Market Simulation (WOMS) model.
Demand is estimated as log-linear function of income, price (adjusted for exchange rate) and
technological change. Non-OPEC production is estimated as a function of geologically forecasted
production and oil prices. In WOMS, OPEC is simulated with two models. In the first approach,
OPEC employs a price reaction as a function of capacity utilization level, in which the solution to
production and price is found to clear the market. In the second, OPEC chooses its production
level, in which world price is found such that the market clears. It is argued that the first model of
OPEC is not capable of describing the price fall of 1986. WOMS has not been used to provide
forecasts of future prices.
Powell (1990) presents a criticism of the capacity utilization framework both by considering the
historical performance of the model and by analyzing a target capacity utilization (TCU) model of
his own. He first critiques the empirical support for the model: illustrating its recent poor out- of-
sample performance, its dependence on the EIA’s particular data set, and the fact that most analyses
use the price of oil in dollars. The larger part of his paper, however, is devoted to developing and
testing a simple target capacity utilization model. The model exhibits long-lasting oscillatory
behavior, and the outcome of the capacity utilization strategy has no systematic relationship to a
revenue-maximizing outcome. These results uncover a fundamental assumption in the TCU
framework: that OPEC’s reaction is mechanical and does not change dynamically over time. With
this assumption, OPEC remains helpless to dampen the unstable market cycles it creates and is
unable to obtain prices consistent with profit maximization.
A problem with this simulation rule is that OPEC capacity must be determined before the
analysis tracks its rate of utilization. Smith (2009) suggests that OPEC has been restraining
investment in new oil production capacity in recent years and thereby has contributed to higher
prices in a market with very rapid demand growth.
4.4.4 Target Price Zone
An alternative rule-of-thumb often considered for OPEC is a target price. In this framework OPEC
selects its output quotas with the goal of maintaining a stable price range.
Based on monthly data between 1988 and 1999, Tang and Hammoudeh (2002) develop an
econometric test, finding that not only did OPEC intervene to maintain prices in a target band, but
also that the movement of oil price is tempered by market participants’ expectations of those
interventions. While the theory remains silent on price changes that occur fully within the specified
target zone, it has strong predictive power as prices move towards the boundaries of the zone.
4.5 Optimization Models
In optimization models a single agent finds its best strategy while the responses of other agents are
simulated. The optimizing agent usually knows the response of other agents and hence is able to
incorporate that into its decision. Some modelers consider Saudi Arabia to be the agent with market
power and solve the optimization on its behalf. In other models, OPEC or a part of OPEC is
considered to be the single agent who optimizes its strategy. This approach can often provide useful
insights about the economic incentives of large producers but it may be more limited in terms of its
ability to predict actual market outcomes.
It should be added that not all models that use optimization techniques are considered as
optimization models in this paper. For instance, before the price rise of 1973, Deam et al (1973)
develop a model based on an assumed competitive market. They assume that short-term prices are
weighted averages of marginal costs, and long-term prices are found by solving a linear program that
minimizes the total cost (extraction, refinery and transportation) to consumers. Such models
optimize society’s welfare by producing at the lowest cost but they are not categorized as
optimization approaches in this paper because the individual producer has no ability to influence
Nordhaus (1973) develops an intertemporal model for the efficient allocation of energy
resources using a depletable resource theory. He considers petroleum, shale oil, coal, nuclear, and
natural gas. Each of these fuel sources has four cost components: production, royalty,
transportation, and processing. The royalty component could be viewed as the depletion cost. A
critical element in his depletable resource model is the existence of a backstop technology which sets
the upper bound on prices and provides the source of energy when resources become scarce. This
important feature is often missing in other models of OPEC decision-making, leading to rapid
increases in future OPEC prices (e.g., see Gately (2004)). In Nordhaus’s model, nuclear breeder
reactors provide that source for total energy. An appropriate backstop for oil would be certain
sources of unconventional oil like oil sands, electric vehicles, or liquid fuels made from natural gas
through gas-to-liquid technologies. The model ultimately finds a very small royalty cost across all
fuel sources and projects how fuel substitution will occur across different end uses over time.
Kalymon (1975) builds several models to explore OPEC behavior through two different
approaches. First he considers OPEC faced with an intertemporal optimization problem. The
organization attempts to maximize the present value of its export profits and the consumer surplus
for its internal consumption. Under this framework two approaches are presented: either a single
stable cartel or with Saudi Arabia and Iran acting as the residual producers. In the second approach
he creates a simulation model to explore different OPEC market sharing structures: maintaining
current market shares or maintaining current production levels with Saudi Arabia / Iran acting as
residual producers. In general he finds the optimal price for OPEC is sensitive to the opportunity
cost of capital, the substitution cost for importing countries, and the coalition structure within
OPEC. On the other hand he finds that the optimal price is not very sensitive to either their total
reserve size or the rate of domestic market growth.
Ben-Shahar (1976) models OPEC as a monopolist deciding on future price levels while the
supply from non-OPEC producers is simulated by a simple price rule. Ben-Shahar also discusses the
investment issues and conflicts of interest among OPEC members. He also develops an
optimization model exploring how oil-producing companies can invest their revenues domestically
and internationally.
Ezzati (1976) develops a macro economic framework and a linear programming optimization
for world energy markets based upon a weighted sum of OPEC members’ utilities. Each producer’s
utility is the present value of its consumption plus a coefficient times the GNP growth rate after the
optimization period. The constraints for maximization include the physical clearance of production
and consumption, and macro-economic relations between oil revenue and nations’ consumption and
policy constraints. He estimates important factors in the world energy market using econometric
models (usually with constant-elasticity functions) and uses a discrete approximation of those
functions in the linear program.
Cremer and Weitzman (1976) develop a model that considers two players: a monopolist (e.g.
OPEC) and a competitive producer. Each of them solves a Hotelling-like problem where the
monopolist sets all the future prices and the competitive producers take these prices as given.
Demand is considered to be linear and grows at a constant rate through time. The solution to this
problem provides a projection for prices. Their numerical values chosen for reserves, costs,
demands are based upon expert opinion.
Daly et al. (1982) have taken into account different goals of OPEC members. In their model
demand is a log-linear function of economic activity and lag distribution on previous prices of oil
relative to other goods. They have divided OPEC members in three groups: Cartel Core (Saudi
Arabia, Kuwait, Qatar, Libya, and UAE), Price Maximizers (Iran, Algeria, Venezuela) and Output
Maximizers (Iraq, Nigeria, Indonesia, Ecuador, Gabon). Output Maximizers and non-OPEC
producers are modeled the same: their production is represented as a function of the world oil price.
