### Topic Page: Oil prices

**Oil Price Volatility**from

*Encyclopedia of Energy*

- 1. Introduction
- 2. Microeconomic Foundation of the Price Elasticity of Demand and Its Estimation
- 3. Volatility of an Oil Price Change and Macroeconomic Activity
- 4. Conclusion

crude oil price

Crude oil is sold through many contract arrangements, in spot transactions, and on futures markets. In 1971, the power to control crude oil prices shifted from the United States to OPEC when the Texas Railroad Commission set prorating at 100% for the first time.

demand elasticityThe relative responsiveness of quantity demanded to changes in price. The price elasticity of demand is important in affecting the pricing behavior of OPEC.

economic impactThe study of oil price shocks and their effects on economic activities.

oil price volatilityThe volatility of crude oil prices is influenced more by both demand structure and shifting demand and supply conditions and less by the cost of producing crude oil. Oil price volatility creates uncertainty and therefore an unstable economy.

Organization of Petroleum Exporting Countries (OPEC)Formed in 1960 with five founding members: Iran, Iraq, Kuwait, Saudi Arabia, and Venezuela. By the end of 1971, six other countries had joined the group: Qatar, Indonesia, Libya, United Arab Emirates, Algeria, and Nigeria. OPEC effectively controlled oil prices independent from the United States during the Arab oil embargo.

The world oil price has been extremely volatile in the past three decades. The cartel pricing is largely affected by the aggregate demand the cartel faces and related elasticity. The stable and unstable cases of price elasticity of demand are investigated in this article to shed light on the seemingly mysterious Organization of Petroleum Exporting Countries pricing behavior. We estimate the elasticity of oil demands in the U.S. market (the world's largest energy consumer) and use this information to probe and predict movements in the market price of crude oil. The volatility of crude oil prices creates uncertainty and therefore an unstable economy. Employing recent data, our empirical results indicate that a higher oil price seems to have a greater impact on the stock market than on the output market.

The world oil price has been extremely volatile in the past three decades. It was as low as $2.17 per barrel in 1971 but spiked to $34 in 1981. It soared to approximately $40 per barrel toward the end of February 2003. The Organization of Petroleum Exporting Countries (OPEC) price increases of the 1970s drove Western industrialized economies into recession. During the 1950s and 1960s, many competitive independent producers characterized the crude oil industry. The demand facing the individual producer is relatively elastic, even though the demand curve for the entire industry is rather inelastic. The price of crude oil was close to the marginal cost during that period of time. OPEC emerged as an effective cartel in approximately 1971 when it successfully raised the pattern of world prices with the Tehran and Tripoli agreements. With the Arab-Israeli war of 1973, its consequent oil embargo, and the nationalization of oil production in member countries, the structure of the cartel provided the means to raise prices substantially from $4.10 per barrel in 1973 to $11.11 in 1974 to reap a monopoly profit.

With the beginning of political problems in Iran, another large increase in oil prices occurred in 1978 when Iranian production declined from a peak of 6 million barrels per day to 0.5 million barrels. Even though half of the reduction in Iranian oil was offset by expanded production by other OPEC producers, the effect was immediate and substantial, causing the price to increase to $13.49 in 1978, because the elasticity of demand was rather inelastic in the short term. Because of the war between Iraq and Iran, Iraq's crude oil production declined by 2.7 million barrels per day and Iran's production declined by 600,000 barrels per day. As a result, the price of crude oil more than doubled from $13.49 per barrel in 1978 to $34 in 1981.

