Download OPEC`s Kinked Demand Curve

April 9, 2014
OPEC’S KINKED DEMAND CURVE
Marc H. Vatter∗
Economist
Economic Insight, Incorporated
9 Underhill Street, Nashua, NH 03060-4060
603.402.3433; 503.227.1994; [email protected]
Abstract
I estimate world demand for crude oil, non-OPEC supply, and the effects of changes in price on world
GDP using quarterly data covering 1973 to 2010. World GDP falls more with increases in price than it
rises with decreases in price. Therefore, instability in price negatively impacts GDP. World demand and
net demand to OPEC are kinked due to the asymmetric effects. The kink implies a vertical discontinuity
in OPEC’s marginal revenue curve. Shifts in cost and horizontal shifts in demand are less destabilizing
with the kink. However, vertical shifts cause larger changes in price, and this accentuates destabilizing
feedback between changes in price and GDP. The kink also implies a range of equilibrium prices and
quantities of production for the cartel. If OPEC’s long run marginal cost, inclusive of marginal user cost,
is $35/bl in 2014, I estimate that any price between $99/bl and $106/bl would provide OPEC no incentive
to change under its long run demand schedule. Using a demand curve applicable to a twelve month
period, an increase (shock) to prices above $142/bl would be profitable for OPEC. Net demand to OPEC
is quite inelastic in the short run, and estimated contemporaneous effects of price on GDP are negative.
Therefore, unstable prices generate countercyclic profits for OPEC, which have hedging value in
financial markets, further incenting OPEC to set unstable prices.
JEL Classification Numbers: Q34; Q41; Q43
Keywords: OPEC; Crude Oil; Price Shock
I thank Sophocles Mavroeidis, Harumi Ito, Talbot Page, Sam Van Vactor, John Driscoll, Andres Rosas,
Chun Chung Au, and David Weil for helpful comments. I thank my mother, Barbara Hudson, Elizabeth
Ferreira, and Micki Spenst for personal support. I thank Barbara and Marshall Hudson for financial
support. I thank my father, Harold Vatter, for his support, including many discussions about the U.S.
economy after the 1970’s oil shocks. I am grateful that I am someone who can “rejoice in his labor, this
is a gift of God” (Ecclesiastes 5:19; Young’s Literal Translation). Errors and views expressed are mine
and do not necessarily reflect those of Economic Insight, Inc.
∗
This project began as dissertation research in Economics at Brown University and has continued in affiliation with
Economic Insight, Inc., P.O. Box 2295, Sisters, OR 97759; www.econ.com. Contact information for Marc Vatter:
vatter.econ.com; [email protected]; 603.402.3433; 503.227.1994; 9 Underhill Street, Nashua, NH 03060-4060.
1
1 Introduction
The price of crude oil has been less stable, and marked by upward shocks, and world economic
growth has been slower, since the Organization of Petroleum Exporting Countries first wielded its
market power assertively in 1973.1 Figure 1 shows the log real price of West Texas Intermediate
crude oil and the real rate of growth of the world economy from 1951 to 2010.
Figure 1: Log Price of WTI and Annual Growth Rate of World GDP; 1951-2010
8
7
6
5
4
3
2
1
0
-1
GDP
2008
2006
2003
2001
1998
1996
1993
1991
1988
1986
1983
1981
1978
1976
1973
1971
1968
1966
1963
1961
1958
1956
1953
1951
WTI
Sources: Federal Reserve Bank of St. Louis; Angus Maddison Project; IMF
From the 1930’s through the 1960’s, major international oil companies known as the “seven sisters”2
colluded through periodic agreements whose terms effectively stabilized the price of crude oil above
marginal cost. Moran (1993) wrote
Taken together, the IPC and the As Is Agreements, operating in tandem with the Texas
Railroad Commission in the United States, stabilized 1935-40 world prices at a level ten to
eleven times the marginal cost of production in the Persian Gulf. (p. 176; emphasis added)
Beyond the automatic execution of standing agreements, much of the short term collusion among
these firms had to be secret or tacit.
1
See Greenhouse (1987) for journalistic observations.
Their names changed with time. Moran (1993) listed them as Exxon, British Petroleum, Royal Dutch-Shell,
Gulf, Mobil, Texaco, and Chevron.
2
In 1954, sales agreements became the principal focus of the Justice Department's anti-trust
case against the oil companies. In 1960, the corporations signed a consent decree promising
not to engage in any further explicit market-division practices. (p. 178; emphasis added)
This also stabilized price because the cost of coordinating a change in price secretly or tacitly was
high. The sisters risked uncoordinated changes in price being seen by one another as violations of
contracted, secret, or tacit agreements, rather than as price leadership. OPEC was also founded in
1960. Unlike the sisters, OPEC can meet openly to discuss and agree on changes in price and output.
Individual members can have much more confidence that other members will raise price (cut output)
when they themselves do as part of a price increase that is profitable to the cartel, more confidence
than if the price increase had to be accomplished through secret or tacit cooperation.
...the challenge of maintaining an oligopoly should have been and should continue to be
easier for the Organization of Petroleum Exporting Countries (OPEC) than it was for the
international oil companies: OPEC can meet and negotiate openly, while the companies had
to be furtive and wary of public attack..." (p. 159)
But maintaining an oligopoly and maintaining price are not the same thing. OPEC generally
maintains price above marginal cost in the long run, as the sisters did, but it does not need to accept
an unprofitably stable price in the short run. OPEC can effect changes in price ad hoc.
OPEC has turned its back on, and relinquished access to, the most important mechanisms of
restraint the companies managed to impose on themselves. It has systematically unraveled
the corporate structure of supra-sovereign limitations, self-denials, and automatic penalties on
the members’ own behavior... (p. 161; emphasis added)
Collusion within OPEC in the short run is overt, so it does not have the same stabilizing effect on
price that tacit collusion would. Nor is OPEC constrained by non-OPEC producers from changing
price. OPEC’s unrivaled market power means that it need not hesitate to increase price for fear that
others with market power will quickly raise production and usurp its market share. Non-OPEC
production rises significantly with price in the long run, but is insensitive to price in the short run.
Here, I argue that OPEC as a whole faces a kinked demand curve, because of asymmetric effects of
changes in the price of crude oil on world GDP, not because non-OPEC suppliers have market power.
Increases in the price of crude oil lower world GDP, and, therefore, demand for crude oil, more than
decreases in price raise them. The kink in OPEC’s demand curve implies a vertical discontinuity in
its marginal revenue curve. Within a corresponding range, decreases in production and sales raise
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price, but reduce revenue by more than they reduce cost, and increases in production and sales lower
price, but raise revenue by less than they raise costs.
Shifts in cost and horizontal shifts in demand cause less instability in price under a kinked demand
curve than under a non-kinked demand curve. With a kinked demand curve, a modest shift in
marginal cost will not change the profit-maximizing quantity of production and sales, or price. A
proportional horizontal shift in demand will also cause no change in price. A parallel horizontal
increase in demand will cause no change or an increase in price, while such a shift always increases
price when there is no kink in demand.3
That said, I still argue that the kink likely has de-stabilizing effects on price that exceed the stabilizing
effects. First, while the kink gives OPEC stronger incentive not to deviate from any
profit-maximizing price/production combination, there is a range of combinations from which OPEC
has such a strong incentive not to deviate, rather than the single such combination that would obtain
without the kink. Thus, modest “cheating” on quotas, disruptions in production, and the like do not
necessarily motivate any stabilizing correction by the cartel. OPEC has been described as “clumsy”.4
The apparent clumsiness may result, in part, from a multiplicity of equilibria in the cartelized market.
Second, a vertical shift in demand causes a greater change in price than it would absent the kink.
Marginal cost passes through the discontinuity gap in marginal revenue before and after a modest
vertical shift in demand, incenting no change in output, leading to a change in price equal to the full
vertical shift in demand. I show this in Figure 2. Demand shifts from D to D′ , and price shifts by
the same amount, from P to P′ , with no change in quantity produced.
3
4
See Frasco (1993).
See Adelman (2004).
4
Figure 2: Vertically Shifting Kinked Demand Curve
P’
P
MC
D’
D
Q
MR’
MR
In contrast, with a non-kinked demand curve, an increase in demand would lead to an increase in
price less than the full vertical shift in demand because the firm would increase output as marginal
revenue intersected marginal cost at a greater quantity of output.
Third, the kink accentuates feedback between the macroeconomy and the price of crude oil.
According to Shepherd (1933; pp. 724-5), a change in GDP per capita is best represented by a vertical
shift. Exogenous changes in world GDP, then, cause larger changes in the price of crude oil in the
presence of the kink. This instability in price will, in turn, further destabilize the macroeconomy.
Fourth, the instability in price fostered by the kink produces a countercyclic stream of profits for
OPEC, which has hedging value in financial markets. Since changes in price negatively impact the
macroeconomy, OPEC’s profits when price is unstable are countercyclic. Demand is inelastic in the
short run. Assuming increasing marginal costs, an increase (decrease) in price will raise (lower)
revenue, lower (raise) cost, and lower (raise) world GDP. The countercyclic stream of profits can be
bundled into a financial instrument that commands a risk premium in financial markets. The
premium obtains because such an instrument can be used to smooth out undesirable fluctuations in
consumption associated with the macroeconomic instability caused by the changes in price.
