Reducing U.S. vulnerability to oil supply shocks.

I. Introduction

The 1990 crisis in the Middle East has raised concern about the United States's vulnerability to oil supply disruptions. In addition, a number of trends point to increased U.S. dependence on imported oil. Oil imports have increased and production has declined in the United States for the last eight years. Imports now comprise 42 percent of total oil consumption and U.S. dependence on oil imports is projected to increase over the next 20 years. The Energy Modeling Forum forecasts imports to be more than twice domestic production by the year 2010 [14].

Realizing that we will be importing oil from unstable regions of the world, policies have been considered which would lower our dependence on foreign oil. Congress approved legislation in September 1990 to increase the Strategic Petroleum Reserve (SPR) to one billion barrels, which would be released when an oil supply disruption occurred. The gasoline tax was increased 5 cents per gallon in December 1991. More recently, the Clinton administration considered a gasoline tax and an import fee among other energy taxes, and a 4.3 cent per gallon gasoline tax passed Congress in August 1993.

There are many studies examining the effects of various policies to protect U.S. energy security.(1) Not many consider the SPR, which can be a powerful tool in combating energy supply shocks. After the oil price shock of the early 1970s, several studies analyzed the effects of stockpiles [1; 16; 17; 19; 23; 25]. Tiesberg [22] developed a model for determining optimal acquisition and sale strategies of SPR oil. He showed that the expected cost of an oil disruption declined with the use of the SPR. Tiesberg found that an optimal tariff policy together with an optimal stockpile policy would be more effective than stockpiling alone.

The SPR can dramatically increase the domestic short run supply elasticity, which has been found to be a key clement in the welfare cost of protectionist policies. Yucel and Dahl [27] find that U.S. vulnerability to oil supply disruptions is lowered with a tariff and the higher the supply elasticity, the lower the vulnerability. To gauge the effects of the SPR on protectionist policies, this paper analyzes five specific policies--a drawdown of oil from the SPR, a 25 cent gasoline tax, an equal revenue per-unit import tariff of $5.92 per barrel, the gasoline tax with drawdown from the SPR and the tariff with drawdown from the SPR. Using a measure of vulnerability to oil supply shocks, I find, as did Tiesberg, that the SPR together with a protectionist policy works best against a supply disruption. However, unlike Tiesberg, when intertemporal depletion effects are factored in, a gasoline tax together with a drawdown from the SPR is the best protection against a supply disruption.

II. Model

Simulation Model

The model is a dynamic partial equilibrium model of the international oil market. The supply side of the model captures the interactions between U.S. policies and world oil prices, where U.S. producers are profit maximizing price takers and OPEC is a dominant firm. U.S. demand constitutes 15 percent of total OPEC demand and is satisfied by domestic production, non-OPEC imports and OPEC imports. Both U.S. producers and OPEC own oil reserves and maximize the present value of their total profits over a 30-year time horizon, subject to their reserve constraints. The problem is simulated for a base case as well as a per unit oil tariff [Tau] and a gasoline tax of [Gamma]. The demand for oil is normalized around 1992 product demand.

After the model is solved numerically, the vulnerability measure is calculated for the base case, the tariff and the gasoline tax with and without a drawdown from the SPR. The SPR enters the model through increased domestic supply in the vulnerability measure in the case of a disruption.

The general maximization problem for U.S. producers is to choose the production path of Qu that maximizes:

[integral of] [P - [Beta][Gamma] - Cu(Ru)][Que.sup.-rt] between limits T and 0 (1a)

subject to the constraint 

[Mathematical Expression Omitted]

while OPEC chooses the production path for Qo that maximizes

[integral of] [f(Qu, Qo) - [Tau] - [Beta][Gamma] - Co(Ro)][Qoe.sup.-rt] between limits T and 0 (2a)

subject to

[Mathematical Expression Omitted].

In the above expressions, P is the price of oil, [Beta] is the percent of the barrel going to gasoline, f is the inverted demand function for domestic and OPEC oil by U.S. consumers, Qo is OPEC production going to U.S. markets, Qu is U.S. domestic production, Ru and Ro are reserve levels, r is the real interest rate, and Cu and Co are costs of production.

