Fiscal Policy Formulation and Implementation in Oil-Producing Countries

5 Statistical Properties of Oil Prices: Implications for Calculating Government Wealth

Jeffrey Davis, Annalisa Fedelino, and Rolando Ossowski
Published Date:
August 2003
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I. Introduction

Understanding the statistical properties of oil prices is important for fiscal policy formulation in oil-producing countries. Specifically, the extent to which oil price changes are believed to be persistent or temporary is likely to have substantial implications for the optimal fiscal policy. Barnett and Ossowski (see Chapter 3 in this volume) argue that government oil wealth—defined as the present discounted value of government oil revenue—is a key input for assessing the sustainability of fiscal policy. Therefore, and looking only at sustainability considerations, the optimal fiscal response to an oil price shock depends on how much the shock changes government wealth.2 This, in turn, hinges on the extent to which the shock is permanent or transitory.

The reasoning is identical to the standard permanent income consumption argument (Friedman, 1957). Specifically, consumption should respond to permanent income shocks but not to transitory ones that leave wealth largely unchanged. Davis and others (see Chapter 11 in this volume) find strong empirical evidence that in a number of oil-producing countries government spending is indeed positively related to oil export earnings. Whether such responsiveness is warranted—based on sustainability considerations—depends on the extent to which changes in current oil revenue translate into changes in oil wealth.

Empirically, therefore, the objective of this paper is to assess the extent to which oil price shocks are transitory or permanent. Conventional tests for unit roots (nonstationarity) are informative in this regard, but at the same time are not decisive. At the simplest level, empirical evidence of nonstationarity (that is, a unit root) in oil prices would suggest that wealth could be quite sensitive to price shocks, and, by extension, government spending as well. However, evidence of a unit root needs to be interpreted carefully on several grounds. First, as argued by Rudebusch (1993), tests for unit roots have low power against near alternatives. Or, more plainly, it is nearly impossible with the available sample sizes to distinguish between a true unit root and a stationary process with slow mean reversion. Second, even if there is a unit root or permanent component to price changes, the process could be dominated by transitory shocks. In this case, most of a given shock is transitory; thus, even though a price shock contains a small permanent component, the value of oil wealth may not change much. Finally, the possibility of structural breaks in the oil price process further complicates matters. The presence of a structural break in a series—for example a one-time shift in the mean—would generally bias results in favor of a unit root, and the erroneous conclusion that all shocks are permanent (when in fact most shocks could actually be transitory).

II. Review of the Literature

There is a diverse literature that examines the statistical properties of oil prices, and many studies do find evidence of mean reversion. The findings from the literature can be roughly grouped as follows. In the very long run, that is, periods of more than 100 years, there is evidence of mean reversion in real oil prices. Studies looking at just the post-World War II period, however, usually find that oil prices are not mean reverting. Nonetheless, when the sample is further divided, many studies find evidence of mean reversion during the more recent periods (since the mid-1970s or mid-1980s).

Pindyck (1999) finds strong evidence of mean reversion in real oil prices looking at an extremely long sample; the sample includes 127 years, 1870–1996, of data on real oil prices. In the longest samples, 1875–1996 and 1900–1996, the null hypothesis of a unit root is rejected using the augmented Dickey-Fuller test.3 Variance ratio tests also indicate that the transitory component of shocks is quite large, further supporting the finding of mean reversion. The paper also develops a model with richer dynamics, allowing for both a stochastic mean and trend, but still finds substantial reversion in price shocks. Moreover, despite the richer dynamics, the long-run out-of-sample forecasts appear to converge to a relatively narrow range (whether the forecast begins in 1970, 1980, 1981, or 1996), and outperform a simpler AR(1) process. The richer dynamics stem from consideration of a model that strives to capture the supply and demand considerations that govern the evolution of prices.

Videgaray (1998) also finds strong evidence of mean reversion using a similar dataset. He estimates a two-state Markov switching model, with the parameters suggesting mean reversion in each state. In particular, he finds that most of the time—around 80 percent—oil prices are in a low mean, low volatility, and high persistence state (slower mean reversion), and the remainder of the time are in a high mean, high volatility, and low persistence state. The possibility of switching states introduces another form of uncertainty, that all else being equal would be expected to increase the variance of long-run price forecasts (and therefore oil wealth).

Focusing on the post-World War II period, Cashin, Liang, and McDermott (2000) find evidence of strong persistence in oil price shocks. They use monthly data on oil prices in real terms from 1957 to 1998 and a median-unbiased estimator to help mitigate the problems associated with regressions on series that may have a unit root. They find strong evidence that oil price shocks are persistent, with the estimate that the half-life of a shock is infinite (that is, no mean reversion). The 90 percent confidence interval for the half-life of a shock ranges from a minimum of more than seven years up to infinity.

