Reprinted from The Atlantic Economic Journal.
Copyright March, 2003 by International Atlantic Economic Society.
Posted on Energy Information Administration Website with permission of
International Atlantic Economic Society.
Elasticity of Demand for Relative Petroleum
Inventory in the Short Run
MICHAEL YE,∗ JOHN ZYREN,∗∗ AND JOANNE SHORE∗∗
To better understand petroleum markets, the authors established the importance of
the deviation of inventory levels away from a normal level, where the normal level is
comprised of seasonal movement and a general trend. Since supply and demand for
petroleum are less elastic to price in the short run than is inventory, it is this deviation
or relative inventory level that plays the role of absorbing unexpected shifts in demand
and supply. They demonstrated theoretically that the demand for relative inventory must
be negatively related to price. They estimated the relative inventory levels and associ-
ated short-run price elasticity for several OECD countries and groups of countries, and
found that short-run price elasticity of demand for relative inventory is negative and
statistically signiﬁcant, supporting the theoretical arguments. (JEL Q40)
In this paper, the authors explored the importance of the deviation of inventories away
from some expected or normal level in understanding petroleum markets. They refer to this
deviation from normal as the relative inventory level. Since supply and demand for petroleum
are less elastic to price in the short run than is inventory, it is this relative inventory level
that plays the role of absorbing unexpected shifts in demand and supply. This observation
stimulated exploring the price elasticity of demand for relative inventory levels theoretically
and empirically. This paper describes why relative inventory level is an important variable to
understanding petroleum markets and demonstrates theoretically that the demand for relative
inventory must be negatively related to price. Then the paper estimates the short-run price
elasticity of demand for relative inventories for several OECD countries and country groups
and Þnd it to be negative and statistically signiÞcant, supporting the theory they developed.
The petroleum market since the Gulf War exhibited several features that allowed the
investigation of short-run petroleum market behavior in terms of supply, demand, and inven-
tory. Over much of the time between 1991 and the present, the Organization of Petroleum
Exporting Countries (OPEC) did relatively little to adjust production in order to accommo-
date consumption changes, and sometimes, when action was taken, it was either insuﬃcient
or excessive to stabilize prices. Thus, there was a fairly long period in which prices varied
considerably. In particular, from 1996 to the present, prices exhibited large cyclical swings.
As shown in Figure 1, monthly average West Texas Intermediate (WTI) crude oil spot price
(nominal) dropped to nearly $11 per barrel early in 1999 and rose to a peak of nearly $35
per barrel towards the end of 2000.1
∗St. Mary’s College of Maryland and ∗∗Department of Energy–U.S.A. This work is partially
sponsored by the Oﬃce of Strategic Petroleum Reserve, U.S. Department of Energy, and was pre-
sented at the Fifty-Second International Atlantic Economic Conference, Paris, France, March 2002.
AEJ: MARCH 2003, VOL. 31, NO. 1
Figure 1: Western Texas Intermediate Spot Price
The level of petroleum inventories also varied considerably during the 1990s. Figure 2
shows the combined government and industrial inventories of both crude oil and petroleum
products in all Organization of Economic Cooperation and Development (OECD) countries.2
Two things can be observed from the Þgure. First, there appeared to be a seasonal pattern
in the early 1990s when the WTI prices were relatively stable. Second, since 1996, a negative
relationship between petroleum inventory and crude oil price is evident when WTI prices
experienced large swings. As the crude oil price dropped from 1996 to 1998, OECD total
inventories climbed to record levels in 1998. Later, when the price climbed to its peak in
late 2000, total inventories declined. Intuitively, the authors suspect that the relationship
between inventory and price was masked by the seasonal pattern in the early 1990s and that
the seasonal pattern was overwhelmed by the large price swings since 1996. Thus, further
careful analysis of petroleum inventory is needed to understand its relationship to WTI price.
The relationship between commodity inventory levels and spot prices has been theoreti-
cally as well as empirically studied for nearly a century.3 There also have been many studies
on petroleum demand and price elasticity of demand for crude oil and oil products in the
mid to long run.4 However, no previous studies on short-run price elasticity for petroleum
inventory were available.
In this paper, the price elasticity of demand for petroleum inventory in the short run
is investigated. A better understanding of the relationship between price and inventory
was found by decomposing observed inventory movement into an expected component of
normal seasonal movement and general trend and into an unexpected component that reßects
responses to the short-run atypical variations in market supply and demand. This unexpected
component is called the demand for relative inventory. The authors estimated the normal
seasonal and trend components and relative inventory level for the Post Gulf War period
from March 1991 to June 2001.