The Hamiltonian for U.S. producers is

H = [P - [Beta][Gamma] - Cu][Que.sup.-rt] + [[Mu].sup.u](-Qu).(3)

The first order conditions are

[H.sub.Qu] = [(P - [Beta][Gamma] - Cu][e.sup.-rt] - [[Mu].sup.u] = 0(4)

[Mathematical Expression Omitted].

Similarly, for OPEC we have

H = [f(Qu, Qo) - [Tau] - [Beta][Gamma] - Co][Qoe.sup.-rt] + [[Mu].sub.o](-Qo)(6)

[H.sub.Qo] = [([f.sup.Qo]Qo + f) - [Tau] - [Beta][Gamma] - Co][e.sup.-rt] - [[Mu].sub.o] = 0(7)

[Mathematical Expression Omitted].

The system is solved numerically to obtain optimal paths for U.S. and OPEC oil output. The domestic and world price of oil, producer profits, and tax revenues are calculated given these production levels.

Vulnerability Measure

After numerically solving the maximization problem(2) the cost of a supply disruption is calculated for the base case and with the two policies. The vulnerability measure calculates the welfare loss due to a marginal disruption in oil imports. It is assumed that the disruption could happen at any time during the 30 year time horizon with equal probability and is calculated at each point in time as if it had happened at that time. The measure of vulnerability to supply disruptions is the change in welfare, calculated as the sum of losses or gains in consumers' and producers' surplus. At the margin this change in welfare is imports multiplied by the infinitesimal change in price, i.e.,

dW = -MdP = QudP - QdP (9)

where Qu is domestic production, Q domestic consumption and M is imports.

dM = [Q.sub.p]dP - Q[u.sub.p]dP (10)

Substituting into dW and rearranging, we obtain the vulnerability measure:

VM = dW/dM = M/(Q[u.sub.p] - Qp).(11)

VM can also be expressed in terms of elasticities,

VM = MP/([[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q).(12)

One can similarly calculate the following modifications of VM when the different policies are in effect.

Per-Unit Tariff. With a tariff, the supply shock also affects tariff revenues. The change in tariff revenues affects welfare and hence enters into the vulnerability measure. Vulnerability to a supply shock, with a per-unit tariff already in effect, is

VM = M[P.sup.D]/([[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q) + [Tau]. (13)

[P.sup.D] is demand price, [[Epsilon].sub.S] is short-run supply elasticity and [[Epsilon].sub.D] is the short-run demand elasticity.

To see the effect of [[Epsilon].sub.S] on the vulnerability measure, we differentiate (13) with respect to [[Epsilon].sub.S] and obtain

[Delta]VM/[Delta][[Epsilon].sub.S] = -MPQu/[([[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q).sup.2] [is less than] 0. (14)

Hence, vulnerability is decreased as domestic producers are better able to increase production in response to an oil supply shock. In a similar fashion, it can be shown that vulnerability increases as the elasticity of demand increases.

Gasoline Tax. With a gasoline tax, a supply disruption changes gasoline consumption and gasoline tax revenues. The vulnerability measure is calculated to be

VM = (M[P.sup.D][P.sup.S] - [Gamma][[Epsilon].sub.D][P.sub.D]Q)/([[Epsilon].sub.S]Qu[P.sup.D] - [[Epsilon].sub.D]Q[P.sup.S]). (15)

To check the sensitivity of VM to changes in domestic supply elasticity, we have

[Delta]VM/[Delta][[Epsilon].sub.S] = [-[P.sub.D]Qu(M[P.sub.D][P.sub.S] - [Gamma][[Epsilon].sub.D][P.sup.D]Q)/[([[Epsilon].sub.S]Qu[P.sub.D] - [[Epsilon].sub.D]Q[P.sup.S])].sup.2] [is less than] 0. (16)

As with the tariff, an increase in domestic elasticity of supply lowers the vulnerability to supply shocks. To see which measure is more responsive to changes in the elasticity of supply, I compare the magnitudes of (15) and (16).

With a little manipulation, we have

[Delta]VM/[Delta][[Epsilon].sub.S] = MP/[([[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q).sup.2] (17)

compared to

[Delta]VM/[Delta][[Epsilon].sub.S] = M[P.sup.D][P.sup.S]/[[[[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q(1 - [Tau])/[P.sub.D]].sup.2] + [Gamma][absolute value of][[Epsilon].sub.D][P.sup.D]Q)/[[[[Epsilon].sub.S]Qu - [[Epsilon].sub.D]Q(1 - [Tau])/[P.sub.D]].sup.2]. (18)

The numerator of expression (17) is less than the numerator of each component of expression (18). The denominator of expression (17) is greater than the denominator of expression (18). Hence, ceteris paribus, expression (17) is less than expression (18). This implies that vulnerability with the gasoline tax is more sensitive to changes in the elasticity of supply than vulnerability with the tariff. Simulation results bear out this observation.

