Is the Strategic Petroleum Reserve our ace in the hole?

The Strategic Petroleum Reserve (SPR) is often touted as a vital asset in mitigating the adverse effects of oil supply disruptions on the economy. The importance of SPR, however, largely depends upon the effect of stock sales on market prices. To address this question, this study develops a

monthly econometric model of the world crude oil market. Inventories, consumption, production, and prices for crude oil are determined within a dominant producer pricing framework in which Saudi Arabia adjusts output based upon market demand and competitive fringe supply. The estimation results provide additional support for the dominant producer pricing model for world oil markets and reasonable estimates of short-run supply and demand elasticities. Several model simulations are conducted to assess the impacts of SPR policies. For example, the gradual build-up of the SPR by the Bush Administration resulted in a very small, almost imperceptible increase in world prices. Similarly, the Clinton sale from SPR had minor impacts on market prices. Another simulation indicates that while SPR sales can lower world prices during a supply shock, the required drawdown would be so substantial the reserve would be significantly depleted after just a few months. These findings suggest that once played, the SPR card has modest impacts on world prices and could be easily trumped by actions of other players, including output adjustments by world oil producers.

1. INTRODUCTION

"Gas prices are burning a hole in New Yorkers' wallets, putting at risk the economic recovery, and the Administration insists on throwing fuel on the fire. Instead of playing our one ace in the hole and releasing oil from the Strategic Petroleum Reserve to help cut prices, they are buying oil on the market and driving up prices even higher,"

--US Senator Charles E. Schumer, May 19, 2004

Senator Schumer's statement suggests that the Strategic Petroleum Reserve (SPR) can be used to significantly affect world oil prices. In fact during late 2000, the Clinton Administration did exactly what the Senator wanted and released nearly 30 million barrels of oil from the SPR. How much did this stock sale reduce prices? The Senator correctly points out that the Bush Administration decided to expand the size of the SPR, increasing it from 550 million barrels in late 2001 to over 690 million barrels in early 2005. Did this stock build "throw fuel on the fire," by contributing to higher prices as the Senator claims and, if so, by how much? To address these questions, a framework is needed of how SPR stock changes affect world oil supply and demand. In developing such a framework, market structure is a central question.

While the oil market has been characterized as a cartel run by the Organization of Petroleum Exporting Countries (OPEC), the research that supports this view is more than 20 years old, see for example Adelman (1982) and Griffin (1985). More recent research by Alhajji and Huettner (2000), suggests that the oil market is a constrained monopoly with Saudi Arabia operating as a dominant producer, adjusting output based upon residual demand and competitive supply. Allhaji and Huettner (2000), however, did not develop an explicit model for prices and the role of inventories in price determination. This study takes these next steps with the estimation of a monthly econometric model of crude oil consumption, production, inventories, and prices. The model is then simulated to determine whether the SPR should be considered "our ace in the hole."

The specification of a crude oil market model is to a considerable extent dictated by the availability of data. The next section discusses these constraints and provides a context for the model presented in the third section. The econometric specification and estimation methods are discussed in section four. The empirical results are presented in the fifth section. Model simulations of supply and demand shocks are in the sixth section along with an analysis of the Clinton SPR sale and the Bush SPR stock-build. The market impacts of a supply shock scenario with and without SPR sales are also presented. The paper concludes with an economic perspective of Senator Schumer's statement and the policy implications from this research.

2. THE WORLD OIL MARKET

Crude oil is the world's most important commodity with gross sales at the wellhead of more than $1.1 trillion during 2004. Significant crude oil production occurs in over 65 countries around the world. In addition to a wide array of extraction wells, a network of pipelines and ships deliver crude to the first "consumers" of crude oil, petroleum refineries. These plants, often owned by large integrated oil companies, refine crude oil into an array of petroleum products, such as gasoline, distillate fuel oil, kerosene, jet fuel, and other petroleum products, including naphtha, asphalt, and other petrochemical products. Hence, the demand for crude oil is derived from the demand for petroleum products. Sales of these products have pronounced seasonality with gasoline sales rising during the summer and distillate sales increasing during the fall and winter. As a result, there are corresponding seasonal swings in crude oil demand.

Inventories of crude oil are held at various locations in the distribution network--at oil fields, in tankers and pipelines, in bulk terminals, at refineries, and of course by governments as strategic reserves. Commercial inventories of crude oil held in so-called primary markets--the United States, Japan, and Europe--averaged slightly more than 775 million barrels from January 1991 through March 2005 (see Table 1). An additional 830 million barrels are in transit at sea, also known as "floating inventories." As noted above, the US SPR increased significantly since 2001 and now is close to its capacity of 700 million barrels. Additional commercial inventories are held in the rest of world but estimates of monthly stocks in these areas are unavailable. While there is reliable information on crude oil stocks and refinery consumption in primary markets, direct measurements at a monthly frequency for the rest of the world are incomplete.

Monthly wellhead crude oil production is readily available so that inventories and consumption in primary markets can be used to determine consumption and net stock changes of crude oil in the rest of the world. Consider the following identity linking production of crude oil in month t, [Y.sub.t], with refinery use, [Q.sub.t], and stocks of crude oil, [X.sub.t],:

[Y.sup.s.sub.t]+[Y.sup.ns.sub.t] = [Q.sup.pm.sub.t] + ([X.sup.obs.sub.t] - [X.sub.t-1.sup.obs]) / [D.sub.t] + [Q.sup.row.sub.t] + ([X.sup.row.sub.t] - [X.sub.t-1.sup.row])/[D.sub.t], (1)

where [X.sup.obs.sub.t] = [X.sup.pm.sub.t] + [X.sup.sea.sub.t] + [X.sup.gov.sub.t] and D is the number of days in a month and where the superscripts are defined as follows: "s" indicates Saudi Arabia, "ns" non-Saudi Arabian sources, "pm" defines primary markets, "obs" denotes observed, "sea" indicates on the ocean, "row" rest-of-world, and 'gov" for government. By definition, world crude oil production is equal to refinery use of crude plus net crude oil stock changes.

Most of the stocks and flows in (1) are reported by the Energy Intelligence Group (EIG) except crude oil refinery runs, [Q.sup.row.sub.t], and net stocks changes in the rest of the world, [X.sup.row.sub.t] - [X.sub.t-1.sup.row]), which together constitute world rest-of-world demand:

[R.sub.t] = [Q.sup.row.sub.t] + ([X.sup.row.sub.t] - [X.sub.t-1.sup.row] / [D.sub.t] = [Y.sup.s.sub.t] + [Y.sup.ns.sub.t] - [Q.sup.pm.sub.t] - ([X.sup.obs.sub.t] - [X.sup.obs.sub.t-1]) / [D.sub.t], (2)

For example, total world crude oil production during January 2005 was 72.9 million barrels per day, refinery runs in primary markets were 32.4 million, and observed crude oil stocks declined the equivalent of 0.1 million barrels per day so that rest-of-world world demand was 40.6 million barrels per day.

