474
SEPARATING STATIC AND DYNAMIC EFFECTS IN AN OIL PRICE MODEL
by
Brling Moxnes
Chr. Michelsen Institute
Fantoftvegen 38
N-5036 FANTOFT
ABSTRACT
A static and a dynamic model of the oil market are compared. Three
major differences appear in forecasts. The dynamic model fluctuates
around the static model equilibrium price. The dynamic model shows
greater uncertainty in trend development. The dynamic model forecast
overshoots the cost level of synthetic oil.
INTRODUCTION
In this paper I examine behaviour of a static and a dynamic version
Of the same oil price model. ‘The purpose of separating static and
dynamic effects is to understand model behaviour and to assess the
importance of dynamic formulations. Starting with a static model
also helps communicating the results.
The static model produces an equilibrium 011 price forecast. The
structure of this model 1s explained in Chapter 2; its behaviour is
explained in Chapter 3. In Chapter 4 the static model is extended
into a dynamic model. (This dynamic model is a very simple version
of the OILTANK model, Endress & Ervik, Moxnes (1982), and Moxnes
(1983)). Lags are introduced in both supply and demand. This
reflects high capital intensity and long construction delays in oil
production and capital-imbedded technologies for consumption of ofl.
Instead of requiring that the oil price equilibrates supply and
demand at each point in time, a price theory is formulated. The
chosen price formulation aims at an equilibrium situation, which is
never quite reached. In chapter 5 the behaviour of the dynamic model
4s examined. A forecast made by the dynamic model is compared to the
static model forecast. Three major differences appear. The dynamic
model fluctuates around the static model equilibrium price. The
dynamic model shows greater uncertainty in trend development. The
dynamic model forecast overshoots the cost level of synthetic oil.
All prices are assumed to be in real 1984 USD.
A STATIC OIL MARKET MODEL
Figure 1 shows the static oi] market model in terms of long-term
supply and demand curves. The long-term equilibrium price is given
by the intersection of the supply and the demand curve. Four actors
are represented in the diagram: consumers, OPEC producers, non-OPEC
Producers and producers of synthetic oil.
Figure 1. Long-term supply and demand curves for the static oi]
market model.
Consumers conserve oil or substitute it with other types of energy
when the ofl price increases, and consumption increases in step with
economic activity. These effects can be expressed
formally by the equation:
475
. yyy pte je
% 7 Ie GD? (ogre os
q = demand for o11 (mb/d)
Ign = 44 mb/d - equilibrium demand for of] in initial year (1984).
y ~ index for economic activity
Yo = 100 - index for economic activity in initial year
v = 0.75 - income elasticity
P - crude ofl price (USD/b)
Po = 30 USD/b - ofl price in initial year (1984)
¢ = 20 USD/b - additive taxes plus costs of refining and distribution
e = -2.0 - of] product price elasticity
The sum of crude oil price, p, and additive taxes and costs, c, make
up oil product prices. Consumers react to product prices relative to
initial product prices through a product price elasticity, e. This
elasticity combines the effects of conservation and substitution.
Because crude oil prices are buffered by additive taxes and costs,
the resulting crude oil price elasticity always stays below the
product price elasticity. when crude oil price equals zero, demand
4s only limited by additive taxes and costs. This explains the
interception between the demand curve and the quantity axis in
Figure 1. A constant price elasticity 1s a very crude assumption on
how demand reacts to price changes. However, it is sufficient for
the purpose of this paper.
Expected growth in economic activity is set to 3 percent per year.
The effect of economic growth in Figure 1 is shown by a rightwards
shift of the demand curve.
Non-OPEC producers invest in exploration and development of oil
fields according to current crude oil prices. The success of these
investments depends on the availability of oil. Availability
declines as remaining resources are depleted. A formal expression
for total o11 supply is given by the equation:
Wtdp, + O<P <P, «2)
Le + PRs
= dey by P
q, - total supply of of] (mb/d)
yy ~ supply of non-OPEC oil (mb/d)
gy = 43 mb/a > initial equilibrium non-oPgc oi] production.
a =0.3 - non-OPEC supply elasticity
R - remaining resources (mb)
= 600000 mb =~ remaining resources initially (1984)
Yop = 26 mb/a—~ OPEC product ion
dy - demand for of1 (mb/a)
P, = 50 USD/b —- ‘cost of synthetic of}
A long term supply elasticity as low as 0.3 indicates limited access
to ol fields for oil companies. Limits are imposed by governments
in order to stretch out oil production and income generation in time.
