Appendix: Modeling Oil Price Behavior
45. Oil prices over the last century have exhibited considerable variability, which was eclipsed by dramatic changes (upward in 1973 and 1979, and downward in 1985), as well as sudden spikes (in 1990 and possibly 2004-05). This appendix looks at the statistical properties of past oil prices that have been used in the Monte Carlo simulations of the fiscal policy model in the main text. We reestimate some of the results of Pindyck (1999) and Engel and Valdès (2000), who argue that past oil prices can best be described by a simple autoregressive process.25 The generic form of these models links today’s price to a trend, at least one lagged price, and a “white noise” random variable.
46. Simple tests show that lags of more than one period are not relevant. Engel and Valdes test the forecasting ability of different oil price determination models, including random walk and autoregressive models. They estimate each model repeatedly using quarterly data that ended in the second quarter of the years 1994 to 1998 and forecast from the estimating sample. They then compute the root mean square error using forecast errors at horizons of one and two years.
47. They conclude that none of the models provides superior forecasting ability to a simple random walk without drift; that is, i.e. αt is zero, the coefficient of the trend variable,
48. Looking at real oil prices over the past 140 years (Figure 6), one wonders whether the large variations are indicative of structural changes in the oil market. In fact, the creation of OPEC, and the changes in its market management behavior over time, would lend support to the hypothesis that structural changes have occurred several times during the course of oil price history. Using dummy variables, we can test the validity of this hypothesis.
49. Simple unit root tests (augmented Dickey-Fuller, ADF) on the log of oil prices between 1861 and 2003 have been performed with different dummy variables: D1 for the period 1974 to 2003, D2 for 1979-03, and D3 for 1974-85.26 The tests strongly support the inclusion of a one-year lag of the oil price in a regression model, but the dummies all come short of significance at the 5 percent level, although D3 may be significant at the 10 percent level. In a linear, ordinary least squares AR(1) regression, D3 is significant at the 5 percent level and its inclusion in the model improves its fit.
50. In addition, market volatility seems to have been very large during the early years shown in the series. One could easily argue that, until about the turn of the twentieth century, oil was an exotic commodity, and markets were thin and did not function well. In fact, when the period prior to 1904 was left out, model fit improved.27 Therefore, the best-fit model of oil price behavior was estimated as shown below (t-values in parentheses).28
51. The calculated standard deviation of the regression was used to produce 5,000 series of 15 random error terms. The random terms were then plugged into the regression equation to produce 5,000 oil price series of 15 years’ duration (omitting the dummy term), and the resulting logs were converted into real oil prices. Real oil prices were used in the fiscal policy model to calculate probabilities of stabilization fund exhaustion.
Arrau, Patricio, and Stijn Claessens, 1992, “Commodity Stabilization Funds,” Policy Research Working Paper No. 835 (Washington: World Bank.
Caballero, Ricardo, 2000, “Macroeconomic Volatility in Latin America: A View and Three Case Studies,” NBER Working Paper No. 7782 (Cambridge, Massachusetts: National Bureau of Economic Research.
Claessens, Stijn, and Panos Varangis, 1994, “Oil Price Instability, Hedging, and an Oil Stabilization Fund: The Case of Venezuela,” Research Working Paper No. 1290 (World Bank).
Davis, Jeffrey, Rolando Ossowski, James Daniel, and Steven Barnett, 2001, Stabilization and Savings Funds for Nonrenewable Resources, IMF Occasional Paper No. 205 (International Monetary Fund).
Engel, Eduardo, and Rodrigo Valdes, 2000, “Optimal Fiscal Strategy for Oil-Exporting Countries,” IMF Working Paper 00/118 (Washington: International Monetary Fund).
Engel, Eduardo, and Patricio Meller, 1993, External Shocks and Stabilization Mechanisms, Inter-American Development Bank, Washington, DC.
Flood, Robert, and Nancy Marion, 2002, Holding International Reserves in an Era of High Capital Mobility, IMF Working Paper 02/62 (Washington: International Monetary Fund).
Greenspan, Alan (1999), Currency Reserves and Debt, remarks before the World Bank Conference on Recent Trends in Reserves Management, Washington DC, April 29, 1999.