Engel and Valdés (2000) use quarterly real oil price data from first quarter (QI) 1957 to second quarter (QII) 1999 and come up with somewhat mixed results. Similar to the findings of this paper, they find that the unit root hypothesis cannot be rejected for the entire sample, but that it can be rejected in smaller samples. In particular, in the 1974QI-1999QII and 1986QI-1999QI samples the unit root hypothesis is rejected. They find that the variance ratio tests support evidence of shocks having both a transitory and a permanent component; however, the small samples (especially the sample 1974QI-1998QIV) make it difficult to draw firm conclusions from this test. They also run 15 different models or forecasting techniques and conclude that none performed significantly better than the random walk over a two-year horizon. However, it is not clear whether these results would generalize to longer forecast horizons—which is relevant for calculating wealth—or different forecasting periods.

Akarca and Andrianacos (1995, 1997, and 1998) have a series of papers that find results similar to, and supportive of, the findings in this paper. Their studies focus on the natural log of monthly real oil prices from January 1974 to October 1994. In their 1995 paper, they find evidence of a structural break in oil prices following January 1986 using regression techniques, corroborated by the examination of the variance ratios in the different periods. Building on this, Akarca and Andrianacos (1997) find that oil prices in the earlier period (January 1986 and earlier) are nonstationary, but that in the latter period oil prices are stationary. In their 1998 paper, they refine this argument, and argue that with the exception of two shocks, oil price shocks have all been transitory. In particular, they find that there was a permanent upward shift in the mean oil price in March 1979 and a permanent decline in January 1986, but that all other shocks have been transitory. This supports one of the main conclusions of their paper, namely that most oil shocks should be viewed as being transitory.

Bessembinder and others (1995) find strong evidence, based on the term structure of futures prices, that markets expect oil prices to be mean reverting. Based on daily futures prices from March 1983-December 1991, they find that 44 percent of an oil price shock is expected to be reversed in eight months. They also argue that among the possible causes of mean reversion in oil futures prices, the main factor is an expected mean reversion in actual prices. That is, market participants expect that there is a large temporary component to oil price shocks. Moreover, the authors highlight that one possible explanation for the mean reversion is that oil supply is more elastic in the long run than in the short run.

Cashin, McDermott, and Scott (2002) take an alternative approach to studying oil prices, characterizing a cycle in oil price movements. Similar to the techniques used to date business cycles, they date the cycles in oil prices. They examine numerous commodity prices, including oil, from January 1957 to August 1999. For oil, while they find that there is a good deal of variability in the duration of booms and slumps, on average an oil boom lasts 22 months with prices rising nearly 50 percent, and a slump lasts 51 months with prices also falling nearly 50 percent. Loosely speaking, therefore, oil prices are characterized by relatively fast rises in prices followed by more prolonged declines.

Oil prices are the outcome of a market process—a fact that is easily overlooked in the quest to model prices as if they were random drawings from a statistical process. It is supply and demand considerations that ultimately drive oil prices (see, for example, Wickham, 1996, or Pindyck, 1999, for a discussion). Market forces, moreover, could point to some mean reversion in oil prices. For example, whereas oil supply may not be able to respond immediately to an uptick in prices, over time production may increase, causing prices to fall back over the medium term. Likewise, higher oil prices may cause demand to fall over time as alternatives to oil are exploited. Focusing just on oil prices, as is done below, abstracts from these structural demand and supply considerations that underlie the observed movements in oil prices.

III. Futures Market Evidence

In the last two decades financial derivatives for oil have been developed and reached significant levels of liquidity. Oil futures embody market expectations about future prices and, therefore, provide clues as to the degree that markets regard oil shocks as permanent or transitory. An analysis of the futures market data strongly suggests that there is—or market participants believe that there is—a substantial amount of mean reversion in oil prices. This is demonstrated using more informal evidence, based in part on Daniel (see Chapter 14 in this volume), and some econometric evidence along the lines of Bessembinder and others (1995).

Informal Evidence

Futures market data support the hypothesis that there is a large transitory component to most oil price shocks—or, to be more precise, that markets expect that there is.4 We demonstrate this by comparing the properties of spot and futures prices and examining the term structure of oil prices.

Futures oil prices exhibit substantially less variation than spot prices, suggesting that there is an important transitory component to oil price shocks. Figure 5.1 compares a proxy for the spot price with the 12-month- and 18-month-ahead futures prices.5 The futures prices fluctuate much less than the spot price proxy, as seen by the fact that the futures have smaller-size peaks and higher-size troughs. Indeed, the standard deviation of the spot proxy is US$4.98 compared to only US$2.97 and US$2.44 for, respectively, the 12- and 18-months-ahead futures prices. Moreover, the ratio of the standard deviation for a given futures price to the spot proxy is monotonically declining with the time to maturity of the contract.6 It falls from 96 percent for the 2-month-ahead futures price (which matures 1 month after the spot proxy), to 60 percent for the 12-month-ahead and 49 percent for the 18-month-ahead.

Figure 5.1.Oil Futures Prices

(In U.S. dollars per barrel)

Source: NYMEX.

