0

The Role of Inventories and Speculative Trading in the 

Global Market for Crude Oil 

 Lutz Kilian Dan Murphy 

 University of Michigan University of Michigan 

CEPR 

March 16, 2010 

Abstract: We develop a structural model of the global market for crude oil that for the first time 

explicitly allows for shocks to the speculative demand for oil as well as shocks to the flow 

demand and flow supply. The forward-looking element of the real price of oil is identified with 

the help of data on oil inventories. The model estimates rule out explanations of the 2003-08 oil 

price surge based on unexpectedly diminishing oil supplies and based on speculative trading. 

Instead, we find that this surge was caused by fluctuations in the flow demand for oil driven by 

the global business cycle. There is evidence, however, that speculative demand shifts played an 

important role during earlier oil price shock episodes including 1979, 1986, and 1990. Recently, 

it has been suggested that it is possible for speculative trading to occur even without any change 

in oil inventories, if the short-run price elasticity of oil demand is zero. Our structural model 

allows us to obtain an estimate of this elasticity based on shifts of the supply curve along the 

demand curve. We show that, even after accounting for the role of inventories in smoothing oil 

consumption, our estimate of the price elasticity of oil demand is not close to zero and much 

higher than traditional estimates from dynamic models that do not account for price endogeneity. 

This eliminates speculation as an explanation of the 2003-08 oil price surge. 

Key words: Oil market; speculation; fundamentals; peak oil; inventories; demand; supply; oil 

demand elasticity; gasoline demand elasticity; structural model; identification. 

JEL: Q41, Q43, Q48, D84 

Acknowledgements: We thank Christiane Baumeister, Ana María Herrera, Ryan Kellogg, Chris 

Knittel, and Whitney Newey for helpful discussions. 

Correspondence to: Lutz Kilian, Department of Economics, 611 Tappan Street, Ann Arbor, MI 

48109-1220, USA. Email: lkilian@umich.edu. 
1

1. Introduction 

The dramatic price fluctuations in the global market for crude oil since 2003 have renewed 

interest in understanding the evolution of the real price of oil. There is much debate in policy 

circles about whether the surge in the real price of oil between 2003 and mid-2008 was caused 

by speculative trading. An alternative view is that unexpected reductions in oil supplies are to 

blame in the form of OPEC withholding oil supplies from the market or because global oil 

production has peaked, as predicted by the peak oil hypothesis. Yet another view is that this 

surge in the real price of oil was driven instead by unexpectedly strong economic growth in the 

global economy, in particular in emerging Asia. 

 The relative importance of these explanations is important to policymakers. To the extent 

that speculative trading is perceived to be the core of the problem, for example, there has been 

considerable political pressure recently to impose regulatory limits on trading in oil futures 

markets.1 If dwindling global oil supplies are the problem, in contrast, there is little U.S. 

policymakers can do to avoid similar price surges but to promote energy conservation and the 

use of alternative sources of energy. Finally, if surges in the global business cycle are the chief 

cause of high oil prices, then efforts aimed at reviving the global economy after the financial 

crisis are likely to cause the real price of oil to recover as well, creating a policy dilemma. 

 This policy discussion has been accompanied by renewed debate among academic 

researchers about how much oil supply shocks matter for the real price of oil relative to 

speculative demand shocks and business-cycle driven demand shocks.2

 This debate has farreaching implications for the specification of empirical models and for the design of theoretical 

models of the transmission of oil price shocks. Despite much progress in recent years, there is no 

consensus in the academic literature on how to model the global market for crude oil. One strand 

of the literature views oil as an asset, the price of which is determined by desired stocks. In this 

interpretation, shifts in the expectations of forward-looking traders are reflected in changes in the 

real price of oil and changes in oil inventories. The other strand of the literature views the price 

of oil as being determined by shocks to the flow supply of oil and flow demand for oil with little 

attention to the role of inventories in smoothing oil consumption. Much of the research on oil 

supply shocks is in that tradition, as are recent economic models linking the real price of oil to 

                                                           

1

 For a discussion of the link between oil futures and oil spot markets see Alquist and Kilian (2010). 2

 See, e.g., Baumeister and Peersman (2008, 2009); Einloth (2009); Hamilton (2009a,b); Kilian (2008a, 2009a,b). 
2

fluctuations in the global business cycle. 

 Recently, there has been increasing recognition that both elements of price determination 

matter in modeling the market for oil (see, e.g., Dvir and Rogoff 2009; Frankel and Rose 2010; 

Hamilton 2009a,b; Kilian 2009a; Alquist and Kilian 2010). In section 2, we propose a structural 

vector autoregressive (VAR) model of the global market for crude oil that explicitly embeds 

these two explanations of the determination of the real price of oil. Using a new approach to 

identification, discussed in section 3, we show how the forward-looking element of the real price 

of oil can be identified with the help of data on crude oil inventories. The proposed dynamic 

simultaneous equation model allows us to separate the speculative component of the real price of 

oil from the components driven by flow demand and flow supply and to characterize the relative 

importance of each type of demand and supply shock for the real price of oil and for changes in 

oil inventories. This feature allows to study the role of storage in oil markets and to shed light on 

the extent of speculation in oil markets in section 4. 

The model provides several new insights. First, the model estimates rule out speculation 

as a cause of the surge in the real price of oil between 2003 and mid-2008. This finding implies 

that additional regulation of oil futures markets would not have stemmed the increase in the real 

price of oil. Second, although speculative trading does not explain the recent surge in the real 

price of oil, we show that it played an important role in several earlier oil price shock episodes. 

For example, it was a central feature of the oil price shock of 1979, following the Iranian 

Revolution, consistent with the narrative evidence in Barsky and Kilian (2002), and it helps 

explain the sharp decline in the real price of oil in early 1986 after the collapse of OPEC. It also 

played a central role in 1990, following Iraq’s invasion of Kuwait. Although, neither negative 

oil supply shocks nor positive speculative demand shocks alone can explain the oil price spike 

and oil inventory behavior of 1990/91, their combined effects do. 

Third, we document that unexpected fluctuations in global real activity explain virtually 

the entire surge in the real price of oil between 2003 and mid-2008, even acknowledging that 

negative oil supply shocks raised the real price of oil slightly. Business cycle factors were also 

responsible for the bulk of the 1979/80 oil price increase in conjunction with sharply rising 

speculative demand in 1979. In contrast, oil supply shocks played only a minor role in 1979. The 

continued rise in the real price of oil in 1980 reflected negative oil supply shocks (largely caused 

by the outbreak of the Iran-Iraq War) as much as continued (if slowing) global growth, amidst 
3

declining speculative demand. Finally, there is evidence that the recovery of the real price of oil 

starting in 1999, following an all-time low in postwar history, was aided by coordinated oil 

supply cuts. Although our analysis assigns more importance to oil supply shocks than some 

previous studies, we conclude that, with the exception of 1990, the major oil price shocks were 

driven primarily by global oil demand shocks. 

Much of the prima facie case against an important role for speculative trading rests on the 

fact that there has been no noticeable increase in inventory accumulation in recent years (see, 

e.g., Kilian 2010). Recently, Hamilton (2009a) suggested that, as a matter of theory, speculative 

trading may cause a surge in the real price of oil without any change in oil inventory holdings if 

the short-run price elasticity of demand for gasoline (and hence the short-run price elasticity of 

oil demand) is zero. Thus, it is essential that we pin down the value of these elasticities. 

Hamilton observed that existing estimates of this elasticity in the literature are close to 

zero, lending credence to this model of speculation. These estimates, however, are based on 

dynamic reduced form regressions that ignore the endogeneity of the real price of oil. They have 

no structural interpretation and suffer from downward bias. In section 5, we address this 

limitation with the help of our structural VAR model. That model nests the limiting case 

discussed in Hamilton. Not only do our response estimates show that speculative demand shocks 

are associated with systematic inventory building, but the econometric model allows us to 

construct a direct estimate of the elasticity parameter based on exogenous shifts of the oil supply 

curve along the oil demand curve. Our median estimate of the short-run price elasticity of oil 

demand of -0.44 is seven times higher than standard estimates in the literature, but more similar 

in magnitude to recent estimates by Baumeister and Peersman (2009) from an alternative 

structural VAR model. 

This elasticity estimate of -0.44, however, like all existing estimates, is misleading 

because it ignores the role of oil inventories in smoothing oil consumption. Refiners hold crude 

oil inventories as insurance against unexpected disruptions of crude oil supplies or unexpected 

increases in the demand for refined products such as gasoline.3

 The decline in crude oil 

inventories in response to a negative oil supply shock increases the magnitude of oil available to 

refiners and must be incorporated in constructing the elasticity of oil demand. Our structural 

                                                           

3

 For further discussion of this convenience yield provided by oil inventories see Alquist and Kilian (2010) and the 

references therein. 
4

model is designed to allow the estimation of this short-run oil demand elasticity in use. The 

median estimate is -0.24. Although much lower than the traditionally defined elasticity estimate 

from structural models, even this estimate is four times higher than the consensus view in the 

literature and distinctly higher than zero. 