Cartel Core chooses the price levels and provides the residual demand. Price Maximizers follow a
target revenue model. The model can project future paths of production. Daly et al. use the ratio of
reserves to production and market shares as a measure of OPEC cartel stability and question
whether different price paths are stable given the current behavior.
Celta and Dahl (2000) develop a model in which OPEC is maximizing social welfare rather than
purely profit maximizing. They define OPEC’s social welfare as the profits from selling oil to the
international market plus consumer surplus for the local consumers minus total extraction cost.
They conclude that for welfare maximization OPEC countries should set domestic oil price equal to
the marginal revenues from the oil export market. Although the problem is well mathematically
formulated, the modeling of domestic welfare is very simplistic.
Horn (2004) develops a model in which OPEC maximizes net present value of its cash flow for
the time horizon of 2000 to 2020. In the reference case, income and price elasticities of demand and
projection of economic growth in each region are calibrated to match EIA (2001) projection of
demand (assuming that the future prices are the prices projected by EIA). He imposes an upper limit
or asymptote on Non-OPEC production due to geologic constraints in two different ways. First, he
fits oil production to the past data as a depletable resource consistent with the Hubbert curve. And
second, he fits the data to a Gompertz function that allows a more gradual approach to the upper
limit or asymptote. In both cases a price elasticity of 0.1 is added to the Non-OPEC supply forecast
to allow production to respond very modestly to better economic conditions. Again, both models
are calibrated to match EIA’s projections of non-OPEC supply. Furthermore there is no capacity
constraint on non-OPEC production. OPEC production is assumed to meet the gap between
demand and non-OPEC supply for a projection of prices.
Based on the structure of the reference case, Horn has searched for a set of prices that will
maximize OPEC’s surplus. He represents OPEC surplus, the extraction costs, and the value of the
resources in the ground. In this approach, resources after 2020 are ignored and investment cost is
modeled by a single number for each additional barrel of capacity. Since the only linkage between
subsequent years is OPEC capacity and OPEC production is a simple function of the price it sets,
the optimization is straightforward. Horn finds higher prices compared to EIA, but all the forecasts
for 2010 are far below the current price of oil. The projections are presented for five cases of
parameters (elasticities and growths) and two models of non-OPEC supply.
Although Horn has developed a simple and transparent model, the numerical assumptions for
parameters are mostly chosen on the basis of expert opinion.
4.6 Game Theoretic Models
In contrast with optimization models, in game-theoretic models there are at least two agents trying
to maximize their net benefits. These sorts of problems are solved by finding the Nash Equilibrium,
a state in which nobody could gain more profit by deviating from its strategy independently.
Although these models are computationally more complicated, they theoretically match the strategic
opportunities to market players more realistically and as a result they have evolved to computational
models described in the next section. Two of the most insightful models are described below.
Salant (1982) has introduced a model integrating the theory of exhaustible resources and the
theory of oligopoly. The structure of the model is similar to Cremer and Weitzman (1976) and it is
extended to a multi-player case. In his model each producer is either one of many competitive sellers
or one of several large but competing sellers (termed Cournot players). A competitive player
essentially allocates their depletable resource over the current and future years (solving the Hotelling
problem) by taking the prices as given. On the other hand, Cournot player(s) adopt almost the
reverse strategy. They set the prices while taking competitive production of other producers as
given. Salant has proved existence of a solution to this problem and introduced an algorithm that is
proved to converge to the equilibrium solution. Although the sample problem in Salant’s paper
solves a simple case with few players, the model could be solved for many players with today’s
detailed data and computational power.
Marshalla and Nesbitt (1986) develop a Hotelling-based framework and find the Stackelberg
equilibrium where OPEC members maximize their joint present value of net income by setting all
future prices. Non-OPEC members take these prices as given and maximize present value of their
profits by setting production levels. This paper can be considered as a detailed numerical application
of Salant (1982).
With a different and unique approach, Hnyilicza and Pindyck (1976) develop a model that
focuses on the interaction between OPEC members. They model demand as growing over time with
a linear function of price and lagged demand. Non-OPEC supply is modeled by a function where
production increases (linearly) with price and decreases (exponentially) with cumulative production
summed over all previous years. Similar to many studies in 1970s, the function structures and
parameters are chosen judgmentally. OPEC countries decide on the price and their production is
determined by total demand and non-OPEC supply.
They have divided OPEC members into Spender Countries (Iran, Venezuela, Indonesia,
Algeria, Nigeria, and Ecuador) and Saver Countries (Saudi Arabia, Libya, Iraq, UAE, Bahrain,
Kuwait, and Qatar). It is assumed that Spender Countries have higher discount rates that encourage
more current production and oil revenues available for immediate spending. In this setting there is a
conflict between interests of these groups on the prices that OPEC should set. A set of efficient
prices could be found by maximizing a weighted average of the net present value of the two groups.
But in this framework the optimal answer gives all the production to one of the groups. Since this
situation is not realistic, they have added the constraint that the two groups maintain their shares of
world production. Hnyilicza and Pindyck have determined the optimal weights of averaging profits
of the groups by Nash bargaining solution and future projections are presented.
Computational models are mainly distinguished by their high computation load. The most important
motivations for emergence of these models are:
Accurate and detailed data availability, econometric advances and more complex description
of agents’ behaviors.
Desire to model systems where many agents are trying to maximize their objective
simultaneously (which leads to a large system of equations).
Enhancements in computation power and numerical methods.
Using these tools, modelers were able to describe and solve much more complicated models. In the
“research models” section, models developed by individual researchers will be described and then
models used by organizations are reviewed.
5.1 Research Models
The academic researchers have mostly focused on providing a better description of oil market using
complicated models considering many agents.
De Santis (2003) creates a computational model of the major supply and demand balances in
the e Saudi Arabian economy (referred to as a computable general equilibrium model) to understand
Saudi behavior and how it influences oil price. An attractive feature of his computational general
equilibrium approach is the ability to examine the impact of subsidies removal on international oil
prices and key macroeconomic indicators such as growth, inflation and consumer and producer
De Santis models Saudi Arabia as the dominant producer in a constrained oil cartel. In the long
run the country sets prices to maximize profits, but in the short run the production of cartel
members is constrained by quotas. Only after meeting to establish new quotas can more optimal
production levels be selected. Building from this assumption, the paper’s core contribution is to
consider the welfare impacts of demand and supply shocks on Saudi Arabia. The country’s economy
is modeled in a computable general equilibrium, where it is a price setter for international crude
prices but a price taker on all other goods. The welfare impacts of demand shocks can be quite large:
increasing welfare substantially for positive shocks and leading to a large reduction for negative
shocks. Taking a 44% negative demand shock (as was witnessed in 1998) the paper finds a
corresponding welfare loss equal to 35-37% of consumer income. Meanwhile, supply shocks--
positive and negative--uniformly lead to welfare losses. Another important finding is that shocks
that can increase profits do not always lead to increased welfare for the nation as a whole due to
trade balance effects on the other sectors of the Saudi economy.