The standard deviations of the futures prices also provide clues as to the expected persistence of shocks. The ratio of the standard deviation of the futures price to the spot proxy can be used to derive a measure of persistence. Specifically, if we assume that the term structure is equal to the expected price (but see below) and that the expected price can be modeled as an AR(1) process, then the ratio of the standard deviation can be used to calculate the implied coefficient on the lagged price. For example, the coefficient in an AR(1) equation consistent with the 18-month standard deviation being 49 percent of the spot proxy is 0.96. Looking at each of the ratios from 2 to 18 months, the implied coefficient varies little, ranging from 0.95–0.96. This has implications for the regressions and unit root tests performed in the next section, as it suggests that the coefficient estimate on the lagged oil price (in the monthly regressions) could be around 0.95—or, if more than one lag is included, that the sum would be close to 0.95.7

The term structure of oil futures provides further evidence that oil prices are expected to be mean reverting. Figure 5.2 shows an average of the futures price curves grouped by the level of the spot price. The mean reversion of futures prices is demonstrated by the fact that, regardless of the spot price, the futures tend to converge to prices close to US$20 per barrel.

Figure 5.2.Average Crude Oil Futures Prices Grouped by Spot Price, 1983–2001

(In U.S. dollars per barrel)

Sources: NYMEX data; and authors’ calculations.

Looking at the term structure from selected days further highlights the underlying mean reversion in futures prices. Figure 5.3 shows the term structure going out to nearly six years on three different days.8

Figure 5.3.Oil Futures Term Structure, Selected Days

(In U.S. dollars per barrel)

Source: NYMEX data from Bloomberg.

Despite substantial variation in the nearby futures price, the six-year-ahead (technically 71-month) futures do not change that much. The January 22, 1998 term structure, coinciding with low spot prices, actually corresponds to higher-priced long-dated futures than the January 18, 2000 term structure (when the spot price was substantially higher). This suggests that while there is most likely mean reversion, the mean that is reverted to may not be constant over time or even necessarily correlated with the spot price.

The finding of mean reversion in the term structure needs to be interpreted carefully. First, the futures prices may not coincide exactly with the actual price expectations. For example, the futures price could also depend on factors such as the interest rate and risk premium, both of which may vary over time, causing the futures price to deviate from the expected price (see Bessembinder and others, 1995). Kumar (1992), however, finds that futures prices for the most part provide unbiased forecasts, although his longest-dated contract is nine months ahead (the sample period also terminates in 1990). Second, the finding of mean reversion, as highlighted above, does not imply that the mean is constant over time. Schwartz (1997) finds strong evidence of mean reversion in oil futures prices, but also finds that a simple model with a constant mean is outperformed by models that allow for time-varying factors.


Futures prices can be used to estimate the expected persistence of oil price shocks, along the lines of Bessembinder and others (1995). In particular, the elasticity of the change in the longer-dated futures prices relative to a change in the spot (or nearby futures) price provides a measure of expected persistence. The following regressions repeat those presented in Bessembinder and others (1995), but using different data. The key differences are that monthly averages instead of daily data are used, the data cover a longer sample period, and longer-dated futures are examined. The sample period is January 1990-August 2001, for which there is continuous data on all contracts out to 18 months. For longer-dated contracts there are missing observations for some months (which, due to the differencing, results in two lost observations).

The results are consistent with those in Bessembinder and others (1995) and suggest that the markets expect price shocks to be largely transitory (Table 5.1). Both the qualitative and quantitative results are strikingly similar. The eight-month future, for example, has a coefficient estimate of 0.535 compared to 0.564 in Bessembinder and others (1995), which implies that 46 percent of a shock is expected to be reversed in eight months. After one year, nearly 60 percent of the shock is expected to be reversed and after 1½ years more than 70 percent is expected to be reversed. The results beyond this are based on smaller samples and thus may not be comparable, but, with this caveat, would seem to imply that after two years more than 80 percent of the price shock is expected to be reversed.

Table 5.1.Elasticities of Futures Price Changes1
StandardBessembinder and others (1995)
FutureElasticityErrorP-valueObservationsR-squaredElasticityStandard Error
Source: Authors’ calculations; and Bessembinder and others (1995).

The dependent variable is the change in the log of the futures price as indicated in the first column, and the independent variable is the change in the log of the nearby future (no constant is included).

Source: Authors’ calculations; and Bessembinder and others (1995).

The dependent variable is the change in the log of the futures price as indicated in the first column, and the independent variable is the change in the log of the nearby future (no constant is included).

The futures market data, both the informal evidence and the econometric results, suggest that markets believe that there is a large transitory component to oil price shocks. However, this does not shed light on whether oil prices are stationary or not. Oil price shocks could have both a permanent and a transitory component, and thus could technically follow a random walk even with the substantial evidence for mean reversion presented above. Nonetheless, the mean reversion is quantitatively significant, which already suggests that the transitory component of price shocks needs to be considered when projecting future revenue from oil production.

