Technical appendix

The most durable economic impacts of a war in Iraq are likely to be the effects on oil markets. Economic models of the oil market are extremely complex because they combine hard geological realities with game-theoretic indeterminacies of oligopolistic behavior, and these difficulties are overlaid with domestic politics and geopolitical strategies in all major countries. The inherent complexities become even greater given uncertainties about post-war oil-market destruction and production scenarios, changes in decisionmakers in the Gulf region, and the potential instability of the OPEC cartel. Finally, from a pure economic point of view, there are technical difficulties in modeling the response of oil demand to price shocks.

The impact of oil prices on economic activity has been well established since the oil-price shocks of the 1970s. Economists do not always agree, however, on the exact mechanism by which oil prices affect the economy. The two major routes are the real-income effect and the business-cycle impact. The real-income effect measures the impact of changing oil prices at full employment on expenditures for imported oil and on productivity as businesses substitute other inputs for high-priced oil. The business cycle effect occurs when higher oil prices trigger lower spending and higher unemployment, either directly through the impact on real incomes and consumption or indirectly through monetary tightening, higher interest rates, and lower investment. These two mechanisms are discussed in turn.

Full employment impacts on real incomes
To tackle the impact on real incomes in a full-employment economy, I have drawn upon recent general-equilibrium economic models of oil demand along with the scenarios laid out by oil-market specialists. This appendix lays out the results of the oil modeling exercise. The model assumes that output is a single homogeneous good. The major component of the model is a production function in which output is produced by other factors and oil inputs, where oil is supplied both by endogenous imports and exogenous domestic production. Aggregate output is produced by a putty-clay technology in oil and other exogenous inputs and is characterized by Cobb-Douglas substitutability ex ante and fixed proportions between output and oil inputs 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 invariant over time.

The parameters central to the model's performance are the following: the initial level and the growth rate of total factor productivity, the elasticity and the rate of growth of the elasticity of output with respect to oil inputs, and the depreciation rate. Note that the depreciation rate is key 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 inputs are a very small share (around 3 per cent) of costs. More precisely, the equations of the model are the following:

(1) Q(t,t) = A(t) E(t, t)^b(t)

(2) Q(t) = Q(t,t) + (1- d) Q(t-1)

(3) E(t) = DP(t) + OI(t)

(4) E(t) = E(t, t) + (1- d) E(t-1)

where Q(t,t) is the output produced in year t from vintage t, A(t) is total factor productivity in year t, E(t, t) is oil inputs used in year t in vintage t, b(t) is the time-varying ex ante elasticity of output with respect to oil inputs in year t, Q(t) is total output, E(t) is total oil inputs, d is the depreciation rate of capital, DP(t) is domestic production of oil, and OI(t) is imports of oil. It is assumed that A(t) and b(t) have constant proportional rates of change over time. The major other variable is P(t), which is the real price of oil, assumed to be set in world markets. The model assumes that, for a given vintage, output, energy inputs, and other inputs decline exponentially at rate d after the initial year.

By manipulating these four equations, we obtain the following two equations for estimation:

(5) E(t) = (1 - d) E(t-1) + [P(t)/(b(t) A(t)]^(1/(b(t)-1))

(6) Q(t) = (1 - d) Q(t-1) + A(t) [P(t)/(b(t) A(t)]^{(b(t)/(b(t)-1))}

The model's five parameters are determined by weighted least squares for the sample period 1970-2002 using annual data; data for 2002 are preliminary through the first nine months of the year. The important depreciation rate variable (d) has an estimated value of 12.2 per cent per year with a standard error of 5.3 per cent per year. These results are consistent with recent studies of the oil market. [1] Figure A-1 shows the value of oil imports (in 2002 prices) for the estimated model along with the actual numbers over the 1970-2002 period. Figure A-2 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 results presented below are, however, quite robust to changes in structure or timing.