Non-OPEC supplies are assumed to be a function of current prices
only, no weight is put on expectations about future prices. This
simplification needs some justification.
Pirst, current prices determine current incomes, which put certain
financial restrictions on investments.
Secondly, “perfect foresight" has to be implemented through the
application of uncertain forecasts. According to Morecroft (1983)
(p. 6) decision makers tend to put less emphasis on uncertain
information from distant sources than on certain information from
close sources. Morecroft seeks support for this view from
representatives of “the behavioural school of economics": Cyert,
March and Simon. In this context, today’s oil price represents the
certain information.
Thirdly, it 1s argued that price forecasts for the long-term are
influenced by current prices.
476
Fourthly, to the extent that ofl companies have other goals than
maximization of profits, the importance of “perfect foresight” is
diminished. Such goals, for example, may be company growth or
stability of operations.
The effect of resource depletion on non-OPEc supply 1s given by the
Linear expression R/Ry. Since R equals R, initially, the effect
on supply is at First neutral. As remaining resources are depleted,
non-OPEC supply 1s reduced; the supply curve shifts leftwards.
Remaining resources are monitored by the equation:
R= - a, + 365 a @)
QPEC-producers are assumed to maintain a given production, q,_,
throughout the forecasting period independent of oil price. this
assumption is motivated by the stress on criteria other than profit
maximation by OPEC members. The assumption becomes more realistic
the more insensitive OPEC considers its profit to be to its om
supply strategies. Brvik (1981) has found that OPEC's profits are
fairly immune to its choice of production capacity.
Producers of synthetic oil are assumed able to supply any demanded
volume, qp, at an oil price equal to costs of synthetic ofl, p,.
This explains the horizontal part of the supply curve.
It is important to note that synthetic of] is defined as a liquid
fuel which can be used by consumers of ordinary oil, without major
adjustments in energy consuming equipment. Thus, gas, coal, and
electricity are not classified as synthetic oil. Market shares for
O11 are lost to gas, coal, and electricity according to oil prices
and the assumed price elasticity.
BEHAVIOUR OF THE STATIC MODEL
Figure 2 shows a prediction from the static model. As the demand
curve moves rightwards because of economic growth, and as the supply
curve moves leftwards because of resource depletion, the oil price
grows until the cost level for synthetic oil is reached. From then
on, demand is met by a mixture of of] and synthetic oi] at a fixed
price of 50 USD/b. (The static model behaviour 1s calculated using
DYNAMO. In order to do so the equilibrium price 1s given by the
equation B = p(K + (q4/a,-1))).
Figure 2 also shows the behaviour of the dynamic model. In the
following, I shall describe how the structure of the static model is
extended to yield a dynamic model.
o+ 2 " ——— ee
1984 es 1994 1999 2004 2009 20K «2019204
THE
Figure 2. Deterministic ofl price forecasts made by the static and
the dynamic oil market model.
477
‘A DYNAMIC OIL MARKET MODEL
Consumers need time to adjust to new price signals. Some
conservation measures can be implemented imeediately, while others
result from slow changes.in production processes and
infrastructures. In the dynamic model, adjustments in consumption,
lag behind price changes by on average eight years. About 63 percent
of the adjustments take place before the eight years have elapsed,
and 37 percent take place afterwards. This means that in the
short-run consumers are less flexible than in the long run; the
short-term demand curve is steeper than the long-term demand curve in
Figure 1.
‘The delayed response to oil price is modelled by introducing a
delayed version of the crude of} price, P,, in Equation 1. (It
makes no difference whether the lag is introduced in the oil price or
in the actual demand equation). ‘The demand equation becomes:
(4)
00 * Ee 5)
Po ee
P, ~ delayed crude oil price for demand
D
250 = 58 mb/d - demand for oil in initial year (1984)
Poo = 18 USD/b - initial level of delayed ‘crude ofl price
The constant Igo is calculated in the initial year before the model
starts simulating. Igo denotes equilibrium demand in the initial
Year, where equilibrium is given by delayed oil price equal to
initial of] price, Py) = Po: Bquation 5 ensures that initial
demand, q in equation 4, equals measured initial demand, Ing"
for any choice of price elasticity, e, and initial level of delayed
crude oil price, Pog: With chosen values for Qn9° Ppg? & and
f+ Gg_ becomes 44 mb/d. This is the value used in the static model.