IV. Oil Price Regressions

Annual and monthly Brent oil price data for the period 1957 to 2001 are used in the following empirical exercises.9 There are certain advantages to working with annual average price data. From a fiscal policy perspective, the average annual price corresponds to the variable of interest for most budgets. Moreover, the lag structure is likely to be simpler, relative to higher-frequency data, thereby avoiding some of the specification selection problems. There are also drawbacks, including the significant loss of observations and intrayear variation. The use of monthly data avoids these problems, but makes the lag structure more complicated. From a technical point of view, however, the larger number of observations is advantageous.

The nominal and the real oil price display qualitatively similar characteristics, although there is more variation in real prices (Figure 5.4). From 1957 to 1970 the price is essentially constant, then in the run-up to the 1974 shocks there is a modest increase in prices before the big spike in 1974, and then another spike in 1979. The 1979 spike, while substantially larger in absolute value, is actually smaller in percentage terms. Prices plunged in 1986 and then went through a period of relative tranquillity until the late 1990s, when, after a dip in 1998, there was a pronounced increase through 2000 that only unwound late in 2001. Comparing the annual and monthly data highlights the extent that the monthly volatility is masked by the annual averages.

Figure 5.4.Nominal and Real Oil Prices

(In U.S. dollars per barrel)

Source: IMF, International Financial Statistics.

Unit Root Tests

There is strong evidence of a unit root in the full (1957–2001) sample of data for both the annual and monthly series. Unit root tests were performed on both real and nominal prices and using a variety of specifications.10 In particular, for the annual data, 12 tests were performed for each price series involving the permutations of (i) zero, one, or two lags; (ii) constant or constant and time trend; and (iii) Augmented Dickey-Fuller or Phillips-Perron test. The results show that the hypothesis of a unit root cannot be rejected in any of the 12 tests on either series. For the monthly series the number of lags was extended to 12 and the same combinations of tests were performed, for a total of 52 tests. The results are similar to those based on annual data as the unit root hypothesis is not rejected in any of the tests. In the post-1973 sample, however, there is strong evidence in favor of rejecting the unit root hypothesis for the annual data using the nominal price. The real oil price series, in contrast, yields somewhat more mixed results. The unit root hypothesis cannot be rejected in the tests that assume no trend in the data. But in the tests that allow for a trend, the unit root is rejected at the 10 percent level in four of the six tests.

The bottom line from this battery of unit root tests is that the answer regarding the presence of a unit root depends on the sample period and whether nominal or real prices are used. The results regarding the sample period are consistent with those in the literature noted above. Specifically, in the longer samples (1957–2001) there is evidence of a unit root, but in shorter samples (1974–2001) oil prices appear to be stationary. This result holds for both annual and monthly data and is strongest for nominal prices, as there is some ambiguity regarding the results for real prices depending on whether a trend is included or not.

Empirical considerations suggest that the nominal oil price is the more appropriate variable to use for the purposes of this study. Testing for a unit root using the log of real oil prices is tantamount to testing for whether the deflator and nominal oil price are cointegrated. Indeed, it imposes that they are cointegrated with a specific vector. This, however, could be problematic on several fronts. First, focusing on the 1974–2001 sample, using both annual and monthly data, the evidence suggests that the unit root hypothesis cannot be rejected for the MUV. Thus, the nonstationarity in the MUV could be behind the seeming nonstationarity of the real oil price—the sum of a stationary (nominal oil prices) and nonstationary variable (MUV) is by construction non-stationary. Second, the failure to find a unit root in the nominal price series for 1974–2001 means that the series cannot be cointegrated, which would require that both series have a unit root. Finally, even in the longer sample (1957–2001), where both the nominal oil price and MUV seem to have a unit root and thus cointegration tests are valid, there is little evidence that the series are actually cointegrated.11

Regression Results

Consistent with the unit root tests, the regression results depend on the sample used. The following discussion focuses on nominal oil prices. For the 1957–2001 annual sample, the coefficient on lagged oil is estimated to be 0.96, quite close to one and lending credence to the failure to reject the unit root hypothesis (Table 5.2). In contrast, the 1974–2001 sample yields an estimate on lagged oil of around 0.5 for the annual data, clearly less than one and suggestive of why the unit root hypothesis is rejected for this sample. Also, the coefficient of around 0.5 on lagged oil would suggest that shocks are not that persistent.

Table 5.2.Regressions of Log of Brent Oil Prices

(Annual Average Series)1

Brent (t-1)0.51*0.69*0.96*0.89*0.73*0.56*
Time Trend0.001
D Brent (t-1)-0.01
Standard error0.260.300.
Number of
Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level.

The dependent variable is the log of Brent oil prices. Dum74–01 is a dummy variable that equals one in 1974–2001, and zero otherwise; Dum74 equals one in 1974 and zero in all other periods.

Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level.

The dependent variable is the log of Brent oil prices. Dum74–01 is a dummy variable that equals one in 1974–2001, and zero otherwise; Dum74 equals one in 1974 and zero in all other periods.