Elasticity of the demand for relative inventory with respect to WTI crude oil spot price
was estimated for a number of countries, groups of countries, and regions in OECD for
YE ET AL.: PETROLEUM INVENTORY
Figure 2: Total OECD Petroleum Inventory
the period of January 1996 to June 2001, during which the market experienced large price
swings.5 They found that the short-run demand for relative inventories of Group-Seven (G-7)
countries (large size economies) is much less elastic than those of non-G-7 OECD countries
(smaller size economies). This supports the intuitive hypothesis that, during times when
crude oil prices are high and volatile, large countries are less sensitive to price changes and
are more likely to have smaller percentage declines in inventory. This has the implication
that poorer countries may back out of high-priced petroleum trading markets before wealthier
countries, thus reducing the eﬀective world demand for crude oil.
In the next section, a theoretical basis is developed to establish a negative relationship
between crude oil price and demand for relative petroleum inventory. Section three presents
the empirical results. It begins with a description of the data used in the study, their sources,
and how the data were processed. Then, empirical results of elasticity at the country level
and elasticity for groups of countries and regions are presented. The last section concludes
The fundamental motivation to have petroleum inventory is much the same as that for
other commodities. Petroleum inventory plays the role of smoothing operations on both
the supply side and demand side and of hedging against price changes.6 More speciÞcally,
inventory levels are determined in the short run by factors such as expected seasonality and
general trends in production and demand as well as unexpected supply or demand shifts, and
price changes caused by these shifts. There may also be other factors such as interest rates
and changes in the cost of physical storage that may be important in the long run.
When dealing with the actual physical commodity (for example, the total of crude oil and
petroleum products), we have two markets, the cash market and the storage market (with
an embedded futures market). Each market has its own separate, yet related, supply and
AEJ: MARCH 2003, VOL. 31, NO. 1
demand. The dynamic equilibrium deÞned by these two markets is depicted by the time
trajectories of spot price, inventory, and convenience yield (the value price of inventory).7
This paper focuses only on the cash market.
The cash market deÞnes equilibrium spot prices and changes in inventory, denoted It−It−1
in period t where I denotes inventory level. In any period t, change in inventory is deÞned
as supply, St, minus demand, Dt, It − It−1 = St − Dt, or,
It ≡ It−1 + St − Dt
Equation (1) is an identity holding for all periods and any crude oil price, assuming that
the storable commodity suﬀers from no destruction or loss of inventory. However, both supply
and demand are functions of price. It is assumed that supply and demand are independent
of each other in the short run. In other words, S = S(P ) and D = D(P ). Since the three
variables I, S, and D are related by (1), I is also dependent on price, or, I = I(P ). Thus,
taking It−1 to be pre-determined in period t, the equilibrium condition can be written as:
It(P ) = It−1 + St(P) − Dt(P) .
Since normal seasonal movements and general trends in inventory exist for each country,
or in aggregate for groups of countries and regions, it is necessary to deÞne a normal level
of inventory for each of them. Such a deÞnition should recognize typical supply and demand
characteristics. More speciÞcally, demand for petroleum products is highly seasonal and is
greatest during the winter months when countries in the Northern Hemisphere increase their
use of distillate heating oils and residual fuels. Supply of crude oil, including both production
and net imports, also shows a similar seasonal variation but with smaller magnitude. During
the summer months, supply normally exceeds demand and OECD countries’ petroleum in-
ventories build; whereas during the winter, demand exceeds supply and inventories are drawn
down. As a result, inventories typically demonstrate seasonality since inventory is a measure
of the balance, or imbalance, between petroleum supply and demand.8 If the market supply
and demand is balanced over the period of a year, the increase in inventories during the
summer will equal the decline in inventories during the winter. In brief, inventories will nor-
mally demonstrate seasonality because their build-ups and draw-downs reßect the seasonal
imbalance between supply and demand as a result of the supply of crude oil showing less
seasonal variation than demand. Long-term trends also exist, mainly due to the trends in
government inventories, increasing economic activities, or new global conservation measures.
Such trends are considered when deÞning a desired normal pattern. 9
Consider that at any given time, t, there is a normal level of inventory reßecting the
typical seasonal demand and supply as well as general trend movements in demand and
supply. Letting ∗ represent the normal level, we have, for a particular time t, from (1),
I∗t = I∗t−1 + S∗t − D∗t
Note that It∗, St∗, and Dt∗ are independent of market price, P , and are determined empiri-
cally by historical information.