We provide a theoretical benchmark for thinking about the relationship between the 

short-run price elasticity of oil demand in use and the short-run price elasticity of gasoline 

demand. We show that under reasonable assumptions about the oil refining industry, the latter is 

about as high as the price elasticity of oil demand in use. That gasoline demand elasticity 

estimate is much larger than some recent estimates in the literature. For example, Hughes, 

Knittel and Sperling (2008) in an influential study report a short-run U.S. gasoline elasticity 

estimate of between -0.03 and -0.08, which is well below our estimate, illustrating the 

importance of structural modeling in constructing estimates of the price elasticity of energy 

demand. Our evidence eliminates speculation as an explanation of the 2003-08 surge in the real 

price of oil. In section 6, we relate our estimate of the short-run price elasticity of gasoline 

demand to the literature on estimating long-run U.S. gasoline demand elasticities from crosssectional data. The concluding remarks are in section 7. 

2. VAR Methodology 

Our analysis is based on a four-variable dynamic simultaneous equation model in the form of a 

structural VAR. Let t y be a vector of endogenous variables including the percent change in 

global crude oil production, a measure of global real activity expressed in percent deviations 

from trend, the real price of crude oil, and the change in oil inventories. All data are monthly and 

the sample period is 1973.2-2009.8. We remove seasonal variation by including seasonal 

dummies in the VAR model. 

2.1. Data 

Data on global crude oil production are available in the Monthly Energy Review of the Energy 

Information Administration (EIA). Our measure of fluctuations in global real activity is the dry 

cargo shipping rate index developed in Kilian (2009a).4

 For more details on the rationale, 

                                                           

4

 This index has also been employed by Alquist and Kilian (2010), Bahattin and Robe (2009), Fukunaga, Hirakata 

and Sudo (2009), Kilian (2009a,b; 2010), Kilian, Rebucci and Spatafora (2009), and Kilian and Park (2009), among 

others. 
5

construction and interpretation of this index the reader is referred to the related literature.5 While 

there are other indices of global real activity available, none of these alternative proxies is as 

appropriate for our purpose of measuring shifts in the global demand for industrial commodities 

and none is available at monthly frequency for our sample period. 

The real price of oil is defined as the U.S. refiners’ acquisition cost for imported crude 

oil, as reported by the EIA, extrapolated from 1974.1 back to 1973.1 as in Barsky and Kilian 

(2002) and deflated by the U.S. consumer price index. We use the refiners’ acquisition cost for 

imported crude oil because that price is likely to be a better proxy for the price of oil in global 

markets than the U.S. price of domestic crude oil which was regulated during the 1970s and early 

1980s. 

Given the lack of data on crude oil inventories for other countries, we follow Hamilton 

(2009a) in using the data for U.S. crude oil inventories provided by the EIA. These data are 

scaled by the ratio of OECD petroleum stocks over U.S. petroleum stocks for each time period. 

That scale factor ranges from about 2.23 to 2.59 in our sample.6 We express the resulting proxy 

for global crude oil inventories in changes rather than percent changes. One reason is that the 

percent change in inventories does not appear to be covariance stationary, whereas the change in 

inventories does. The other reason is that the proper computation of the oil demand elasticity, as 

discussed below, requires an explicit expression for the change in global crude oil inventories in 

barrels. This computation is only possible if oil inventories are specified in changes rather than 

                                                           

5 The idea of using fluctuations in dry cargo freight rates as indicators of shifts in the global real activity dates back 

to Isserlis (1938) and Tinbergen (1959); also see Stopford (1997). One advantage of using this type of index is that it 

automatically accounts for any additional demand for industrial commodities generated by the depreciation of the 

U.S. dollar in recent years. The panel of monthly freight-rate data underlying the global real activity index was 

collected manually from Drewry’s Shipping Monthly using various issues since 1970. The data set is restricted to 

dry cargo rates. The earliest raw data are indices of iron ore, coal and grain shipping rates compiled by Drewry’s. 

The remaining series are differentiated by cargo, route and ship size and may include in addition shipping rates for 

oilseeds, fertilizer and scrap metal. In the 1980s, there are about 15 different rates for each month; by 2000 that 

number rises to about 25; more recently that number has dropped to about 15. The index was constructed by 

extracting the common component in the nominal spot rates. The resulting nominal index is expressed in dollars per 

metric ton and was deflated using the U.S. CPI and detrended to account for the secular decline in shipping rates. 

For this paper, this series has been extended based on the Baltic Exchange Dry Index, which is available from 

Bloomberg. The latter index, which is commonly discussed in the financial press, is essentially identical to the 

nominal index in Kilian (2009a), but only available since 1985. 

6

 Petroleum stocks as measured by the EIA include crude oil (including strategic reserves) as well as unfinished oils, 

natural gas plant liquids, and refined products. The EIA does not provide petroleum inventory data for non-OECD 

economies. We treat the OECD data as a proxy for global petroleum inventories. Consistent series for OECD 

petroleum stocks are not available prior to 1987.12. We therefore extrapolate the percent change in OECD 

inventories backwards at the rate of growth of U.S. petroleum inventories. For the period 1987.12-2009.5, the U.S. 

and OECD petroleum inventory growth rates are reasonably close with a correlation of about 80%. 
6

percent changes.7

2.2. A Model of the Global Market for Crude Oil 

The reduced-form model allows for two years worth of lags. This approach is consistent with 

evidence in Hamilton and Herrera (2004) and Kilian (2009a) on the importance of allowing for 

long lags in the transmission of oil price shocks. The real activity index of Kilian (2009a) is 

stationary by construction. We measure fluctuations in real activity in percent deviations from 

trend. Oil production is expressed in percent changes in the model, whereas oil inventories are 

expressed in differences. Preliminary tests provided no evidence of cointegration between oil 

production and oil inventories. Following Kilian (2009a), the real price of oil is expressed in loglevels.8

 The corresponding structural model of the global oil market may be written as 

24

0

1

, t i ti t

i

B y By  



   (1) 

where t  is a 4 1 vector of orthogonal structural innovations and , 0,...,24, B i i  denotes the 

coefficient matrices. The seasonal dummies have been suppressed for notational convenience. 

The vector t  consists of a shock to the flow of the production of crude oil (“flow supply shock), 

a shock to the flow demand for crude oil and other industrial commodities (“flow demand 

shock”), a shock to the demand for oil inventories arising from forward-looking behavior 

(“speculative demand shock”), and a residual shock that captures all structural shocks not 

otherwise accounted for and has no direct economic interpretation. 

                                                           

7

 Note that we focus on above-ground inventories in this paper. A different strand of the literature has considered oil 

below the ground as another form of oil inventories. We do not pursue this possibility, because oil below the ground 

is not fungible with oil above ground in the short run and because no reliable time series data exist on the quantity of 

oil below the ground. We do discuss, however, how speculation based on below-ground inventories would be 

recorded within our model framework and how it may be detected in section 4.3. 

8

 One reason is that economic theory suggests a link between cyclical fluctuations in global real activity and the real 

price of oil and hence the real price of gasoline (see Barsky and Kilian 2002). Differencing the real price series 

would remove that slow-moving component and eliminate any chance of detecting persistent effects of global 

shocks to the demand for all industrial commodities including crude oil. Moreover, even granting that the real price 

of oil is well approximated by a random walk in prediction, it is not clear a priori whether there is a unit root in the 

real price of oil. The level specification adopted in this paper has the advantage that the impulse response estimates 

are not only asymptotically valid under the maintained assumption of a stationary real price of oil, but robust to 

departures from that assumption, whereas incorrectly differencing the real price of oil would cause these estimates to 

be inconsistent. The potential cost of not imposing unit roots in estimation is a loss of asymptotic efficiency, which 

would be reflected in wider error bands. Since the impulse response estimates presented below are reasonably 

precisely estimated, this is not a concern in this study. It should be noted, however, that historical decompositions 

for the real price of oil rely on the assumption of covariance stationarity and would not be valid in the presence of 

unit roots. 
7

 The flow supply shock corresponds to the classical notion of an oil supply shock, as 

discussed in the literature. The flow demand shock can be thought of as a demand shock 

reflecting the state of the global business cycle. The speculative demand shock is designed to 

capture innovations to the demand for crude oil that reflect revisions to expectations about future 

demand and future supply as distinct from innovations to the current flow supply or flow 

demand. We identify these shocks based on a combination of sign restrictions on the structural 

impulse response functions and other economically motivated restrictions. 

Our model allows for alternative views of the determination of the real price of oil 

conditional on lagged data. One view is that the real price of crude oil is determined by the 

current flow supply of oil and the current flow demand for oil. The flow supply of crude oil is 

measured by the global production of crude oil. An unexpected disruption of that flow 

(embodied in a shift to the left of the contemporaneous oil supply curve along the oil demand 

curve) within the month will raise the real price of crude oil, will cause oil inventories to be 

drawn down in an effort to smooth consumption, and will lower global real activity, if it has any 

effect on real activity at all. 

 The flow demand for crude oil is driven by unexpected fluctuations in global real 

activity. These represent shifts in the demand for all industrial commodities including crude oil 

associated with the global business cycle.9

 An unanticipated increase in global real activity 

(embodied in a shift to the right of the contemporaneous oil demand curve along the oil supply 

curve) within the month will raise the real price of oil, will cause oil inventories to be drawn 

down, and will stimulate global oil production, if it has any effect on oil production at all. The 

latter stimulus, however, is bound to be small on impact, given the consensus in the literature 

that the short-run price elasticity of oil supply is near zero. 