Al-Qahtani (2008) considers six crude types, refinery constraints, seven final products, and a
transportation network and searches for a partial equilibrium. Such a complicated model needs many
parameters describing the objectives and properties of each region/agent and most parameters are
adjusted subjectively or fit to match a base case projection.
Consumers are assumed to be competitive (i.e. they have no market power) and a marginal
benefit function is assumed for customers. Refinery demand in each region for each supplier’s
product depends on the supplier price and elasticities.
In his main model, Al-Qahtani has assumed that Saudi Arabia is the dominant firm and
optimizes its profits. In this case other OPEC members’ behaviors are either similar to the non-
OPEC producers or are assumed to be such that they maintain their historical markups. In another
model OPEC is assumed to be the optimizing firm (i.e. a pure cartel assumption).
The competitive producers supply each crude type at the point where the marginal cost equals
the market-clearing price. To calculate the cost function and the related supply function of
producers, they assume price elasticities, with other parameters of the cost function calibrated to
match the realized productions. The market is cleared by crude market clearance (i.e. extraction
equals refinery input and refinery constraints are satisfied) and product market clearance.
The problem is formulated as single step optimization (by Saudi Arabia or OPEC) subject to
the constraints of other agents’ behaviors. All input data used in the model belong to the year 2004.
Running the optimization for this year and comparing the results with realized outcomes, Al-
Qahtani has concluded that regardless of whether OPEC or Saudi Arabia is maximizing their net
income, they would have gained more profit if they had produced less, implying that neither Saudi
Arabia nor OPEC is fully exercising their potential market power.
Huppmann and Holz (2009) develop a one-step optimization, considering a network of
transportation costs and financial markets behaving as a pool. The producers gain either the
oligopolistic (Cournot) revenue or the competitive revenue. If OPEC is assumed to be a cartel, the
whole OPEC acts as a single player and receives the cartel profit. If Saudi Arabia is assumed to be
the dominant firm, Saudi Arabia receives its oligopolistic profit and the rest of producers obtain
competitive profits.
In their model, production cost are taken from Aguilera et al. (2009) and production capacities
are determined by the assumption that all countries produce at 95% of capacity in the base year
reference values.
In addition to the conventional oil market agents (producers and consumers), Huppmann and
Holz model a trading company that maximizes the profits of distributing oil from producers in
different countries to customers. (Note that because of the network constraints and different
shipping costs this problem is not trivial.) Furthermore, it is assumed that there are some
arbitrageurs that can benefit from differences in prices in different nodes. Huppmann and Holz
demonstrate that considering these arbitrageurs provides a better estimate of the market. Putting the
optimization problem of all these agents together, they numerically solve the corresponding
optimality conditions. They use a mathematical programming approach that is particularly valuable
for computing solutions where more than one agent can exercise some market power (referred to as
a mixed complementarity problem (MCP) approach). While they only run the model for one time-
step in their paper, it should be added that they have claimed that the model can be run as a multi-
year optimization.
Huppmann and Holz use their method to compare the results of their model with the actual
outcome in 2006 to check for a correct descriptive model of producer behavior. Running the model
with different assumption on the set of producers that have market power (Cournot producers),
they have concluded that most OPEC members behave similar to a condition of oligopoly, but that
Saudi Arabia does not fit either the cartel assumption or purely oligopolistic models.
5.2 Energy Information Administration
The Energy Information Administration (EIA) is responsible for official energy information for use
by the United States federal government and approaches oil issues with a variety of tools and
computational models.
5.2.1 Annual Energy Outlook – NEMS
The Annual Energy Outlook (AEO) is a highly detailed annual report derived from the National
Energy Modeling System (NEMS). NEMS is a large multi-purpose, detailed energy model including
numerous energy sectors, end-uses, and markets. The system is decomposed into numerous
modules, each taking specific inputs from other modules and providing specific outputs. Each
module is repeatedly solved as the system as a whole seeks equilibrium in all markets. Different
modules (as well as the different agents within any single module) vary between using optimization
or more simulation-based approaches.
NEMS is the flagship computational model, illustrating both the positive and negative
consequences of creating a highly detailed computer-intensive model. On the one hand, it can be
configured to analyze a wide range of scenarios and evaluate the potential impact of relatively
complex proposed policies. On the other hand, with so many different inputs and interactions it can
be difficult to understand what parameters or assumptions are driving certain behaviors. Such a
model needs constant maintenance and scrutiny.
Like with all models, it is important to put the model in the context of its chartered purpose: to
provide detailed scenario analysis for proposed policies, including impacts at a regional and
stakeholder level. To this end, while oil prices are a critical determinant of behavior in the model,
understanding their dynamics is less prioritized than obtaining evaluations of the impacts of policy.
The impact of those prices is largely evaluated through the use of low and high oil price scenarios.
The EIA is actively designing and building a new module to deal with the liquids fuel market,
but currently most of the oil modeling is handled in two modules: the Petroleum Market Model
(PMM) and the International Energy Module (IEM).
Petroleum Market Module
A diagram showing the Petroleum Market Module’s dependencies with the rest of NEMS is
illustrated in Figure 1. As a tool focused on domestic policy analysis, U.S. production and refining
are modeled in much higher detail than the rest of the world. Currently the model draws
international prices from the International Energy Module. The new Liquid Fuels Market Module
(LFMM) scheduled to replace the PMM may change this simplified treatment (OnLocation Inc.
Figure 1 – Petroleum Market Module Inputs/Outputs.
The PMM is centered on the refining sector, which is optimized with a linear program. Using
refining constraints, refined product demands and prices, and crude supplies and prices, domestic
and international product production are calculated in equilibrium. An overview of the PMM’s
structure is presented in Figure 2 (Office of Integrated Analysis and Forecasting 2010).
Figure 2 – Petroleum Market Module Overview.
International Energy Module
While the module title perhaps connotes a broader scope, the sole current function of the IEM is to
simulate the interaction between the U.S. and global petroleum markets (Office of Integrated
Analysis and Forecasting 2010). Its primary output is an estimate of world oil production available in
each year at different world oil prices (i.e., a world supply curve) and associated world oil prices.
The module interacts closely with two other elements of the NEMS model: the PMM and a set
of exogenous inputs from a file called “omsecon.txt”. The PMM provides the IEM with U.S. crude
supply, demand, crude imports, and product imports by year. The IEM provides the PMM with
computed world oil price and world crude supply curves. The two modules are solved jointly to
ensure equilibrium. The interactions are summarized in Figure 3 below.