Jeanne, Olivier, and Romain Rancière (forthcoming), The Optimal Level of International Reserves for Emerging Market Countries: Formulas and Applications, IMF Research Department, IMF.
Prepared by Ulrich Bartsch.
For macroeconomic stabilization purposes, it is important that the financial assets be kept in foreign currency to limit the domestic liquidity injection from oil exports.
Arrau and Claessens (1992), Valdes (1993), Daniel (2003). Interestingly, a third option to reduce revenue volatility does not seem to attract much attention: governments could design fiscal regimes for private oil companies such that the companies rather than the governments shoulder the price risk.
In principle, governments can print money when resource revenue falls short of expectations. Printing money would not, of course, enable the government to buy foreign goods and would also trigger domestic inflation and currency depreciation. After creating a short-lived illusion, the government would be worse off than before. This option for dealing with revenue uncertainty is therefore not discussed in the literature.
It should be noted that funds in Alaska and Norway and as well as some other countries, including Kuwait and Oman, have also been set up to hold oil revenue for future generations to ensure intergenerational equity.
Jeanne and Ranciere (forthcoming, 2005) develop a maximization model with costs of reserves (interest rate differential) and risk aversion given a probability of facing a financial crisis. The results support the “Greenspan rule.”
Fiscal policy would be based on an oil price rule, that is, it would target a balanced budget at the budget oil price. Actual oil prices higher or lower than the budget oil price would lead to surpluses or deficits. This policy is equivalent to choosing a stable non-oil balance.
The table calculates the root of the mean of squared differences between moving averages over one to nine years and actual prices.
Prices have become more volatile since the 1970s.
Of course, a maximization model would, in this case, choose the optimum level of stabilization given the costs of holding more assets in a stabilization fund.
Venezuela and Chile determined deposits in their stabilization funds on the basis of moving averages of commodity prices, see Arrau and Claessens (1992), Claessens and Varangis (1994), Davis and others (2001).
Non-oil revenue is assumed to be predictable.
Stochastic development of production capacity would complicate the analysis. Risks would obviously increase. Although rising production over time would reduce the risks. Stochastic development also assumes that taxes are a constant fraction of production value, which is a permissible approximation only if tax-deductible production expenses are small relative to production value.
Starting with a balanced budget in 2004, the model produces data denominated by the nonoil deficit. It should be noted that the model uses real U.S. dollars for all variables. It does not take into account exchange rate and dollar deflator feedback effects of oil prices.
In 2004, the federal government targeted a deficit at the reference price to be financed from repatriated looted funds, privatization receipts, and domestic borrowing. In 2005, all three levels of government are targeting deficits to be financed with about one-half of the windfall revenue deposits of 2004. Consolidated spending in 2004 was therefore more in line with the revenue Nigeria would have received had the oil price been $28 per barrel, and 2005 spending is projected to be in line with about $33 per barrel.
It should be noted, however, that the results will overstate Nigeria’s risks because production increases that are highly likely to occur over the next 5 to 10 years are not taken into account.
While the country had net foreign reserves of US$17 billion at end-2004, government deposits in the blocked central bank account for windfall oil revenue amounting to US$6 billion.
While the Nigerian government is discussing a debt buy back with its Paris Club creditors, the analysis in this chapter takes the debt as a given; it is neither repaid using financial assets, nor can the government borrow more domestically or abroad.
If, indeed, the 2004 price is used as the reference price and the authorities target a balanced budget at this price, the probability of asset exhaustion rises to 43 percent.
All tests are performed using logs of oil prices.
Prices started rising in 1971, but the big price increase followed the imposition of supply restrictions by Saudi Arabia during October 1973. A high point was reached in 1980, but the dramatic end to the “OPEC years” came with the decision by Saudi Arabia to move to netback pricing in the fall of 1985.
The choice of 1904 was arbitrary, giving 100 observations for the regression.
Other descriptive statistics:
|R2||0.848708||F(2,97) =||272.1 [0.000]**|
|No. of observations||100||No. of parameters||3|
|R2||0.848708||F(2,97) =||272.1 [0.000]**|
|No. of observations||100||No. of parameters||3|