There are also two material balances that are helpful to understand the link between crude oil refinery runs and refined petroleum product sales. The first concerns the balance between petroleum product sales and refinery production

and finished product inventories:

[Z.sup.pm.sub.t]+ [Z.sup.row.sub.t] = [YZ.sup.pm.sub.t] - ([XZ.sup.pm.sub.t] - [XZ.sup.pm.sub.t-1] / [D.sub.t] = [YZ.sup.row.sub.t] - ([XZ.sup.row.sub.t] - [XZ.sup.row.sub.t-1] / [D.sub.t], (3)

The left side of this equation is total world demand for petroleum products, such as gasoline, fuel oil, and other products, which is the sum of demand in primary markets [Z.sup.pm.sub.t], and in the rest of the world, [Z.sup.row.sub.t]. The right side includes refinery production of petroleum products in primary markets, [YZ.sup.pm.sub.t], and in the rest of the world, [YZ.sup.row.sub.t]. Product sales are also supplied by changes in final product inventories, [XZ.sup.pm.sub.t] & [XZ.sup.row.sub.t] respectively.

The second balance links refinery production with inputs of crude and other hydrocarbon supplies. The physical amount of refinery production reflects inputs of crude oil and other hydrocarbons, such as natural gas liquids. There is also a volumetric increase known as refinery processing gains that occurs during the transformation of crude oil into lighter and less dense refined petroleum products. Hence, the mass balance for refinery production is as follows:

[YZ.sup.pm.sub.t] + [YZ.sup.row.sub.t] = [Q.sup.pm.sub.t] + [Q.sup.row.sub.t] + [QL.sub.t] + [QG.sub.t] (4)

In other words, refinery production is equal to the sum of crude oil inputs into refining also known as crude oil refinery runs, [Q.sup.pm.sub.t] + [Q.sup.row.sub.t], natural gas liquids [QL.sub.t], and processing gains, [QG.sub.t].

The above balances do not include net trade balances because they are zero on an aggregate world basis. Regional product balances, however, would include net trade flows. For example, the product balance for primary markets is as follows:

[Z.sup.pm.sub.t] = [YZ.sup.pm.sub.t] - ([XZ.sup.pm.sub.t] + [XZ.sup.pm.sub.t-1]) / [D.sub.t] + [IZ.sup.pm.sub.t] - [EZ.sup.pm.sub.t],

which states that the sales of petroleum products is equal to regional production less the change in product stocks plus imports of petroleum products, [IZ.sup.pm.sub.t], less product exports, [EZ.sup.pm.sub.t]. Rearranging this equation expresses total product demand in primary markets as follows:

[Z.sub.t] = [Z.sup.pm.sub.t] + ([XZ.sup.pm.sub.t] - [XZ.sup.pm.sub.t-1]) / [D.sub.t] = [YZ.sup.pm.sub.t] + [IZ.sup.pm.sub.t]- [EZ.sup.pm.sub.t] (5)

This measure of the demand-pull on crude oil refinery runs, [Z.sub.t], includes both final product use and product inventory demand and will be used below in the demand equation for crude oil in primary markets. Crude oil refinery runs in primary markets generally increased until 1998 and then followed a flat trend since then. Total product demand in this region shows a similar pattern with pronounced seasonality. Lagged refined petroleum product demand is used below as an instrumental variable in estimation because it serves as a good proxy for the seasonal swings in petroleum product consumption, such as the increase in heating oil use during winter and gasoline consumption during the summer driving season.

Data limitations do not allow inventory adjustments to total product demand in the rest of the world. Instead, unadjusted total product demand in the rest of the world is used as the demand pull on crude consumption in these areas. This region includes net exporters of petroleum product to primary markets. As a result, rest-of-world demand, which again is crude oil refinery runs and net changes in crude oil stocks, sometimes exceeds total product demand in the rest of the world. During the late 1980s and early 1990s rest-of-world on demand was declining but then steadily increased from 1995, reflecting strong economic growth in China and other developing regions. The simple correlation between rest-of-world crude demand and total product demand in the rest of the world is 0.82, the exact same correlation between refinery runs and the inventory adjusted product demand in primary markets. So in summary, petroleum product sales in primary markets and other areas of the world serve as the two key demand drivers in our model of world crude oil markets. (1)

On the supply side, the world's most important producer, Saudi Arabia, often has excess capacity and acts as a swing producer. Saudi production averaged 8.1 million barrels per day (mmbd) over the sample period (see Table 1). Saudi output increased sharply during the Iraqi occupation of Kuwait in 1990 and then remained at this higher level, fluctuating between 7.5 and 9.5 million barrels per day from 1991 through the first quarter of 2005. Non-Saudi crude oil production averaged 57.3 million barrels per day and displays a rather smooth upward trend during the sample.

While there are many types of crude oil with different prices reflecting quality differentials, this study uses the price for West Texas Intermediate (WTI) crude as the market clearing price. In part this reflects the very active and sizeable market for futures contracts for WTI crude at the New York Mercantile Exchange (NYMEX). Saudi Arabian output fluctuates considerably and at times seems to follow prices for WTI crude (see Figure 1). For example, during the 1998 decline in prices, Saudi production was lowered and, after prices began to recover sharply during 1999, increased. The sharp fall in prices during 1998 without any major cutback in Saudi output suggests that other events, such as demand shocks, also affect market prices. Prices for the first nearby contract averaged $23.8 per barrel over the sample period, ranging from below $12 during late 1998 to a high of over $54 in March 2005 (see Table 1).

[FIGURE 1 OMITTED]

3. A DOMINANT PRODUCER PRICING MODEL FOR OIL

The model developed in this study has two major dimensions: the supply and demand for flows and stocks of crude oil. The demand for crude oil is derived from the demand for refined petroleum products. The supply of crude from current production includes supply from competitive producers and production from the dominant producer, Saudi Arabia. The demand for crude oil inventories is determined by transporters, distributors, and refiners of crude oil. A supply of storage relation determines the forward price spread, which affects the user cost of holding inventories.