 This standard view of the global crude oil market is incomplete, however. Given that 

crude oil is storable, it may also be viewed as an asset, the real price of which is determined by 

the demand for inventories (see, e.g., Frankel and Rose 2010; Kilian 2009a; Alquist and Kilian 

2010). This means that we must allow the price of oil to jump in response to any news about 

future oil supply or future oil demand. For example, upward revisions to expected future demand 

for crude oil (or downward revisions to expected future production of crude oil), all else equal, 

                                                           

9

 A well documented fact is that there is considerable comovement between the real price of crude oil and the real 

price of other industrial commodities during times of major fluctuations in global real activity (see, e.g., Kilian 

2009b). 
8

will increase the demand for crude oil inventories in the current period, resulting in an 

instantaneous shift of the contemporaneous demand curve for oil along the oil supply curve and 

an increase in the real price of oil. Although there is no direct effect of such a shock on global 

real activity within the month by construction because the shock is defined as an innovation 

about future global real activity or oil production, to the extent that the real price of oil jumps on 

impact, one would expect this shock to lower global real activity indirectly, if it has any impact 

on real activity at all. One would also expect the impact response of global oil production to such 

an expectations shock to be positive, if oil production responds at all. This follows from the 

premise that any news about future oil production shortfalls will not have any direct effect on 

current oil production by construction.10 

News about future oil production and future demand for crude oil are but one example of 

shocks to expectations in the global market for crude oil. An unexpected increase in the 

uncertainty about future oil supply shortfalls would have much the same effect. This point has 

been demonstrated formally in a general equilibrium model by Alquist and Kilian (2010). The 

main difference is that uncertainty shocks would not be associated with expected changes in 

future oil production or real activity.11 In this paper we refer to any oil demand shock that 

reflects shifts in expectations about future oil production or future real activity as a speculative 

oil demand shock. The next section discusses how we distinguish speculative demand shocks 

from flow demand shocks and flow supply shocks in practice. 

3. Identification 

The structural VAR model is set-identified based on a combination of sign restrictions, shape 

restrictions, and bounds on the implied price elasticities of oil demand and oil supply. Some of 

these restrictions are implied by the economic model discussed in section 2, while others can be 

motivated based on extraneous information. We impose six sets of identifying restrictions, each 

of which is discussed in turn.12

                                                           

10 If there is an effect, it must arise from the price incentive for higher production created by the speculative demand 

shock. That effect is likely to be small, given the consensus in the literature that the short-run price elasticity of oil 

production is near zero. 

11 Our approach is consistent with the observation in Dvir and Rogoff (2009) that the role of storage is speculative 

when rapid industrialization coincides with uncertain oil supplies, as has been the case in the post-1973 period that 

we focus on in this paper. 

12 The use of sign restrictions in oil market VAR models was pioneered by Baumeister and Peersman (2008, 2009). 

Our approach differs from theirs in many dimensions including the nature of the sign restrictions imposed. 
9

3.1. Impact Sign Restrictions 

The sign restrictions on the impact responses of oil production, real activity, the real price of oil 

and oil inventories are summarized in Table 1. These restrictions directly follow from the model 

discussed in section 2. All sign restrictions involve weak inequalities and allow for the response 

to be zero. Implicitly, these restrictions also identify the residual innovation. Given the difficulty 

of interpreting this residual economically, we do not report results for the residual shock, but 

merely note that it is not an important determinant of the real price of oil. 

 Sign restrictions alone are typically too weak to be informative about the effects of oil 

demand and oil supply shocks. As demonstrated in Kilian and Murphy (2009) in the context of a 

simpler model, it is important to impose all credible identifying restrictions to allow us to narrow 

down the set of admissible structural models.13 One such set of restrictions relates to bounds on 

impact price elasticities of oil demand and oil supply. 

3.2. Bound on the Impact Price Elasticity of Oil Supply 

An estimate of the impact price elasticity of oil supply may be constructed from the dynamic 

simultaneous equation model (1) by evaluating the ratio of the impact responses of oil production 

and of the real price of oil to an unexpected increase in aggregate demand or in speculative 

demand. There is a consensus in the literature that this short-run price elasticity of oil supply is 

close to zero (see Hamilton 2009a, Kilian 2009a). Neither Hamilton (2009a,b) nor Kilian (2009a) 

provide econometric estimates of the short-run elasticity of oil supply. Here we follow Kilian 

and Murphy (2009) in imposing an upper bound on the impact oil supply elasticity. This bound 

is important because many models identified purely based on sign restrictions imply an impact 

oil supply elasticity that is far too large to be economically plausible. 

An empirically plausible bound may be obtained by focusing on the historical episodes of 

well-defined and exogenous oil price shocks such as the outbreak of the Persian Gulf War on 

August 2, 1990. That event caused a sharp spike in the real price of oil. Given the timing of that 

event, production data for August of 1990 are informative about the oil supply response in the 

rest of the world. Because prior to the war there had been spare capacity in oil production, as 

discussed in Kilian (2008a), and because there was a concerted effort to increase global oil 

production following the invasion, this response provides a plausible upper bound for the withinthe-month elasticity of oil supply. In August of 1990, the global production of crude oil from all 

                                                           

13 For a similar point also see Canova and De Nicolo (2002), Uhlig (2005), and Canova and Paustian (2007). 
10

oil producers excluding Iraq and Kuwait increased by 1.17%, whereas the real price jumped by 

44.3% which suggests an oil supply elasticity of 0.0258.14 We impose this upper bound on the 

impact price elasticity of oil supply in selecting the set of admissible models. It is important to 

stress that this additional identifying restriction only relates to the impact elasticity rather than 

the dynamic responses and that it does not constrain the level of the impact responses, but merely 

imposes a bound on their relative magnitude.15 

3.3. Bound on the Impact Price Elasticity of Oil Demand 

A preliminary estimate of the impact price elasticity of oil demand may be constructed from the 

estimated model (1) by evaluating the ratio of the impact responses of oil production and of the 

real price of oil to an unexpected oil supply disruption. This oil demand elasticity in production

corresponds to the standard definition of the oil demand elasticity used in the literature. It 

equates the production of oil with the consumption of oil. In the presence of changes in oil 

inventories that assumption is inappropriate. The relevant quantity measure instead is the sum of 

the flow of oil production and the depletion of oil inventories triggered by an oil supply shock. 

To our knowledge, this distinction has not been discussed in the literature nor has there been any 

attempt in the literature to estimate this oil demand elasticity in use. A natural additional 

identifying assumption is that the impact elasticity of oil demand in use must be weakly negative 

on average over the sample. We defer a formal definition of this elasticity to section 5.2. Note 

that we do not need to restrict the oil demand elasticity in production. Our impact sign 

restrictions ensure that this elasticity is weakly negative on impact. 

3.4. Relative Order of Magnitude Restrictions on Impact Responses 

The impact elasticity of oil supply is estimated based on a shift of the oil demand curve along the 

supply curve. Because there are two oil demand shocks in the model, the model allows the 

construction of two estimates of the impact price elasticity of oil supply. In population, these 

elasticities must be identical. The reason is that the effect of both oil demand shocks on oil 

production in the impact period by construction operates exclusively through the real price of oil. 

                                                           

14 Source: Energy Information Administration. In July 1990 dollars, the real price of oil increased from $16.54 per 

barrel to $24.04 per barrel from July to August. Oil supply from all producers excluding Iraq and Kuwait increased 

from 55,197 barrels per day to 55,844 barrels per day. 

15 While we prefer to work with an empirically grounded bound on this elasticity, it can be shown that relaxing this 

bound somewhat, say to 0.05, has little effect on the impulse response estimates. Even for a bound of 0.10 our 

results remain qualitatively similar. Moreover, the elasticity estimates reported in section 5 change only in the 

second decimal place. 
11

Although we would expect some sampling variation in these estimates, it seems reasonable to 

discard all structural models that imply estimates of the same elasticity that are different by an 

order of magnitude. This means, for example, that we would discard a model solution in which 

one of the impact elasticities of oil supply is 0.001, while the other is 0.023. 

Likewise the model implies that the ratio of the impact response of real activity to the 

impact response of the real price of oil should be the same in response to negative oil supply 

shocks as in response to positive speculative demand shocks. In both cases, the impact response 

of real activity is driven by the response of the real price of oil. In particular, a speculative 

demand shock by construction will not affect real activity directly within the month. It is 

important to stress that these additional identifying assumptions impose no further restrictions on 

the ratio or the magnitude of the level of the impact responses. They merely represent crossequation restrictions. 

3.5. Shape Restrictions 

Rather than impose any dynamic sign restrictions on these responses, we exploit the fact that 

expectations shocks should result in a jump of the real price of oil on impact followed by a 

decline in the long run (see Alquist and Kilian 2010). This motivates the additional identifying 

restriction that the response of the real price of oil to a speculative demand shock must not be 

higher at the highest horizon considered than it is on impact. We do not take a stand on the 

evolution of the response function at intermediate horizons. 

3.6. Dynamic Sign Restrictions 

Our final set of restrictions relates to the dynamic responses to an oil supply shock. This set of 

identifying restrictions is necessary to rule out structural models in which unanticipated oil 

supply disruptions cause a strong decline in the real price of oil below its starting level which is 

at odds with the standard view in the literature. Specifically, we impose the additional restriction 

that the response of the real price of oil to a negative oil supply shock must be positive for at 

least twelve months, starting in the impact period. Because the positive response of the real price 

of oil tends to be accompanied by a persistently negative response of oil production, once we 

impose this additional dynamic sign restriction, it furthermore must be the case that global real 

activity responds negatively to oil supply shocks. This is the only way for the oil market to 

experience higher prices and lower quantities in practice, because in the data the decline of 
12

inventories triggered by an oil supply disruption is much smaller than the shortfall of oil 

production. This implies a joint set of sign restrictions such that the responses of oil production 

and global real activity to an unanticipated oil supply disruption are negative for the first twelve 

months, while the response of the real price of oil is positive. 

