**Technical Appendix on the Oil Market:**
**The Economic Consequences of a War with Iraq**
William D. Nordhaus, Yale University
October 29, 2002
Models of the oil market are extremely complex. The estimates prepared by Perry have been compared with a simplified growth model of the U.S. economy. This appendix explains the model and the basic results. The model assumes that output is entirely consumption goods. The major component is a production function in which the only endogenous input is oil imports. Production is a putty-clay technology in oil inputs and other exogenous inputs, with Cobb-Douglas substitutability ex ante and fixed proportions between output and oil imports ex post. The model is a full-employment model that calculates the terms of trade effects along with the effects of substitution of other inputs for oil. The investment-output ratio is assumed to be constant over time.
Five parameters are central to the model’s performance: the initial level and the growth of total factor productivity, the elasticity and the rate of change of the elasticity of output with respect to oil imports, and the depreciation rate of the capital stock. Note that the depreciation rate is central because it determines the speed with which oil demand responds to changes in oil prices. It is assumed that capital is never scrapped, which is realistic when oil imports are a very small share (roughly 2 percent) of costs. The model’s five parameters are determined by minimizing a loss function that is a weighted sum of the squared errors of GDP and oil imports over the period 1960-2000. The central estimate is for a depreciation rate of 0.018 percent per year. One final parameter is the time path of the response of oil prices to shocks. These results are consistent with recent studies of the oil market.^{1}
Real oil prices are exogenous during the historical period. Based on the behavior of oil prices in the 1970-2000 period, I estimate that oil regresses back to the trend at a rate of 20 percent per year after either a good or bad shock.
Using the model, we estimate the impact of both Perry’s “worse” case as well as the “happy” case of an increase in oil production. Figure 3 shows the value of oil imports (in 2002 prices) for the estimated model along with the actual numbers. Figure 4 shows the estimated and actual physical oil-real GDP ratios. The fit looks misleadingly good because most of the movement is due to the to oil prices. Figure 5 shows the actual and calculated volume of oil imports. The model captures the broad trends but cannot resolve the short-run turning points precisely.
The base case assumes that real oil prices grow at 2 percent per year after averaging $25 per barrel in 2002. I estimate Perry’s “worse” case by setting the real oil price at $75 per barrel in 2003 and then allowing the real price to regress 20 percent per year back to the baseline. The “happy” outcome is somewhat more complex. It assumes that Iraq builds up its production by 1 mbpd relative to the baseline; that Saudi Arabia and other supplier countries reduce their supply by one-third of the increased Iraqi production; that oil production then regresses back to the baseline at 20 percent per year after 2008; and that world oil demand is four times as large as U.S. demand and has equal elasticities. The model then solves for the price trajectory that balances supply and demand.
The important results of the model are shown in Table A-1. The first column shows the terms of trade impacts – that is, the impacts of the shocks on the real cost of oil imports. The second column shows the impact on real net domestic product (which is the appropriate welfare measure of output). The final column shows real national income, which is real output corrected for the terms of trade effect. The third column equals the sum of the first two. The bottom rows show the elasticities of the demand for imported oil with respect to the crude oil price. These are close to the estimates used by Perry and found in the literature.
The effects of oil shocks are actually quite subtle. When capital adjustment is slow, most of the impacts are on the terms of trade in the first column. When capital adjustment is very fast, most of the impacts are on output through the requirement of substitution of other inputs for oil. And the effect is obviously larger if prices regress more slowly back to their baseline path.
The high-cost case of $500 billion is consistent with a number of possible combinations of parameters in the oil model. Looking at the last column of Table A-1, a long lifetime and rapid regression of price to trend yields $468 billion. A short lifetime and a slow regression of price to trend yield $650 billion. Even instantaneous adjustment and slow regression yield a number near the high-cost figure in Table 7. Note as well that these assume perfect competition, no economic frictions, and no political sand in the gears of market reactions.
Table A-1. **Cost of Perry’s “Worse” Oil Shocks in Full Employment Model**
**Figure 1. **Estimated and Actual Value of Oil Imports, 1970-2000 (billions in constant prices)
**Figure 2. **Share of Oil Imports in GDP, 1970-2000
**Figure 3. **Actual and Projected Volume of Imports (billions of barrels)
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