5
Fifth and finally, though a change in population is better represented by a horizontal shift, if the
macroeconomy is less stable than costs of extracting crude oil and world population, shifts in cost and
demand taken together will cause greater instability in the price of crude oil under a kinked demand
curve than under a non-kinked curve.
OPEC, then, may well find unstable prices more profitable than stable prices.
The Seven Sisters as a whole may also have faced a kinked demand curve, but oil prices were more
stable before 1973 because the Sisters’ collusion had to be tacit, and because of their greater
accountability in general to the government of the United States and other large oil-consuming
nations.
I estimate world demand for crude oil, non-OPEC supply, the effect of crude oil prices on world
GDP, and, therefore, net demand to OPEC. In their survey of literature on energy demand, Atkins
and Jazayeri (2004) discuss three major areas of refinement to the traditional model of demand that
apply to crude oil: asymmetry; regime change; and changing seasonal patterns. Increases in the price
of crude oil affect quantity demanded and GDP differently from decreases. Regarding demand,
according to Atkins and Jazayeri (p. 31), “To say that there is an asymmetry of response appears to be
observationally equivalent to saying that there is some underlying, longer run decrease in demand due
to some kind of energy efficiency of use.” Griffin and Schulman (2005) make a case that a
symmetric specification with a trend toward energy saving technical change is superior. Such a trend
may include deterministic and stochastic elements. Wing (2008; p. 24) states “Of the changes that
occur within industries, disembodied exogenous technical progress is the predominant energy-saving
influence.” I model the direct effects of price on demand as symmetric, and I include both a
deterministic trend and lagged dependent variables in my regression. I allow for asymmetric effects
of crude oil prices on the world economy. In short, I model the market as though all asymmetric
impacts of price on demand result from asymmetric impacts of changes in price on GDP.
Regression analysis of nonstationary time series can produce spurious estimates. Atkins and Jazayeri
argue against the hypothesis of unit roots in oil market data and in favor of multiple structural breaks,
or “regime change”. When modeled as dynamic processes with no changes in intercept or trend,
world GDP and world production, non-OPEC production, and the price of crude oil are nonstationary.
With one major exception, the 1990-91 Gulf War, these apparent nonstationarities are cointegrated by
the estimated coefficients. To the considerable extent that the apparent nonstationarities actually
6
reflect structural breaks, the regressions use most of the information the breaks provide in a way that
leaves stationary residuals and makes economic sense. The exception, as noted, is that I did model
structural breaks in non-OPEC supply around the time of the Gulf War.
Changing seasonal patterns observed in the market for crude oil may be the result of global climate
change. I make no estimate of such a trend, but I purge the data of sample-wide seasonal regularity,
so forecasts based on the estimates do not reflect outdated seasonal patterns in a static sense.
I discuss the data in Section 2. I describe the estimates of world demand for and non-OPEC supply of
crude oil in Section 3, and the effects of crude oil prices on world GDP in Section 4. In Section 5, I
discuss OPEC per se: I calculate net demand to OPEC and present estimated elasticities, marginal
revenue gaps, and ranges of profit-maximizing prices. I conclude in Section 6.
2 Data
Table 1, at end, shows the basic data, various transformations of which I use to make the estimates.
The footnotes to Table 1 explain most of the columns, but Column A is the U.S. refiners’ acquisition
cost of imported crude oil, tabulated and defined by the U.S. Energy Information Administration
(EIA) as the “world price” of crude oil in its analyses and forecasts. I assume that the world market
for crude oil is integrated. According to Adelman (2004; p. 19), “Most oil moves by sea, and ships
can be diverted from one destination to another relatively easily. Moreover, much additional oil can
be diverted from land shipment to sea. Hence, it is fairly easy to reroute shipments of oil from
nations that have a sufficient supply to nations that are experiencing a shortage. It is only a minor
exaggeration to say that every barrel in the world competes with every other.”
7
Between early 2011 and mid-2013, oil prices in the North American interior, as measured by the
West Texas Intermediate (WTI) New York Mercantile Exchange (NYMEX) benchmark, fell relative
to their historic relationship with oil prices elsewhere. Historically high world prices made large
quantities of unconventional crude oil economically recoverable. The additional production
congested pipelines between Cushing, OK, where the benchmark is priced, and the U.S. Gulf Coast,
separating WTI from the world market. The Brent-WTI split stood at $6.31/bl as of March 6, 2014,
much narrower than its $27.31/bl average in September, 2011, but still higher than its, slightly
negative, historical norm.5
The separation in markets extended to that for retail products. Figure 3 shows the Brent – WTI split
(in $/bl) along with the difference between the simple average of retail gasoline prices (in ¢/gallon)
across PADDs 1, 3, and 5 (U.S. coastal areas) and that across PADDs 2 and 4 (U.S. interior).6 As the
Brent – WTI split became large, so did the difference in gasoline prices. A regression of the
difference in gasoline prices on the split, monthly dummies, and twelve lags of the dependent variable
gives a coefficient on the split with a t-statistic of 2.14; there is no autocorrelation in the residuals.
When the split is small, so is its effect on gasoline prices, but in September 2011, this coefficient
implies an elasticity of the difference in gasoline prices with respect to the Brent – WTI split of 0.45,
which is significant. I conclude that the North American interior has been a distinct and separate
market for crude oil and products since early 2011, and I do not use data from after 2010 in my
analysis. Apart from its simplicity, this way of dealing with the fragmentation of the market in recent
years means that when I later apply the estimates in a more current (2014) context, I am doing so well
out of sample, a good test of the accuracy of a model.
5
More information is available at http://www.eia.gov/todayinenergy/detail.cfm?id=11891, accessed July 15,
2013.
6
“PADD” stands for “Petroleum Administration Defense District”. See
http://www.eia.gov/todayinenergy/detail.cfm?id=4890, accessed March 6, 2014, for a map.
8
Figure 3: Brent - WTI Split and U.S. Regional Gasoline Prices
50
40
30
20
10
0
-10
PADDs 1, 3, & 5 less PADDS 2 & 4
2013
2012
2011
2010
2010
2009
2008
2007
2006
2005
2005
2004
2003
2002
2001
2000
2000
1999
1998
1997
1996
1995
1995
1994
1993
-20
Brent less WTI
Source: U.S. Energy Information Administration,
http://tonto.eia.gov/dnav/pet/hist/LeafHandler.ashx?n=PET&s=EMM_EPM0_PTE_R10_DPG&f=M, accessed
March 6, 2014.
I estimate the price of crude oil for October-December of 1973 based on monthly data on the rest of
this series and free-on-board and landed costs of crude oil imported to the U.S. from January 1974 to
April 2009. The prices of crude oil for October-December 1973 used to calculate the quarterly
average, highlighted in yellow in Table 1, are predicted values based on the following regression:
∆Pt world = −0.0083+ 0.5037 ∆Pt fob + 0.5435 ∆Pt landed
0.0276
0.0828
0.0856
(1)
where t is in months, ∆Pt world is the month-to-month change in the world price, ∆Pt fob the change in
the free-on-board price, and ∆Pt landed the change in the landed price. The R 2 = 0.9640 . A dynamic
process can be described as I ( d ) , where d = 1 corresponds to a unit root and d = 0 to perfect
covariance level stationarity. A generalization of this distinction is to allow d to assume non-integer
values. Robinson tests7 estimate the degree of fractional differencing, d, needed to render an I(d)
series I(0) using a log-periodogram regression. According to Baillie (1996; p. 21), “For
−0.5 < d < 0.5 , the process is covariance stationary, while d < 1 implies mean reversion.” A
7
See Robinson (1995).
9
(
)
Robinson test of the residuals in (1) estimates them to be I −0.2173 , where the number below is
0.0435
the standard error of the estimate.
Column H is the percent drop in world output of crude oil caused by war or civil conflict. The
episodes of war and civil conflict include the November 1973 Yom Kippur war, the November 1978
onset of the Iranian Revolution, the October 1980 onset of the Iran-Iraq war, the August 1990 Iraqi
invasion of Kuwait, civil unrest in Venezuela beginning in December 2002, and the U.S. invasion of
Iraq in March of 2003.
I derived real crude oil prices using Columns A and B.
I derived quarterly world GDP by applying quarterly variation in U.S. GDP, Column F, to annual
world GDP, Column E. Both U.S. GDP and U.S. consumption of crude oil declined from a fourth to
a fifth of the worldwide totals, and the oil intensity of the U.S. economy was about the same as that of
the world economy, throughout the sample. I used world GDP rather than OECD GDP as a measure
of income. The non-OECD share of world consumption of crude oil has increased from 25% to 50%
since 1970.8 Rapid economic growth has caused demand for oil to grow especially fast in some
non-OECD countries such as China and India. I used purchasing power parity (PPP) because market
exchange rates are subject to political and speculative influences that do not reflect the real incomes
of consumers of crude oil and those affected by the market for it. National GDPs calculated using
market exchange rates can deviate from purchasing power parity for extended periods.9
For each series in Table 1, I either used seasonally adjusted data, made adjustments for seasonality, or
found no seasonal variation when regressing them on seasonal dummy variables, so I made no
seasonal adjustments. I made no adjustments to my methods of estimation to account for the extent to
which the data used were estimated or constructed.