The supply relation in the model determines price based upon marginal extraction cost and a markup that depends upon the elasticity of demand and the elasticity of supply from the competitive fringe. Unlike many oil market studies, such as Griffin (1985) and Alhajji and Huettner (2000), that infer markup pricing from the elasticities of supply and demand, this study adopts the approach used by Morrison (1992) that involves direct estimation of a supply relation. (2)

Based upon the considerations discussed in the previous section, this study examines the demand for crude oil in two regions of the world: primary markets defined to include the US, Japan, and fifteen European countries (EU15) (3) and the rest of the world. Crude oil demand in primary markets, [Q.sup.pm.sub.t], is a function of the real price and petroleum product sales:

[Q.sup.pm.sub.t] = [[alpha].sub.0] + [[alpha].sub.1] 1n ([P.sub.t] / [CPI.sup.q.sub.t]) + [[alpha].sub.2] 1n [Z.sub.t] + [[epsilon].sup.q.sub.t], (6)

where [P.sub.t] is the price on the first nearby contract at the NYMEX for WTI crude oil, [CPI.sup.q.sub.t] = [CPI.sub.t] / [w.sup.usa,q.sub.t] + (1-[w.sup.usa,q.sub.t])[DI.sub.t]] is the U.S. consumer price index, [CPI.sub.t], adjusted by an index of the trade-weighted real value of the U.S. dollar, [DI.sub.t], where [w.sup.usa,q.sub.t] is the share of US crude oil consumption in primary markets, and [Z.sub.t] is defined by (5) above, and the [alpha]'s are unknown parameters. The index for the real value of the US dollar is from Loretan (2005) and is defined as [e.sub.jt][p.sub.t]/[p.sub.jt], where [e.sub.jt] is the price of the US dollar in terms of foreign currency j in period t and where [p.sub.t] and [p.sub.jt] are consumer price indexes for the US and economy j respectively. Hence, the real price term in (6) is a weighted average of real prices in the US and real prices in other primary markets. A semi-log specification is adopted to make the model more tractable, allowing a closed form solution for price and the inverse price elasticity that enters the supply relation.

As discussed in the previous section, crude oil demand outside primary markets is really rest-of-world demand given by (2) above. Rest-of-world crude oil demand, [R.sub.t], is a function of real price and refinery production in the rest of the world as follows:

[R.sub.t] = [[beta].sub.0] + [[beta].sub.1] 1n ([P.sub.t]/[CPI.sup.r.sub.t]) + [[beta].sub.2] 1n [Z.sup.row.sub.t] + [[epsilon].sup.r.sub.t], (7)

where [CPI.sup.r.sub.t] = [CPI.sub.t]/[DI.sub.t], [Z.sup.row.sub.t] is sales of refined petroleum products in other regions during period t, and the [beta]'s are parameters to be estimated.

The other portion of the demand side involves crude oil stocks. Inventories provide a physical bridge between market balance today and tomorrow. Currently available supplies depend in part upon inventories carried over from last period. Likewise, stocks at the end of this period for carryover next period affect commodity availability in the future. Since prices in any specific period reflect the balance between demand and availability, inventories link prices between time periods.

The study by Blinder and Maccini (1991) suggests that firms may use finished goods inventories to smooth production and avoid costly start-up and shutdown costs to meet changes in sales. In addition, the study by Eichenbaum (1989) finds that firms may hold inventories of inputs to smooth costs by accumulating raw materials stocks when prices are low and drawing down inventories when input prices escalate.

Ramey (1989) models inventories as just another factor of production with inventory demand as a function of the cost of using inventories and the level of output. This study adopts a similar approach, assuming that the demand for commercial crude oil stocks in primary markets, [X.sup.pm.sub.t], depends upon real user costs, refinery production, and lagged stocks:

[X.sup.pm.sub.t] = [[delta].sub.0] + [[delta].sub.1] [1n(P.sub.t]/ [P.sub.f.sub.t]) + [r.sub.t] - [i.sub.t]] + [[delta].sub.2] 1n [Z.sub.t] + [[delta].sub.3] [X.sup.pm.sub.t-1] + [[epsilon].sup.x.sub.t], (8)

where the first expression in square brackets on the right of (8) is the real user cost; [P.sup.f.sub.t] is the price on the second nearby NYMEX contract for WTI crude oil; [r.sub.t] is the monthly rate on three month U.S. Treasury bills; and [i.sub.t] is the monthly rate of change in the [CPI.sub.t]. The expectation is that stocks fall with higher user costs and decline with higher refinery production, the latter reflecting production smoothing by refiners and transporters of crude oil. The use of the next nearby futures in this equation implicitly captures expectations. A rational expectations model would include the realized price next period but this would substantially increase the complexity of model simulation. Alternative methods of introducing market expectations deserve further study and analysis.

The relation for crude oil stocks at sea, [X.sup.sea.sub.t], follows a similar specification:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

where [Y.sup.sa.sub.t] is production by Saudi Arabia, and [Y.sup.ns.sub.t] is non-Saudi production. Again, our expectation is that stocks at sea should fall with higher user costs. Unlike inventories on land, stocks at sea depend upon world production. Given the time lags in transmitting demand shocks back to crude oil producers and in shipping crude from distant producing areas to the main consuming regions, stocks at sea should move directly with world oil production. Hence, the expectation here is that stocks at sea rise (fall) with higher (lower) world oil production. The two flow demand equations (6)-(7) and the two inventory demand equations (8)-(9) constitute the demand side of the model.

The supply side of the model determines production levels and prices for immediate and future delivery of crude oil. The speculative net benefit of holding title to a commodity in storage is simply equal to the difference between the future and current price. To justify the cost of holding a commodity in storage, this return should cover the cost of insuring and warehousing the commodity. There is also a financial opportunity cost to holding an inventory asset because the owner could have sold the commodity and invested the proceeds in an asset that pays interest. These arguments suggest that prices for delivery in the future should be higher than those currently prevailing in spot or cash markets by the amount of these carrying charges. In the parlance of the British, markets with prices that justify these carrying charges are in contango.

Oftentimes, however, spot or cash prices substantially exceed prices for future delivery. In this case, the market implies inverse carrying charges or is in, using the British term, backwardation. Under these conditions, there are no incentives for holding stocks. Aggregate stocks-outs, however, are not observed in petroleum markets. Kaldor (1939), Working (1934) and Telser (1958) argue that producers and distributors never completely sell-off inventories because they earn a convenience yield from holding them. In contrast, Keynes (1938) argued that spreads between futures and spot prices reflect a risk premium. Litzenberger and Rabinowitz (1995), Brennan and Schwartz (1985) and Gibson and Schwartz (1990) develop this idea further by showing that price spreads contain option values related to price uncertainty.