Higher oil prices create inflationary pressure and slow worldwide economic activities. The recession of the early 1980s reduced demand for oil. From 1982 to 1985, OPEC tried to stabilize the world oil price with low production quotas. These attempts were unsuccessful because various members of OPEC produced beyond their quotas, causing crude oil prices to decrease below $10 per barrel by mid-1986. In particular, Saudi Arabia's increases in oil production frequently depressed the oil price. The price of crude oil remained weak until the start of the Gulf War in 1990, when it eclipsed $40 per barrel. Because of the uncertainty associated with the invasion of Kuwait by Iraq and the ensuing Gulf War, the oil price spiked again to $34 in late 1990. After the war and the recession of the early 1990s, the crude oil price began a steady decline. The economy, however, started to turn around in 1994. With a strong economy in the United States and a booming economy in Asia, increased demand led to a steady price recovery well into 1997. The financial crisis and subsequent economic setbacks in Asia started in 1997 and oil prices plummeted to approximately $10 in late 1998 and early 1999. With the recovery in Asia and the decrease in oil quotas by OPEC, the price has recovered to approximately $30 a barrel in recent years. In 2002, for the first time, Russia's oil production surpassed that of Saudi Arabia, signaling a more complicated pricing scheme for oil.

The literature on the volatility of crude oil prices relates oil price changes either to the effect of the price elasticity of demand or to the instability of the market structures. It is apparent that the stable price is established through the equilibrium of total world demand and supply, including OPEC and non-OPEC production. In the short term, the price change is largely impacted by the immediate substantial increase or decrease in oil production from OPEC members and political events. The cartel's pricing policy is largely affected by the aggregate demand it faces and related elasticity.

The volatility of crude oil prices in turn creates uncertainty and therefore an unstable economy. In his pioneering work, Hamilton indicated that oil price increases have partially accounted for every U.S. depression since World War II. Many researchers, using different estimation procedures and data, have tested the relationships between the oil price increases and many different macroeconomic variables. Using a multiequation statistical approach incorporating the U.S. interest rate, oil price, industrial production, and real stock returns with daily data from 1947 to 1996, Sadorsky found that oil price volatility does have an impact on real stock returns. Recently, emphasis has shifted to the asymmetry of the impact of oil price shocks on economic activities and on stock markets. Mork was the first to provide the asymmetry of oil price shocks or its volatility on economic activities. Using data from industrial nations, Mork and Olson verified that there is a negative relationship between an oil price increase and national output, whereas no statistical significance can be attributed to them when the oil price declines. Lee et al. estimated oil price shocks from a generalized econometric model and investigated the impacts of positive and negative oil price shocks on economic activities. They came to the same conclusion that positive shocks have a statistically significant impact on economic activities, whereas negative shocks have no significant impact.

This article examines the volatility of crude oil prices by first determining the potential maximal price that OPEC can extract based on the microeconomic foundation of the elasticity theory proposed by Greenhut et al. The market structure of OPEC, the stable and unstable demand structure, and related elasticity of demand are discussed. In particular, the theory of unstable price elasticity of demand helps explain some of the pricing behavior of OPEC. The price elasticity of demand is then estimated to shed light on the volatility of oil prices. This article further investigates the significance of changing oil prices on the economy by examining the relationship between oil price volatility and industrial production and/or the stock market.

Consider a cartel (e.g., OPEC) whose objective is to maximize joint profit:

_{i}, is the sum of outputs of n cartel members (q

_{i}), and TC

_{i}is the total cost function of cartel member i. Note that OPEC behaves much like a monopoly or an effective cartel despite occasional squabbles over output quotas. Under recent OPEC arrangements, if the price becomes too low, OPEC would reduce output by half a million barrels per day (ΔQ = 500,000) at one time. A 500,000-barrel decrease (increase) in Q is approximately 2% of the total cartel output, and each member must accept a 2% decrease (increase) in its quota in the case of a tightly controlled cartel. Within this framework, it is the total cartel output Q, instead of qi that plays a crucial role in the pricing decision. The first-order condition requires

Equation (2) states that the marginal revenue (MR) equals the common cartel marginal cost (MC, or horizontal summation of marginal cost curves for all cartel members) in equilibrium. Note that if some MC_{i} 's exceed the going market price, these members have no role to play in the pricing decision. However, this is not likely the case for OPEC because production costs fall far short of the market price.

Substituting MR = P(1-1/e) into Eq. (2) yields

The second-order condition plays a critical role in describing the switching demand conditions. Here, we classify two major demand cases via expanding the elasticity theory formulated by Greenhut et al. in terms of the second-order condition.