8
Source: U.S. Energy Information Administration, http://www.eia.gov/finance/markets/demand-oecd.cfm,
accessed March 7, 2014.
9
See Cashin and McDermott (2001).
10
2.1 Seasonal Adjustment
I removed seasonal variation in world production, non-OPEC production, and price in the following
manner: I regressed each series and its first differences on seasonal dummy variables; I added the
residuals from each regression to the mean of the dependent variable to get preliminary seasonally
adjusted levels and first differences, respectively; I added the cumulative sum of the preliminarily
seasonally adjusted first differences to the initial value of the preliminarily seasonally adjusted levels
to get secondarily seasonally adjusted levels; I added a constant to the secondarily seasonally adjusted
levels so that the mean of the resulting series was the same as that of the original series; this gave me
a final seasonally adjusted series. I found that this extensive process was necessary to purge both the
series and their first differences of regular seasonal variation, as measured by the (in)significance of
the coefficients when the final series and their first differences were regressed on seasonal dummy
variables.
3 World Demand for and Non-OPEC Supply of Crude Oil
I assume that the quantity of crude oil demanded equals the quantity supplied, as measured by world
production of crude oil. The quantity demanded, then, includes that amount added to inventory.
3.1 Specification of World Demand
I estimate quarterly world demand for crude oil as a linear function of a constant, price, world GDP, a
linear time trend, one lag of quarterly quantity demanded, and annual quantity demanded lagged one
quarter:
Dt = δ 0 + δ P Pt + δ G Gt + δ t + δ D Dt −1 + δ Dave Davet −1 + ε tD
(2)
Dt is quarterly quantity of crude oil demanded worldwide in billion barrels per year, Pt is the real
price of crude oil in 2005$/bl, Gt is world gross domestic product (purchasing power parity;
normalized to average 1 in 2005), t is time in quarters (t = 0 in 2011:II), Davet −1 is annual demand
11
for crude oil for the four quarters ending with quarter t − 1 , and ε tD is potentially heteroskedastic,
autocorrelated, and correlated with ε tS from (3), below.
The price term δ P captures the effect of contemporaneous price on the quantity of crude oil
demanded worldwide. I treated quantity demanded as a linear function of price so that the price
elasticity of demand would increase with price. Numerous substitutes for crude oil, including
potential conservation measures, exist, but they have only become competitive as oil prices have
reached new highs. These may include ethanol from cellulose as well as corn, biodiesel, coal to
liquids, natural gas to liquids, potentially huge reserves of natural gas hydrates below the ocean floor,
nuclear power, wind power, photovoltaic solar power, electric cars, and denser urban design. The
choice of price rather than log price as a regressor, then, is motivated by the assumption that greater
competitiveness of alternatives to crude oil increases the price elasticity of demand for crude oil as
the price reaches new highs. If price trends up faster than demand, the associated percentage drop in
quantity demanded increases as the price increases. Adelman (1990; p. 11) wrote “…the higher the
price, the greater the incentive to consumers to substitute other comparable goods; and to producers,
to substitute labor and capital or other inputs. In addition, for both consumers and firms, there is an
income effect pushing the same way: the greater the importance of the product in the total budget, the
more important the impact of a further increase. Hence the higher the price, the greater the response
to a given price change.” Statistically, price performed better than log price in specification tests.
I include a time trend to account for increasing efficiency in the use of crude oil. From Table 1, the
ratio of world crude oil consumption to GDP in 2009 was a fifth of what it was in 1974. While some
of this resulted from substitution of other fuels for oil, most did not. In 2010, worldwide consumption
of primary energy of all kinds per unit of GDP was a fourth of what it was in 1980.10 According to
Atkins and Jazayeri, inclusion of the time trend obviates the need to model the direct effects of price
on demand as asymmetric, since the two are observationally equivalent. According to Griffin and
Schulman, the trend is superior. According to Wing, the deterministic trend is important, at least in
the U.S.
I model persistence in demand for crude oil using both quarterly and annual quantity demanded of
crude oil lagged one quarter; Dt −1 and Davet −1 . Rather than using a series of quarterly lags, I use an
10
Source: U.S. Energy Information Administration;
http://www.eia.gov/cfapps/ipdbproject/IEDIndex3.cfm?tid=44&pid=44&aid=2, accessed July 15, 2013.
12
annual average to emphasize long term persistence.11 Short term persistence results from rigidity in
planning for the use of oil-specific capital and durables, such as travel planning. Long term
persistence results from the sunk costs of large amounts of substantially oil-specific physical and
human capital and durables, beginning at the refinery and continuing downstream to such things as
gasoline-powered vehicles and auto-oriented urban design. The sunk costs make maintenance of
existing capital cheaper than replacement with new capital better optimized to a current price of crude
oil. Both “short term” and “long term” persistence are short run phenomena, in that there are no sunk
costs of oil-specific capital and durables, and, therefore, no persistence, in the long run. Although its
coefficient is only statistically significant at the “85% level” in the regression below, including
Davet −1 improves the model’s performance in specification tests.
3.2 Specification of Non-OPEC Supply
I modeled non-OPEC supply as a linear function of a constant, a dummy variable for the quarters
surrounding the Gulf War, log price, cumulative non-OPEC supply lagged one quarter, a one quarter
lag in interest on three-month U.S. treasury bills, a one quarter lag in the trade-weighted exchange
value of the U.S. dollar, a linear time trend, and quarterly non-OPEC production lagged one quarter.
St = η0 + ηGW M t90 III 92 IV + η p pt + ηCS Ct −1 + ηi it −1 + η X X t −1 + η t + η S St −1 + ε tS
(3)
where St is quarterly non-OPEC quantity supplied, M t90 III 92 IV is a dummy variable equaling 1 from
1990:III through 1992:IV, pt ≡ ln Pt is log price, Ct −1 is cumulative non-OPEC production lagged
one quarter, it −1 is interest on three-month U.S. treasury bills lagged one quarter, X t −1 is the
trade-weighted exchange value of the U.S. dollar lagged one quarter, t is a linear trend measured in
quarters and equaling zero in 2011:II, and ε tS is potentially heteroskedastic, autocorrelated, and
correlated with ε tD from (2).
Iraqi and Kuwaiti production fell during and after the Gulf War, the International Energy Agency
tapped strategic stocks, expectations changed significantly and frequently, and short term volatility in
price increased at the time of and following Iraq’s August 1990 invasion of Kuwait. Allowing a
11
This also keeps down the number of regressors and, therefore, the variances of the estimates.
13
temporary shift in intercept during this time improved the results of tests of specification and
stationarity.
I use log price so that the price elasticity of non-OPEC supply decreases in quantity supplied. While
many sources of crude oil may be available, there is substantial variability in the cost of extracting
and finding them. The decreasing short run elasticity reflects the effect of increasing costs of
extraction as existing sources are used more intensively. Decreasing long run elasticity and lagged
cumulative supply reflect increasingly costly sources being exploited.
The U.S. interest and exchange rates reflect the importance of the U.S. dollar to commodity markets
in general and that for crude oil in particular. Both organized exchanges and contracts for crude oil
typically quote prices in dollars. The dollar was the world’s “petro-currency” throughout the sample
period and remains so today. The nominal rate of interest on dollar-denominated securities
essentially measures the degree of inflationary expectation for the U.S. economy: The “real interest
rate” component measures the extent to which the Federal Reserve tightens credit to prevent inflation,
and the remaining component represents the extent to which it accommodates inflation. A change in
the exchange value of the dollar can affect the incentive to produce under non-indexed lease
agreements and forward contracts, but it will only shift demand for crude oil between the U.S. and
other countries, without having much affect on world demand, since the U.S. economy is about as
oil-intensive as the world economy as a whole. Empirically, if I include it −1 and X t −1 in the demand
equation, both when retaining them in and when removing them from the supply equation, they are
not at all statistically significant in the demand equation.
The time trend captures the effect of advancing technology of exploration, development, and
extraction. Lagged quantity supplied reflects persistence in supply resulting from the presence of
physical and human capital specific to exploration and extraction of crude oil.
I tried including an annual moving average term lagged one quarter, Savet −1 , like Davet −1 in (2), in
(3). While including Davet −1 in (2) improved the results of specification tests, excluding Savet −1
improved the results of specification tests. The re-optimization of investment in exploration and
extraction in response to changes in the price of crude oil is less complicated than that of the capital,
durables, and other factors used in combination with crude oil, so long term persistence does not
warrant emphasis in a separate variable in the case of non-OPEC supply, as it does in demand.
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3.3 Identification and Estimation of World Demand and Non-OPEC Supply
Identification of world demand and non-OPEC supply is the most challenging aspect of making these
estimates. I treat the price term in (2) as an endogenous regressor because innovations in demand can
cause contemporaneous changes in price. I treat log price in (3) as endogenous because it depends on
shifts in supply. I also treat GDP, in (2), as endogenous because, for example, a war could affect both
demand for crude oil and GDP. Price and log price are codetermined, so there are, effectively, two
endogenous regressors in the system.