 In contrast, we do not impose any dynamic sign restrictions on the responses to oil 

demand shocks. In this respect our approach differs from Baumeister and Peersman (2009), for 

example. In particular, we do not impose any dynamic sign restrictions on the responses of 

global real activity and oil production to speculative oil demand shocks. The reasoning is as 

follows. The speculative demand shock in our model is a composite of three distinct types of 

expectations shocks. For example, a pure uncertainty shock (such as a mean-preserving increase 

in the spread) that raises precautionary demand will be associated with an increase in the real 

price of oil and higher oil inventories without any change in expected oil production or expected 

real activity (see Alquist and Kilian 2010). As a result, one would expect no response in oil 

production or in real activity, except to the extent that higher oil prices all else equal stimulate oil 

production over time or may reduce global real activity. 

 To the extent that a speculative shock involves upward revisions to expected future 

demand for crude oil instead, one would expect that shock to increase the real price of oil, oil 

inventories and future global real activity, but not to change oil production, except to the extent 

that higher oil prices stimulate global oil production over time. A classical example of such a 

situation would be speculation in anticipation of a booming world economy (or – with reverse 

signs – the anticipation of a major recession driven by a financial crisis). 

In either of these first two cases, the response of oil production is expected to be weakly 

positive over time. In contrast, a speculative shock involving downward revisions to expected 

future crude oil production would be expected to cause higher oil prices, higher inventories, and 

lower future oil production, and possibly a decline in global real activity over time driven by 

higher oil prices. Thus, unlike in the earlier two cases, there is reason to expect the response of 

oil production to be negative over time. For example, it has been argued in the literature that the 

oil price spike of 1990, following the invasion of Kuwait by Saddam Hussein, did not only 

reflect the oil supply shock associated with the cessation of oil production in Iraq and Kuwait, 

but the specter of Iraq invading Saudi Arabia and future Saudi oil production ceasing (see Kilian 

2008a). Likewise, Barsky and Kilian (2002) made the case that the increase in the price of oil 
13

following the Iranian Revolution of 1979 reflected in part the fear of a wider regional 

conflagration involving the U.S. and/or moderate Gulf oil producers. A third example would be 

speculation by traders driven by the anticipation of declining future oil supplies (as implied by 

the peak oil hypothesis). Such speculation, if it did indeed occur, would have been associated 

with higher oil prices, higher inventories, and lower future oil production.16 

Given the fact that historically expectations of future oil production reductions more 

often than not have failed to materialize within the sample, one would not expect the estimated 

response of oil production to the speculative demand shock to be strongly negative and it is 

conceivable that this response may actually be positive. Likewise, it is not clear whether the 

dynamic response of real activity should be positive, reflecting the realization of expectations of 

increased real activity, or negative, reflecting declines in real activity triggered by higher oil and 

other industrial commodity prices. Hence, we do not impose restrictions on the sign of the 

responses of real activity and oil production to speculative oil demand shocks beyond the impact 

period. 

3.7. Implementation of the Identification Procedure 

Given the set of identifying restrictions and consistent estimates of the reduced-form VAR 

model, the construction of the set of admissible structural models follows the standard approach 

in the literature on VAR models identified based on sign restrictions (see, e.g., Canova and De 

Nicolo 2002; Uhlig 2005). Consider the reduced-form VAR model ( ) , ALy e t t  where t y is the 

N -dimensional vector of variables, A( ) L is a finite-order autoregressive lag polynomial, and 

t e is the vector of white noise reduced-form innovations with variance-covariance matrix .

t e

Let t  denote the corresponding structural VAR model innovations. The construction of 

structural impulse response functions requires an estimate of the N N matrix B in . t t e B   17

Let t  e P P and 0.5 B  P such that B satisfies . t e  BB Then B  BD also satisfies 

t BB e     for any orthonormal N N matrix D. One can examine a wide range of possibilities for 

B by repeatedly drawing at random from the set D of orthonormal rotation matrices D.

                                                           

16 In contrast, speculation by oil producers, who choose to leave oil below the ground in anticipation of rising prices, 

as discussed in Hamilton (2009b), in our modeling framework would be classified as a shock to the flow supply of 

crude oil. 

17 For a review of the construction of these structural impulse responses the reader is referred to Fry and Pagan 

(2010), for example.
14

Following Rubio-Ramirez, Waggoner and Zha (2005) we construct the set B of admissible 

models by drawing from the set D of rotation matrices and discarding candidate solutions 

for B that do not satisfy a set of a priori restrictions on the implied impulse response functions. 

The procedure consists of the following steps:

1) Draw an N N matrix K of NID(0,1) random variables. Derive the QR decomposition 

of K such that K QR   and . QQ IN  

2) Let D Q . Compute impulse responses using the orthogonalization . B  BD If all 

implied impulse response functions satisfy the identifying restrictions, retain D.

Otherwise discard D.

3) Repeat the first two steps a large number of times, recording each D that satisfies the 

restrictions (and the corresponding impulse response functions). 

The resulting set B comprises the set of admissible structural VAR models. 

4. Estimation Results 

The identifying restrictions described in section 3 do not necessarily yield point-identified 

structural impulse responses. We generated 60 million rotations based on the reduced-form VAR 

estimate. 13 candidate models satisfied all identifying restrictions. For further analysis, we select 

the model that yields an impact price elasticity of oil demand in use (defined in detail in section 

5.2) closest to the posterior median of this elasticity. This can be done without loss of generality, 

as the other admissible models yield virtually indistinguishable response estimates. 

4.1. Responses to Oil Supply and Oil Demand Shocks 

Figure 1 plots the responses of each variable in this benchmark model to the three oil supply and 

oil demand shocks (together with the corresponding pointwise 68% percentiles of the posterior 

distribution). All shocks have been normalized such that they imply an increase in the real price 

of oil. In particular, the oil supply shock refers to an unanticipated oil supply disruption. 

 Figure 1 illustrates that the role of storage differs depending on the nature of the shock. 

An oil supply disruption causes inventories to be drawn down in an effort to smooth production 

of refined products. A positive flow demand shock causes an initial decline in oil inventories, 

again reflecting production smoothing, followed by a complete rebuilding of inventories within 

the first year. A positive speculative demand shock causes a persistent increase in oil inventories. 
15

 An oil supply shock is associated with a reduction in global real activity and a persistent 

drop in oil production, but much of the initial drop is reversed within the first year. The real price 

of oil rises only temporarily. It peaks after two months and falls as oil production recovers. After 

one year, the real price of oil falls below its starting value, as global real activity drops further. 

A positive shock to the flow demand for crude oil, in contrast, is associated with a persistent 

increase in global real activity. It causes a persistent hump-shaped increase in the real price of oil 

with a peak after one year. Oil production also rises somewhat, but only temporarily. Finally, a 

positive speculative demand shock is associated with an immediate jump in the real price of oil. 

The real price response overshoots, before declining gradually. The effects on global real activity 

and global oil production are largely negative, but small. These estimates imply a larger role for 

oil supply shocks than the structural VAR model in Kilian (2009a), for example, illustrating the 

importance of explicitly modeling speculative demand shocks and oil inventories. 

4.2. What Drives Fluctuations in Oil Inventories and in the Real Price of Oil? 

Table 2 illustrates the relative importance of each of the structural shocks in driving the change 

in oil inventories. In the short run, 41% of the variation is driven by speculative demand shocks, 

followed by oil supply shocks with 23%. Flow demand shocks have a negligible impact with 

1%. At long horizons, in contrast, the role of speculative demand shocks declines to 36% and 

that of flow demand shocks increases to 15%, while the contribution of oil supply shocks 

remains essentially unchanged at 21%. This evidence suggests that, on average, fluctuations in 

oil inventories mainly reflect speculation, but there also is an important element of production 

smoothing by refiners in response to oil supply shocks. This contrasts with a much larger role of 

flow demand shocks in explaining the variability of the real price of oil. For example, in the long 

run, 85% of the variation in the real price of oil can be attributed to flow demand shocks, 

compared with 9% due to speculative demand shocks and 4% due to flow supply shocks. 

Impulse responses and variance decompositions are useful in studying average behavior. 

To understand the historical evolution of the real price of oil, especially following major 

exogenous events in oil markets, it is more useful to compute the cumulative effect of each shock 

on the real price of oil and on the change in oil inventories. Figure 2 allows us to answer not only 

the question of how important the speculative component in the real price of oil was between 

2003 and mid-2008, but we can assess the quantitative importance of speculation at each point in 
16

time since the late 1970s.18

4.3. Did Speculators Cause the Oil Price Shock of 2003-2008?

A common view in the literature is that speculators caused part or all of the run-up in the real 

price of oil between 2003 and mid-2008. Especially the sharp increase in the real price of oil in 

2007/08 has been attributed to speculation. The standard interpretation is that oil traders in spot 

markets buy crude oil now in anticipation of higher oil prices with the expectation of selling later 

at a profit. Unless the oil demand elasticity is zero – a possibility that we discuss below – a 

necessary implication is that all else equal oil inventories must increase. The response estimates 

in Figure 1 confirm this prediction. A positive shock to speculative demand increases both the 

real price of oil and oil inventories. 