Using the longer 1957–2001 sample, but allowing for a shift in the mean beginning in 1974, yields results similar to the 1974–2001 sample. The persistence of shocks is about the same and the implied unconditional mean for the post-1974 period is US$21.65, only slightly different than that from the US$21.35 for the 1974–2001 sample.

However, even if we allow for a structural break in 1974, formal tests are still unable to reject the unit root hypothesis for the full 1957–2001 sample. Perron (1989) suggests a testing procedure and critical values applicable to such situations, and neither the residual-based tests nor the one based on regressions reject the null hypothesis of a unit root.

The failure to formally reject the unit root hypothesis, even with a structural break, is not surprising. As it is well known, unit root tests have low power against local alternatives, especially in the relatively small sample sizes used here. Moreover, the failure to reject the unit root does not mean that there is indeed a unit root. Thus, we are left in the position of having to rely on more subjective assessments as to whether there is a unit root or not, and whether to rely on the longer 1957–2001 sample or the shorter 1974–2001 sample. The subsequent exercises rely on the shorter 1974–2001 sample. There is clearly evidence of a structural break in 1974, as a regime of essentially constant oil prices was coming to an end and a new regime with much more volatile—and higher—oil prices was beginning.

Mean Oil Prices

The regressions have implications regarding the mean oil price, a notion that needs to be interpreted carefully. While an unconditional mean oil price may be readily calculated from the above regressions, it is really better viewed as a conditional mean, that is, a mean conditional on there being no further structural breaks in oil prices. Indeed, by basing the assessment on the presumption that there was a structural break in 1974, the analysis actually admits that there are, at least occasionally, permanent shocks to the oil price series. By definition, therefore, the oil price series is not stationary. The following, therefore, is not only conditional, but explicitly assumes that there would be no further structural breaks or permanent shocks to oil prices.

The assumption that there would be no further structural breaks warrants further discussion. It is justified on the grounds that such shocks are infrequent and little is known about their likely distribution or arrival rate. By ignoring the possibility of such shocks, the analysis effectively says that policymakers can quantitatively do no better than to assume that the present regime will exist into the future. By ignoring the possibility of there being a future permanent shock, the following exercise underestimates the true degree of uncertainty.

The reasoning, more heuristically, is that most shocks to oil prices seem to be temporary and not permanent. That is not to say that there are not permanent shocks as well, but rather that most shocks are not, and that from a policy point of view it is better to assume that a given shock is transitory. This leaves open perhaps the most difficult question, which is to identify in real time when a permanent shock has occurred. That is a question beyond the realm of this study, although clearly one that policymakers have to confront.

With the caveats above, it is relatively straightforward to derive the mean oil price from the above regressions.12 Ultimately, however, it is not just the mean but also the variance (and perhaps higher moments) of oil prices—and therefore oil wealth—that need to be considered. The imprecision in the underlying parameter estimates translates directly into uncertainty about the mean oil price, and a few dollars plus or minus could have significant implications for oil wealth.

Parameter Uncertainty

Parameter uncertainty introduces a good degree of variation into the estimated mean. While the unconditional mean oil price for the 1974–2001 sample, using annual data, is estimated to be US$21.35, the standard deviation is US$2.29. If we take ±2 standard deviations—corresponding roughly to the 95 percent confidence interval—then the range for the estimated mean price goes from US$16.77 to US$25.92 (Table 5.3). This is a relatively large range that, in turn, translates into a fair amount of uncertainty about oil wealth.

Table 5.3.Regressions of Log of Brent Oil Prices(Nominal, Annual Average Series)
Brent (t-1)0.51*0.52*0.72*0.67*0.65*0.62*0.62*0.72*0.61*0.53*
Standard error0.
Number of observations28202020202020202020
Unit root test11NRNRNRNRNRNRNR10
Unconditional mean
Standard deviation
-2 Standard deviations16.7716.0412.3914.2415.1615.6214.6612.3414.8612.57
+2 Standard deviations25.9228.0429.9629.6029.6429.1028.3526.7225.7224.18
Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level; NR means that the unit root hypothesis is not rejected.
Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level; NR means that the unit root hypothesis is not rejected.

Using the monthly data for the 1974–2001 sample, we find a lower unconditional mean and standard deviation, US$20.83 and US$1.78, respectively (Table 5.4). This translates into a shorter range for the 95 percent confidence interval from US$17.27 to US$24.39. This result is expected given the number of observations used for each specification.

Table 5.4.Regressions of Log of Brent Oil Prices(Nominal, Monthly Average Series)










Brent (t-1)1.10*1.12*1.35*1.34*1.33*1.32*1.32*1.28*1.23*1.20*
Brent (t-2)-0.16*-0.19*-0.38*-0.37*-0.37*-0.36*-0.35*-0.32*-0.28*-0.27*
Standard error0.
Number of observations336240240240240240240240240240
Unit root test11NRNRNRNRNR1055
Unconditional mean
Standard deviation
-2 Standard deviations17.2716.8714.5615.9016.6416.6714.2115.6915.9816.14
+2 Standard deviations24.3925.7727.2827.3127.7527.0526.8925.0724.0323.01
Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level; NR means that the unit root hypothesis is not rejected.
Sources: WEO database; and authors’ calculations.Note: * significant at the 1 percent level; ** at the 5 percent level; and *** at the 10 percent level; NR means that the unit root hypothesis is not rejected.