The omsecon.txt file essentially calibrates the model results to be consistent with key NEMS
supply and demand curves but allows prices and quantities to deviate from their original projected
values to reflect the new conditions being simulated. The file contains four conditions represented
as time series from 2007 to 2035 to be used as inputs for the IEM. The four conditions are: 1)
Global total crude-like liquids demand curves, 2) U.S. total crude-like liquids demand curves, 3)
Global total crude-like liquids supply curves, and 4) U.S. total crude-like liquids supply curves. Each
of these curves is expressed as a function: 𝑄=𝛼𝑃!, where 𝜖 is the elasticity (constant for each
curve, but allowed to vary from year to year), and 𝛼 is a parameter determined by a point on the
curve. The values for 𝑃, the expected world oil price, are provided by assumption, and the values for
𝑄 are assumed based on previous runs of NEMS. In order to estimate the values for 𝜖 and 𝛼 in a
given year, the first three points on the curve are estimated using three scenarios considered in the
previous year’s AEO.5 The parameters are then chosen to fit a demand curve with constant price
elasticity (an isoelastic curve) through these three data points, intersecting the point of the reference
case. While the model runs and as the PMM produces U.S. demand levels that differ from the
exogenously projected path, the IEM translates the supply and demand curves (maintaining the
exogenous elasticities) to produce an equilibrium world oil price and demand.
Figure 3 – International Energy Module Inputs/Outputs.
5.2.2 Short-term Energy Outlook
The short-term energy outlook (STEO) is developed using the Short-Term Integrated Forecasting
(STIFS) model. The STIFS is an aggregated national model without regional detail. The model is
estimated from econometric methods, drawing data from the EIA’s time series as well as other data
sources. The EIA has plans to update the model to the Regional Short-Term Energy Model.
For the STIFS model, crude import prices are taken as exogenous, projected through the
forecast period. Additionally, domestic crude production is also exogenous (Energy Information
Administration 2000). The purpose of the model is to understand and project product prices and
usage patterns in the short-run (at most two years). The EIA releases a new STEO monthly.
5 The three point estimates correspond to the world oil price and global crude-like liquids demand from the following
three scenarios: 1) Reference Case Scenario, 2) High Oil Price Case Scenario, 3) Low Oil Price Case Scenario
It is worth mentioning, that consistent with findings by econometricians (Szakmary and et al.
2003) the short-term outlook uses implied volatility (estimated by futures markets) instead of
historical volatility in establishing the interval estimates provided by its oil price forecasts (Energy
Information Administration 2009).
5.2.3 International Energy Outlook
The IEO is driven by another set of models under the World Energy Projects Plus (WEPS+)
modeling system. The model converges to a price-consumption equilibrium, modeling 16 regions
and several countries. Similar to the NEMS framework, the WEPS+ system is modular in nature,
allowing multiple distinct modules to interact over a shared database. Oil supply and prices are
generated “bottom up” using the Generate World Oil Balance (GWOB) application, and then
integrated with projections from the STEO and NEMS to ensure consistency across the models
(Energy Information Administration 2010). Non-conventional liquid fuels are projected in
exogenous analysis. Similar to NEMS, a refinery model determines refined petroleum product
prices, accounting for crude prices, transportation, and historical markups.
5.3 Energy/Climate Change Models
In the last two decades there has been very rapid growth in the number of comprehensive energy
market and climate change policy models developed. These approaches have particular strengths in
that they represent inter-fuel substitution opportunities that may have very important influences on
oil markets in the future. However, they suffer from a serious problem for evaluating oil prices and
oil markets because they represent oil-market actors in very simplistic terms, often downplaying the
role of OPEC. A key future challenge in energy modeling will be to merge the advantages of these
climate change approaches with more realistic assessments of key market structure considerations in
the oil market.
Crude oil availability and prices are key factors in every energy and climate change model. In
order to study the effects of a climate change policy, one should measure the effect of such policies
on world energy demand and specifically the demand supplied by conventional resources. As a result
there has been substantial effort developing world energy models in the previous decade. In this
section, four of these models (WEM-ECO, WITCH, MESSAGE and EPPA) are reviewed. Energy
and climate change models are not intended to be accurate forecasters of oil prices: their main goal
is providing long-term energy production, consumption and greenhouse gas emissions projections
and policy analysis rather than forecasting oil prices. They usually do not consider OPEC’s market
power and its consequences in modeling the supply side of the oil market. In all the following
models the oil price is found endogenously by solving market-clearing conditions for all major
energy sources and sectors represented within the framework as well as for other non-energy
sectors. Unlike the structural models considered previously, these frameworks are based upon a
general equilibrium solution that solves for many other markets in the world economy in addition to
the oil market.
5.3.1 World Energy Model (WEM-ECO)
International Energy Agency (IEA) uses WEM-ECO - a hybrid model coupling the bottom-up
WEM model with the top-down general equilibrium model IMACLIM-R. The World Energy Model
(WEM) has been developed internally to the IEA since 1993. WEM is an energy sector partial
equilibrium model which provides short to medium-run energy demand and supply projections in 21
regional or country blocks. Contrary to optimization models, the WEM model is a simulation model
with a yearly step based on a modular structure and provides projections for 20 to 30 years (IEA
Regarding the oil market, WEM takes prices as an exogenous assumption and finds trajectories
of supply and energy demand. In fact, the projection of the price is found by IMACLIM-R, the
other main module of WEM-ECO.
Oil demand is determined directly from the prices, elasticities, and other assumptions (e.g.
technologies and economic growth). In WEM, MENA (Middle East and North Africa) plays the
role of OPEC. Non-MENA production is determined based on the level of ultimately recoverable
resources and a depletion rate estimated by using historical data and industry sources.
In WEM’s reference scenario, MENA producers are assumed to be the residual suppliers i.e.
their production fills the gap between total world oil demand and non-MENA added to non-
conventional oil production.
IMACLIM-R is a hybrid recursive general equilibrium model of the world economy that
considers 12 regions and 12 sectors (Sassi, Crassous et al. 2010). The base year of the model is 2001
and it is solved in a yearly time step. IMACLIM-R solves the general equilibrium problem of these
agents and provides projections of macroeconomic variables.
Regarding the oil prices, in IMACLIM-R, all sectors apply a constant mark-up rate to their
inputs’ costs. Sassi et al. state that “such a constant markup corresponds to a static profit-
maximization for producers whose decreasing return factor can be approximated by an exponential
function of utilization rate”.
The WEM-ECO model, resulting from the coupling of WEM and IMACLIM-R, is built on an
iterative exchange of information between the two models.