Notwithstanding the popular perception that speculative demand helped cause the run-up 

in the real price of oil after 2003 and in particular in 2007/08 – either in anticipation of stronger 

economic growth or in anticipation of declining oil supplies as predicted by the peak oil 

hypothesis – there is no indication in Figure 2 that this oil price surge had much to do with 

speculative demand shocks. Instead, the model supports the substantive conclusions in Kilian 

(2009a) and Kilian and Hicks (2009) – based on alternative methodologies – that the surge in the 

real price of oil between 2003 and mid-2008 was mainly caused by shifts in the flow demand for 

crude oil driven by the global business cycle. This finding is important because it tells us that 

further regulation of these markets would have done nothing to stem the increase in the real price 

of oil. 

 An alternative view of speculation is that OPEC in anticipation of even higher oil prices 

held back its production after 2001, using oil below ground effectively as inventories (see, e.g., 

Hamilton 2009a, p. 239).19 One way of testing this hypothesis is through the lens of our 

structural model. In the model, OPEC holding back oil production in anticipation of rising oil 

prices would be classified as a negative oil supply shock. Figure 2 provides no indication that 

negative flow supply shocks played an important role between 2003 and mid-2008. Nor does the 

evidence provide any support for the notion that negative oil supply shocks associated with the 

                                                           

18 We do not include the contribution of the residual inventory shock because that shock makes no large systematic 

contribution to the evolution of the real price of oil. 

19 We do not consider oil below the ground as part of oil inventories in this paper. Unlike above-ground oil 

inventories that can be drawn down at short notice, oil below the ground is inaccessible in the short run and not 

available for consumption smoothing. Thus, it must be differentiated from inventories in the usual sense. 
17

peak oil hypothesis explain the surge in the real price of oil after 2003.20 Any unanticipated 

exogenous decline in oil supplies associated with that hypothesis likewise would be captured by 

an unexpected flow supply reduction, yet there is no indication of such shocks persistently 

driving up the real price of oil toward the end of the sample. What evidence there is of a small 

supply-side driven increase in the real price of oil is dwarfed by the price increases associated 

with flow demand shocks. Moreover, the sharp V-shaped dip in the real price of oil in late 2008 

is unambiguously driven by a similar dip in the global real activity measure associated with the 

global financial crisis. 

Whereas the recovery from the all-time low in the real price of oil in 1999-2000 resulted 

from a combination of coordinated OPEC oil supply cuts, a gradual increase in global real 

activity (often associated with the U.S. productivity boom) and increased speculative demand in 

anticipation of increased future real activity and/or further oil supply reductions, the resurgence 

of the real price of oil starting in early 2009 reflected primarily a recovery of global real activity 

(see Figure 2). 

4.4. The Inventory Puzzle of 1990 

Although speculative motives played no important role after 2003, there are other oil price shock 

episodes when they did. One particularly interesting example is the oil price shock associated 

with the Persian Gulf War of 1990/91. In related work, Kilian (2009a) presented evidence based 

on a model without oil inventories that the 1990 oil price increase was driven mainly by a shift in 

speculative demand (reflecting the uncertainty about future oil supplies from neighboring Saudi 

Arabia) rather than the physical reduction in oil supplies associated with the war. As noted by 

Hamilton (2009a), this result is puzzling upon reflection because oil inventories moved little and, 

if anything, slightly declined following the invasion of Kuwait. This observation prompted 

Hamilton to reject the hypothesis that shifts in speculative demand were behind the sharp 

increase in the real price of oil in mid-1990 and its fall after late 1990. Given the consensus that 

flow demand did not move sharply in mid-1990, Hamilton suggested that perhaps this price 

increase must be attributed to oil supply shocks after all. The inventory data, however, seem just 

as inconsistent with this alternative hypothesis. Inventories declined in August of 1990, but only 

by one third of a standard deviation of the change in inventories. Given one of the largest 

unexpected oil supply disruptions in history, one would have expected a much larger decline in 

                                                           

20 For a critical review of the peak oil hypothesis see Einloth (2009). 
18

oil inventories given the impulse response estimates in Figure 1. In light of this evidence, neither 

the supply shock explanation nor the speculative demand shock explanation by itself seems 

compelling. 

Our econometric model resolves this inventory puzzle. The explanation is that the 

invasion of Kuwait in August of 1990 represented two shocks that occurred simultaneously. On 

the one hand it involved an unexpected flow supply disruption and on the other an unexpected 

increase in speculative demand. Whereas the flow supply shock caused a decline in oil 

inventories, increased speculative demand in August caused an increase in oil inventories, with 

the net effect being a slight decline in oil inventories. At the same time, the observed increase in 

the real price of oil was caused by both shocks working in the same direction. 

The historical decomposition in Figure 3 contrasts the price and inventory movements 

caused by each shock during 1990/91. It shows that overall two thirds of the price increase in 

August of 1990 was caused by the oil supply shock and only one third by the speculative demand 

shock. This result is in sharp contrast to the estimates in Kilian (2009) who found no evidence of 

oil supply shocks contributing to this increase, illustrating again that the inclusion of inventories 

in the structural model matters. Figure 3 also highlights that the decline in the real price of oil, 

starting in late 1990 when the threat of Saudi oil fields being captured by Iraq had been removed 

by the presence of U.S. troops, was almost entirely caused by a reduction in speculative demand 

rather than increased oil supplies. The latter observation is consistent with evidence in Kilian 

(2008a) that it is difficult to reconcile the sharp decline in the real price of oil starting in late 

1990 with data on oil production. 

It is also noteworthy that according to Figure 2 there was a substantial increase in 

speculative demand and a substantial increase in oil supplies in the months leading up to the 

invasion with offsetting effects on the real price of oil. This result is consistent with a sharp 

increase in oil inventories in the months leading up to the invasion. One interpretation is that the 

invasion was anticipated by informed oil traders or, more likely, that traders responded to 

evidence of increased political tension in the Middle East. Gause (2002) notes a shift in Iraqi 

foreign policy toward a more aggressive stance in early 1990. This shift was caused in part by 

economic and financial pressures which Iraq attributed to unexpectedly rising oil production in 

countries such as Kuwait and hence falling oil prices, consistent with the evidence in the upper 

panel of Figure 2. 
19

4.5. What Caused the 1979 and 1980 Oil Price Shocks?

Speculative demand played an even more important role in 1979. The traditional interpretation is 

that this oil price increase was driven by flow supply disruptions associated with the Iranian 

Revolution of late 1978 and early 1979. Much of the observed increase in the real price of oil, 

however, only occurred after Iranian oil production had resumed later in 1979. Barsky and Kilian 

(2002) therefore attribute the price increase starting in May of 1979 and extending into 1980 in 

part to increased flow demand for oil and in part to a substantial increase in speculative demand 

for oil, consistent with anecdotal evidence from oil industry sources and with the perception of a 

noticeable increase in the risk of an oil supply disruption in the Persian Gulf in 1979.21 

 This hypothesis is testable in our model. Figure 2 shows that not only was there a 

dramatic and persistent increase in the real price of oil driven by positive flow demand shocks in 

1979 and 1980 (not unlike the persistent price increase after 2003), but that increase was 

reinforced in 1979 by a sharp increase in speculative demand, exactly as conjectured in Barsky 

and Kilian (2002). Whereas flow demand pressures on the real price of oil gradually receded 

starting in 1981, speculative demand pressures remained high until the collapse of OPEC in late 

1985. In contrast, there is little evidence of flow supply shocks being responsible for the oil 

price surge of 1979, consistent with the fact that overall global oil production increased in 1979, 

reflecting additional oil production outside of Iran. Only in late 1980 and early 1981 is there a 

moderate spike in the real price of oil driven by flow supply shocks, largely associated with the 

outbreak of the Iran-Iraq War (see Figure 2). 

 It is useful to explore the price and inventory dynamics in 1979 in more detail. The 

historical decompositions in Figure 4 show that indeed flow supply shocks caused a temporary 

drop in oil inventories in December of 1978 and January of 1979, but for the next half year 

positive flow supply shocks increased oil inventories. This result is also consistent with the fact 

that global oil production starting in April of 1979 exceeded its level prior to the Iranian 

Revolution. At the same time, after March of 1979, repeated speculative demand shocks caused a 

persistent accumulation of inventories, while driving up the real price of oil. The inventory 

                                                           

21 For example, Terzian (1985, p. 260) writes that in 1979 “spot deals became more and more infrequent. The 

independent refineries, with no access to direct supply from producers, began to look desperately for oil on the socalled ‘free market’. But from the beginning of November, most of the big oil companies invoked force majeure and 

reduced their oil deliveries to third parties by 10% to 30%, when they did not cut them off altogether. Everybody 

was anxious to hang on to as much of their own oil as possible, until the situation had become clearer. The shortage 

was purely psychological, or ‘precautionary’ as one dealer put it.” 
20

accumulation continues into 1980. There is no indication that flow supply shocks played an 

important role in the oil price surge of 1979. 

 It was not until September of 1980 when the Iran-Iraq War broke out that the oil market 

experienced another major disruption of flow supply. This event is once again associated with 

declining oil inventories initially and subsequently rising inventories driven by unexpected flow 

supply increases, reflecting in part the growing importance of new non-OPEC oil producers. 

As Figure 5 shows, the increase in the real price of oil in response to this flow supply shock is 

larger than the price response to the 1979 shock. There is also evidence of a resurgence of 

speculative demand in the months following the outbreak of the war, reflected in rising 

inventories and a higher real price of oil. 