Rolling regressions are performed to examine the robustness of the above results. The 1974–2001 sample is broken up into nine subperiods of 20 observations (Table 5.3). The results are broadly consistent with those for the whole 1974–2001 sample, but would point to relatively more uncertainty as to the unconditional mean. The estimates of the unconditional mean range from a low of US$19.53 for the 1980–1999 sample to a high of US$22.40 for the 1977–1996 sample. Moreover, the standard deviation is also higher in all of the subsamples, peaking at US$4.39 for the 1975–1994 subsample—implying a 2 standard deviation range from US$12.39 to US$29.96. Given the smaller sample and higher estimates on the coefficient of lagged oil, the unit root hypothesis could not be rejected for most of these subsamples. Only in two cases is it rejected, although the estimate on lagged oil never exceeds 0.72.

The same time periods are used to run rolling regressions on the monthly data, each with 240 observations (Table 5.4). The estimates of the unconditional mean range from a low point of US$19.57 for the 1982–2001 period to a peak of US$22.19 for the period between 1977–1996, again showing slightly less volatility than the annual series. The standard deviation is also higher for most of the subsamples, but it is contained within a smaller range, going from a low point of US$1.72 for the 1982–2001 sample to US$3.18 for 1975–1994. The hypothesis of the unit root is rejected for the first subperiod (1974–1993), and for all the samples starting after 1980. The rolling regressions are also performed on the monthly data for the post-1987 sample to allow for the possibility of a break in 1986 as found by Akarca and Andrianacos (1995, 1997, and 1998). These results (not presented) suggest a lower mean price (US$18.71) relative to the 1974–2001 sample and a lower standard deviation.

The above regressions provide strong evidence of mean reversion, but also highlight that there is uncertainty as to the true underlying parameters. The implied unconditional mean of oil prices varies depending on the sample period, as does the standard deviation. This could reflect normal sample fluctuation, or the fact that despite strong evidence in favor of mean reversion, the underlying mean that is being reverted to fluctuates modestly over time.

V. Oil Wealth

One of the objectives of this paper is to understand how movements in oil prices affect estimates of government oil wealth. As noted above, oil wealth is a key determinant of the size of the sustainable non-oil fiscal deficit, and thus an important variable for fiscal policy formulation. For example, if oil price shocks have a large impact on estimates of government oil wealth, then, at least on sustainability grounds, there would be a basis for adjusting the non-oil balance in line with oil price movements.13 At the same time, the variance of the oil wealth estimates also matters. The larger the uncertainty about the estimate of wealth, the stronger the precautionary savings motives would be.

Translating oil price movements into changes in fiscal oil wealth, however, is complicated and requires making numerous assumptions. The first set of complications relates to the calculation of the present discounted value of total oil revenue. In addition to the path of prices, such a calculation depends on the interest (discount) rate, the amount of oil reserves, the number of years that it will take to exhaust the reserves, and the amount of extraction that will take place in any given period. Moreover, these factors may themselves depend on oil prices. For example, price movements could affect decisions on how much oil to extract in a given period, or might induce more exploration that may result in finding additional reserves.

The second set of complications relates to translating the flow of gross oil revenue into government oil revenue. This would depend on the profits in the oil sector, which are likely to be a nonlinear function of oil prices. In particular, if extraction costs contain a large fixed component (as they probably do), then a given percentage change in prices would translate into an even larger change in profitability. For example, if the cost of extraction per barrel is US$10, a 20 percent increase in the price from, say, US$20 to US$24 results in a 40 percent increase in profitability, from US$10 to US$14 per barrel. Another consideration is the financial relationship between the government and the oil sector, including whether most fiscal oil revenue comes from ownership in the oil company, royalties, or taxation—a fiscal regime, moreover, which could be nonlinear in profitability. These considerations suggest that some caution is warranted in translating oil price movements into changes in fiscal revenue.

In light of the above considerations, the following examples should be seen as illustrative. In any event, country-specific estimates could be calculated by making the corresponding adjustments to the assumptions. To keep matters simple, it is assumed that extraction lasts for a fixed number of years, a constant amount of oil is extracted in each period, and the discount rate is constant. The per-period extraction is also normalized to one—the results, therefore, could be equivalently viewed as the expected return for producing a barrel of oil each year for the given number of years. Finally, the cost of extraction is assumed to be a fixed amount per barrel.

The specific values of these parameters are varied in the calculations below to assess the sensitivity of the results. In all cases, however, the interest rate is fixed at 3 percent. This is somewhat low for a nominal interest rate—given that nominal prices are being projected—but it could also be interpreted as a proxy for the real interest rate under the assumption that in the very long run oil prices grow in line with inflation. The period during which extraction is projected to take place is set at either 25 years, 50 years, or infinite. The extraction costs are either set at zero—implying that gross oil revenue is actually being calculated—or US$10 per barrel, to proxy for a relatively high-cost producer.