By using the chain rule, we have

For a given output elasticity β, if the marginal cost is an insignificant portion of price (i.e., a large k) or the marginal cost is constant (β → ∞, as is true in a large-scale crude oil production with a sizable fixed cost), the second term on the right side of Eq. (6) plays a trivial role and can be ignored. It follows that dπ'/dP>0 for dπ'/dQ < 0, and it is sufficient that relation A holds:

The residual term e/βk would reinforce the relation, but its magnitude may be insignificant, with k and/or β being large enough.

On the other hand, the unstable relation B would follow if the second-order condition is not satisfied:

Relation A indicates that no matter what the value of e is, the marginal profit π' will increase with price less than, proportionately equal to, or more rapidly than price if and only if 1-e<η<1, η = 1, or η>1, respectively. If prior market conditions establish a price at a level at which the elasticity of demand is less than unity and MR is below MC (i.e., the marginal profit being negative), an OPEC price hike could be favorable. Under relation A, an increasingly elastic demand at higher prices (e.g., η>0) would generally create conditions in which alternative fuels become more competitive following the price hike. The desired result under profit-maximizing principles is to have the marginal profit increase to 0 and elasticity close to e^{*} = k/(k— 1) depending on the ratio k(k = P/MC).

Since the marginal cost for OPEC countries is very low relative to price, and k is accordingly large, e^{*} should be very close to 1. Under the condition η = 1 or η > 1, the increase in elasticity at a higher price is proportionately equal to or greater than the increase in price, and we reach the point at which negative marginal profit increases to zero more rapidly than under 1-e<η<1. On the other hand, if the price elasticity of demand is greater than unity and MR is greater than MC, it becomes advantageous for OPEC to lower its price. In general, the elasticity of demand would converge toward e^{*} = k/(k— 1) and the marginal profit to zero. That is, the market system would adjust itself under stable relation A.

Relation B indicates that if η - (1 - e)<0, the marginal profit will decline (increase) as the price of crude oil is raised (lowered). This relation is an unusual and basically unstable case. Relation B also implies that the second-order condition in Eqs. (5) or (6) is not satisfied. The elasticity will therefore diverge from e^{*} = k/(k— 1). A cartel can benefit from an increase in price if demand is inelastic. Under the unstable relation B, the elasticity of demand decreases markedly as the price is raised. Inasmuch as marginal profit decreases and is negative, output will be curtailed and the price will be raised further. This can occur only in unusual circumstances (e.g., the energy crisis of 1973-1974). It is not a mathematical curiosity to have relation B—that is, an unusually strong convex demand curve. This could be a direct result of a structural break in the world oil market from a preembargo competitive oil market to an after-embargo cartel market. For example, the market demand changed from an elastic competitive market demand (before the 1973 embargo) to an inelastic cartel demand (after the embargo, from point F to C in Fig. 1).

The regime shift occurred when OPEC emerged as an effective cartel in 1971 after the Tehran Agreement. The ensuing Arab-Israeli War of 1973, subsequent oil embargo, and the nationalization of oil production in member countries enabled the cartel to raise the price of crude oil from $2 per barrel in 1971 to $34 in 1981. The price skyrocketed again to $37 in 2000 and $39.99 in late February 2003. The market changed from a competitive one to one in which OPEC was able to exercise a considerable degree of monopoly power. Demand, in turn, changed from a relatively elastic individual market demand curve to a relatively inelastic industry cartel demand curve. The OPEC countries could therefore raise the oil price even further under this structural break in demand. This was the direct result of the unstable relation B.