Accordingly, this study assumes that the nominal returns from storage reflect a marginal convenience yield and a risk premium related to price uncertainty:

1n([P.sub.t]/[P.sup.f.sub.t])-r = [[phi].sub.0] + [[phi].sub.1] 1n ([X.sup.obs.sub.t-1t]/[Q.sup.pm.sub.t]) + [[phi].sub.2] 1n [V.sub.t] + [[epsilon].sup.f.sub.t], (10)

where beginning inventories, [X.sup.obs.sub.t-1], are defined as above. The left side of (10) is the nominal returns from storage while the first two terms on the right represent fixed storage costs and the convenience yield, respectively. The parameter [[phi].sub.1] is expected to be positive because higher beginning inventories this period imply that first nearby prices are lower relative to second nearby prices, which increases the returns to storage. The last term in (10) is a risk premium, which is a function of price volatility, [V.sub.t], measured as a 20-day moving average of the standard deviation in the price for the first nearby contract, see Considine and Larson (2001). In this case, the returns to storage are expected to fall with higher price volatility because greater uncertainty often raises prices today relative to those for future delivery. Equation (10) is essentially a risk adjusted version of the basic arbitrage condition for commodities discussed by Brealey and Myers (2003). Over the sample, the average returns to storage are -11.1 percent at an annual rate, which indicates the market is most often in backwardation. This return also displays enormous volatility ranging from -117 percent to over 64 percent (see Table 1).

Now consider the supply of crude oil from Saudi Arabia. Marginal revenue facing Saudi Arabia is:

[[partial derivative][RV.sup.sa.sub.t] / [partial derivative] [Y.sup.sa.sub.t]] = [P.sub.t] + [Y.sup.sa.sub.t] [[partial derivative] [P.sub.t] / [[partial derivative][Y.sup.sa.sub.t]], (11)

where [Y.sup.sap.sub.t] is crude oil production by Saudi Arabia in period t. (4) Equating marginal revenue with marginal cost and solving for price yields:

[P.sub.t] = [MC.sup.sa.sub.t] - [[partial derivative][P.sub.t] / [partial derivative]1n[Y.sup.sa.sub.t]], (12)

where full marginal cost, [MC.sup.sa.sub.t] = [LC.sub.t] + 0.17[P.sub.t] in which [LC.sub.t] is lifting costs or marginal extraction costs. Marginal cost is approximated using the procedures discussed by Allhaji and Huettner (2001) and consists of incremental extraction cost of roughly $4 in 1980, which is escalated at the rate of producer price inflation in the US, and royalty payments that are assumed to be 17% of price.

Equilibrium Saudi output is a residual demand:

[Y.sup.sa.sub.t] = [Q.sup.pm.sub.t] + [R.sub.t] + ([X.sup.obs.sub.t] - [X.sup.obs.sub.t-1]) / [D.sub.t] - [Y.sup.ns.sub.t], (13)

For this study, output by the competitive fringe, [Y.sup.ns.sub.t], is hypothesized as a simple function of the real market price:

[Y.sup.ns.sub.t] = [[pi].sub.0] + [[pi].sub.0] 1n ([P.sub.t]/[CPI.sup.y.sub.t]) + [[epsilon].sup.ns.sub.t], (14)

where [CPI.sup.y.sub.t] = [CPI.sub.t]/[[w.sup.usa,y.sub.t] + (1-[w.sup.usa,y.sub.t])[DI.sub.t]] in which [w.sup.usa,y.sub.t] is the US share of world crude oil production.

All the elements to derive the derivative in equation (12) now exist. The first step is to note that the supply of storage relation implies that the second nearby futures price is affected by first nearby prices. Hence, the user costs from the two inventory demand equations must be eliminated by substituting the relevant portion of (10) into (8) and (9) to obtain:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (15)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (16)

respectively. The demand for OPEC crude follows from substituting (6), (7), and (14)-(16) into (13) resulting in:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

where

[[epsilon].sub.t] = [[epsilon].sup.q.sub.t] + [[epsilon].sup.r.sub.t] - [[epsilon].sup.ns.sub.t] + [[[epsilon].sup.x.sub.t] + [[epsilon].sup.s.sub.t] - ([[delta].sub.1] + [[gamma].sub.1]) [[epsilon].sup.f.sub.t]] / [D.sub.t]

Solving (17) for Pt and using the superscript "e" to denote equilibrium price yields the following expression:

[P.sup.e.sub.t] = exp [[Y.sup.sa.sub.t] - [A.sub.t]) / ([[alpha].sub.1] + [[beta].sub.1] - [[pi].sub.1])], (18)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Taking the partial derivative of (18) with respect to Saudi output, substituting the result into (12), and solving for observed prices yields the following empirical model for the supply relation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

This behavioral condition provides the equilibrium price for Saudi Arabia that maximizes profits subject to residual demand, which reflects the flow and stock demand for crude oil and supply from other producers. The complete econometric model consists of seven behavioral equations, (6)-(9), (10), (14), and (20), and one identity (13) containing eight endogenous variables, [Q.sup.pm.sub.t], [R.sub.t], [X.sup.pm.sub.t], [X.sup.sea.sub.t], [Y.sup.ns.sub.t], [X.sup.sa.sub.t], [P.sub.t], and [P.sup.f.sub.t].

4. ECONOMETRIC ESTIMATION

An earlier version of the model presented above allowed first order autocorrelation in all behavioral equations, except the two partial adjustment models for inventories. These autoregressive parameters were all very close to one. (5) As a result, a first difference version of the model is estimated in this study. Hence, the demand for crude in primary markets, rest-of-world demand, competitive fringe supply, and the supply of storage are estimated in first differences, which eliminate their respective intercept terms. These relations appear in implicit form as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

The two inventory equations are also estimated in implicit form:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

Following the same procedure as described above provides a new equilibrium price:

[P.sup.e.sub.t] = exp [([Y.sup.sa.sub.t]-[A.sup.d])/ ([[alpha].sub.1]-[[beta].sub.1]-[[pi].sub.1])] (27)

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Taking the derivative of (27) with respect to [Y.sup.sa.sub.t], substituting into the price markup equation (12), and taking first differences results in the following estimated form of the price markup equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (28)

The simultaneous nature of the model requires either full information maximum likelihood estimation or some estimator that employs instrumental variables. Maximum likelihood assumes normally distributed errors. A less restrictive estimator adopted in this study is the generalized method of moments (GMM), which allows correction of the standard errors for heteroscedasticity and autocorrelation. The instrumental variables include a constant term; lagged values of crude oil inventories held on land, [[X.sup.pm.sub.t-1] and at sea, [X.sup.sea.sub.t-1]; lagged, stock adjusted sales in primary markets, [Z.sub.t]; lagged product sales in the rest of the world, [Z.sup.row.sub.t-1]; heating and cooling degree days in the United States; the three lagged adjusted consumer price indices discussed above; and lagged rates on US three month treasury bills. (6) Three-stage least squares estimation of (21)-(26) provide starting values for full GMM estimation of the complete system, (21)-(26) and (28). The GMM estimation routine includes a correction of the standard errors for heteroscedasticity and a first-order moving average in the error terms.