5.3.2 OPEC World Energy Model (OWEM)
OPEC Secretariat constructed the OPEC World Energy Model (OWEM) which is an econometric
energy model, based upon annual data, to assess the impact of energy scenarios on OPEC. The
Model was first consolidated in 1987 and was subsequently updated and revised to take account of
the changes in the country groupings, OPEC membership, environment modeling, etc. The model
consists of 194 scholastic equations and 459 identities.
Within OWEM, the energy demand module (ENDEM) is an Energy Demand Model which
explains requirements in the OECD regions for oil, solid fuels, gas and electricity by the energy
users in industry, the household/commercial sector, transportation, electricity generation and marine
bunkers. It combines aggregate energy demand equations with fuel shares. The model for non-
OECD regions (ODEC) explains oil demand for developing country regions, by sector. It differs
from the treatment of ENDEM inasmuch as oil volumes are estimated
The Price of Energy Model (PEM) explains energy prices paid by the OECD energy users in
ENDEM in terms of world crude oil prices, domestic unit costs in the OECD regions and energy
tax rates. The Supply of Energy Model (SEM) explains energy supplies, in particular the supply of
oil, by region.
The MACROGEM-TRAM model, forecasts non-energy imports for OECD regions and uses
export and import shares as weights to obtain aggregate indexes of market demand and competing
prices. The purpose of the TRAM module of OWEM is to link the world regions together so that
regional non-energy exports are calculated from regional non-energy imports, estimated as equations
for the OECD in this module and regional nonenergy import prices are calculated from regional
export prices. MACROGEM-TRAM provides real GDP (exogenous) and the overall levels of prices
in the OECD regions as required by ENDEM. Real GDP is the main activity variable in the
aggregate energy equations. Assumptions for the share of industry in the economy are also made to
generate industrial value-added. The GDP deflators are used to convert nominal prices of oil, coal,
gas and electricity given by PEM into the real prices which enter the fuel-share equations. The prices
are weighted together to give the aggregate-energy price relative to the GDP deflator, which enters
the aggregate-energy equations.
5.3.3 World Induced Technical Change Hybrid (WITCH)
The World Induced Technical Change Hybrid (WITCH) model divides the world into 12 regions
and considers each region as a player with forecasted oil demand who can decide on
production/export levels (that are constrained by production capacities) and investments in the oil
industry (that can increase production capacity) (Massetti and Sferra 2010). Specifically, they have
provided a rather complicated model that calculates the investment needed for capacity expansion.
The objective of each player is to maximize the net present value of the utility derived from
aggregate consumption for all goods and services and for leisure. In this model, the market is cleared
globally and prices are determined endogenously. The cost of each barrel of oil emerges as a shadow
cost of resources invested in the oil sector. It should be added that similar to many integrated
assessment models (IAMs), each player in this model behaves as a price taker. Therefore, the
noncompetitive aspect of oil market is not captured in the results. WITCH provides forecasts until
2100 for different scenarios of carbon reduction policies.
MESSAGE (Model for Energy Supply Strategy Alternatives and their General Environmental
impact) is developed by the International Institute for Applied Systems Analysis (IIASA 2001).
MESSAGE considers various sources of energy from extraction and storage to transportation,
distribution and final user. MESSAGE divides the world into 11 groups and minimizes the total cost
to the system subject to a set of constraints on supplies and infrastructure. In this framework the
price is found endogenously. As with WITCH and many of the other models of this type, oil
producers cannot exert market power and influence prices. Since all energy resources in MESSAGE
are treated the same, the special role of OPEC in the oil market is neglected.
5.3.5 Emissions Prediction and Policy Analysis (EPPA)
The Emissions Prediction and Policy Analysis (EPPA) model forms a part of the MIT Integrated
Global Systems Model (IGSM). It is a recursive-dynamic multi-regional general equilibrium model
of the world economy (Paltsev, Reilly et al. 2005). In each of the 16 regions it maximizes the utility
of Households and Firms subject to the technologies of production and consumption, consumer
endowments of primary factors and imposed policies. Production technologies in different sectors
are described by nested constant elasticity of substitution (CES) functions that exhibit constant
returns to scale. This special structure simplifies the optimization problem but also implies that in
equilibrium firms make only normal economic profits. Hence, prices are determined endogenously
equal to the per-unit costs. A main difficulty in this approach is its inability to model OPEC’s
market power in the oil market. EPPA has explicit assumptions on cross resource elasticities and
provide forecasts for a long-time horizon extending through the year 2100.
Financial models are a somewhat newer brand of oil price models, taking advantage of the recent
“financialization” process where the vastly expanded role of financial motives, markets and
institutions have dominated commodity and oil trading.. In addition to the data from oil futures and
options being relatively new, many of the relevant findings from finance that serve as the basis for
these models are also recent. These models attempt to understand the behavior of the financial
market and use any information contained therein for predicting future prices or volatility. The
discussion below focuses on how these techniques have been applied to understand oil price
movements but not necessarily the financialization process. Typically these models have a short-
term view limited by the number of future periods over which the forward market remains liquid
and balanced.
The main differences between the structural econometric models and financial (reduced form)
models are three fold. First, most structural econometric models explicitly specify oil demand and
supply, whereas financial models mainly focus on oil price and its time series properties. Although
the fundamental demand and supply variables can be incorporated into the financial models, they
are typically introduced with the aim to improve the model fit to the price data. Second, estimates of
the econometric models have economic interpretation and thus can be used for policy analysis, while
the reduced-form parameters in the financial models have much less economic meaning and are
mostly used for the purpose of forecasting, derivatives pricing or risk management. Third, reduced
form models use data with higher frequencies, like monthly, weekly or daily, than econometric
models that usually use yearly or quarterly data as higher frequency consumption and production
data are generally not available.
6.1 Models
6.1.1 ARMA Model: The Benchmark Model
The univariate (single variable) autoregressive moving average (ARMA) model, sometimes called
Box-Jenkins models, is the benchmark time series model for oil prices. The notation ARMA(p, q)
refers to the model with p autoregressive terms (lagged values of the dependent variable) and q
moving average terms (lagged values of the error terms). The oil price can be modeled as
The error terms 𝜖! are generally assumed to be independent identically-distributed random
variables (i.i.d.) sampled from a normal distribution with zero mean: 𝜖!~N(0,𝜎!) where σ! is the
variance. These assumptions may be weakened but doing so will change the properties of the model.
Sometimes a time trend will be included in the model.
When exogenous variables are included, the model is called autoregressive moving average
model with exogenous inputs model (ARMAX). In principle, any variables that contain useful
information about oil prices, such as the fundamental supply and demand information or aggregate
macroeconomic variables, could be included as the exogenous variables.
The ARMA model is well-known for its simplicity and its capacity to capture the time variation
of a time series and the ability to forecast the future prices. The model can be estimated using
various econometric methods and the number of lag periods for both autoregressive and moving
average terms will be chosen according to some statistical criteria.