In order to estimate the demand relations, we use data from “The Annual Energy Review” and “The Economic Report of the President.” The price of coal (PC) is measured in cents per million Btu (cost, insurance, and freight price to electric utility power plants), as are prices of petroleum (P) and natural gas (PN). The quantity of petroleum consumption (Q) is in quadrillion Btu (10^{15}) and real gross domestic product is used to reflect income (Y). The sample period extends from 1949 to 1998. As with other economic variables, the unit root (unstable variables or not stationary) property needs to be examined before the estimations. Note that we fail to reject the null hypothesis of a unit root for all the variables even after the logarithmic transformation. That is, these variables are not stationary for the ordinary least squares technique: A technique is needed that relates a set of independent variables and dependent variables in terms of a linear equation. Since all the variables in our model are not stationary, we apply the two-step technique by Engle-Granger to explore the cointegration relation (comovements of unstable variables). The cointegration model, used in the presence of unstable variables, suggests the use of the error correction model (ECM) in estimating the demand relation. That is, demand for petroleum can be appropriately formulated as

_{t}denotes consumption of crude oil; ECMt-1 is representing past disequilibrium; P

_{t}denotes the price of crude oil; Y

_{t}is income; PC

_{t}is the price of coal; and PN

_{t}represents the price of natural gas. Despite its complexity, the model is more general because it allows past disequilibrium or perturbations to be included in explaining oil consumption. The estimated results for the entire sample period are shown as follows:

^{2}is the adjusted R square, which reflects general fitness of the model; t statistics in parentheses indicate the significance of estimated coefficients. Within the framework of the partial adjustment model (or model with lagged dependent variable) with ECM, the price elasticity tends to converge approximately to -0.198 = [-0.0502/(1-0.7426)] when estimated in the level of first difference. Similarly, we report the estimation results for the two-subsample periods (1949-1975 and 1976-1998):

The short-term price elasticities before and after the structural break can thus be estimated as -0.1778 and -0.0625, respectively. The empirical results indicate that (i) the elasticity after the energy crisis decreased in absolute value from 0.1778 to 0.0625 (a 65% decrease), clearly an unstable case of η<0 (i.e., the price elasticity decreases as price increases), and (ii) there seems to be considerable room for a price hike because the long-term elasticity from Eq. (8) of -0.198 falls far short of k/(k - 1).

Neither the long-term price elasticity for the entire sample period (-0.198) nor the short-term price elasticity after the structural break (-0.0625) are close to the theoretical limit: k/(k— 1)≈1.05 as is expected by a profit-maximizing cartel. The discrepancy may be explained by the significant income elasticity of 1.3127 in Eq. (10). Since the business cycle is both inevitable and unpredictable, a recession could certainly shift the demand curve to the left (Fig. 1). Continuous and gradual price hikes without disruptions in demand would render price elasticity toward k/(k— 1) in the long term. A recession would generally depress both price and quantity, as shown in Fig. 1 from point A to B. Given that the price elasticity can be geometrically measured as e_{A} = tanγ/slope (d_{1}) at point A, the size of the price elasticity does not appear to have changed appreciably. That is, e_{A}= tanγ/slope (d_{1}) and e_{B} = tanθ/slope (d_{2}) are similar because both tan θ and the slope of the line d_{2} have decreased. Unless the U.S. economy is recession-proof in the long term, it does not seem possible that the long-term price elasticity would approach k/(k— 1) as implied by the theory. The wild swings in oil price after 1973 speak to the fact that demand for and supply of crude oil are not independent of political events. The significant change in the oil price was and can be detrimental to the suppliers with limited capacity and relatively higher marginal cost. In contrast, producers with lower marginal cost and greater capacity (e.g., Saudi Arabia) would benefit from greater output quota. To prevent such violent price changes, it is advantageous to OPEC to have a price band in which the price elasticity is not too low. However, can k/(k— 1) x 1.05. a theoretical limit developed previously, ever be reached? There are at least three reasons in favor of this argument. First, switching to alternative fuels becomes more plausible at high oil prices and thereby tends to push long-term price elasticity close to k/(k— 1). Second, noncartel output (e.g., 5-7 million barrels per day from Russia) in the long term can present a credible threat when the price is high enough. This renders OPEC's residual demand curve flatter for every high price. Third, significant ad valorem tariffs in G8 countries would effectively pivot the demand curve downward.