478
The delayed crude oil price, Py is given by a first order delay
Corresponding to a simple one parameter Koyck lag:
Py (PR Pty (6)
T, = 8 years - average time delay for demand adjustments.
Total supply is given as the sum of non-OPEC, OPEC, and synthetic
supply
4g "Wy * dp + ay
Non-OPEC producers need time to adjust production capacity when the
o11 price changes. It takes time to make plans, to explore, and to
develop new fields. In this respect oil production 1s similar to oil
consumption: The supply curve, like the demand curve, is steeper in
the short-term than in the long-term. Non-OPEC production is assumed
for equal non-OPgC production capacity; non-OPEC producers maintain
full capacity utilization.
As with demand, supply is delayed.by the introduction of a delayed
crude oil price, P,. Non-OPEC production is given by the formula:
= . ok
Wy 7 Igy Ds mM
P
a NO,a
Seu yo! GE (8)
Py - delay crude of] price for non-oPRc supply
Wo = 38 mb/d ~ initial non-opgc ‘supply
Pyg ~ 20.4 USD/b - initial level of délayed crude ofl price for
non-OPEC supply
As in equation 5 for demand, equation 8 for non-OPE&C supply ensures
that initial non-OPsc supply, 9, in equation 7, equals measured
initial supply. Wyo” Initial equilibrium non-OPgC supply, Igy?
equals 43 mb/d with the chosen values for 4. Pugs Po+ and a.
Delayed crude oil price for non-OPEC supply is given by the equation:
Py = (PR - PY)/Ty (9)
Ty = 6-years - averge time delay for non-oPEc supply
adjustments.
‘The delay time in this simple model is an average of the average time
needed to increase and to decrease production.
OPEC acts as a “swing producer”. When total supply increases above
demand, OPBC cuts back on production to maintain a desired price
level. Since OPEC capacity is given exogenously, cutbacks result in
lower capacity utilization. OPEC production is given by the equation
op 7% ~ Wy > Sy ; Qo)
Capacity utilization is given by:
™: MN -
Yop op Cop qi)
- OPEC capacity utilization
U,
op
Cop 7 32-5 mb/d - OPEC capacity
. OPEC's desired price level is influenced by current market
conditions. The best information about the market is given by OPEC's
ow capacity utilization. Since nobody knows exactly the best price
level for OPEC to choose, practical OPEC policies must, to a large
extent, be based on today's price and on current market conditions.
In the dynamic model, OPEC lowers its desired price from today's
level if capacity utilization falls below 80 percent. When capacity
utilization approaches 100 percent, OPBC is no longer in control of
the oll price, and a rapid price escalation occurs. This means that
=40=
the model does not calculate an equilibrium price. Rather, the model
constantly produces exploratory price changes in order to restore an
equilibrium characterized by 80 percent capacity utilization.
Ignoring short-term spot market fluctuations, outside the control of
OPC, the crude oil price equals OPEC's desired price. The crude oil
price is given by the equation:
B= p+ £Wy) (2)
£05) ~ growth rate (fractional change per year)
‘The chosen functional relationship between OPEC capacity utilization,
Yop" and fractional change in oil price, EWU.) is shown in
Figure 3. Historical observations give an indication of the quality
of this assumption.
| @ CONTRACT PRICES
opec capacrry
CHLEATION
PERCENT
Figure 3. Fractional yearly change in ol price from OPEC capacity
utilization.
479
-iu-
At the desired 80 percent capacity utilization OP&C production is
26 mb/d, which 1s the production rate in the static model.
Producers of synthetic oil also need time to increase production.