In practice when forecasting is the main purpose, the observed data will be divided into two
sub-sample periods: in-sample and out-of-sample intervals. The parameters of an equation are
initially estimated using data from the in-sample interval. Out-of-sample values for the exogenous
or explanatory variables are then entered into the estimated model to generate a series of forecasted
values. Measures of out-of-sample fit are used to evaluate and compare different model
specifications. One common measure is the mean squared prediction error (MSPE), which is
defined as
where h is the number of the out-of-sample observations.
The model with lower MSPE is believed to have better predictive performance. Using a number
of measures for predictive fit, Alquist, Kilian and Vigfusson (2010) do a comprehensive survey of
the predictive performances for a number of models under different scenarios.
6.1.2 Random Walk Model and Mean-reverting Model
Plenty of attention has been paid to two special classes of ARMA model in empirical studies, the
random walk model and the mean-reverting model. The random walk model, also called the unit
root model, is consistent with the efficient market hypothesis (EMH) that claims nobody can
outperform the market. That is,
Thus the price change (𝑋!!!𝑋!)!is pure noise and the best forecast for tomorrow’s price is the
price today. This prediction rule is called the ‘no change rule’.
In comparison, in the mean-reverting model, the oil price converges to a long-term equilibrium
level of oil price. That is,
where X is the long-term mean and 𝜅, typically positive, is the speed of convergence. A larger
deviation from the long-term mean implies greater correction to the long-term mean in the next
period. The mean-reverting model is consistent with the fundamental-driven story. When the
current oil price is higher than the equilibrium level, oil demand will be lower and oil production will
start to expand, forcing the oil price to fall.
Pindyck (1999) uses such models and their variants to study the long-term dynamics of energy
prices. For empirical comparison of the two models, see Geman (2007) and Maslyuk and Smyth
(2008). Alquist, Kilian and Vigfusson (2010) also examine a number of variants of the no-change-
6.1.3 Non-linear Models
Non-linear models have been proposed to model oil prices as the extension of the linear models.
The idea of non-linearity is not limited to the ARMA models and can be incorporated into the more
complicated models introduced in later sections.
6.1.4 Asymmetric models
In the linear ARMA model, the parameters are assumed constant. Motivated by the economic story
that the price response may be asymmetric depending on the signs or values of some variables,
parameters are allowed to be different in the asymmetric models. This intuition can also be applied
to the parameters on autoregressive, moving averaging, or the exogenous parts of the ARMAX
model or the models that will be discussed later. Here we present simply one example as follows,
where 𝑋𝑋!
! are price increases and 𝑋𝑋!
! are price decreases. When both 𝜅!and 𝜅! are
positive, 𝑋!!! will increase when 𝑋𝑋!>0!and will decrease when 𝑋𝑋!<0.
Papapetrou (2009) is an example of the asymmetric model for explaining aggregate output as a
function of oil prices. Hamilton (2003), Hamilton (2009), and Kilian and Vigfusson (2009) use non-
linear autoregressive models to study the asymmetric macroeconomic effect of oil price increases
and decreases.
6.1.5 Regime-switching models
Another family of non-linear models is the regime-switching models in which some parameters
depend on the unobserved state of the world, summarized by Hamilton (2008). For example, the oil
market can be divided into three states: the markets with plenty of excess oil supply, balanced supply
and tight supply. One illustrative example of regime-switching model is give as follows,
where s! is a random variable that could be 1 or 2, that is, there are totally two states of the world. A
complete description of the probability law governing the observed data would then require a
probabilistic model of what caused the change from 𝑠!=1 to 𝑠!=2. The simplest such
specification is that s! is the realization of a two-state Markov chain with,
Pr 𝑠!=𝑗𝑠!!!=𝑖,𝑠!!!=𝑘,,𝑦!!!,𝑦!!!,=Pr 𝑠!=𝑗𝑠!!!=𝑖=𝑝!"
The model can be estimated by the maximum likelihood estimation (MLE) method as we can
explicitly specify the analytical log-likelihood function under Gaussian assumption.
Studies using the regime-switching models include Cologni and Manera (2009) and Papapetrou
(2009). Cologni and Manera (2009) evaluate the aggregate economic output effects of oil price
changes in the G-7 countries. Using regime-change techniques, they attribute the major changes in
the relationship to improvements in energy efficiency and better monetary and fiscal to external
supply and demand shocks. Papapetrou (2009) estimates the response of aggregate Greek industrial
output to oil price movements by differentiating between a regime of high oil price changes (greater
than 3% per month) from one of low oil price changes.
6.1.6 Time-varying Volatility and GARCH Model
Another popular family of models is the generalized autoregressive conditional heteroskedasticity
(GARCH) models and their variants, in which the volatility of oil shocks are assumed to be time
varying, in contrast to the constant variance assumption. The time varying variance assumption is
believed to be consistent with the empirical behavior of oil prices. In the classical GARCH (1,1)
model proposed by Engle (1982) and Bollerslev (1986), the volatility is modeled recursively by,
The literature using GARCH models to study oil volatilities is extensive. See Sadorsky (1999;
2003; 2006), Morana (2001), Adrangi et al. (2001), Sadeghi and Shavvalpour (2006), as representative
examples. Sadorsky (1999) finds that both oil prices and oil price volatility influence real stock
returns, while Sadorsky (2006) concludes that GARCH specifications often produce better forecasts
of oil price volatility than other specifications.
6.2 Vector Autoregressive Model (VAR)
Oil prices often interact with other economic variables, such as macroeconomic variables, prices of
other energy products, and stock prices. Vector autoregression (VAR) models, generalizing the
univariate AR models, are often used to capture the evolution and the interdependencies between
multiple time series. A reduced form unrestricted p-th order VAR model for k variables, denoted
VAR(p), is given by
where y is a kx1 vector of the variables of interest, c is a k×1 vector of constants (intercept), B is a
k×k matrix (for every i = 1, ..., p) and 𝑒! is a k×1 vector of error terms. Equivalently, the model can
be written as
where L is the lag operator and B(L) is a polynomial function. Similar to the ARMA models,
parameters of the VAR models do not have much economic interpretation.
6.2.1 Co-integration Model
A particular class of VAR models, the co-integration model developed by Granger (1986) and Engle
and Granger (1987), has received a lot of attention by economists and has been applied widely in the
analysis of the interaction between oil price and other economic variables. In a bivariate co-
integrated system, both of the two time series are non-stationary, for which the historic values of the
variable cannot forecast the future. However, the linear combination of the two variables could be
stationary; that is, mean reverting. This linear combination suggests an economic equilibrium
relationship and the deviation from the equilibrium relationship provides some predictive power for
the future values. The co-integration model is presented as,
In this system, 𝑦=𝛽𝑥 is a co-integrated relationship and β is called the set of co-integrated
coefficients. When the two variables are deviating from the equilibrium relationship, there exists an
economic force that pulls the two variables back to the equilibrium level. 𝛼! and 𝛼! are
adjustment coefficients, measuring the speeds of the two variables converging to the equilibrium
The VAR and co-integration models have been widely used to study the relationship between oil
prices and other variables including macroeconomic variables, industrial variables, and financial
market variables. As the literature using this method is huge, we only list a few representative studies
in each category.