Substantial price fluctuations have been witnessed for the past three decades, especially since the 1973 energy crisis. Based on our estimate, the average price elasticity was very low,-0.1778 before 1975, but the change in market structure has given rise to the unstable demand case. It has been borne out with the short-term elasticity of -0.0625 after 1975. Notice that the negative and significant ECM coefficient (-0.1643) in Eq. (10) suggests a convergent trend toward equilibrium values after the structural break. In the absence of major war, it does not seem plausible that the price of oil will significantly exceed $40 due to the income effect in the demand structure. The price elasticity, hovering at -0.0625 after the structural break, suggests that the oil price would more likely approach the upper limit of the price band ($28) than the lower limit ($22) if OPEC members strictly adhered to the production cut (e.g., from Q_{1} to between Q_{2} and Q_{3}; Fig. 1) in the presence of a recession. The result is borne out because oil prices lingered around $28 at the beginning of May 2001, 1 month after the production cut. As the recession deepened after the September 11, 2001, terrorist attacks, the price of crude oil dropped to $20 in November 2001 when the OPEC cartel was reluctant to further reduce production. Failing to do so would result in a drastic price reduction (from point C to point D in Fig. 1) as occurred before. On the other hand, the upward pressure on price could be too irresistible because -0.0625 is far below the theoretical limit of -1.05, as inelastic demand promotes price increase.

Given that oil is of great importance in the production process, its impact on industrial output cannot be ignored. Furthermore, the growing magnitude of oil price changes reflects the major role of uncertainty in statistical modeling. For instance, Lee et al. found that uncertainty in oil price (conditional variance of an oil price change) could significantly impact economic growth. In particular, one unit of positive normal shock (a large price increase) gives rise to a decreased output, whereas one unit of negative shock does not necessarily lead to an increased output. Similarly, the impact of an oil price change on the financial market has received increased attention. Sadorsky was among the first to apply a formal statistical model to investigate such an impact. To capture the uncertainty inherent in the macroeconomic foundation, we need to first define the real oil price after adjusting for the consumer price index or roilp_{t}. To ensure stationarity property, let Δroilp_{t} represent the first difference of the logarithmic transformation on roilp_{t}. One of the common ways to measure the volatility of oil price is to apply an econometrical model called autoregressive and conditional heteroskedastic (ARCH) by Engle or its generalized version, the GARCH model, by Bollerslev. The GARCH model shown below is fairly general in describing the behavior of a volatile time series such as oil price in macroeconomics:

_{t}is the conditional variance often used to represent volatility, and z

_{t}= ε

_{t}/→ √h

_{t}denotes a standardized disturbance term. Note that optimal lags of the GARCH (1,1) -ARMA(p, q) are selected based on the criterion that a series correlation (correlation via residuals) is not found in Z

_{t}and z

^{2}

_{t}Finally, z

_{t}is normally distributed with zero mean and unit variance or N(0,1). Even though h

_{t}is frequently chosen to measure the volatility, the major problem is that variance masks the direction of changes to which shocks are administered. The asymmetric impact—only positive shocks (or price increases) slow economic activity and/or the stock market—begs the use of z

_{t}instead of h

_{t}as a proxy for volatility. As such, we use z

_{t}as the proxy in our research model.

Monthly data of industrial production (ip_{t}), real stock return (Δrstkp_{t}), consumer price index (cpi_{t}), exchange rate (exch_{t}), interest rate (r_{t}), and stock indices from July 1984 to March 2002 were obtained from the International Financial Statistics (IFS) data bank. Data for oil prices are from “Energy Prices and Taxes” published by the International Energy Agency. Note that we include exchange rates because oil is exported to many industrialized economies. In addition, the interest rate is incorporated to account for monetary policy. Major industrialized countries included in the study are the United States, Canada, Italy, Japan, Germany, and the United Kingdom.