Finding excluded instruments that are both strong and exogenous to a global market with
macroeconomic externalities is difficult to do perfectly. I use one- and two-year (i.e. four and eight
quarter) lags of disruptions in world supplies of crude oil resulting from war or civil conflict, Qt − 4
and Qt −8 , and one- and two-year lags of world GDP, Gt − 4 and Gt −8 . All of the excluded
instruments are lagged and, therefore, not causally impacted by innovations in demand for or supply
of crude oil. Hamilton (2003) uses disruptions to crude oil supplies to extract variation in price that
was exogenous to U.S. GDP. The variable Qt is the percent drop in world supply of crude oil during
Quarter t associated with the episodes listed in the description above of Table 1, all of which occurred
in OPEC countries. It is an extension of Hamilton’s instrument. Qt represents changes in OPEC
production associated with conflict.
Lagged GDP is a strong instrument for current GDP, and it is unlikely that the four- and eight-quarter
lags would correlate with current demand without also correlating with lagged demand, which is well
controlled for in (2). More generally, because current and lagged market quantities, prices, incomes,
and technological change are controlled for as well, the excluded instruments correlate with these
and, therefore, need not correlate with the current error term. In a recursive dynamic process such as
that followed by demand in (2), lagged values of the regressors affect the dependent variable through
its lags in a way that declines geometrically with the length of the lag. When lagged GDP affects
lagged price, it will also, in turn, affect current demand through lagged demand. GDP can be
modeled as having its own recursive process, but its dynamics are modeled in a manner in the
recursive process describing demand, as well. Finally, inasmuch as, beyond these effects, lagged
GDP still affects the error term, it will likely have a greater effect on lagged errors than current ones,
15
and these effects will also be captured in the dynamic process followed by demand. The current error
term, ε tD , may be unaffected if it is not correlated with lagged errors; Figure 4, below, shows no 95%
statistically significant autocorrelation in the residuals from estimation of (2), and the p-value in a
Portmanteau’s Q test of the null hypothesis that the residuals associated with (2) are white noise is
0.9985. In sum, Equation (2) substantially provides ways for Gt − 4 and Gt −8 to affect Dt through
ε tD−8...1 , Gt −7...0 , Pt −8...0 , Dt −8...1 , and Davet −8...1 , rather than through ε tD , and there is no evidence of
correlation between ε tD−8...1 and ε tD . Furthermore, the p-value in a Sargan test of the joint null
hypothesis that Gt − 4 , Gt −8 , Qt − 4 , and Qt −8 are uncorrelated with ε tD and ε tS and correctly excluded
from (2) and (3) is 0.69. Perhaps most tellingly, in a first stage regression of Dt on all exogenous
variables, neither Gt − 4 nor Gt −8 is statistically significant ( t = 0.04 and − 0.77 , respectively), while
Dt −1 is highly significant ( t = 6.92 ).
3.4 Results and Testing of Estimated World Demand and Non-OPEC Supply
Three stage least squares accounts for correlations in errors across equations. I used ®Stata’s reg3
command to estimate Equations (2) and (3) simultaneously using iterated generalized least squares. 12
The estimates, shown in Equations (4) and (5), converged in five iterations.
Dt = -1.7283 − 0.0125 Pt + 0.0441Gt − 0.0715 t + 0.7655 Dt −1 + 0.1526 Davet −1 + etD
1.6155
0.0044
0.0184
0.0362
0.0956
0.1010
St = 8.1301− 0.0750 M t90 III 92 IV + 0.2376 pt − 0.0227 it −1
3.2638
0.0385
0.0764
0.0086
+ 0.3520 X t −1 − 0.0416 Ct −1 + 0.2211t + 0.9416 St −1 + etS
0.1479
0.0162
0.0892
(4)
(5)
0.0192
The R 2 = 0.99 for demand and 0.98 for non-OPEC supply. All of the coefficients are significantly
different from zero at the 99% level except: the Gulf War dummy variable, which is significant at the
90% level; the demand constant, which is not significant; the deterministic trend in demand, which is
significant at the 95% level; and Davet −1 , which is “significant at the 85% level”. Portmanteau’s Q
12
I performed my calculations using Stata/SE Version 10.1 for Windows.
16
tests of the null hypothesis that etD and etS are statistical “white noise” give p-values of 0.9985 and
0.5243, respectively. Figure 4 shows the autocorrelations among the residuals from (4) and (5).
Figure 4: Autocorrelations
_____________________________________________________________________________
Supply Residuals
-0.20
-0.20
-0.10
-0.10
0.00
0.00
0.10
0.10
0.20
0.20
Demand Residuals
0
10
20
Lag
30
40
0
Bartlett's formula for MA(q) 95% confidence bands
10
20
Lag
30
40
Bartlett's formula for MA(q) 95% confidence bands
______________________________________________________________________________
Robinson tests estimate the degree of fractional differencing, d, needed to render etD and etS level
(
)
stationary I ( 0 ) to be d = −0.0410 and d = 0.0918 , respectively. The residuals are sufficiently
0.0572
0.0872
stationary to dismiss the possibility that the estimates in (4) are spurious because of any
nonstationarity in the regressors. Whatever non-stationarity exists in the regressors is cointegrated.
4 The Price of Crude Oil and World GDP
The price of crude oil affects world GDP which, in turn, affects demand for crude oil. OPEC must
account for the effects of its pricing and production on the world economy when deciding what will
be most profitable for the cartel.
Figure 5 shows the real (2005$) price of crude oil from 1973:IV to 2011:II. Worldwide recessions in
my constructed data are shown in red. Three of the five recessions were preceded by oil price shocks,
and none of the oil price shocks failed to precede a recession. Far and away the two largest
quarter-to-quarter price increases in the OPEC era were $21.41 between 1973:IV and 1974:I and
17
$22.04 between 2008:I and 2008:II. There was a slowdown in the world economy in 1974:II, a
recession beginning in 1974:III, and a recession beginning in 2008:III. The third largest increase in
price during the OPEC era of $12.63 occurred between 2007:III and 2007:IV. The large shock in
1973 preceded a long term slowdown in world economic growth, and the 2008 recession has been
termed “Great”. Over two quarters, from 1978:III to 1980:I, price increased $39.51. GDP declined at
an annual rate of more than 8% from 1980:I to 1980:II and 0.7% the following quarter.
0
20
40
60
80
100
Figure 5: Real (2005$) Price of Crude Oil from 1973:IV to 2011:II
1972
1977
1982
1987
1992
1997
2002
2007
2012
4.1 Specification of World GDP
A good deal has been written about asymmetry in the response of the macroeconomy to changes in
the price of crude oil.13 Increases in price damage the economy more than decreases help. To
illustrate one reason why, suppose wages are sticky in the downward direction. Figure 6 describes
the market for labor when the price of crude oil fluctuates.
18
Figure 6: Labor Market with Downwardly Sticky Wages and Fluctuating Price of Crude Oil
W
S LS
W1
W0
S L1
DL
S L0
L0
L1
L
The price of crude oil changes from P 0 to P1 (not shown), raising the cost of fuel used to travel to
work and back, shifting the competitive supply of labor from S L0 to S L1 . The equilibrium wage
increases from W 0 to W 1 , and the quantity of labor demanded decreases from L0 to L1 . Next, the
price of crude oil returns to P 0 , but workers continue to require wage W 1 , so the supply curve
changes to S LS , the quantity of labor supplied remains at L1 , and less output is produced than before
the price of crude oil increased and subsequently decreased to its original level.
To capture the asymmetric effects econometrically, I specify increases and decreases in the price of
crude oil separately, using first differences in log price to explain first differences in log GDP. With
this functional form, regression coefficients represent the, constant, elasticities of GDP with respect to
the price and lagged prices of crude oil. I allow for response in the first difference in the log of GDP
to zero through five quarter lags in increases and decreases in the log price of crude oil. I also include
five lagged dependent variables, first differences in log GDP, in the regression.
gt − gt −1 = γ 0 +
13
t
∑γ
s =t −5
+
s
max ( ps − ps −1 , 0 ) +
t −1
∑γ
s =t −5
−
s
min ( ps − ps −1 , 0 ) +
t −1
∑ γ (g
s =t − 5
g
s
s
− g s −1 ) + ε tg (6)
See, for example, Hamilton (2003), Greene and Ahmad (2005), or Gately and Huntington (2002).
19
where gt is the natural logarithm of world GDP in quarter t, ( Gt , (normalized to 100 in 2005),
gt ≡ ln Gt ), and ε tg is a potentially heteroskedastic and autocorrelated error. With the lagged
dependent variables, changes in price beyond the fifth lag may impact current GDP. The lag structure
is just long enough to include the lag with the largest impact. Impacts through the lagged dependent
variables decline with their distance in time from t .
4.2 Identification of World GDP
I treat contemporaneous changes in log price, max ( pt − pt −1 , 0 ) and min ( pt − pt −1 , 0 ) as
endogenous because GDP can affect current price. The excluded instruments include lags of
positive and negative differences between the residuals from the demand and non-OPEC supply
(
)
equations (unexplained changes in OPEC production), specified separately, max etD−1 − etS−1 , 0 and
min ( esD=t −1...3 − esS=t −1...3 , 0 ) . In first-stage regressions, only the first lag of the positive changes in
unexplained OPEC production was significant, while the first three lags of negative changes were, so
I did not use the longer lags of the positive changes. One interpretation is that the cooperative game
among OPEC members in which prices are raised through cuts in production must be repeated to
succeed; cooperation is easier to establish in repeated than in one-shot cooperative games. On the
other hand, when OPEC wants prices to fall, it may simply allow cooperation to break down, and this
can be done quickly and easily.