The relative level of inventory is deÞned as the deviation of the actual level from the
normal level. Letting the preÞx R mean relative level and subtracting (3) from (1):
RIt = RIt−1 + RSt − RDt
where RIt = It − I∗t, RSt = St − S∗t, and RDt = Dt − D∗t. Referring to (2), equation (4)
may also be re-written with each term explicitly expressed as a function of P , except RIt−1,
which is treated as pre-determined in period t:
YE ET AL.: PETROLEUM INVENTORY
RIt(P ) = RIt−1 + RSt(P) − RDt(P) .
Given It−1 (and thus RIt−1) as predetermined, (5) says that in the short run, demand for
relative inventory, RIt, responds to unplanned variations in the supply, RSt, and unplanned
variations in demand, RDt. Inverting equation (5) to express price explicitly:
P = f(RSt, RDt)
Equation (6) says that market equilibrium price is determined by relative supply and
relative demand because of the relationship between relative inventory, relative supply, and
relative demand expressed by (4).
Equilibrium inventories may be disturbed by three exogenous factors: shifts in supply,
shifts in demand, and shifts in the value of inventory (convenience yield). This paper focuses
only on the Þrst two.10 Typical examples of shifts in supply for which RSt < 0 are OPEC
production cuts or pipeline accidents. Examples of shifts in demand for which RDt > 0 are
abnormal severe cold weather conditions or unexpected economic recoveries.
Note that any supply and demand shifts are directly translated into shifts in relative
supply and relative demand because the normal levels of supply and demand are independent
of price, that is, they are historically determined. In other words, we have ∆RS = ∆S and
∆RD = ∆D since RS = S − S∗ and RD = D − D∗ within a given time period t. Note
that ∆S, ∆RS, ∆D, and ∆RD are not the usual time diﬀerences between values in period t
minus values in period (t −1). Rather, it is the additional change within period t, taking the
value in period (t − 1) as given. Therefore ∆S∗ = ∆D∗ = 0, that is, the normal levels stay
always unchanged in period t since they are determined historically and are independent of
current market conditions. (To avoid any possible confusion, subscript t has been omitted
whenever ∆ is used).
To see what happens to the relative inventory level when there is an unexpected decrease
in supply or increase in demand in a particular period, we have from (5), taking RIt−1 as
∆RI = ∆RS − ∆RD .
Consider Þrst the impacts of a shift in supply. Dividing both sides of (7) by ∆RS yields:
∆RS − ∆RS
where the shift in demand (the second term on the RHS) is due to the change in the market
price caused by the shift in supply. To explicitly express the demand response to price, we
re-write ∆RI/∆RS = (∆RI/∆P )·(∆P/∆RS) and ∆RD/∆RS = (∆RD/∆P)·(∆P/∆RS),
recalling particularly (5). Thus, (8) becomes:
If there were no inventory or if inventory were not responsive to price changes, that is,
∆RI/∆P ≈ 0, we would have 0 = 1 − (∆RD/∆P)·(∆P/∆RS) from (9), which implies
∆RD = ∆RS. In other words, demand would have to drop exactly the same amount of any
supply loss in period t. To achieve ∆RD = ∆RS when ∆RS < 0 and no usable inventories
exist, price would have to increase signiÞcantly in the short run. However, in the real world,
demand would rarely, if ever, accommodate one-hundred percent of the drop in supply in the
AEJ: MARCH 2003, VOL. 31, NO. 1
short run. In other words, when inventories exist, the change in demand is observed to be
smaller than the change in supply, |∆RD| < |∆RS|, in the short run. This is the case because
many end users are unable or unwilling to alter their lifestyles, the production technologies
involved, organizational structures, or other capital investments in the short run, unless the
increase in price is so large that the cost of operating in status quo becomes greater than the
cost of changing.
Assuming availability of usable inventories, one has, from (9) for ∆RD/∆RS < 1, or
|∆RD| < |∆RS|: !∆RI" "=1 " ">0 .
It can be concluded that ∆RI/∆P < 0 from (10) since a decrease in supply increases price,
that is, ∆P/∆RS < 0.