Vulnerability with the SPR

The U.S. government has stockpiles of oil in the SPR. In the most recent oil disruption during the Middle East crisis, the government drew oil from the SPR. Currently, the maximum rate of draw-down from the SPR is 3.5 million barrels for the first 90 days. The rate gradually decreases to 1.2 million barrels per day after 180 days. If the SPR is utilized in the event of a supply disruption, the short run elasticity of domestic supply will be greatly increased.

Since it is impossible to know how an oil supply disruption in one part of the world will be distributed to consumer countries, I assume that the supply disruption causes a given increase in the world price of oil. Given this increase in oil prices, I consider two scenarios: an additional domestic supply of 3.5 million barrels per day from the SPR and a second scenario where the drawdown from the SPR is only 1 million barrels per day. I then calculate the vulnerability measure for the base case and with the two policies incorporating the additional supplies from the SPR.

III. Model Inputs

The demand for oil is derived from the demand for oil products and is a constant elasticity function of price and income. The price elasticity of oil is a weighted average of product elasticities and is calculated to be -0.9. The income elasticity is chosen to be 0.8.(3) Imports from Non-OPEC producers are assumed to remain constant at the 1992 level of 1385.5 million barrels per year. Variables are normalized around 1992 values, giving the inverted demand function:

P = 119.61[(Qu + Qo + 1385.5).sup.-1.1][Y.sup..89].

On the supply side of the market, estimated proven reserves for the U.S. are taken as 100.6 million barrels. U.S. reserves includes an allowance for future oil to be found and is derived from U.S. Bureau of the Mines estimates. The reserves for OPEC are taken to be 769.2 million barrels [21]. The average cost functions for OPEC and the U.S. are from Dahl [8; 9]. They are a function of reserves and have a time trend built in. The cost of extraction increases as reserves are used up.

Cu = 33.13 - 0.0002832Ru + 0.21t

Co = 23.232 - 0.000026Ro + 0.016t.

The real interest rate is taken to be 8 percent for both U.S. and OPEC and income is assumed to grow at 2.5 percent.

Short-run supply and demand responses to the disruption are important factors affecting vulnerability. After conducting a sensitivity analysis using various fractions of the long run price elasticity of demand, the short-run demand elasticity was taken to be one-tenth of the long-run elasticity of -0.9. This is in accord with short-run elasticity estimates in the literature [7; 13; 18].

The short-run supply elasticity for oil production is generally estimated to be very low, ranging from 0 to 0.01 [6; 13]. However, with a drawdown from the SPR, short-run supply elasticities could be quite high. To check the sensitivity of the vulnerability measure to changing supply elasticities, the measure is first calculated with various short-run elasticities ranging from 0.01 to 3.0. These elasticities are obtained by taking various fractions of the supply elasticities inherent in the model simulations.

To calculate how the SPR alters vulnerability in the event of a supply disruption, I consider several scenarios. I assume that the supply disruption gives rise to an increase in world prices of 25, 50, 75, 100, and 200 percent. Given the increases in oil prices, 3.5 million barrels of oil per day are drawn from the SPR for 90 days. The vulnerability measure is calculated with this additional supply for the base case, the import tariff and the gasoline tax. The vulnerability measure is also calculated with drawdowns of two and one million barrels per day.

Table 1. Vulnerability Measure with Different Supply Elasticities (Discounted
Value of Total Vulnerability over the 30 Years)

[[Epsilon].sub.S]     0.01     0.05     0.1     0.5     1.0     2.0     3.0

Base                  3633     3132     2673    1231    735     407     282
Tariff                3595     3054     2577    1194    755     473     367
Gas Tax               3989     3370     2822    1227    719     393     271

IV. Discussion of Results

Optimal time paths are simulated for U.S. production, OPEC production and oil prices for the base case, the tariff and the gasoline tax. The vulnerability measure is first calculated using these time paths for all three cases to see whether the policies make us less or more vulnerable to oil supply shocks. A supply disruption is then assumed to occur which gives rise to an increase in oil prices and leads to a drawdown of oil from the SPR. The vulnerability measure is again calculated for the base case and two policies, incorporating the additional supply from the SPR.