Estimates of coefficients are consistent in OLS regressions with “generated regressors”. In 2SLS, the
transformations of etD− s − etS− s are “generated instruments”. According to Wooldridge (2002; p. 117),
“…there are practical reasons for using 2SLS with generated instruments rather than OLS with
generated regressors.” Whether the generated instruments are included or excluded, inference using
heteroskedasticity- and autocorrelation-robust standard errors in a GMM context, a generalization of
both OLS and 2SLS done here, is consistent and asymptotically efficient.
I assume that OPEC producers are the only strategic decision-makers impacting the price of crude oil,
and the price of crude oil impacts world GDP. Thus, OPEC production is a driver of both the price of
crude oil and world GDP, through price. This does not mean that OPEC producers do not also
20
respond to GDP, but lagged OPEC production would only depend on current innovations in GDP
through accurate expectations of those innovations. The innovations in (6) are independent of lagged
changes in price and GDP. I assume that OPEC producers are not able to anticipate these
innovations.
The excluded instruments for contemporaneous changes in log price also include a dummy variable
equaling 1 from the beginning of the dataset through 1985:I, M t1985I . The assumed shift in volatility
of price in 1985:II coincides with the maturation of crude oil as an actively traded commodity. The
coefficient of determination (standard deviation over mean) of price equals 0.30 through 1985:I and
0.57 thereafter. Verleger (2005; p. 5) explains that as prices dropped in the early 1980’s, the world
crude oil market was in transition from a vertically integrated one to one characterized by active
commodity markets. In particular, “...the development of North Sea production introduced classic
commodity market institutions into the global oil market. A true spot market was created.” The
development of the commodity market preceded, and facilitated, the “price collapse of 1986”, which
likely resulted from OPEC’s increasing excess capacity associated with falling short term demand.
Examples of dummy variables as excluded instruments can be found in Evans and Schwab (1995) and
Djankov and Reynal-Querol (2007).
21
4.3 Results and Testing of Estimated World GDP
Continuously updated GMM estimates of (6), shown in Table 2, converged after 153 iterations.
Table 2: Estimated Effects of Changes in Crude Oil Prices on the First Difference in
World GDP, ∆gt ≡ gt − gt −1
__________________________________________________________________________________________
Coefficient Standard. Error
Coefficient Standard. Error
∆ + pt
-0.086
0.020
∆gt −1
0.181
0.116
−
∆ pt
-0.039
0.016
∆g t − 2
-0.053
0.042
+
0.012
0.006
∆gt −3
-0.293
0.063
−
0.016
0.008
∆gt − 4
0.463
0.121
+
-0.009
0.008
∆g t −5
0.001
0.077
−
-0.011
0.007
Constant
0.009
0.002
+
-0.006
0.005
−
∆ pt −3
-0.003
0.005
∆ + pt − 4
∆ pt −1
∆ pt −1
∆ pt − 2
∆ pt − 2
∆ pt −3
0.005
0.004
−
-0.015
0.010
+
-0.021
0.005
−
-0.014
0.004
∆ pt − 4
∆ pt −5
∆ pt −5
__________________________________________________________________________________________
∆g s = g s − g s −1 is the quarterly first difference in the natural logarithm of world GDP.
∆ + ps ≡ max ( ps − ps −1 , 0 ) is the positive change in the natural log price of crude oil between
Quarter s − 1 and Quarter s , and ∆ − ps ≡ min ( ps − ps −1 , 0 ) the negative change.
Of the 18 regressors, including the constant, six have coefficients that are significantly different from
zero at the 99% level, two others at the 95% level, and one more at the 90% level. I retained the
remaining nine so as to maintain the contiguity and consistency of the lag structure. The test statistics
are robust to heteroskedasticity and autocorrelation of any form. However, A Pagan-Hall test using
22
the predicted values, gˆ t , associated with Table 2 as an indicator variable fails to reject
homoskedasticity in the errors ( p = 0.970 ) . There is no statistically significant autocorrelation in
the residuals at any specific lag, as shown in Figure 7, and a Cumby-Huizinga test fail to reject a null
hypothesis that there is no autocorrelation at any lag up to 25 ( p = 0.985 ) .
-0.20
-0.10
0.00
0.10
0.20
Figure 7: Autocorrelations Among GDP Residuals
0
10
20
Lag
30
40
Bartlett's formula for MA(q) 95% confidence bands
A Bartlett cumulative periodogram test puts a p-value of 0.857 on a null hypothesis that the residuals
were generated by a white noise process. They are stationary; Estimated d = -0.009 in a Robinson
0.075
test.
There are five excluded instruments and two endogenous regressors in a dataset of 158 observations,
used to perform a regression with five lags in the regressors. The p-value in a Hansen test of a null
hypothesis that the excluded instruments are independent of the error term is 0.882. When I omit
max ( etD−1 − etS−1 , 0 ) and min ( etD−1 − etS−1 , 0 ) from the set of instruments, the p-value is 0.515, and
(
)
(
)
when I test a null that max etD−1 − etS−1 , 0 and min etD−1 − etS−1 , 0 are independent of the error term,
assuming the other excluded instruments are also, the p-value is 0.888. The value of a
23
Kleibergen-Paap Wald rk F-statistic is 23.80, which exceeds the highest, 90%, critical value reported
by Stata of 4.32, leading to a rejection of a null hypothesis that the excluded instruments are weak.
4.4 The Effect of Changes in Crude Oil Prices on World GDP
Oil prices are important to the macroeconomy, but are not all important. A clear example is shown in
Figure 8, which plots the residuals associated with the estimates of (6) appearing in Table 2. The
deepening of the “Great Recession” in the fall of 2008 stands out, a result of a collapse in private
lending, but the oil shock of the previous summer was a contributing factor.
-.06
-.04
-.02
0
.02
.04
Figure 8: GDP Residuals
1972
1977
1982
1987
1992
1997
2002
2007
2012
Table 2 indicates that decreases in the price of crude oil raise GDP less than increases lower it. There
is some oscillation in the effects of either an increase or a decrease in price, but at no lag is the
cumulative effect of an increase (decrease) in price on GDP non-negative (non-positive). t-tests reject
negativity of the sum of the coefficients on increases and of those on decreases with 99% confidence.
As to asymmetry, a null hypothesis that the effects of decreases are greater than those of increases is
rejected with 95% confidence: The p-value associated with a null hypothesis that the sum of the
absolute effects of increases in price is greater is 0.963; that on the alternative is 0.037.
24
The asymmetry in Table 2 echoes that in a number of estimates. Hamilton (2003) explains the
asymmetry in the relationship as the result of allocative disturbances and uncertainty. An unexpected
change in oil prices in either direction changes the optimal mix of industrial equipment and consumer
durables that firms and consumers, respectively, desire. If the change makes them uncertain about the
future direction of prices, then they are likely to postpone major purchases until the uncertainty is
resolved. This would also apply to governments, in particular with regard to transportation
infrastructure and urban planning. (Hamilton (2009; pp. 39-40) notes “…house prices in 2007 were
likely to rise slightly in the zip codes closest to the central urban areas but fall significantly in zip
codes with longer average commuting distances.”) Thus, there is a contractionary element in the
effects of either increases or decreases in the price of crude oil, but no corresponding expansionary
element in the effects of increases.
Another reason for the strong asymmetry is downward stickiness of wages in the short run, as shown
in Figure 6, which illustrates effects through the supply of labor. Demand for labor may also shift.
When the price of oil rises, to the extent that labor and oil are complements, demand for labor falls,
causing only unemployment. To the extent that labor and oil are substitutes, demand for labor rises,
raising wages and employment. When the price of oil falls, to the extent that labor and oil are
complements, demand for labor rises, raising wages and employment. To the extent that labor and oil
are substitutes, demand for labor falls, causing only unemployment. There is no reason before the
fact to suppose that the sum of these effects is zero. Most workers in countries that are not poor use
oil products or close substitutes, such as natural gas, to travel to and from work, so oil is related to
labor in the production of a large majority of goods. Other inputs related to oil in production of goods
may also have downwardly sticky prices, and this may contribute to the asymmetry.
A third reason for the asymmetry is income and liquidity effects. Since oil products and their
substitutes take a large share of many budgets, increases from a given price level reduce spending
more than decreases from that level increase spending. These effects can be especially strong in poor
countries. Teitenberg (2007; p. 202) writes “The lack of foreign exchange has been exacerbated
during periods of high oil prices. Many developing nations must spend large portions of export
earnings merely to import energy.
Fourth, investors whose wealth and income are sensitive to the price of oil will hold increases therein
in liquid form for a time before committing to a less liquid investment. A large change in price in
25
either direction will redistribute wealth and income and, as a result, tend to slow down real
investment.