Mean of Wealth

Variations in the current price do not have a very strong impact on estimates of oil wealth. Intuitively, this follows from the finding that oil shocks are not that persistent, as embodied in the relatively fast mean reversion. Thus, whether oil prices at a particular point in time are high or low only affects the near-term price forecasts. The medium- to long-horizon forecasts are unchanged, so the impact on oil wealth would be limited to the impact of a few years of higher or lower prices. The sensitivity, therefore, would also depend on the remaining years of production, with short-term price changes more important for producers with fewer years of production remaining.

To illustrate this, oil wealth is simulated using a continuum of oil prices. Figure 5.5 shows the deviation of wealth from a reference value as a function of the current price, where the reference value of wealth is calculated by setting the price to its long-run average. The parameters from the regressions on annual data (1975–2001) are used, which, as an AR(1), has the advantage that the current price is all that is needed to determine the future path of prices and therefore wealth. Focusing on the top panel, which assumes that extraction costs are zero, the sensitivity to changes in price is greater (as seen by the higher slope) the fewer years of production remaining. The magnitude of the changes, however, are not that large even for the producer with only 25 years of production remaining; for example, an increase in the price from US$10 to US$30 would only increase wealth by around 12 percent. The bottom panel of Figure 5.5 repeats the exercise with extraction costs set to US$10 per barrel. The sensitivity, as expected, increases; for example, an increase from US$10 to US$30 for the high-extraction-cost producer with 25 years of oil remaining results in a 24 percent increase in wealth.

Figure 5.5.Oil Wealth Simulations

(In percent of reference value of wealth)1

Source: Authors’ calculations.

1Reference value of wealth is calculated by setting the oil price to its long-run average.

It follows, therefore, that the changes in oil wealth induced by the yearly fluctuations in oil prices are generally not too large (see Table 5.5).14 For example, when oil prices increased by 60 percent in 2000, a “no extraction cost” producer would have experienced an increase in oil wealth ranging from 5½ percent to around 3 percent depending on the years of production remaining. As highlighted above, a high-cost producer would experience a larger change in wealth, but the amounts still are not that large. Again looking at 2000, oil revenue would have increased by nearly 140 percent for the high-cost producer, yet wealth would have grown by only 10 percent or so (for a producer with 25 years of production remaining) and less for a producer with more years of production remaining. On the rough assumption that the sustainable non-oil deficit moves in line with oil wealth, the implied elasticity (which depends on the price) of the sustainable non-oil deficit with changes in oil prices is generally well below 10 percent.15

Table 5.5.Annual Change in Oil Wealth and Revenue(In percent)
No Extraction CostHigh Extraction Cost
Brent PriceWealth (production years)Wealth (production years)
Sources: IMF, International Financial Statistics; and authors’ calculations.Note: The wealth estimates assume that the log of oil prices follows an AR(1) with a constant of 1.487 and AR(1) coefficient of 0.514.
Sources: IMF, International Financial Statistics; and authors’ calculations.Note: The wealth estimates assume that the log of oil prices follows an AR(1) with a constant of 1.487 and AR(1) coefficient of 0.514.

Videgaray (1998) finds qualitatively similar but generally larger effects of oil price changes on wealth. His calculations are roughly comparable to the no-extraction-cost infinite producer in Table 5.5. Whereas he estimates a decrease in wealth of 26 percent in 1986 (the largest decline in his table), Table 5.5 implies a decrease in wealth of only 3.6 percent. Nonetheless, he reports a change in wealth greater than 5 percent in only 7 of the 17 years of data (1980–1996). The main reason for the higher sensitivity is that there is more persistence of the shocks in his model and thus slower mean reversion.

Variance of Wealth

The impact of oil price changes on wealth needs to be viewed in the context of the more general uncertainty surrounding wealth expectations. As highlighted above, the parameters of the oil price equation are themselves unknown. This implies that the variance (or standard deviation) of wealth expectations could be calculated by factoring in the parameter uncertainty. The parameter uncertainty affects both the long-run average price and the persistence of price shocks—both of which would have an impact on the variance of wealth expectations. In particular, the sensitivity of wealth to changes in the oil price depends on the persistence of shocks. If the persistence is underestimated, for example, then the sensitivity of wealth to price changes—as analyzed above—is also underestimated. While this effect is potentially quite important, the uncertainty about the long-run prices is algebraically easier to examine and sufficient to demonstrate that there is a good degree of uncertainty surrounding wealth expectations.