4.6. The Collapse of OPEC in 1986 

In late 1985, Saudi Arabia decided that it would no longer attempt to prop up the price of oil by 

reducing its oil production, creating a major positive shock to the flow supply of oil. The same 

event also markedly changed market perceptions about OPEC’s market power. Figure 6 shows 

that, as expected, the positive flow supply shock in early 1986 drove down the real price of oil, 

while oil inventories rose in response. Simultaneously, a drop in speculative demand reinforced 

the decline in the real price of oil, while lowering inventory holdings. This pattern is similar to 

the pattern in Figure 3, except in reverse. Although OPEC attempted to reunite and control 

production in 1987, amidst increased speculation, as shown in Figure 2, these attempts proved 

unsuccessful in the long run. 

4.7. The Venezuelan Crisis and Iraq War of 2002/03 

Figure 7 focuses on the oil supply shock of 2002/2003 when within months first Venezuelan oil 

production slowed considerably at the end of 2002 and then Iraqi oil production ceased 

altogether in early 2003. The combined cutback in oil production was of similar magnitude to the 

oil supply shocks of the 1970s (see Kilian 2008a). Figure 7 shows that this event reflected a 

combination of flow supply shocks and speculative demand shocks. 

The Venezuelan oil supply crisis of late 2002 was associated with declining oil 

inventories, consistent with an unexpected oil supply disruption, but it also was associated with 

an increase in speculative demand in anticipation of the Iraq War that dampened the decline in 

inventories, while reinforcing the increase in the real price of oil. The military conflict in Iraq 
21

lasted from late March 2003 until the end of April 2003. Despite the additional loss of Iraqi 

output in early 2003, global oil production unexpectedly increased. The production shortfalls in 

Iraq and Venezuela were more than offset at the global level by increased oil production 

elsewhere. These positive flow supply shocks lowered the real price of oil starting in early 2003 

and resulted in positive inventory accumulation. At the same time, as early as March 2003, lower 

speculative demand caused the real price of oil to drop and oil inventories to fall. Again the 

effect of the two shocks on inventories was offsetting, whereas the effect on the price worked in 

the same direction. This last example again underscores that geopolitical events in the Middle 

East matter not merely because of the disruptions of the flow supply of oil they may create, but 

also because of their effect on speculative demand. 

5. Can Speculation Occur Without a Change in Oil Inventories? 

Our structural model of the oil market not only sheds light on the historical evolution of prices 

and quantities, but it may be used to obtain direct estimates of the short-run price elasticities of 

oil supply and oil demand. The elasticity of oil demand in particular plays a central role in 

assessing the empirical content of a recently proposed alternative model of speculation in oil 

markets. Specifically, Hamilton (2009a) shows that speculation could result in a surge in the real 

price of oil without any oil inventory accumulation, provided the short-run price elasticity of 

gasoline demand is zero. As shown below, that elasticity is closely related to the short-run price 

elasticity of oil demand, estimates of which can be obtained from our structural model. 

5.1. The Short-Run Oil Demand Elasticity in Production 

While there is little doubt that the price elasticity of oil supply is near zero in the short run, the 

literature does not offer much direct evidence on the short-run price elasticity of oil demand.22

The identification of this demand elasticity requires an exogenous shift of the contemporaneous 

oil supply curve along the contemporaneous oil demand curve within the context of a structural 

model. In contrast, much of the existing literature on estimating oil demand elasticities has been 

based on models that do not distinguish between oil demand and oil supply shocks (see, e.g., 

Dahl 1993; Cooper 2003).23

                                                           

22 Indeed our estimate of the price elasticity of oil supply is only about 0.01 or 0.02 on impact, consistent with the 

conventional view that the short-run oil supply curve is nearly vertical. 

23 A recent exception is Baumeister and Peersman (2009) who proposed an alternative structural VAR model of the 

oil market and used this model to estimate the oil demand elasticity. 
22

 Existing estimates of the oil demand elasticity in the literature have equated the percent 

change in quantity with the percent change in the production of crude oil. In this paper, we refer 

to the resulting elasticity measure as an oil demand elasticity in production, denoted by 

, Pr . O oduction  In model (1), this elasticity can be estimated as the ratio of the impact response of oil 

production to an oil supply shock relative to the impact response of the real price of oil. There is 

a consensus in the literature that the short-run price elasticity of oil demand in production is very 

low. For example, Hamilton (2009b) conjectures that this elasticity is -0.06. Our posterior 

median estimate of the oil demand elasticity estimate, as shown in the first column of Table 3, is 

-0.44. This estimate is seven times higher than typical conjectures in the recent literature. It is 

also much higher than conventional regression estimates of this elasticity. For example, Dahl 

(1993) and Cooper (2003) report estimates between -0.05 and -0.07. 

One reason for this difference is that standard econometric estimates of the crude oil 

demand elasticity fail to account for the endogeneity of the price of crude oil. Standard concerns 

about price endogeneity with respect to quantity suggest that these elasticity estimates are biased 

toward zero. For example, if we employed the conventional log-level specification used in the 

earlier literature on our data the implied elasticity estimate would be only -0.02. The use of a 

fully structural econometric model allows us to overcome this bias problem.24 

While the precise value of the oil demand elasticity estimate may be sensitive to the 

number of rotations and the choice of seed, accounting for estimation uncertainty does not 

overturn this result. Table 3 shows the posterior median of the oil demand elasticity estimate 

along with the 68% error band. The model assigns substantial probability mass to values between 

-0.64 and -0.28. The posterior standard error is 0.17. 

5.2. The Short-Run Oil Demand Elasticity in Use 

The oil demand elasticity in production in Table 3 is based on the conventional definition in 

empirical work. The definition of the price elasticity of oil demand that matters for policy 

questions is the oil demand elasticity in use, however. The latter elasticity is based on the change 

in quantity from both oil production and the depletion of oil inventories and hence more 

                                                           

24 Baumeister and Peersman (2009) based on a time-varying quarterly structural VAR model obtain an average 

median estimate of the short-run oil demand elasticity in production of -0.38. Their model differs from ours in 

several dimensions including the choice of the data, data frequency, and sample period, in the variables included, the 

dynamic specification and the identifying assumptions. Their analysis abstracts from oil inventories. Nevertheless, 

their elasticity estimate like ours is much higher than conventional estimates from non-structural models and similar 

to ours in magnitude.
23

accurately captures the behavior of oil consumers. To our knowledge, this distinction has not 

been discussed in the literature nor has there been any attempt to estimate the price elasticity in 

use. Doing so requires a structural model that explicitly includes oil inventories. In this section 

we show how the oil demand elasticity in use can be approximated with the help of our structural 

dynamic model of the oil market. By construction, allowing for inventory responses will tend to 

lower the price elasticity of oil demand. An important question is how much of a difference the 

inclusion of oil inventories makes for the elasticity estimate. 

 The amount of oil used in period t , denoted by , Ut equals the quantity of oil produced in 

that period ( ) Qt minus the oil that is added to the stock of inventories ( )t S : 

. UQ S tt t    

The change in oil used over time therefore equals the change in oil produced minus the change in 

the addition to inventory stocks: 2 .    UQ S tt t The price elasticity of oil demand in use is 

defined as: 

2

% 1 1 , % %

t t

Use tt t

t

t t

Q S

UQ S

P P   

 

     

where represents changes and % indicates percent changes in response to an oil supply 

shock in period t, and Pt denotes the real price of oil. Denote by B11

 the impact response of the 

percent change in oil production to an oil supply shock, where Bij

 refers to the ij th element of 

B. Then the implied change in oil production is 1 11 1 1 11 /100 /100.      QQ B Q Q B tt t t    

Moreover, 2

1 41 41, t tt        S S S SB SB    where the change in oil inventories in 

response to the oil supply shock equals the impact response B41

 and, prior to the shock, the 

change in crude oil inventories is equal to its mean S, which is observable. Finally, the impact 

percent change in the real price of oil in response to an oil supply shock is 31 B .  Hence, the 

demand elasticity in use can be expressed equivalently as 

1 11 41

1

31

( /100)

. /100

t

Use t

t

QB B

Q S

B 





 

  

 


24

Note that by construction Use t depends on Qt1 and hence will be time-varying even though the 

oil demand elasticity in production is not. We therefore report the average oil demand elasticity 

in use over the sample period throughout this paper, denoted by , . O Use  This allows for the 

possibility that the estimate of Use t may be slightly positive merely by chance, which seems 

especially likely if Use t is close to zero in population because this elasticity depends on reducedform parameters that may be imprecisely estimated. 

The second column of Table 3 shows that, as expected, the demand elasticity in use is 

much lower than the elasticity in production. The median estimate is only -0.24 compared with 

an estimate of -0.44 for the demand elasticity in oil production. The 68% error bands range from 

-0.42 to -0.09. This finding is important in that it suggests that even the inclusion of inventories 

does not overturn our findings that the short-run price elasticity of oil demand is much higher 

than previously thought. 

5.3. Bounding the Short-Run Gasoline Demand Elasticity 

The magnitude of the short-run price elasticity of oil demand has important implications for 

theoretical models of speculative demand. In the absence of changes to oil production, standard 

models of speculation imply that oil inventories must increase to enable the price of oil to 

increase. Recently, it has been suggested that under certain conditions speculation may drive up 

the real price of oil without any change in oil inventories (see Hamilton 2009a). Specifically, this 

may occur if refiners are able to pass on fully to gasoline consumers an exogenous increase in 

the real price of oil driven by speculation. This requires the demand for gasoline to be 

completely price-inelastic. Whether the alternative model of speculation in Hamilton (2009a) 

could explain our data depends on the magnitude of the short-run price elasticity of gasoline 

demand. 