Similarly, in the short run, an unexpected increase in demand for petroleum may not be
fully accommodated by an increase in supply. Price would increase signiÞcantly if there were
no inventory or if inventory did not respond to price changes. In reality, crude oil supply
may not increase at all and petroleum product production may increase somewhat, resulting
in a draw down of inventories of both crude oil and petroleum products to accommodate
the increased demand and mitigate the increase in price in the short run. Using similar
arguments to those made on the eﬀect of a supply shift, it can be shown that ∆RI/∆P < 0
when the source of the price change is the shift in demand.
Thus, the authors conclude that relative inventory is negatively related to price in the
short run, irrespective of whether a price change is caused by an unexpected supply shift or
an unexpected demand shift. In the next section, they empirically estimate the short-run
price elasticity of demand for relative petroleum inventory in a number of OECD countries
as well as regions and country groups.
The Data and Empirical Results
Petroleum inventories can be deÞned as the sum of government and industrial stocks of
both crude oil and petroleum products. The authors carried out the analysis on the total
of industry and government inventories, rather than industry only, because several countries
appeared to have reclassiÞed inventories between government and industrial categories. They
also decided to investigate the behavior of demand for inventories for both crude oil and
petroleum products because crude oil inventories at reÞneries are essentially exchangeable
with product inventories in a monthly time frame, and even crude oil inventories located in
distant places might only be a month from conversion to products.
Data for government and industrial inventories of crude oil and petroleum products for all
OECD countries are available from March 1984 to the present, but the International Energy
Agency (IEA) changed its data collection methodology in December 1990. The study on
elasticity was limited to the period from January 1996 to July 2001 because, at the country
level, the data appeared most consistent (that is, fewer one-time readjustments) from 1996
onwards. Furthermore, this time period contains some of the largest price swings and also
avoids the Gulf War impacts on the market. The normal levels, however, were established
using the data beginning in early 1991.
For crude oil prices, WTI spot price was used, which is considered a world marker price.
Another price also viewed as a marker price is Brent. However, it was found that the two
price series are highly correlated and move in very much the same pattern, with monthly WTI
crude oil spot price being higher than Brent throughout the period, except for temporary
YE ET AL.: PETROLEUM INVENTORY
daily or weekly price inversions.11 These daily spot prices were obtained from Standard and
Poor’s Platts Data Service. Since OECD inventory data are only available monthly, the daily
crude oil spot prices were aggregated to a monthly frequency.
In order to estimate a constant elasticity measure of the demand for relative inventory for
individual OECD countries, the G-7 aggregate, non-G-7 aggregate, and each of the several
regional aggregates, the authors Þrst de-trended and de-seasonalized the log values of observed
inventories to identify the normal levels in log form. Let Dk, k = 2, 3, . . . , 12, represent the 11
monthly seasonal variables and T the trend variable. Let Iit be the observed total petroleum
inventories in the ith country, region, or group in period t. The following regression equation
deÞnes the normal and relative levels of the log values of total inventories in the ith country,
region, or group in period t:
ln(Iit) = ci0 + ci1T + #cikDk +residualit ,
in which ci0 , ci1, and cik, k = 2, . . . , 12 are estimated coeﬃcients from the regression.
The normal level of demand for inventory, denoted Iit∗ for the ith country, region, or
group in period t, is empirically deÞned as:12
ln(I∗it) = [ln(Iit)]∗ = ci0 + ci1T + #cikDk ,
and the demand for relative inventory level for the ith country, region, or country group in
period t, denoted by RIit, is empirically deÞned as:13
ln(RIit) = ln(Iit) − ln(I∗) ,
where ln(Iit) − ln(I∗) = residual
it in (11).
Regression results show statistically signiÞcant seasonal patterns and consistent trends in
inventory for many OECD countries, regions, and country groups from the period beginning
in March 1991 through June 2001.14 The seasonality is particularly strong during the early
years in the 1990s.15 Later in the decade, the seasonality is often overwhelmed by the warm
winters that limited the usual inventory draws and a large over-supplied market that was
followed by an under-supplied market.16
Figure 3 shows the inventory trend and seasonality using the log values of total OECD
inventory data from March 1991 to June 2001 in which relative levels, or the residual, are
shown as the diﬀerence between actual and normal.
Comparing to WTI price shown in Figure 4 below, the negative relationship between
relative inventory level and WTI price is obvious since 1996 and can be seen to a lesser
extent in the early 1990s. This is particularly revealing when recalling that the negative
relationship cannot immediately be observed between the inventory level and WTI price in
the early 1990s in Figure 2.