5. ESTIMATION RESULTS

The GMM parameter estimates appear in Table 2 using 157 monthly observations from March 1992 to March 2005. (7) The objective function of the GMM estimator is distributed as a Chi-Squared statistic with degrees of freedom equal to the number of instruments (10) times the number of equations (7) less the number of parameters (15), which is equal to 55. The value of the test statistic is 48.3 with a probability value of 0.725. Hence, the null hypothesis that the model is valid fails to be rejected. The relatively high probability value provides additional support that the dominant firm pricing model is appropriate to characterize the world oil market.

All estimated coefficients have the anticipated signs and only two parameters, [[gamma].sub.1], the effect of user costs on stocks held at sea and [[phi].sub.1], the effect of the inventory to sales ratio on the returns from storage, are insignificantly different from zero. The former is not surprising since the crude transportation network is rather inflexible. The insignificance of the inventory to sales ratios in explaining the returns to storage has also been found by Considine and Larson (2001).

Summary fit statistics appear in Table 3. The correlations between the fitted and the actual endogenous variables range from a low of 0.58 for inventories held in primary markets to 0.98 for the first nearby price. The other correlations range from 0.86 to 0.97 (see Table 3). The Durbin-Watson statistics generally indicate the absence of serious autocorrelation. The mean squared errors from static and dynamic simulations of the model also appear in Table 3. The static simulations use the actual values for the lagged dependent variables while the dynamic simulations use the lagged predictions. The static mean squared errors for consumption, inventories, and non-Saudi production are all less than 5 percent. The mean squared errors for Saudi production and prices, however, are somewhat higher (see Table 3). The dynamic mean squared errors are higher as expected but generally indicate the model is stable in dynamic simulations.

All parameters in the model yield sensible elasticities, which are presented in Table 4. The first set of elasticities discussed involves the market price. If the price of crude oil goes up 10% current crude oil demanded by refineries in the U.S., Japan, and the 15 European countries listed in footnote 3 would go down 1.39%, and the sum of refinery demand and inventory adjustment from other countries would go down 1.85% (see Table 4). For a 10% increase in crude oil prices assuming futures prices are constant, commercial crude oil inventories held in primary markets would decline 6.52% but crude oil inventories held at sea decline only 0.72%. The weighted average of these stock and flow price elasticities of demand imply that for a 10% increase in crude oil prices, the inventory changes and flows of crude drop 4.46% (see Table 4).

The elasticities of demand for stocks and flows with respect to refined product sales and world crude oil production are also correctly signed and have reasonable magnitudes. For example, if refinery product sales increase 10%, crude oil demand increases 9.4% and 5.3% in the primary markets and other regions respectively. If refined product sales increase 10%, commercial crude oil inventories decline 2.35% (see Table 4). Our estimates also indicate that for a 10% increase in world crude oil production, stocks of crude oil held at sea increase 2.16%.

The widely held belief that crude oil production is relatively unresponsive to price in the short-run is confirmed with an elasticity that suggests a 10% increase in crude oil prices increases non-Saudi oil production 1.7%. The elasticities of demand for Saudi Arabia are not a simple weighted average of the market flow and stock demand elasticities because there is no closed form solution for equilibrium Saudi production. To determine Saudi demand elasticities, an implicit differential equation must be solved for Saudi Arabia's residual demand. (8) The estimated own price elasticity of demand suggests that for a 10% increase in price, the demand for Saudi crude declines 27.9%. This elasticitiy of demand for Saudi crude oil of -2.79 is measured at the mean and ranges from -3.26 to -2.37 during the sample (see Table 4). Hence, Saudi Arabia is operating as a constrained monopolist and marginal revenue is positive.

The supply of storage relation also conforms to economic theory. The returns to storage decline with lower stock levels indicating the presence of a convenience yield, which offsets these low returns when stocks are low. The probability value, however, indicates that there is more than a 12 percent chance that this elasticity is zero. In addition, the returns to storage decline with higher price volatility, consistent with Considine and Larson (2001) indicating that periods of greater uncertainty force prices on nearby futures contracts substantially above prices on distant contracts, reducing benefits from holding oil in storage today.

The partial equilibrium elasticities of markups with respect to the main exogenous factors in the model are also presented in Table 4. Price markups over marginal cost show a significant inverse relationship with stocks held at sea and by governments (see Table 4). Markups increase with refinery product sales in both primary markets and the rest of the world (see Table 4). Computation of a complete set of market equilibrium elasticities of supply and demand involves the solution of a set of nonlinear, implicit differential equations. The following model simulations, however, essentially provide a numerical simulation of the elasticities with respect to government stock changes and supply and demand shocks.

6. IMPACTS FROM MARKET SHOCKS AND SPR POLICIES

To illustrate the policy simulation capabilities of the model, consider three sets of simulations that involve comparisons between a base simulation and three scenarios over a three-month period from October to December 2004:

* 30-million-barrel stock sale from the SPR,

* 1-million-barrel per day supply disruption, and

* 1-million-barrel per day demand shock.

The results appear below in Tables 5 and 6. The first scenario, which is equivalent to the Clinton Administration's SPR sale prior to the 2000 presidential election, results in a 3.5 percent decrease in price, or a $1.30-per-barrel decline (see Table 6 for the absolute changes), with most of the stock sale offset by lower world production. These are very modest changes and suggest that SPR stocks sales, even a rather sizeable 30 million barrel sale, equivalent to 1 million barrels per day for 30 days, have minimal impacts on the market because Saudi Arabia as the dominant firm cuts back production and with lower world prices other producers also reduce output.

A supply disruption is simulated by including an exogenous intercept shifter in the Saudi supply relation that is calibrated to result in a one-million-barrel-per-day reduction in Saudi crude oil production. This scenario also results in a modest impact on prices, with an increase of $2.0 per barrel in equilibrium prices, or 5.2 percent. The supply response by non-Saudi producers offsets about half of the production cut by Saudi Arabia. It is important to note that this simulation would not reflect a capacity constrained market, which is simulated below.

The simulation results for the third scenario suggests that a demand shock of one million barrels per day increases prices more than 3.9 percent, or about $1.50 per barrel. This scenario was accomplished by simulating the model with higher refinery production in the primary market and world rest-of-world demand equation. The one million per day demand shock results in a proportionately smaller price increase because the decline in commercial inventories acts as a buffer on the market.

The impacts of the Bush Administration's increase in the SPR are estimated by simulating the model from November 2001 to March 2005 with and without the SPR stock build. The changes in prices resulting from no stock-build are plotted in Figure 2. The Bush stock build increased crude oil prices but the average change was a miniscule $0.2 per barrel, equivalent to 1/2 cent per gallon. These results clearly illustrate that a gradual increase in the SPR has virtually no impact on market prices. The incremental stock additions are simply too small to affect world prices.