 That magnitude is directly related to the impact price elasticity of oil demand in use. 

Rather than extend the econometric model to permit a joint analysis of the crude oil and gasoline 

markets, which does not seem feasible given the limited degrees of freedom, in this section we 

derive an explicit relationship between consumers’ demand for gasoline and refiners’ demand for 

crude oil in a model in which refiners are allowed to, but not required to have market power in 

the gasoline market. Refiners are treated as price-takers in the crude oil market. Our analysis is 

strictly short-term, as is appropriate in constructing impact price elasticities. In the interest of 
25

tractability, we abstract from the fact that gasoline is only one of several refined products jointly 

produced from crude oil. 

 We postulate that gasoline is produced according to a Leontief production function over 

capital, labor, and oil, G KL O  min , , .    If capital is fixed in the short run and refiners’ labor 

input can be varied on the intensive margin, which seems plausible in practice, refiners produce 

gasoline in fixed proportion to the quantity of oil consumed, G O  , and pay a marginal cost 

equal to the price of oil, , PO plus the marginal cost of labor, . MCP c  O  

Consumers maximize 

1/ ( 1) 1/ ( 1) 1 U BG B G ( , ) (1 ) ,



                

where B is a bundle of non-gasoline consumer goods and G is gasoline consumption at price . PG

The term  is the constant elasticity of substitution and 1 denotes the expenditure share of 

gasoline. Consumers choose 1 ( ) (1 ) , GP X P P G G

       where X is the total expenditure on all 

goods, P is the consumer price index, and the price elasticity of demand for gasoline, , G 

equals . Equivalently, 1/ ( ) PG G G

    where 1 (1 ) . X P      

In the Cournot-Nash equilibrium, each of J identical refinery firms will choose its own 

quantity of gasoline output, , 1,..., , j gj J  given the outputs of other firms, to maximize profits 

    1/ ( ) j G j Oj j Oj P Gg c P g f G g c P g f         

with respect to ,j g where j j G g   and f represents short-run fixed costs. This yields the 

first order conditions 

  1/ ( 1)/

0 / 0 1,..., . P gP G gG c p j J G jG j

            

Summing over j and solving for the market price and gasoline production yields 

 

 

( 1) . 1

O

G

O

JPc J P G

J JPc



  

 

       

   

Given , G O  we obtain 
26

 

 

1 .

O

J

O

JPc



 





     

  

Log-linearization yields 

, , O Use G O

O

P

P c   



where O Use ,  denotes the price elasticity of demand for crude oil in use. Thus, if O Use ,  were zero, 

then by construction so would be . G  

 Given the evidence that O Use ,  is not even close to zero, we need to be more specific about 

the link. If the price of oil constitutes the largest component of refiners’ marginal cost, consistent 

with the evidence presented in Considine (1997), then 0 , O  c P  which in turn implies 

, , 2 . O Use G O Use     Thus, the price elasticity of gasoline demand must be between one and two 

times as high as the price elasticity of the demand for crude oil. This result includes as a limiting 

case the view expressed in Hamilton (2009a) that the gasoline demand elasticity is 

approximately twice as high as the oil demand elasticity. 

In light of the marginal cost estimates presented in Considine (1997), however, who 

provides evidence that 0, c  the factor of proportionality is likely to be closer to unity. This 

allows us to conclude based on Table 3 that the posterior median estimate of the short-run price 

elasticity of gasoline demand must be about -0.24.25 That estimate is much larger than some 

recent estimates in the literature. For example, Hughes, Knittel and Sperling (2008) in an 

influential recent study report a baseline elasticity estimate of only -0.04 for the United States 

based on data for 2001-06. Their estimate, however, like earlier studies, fails to account for price 

endogeneity and cannot be interpreted as an elasticity in the textbook sense.26 Moreover, it is 

sensitive to the sample period. Similar estimates of this elasticity based on older data are near 

-0.20 (see, e.g., Dahl and Sterner 1991). The average of the least-squares estimates in Hughes et 

                                                           

25 Based on the 68% error band, the price elasticity of gasoline demand could be anywhere between -0.09 and -0.42.

26 The baseline results in Hughes et al. (2008) are ordinary least squares estimates of monthly reduced-form time 

series regressions of quantity on price in log-levels (with additional controls included). As part of their sensitivity 

analysis for 2001-06, they also use as an instrument unpredictable changes in global crude oil production driven by 

events such as Hurricanes Rita and Katrina. This results in gasoline demand elasticity estimates as high as -0.08 for 

2001-2006. However, the weak instrument diagnostics in Hughes et al. are not informative, raising concerns about 

downward bias in the elasticity estimates. 
27

 al. for 1975-80 and for 2001-06 is -0.19.27 

Our bounds on the impact price elasticity of gasoline demand allows us to discount the 

possibility discussed in Hamilton (2009a) that speculation may arise without any change in 

inventories. This finding is also consistent with the large positive inventory response to 

speculative demand shocks in Figure 1. It is important to stress that our identifying assumptions 

encompass the model discussed in Hamilton (2009a) as a special case. Hence, we can 

unambiguously rule out the hypothesis that increases in the real price of oil in 2003-08, in 

particular, were driven by speculation. 

6. Related Estimates of the Price Elasticity of Gasoline Demand in the Literature 

Although there is no alternative to the use of dynamic simultaneous equation models in 

estimating the short-run price elasticity of oil demand or gasoline demand, it is useful to compare 

our findings to the related literature on estimating long-run price elasticities of gasoline demand. 

There is widespread recognition that the long-run adjustments to changes in energy prices are 

potentially much greater than the adjustments occurring within the first month. It is commonly 

thought that the adjustment toward more energy-efficient technologies occurs over a horizon of 

perhaps five or ten years (see, e.g., Sweeney 1984). 

 Such long-run price elasticities may be estimated from cross-sectional household data.28

The premise of cross-sectional estimates of the price elasticity of gasoline demand is that, 

controlling for region-specific and time effects (as well as other relevant controls such as 

demographics or income), consumers on average are in steady state. Identification in these 

regressions arises from the within-region variation in U.S. gasoline prices. Thus, an obvious 

plausibility check is that estimates of the short-run price elasticity of gasoline demand from 

structural dynamic models must not exceed the corresponding long-run estimates from structural 

cross-sectional models. It can be shown that our short-run estimates are compatible with the 

cross-sectional evidence. For example, studies of nonparametric gasoline demand functions 

                                                           

27 Indeed, one of the main points in Hughes et al. (2008) is that there appears to have been a structural change with 

recent estimates of the price elasticity of gasoline demand being lower. This interpretation overlooks that their 

model makes no allowance for changes in the composition of demand and supply shocks in the gasoline market. 

Recent work by Kilian (2010) has demonstrated that ignoring the distinction between shifts in the contemporaneous 

oil supply curve and shifts in the contemporaneous demand curve for oil can account for the apparent instability in 

the expected response of gasoline consumption to gasoline price shocks. In the model proposed in section 3, we 

similarly control for this source of time variation. 

28 This is not an issue that can be addressed with our VAR methodology. That methodology is not suitable for 

assessing responses at horizons of five or ten years. Given the short time series available, estimates of dynamic 

responses from structural VAR models tend to become unreliable at horizons beyond one or two years. 
28

based on U.S. household survey data such as Hausman and Newey (1995) have consistently 

produced long-run price elasticity estimates near -0.8, far in excess of our median estimate of 

-0.24 of the short-run elasticity.29 

7. Conclusion 

Standard structural VAR models of the market for crude oil implicitly equate oil production with 

oil consumption and ignore the role of oil inventories. Traditionally these models have focused 

on shocks to the contemporaneous flow supply of oil and the contemporaneous flow demand for 

oil. In this paper we augmented the structural model to include shocks to expectations about 

future oil supplies and future oil demand. Such shocks must be represented as shifts of the 

contemporaneous oil demand curve rather than the contemporaneous oil supply curve, even if the 

shift in expectations is about a cut in future oil supplies. The reason is that traders in anticipation 

of the expected oil shortage will buy and store crude oil now with the expectation of selling later 

at a profit. Such speculative demand shocks will typically be associated with inventory building. 

In contrast, oil consumption smoothing in response to positive flow demand shocks and negative 

flow supply shocks will involve a drawing down of oil inventories. We proposed a dynamic 

simultaneous equation model including oil inventories that allows the identification of all three 

types of shocks. 

The inclusion of oil inventories matters. The structural model proposed in this paper 

implies a larger role for oil supply shocks in explaining fluctuations in the real price of oil than 

previous estimates. The added explanatory power of oil supply shocks in explaining fluctuations 

in the real price of oil, especially in 1990, comes at the expense of the explanatory power of 

speculative demand shocks. Nevertheless, the largest and most persistent fluctuations in the real 

price of oil since the 1970s such as the oil price increase in 1979/80 were driven primarily by 

business cycle fluctuations affecting the demand for crude oil. Of particular interest in this paper 

has been the oil price increase from 2003 until mid-2008. We were able to provide direct 

evidence against the popular view that the sharp increase in the real price of oil during this 

period (and in 2007/08 in particular) was driven by speculation among oil traders. Shifts in 

speculative demand played a more important role during several earlier oil price shock episodes, 

                                                           

29 Schmalensee and Stoker (1999) question the reliability of the price data and the specification used in Hausman 

and Newey (1995), but Yatchew and No (2001) address those concerns using more detailed Canadian data and 

arrive at a gasoline demand elasticity estimate of -0.9, very close to Hausman and Newey’s original estimate. 
29

however, notably in 1979, 1986 and in 1999/2000. We showed that, without accounting for shifts 

in the speculative demand for oil, it is not possible to understand the evolution of the real price of 

oil during these episodes. 