To obtain the constant elasticity of demand for relative inventory for the ith country,
region, or group, the following regression equation was estimated:
ln(RIit) = ai + ei ln(W T It) + residualit + AR or MA terms17
in which ei is the elasticity.
Table 1 summarizes the results for the short-run demand elasticity of relative inventory
for OECD total, G-7, non-G-7, and several geographic regions. These results are calculated
for the period from March 1996 to June 2001 based on the relative inventory levels derived
from the period of 1991-2001.
AEJ: MARCH 2003, VOL. 31, NO. 1
Figure 3: The Actual, Normal, and Relative Levels of Inventory∗
Figure 4: The Relative Inventory and WTI Price
YE ET AL.: PETROLEUM INVENTORY
Two things are readily observed. First, as expected, there is a signiÞcant negative demand
response for relative inventory to price changes in the short-run, ranging from -0.026 to -
0.110, which is supported by the theory they developed in the last section. Second, the main
distinction in elasticity values is not among various geographical regions, but between the
G-7 aggregate (-0.0263) and non- G-7 aggregate (-0.0827). As expected, G-7 dominates the
total OECD’s elasticity of demand for inventory (-0.0263).
At the country level, despite the fact that data are much noisier due to sudden shifts in
inventories, Table 2 and the following scatter diagram demonstrate a positive relationship
between the crude oil price elasticity of demand for relative petroleum inventory and the log
value of GDP for a subset of OECD countries.18 While the correlation may not look strong
to the naked eye, the coeﬃcient of correlation between log(GDP) and elasticity is 0.50 and
signiÞcant at 94.7 percent.
Group and Regional Elasticity
N. Europe 10
N. Europe 8
S. Europe 5
aRegions are deÞned as follows: Europe 2 excludes U.K. and Ireland; N. Europe 10 includes Austria,
Belgium, Denmark, France, Germany, Ireland, Luxembourg, the Netherlands, Switzerland, and U.K.;
N. Europe 8 includes Austria, Belgium, Denmark, France, Germany, Luxembourg, the Netherlands,
and Switzerland; Scandinavia includes Norway, Sweden, and Finland; S. Europe 5 includes Spain,
Italy, Portugal, Greece, and Turkey; and N. America includes Canada, the United States, and Mexico.
bThe total excludes Czech Republic, Hungary, and Poland. Also note that Iceland and Slovak
Republic have no petroleum inventory.
cElasticity values are for the single period lagged for two months from the current month.
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GDP (in Billions $)g
aThe results for Canada and Turkey were derived by using a combined estimation for both the
elasticity and normal (that is, de-seasonalized and detrended) inventory level using data from January
1996 to June 2001.
bThe results for France and Mexico were derived for the one month lagged WTI crude price.
cThe results for Ireland and Japan were derived for the industrial inventories only, excluding gov-
ernment controlled inventories.
dLuxembourg had only petroleum products inventories.
eNorway’s elasticity is for the single period lagged for two months from the current month.
f While the United States’ demand for relative inventories respond to both the current month price
as well as last month price signiÞcantly, this is the elasticity for the current month only.
g See footnote a in Table B-1 in Appendix B.
Overall, results shown in Tables 1 and 2 and Figure 5 demonstrate that the demand for
relative petroleum inventory is indeed signiÞcantly negatively related to spot price, indicating
that, in the short run, relative inventory plays a crucial role of absorbing unplanned variations
in the petroleum market. Moreover, they also show that, in the short run, large OECD coun-
tries, individually and in aggregate, appear to be less elastic than smaller OECD countries,
individually and in aggregate.19 This supports the intuitive hypothesis that, during times
when markets have high, volatile crude oil prices, large countries are less sensitive to price
changes, and are more likely to have a slower rate of change in inventory levels. This may
imply that small or poor countries may back out of high-priced petroleum trading markets
before big or wealthy countries, thus reducing the eﬀective world demand for crude oil.
The authors focused on short-run petroleum cash market behavior in this paper. They
found strong evidence to support the theoretical Þnding that it is inventory that plays the
pivotal role in absorbing the unplanned variations in the petroleum market, since neither
supply nor demand fully accommodate changes in price in the short run. One of the impor-
tant concepts developed in this paper is the normal level and relative level of demand for
inventory, where the former reßects the typical seasonal and trend movements and the latter
the unexpected supply or demand shifts in the market. They derived a negative relationship