[FIGURE 2 OMITTED]

The last simulation considers the market impacts of a major supply shock and the effects of an SPR release during such a market disruption. The supply shock scenario involves a five million barrel per day reduction in non-Saudi production during the first three months along with a 50 percent increase in price volatility. During the next three months, the supply reduction diminishes to two million barrels per day and the increase in price volatility also subsides (see Table 7). This scenario also assumes that Saudi marginal cost increases, which acts essentially as a short-run capacity constraint. This is modeled as an exogenous increase in marginal cost. Indeed, Saudi output expansion may face such constraints because incremental supplies are located farther away from existing infrastructure and involve substantial security costs. As a result, Saudi output expands to offset the world supply reduction but not more than 1.5 million barrels per day (see Table 7). The impacts are as expected with prices rising from $12 to $14 per barrel. Also notice the substantial reduction in commercial inventories and the reductions in crude oil consumption (see Table 7).

In response, suppose the US and other International Energy Agency countries releases 90 million barrels per month from the SPR during the first three months, 60 million per month during the next two months, and 30 million barrels during the sixth month of the supply shock. Also, assume that these actions reduce price volatility 25 percent from the supply shock scenario. The price paths under these scenarios are illustrated in Figure 3. These SPR sales mitigate more than two-thirds of the price increase. Notice, however, that Saudi Arabia reduces output under the SPR scenario. This behavior is consistent with a dominant producer pricing market structure, although the Saudis would possibly consider the political ramifications of these actions, which are fascinating but beyond the bounds of this study. (9)

[FIGURE 3 OMITTED]

7. SUMMARY AND POLICY IMPLICATIONS

This study develops a short-run econometric model of the world market for crude oil. The model involves the simultaneous determination of flows and stocks of crude oil, using the spot price to equilibrate crude oil availability with demand for immediate processing into refined products and using futures prices to balance current and future uses of crude oil. The econometric analysis provides quantitative estimates of several widely held notions by crude oil market and policy analysts:

* Saudi Arabia is a possible dominant producer,

* The demand for crude oil is very price inelastic,

* The supply elasticity is also price inelastic,

* Inventories respond to user costs,

While user costs are significant, the elasticity of stocks with respect to user costs is relatively small. Inventories of crude oil held on land are relatively more sensitive to shifts in the production of refined petroleum products. Stocks of crude in tankers at sea move directly with world oil production, acting essentially as a floating inventory for crude oil exporters.

The model simulations indicate that gradual accumulation of government strategic stockpiles is unlikely to cause significant upward pressures on prices. Indeed the simulations conducted in this study reveal that the Bush Administration's policy to fill the SPR raised crude oil prices by only 20 cents per barrel. Similarly, the model simulation of a 30 million barrel sale from the SPR or some combination of SPR and government held stocks in other IEA countries would reduce prices by only 3.5 percent. The last simulation reveals that while a government strategic reserve release from the SPR and other IEA countries during a supply shock would reduce world prices significantly, nearly 30 percent of the reserve would be depleted after a six month disruption. In all of these simulations, the market impacts of SPR are partially offset by output adjustments by the dominant world producer, Saudi Arabia.

Should the SPR be considered our ace in the hole? This study finds that sales of strategic reserves may be futile because the price impacts of stock sales can be partially or completely offset from output reductions by world oil producers. On the other hand, this study demonstrates that stock sales can substantially reduce market prices in the event of a major supply disruption, although the strategic reserves may be significantly depleted after a relatively short period of time. As Considine and Dowd (2005) demonstrate the experience with exercising these options is mixed. For example, it took the Bush Administration six months to sell oil from the SPR during the Persian Gulf War of 1990-91 and by then it was too little and too late. Taylor and Van Doren (2005) argue that the costs of the building and holding the SPR exceed the benefits from releasing oil during disruptions. Overall, the evidence suggests that the SPR should not be considered our ace in the hole. While the SPR may have a strategic value, it remains to be convincingly demonstrated. The implication is that policy makers may wish to consider shifting the focus from mitigating the effects of oil supply disruptions to making the economy more resilient with measures to stimulate domestic energy supply and to encourage conservation and greater energy efficiency.

REFERENCES

Adelman, Morris A. (1982). "OPEC as a Cartel," in J.M. Griffin and D.J. Teece, eds., OPEC Behavior and World Oil Prices. London: Allen & Unwin.

Alhajji, A.F. and D. Huettner (2000). "OPEC and World Crude Oil Markets from 1973 to 1994: Cartel, Oligopoly, or Competitive," The Energy Journal 21(3): 31-59.

Blinder, A., and L. J. Maccini (1991). "Taking Stock: A Critical Assessment of Recent Research on Inventories," Journal of Economic Perspective 5(1): 73-96.

Brealey, R.A. and S.C. Myers (2003). Principles of Corporate Finance. New York: McGraw-Hill Irwin, Inc.: 762-763.

Brennan, M.J., and E. S. Schwartz (1985). "Evaluating Natural Resource Investments," Journal of Business LVIII, 135-157.

Considine, T.J., and D.F. Larson (2001). "Risk Premiums on Inventory Assets: The Case of Crude Oil and Natural Gas," Journal of Futures Markets 21(2):109-126.

Considine, T. J. (2001). "Markup pricing in petroleum refining: A multiproduct framework," International Journal of Industrial Organization 19(10): 1499-1526.

Considine, T. J. and K. M. Dowd (2005). "Oil markets and the Strategic Petroleum Reserve," Regulation 28(2):18-25.

Eichenbaum, M.S. (1989). "Some Empirical Evidence on the Production Level and Production Cost Smoothing Models of Inventory Investment," American Economic Review 89(4): 853-864.

Gibson, R., and E. S. Schwartz (1990). "Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," The Journal of Finance 45(3): 959-975.

Griffin, J. M. (1985). "OPEC Behavior," The American Economic Review, 75(5): 954-963.

Kaldor, Nicholas (1939). "Speculation and Economic Stability," Review of Economic Studies 7(1): 1-27.

Keynes, John Maynard (1938). A Treatise on Money: Volume II: The Applied Theory of Money. London: Macmillan.

Litzenberger, Robert H., and Nir Rabinowitz (1995). "Backwardation in Oil Futures Markets: Theory and Empirical Evidence," Journal of Finance 50(5): 1517-1545.

Loretan, M. (2005). "Indexes of the Foreign Exchange Value of the Dollar," Federal Reserve Bulletin, 92(4): 1-8.