Consider the response in GDP in Quarter t to a change in price s quarters earlier. From (6), the
short run elasticity of world GDP s quarters hence with respect to a change in price lasting one
quarter is
t
 t

∆g t
= ∑ γ i+ / −  Π γ gj 
∆pt − s i =t − s
 j = 2 t − s −i 
where γ tg ≡ 1 and γ i+ / − is the coefficient on an increase/decrease in log price in Quarter i and γ gj
the coefficient on the change in log GDP in Quarter j.
Evaluating this at s = 5 in 2009:III gives an estimate of the impact of the large increase going into
summer 2008. Price (2005$) in 2008:II was Pt −5 = $106.31 , and in 2008:I was Pt −5−1 = $84.05 .
The estimated elasticity is -0.0203, and the price change was 23.5%, so the estimated effect is that
world GDP was 0.48% lower in 2009:III due to that largest ever quarter-to-quarter increase in the real
price of crude oil. In my constructed data, world GDP was 2.14% lower in 2009:III than in 2008:II,
so Table 2 implies that a fifth of the decrease was caused by the upward shock in 2008:II. The oil
shock contributed significantly to the Great Recession, but was not its primary cause.
These negative short run effects reduce GDP in the long run because lower current GDP means lower
current investment, which is the only way to provide now for future GDP. Short run dips in GDP
lower future GDP because investment varies directly and elastically with GDP. Hysteresis also sets
in among unemployed workers, lowering their future productive capability; a recession in
employment implies less current investment in human capital through accumulation of work
experience. The long run elasticity of world GDP with respect to a temporary, one quarter, change in
the price of crude oil is
∑
γ + − ∑ i =t −5 γ i−
i =t − 5 i
t
t
1 − ∑ i =t −5 γ ig
t −1
≈ −0.056 using Table 2.
26
A 1% increase in the price of crude oil lasting exactly one quarter lowers world GDP in the long run
by 0.056% . Thus, if it had been exactly reversed in 2008:III, the largest-ever, $22.27/bl in 2005$,
increase the previous quarter would have caused world GDP to be 1.32% lower in each quarter over
the long run. In my constructed data, world GDP grew about 1.96% quarterly. The shock of 2008,
then, set the world economy back about two months.
5 OPEC
The supply curve of a monopolist does not exist. OPEC is not a monopolist in the literal sense, but its
market power in the world market for crude oil is unrivaled, so, as a whole, its profit-maximization
problem is like that of a monopolist. OPEC does not interact strategically with non-OPEC suppliers,
with the possible exceptions, ignored here for simplicity, of the governments of Mexico, Norway, and
Russia; OPEC takes account of its influence on non-OPEC production when deciding its own
production, but non-OPEC producers do not take account of their influence on OPEC in deciding
their production14. Since OPEC’s market power is substantial and unrivaled, it decides the world
price of crude oil as it decides its own production.
Celta and Dahl (2000) estimated OPEC’s short run marginal costs in 1995 dollars as
ln ( MC ) = 46.3263 + 0.3026 ln ( QOPEC ) − 2.3356 ln ( ROPEC )
(7)
where QOPEC is OPEC production in thousand b/d and ROPEC is proven OPEC reserves in thousands
of barrels. In 2012, OPEC production was 36.599 million b/d, and proved reserves were 1.113
trillion barrels. (7) implies short run marginal costs in 2012 dollars of $2.76/bl. In that year, the price
of Brent crude oil averaged $111.63/bl, and that of WTI averaged $94.05/bl.15 A graphic on page 33
of Van Vactor (2010) puts long run marginal cost in OPEC countries, including Venezuela, between
$15/bl and $30/bl in 2009. Though competitive producers whose future marginal costs increase in
current production will produce where current marginal cost is less than price, such a large difference
between price and marginal cost suggests something other than price-taking behavior.
14
Other overlooked exceptions include non-OPEC governments who subsidize production of crude oil to
reduce “dependence on foreign oil”, who can be said to interact strategically with OPEC.
27
5.1 Net Demand to OPEC
Since OPEC output is identically the difference between world quantity demanded and non-OPEC
quantity supplied, Ot = Dt − St , I calculate net demand to OPEC by subtracting (3) from (2).
Ot = δ 0 − η0 + δ P Pt − η p pt + δ G Gt + (δ − η ) t + δ D Dt −1 + δ Dave Davet −1
−ηGW M t90 III 92 IV − ηC Ct −1 − ηi it −1 − η X X t −1 − η S St −1 + ε tD − ε tS
Using the estimates in (4) and (5) gives the values in Table 3.
Table 3: Net Demand to OPEC, Ot ≡ Dt − St
_________________________
Variable
Coefficient
Pt
-0.013
pt
0.238
Gt
0.044
t
-0.293
Dt −1
0.766
Davet −1
0.153
M t90 III 92 IV
-0.075
Ct −1
-0.042
it −1
-0.023
X t −1
0.352
St −1
0.942
-9.858
Constant
15
Reserve, production, and price data come from EIA.
28
(8)
The asymmetric effects of the price of crude oil on world GDP imply asymmetric effects of price on
world demand and net demand to OPEC. Increases in price lower quantity demanded more than
decreases in price raise quantity demanded. OPEC’s demand curve is concave to the origin.
Table 4 shows estimated elasticities of world demand, world GDP, non-OPEC supply, and net
demand to OPEC. I assume in my calculations of elasticities that it is 2014:II, price is $100/bl,
annual quantity demanded is 27.80 billion barrels per year, GDP flows at an annual rate of 123.1,
where GDP in 2005 ≡ 100 , and non-OPEC quantity supplied is 15.79 billion barrels per year,
implying OPEC production of 12.00 billion barrels per year. Long run demand is elastic at the price
of $100/bl, and net demand to OPEC at time-horizons of twelve months or less is inelastic.
The next to last column of Table 4 shows prices at which demand over various time-horizons is
unit-elastic for upward changes in price. Net demand to OPEC over a twelve month time-horizon
becomes unit elastic for increases in price at $142.41/bl. This suggests that an oil price shock lasting
up to a year in which prices would fluctuate around $150/bl is a real possibility. Had private
borrowing not collapsed at about the same time, it might well have been profitable for OPEC to
sustain the shock of 2008, which went about to this level, longer than it did. At shorter time-horizons,
net demand to OPEC only becomes elastic at prices significantly higher than any in the data from
which these estimates were derived, so these numbers should be viewed skeptically. I include them
for the sake of completeness.
The discontinuity gap in marginal revenue is shown in the last column of Table 4. I calculate the gap
(
)
as P ∗ 1 ε + − 1 ε − , where ε + is the elasticity with respect to an increase in price, and ε − is the
elasticity with respect to a decrease in price. OPEC’s long run marginal cost curve may pass through
the discontinuity gap in marginal revenue over a wide range of prices and quantities. Since 1973,
historic changes in the world economy, as with the deep recession in the early 1980’s and rapid
growth beginning in the late 1990’s, have preceded large lasting changes in the price of crude oil.
(See Figure 1.)
29
Table 4: Elasticities and MR Gaps at $100/bl and Upwardly Unit-Elastic Prices
in 2014:II (2013$)
Price+
Price-
Income
-0.0557
-0.0863
0.0150
-0.1488
-0.0464
-0.0389
0.0150
-0.1274
0.1955
-0.1019
-0.0934
0.0292
-0.2744
-0.0824
-0.0318
0.0292
-0.2292
0.3526
Upwardly
Unit-Elastic
Price
MR Gap
$554.36
-$571.96
-$685.18
=
$113.22
$377.36
-$264.49
-$336.24
=
$71.75
$240.25
-$115.83
-$158.30
=
$42.46
$142.41
-$32.62
-$58.67
=
$26.05
$67.95
$36.71
$26.74
=
$9.97
3 Month
Demand
GDP
NO Supply
OPEC Demand
0.4527
6 Month
Demand
GDP
NO Supply
OPEC Demand
0.8166
9 Month
Demand
GDP
NO Supply
OPEC Demand
-0.1759
-0.0935
0.0425
-0.4633
-0.1430
-0.0368
0.0425
-0.3872
0.4820
1.1164
12 Month
Demand
GDP
NO Supply
OPEC Demand
-0.2943
-0.0780
0.0551
-0.7541
-0.2408
-0.0325
0.0551
-0.6302
0.5921
Demand
-0.7896
GDP
-0.1518
NO Supply
0.3347
OPEC Demand
-1.5799
Quarter =
Price =
World Quantity Demanded =
World GDP =
Non-OPEC Quantity Supplied =
-0.6634
-0.0958
0.3347
-1.3649
2014
100.00
27.80
123.10
15.79
2.3875
1.3714
Long Run
30
5.5296
II
in 2013$
in bbl/yr
; 2005=100
in bbl/yr
In a purely static exercise, one would expect OPEC to produce and price where long run marginal
cost, between $15/bl and $30/bl in Van Vactor, fell in the marginal revenue gap for the appropriate
time-horizon. However, two (upward) adjustments to these figures are appropriate. First, the
numbers in Van Vactor applied in 2009, and one would expect costs to be higher in 2014. Second,
they do not consider the effect of present production on future costs, which increases the opportunity
cost of present production. OPEC’s marginal costs, inclusive of “marginal user cost”, may be
considerably higher than those indicated in Van Vactor. Though interest rates as of early 2014 are
low, marginal user cost is increasing in the discount rate, and OPEC is generally thought to have a
high discount rate.16 Table 5 shows upper and lower bounds of ranges of prices (UB − LB ) within
which OPEC cannot increase profits by change price and production in the long run assuming the
long run marginal costs, inclusive of marginal user cost, LRMC , indicated in the column headings.