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. To estimate the impacts of alternative outcomes, the trend case assumes that real oil prices grow at 2 per cent per year after 2002. The "worse" or price-shock case starts with an initial price of $75 per barrel in 2003. Based on the behavior of oil prices in the 1970-2000 period, oil prices in the worse case are assumed to regress back to the trend path at a rate of 20 per cent per year of the difference between the trend and worse prices in the prior year.

The "happy" outcome is somewhat more complex to model. It assumes that the net increase in OPEC production (due to an increase in productive capacity in Iraq less any reduction in production in Saudi Arabia and other supplier countries) totals 2/3 million barrels per day, which is attained five years after the beginning of a war. It further assumes that world oil demand is four times as large as US demand and has equal elasticities. The model then solves for the price trajectory that balances supply and demand over the 2003-2012 period.

The key 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 cost in the adverse case totals slightly under $800 billion for the decade. About one-seventh of this is higher expenditures on imported oil, while the balance comes from a decline in real output. The increase in oil expenditures comes in the early years, before the economy has a chance to adapt to the higher prices. Most of the production decline, by contrast, comes in later periods as the economy substitutes other inputs for higher-cost oil. Note that these results exclude any business cycle impacts, which are considered next, and additionally they assume perfect competition, no economic frictions, and no political sand in the gears of market reactions.

Business cycle impacts
Sharp oil price increases have been associated with most of the recessions of the last three decades. There have been numerous studies of the impact of oil prices on output in the short run. We can use a simple one-equation model to capture the fundamental dynamics. An instrumental-variables estimate over the period 1962 to 2002 relating real GDP to real oil prices, lagged real GDP, and a trend produces the following:

(7) log[Q(t)] = constant - 0.011 log[P(t)] - 0.023 log[P(t-1)] + 0.22 log[Q(t-1)]

                                     (0.013)              (0.014)               (0.214)

                                     + trend + autoregressive error correction

SEE = 0.0172 R2 = 0.998

The variable definitions are the same as in the previous section. In this equation, I have used twice-lagged real oil prices as the instrument for lagged real GDP. The numbers in parentheses underneath the coefficients are the standard errors of the coefficients, SEE is the standard error of estimate of the equation, and R² is the fraction of the variance of the dependent variable explained by the equation.

We can use this equation to project the impact of the oil-price shock on output. The equation predicts for the worse price case a decline in real GDP reaching a maximum of 3.5 per cent of GDP, which is much larger than maximum decline of 0.5 per cent predicted by the full-employment model in the last section. The reason why output reacts so much to oil price increases - almost 10 times more than would be predicted by standard neoclassical growth models - has been observed in earlier research and remains controversial. One possible reason for the large discrepancy is that oil price increases tend to fuel inflationary pressures and thereby trigger anti-inflationary monetary policies. Inflationary impulses also tend to redistribute income from labor to property incomes and thereby lower consumption expenditures.

We can use equation (7) to estimate the impact of the "worse" oil-price shock on the business cycle. For this purpose, I assume that the business-cycle impacts last only two years, and that monetary and fiscal policies close the gap between the trend and worse output paths after that time. I also subtract the full-employment impact on output estimated in the first section to prevent double counting.

Under these assumptions, the net cyclical impact of the worse price increase is $391 billion. This net number represents $492 billion of gross loss in output less $101 billion of loss in potential output which was counted in the numbers in Table A-1. The gross loss estimate is consistent with Perry's estimate, being approximately 1.5 years of Perry's estimate of the GDP impact of the worse oil price scenario. Additionally, this estimate is close to the loss in output from the recession triggered by the First Persian Gulf War, which reduced output over the 1990:3 to 1992:2 period by $490 billion relative to the pre-war trend.

The impact of the happy oil price scenario is likely to be very small. Most of the macroeconomic impacts will come well into the future and are likely to be anticipated. Using the same methodology as is employed for the oil-shock case, the impact is estimated to be $17 billion in net cyclical gain in the first two years.

Figure A-1. Estimated and actual value of oil imports, 1970-2002 (billions in constant prices)

Figure A-2. Actual and projected volume of imports, 1970-2002 (billions of barrels)