Morrison, Catherine J. (1992). "Markups in U. S. and Japanese Manufacturing: A Short-Run Econometric Analysis," Journal of Business and Economic Statistics 10(1): 51-63.

Ramey, Valerie A. (1989). "Inventories as Factors of Production and Economic Fluctuations," The American Economic Review 79(2): 338-354.

Taylor, Peter, and Peter Van Doren (2005). "The Case Against the Strategic Petroleum Reserve," Policy Analysis, The Cato Institute, 555(1): 1-24.

Telser, Lester G.(1958). "Futures Trading and the Storage of Cotton and Wheat," Journal of Political Economy 66(2): 233-255.

Working, Holbrook (1934). "Theory of Inverse Carrying Charge in Futures Markets," Journal of Farm Economics 30(1): 1-28.

(1.) The natural next step is to model refined petroleum markets but this would add considerable complexity to the model given the multiproduct nature of petroleum refining, see Considine (2001).

(2.) An earlier version of this paper considered a supply relation that includes a user cost for reserves based upon the study by Pindyck (1985), which develops a theory that shows competitive commodity prices reflect marginal extraction cost plus the user cost of reserves. This particular user cost effect, however, was statistically insignificant.

(3.) The fifteen countries are Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxemburg, Netherlands, Portugal, Spain, Sweden, United Kingdom.

(4.) Note natural gas liquids and petroleum condensates are not included because OPEC does not report these hydrocarbon flows by country.

(5.) This is consistent with the unit roots found in crude oil supply, demand, and prices as well as petroleum product demands.

(6.) Alternative instruments were tried with minor changes in the estimated coefficients.

(7.) Prior to 1992, crude oil consumption data are incomplete and, therefore, inconsistent with subsequent data.

(8.) The derivation is available from the author upon request.

(9.) Modeling the political calculus for Saudi output decision making is an interesting topic for additional research.

Timothy J. Considine, The Pennsylvania State University, 125 Hosler Building, University Park, PA 16802. Email address: cpw@psu.edu.

Table 1. Summary Statistics on World Crude Oil Markets,
January 1991 to March 2005

                                     Standard
                             Mean    Deviation   Minimum   Maximum

                                     Million barrels per day

Sales, primary markets        30.8         1.8      26.1      33.7
Net requirements, rest of
  the world                   34.6         2.5      29.9      41.7
World Production              65.4         3.8      59.1      73.9
  Saudi Arabia                 8.1         0.5       6.9       9.4
  Non-Saudi                   57.3         3.7      51.5      64.9

                                     Million barrels

Inventories                  775.7        30.0     707.0     834.0
  Primary Markets            833.9        52.0     732.0     948.0
  At Sea                    1324.2        74.1    1209.0    1522.0
  Government

Prices                               Dollars per barrel

  First nearby                23.8         8.1      11.3      54.6
  Second nearby               23.6         8.0      11.6      55.3

Other Measures                       Percent per annum

  Volatility                  33.5        14.5      11.7     122.3
  Returns to storage         -11.1        24.0    -117.1      64.2
  Real user costs              8.5        23.6     -65.6     112.5

Table 2. Generalized Method of Moment Estimates

Parameter         Estimate   t-statistic   P-value

[[alpha].sub.1]      -4.31      -2.30      [.021]
[[alpha].sub.2]      29.13      13.78      [.000]
[[beta].sub.1]       -6.43      -2.14      [.032]
[[beta].sub.2]       18.53       3.07      [.002]
[[delta].sub.0]    1040.52       7.29      [.000]
[[delta].sub.1]    -506.96      -4.52      [.000]
[[delta].sub.2]    -183.09      -6.50      [.000]
[[delta].sub.3]       0.52       8.16      [.000]
[[gamma].sub.0]    -573.39      -5.04      [.000]
[[gamma].sub.1]     -60.40      -0.82      [.414]
[[gamma].sub.2]     180.81       5.32      [.000]
[[gamma].sub.3]       0.78      20.78      [.000]
[[pi].sub.1]          9.71       3.77      [.000]
[[phi].sub.1]         0.64       1.52      [.128]
[[phi].sub.2]        -0.29      -3.41      [.001]

Table 3. Summary Fit Statistics

                      Correlation      Durbin-   Mean   Square Errors
                   Actual & Predicted  Watson   Static     Dynamic

Consumption
Primary markets           0.95          2.40    0.016       0.085
Rest of the world         0.86          3.03    0.038       0.054
Inventories
  On land                 0.58          1.63    0.049       0.180
  At sea                  0.90          2.57    0.027       0.077
Production
  Non-Saudi               0.97          2.03    0.016       0.080
  Saudi                    na            na     0.093       0.267
Prices
  First nearby            0.98          2.33    0.088       0.267
  Second nearby           0.94          2.52    0.131       0.263

Table 4. Supply, Demand, and Markup Elasticities
(Evaluated at Sample Mean)

                                           Estimate   t-statistic

Primary markets consumption
  Price                                     -0.139      -2.302
  Petroleum product sales                    0.938      13.777
Rest of world consumption
  Price                                     -0.185      -2.143
  Petroleum product sales                    0.534       3.068
Primary stocks
  Price                                     -0.652      -4.519
  Petroleum product sales                   -0.235      -6.503
Stocks at sea
  Price                                     -0.072      -0.817
  World crude production                     0.216       5.320
Supply of storage
  Primary stocks                             0.644       1.522
  Price volatility                          -0.289      -3.412
Non-Saudi own price elasticity of supply     0.168       3.774
Own price elasticities of demand
  Market                                    -0.446      -5.840
  Saudi                                     -2.790      -7.352
Markup elasticities
Primary stocks                              -0.002      -0.031
  Stocks at sea                             -0.049      -2.692
  Government stocks                         -0.357      -3.277
  Primary product sales                      0.238       3.198
  Rest of world product sales                0.151       2.397

                                           P-value

Primary markets consumption
  Price                                     [.021]
  Petroleum product sales                   [.000]
Rest of world consumption
  Price                                     [.032]
  Petroleum product sales                   [.002]
Primary stocks
  Price                                     [.000]
  Petroleum product sales                   [.000]
Stocks at sea
  Price                                     [.414]
  World crude production                    [.000]
Supply of storage
  Primary stocks                            [.128]
  Price volatility                          [.001]
Non-Saudi own price elasticity of supply    [.000]
Own price elasticities of demand
  Market                                    [.000]
  Saudi                                     [.000]
Markup elasticities
Primary stocks                              [.975]
  Stocks at sea                             [.007]
  Government stocks                         [.001]
  Primary product sales                     [.001]
  Rest of world product sales               [.017]

Table 5. Impacts of SPR Sale and Supply and Demand Shocks in
Percent Changes, 2004

                                 Percent Changes from
                                 Base Simulation

                                    30 million
                                     SPR Sale

                                 Oct.   Nov.   Dec.