This is because planning, construction etc. take time. Furthermore,
absolute growth in production of synthetic oil is limited by lack of
resources in an infant industry. For example, lack of trained
manpower slows down growth directly or through wage and cost
escalations. Supply of synthetic oil, 4,, 1s given by the equation:
dy * 4° 9(P/PL) qa)
P, = 50 USD/bbl ~ cost of synthetic oi]
9(b/P,) - growth rate (fractional change per year)
Gag * 9-5 mb/d - initial synthetic oi] production
Pigure 4 shows the assumed relationship between return on investments
in synthetic of, p/p, and the yearly growth rate for this
industry. At low return, capacity is slowly depreciated because of
long lifetimes of capital equipment. Factories tend to operate as
long as prices are higher than operating costs, which are much lower
than the total costs of synthetic oll, p,. The higher the return,
the faster the growth. As return becomes very high, physical
constraints become more and more dominant. This explains why growth
is limited at very high returns.
-12-
°.
.
of
Pigure 4. Relationship between return on investments and synthetic
of] production growth.
Initial synthetic of] production, q,,. reflects the initial status
of synthetic oil producton with respect to capital equipment and
experienced manpower. As this is the resource base the industry will
be built on, its size is of great importance with regard to the
market penetration of synthetic ofl.
480
eqs
BEHAVIOUR OF THE DYNAMIC MODBL
The static model is characterized by static equations for supply and
demand, and an oil price which equilibrates supply and demand. In
the dynamic model, both supply and demand are delayed reactions to
oil price, and the ofl price is given by an explicit price theory.
Figure 2 shows the different forecasts resulting from the two
models. There are three important differences:
- The dynamic model produces price cycles
- Uncertainty in the long term trend is greater in the dynamic than
in the static model
~ ‘The dynamic model forecast overshoots the cost level of synthetic
oil
Price cycles
‘The structure of the oil market has changed remarkably since 1973.
Prior to the 1973 o11 embargo, oil prices were well controlled by a
few large oi! companies. Instabilities appeared only in volumes.
During the years 1973 to 1976 of11 companies operating in OPEC
countries were progressively nationalized. For example, the
Saudi-Arabian government had acquired a 100 percent interest in
‘Aramco's crude oil concessions in mid-1976, OPEC (1983) p. 115. The
number of actors in the oil market increased. “During 1979-80 the
very long terms of many contracts were reduced. Total volumes traded
to former concessionary companies fell to around 50% of the total.
Direct trade to Government-importing agents increased and the volume
traded at spot prices expanded from 5-10% to perhaps 10-15%",
Mitchell (1982) p. 89. These latter changes broke up the old market
structure even more. By the beginning of the 1980s the structure of
the of] market had become much like the structure of other raw
material markets. ‘thus it has become more likely that traditional
commodity price cycles will appear in the ofl market. The two price
hikes in 1973 and in 1979 will in fact be viewed as two such
fluctuations around an increasing long-term trend.
-4-
The Cobweb theory, Henderson & Quant p. 142, gives an explanation of
the commodity cycle in the case of supply only lagging behind price.
A high price in one period means that supply will be high in the next
period, with the result that price falls. A low price means low
supply in the next period and so forth. In general, the Cobweb
theory states that fluctuations increase in magnitude over time when
supply 1s more flexible than demand, and decrease in magnitude when
demand is more flexible than supply.
The Cobweb theory can easily be formulated in a dynamic model if one
assumption is altered, Meadows (1970) p. 15. Instead of assuming
that supply changes in steps exactly one period after each price
change, assume that the supply response is distributed in time. This
seems to be a realistic assumption since supply can be changed by
different means, for exemple, capacity utilization, employment, and
investments. In addition, the possibilities for production
enhancements differ among producers. when the distribution is as
wide as that implied by the delay-function in equation 9, cycles will
no longer appear in the Cobweb model. Thus the Cobweb theory 1s not
sufficient to explain fully the cycles in the presented dynamic o11
market model.
‘The price formulation is also of importance for the cyclical
tendency. This is most easily explained by going through one period
of a typical cycle. (An analytical analysis of instability is very
d@ifficult.). Assume that exports from one oil producing country is
suddenly cut off. This is the event that makes the model reveal its
dynamic properties. Excess demand and very high OPEC capacity
utilization leads to a rapid price escalation more or less outside
the control of OP&C. AS both demand and supply 1s inelastic in the
short run, the price has to rise very high to balance the market.
‘The new price becomes the desired price level that OPEC wants to
maintain. However, after a few years, the high price level has
brought about reductions in demand and increases in production.