Table 5: Profit-Maximizing Prices at Various LRMC’s
in 2014:II (2013$)
LRMC:
UB:
LB:
Size of Range:
20.00
95.14
86.57
8.57
30.00
102.30
94.77
7.54
35.00
105.78
98.69
7.09
40.00
109.19
102.51
6.68
50.00
115.85
109.90
5.95
The price of WTI averaged $97.98/bl in 2013, and that of Brent averaged $108.56/bl, while the
standard deviation in the price of WTI in 2013 was $5.46/bl, and that of Brent was $4.64/bl,
according to EIA. At least recently, the multiplicity of equilibria implied by OPEC’s discontinuous
long run marginal revenue curve, associated with the asymmetric effects of oil prices on world GDP,
is a reasonable explanation for much of the variation in those prices, and large price shocks can also
be explained by applying the model to shorter time-horizons.
16
See, for example, Adelman (1990; pp. 11-13).
31
6 Conclusion
Instability in the price of crude oil does not imply that OPEC is unable to use its market power
effectively. The asymmetric effects of changes in the price of crude oil on the macroeconomy imply
that world demand and demand to OPEC net of non-OPEC production are kinked, that there is a
vertical discontinuity in OPEC’s marginal revenue curve. Therefore, there are multiple combinations
of price and OPEC production at which an increase in price (decrease in production) lowers revenue
more than cost, and at which a decrease in price (increase in production) raises revenue less than cost.
The asymmetry results in multiplicity of equilibria. In 2014, using long run demand, the range of
equilibrium prices appears to be about $7/bl wide, and an increase in price lasting one year to levels
above $142/bl would also appear to be profitable.
In the short run, demand to OPEC is quite inelastic, and the contemporaneous effects of changes in
price on GDP are negative and statistically significant. From Table 2, a 1% increase (decrease) in the
price of crude oil causes a 0.086% decrease (0.039% increase) in world GDP in the same quarter.
Assuming non-decreasing marginal costs, OPEC can collect a countercyclic stream of profits by
promulgating instability in the price of crude oil. The stream can be used to smooth out undesirable
fluctuations in consumption associated with the changes in GDP, so OPEC can sell instruments in
financial markets that command a risk premium. Thus, within some range, OPEC has incentive to
promulgate unstable prices for crude oil. Because increases in the price of crude oil damage the
macroeconomy more than decreases improve it, the instability in price that OPEC has incentive to
promulgate damages the macroeconomy.
The discontinuity in marginal revenue implies that vertical shifts in demand, associated with changes
in world GDP, cause larger changes in the price of crude oil. These, in turn, affect GDP.
32
Table1: Basic Data
A
Obs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
Year
1972
1972
1972
1972
1973
1973
1973
1973
1974
1974
1974
1974
1975
1975
1975
1975
1976
1976
1976
1976
1977
1977
1977
1977
1978
1978
1978
1978
1979
1979
1979
1979
1980
1980
1980
1980
1981
1981
Qrtr
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
B
C
D
E
Price
Implicit
Price
Deflator
NonOPEC
Output
World
Output
Annual
World
GDP
(PPP)
US$/bl
2005:I=1
bbl/yr
bbl/yr
bUS$
1.93
6.51
12.94
12.66
11.99
13.64
14.39
13.29
13.44
15.88
14.70
13.16
12.86
14.64
15.74
14.27
13.88
15.69
15.85
14.21
13.83
15.82
17.28
18.93
23.38
28.04
33.54
33.85
33.81
36.16
40.07
37.49
0.2837
0.2893
0.2949
0.3019
0.3109
0.3202
0.3276
0.3325
0.3386
0.3446
0.3484
0.3521
0.3569
0.3633
0.3694
0.3747
0.3793
0.3876
0.3933
0.4005
0.4072
0.4158
0.4232
0.4336
0.4430
0.4519
0.4614
0.4718
0.4826
0.4959
0.5085
0.5181
9.34
9.58
9.68
9.64
9.59
9.73
9.69
9.76
9.73
9.77
10.11
10.08
10.12
10.27
10.48
10.56
10.77
10.98
11.12
11.29
11.39
11.75
11.81
11.94
11.99
12.16
12.28
12.39
12.42
12.52
12.59
12.51
12.71
12.85
21.33
21.79
22.28
21.19
21.79
22.34
21.38
21.19
20.23
20.26
21.55
20.46
21.26
21.79
22.51
23.67
23.20
23.17
22.95
23.62
22.59
23.28
23.69
24.21
23.74
24.64
24.73
24.68
24.44
23.68
23.18
22.12
23.03
22.64
33
5988
5988
5988
5988
6697
6697
6697
6697
7452
7452
7452
7452
8266
8266
8266
8266
9176
9176
9176
9176
10273
10273
10273
10273
11539
11539
11539
11539
12875
12875
12875
12875
14363
14363
F
G
H
I
Quarterly
U.S. GDP
Nominal
Rate on 3Month
Treasuries
Drop in
World
Supply
TradeWeighted
Exchange
Value of
U.S.$
bUS$
secondary
%
2005:I=1
1381
1418
1437
1479
1495
1534
1563
1603
1620
1656
1714
1766
1825
1857
1891
1938
1993
2060
2122
2169
2209
2337
2399
2482
2532
2596
2670
2731
2797
2800
2860
2994
3132
3167
3.44
3.77
4.22
4.86
5.70
6.60
8.32
7.50
7.62
8.15
8.19
7.36
5.75
5.39
6.33
5.63
4.92
5.16
5.15
4.67
4.63
4.84
5.50
6.11
6.39
6.48
7.31
8.57
9.38
9.38
9.67
11.84
13.35
9.62
9.15
13.61
14.39
14.91
0
0
0
0
0
0
0
4.90064
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1.9533
0
0
0
0
0
0
4.54801
0
0
0.30
0.29
0.28
0.29
0.30
0.29
0.30
0.30
0.30
0.30
0.31
0.32
0.32
0.33
0.33
0.33
0.34
0.34
0.34
0.33
0.33
0.33
0.31
0.31
0.32
0.32
0.32
0.33
0.33
0.33
0.33
0.33
0.35
0.37
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
1981
1981
1982
1982
1982
1982
1983
1983
1983
1983
1984
1984
1984
1984
1985
1985
1985
1985
1986
1986
1986
1986
1987
1987
1987
1987
1988
1988
1988
1988
1989
1989
1989
1989
1990
1990
1990
1990
1991
1991
1991
1991
1992
1992
1992
1992
1993
1993
1993
1993
1994
1994
1994
1994
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
35.28
36.91
36.38
32.86
32.48
34.12
31.55
28.30
28.60
30.40
30.24
28.92
28.21
29.56
28.58
27.21
25.92
27.75
20.44
12.59
11.21
14.52
18.25
18.01
18.39
19.00
16.56
15.41
13.66
14.32
18.16
18.70
16.95
19.93
21.10
15.69
22.90
30.59
20.75
17.88
17.95
19.84
17.51
18.39
18.75
19.27
18.70
17.41
14.93
15.11
14.36
15.50
16.03
17.22
0.5273
0.5369
0.5442
0.5508
0.5586
0.5647
0.5693
0.5735
0.5793
0.5836
0.5910
0.5960
0.6008
0.6047
0.6114
0.6148
0.6174
0.6214
0.6246
0.6279
0.6314
0.6357
0.6416
0.6453
0.6503
0.6553
0.6607
0.6669
0.6744
0.6795
0.6872
0.6940
0.6986
0.7032
0.7117
0.7199
0.7266
0.7324
0.7403
0.7455
0.7513
0.7557
0.7595
0.7642
0.7678
0.7721
0.7768
0.7811
0.7847
0.7890
0.7931
0.7969
0.8016
0.8058
12.75
12.68
12.82
13.01
13.11
13.27
13.28
13.39
13.52
13.48
13.74
13.90
13.94
14.01
14.01
14.06
14.15
14.21
14.12
14.09
14.23
14.19
14.16
14.15
14.31
14.26
14.34
14.28
14.17
14.12
14.04
13.94
14.08
14.02
13.96
13.92
13.76
13.85
13.99
13.73
13.70
13.63
13.40
13.25
13.13
13.03
12.93
12.91
12.86
12.96
13.14
13.17
13.23
13.41
21.47
21.33
21.32
20.82
21.10
21.57
20.34
20.86
21.76
21.63
21.86
22.09
21.56
21.46
21.65
21.26
21.16
22.32
22.12
22.55
22.86
22.12
22.01
22.27
23.31
23.05
22.98
23.20
23.45
24.36
23.44
23.74
24.06
24.41
24.64
24.64
23.64
24.06
24.43
23.97
24.21
24.33
24.49
24.18
24.17
24.35
24.71