Uncertainty about the parameters to use in estimating oil wealth translates into a high variance in wealth expectations. As noted above, the standard deviation for the long-run oil price in the 1974–2001 annual regression (Table 5.5) is around 10 percent of the price. This implies that for the no-extraction-cost producer (with infinite production years remaining) the standard deviation of wealth is also 10 percent. Or, viewed alternatively, the 95 percent confidence interval spans roughly from 80–120 percent of expected wealth. In contrast, an oil price variation from US$10 to US$30 translates into movements equivalent to 96–102 percent of expected wealth (see Figure 5.5). In light of the variance of wealth expectations, such a change in expected wealth would not be statistically significant. For the high-extraction-cost producer, the uncertainty about wealth is substantially greater as the appropriate standard deviation to use would be in excess of 20 percent.

VI. Summary and Conclusions

The empirical investigation of the statistical properties of oil prices suggests that most oil price movements are transitory. In particular, accepting that there are periodic permanent oil shocks (such as in 1973), the evidence suggests that oil prices are mean reverting. Mean reversion is supported both by conventional unit root tests and an analysis of price expectations as embodied in the term structure of futures prices. The futures price data imply that around 60 percent of a given price shock is expected to be reversed after one year. Conventional unit root analysis on nominal oil prices generally rejects the unit root hypothesis using both monthly and annual data—with the important caveat that the sample must begin after 1973.

The presence and the pace of mean reversion in oil prices suggest that the year-to-year fluctuations have only a minor impact on oil wealth. This implies that for the most part (and looking only at sustainability considerations) a government should not adjust the non-oil balance that much in response to oil price changes. Moreover, the change in expected oil wealth from changes in prices is likely to be quantitatively insignificant relative to the uncertainty surrounding projections of oil wealth. This reinforces the view that a given change in oil prices does not convey too much new information about government wealth nor the sustainability of fiscal policy.


The authors are grateful to Paul Cashin, Nigel Chalk, James Daniel, Jeffery Davis, Lucien Foldes, and Rolando Ossowski for helpful comments. The views expressed in the paper, as well as any errors, are the sole responsibility of the authors and do not necessarily represent the opinions of the Executive Board of the IMF or other members of the IMF staff.

Barnett and Ossowski, however, highlight that there are a variety of macroeconomic and fiscal factors that need to be considered in assessing the appropriate fiscal response to an oil shock.

In only one of the six tests reported (longest sample with four lags), the null hypothesis could not be rejected at the 10 percent level. In the shorter samples (1925–1996 and shorter), however, the unit root hypothesis is not rejected, although the author cautions that the sample size is insufficient to reject the unit root hypothesis given the slow mean reversion, and that failure to reject is not the same as accepting. These points are also pertinent for what follows.

The data are monthly averages of futures contracts for sweet oil as traded on the New York Mercantile Exchange between March 1983 and November 2001.

The nearby futures price—that is the futures price that expires next—is used as a proxy for the spot price in this section (see Bessembinder and others, 1995, regarding the advantages of proceeding this way).

This holds for contracts with up to 18 months’ maturity (for which there are no missing observations during the sample period); for longer-dated contracts there are significant missing observations, which makes the comparisons less straightforward.

The regressions and unit root tests below use the log of oil prices; however, repeating the above calculations expressing the futures prices in logs yields very similar results—the range, with rounding, is still 0.95–0.96.

Only contracts that had volume reported for that day are included in the graph. Since we are interested in the longer-dated futures, days (each in January to facilitate comparison) with the most activity in the longer-dated futures were selected. The December futures contracts often have activity six years in advance.

Data are from IMF’s International Financial Statistics unless noted otherwise. Prices in real terms are constructed using the U.S. manufacturing unit value (MUV) index as the deflator.

A11 the empirical exercises, unless otherwise noted, use the natural logarithm of the given price. A description of the unit root tests and results is available upon request from the authors.

Specifically, cointegration tests were performed allowing for either zero or one lag in the data. In none of the five common permutations (that is no trend, linear trend, or quadratic trend in the data combined with various combinations of a trend or constant in the cointegrating relationship) was there evidence of any cointegrating relationship.

The annual regressions use the results from an AR(1) regression, while the monthly regressions are based on AR(2) in line with the results for the Schwarz criterion and consistent with Akarca and Andrianacos (1998).

Barnett and Ossowski (see Chapter 3 in this volume) elaborate on this, and also discuss why, in general, the non-oil balance should often be adjusted cautiously to increases in prices, even if a greater increase might be warranted based solely on sustainability considerations.

The change in oil wealth is approximated by comparing oil wealth for a given type of producer (no cost or high cost, and number of years of production remaining) in a given year with the previous year. For example, the oil wealth of a producer with 25 years of production remaining in 2000 is compared to a producer with 25 years of production remaining in 1999.

For example, suppose that a non-oil deficit equivalent to 5 percent of GDP is deemed sustainable and oil revenue is 6 percent of GDP (implying some wealth accumulation). An elasticity of 10 percent would imply that if oil revenue doubled to 12 percent of GDP (an increase of 6 percentage points of GDP), the sustainable non-oil deficit would rise by only ½ percentage point of GDP. Moreover, most of the implied elasticities in Table 5.5 are well below 10 percent.

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