In base case simulations, the price of oil is initially $18.64 in 1992 and rises to $29.60 (in 1992 dollars) by the end of the 30 year time horizon. U.S. output satisfies 42 percent of domestic consumption initially, but falls to 36 percent of consumption at the end of the time horizon. Domestic production does not fall off dramatically because the initial reserves for the United States account for additions to the reserve base after 1992.

A $5.92 per barrel oil-import tariff raises the domestic price of oil to $20.10 per barrel for both consumers and producers.(4) The price increase decreases domestic consumption and increases domestic production. Over the 30-year time horizon, consumption falls 5.8 percent and domestic production increases 9.9 percent with the imposition of the tariff. Consumers are worse off, but producer profits are increased 22 percent.

The decrease in consumption and the increase in production lead to lower imports with the tariff; imports are reduced 15.4 percent in 30 years. Although the share of imports increases in the later years because of higher domestic production and a quicker depletion of U.S. crude oil reserves, the import share is always less than the base case. The fall in imports depresses the world price of oil because the United States consumes about one-fourth of world oil production and thus has monopsony power in the world oil market.

The 25 cents per barrel gasoline tax lowers producer prices and increases consumer prices. One-third of the tax is borne by producers and two-thirds by consumers, leading to an initial consumer price of $21.03 and a producer price of $17.68. The tax causes a 7.5 percent decrease in total consumption, a 6.6 percent decrease in production and an 8 percent reduction in imports over the thirty years.

Which policy makes us least vulnerable to oil supply disruptions? Table I gives a summary of the vulnerability measure for different policies and short-run supply elasticities. The measure reported in Table I is the 30-year present value of the vulnerability measure for the three cases. The rankings of the policies change with changing short-run supply elasticities.

The tariff makes us less vulnerable to supply disruptions when supply is very inelastic, but becomes less effective as supply elasticity increases. After elasticity reaches unity, the tariff makes us more vulnerable than the base case.

Increased production and decreased consumption with a tariff combat a supply disruption effectively when supply elasticities are low. Consumers bear most of the price increase in a disruption if short run supply is inelastic. However, the loss in consumer's surplus is dampened due to higher prices and lower consumption with the tariff. Producers are better off because they receive a higher price for their relatively unchanged level of output. The overall welfare cost of the oil supply shock is lower with the tariff than the base case.

As the short run supply elasticity rises, high domestic output with the tariff becomes less of a factor in reducing vulnerability. With elastic supply, prices do not rise as much and the gain in producer surplus during the disruption is not as high. The intertemporal distortions of the tariff also become more of a factor. Reserves are depleted more quickly with the tariff, leading to higher future production costs. When supply is elastic, these additional costs become unnecessary. Elastic short-run supply becomes sufficient to combat vulnerability in the event of a disruption.

Contrary to the tariff, the gasoline tax makes us more vulnerable when short-run supply elasticity is low and less vulnerable when elasticity is greater than 0.5. If short run supply is assumed to be in the range of 0 to 0.1 (which is the range of realistic short-run supply elasticities), a disruption in imports becomes costly with the gasoline tax. Low domestic production coupled with unresponsive supply makes the United States more vulnerable to supply shocks.

If short run supply is more responsive to price changes however, the disruption in imports does not increase consumer prices very much. The lower import shares and lower consumption with the gasoline tax become the dominant factors, and vulnerability decreases with the gasoline tax.

Lower domestic oil production with the gasoline tax is another factor helping to lower vulnerability if short run supply is elastic. Because the gasoline tax depresses domestic output, it depletes the resource base less than either the tariff or the base case. A larger resource base means lower production costs with the gasoline tax. In the long run, both factors help to lower vulnerability if short-run supply is elastic.

In the event of a supply disruption, the government could draw down oil from the SPR, substantially increasing short run supply. The preceding analysis suggests that the gasoline tax, along with the SPR may be the best tool against a supply disruption. The effects of releasing 3.5 million barrels of oil per day for 90 days from the SPR in the event of a disruption are shown in Table II. By increasing the short-run supply elasticity, the SPR lowers vulnerability considerably for all policies.