Our analysis also suggests that there is no evidence that the peak oil hypothesis or 

deliberate production cutbacks by oil producers had much bearing on the recent oil price shock. 

Rather our results support recent findings in the literature that the run-up in the real price of oil 

between 2003 and mid-2008 was caused almost entirely by shifts in the global flow demand for 

oil. This implies that the real price of oil is expected to rise, as the global economy recovers from 

the financial crisis, creating a policy dilemma, unless energy consumption can be reduced or new 

energy sources can be found. In contrast, additional regulation of oil traders is unlikely to 

prevent the price of oil from rising again in the future. 

Hamilton (2009a,b) recently has cast doubt on explanations of major oil price increases 

based on shifts in speculative demand during previous oil price shock episodes. He observed in 

particular that following the outbreak of the Persian Gulf War in August 1990, oil inventories did 

not increase as one would have expected in response to a positive speculative demand shock. At 

the same time, the absence of a sharp decline in oil inventories in August of 1990 is inconsistent 

with the view that the price increase reflected a negative oil supply shock. We demonstrated that 

this inventory puzzle can be resolved with the help of a structural oil market model. Our analysis 

showed that the price and inventory data can be explained only based on a combination of these 

two shocks. Because the implied inventory responses are of opposite sign, the net effect in 

inventories is close to zero, where the sharp price increase reflects the fact that the implied price 

responses are of the same sign. Similar relationships were shown to hold during other key 

historical episodes. These examples illustrate that it is essential to rely on structural models in 

interpreting the price and quantity data. 

The use of a structural regression model also is important for the construction of the 

short-run price elasticity of oil demand. For example, Hamilton (2009a,b) suggests that 1978-81 

is one episode where one might clearly and without a regression model attribute cumulative 

changes in the price of oil to exogenous oil supply shifts only, allowing one to construct a 

demand elasticity estimate from the ratio of cumulative changes in quantities and prices for that 

period. The structural model we have analyzed suggests otherwise. We showed that oil demand 

shocks were the main cause of the observed oil price increase in 1978-81. Oil supply shocks 
30

played a small role only, violating the premise of Hamilton’s calculations. 

We observed that there are no credible regression-based estimates of the short-run price 

elasticity of oil demand in the literature. Conventional estimates of this elasticity from dynamic 

regressions, as in Dahl (1993) and Cooper (2003), have ignored the endogeneity of the real price 

of oil, causing the elasticity estimate to be downward biased. Moreover, all existing estimates, 

including the structural estimates recently provided by Baumeister and Peersman (2009), have 

ignored the role of inventories in smoothing oil consumption in response to oil supply shocks. 

We provided a model that allows the estimation of both the traditional oil demand elasticity in 

production and of the more relevant oil demand elasticity in use which incorporates changes in 

oil inventories. Our elasticity estimates are substantially higher than standard estimates cited in 

the literature, and appear to rule out recently proposed models of speculative trading based on a 

zero short-run price elasticity of oil demand. We also provided a theoretical benchmark for the 

relationship between the short-run price elasticity of oil demand in use and the corresponding 

price elasticity of gasoline demand. The latter was shown to be about as high as the oil demand 

elasticity in use under plausible assumptions about the refining industry. The resulting short-run 

gasoline demand elasticity estimates are compatible with alternative estimates of the long-run 

price elasticity of gasoline demand from cross-sectional data.
31

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34

Table 1: Sign Restrictions on Impact Responses in VAR Model 

Note: All sign restrictions involve weak inequalities. All shocks have been normalized to imply 

an increase in the real price of oil. 

Table 2: Percent Contribution to Variability of the Change in Inventories 

Horizon Flow 

supply shock 

Flow 

demand shock 

Speculative 

demand shock 

3 23.1 1.4 41.3 

6 22.7 2.3 41.2 

9 22.7 3.5 41.1 

12 22.5 4.0 41.3 

∞ 21.4 14.8 35.7 

Note: Results from a structural forecast error variance decomposition based on the benchmark 

estimate of the structural model (1) as in Figure 1. The infinite horizon is approximated by 600. 

Table 3: Posterior Distribution of the Short-Run Price Elasticity of Demand for Crude Oil 

O oduction , Pr  O Use , 

16th Percentile -0.64 -0.42 

50th Percentile -0.44 -0.24 

84th

 Percentile -0.28 -0.09 

Standard Deviation 0.17 0.18 

Note: Based on 150 admissible structural models drawn from the posterior. In constructing the 

posterior we impose a uniform prior on the elasticity in use that bounds this elasticity at -0.5. 

This restriction is not binding in the set of admissible models obtained from the actual data. 

O oduction , Pr  refers to the price elasticity of oil demand in production and O Use ,  to the price 

elasticity of oil demand in use. The latter definition accounts for the role of inventories in 

smoothing oil consumption. 

Flow 

supply shock 

Flow 

demand shock 

Speculative 

demand shock 

Oil production - + + 

Real activity - + - Real price of oil + + + 

Inventories - - + 
35

0 10

-2-1

01

Flow supply shock

Oil production

0 10

-5

05

10

Flow supply shock

Real activity

0 10

-5

05

10

Flow supply shock

Real price of oil

0 10

-20-10

0

1020

Flow supply sho

Inventories

0 10

-1

012

Flow demand shock

Oil production

0 10

-5

05

10

Flow demand shock

Real activity

0 10

-5

05

10

Flow demand shock

Real price of oil

0 10

-20-10

0

1020

Flow demand sho

Inventories

0 10

-1

012

Speculative demand shock

Oil production

Months

0 10

-5

05

10

Speculative demand shock

Real activity

Months

0 10

-5

05

10

Speculative demand shock

Real price of oil

Months

0 10

-20-10

0

1020

Speculative demand 

Inventories

Months

Figure 1: Structural Impulse Responses: 1973.2-2009.8 

Note: Results for the admissible structural model with an impact price elasticity of oil demand in use closest to t

of that elasticity. Dashed lines indicate pointwise 16% and 84% posterior quantiles based on 150 admissible drawOil production refers to the cumulative percent change in oil production and inventories to cumulative changes in 
36

1980 1985 1990 1995 2000 2005

-100

-50

0

50

100

Cumulative Effect of Flow Supply Shock on Real Price of Crude Oil

1980 1985 1990 1995 2000 2005

-100

-50

0

50

100

Cumulative Effect of Flow Demand Shock on Real Price of Crude Oil

1980 1985 1990 1995 2000 2005

-100

-50

0

50

100

Cumulative Effect of Speculative Demand Shock on Real Price of Crude Oil

Figure 2: Historical Decompositions for 1978.6-2009.8 

Note: Based on benchmark estimate as in Figure 1. The vertical bars indicate major exogenous events in oil maroutbreak of the Iranian Revolution in 1978.9 and of the Iran-Iraq War in 1980.9, the collapse of OPEC in 1985.1Persian Gulf War in 1990.8, the Asian Financial Crisis of 1997.7, and the Venezuelan crisis in 2002.11, which wIraq War in early 2003. In constructing the historical decomposition we discard the first five years of data in an etransition dynamics. 
37

1990.7 1990.8 1990.9 1990.10 1990.11 1990.12 1991.1 

-30-20-10

0

102030

Real price of oil

Cumulative effect of flow supply shockCumulative effect of speculative demand shock

1990.7 1990.8 1990.9 1990.10 1990.11 1990.12 1991.1 

-50-40-30-20-10

0

1020

Change in oil inventories

Figure 3: Historical Decompositions for the Persian Gulf War Episode of 1990/91 

 Note: Based on estimates of structural model (1) on data for 1973.2-2009.8 
38

1978.10 1979.1 1979.4 1979.7 1980.1

-20

0

2040

Real price of oil

Cumulative effect of flow supply shockCumulative effect of speculative demand shock

1978.10 1979.1 1979.4 1979.7 1980.1

-20

0

2040

Change in oil inventories

Figure 4: Historical Decompositions for the Iranian Revolution of 1978/79 

Note: Based on estimates of structural model (1) on data for 1973.2-2009.8 
39

1980.9 1980.12 1981.3 

-30-20-10

0

1020304050

Real price of oil

Cumulative effect of flow supply shockCumulative effect of speculative demand shock

1980.9 1980.12 1981.3 

-30-20-10

0

1020304050

Change in oil inventories

Figure 5: Historical Decompositions for the Outbreak of the Iran-Iraq War in 1980 

Note: Based on estimates of structural model (1) on data for 1973.2-2009.8 
40

1986.1 1986.3 1986.5

-40-20

0

2040

Real price of oil

Cumulative effect of flow supply shockCumulative effect of speculative demand shock

1986.1 1986.3 1986.5

-40-20

0

2040

Change in oil inventories

Figure 6: Historical Decompositions for the Collapse of OPEC in 1986 

Note: Based on estimates of structural model (1) on data for 1973.2-2009.8 
41

2002.11 2003.1 2003.4

-40-20

0

2040

Real price of oil

Cumulative effect of flow supply shockCumulative effect of speculative demand shock

2002.11 2003.1 2003.4

-40-20

0

2040

Change in oil inventories

Figure 7: Historical Decompositions for Venezuelan Crisis and Iraq War in 2002/03 

Note: Based on estimates of structural model (1) on data for 1973.2-2009.8