Models with macroeconomic variables
o Cunado and Perez de Gracia (2005) study the relationship among oil prices, economic
activity and inflation.
o Chen and Chen (2007) study the interaction between oil prices and real exchange rates.
o Lardic and Mignon (2008) examine the co-integration relationship between oil prices and
o Chevillon and Rifflart (2009) study the effects of OPEC's behavior and the coverage rate
of OECD expected future demand on oil prices.
Models with Industry Information
o Asche et al. (2003) study oil price and the prices for other petroleum products.
o Ye et al. (2006) use relative inventories data to forecast oil prices.
o Grasso and Manera (2007) study the asymmetric relationship between crude oil prices
and gasoline prices.
o Kaufmann et al. (2008) study the role of refinery utilization and futures market
information on oil price.
o Honarvar (2009) and Westgaard et al. (2011) examines the co-integration relationship
between oil prices and natural gas prices.
o Fattouh (2010) studies the dynamics of crude oil price differentials.
Models with financial variables
o Gülen (1998) and Kaufmann and Ullman (2009) examine the co-integration relationship
between spot prices and futures prices for crude oil.
o Miller and Ratti (2009) study the co-integration relationship between oil prices and stock
o Henriques and Sadorsky (2008) investigate oil prices and the prices of alternative energy
6.2.2 The Factor-augmented VAR model (FAVAR)
When a large panel dataset is available to forecast oil prices, there can be too many parameters to
estimate if all of the variables are included in the VAR model. The Factor-augmented VAR model
(FAVAR) can be used to extract useful information from the large panel dataset and reduce the
dimension of the estimated model.
Suppose there is a large panel dataset 𝑋!, for example the aggregate macroeconomic variables,
whose dynamics are defined by the dynamic factor model by Stock and Watson (2002) as follows,
where F! is the vector of unobserved factors that has dimension much smaller than X!. The
dynamics of the factors is defined by a VAR process.
Incorporating the factors into the VAR model, the FAVAR model of Bernanke et al. (2005) is
presented as
where 𝑌
! is the interested variables, L is the lag operator and Φ(L) is a polynomial function. Zagaglia
(2010) uses the FAVAR model to study the dynamics of oil futures using a large panel dataset that
includes global macroeconomic indicators, financial market indices, quantities and prices of energy
6.3 Structural Vector Autoregression Models (SVAR)
Despite the popularity of the reduced form VAR models in forecasting oil prices, demand or supply
quantities and other relevant variables, less can be told about the underlying economic relationship
among these variables with these models. Structural vector autoregression (SVAR) introduced by
Sims (1980) tries to fill this gap by recovering economic shocks from observable variables by
imposing a minimum set of assumptions compatible with a large class of models. The power of this
approach for representing the structural features of the market depends critically upon whether the
restrictions imposed by the modeler are warranted. This approach does not always produce superior
results because modeler judgment can play such a critical role.
A structural vector autoregression model works in the following steps. First, specify a number
of structural equations, motivated from economic theory, for example, the oil demand and supply
functions. Allowing yt to represent price, quantity and other variables, the structural equations have
the following form,
where 𝑤! is the structural shock, for example the demand shock or the supply shock.
Second, a reduced form VAR model discussed earlier is estimated. In order to develop a one-
to-one mapping between the estimated reduced form parameters and the structural parameters, we
have to impose parametric restriction on the structural equations from economic theory; typically in
the form of exclusive restriction, that is, exclude some variables in certain equations. For example,
the analyst would exclude real GDP when he wanted to identify the supply function and input costs
when he wanted to identify the demand function. Finally, we can use structural parameters to draw
economic conclusions.
Studies on crude oil prices using structural VAR models with parametric restrictions include
Herrera and Hamilton (2004), Cologni and Manera (2008), Krichene (2007) and Kilian (2009).
Instead of imposing parametric restrictions, sign restrictions can also be used to identify the
structural VAR models. For example, we can impose upper or lower bounds on the oil demand
elasticity with respect to price from economic intuition. Killian and Murphy (2010) have constructed
one such structural VAR model that includes oil production, inventory, price and a proxy for real
economic activity. A well-known problem of the conventional econometric models about oil
systems that are not estimated in reduced form is the endogeneity issue, that is, variables on the right
side of the regression equation are correlated with the error term.
Using the “sign restrictions” on elasticities and other economic variables, they are able to
distinguish supply shocks, demand shocks and speculative shocks and thus identify the structural
parameters, to some extent. This identification is not conventional point identification but the set
identification, that is, a small of number of admissible models are identified. Their estimate for the
short-run demand elasticity is -0.26, much larger than earlier studies using models without
accounting for price endogeneity.
Using a structural VAR model with sign restrictions, Lippi and Nobili (2010) study the interplay
between oil prices and the US business cycle. They find the correlation between oil prices and the
US business cycle depends on the nature of the fundamental shock: a negative correlation emerges
in periods when oil-supply shocks or global demand shocks occur, while a positive correlation
emerges in periods of supply shocks in the global economy or the US.
Artificial intelligence can be defined as a set of complementary technologies that mimic the human
brain in thinking to solve complex structured, nonlinear and dynamic problems. Data mining is a set
of techniques used to extract hidden patterns from data. Artificial intelligence and data mining
(AI&DM) present a set of solutions outside of the toolbox traditionally available to and used by
engineers and economists, with potential applications to energy markets and the oil and gas
exploration and production industry. Successful use of these tools requires a new way of looking at
problems at hand. Unlike conventional modeling methods, where predefined patterns (parametric
methods) are used to build models, AI&DM tools and techniques are not constrained to any
predefined functional definitions.
AI&DM provides an inductive approach to problem solving that encourages learning by
following intuitive pathways from general to specific as opposed to the traditional regression-based
approach that moves from specifics to general. Instead of using preconceived/pre-defined models
to characterize patterns in data, AI&DM explores and discovers existing patterns in data (no matter
how complex or invisible they may seem at first glance) to build models. AI&DM’s objective is to
mimic the most powerful pattern recognition engine in the universe the human brain.