OPEC's capacity utilization drops. OP& still desires a high price,
but the low capacity utilization forces OPEC to lower the real oil
price. This reduction comes about both through nominal reductions
481
-15-
and general price inflation. Reduced prices stimulate demand and
discourage investments in marginal oil fields. The major results of
these incentives appear after a few more years. As desand approaches
total supply capacity, no small force can change the direction of
this movement. OPEC capacity utilization grows towards one hundred
percent, while the oil price escalates rapidly. This situation is
similar to the starting point. This time there is no exogenous event
that begins the cycle. Rather, instability is passed on from the
previous period.
‘This is how the oil price cycle works in the model. Another
deviation from the Cobweb theory worth mentioning, is the delayed
response in demand. Because of this delay, the short-term price
elasticity is very low. According to the Cobweb theory, this
destabilizes the price cycle.
As the purpose of this paper is to discuss the behaviour of one
particular dynamic mode] compared to a static version of this model,
I will not discuss sensitivity to different model formulations in
detail. I only mention a few possible extentions:
~The price formulation is no doubt a great simplification of
reality. The rationale for the formulation is not that it is the
best policy OPEC can adopt. Rather, it 1s chosen because I
believe that it is a politically feasible policy. In Moxnes
(1982) p. 53, it 1s shown that ofl price development can be
stabilized, 1f OPEC reacts to changes in its ow capacity
utilization as well as in the level of the capacity utilization. |
A policy where capacity utilization influences price directly in
addition to the effect on fractional change in price, also
stabilizes price development. Well-founded expectations about
future supply and demand should also be expected to stabilize
price development. However, policies that prove to work in a
deterministic model are not necessarily acceptable policies in an
environment characterized by much uncertainty.
gers ae
- Adding random disturbances to supply and demand, serves to
propagate the price cycle. This point is well explained by
Frisch (1933) p. 171: "In many cases they (economic
oscillations) seem to be produced by the fact that certain
exterior impulses hit the economic mechanism and thereby initiate
more or less regular oscillations”.
- Adding inventories in the model, also seems to destabilize the
price cycle, Moxnes (1982) p, 49. This is the.case if inventory
holders tend to build-up security stocks when it 1s revealed that
supply is short of demand. ‘This effect works to maintain price
cycles. Release of governmental strategic petroleum reserves in
cases of short supply, counteracts the effect of private
inventory build-ups.
Because of random disturbances and limited knowledge about parameters
and structure, it is very difficult to predict the timing of oi]
price fluctuations beyond one future cycle. A cyclical tendency can
be predicted for a longer period, however. Thus, price cycles
increase total uncertainty in ofl price forecasts. Knowledge about
cycles also helps to sort out short and long-term trends from recent
historical developments.
une: jong- ts
Ifa smooth line is drawn through the price prediction from the
dynamic model in Figure 2, one can see that the dynamic model gives a
higher trend development than the static model. ‘The reason for this
is delay in supply and demand. At each point in time supply and
demand are given by the of] price of a few years ago. Given that the
price trend is increasing, supply and demand are always determined by
a price lower than the current price. This means that demand will
exceed supply persistently, compared to the static case where supply
and demand react to current prices. To obtain the same balance
between supply and demand as in the static case, the ofl price must
increase ahead of time. This is in fact what happens to a large
extent in the model. The price formulation accumulates the pressure
on price from market imbalances and the result is a higher price
trend than in the static model.
482
-1-
In a scenario producing s a declining long-term trend in the of}
price, the dynamic model also produces a price prediction which is
ahead of the static model prediction. This means that in the
declining scenario, dynamics lower the price prediction. Altogether
this means that the dynamic model portrays greater uncertainty in
price predictions than the corresponding static model.
Price overshoot
In scenarios where synthetic oil is demanded, the ofl price
prediction from the dynamic model overshoots the cost level of
synthetic ofl, Figure 2 illustrates this point. The explanation is
that synthetic ofl is not brought quickly enough on to the market to
prevent a supply shortage when non-OPEC oil production tapers off as
demand grows. Figure 4 shows how the growth rate is influenced by
oil price and costs. Because the synthetic of] industry is in its
infant stage as the oil price passes the cost level for synthetic
oil, absolute growth is low in the early years. This is in contrast
to the static model where the implicit growth rate 1s enormous in the
First few years of operation.