24.39
24.40
24.46
25.00
25.03
24.92
25.20
34
14363
14363
15387
15387
15387
15387
16464
16464
16464
16464
17883
17883
17883
17883
19111
19111
19111
19111
20235
20235
20235
20235
21599
21599
21599
21599
23357
23357
23357
23357
25135
25135
25135
25135
26812
26812
26812
26812
28119
28119
28119
28119
29324
29324
29324
29324
30640
30640
30640
30640
32380
32380
32380
32380
3261
3284
3274
3331
3367
3408
3480
3584
3692
3796
3913
4015
4087
4148
4237
4302
4395
4453
4516
4555
4620
4669
4736
4821
4901
5023
5091
5208
5300
5413
5527
5628
5712
5763
5891
5975
6030
6023
6055
6144
6218
6279
6381
6492
6587
6698
6748
6830
6904
7033
7136
7270
7352
7477
15.05
11.75
12.81
12.42
9.32
7.91
8.11
8.40
9.14
8.80
9.17
9.80
10.32
8.80
8.18
7.46
7.11
7.17
6.90
6.14
5.52
5.35
5.54
5.66
6.04
5.86
5.72
6.21
7.01
7.73
8.54
8.41
7.84
7.65
7.76
7.75
7.48
6.99
6.02
5.56
5.38
4.54
3.89
3.68
3.08
3.07
2.96
2.97
3.00
3.06
3.24
3.99
4.48
5.28
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4.07159
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.38
0.38
0.40
0.42
0.44
0.45
0.46
0.47
0.49
0.50
0.52
0.53
0.56
0.59
0.62
0.62
0.61
0.59
0.58
0.57
0.56
0.57
0.55
0.55
0.56
0.55
0.54
0.54
0.57
0.56
0.58
0.61
0.62
0.63
0.65
0.67
0.65
0.64
0.65
0.69
0.69
0.68
0.69
0.70
0.69
0.73
0.75
0.75
0.77
0.79
0.83
0.84
0.83
0.83
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
1995
1995
1995
1995
1996
1996
1996
1996
1997
1997
1997
1997
1998
1998
1998
1998
1999
1999
1999
1999
2000
2000
2000
2000
2001
2001
2001
2001
2002
2002
2002
2002
2003
2003
2003
2003
2004
2004
2004
2004
2005
2005
2005
2005
2006
2006
2006
2006
2007
2007
2007
2007
2008
2008
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
18.35
17.96
15.92
17.83
19.74
19.99
20.06
24.08
22.37
17.64
17.10
18.57
14.68
12.07
11.22
11.88
12.22
15.16
19.09
24.08
28.15
26.25
28.46
29.35
25.51
23.59
22.35
17.97
20.54
23.69
25.27
26.50
31.94
25.35
26.71
28.85
32.34
33.55
37.93
40.82
42.36
45.64
56.09
53.09
56.01
63.26
63.25
54.50
54.57
62.14
69.79
83.50
91.08
115.56
0.8104
0.8140
0.8178
0.8220
0.8267
0.8299
0.8325
0.8371
0.8425
0.8445
0.8474
0.8506
0.8520
0.8540
0.8573
0.8599
0.8637
0.8668
0.8700
0.8731
0.8800
0.8845
0.8898
0.8945
0.9005
0.9067
0.9095
0.9123
0.9156
0.9197
0.9236
0.9289
0.9354
0.9382
0.9434
0.9482
0.9564
0.9645
0.9715
0.9787
0.9878
0.9944
1.0046
1.0130
1.0206
1.0295
1.0372
1.0419
1.0538
1.0610
1.0645
1.0696
1.0759
1.0830
13.39
13.38
13.58
13.53
13.67
13.76
13.79
13.93
14.00
14.01
14.03
14.13
14.19
14.15
14.01
14.03
14.12
13.99
14.14
14.27
14.30
14.33
14.48
14.57
14.54
14.42
14.62
14.70
14.76
14.95
14.86
14.90
15.00
14.98
15.16
15.32
15.30
15.41
15.34
15.31
15.26
15.45
15.14
15.16
15.22
15.22
15.27
15.28
15.30
15.29
15.16
15.10
15.08
15.06
25.48
25.66
25.77
25.69
26.14
26.24
26.18
26.44
26.95
27.03
27.06
27.25
28.01
27.90
27.29
27.26
27.82
27.09
27.23
27.14
27.74
28.33
28.69
28.79
28.80
28.23
28.34
28.06
27.99
27.98
28.06
28.38
28.89
28.80
28.91
29.60
30.07
30.27
30.52
30.48
30.81
31.16
30.81
30.72
30.99
30.93
30.99
30.69
30.87
30.91
30.73
30.94
31.42
31.44
35
34186
34186
34186
34186
36226
36226
36226
36226
38351
38351
38351
38351
39790
39790
39790
39790
41827
41827
41827
41827
44729
44729
44729
44729
46866
46866
46866
46866
49015
49015
49015
49015
51824
51824
51824
51824
55655
55655
55655
55655
59560
59560
59560
59560
63420
63420
63420
63420
68710
68710
68710
68710
72112
72112
7545
7605
7707
7800
7893
8062
8159
8287
8402
8552
8692
8788
8890
8995
9147
9326
9450
9562
9719
9932
10036
10284
10364
10475
10513
10642
10644
10703
10837
10938
11040
11106
11231
11371
11628
11819
11991
12184
12369
12564
12816
12976
13207
13383
13650
13803
13911
14068
14235
14425
14572
14690
14673
14817
5.74
5.60
5.37
5.26
4.93
5.02
5.10
4.98
5.06
5.05
5.05
5.09
5.05
4.98
4.82
4.25
4.41
4.45
4.65
5.04
5.52
5.71
6.02
6.02
4.82
3.66
3.17
1.91
1.72
1.72
1.64
1.33
1.16
1.04
0.93
0.92
0.92
1.08
1.49
2.01
2.54
2.86
3.36
3.83
4.39
4.70
4.91
4.90
4.98
4.74
4.30
3.39
2.04
1.63
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.05313
0
0
0
0.3079
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.85
0.82
0.84
0.86
0.88
0.89
0.89
0.90
0.93
0.94
0.96
0.99
1.05
1.05
1.08
1.05
1.06
1.07
1.06
1.05
1.06
1.08
1.10
1.13
1.13
1.16
1.15
1.16
1.18
1.16
1.14
1.15
1.13
1.09
1.09
1.06
1.03
1.06
1.05
1.01
1.00
1.01
1.01
1.02
1.01
0.99
0.99
0.98
0.98
0.96
0.94
0.91
0.89
0.88
147
148
149
150
151
152
153
154
155
156
157
158
2008
2008
2009
2009
2009
2009
2010
2010
2010
2010
2011
2011
3
4
1
2
3
4
1
2
3
4
1
2
111.12
52.89
41.81
57.30
65.74
74.09
76.54
74.09
72.65
81.94
95.42
108.55
1.0916
1.0930
1.0972
1.0959
1.0966
1.0994
1.1036
1.1079
1.1116
1.1164
1.1240
1.1312
14.86
14.95
15.08
15.10
15.22
15.29
15.38
15.41
15.40
15.48
15.45
15.30
31.16
30.82
30.65
30.75
30.88
30.92
31.22
31.46
31.46
31.43
30.35
29.95
72112
72112
72119
72119
72119
72119
76810
76810
76810
76810
81330
81330
14844
14547
14381
14342
14384
14564
14673
14879
15050
15232
15243
15462
1.49
0.30
0.21
0.17
0.16
0.06
0.11
0.15
0.16
0.14
0.13
0.05
0
0
0
0
0
0
0
0
0
0
3.43509
1.3259
A: refiners' acquisition cost of imported crude oil, U.S. dollars per barrel; 1973:III is official price of Saudi Light; from U.S.
Energy Information Administration
B: U.S. gross domestic product implicit price deflator; quarterly figures from Federal Reserve Bank of St. Louis
http://research.stlouisfed.org/fred2/data/GDPDEF.txt, accessed April 1, 2014.
C: non-OPEC production of crude oil; from U.S. Energy Information Administration,
http://www.eia.doe.gov/emeu/international/oilproduction.html, accessed April 1, 2014.
D: world crude oil production; from U.S. Energy Information Administration, also
http://www.eia.doe.gov/emeu/international/oilproduction.html, accessed April 1, 2014.
E: world gross domestic product; from IMF World Economic Outlook, April 2005,
http://www.imf.org/external/pubs/ft/weo/2005/01/data/dbasubm.cfm and IMF World Economic Outlook, April 2009,
http://www.imf.org/external/pubs/ft/weo/2009/01/weodata/weoselser.aspx?a=1&c=001&t=1
F: quarterly U.S. gross domestic product; from Federal Reserve Bank of St. Louis
http://research.stlouisfed.org/fred2/data/GDP.txt, accessed April 1, 2014.
G: nominal rate on 3-Month U.S. treasury securities, secondary market; from
http://www.federalreserve.gov/releases/H15/data/Monthly/H15_TB_M3.txt
H: percent drop in world output due to violence; from EIA Monthly Energy Review
http://www.eia.doe.gov/emeu/international/oilproduction.html, accessed April 1, 2014.
I: Trade-Weighted Exchange Value of U.S. Dollar; from Federal Reserve Bank of Saint Louis
http://research.stlouisfed.org/fred2/data/TWEXBMTH.txt, accessed April 1, 2014.
36
0.89
0.99
1.01
0.98
0.95
0.92
0.93
0.95
0.93
0.91
0.89
0.87
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