Table II shows that gasoline tax together with the SPR always makes the U.S. less vulnerable to a supply disruption, compared to just releasing oil from the SPR. The lower consumption and lower imports with the gasoline tax and the additional supply from the SPR lower vulnerability.

On the other hand, the tariff together with the SPR is not much help in combating a disruption unless the price increase from the disruption is about 100 percent. In cases where prices do not rise as dramatically, an SPR drawdown on its own is preferable to an SPR drawdown in combination with a tariff. When the price increase due to the disruption is small, the short run elasticity, calculated with additional supply from the SPR, is relatively high compared to the short run response when the price increase is more than 100 percent. The previous analysis has shown that the tariff is more effective when short-run elasticities are low. Therefore, the tariff coupled with the SPR is effective only when prices increase dramatically with a disruption.

Table II. Vulnerability Measure with Price Shocks and an Additional Supply of
3.5 mb/d from the SPR (Discounted Value of Total Vulnerability over the 30
Years)

Price Change         25%         50%         75%         100%         200%

Base                 232         443         642         835          1580
Tariff               323         496         660         819          1435
Gas Tax              201         384         558         725          1368
Table III. Vulnerability Measure with Price Shocks and an Additional Supply of
1.0 mb/d from the SPR (Discounted Value of Total Vulnerability over the 30
Years)

Price Change         25%         50%         75%         100%         200%

Base                 949         1653        2269        2845         4993
Tariff               985         1624        2187        2713         4681
Gas Tax              873         1534        2113        2650         4633

A smaller drawdown, such as 1 million barrels per day has qualitatively the same results, although the supply elasticity is much lower than with a 3.5 million barrels per day drawdown. Table III shows the vulnerability measure with this smaller drawdown. The gasoline tax is still the best policy when used together with the SPR.(5)

V. Conclusion

The recent Middle East crisis has increased concerns about our vulnerability to oil supply shocks. Many policies have been proposed to reduce vulnerability. This paper analyzes U.S. vulnerability to an oil supply disruption with a drawdown of oil from the SPR at time of disruption, a tariff, a tariff with SPR drawdown at time of disruption, a gasoline tax and a gasoline tax with SPR drawdown at time of disruption.

Based on the measure of vulnerability, the tariff decreases vulnerability if the short-run oil supply elasticity is low, but increases vulnerability if the short-run supply elasticity is more than 1.0. The gasoline tax, on the other hand, increases vulnerability if short-run supply is very inelastic, but decreases vulnerability if elasticity is higher than 0.5. However, in the event of a supply disruption, short-run elasticities could be very high. A governmental drawdown of oil from the SPR as happened during the most recent crisis would substantially increase short-run elasticities. Then, the gasoline tax along with an SPR drawdown would be the best weapon against supply disruptions.

1. See Bergstrom [2], Bizer and Stuart [3], Broadman and Hogan [6], Nesbitt and Choi [15], and Walls [24] on tariffs, French [12], and Uri and Boyd [20] on gasoline taxes and Dahl and Yucel [11] for a literature review of papers that consider the macroeconomic effects of protectionist policies.

2. The mathematical details of the problem can be found in Yucel and Dahl [26].

3. For surveys of these elasticities see Bohi [4], Bohi and Zimmerman [5], and Dahl [10]. Many of the derived estimates for product price elasticity are between -.3 and - 1.6, while many of those for income elasticity are between .6 and 1.4. The elasticities are normalized around 1992 product demand minus net product imports of 6.938 million barrels per day, GDP of $5.907 trillion, and an oil supply price of $18.43.

4. A per-unit rate of $5.92 per barrel equates tariff revenues to gasoline tax revenues.

5. If OPEC market structure was competitive rather than monopolistic, the SPR's role in combating supply disruptions would be enhanced. With a competitive OPEC, world oil prices would be lower and OPEC would have a larger market share. Lower oil prices would lower U.S. oil production and increase consumption. The U.S. would bear a higher share of the welfare burden of both the tariff and the gasoline tax and U.S. vulnerability to oil supply shocks would be greater with lower oil prices. In such a case, a drawdown from the SPR which would increase short run supply elasticity, especially when domestic production was low, would greatly reduce our vulnerability to oil supply shocks.

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