‘The price overshoot means that forecasts made by the dynamic model
portray greater uncertainty than forecasts made by the static model.
The uncertainty only extends upwards.
- 18 -
CONCLUSION 483
This paper has demonstrated that there are important differences
between a static and a dynamic model of the ofl market. ‘The explicit
investigation of a static and a dynamic version of the same oil price
model has been a very useful approach to understand and explain the
importance of dynamic formulations.
First, the dynamic model produces fluctuations in the smooth trend of
the static model's equilibrium price prediction. Understanding such
fluctuations is imperative for those who want to extract short and
long-term trends from recent history. Also, price fluctuations call
for further policies by oil companies and oil producing countries,
than do smooth trend-developments.
Secondly, when model parameters are chosen to give an increasing
trend in predictions, the trend development of the dynamic model is
higher than the trend development of the static model. In the
exemple used in this paper, the difference 1s about 12 USD/b. When
Parameters are chosen to give a downward price trend, the dynamic
model gives a lower trend development than the static model. Thus,
the dynamic model portrays greater uncertainty in price forecasts
than the static model when input parameters are uncertain.
Thirdly, the dynamic model forecast overshoots the cost level of
synthetic oil. This happens while synthetic of] production 1s going
through the first part of its s-shaped growth curve. As demand for
synthetic ofl grows faster than supply, the oil price rises above the
cost level of synthetic oil. this effect introduces upwards
uncertainty in ofl price predictions.
‘The latter two differences between the two models are relatively easy
to understand. Thus, they need leas justification than the first and
more complicated difference, namely the cycles. It is clear from
model experiments that the Fluctuations are sensitive to model
formulations. It is the “second best” OPEC policy that leads to the
strongest fluctuations. Therefore, the current model version is
based on the assumption that the best OPEC policy is politically
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infeasible. Furthermore, several important variables are left out of
the model, for example inventories. Thus, the cycles in the dynamic
model predictions should not be judged by their relation to future
development. Rather, the purpose of the model and its presented
behaviour, is to gain an understanding of a complicated phenomenon.
AS reasonable assumptions about the market produce fluctuations, the
phenomenon 1s likely to occur.
That “commodity cycles" in the of] price are likely to occur, can
also be concluded from the recent development of the structure of the
real oil market. The structure is more like a regular raw material
Commodity market today than ten years ago. Regular raw material
commodity markets are characterized by price fluctuations.
REFERENCES
1, Endress and Ervik
2. Ervik (1981)
3. Frisch (1933)
4. Henderson and Quant
5. Meadows (1970)
6. Mitchel (1982)
7. Morecroft (1983)
8. Moxnes (1982)
9. Moxnes (1983)
10. OPEC (1983)
01600
25.06.84
~ 20-
“OILTANK-2, Technical report”. Christoph
Endress and Leif K. Brvvik.
CHI-no. 790313-1.
Panel discussion p. 469 and p. 471 in
“Mathematical Modeling of Energy Systems”
ed. by Ibrahim Kavrakoglu. - Nato Advanced
Study Institute Series &: Applied Sciences
No. 37.
“Propagation problems and impulse problems
4m dynamic economics", Ragnar Frisch.
Economic Essays’ in honour of Gustav
Cassel. London, George Allen & Unwin Ltd.
“Micro economic theory: A mathematical
approach". McGraw Hill.
“Dynamics of commodity production cycles".
Dennis L. Meadows. Wright-Allen Press Inc.
238 Main Street, Cambridge, MA 02142.
“Anatomy of an oil crisis". John Mitchell
Zeitung fiir Energiwirtschaft 2/1982.
“System dynamics: Portraying bounded
rationality". John W. Morecroft.
Proceedings of the 198] system Dynamics
Conference in Rensselaervill, New York.
“Usikkerhet 1 trendutvikling og grad av
ustabilitet for oljeprisen". Erling
Moxnes, CMI-nr. 822125-2.
“Usikkerhet i den langsiktige
oljeprisutviklingen". @rling Moxnes,
CMI-822260-2.
“OPEC member country profile”. OPEC's
secretariat, Obere Donaustrasse 93, A-1020,
Vienna, Austria.”
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