(Mohaghegh, Al-Fattah, and Popa 2011)
Artificial neural networks, fuzzy logic and genetic algorithms are among the artificial intelligence
paradigms. Artificial neural network (ANN) technology has seen a surge of new applications in
recent years in various areas of science, engineering, and finance because of its power and ease of
use in solving complex structured and nonlinear problems. ANNs are an information processing
technology inspired by the studies of the brain and nervous system. In other words, they are
computational models of biological neural structures. Neural networks are nonlinear statistical
models. Inputs are combined linearly to derive features that predict the target variable(s) using a
nonlinear function. These procedures are especially powerful when applied to situations where the
desired signal is high relative to the level of background noise and when the goal focuses on
prediction without interpretation or explanation. They are less effective for problems where the goal
is to understand the roles of the separate independent variables or to describe the behavioral and
expectations process that generate the data (Hastie, et al, 2009, chapter 11). For the oil price issue,
this approach may have value in extracting key information and patterns related to price volatility.
Each neural network (NN) generally consists of a number of interconnected processing
elements (PE) or neurons grouped in layers. Figure 4 shows the basic structure of a three-layer
network: one input layer, one hidden layer, and one output layer. The neuron consists of multiple
inputs and a single output. Input consists of the values of independent variables and output is
comprised of the dependent variables. Each input is modified by a weight, which is attached to the
input value. The input can be raw data or output from other PEs or neurons. With reference to a
threshold value and activation function, the neuron will combine these weighted inputs and use
them to determine its output. The output can be either the final product or an input to another
neuron (Al-Fattah 2011).
Fuzzy logic on the other hand is a form of many-valued logic or probabilistic logic; it deals with
reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory,
where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value
that ranges in degree between 0 and 1. Fuzzy logic has been extended to handle the concept of
partial truth, where the truth value may range between completely true and completely false.
Figure 4- An example of a three-layer MLP neural network structure.
The design and development of an ANN model involve seven important procedures. These
procedures include: 1. Data acquisition and preparation, 2. Data preprocessing, 3. Inputs selection
and dimensionality reduction, 4. Network design, 5. Network training, 6. Verifying, and 7. Testing.
Figure 5 is a flowchart illustrating the ANN development strategies implemented by Al-Fattah and
Al-Naim (2009).
Artificial intelligence evolving technology has been recently applied for modeling, analyzing,
and forecasting critical problems in the area of energy markets and economics. One important
problem, for example, that can be addressed using the ANN technology is modeling energy market
volatility (Al-Fattah, 2012 & 2013). Price volatility is an important measure used in derivative option
pricing, and portfolio construction, and risk management. To the extent that traditional statistical
and econometric tools have failed to fully resolve the sources and behavior of price volatility, ANN
is a promising approach that may with further development overcome the shortcomings of the
conventional modeling methods.
In his study, Al-Fattah (2012 & 2013) developed two ANN models for forecasting oil price
volatility: one for WTI futures price volatility and the other for WTI spot prices volatility. It was
noted that the intention of his work is not to predict the oil prices in absolute terms; rather the
objective is to reasonably predict the direction of its volatility. The models were successfully
designed, trained, verified, and tested using historical oil market data. The estimations and
Input layer Output layerHidden layer
predictions from the ANN models closely match the historical and calibrated data of WTI from
January 1994 to April 2012. They also appear to capture very well the dynamics and the direction of
the oil price volatility. These ANN models can be used at least as a short-term predictive tools for
the direction of oil price volatility, to quantitatively examine the effects of various physical and
economic factors on future oil market volatility, to understand the effects of different mechanisms
for reducing market volatility, and to recommend policy options and programs incorporating
mechanisms that can potentially mitigate the oil market volatility.
Figure 5- Flowchart of ANN design and development procedure deployed in this study.
Source: Revised from Al-Fattah and Al-Naim, 2009.
In this review we have considered a wide array of models, each with their own strengths, weaknesses
and contributions to the literature. Motivated by different objectives, modelers have turned to
methods from economics, game theory, statistics, finance, and artificial intelligenece to model the oil
market. We have seen structural models used to gain insights into the underlying forces in the
market, computational models used to study detailed impacts across stakeholders at a national and
global scale, reduced form models used to forecast short-term prices and validate empirical
relationships in the data, and artificial neural network models used to forecast energy markets and
economic problems such as the price volatility.
A single model cannot do everything. In focusing on certain attributes others are simplified.
Unforeseen events--wars, natural disasters, advances in technology, the macroeconomic cycle--can
have drastic impacts on prices and defy even the most thorough modeling effort. The right
modeling approach answers the central question to the research, while considering only the details
necessary to support the analysis.
This paper summarized existing modeling approaches without trying to identify research gaps in
this literature. Nevertheless, one can observe several key limitations in the previous attempts to
model the oil market.
First, none of the major energy organizations, central banks, or international organizations like
the World Bank actually use models to project prices. Instead, they use models to project supply
outside of OPEC and demand and allow OPEC to satisfy the net demand for oil. The organizations
then determine whether the residual oil supplied by OPEC appears reasonable based upon a series
of judgmental factors about geology, politics and economics.
Second, many policy models are used to forecast the most likely future path for oil prices. Used
in this manner, many projections across different organizations appear very similar to each other,
creating a false sense that models can track oil prices accurately. In contrast, these models are
infrequently used to their full capacity to explore the complete range of possible outcomes and
technological developments that might be possible under different conditions.
Third, most recent energy models for evaluating climate change policy emphasize the long-run
adjustment of energy-consuming economies in shifting away from fossil fuels with little attention to
the market structure currently existing in today’s petroleum sector. These more comprehensive
energy models have certain advantages, including the ability to evaluate detailed impacts of various
policies and decisions and how society’s welfare will change with different economic and energy
policies. Among their limitations, however, is that they will disappoint policymakers who consider
oil market structure issues and OPEC pricing decisions to be important, because they largely ignore
these issues. Efforts to integrate world oil and climate change models will require substantial
improvement in the representation of oil market structure. Artificial neural network models appear a
promising approach for capturing these dynamic factors.
This paper is based on research supported by the King Abdullah Petroleum Studies and Research
Center (KAPSARC). We would like to acknowledge the careful comments and review on our previ-
ous work by Bassam Fattouh, James Smith, Fred Joutz, and Awwad Al-Harthi. We also benefitted
from the valuable advice from and discussion with John P. Weyant, Stephen P.A. Brown, James L.
Sweeney and participants at the Oil Metric Forum workshop in Washington, D.C. on September 16-
17, 2010, and the National Energy Policy Institute Conference on OPEC at 50: Its Past, Present and
Future in a Carbon-Constrained World in Tulsa, OK on March 23, 2011. All responsibility for the
contents of this paper belongs to the principal authors, and none of the views and conclusions can
be attributed to any of the above individuals or the King Abdullah Petroleum Studies and Research
Center (KAPSARC).
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