Demand primary markets            0.5    0.0    0.0
Net requirements rest of world    0.6    0.1    0.0
Stocks in primary markets        -0.2   -0.5    0.8
Stocks at sea                    -0.2   -0.2    0.2
Non-Saudi output                 -0.5    0.0    0.0
Saudi output                     -4.1   -0.4    0.2
First nearby price               -3.5   -0.3    0.2
Second nearby price              -3.9     -1    0.9
Markup                           -4.5   -0.4    0.2

                                 Supply disruption
                                 1 million barrels
                                      per day

                                 Oct.   Nov.   Dec.

Demand primary markets           -0.7    0.0    0.0
Net requirements rest of world   -0.9    0.0    0.0
Stocks in primary markets         0.3    0.2    0.1
Stocks at sea                    -0.1   -0.1   -0.1
Non-Saudi output                  0.8    0.0    0.0
Saudi output                      -12   -0.1   -0.1
First nearby price                5.2   -0.1    0.0
Second nearby price               5.5   -0.1    0.0
Markup                            6.7   -0.1   -0.1

                                    Demand shock
                                  1 million barrel
                                       per day

                                 Oct.   Nov.   Dec.

Demand primary markets            1.7   -0.1    0.0
Net requirements rest of world    1.2   -0.1    0.0
Stocks in primary markets        -1.2   -0.8   -0.5
Stocks at sea                     0.1    0.1    0.1
Non-Saudi output                  0.6    0.1    0.0
Saudi output                      4.2    0.6    0.3
First nearby price                3.9    0.4    0.2
Second nearby price               2.7    0.3    0.2
Markup                            5.0    0.6    0.3

Table 6. Impacts of SPR Sale and Supply and Demand Shocks
in Absolute Changes, 2004

                              Absolute Changes from
                                 Base Simulation

                                   30 million
                                    SPR Sale

Barrels per day                Oct.    Nov.    Dec.

  Demand primary markets        0.2     0.0     0.0
  Demand rest of world          0.2     0.0     0.0
  Non-Saudi output             -0.3     0.0     0.0
  Saudi output                 -0.4     0.0     0.0

Barrels
  Stocks in primary markets    -1.6    -4.3    -6.1
  Stocks at sea                -1.9    -2.1    -2.2

Dollars per barrel
  First nearby price           -1.3    -0.1    -0.1
  Second nearby price          -1.6    -0.4    -0.3
  Markup                       -1.1    -0.1    -0.1

                                Supply disruption
                                1 million barrels
                                    per day

Barrels per day                Oct.    Nov.    Dec.

  Demand primary markets       -0.2     0.0     0.0
  Demand rest of world         -0.3     0.0     0.0
  Non-Saudi output              0.5     0.0     0.0
  Saudi output                 -1.0     0.0     0.0

Barrels
  Stocks in primary markets     2.3     1.3     0.7
  Stocks at sea                -1.0    -0.8    -0.7

Dollars per barrel
  First nearby price            2.0     0.0     0.0
  Second nearby price           2.4     0.0     0.0
  Markup                        1.7     0.0     0.0

                                  Demand shock
                                1 million barrel
                                    per day

Barrels per day                Oct.    Nov.    Dec.

  Demand primary markets        0.6     0.0     0.0
  Demand rest of world          0.5     0.0     0.0
  Non-Saudi output              0.4     0.0     0.0
  Saudi output                  0.4     0.0     0.0

Barrels
  Stocks in primary markets   -10.1    -6.1    -3.5
  Stocks at sea                 1.1     1.0     0.9

Dollars per barrel
  First nearby price            1.5     0.2     0.1
  Second nearby price           1.2     0.1     0.1
  Markup                        1.2     0.1     0.1

Table 7. Impacts of Supply Shock & SPR Release

                                      Months

                          1        2        3        4

Variables                        Supply Shock Absolute
                                 Changes from Base

Barrels per day
  Demand PM                0.0     -0.5     -0.9     -1.0
  Demand ROW               0.0     -0.8     -1.3     -1.5
  Non-Saudi output         0.0     -5.0     -5.0     -5.0
  Saudi output             0.0      1.5      1.3      1.4

Barrels
  Stocks in PM             0.0    -54.3    -86.4   -106.7
  Stocks at sea            0.0    -15.3    -28.2    -38.4

Dollars per barrel
  First nearby price       0.0      6.0     10.1     12.0
  Second nearby price      0.0      0.5      3.8      4.6

                                  Percent Change

Volatility                 0.0     50.0     50.0     50.0

                        SPR Release Absolute Changes from
                                  Supply Shock

Barrels per day
  Demand PM                0.0      0.3      0.6      0.8
  Demand ROW               0.0      0.4      0.9      1.1
  Non-Saudi output         0.0      0.0      0.0      0.0
  Saudi output             0.0     -1.2     -1.5     -1.8

Barrels
  Stocks in PM             0.0     30.1     36.6     28.3
  Stocks at sea            0.0      0.5     -1.1     -4.4
  Government               0.0    -88.0   -181.0   -283.0

Dollars per barrel
  First nearby price       0.0     -3.1     -6.9     -9.1
  Second nearby price      0.0      0.0     -4.0     -6.1

                                 Percent Change

Volatility                 0.0    -25.0    -25.0    -25.0

                               Months

                          5        6        7

Variables               Supply Shock Absolute
                          Changes from Base

Barrels per day
  Demand PM               -1.1     -1.1     -0.9
  Demand ROW              -1.6     -1.6     -1.4
  Non-Saudi output        -4.0     -3.0     -2.0
  Saudi output             1.0      0.6      0.2
Barrels
  Stocks in PM          -110.0   -102.3    -86.7
  Stocks at sea          -44.1    -45.8    -44.0
Dollars per barrel
  First nearby price      12.9     14.1     12.6
  Second nearby price      5.9      8.0      8.6

Volatility                40.0     30.0     20.0

                        SPR Release Absolute Changes from
                                 Supply Shock

Barrels per day
  Demand PM                0.6      0.7      0.5
  Demand ROW               0.9      1.1      0.7
  Non-Saudi output         0.0      0.0      0.0
  Saudi output            -1.1     -1.4     -0.6
Barrels
  Stocks in PM            10.8    -10.1    -29.3
  Stocks at sea           -6.7    -10.6    -12.6
  Government              -345   -408.0   -443.0
Dollars per barrel
  First nearby price      -7.7     -9.9     -7.0
  Second nearby price     -6.1     -9.9     -9.3

Volatility               -25.0    -25.0    -25.0

PM = Primary markets, ROW = rest-of-world