As in many other time series analyses, we need to examine the existence of a unit root (unstable) on the variables of lip_{t}, lrstkp_{t}, lr_{t}, and lexch_{t}. The prefix l indicates the logarithmic transformation of the original variables, used to damp unstable variables. If these variables are I(0) or integrated of order zero indicating stationarity or stability of the variable, we could add z_{t} to form a five-variable VAR model. However, if these variables are I(1) or integrated of order 1 (not stationary), we need to first examine the potential existence of any cointegration relation (or comovements of unstable variables). A five-variable vector error correction model can be formulated in the presence of such a cointegration relation. Otherwise, the four-variable (first difference) model along with z_{t} would suffice to analyze the direction of causality among the variables.

The techniques for examining variable stationarity by Phillips and Perron and by Kwiatkwoski et al. are applied to the four variables for the six countries. The result is unanimous in that all the variables are of I(1) or not stationary. Consequently, we examine the potential existence of cointegration relations via the trace method developed by Johansen. An examination of the trace statistics suggests that no cointegration relation exists for the five countries except Japan, and two sets of cointegration relations exist for Japan. That is, we can include the past disturbance term ECM_{t-1} in the model to explain industrial production for Japan as follows:

_{t-1}is the error correction term representing the long-term cointegration. On the other hand, the five-variable vector autoregression model is applied to the other five countries as follows (only the stock return equation is shown):

To purge serial correlation in z_{t} of Eq. (11), for more accurate estimation, a lag of 5 on autoregression and a lag of 1 on moving average are needed. The result indicates that the volatile behaviors of oil prices are best described by an ARCH model for Canada due to its insignificant β_{1}. However, the GARCH model is preferred for the remaining countries, of which Japan has the strongest persistence in oil price volatility (i.e., α_{1} + β_{1} > 1). The United States has the smallest persistence, with α_{1} + β_{1} =0.7866. Except for Japan, in which α_{1} > β_{1} (unexpected shock impacts current conditional variance more than past conditional variance), the reverse is true for other countries. Note that the GARCH model is selected so that z_{t} and Z_{t}^{2} are free of serial correlation, an undesirable property in a regression analysis.

H |
Canada |
Germany |
Italy |
Japan |
United Kingdom |
United States |
---|---|---|---|---|---|---|

* “not →” means “does not Granger cause.” The Granger causality carries the information that variable x causes variable y, whereas the ordinary regression model provides x associates y. A rejection of H | ||||||

z |
Cannot reject |
Cannot reject |
(+) Reject* |
Cannot reject |
Cannot reject |
Cannot reject |

z |
Cannot reject |
Cannot reject |
Cannot reject |
Cannot reject |
Cannot reject |
Cannot reject |

z |
Cannot reject |
Cannot reject |
(-/+) Rejec** |
Cannot reject |
(+) Reject*** |
Cannot reject |

z |
Cannot reject |
(-) Reject** |
(-) Reject* |
Cannot reject |
Cannot reject |
(-) Reject*** |

It is not surprising that the greatest z_{t} (greatest change in oil price) value occurred during the Gulf War in 1990. Table I reports the causality results from the statistical models. The lengths of impacts can be determined from the analysis. In the case of Germany, the volatility of a real oil price change exerts a negative impact on stock returns for three periods before it tapers off to zero. For Italy, the volatility of a real oil price change leads the monthly interest rate to change positively for 7 months, the monthly stock return to change negatively for approximately 4 months, and the monthly industrial production to change negatively in the first month but positively during the next 3 months.

Surprisingly, the same volatility exerts positive impacts on industrial production (3 months) for the United Kingdom before leveling off to zero. The favorable impact of higher oil prices on industrial output can be attributed to the fact that Britain is one of the non-OPEC producers: A higher oil price commands the greater revenue (η<0) from export, which can in turn be reinvested. For the United States, the volatility of a real oil price change leads to negative stock returns for 3 months before diminishing gradually to zero. The same volatility has no appreciable impacts on either industrial production or stock returns for Canada and Japan. It seems that the volatility of oil price changes leads to negative stock returns in three of the six countries. It affects industrial production in only two countries, including a positive impact in the United Kingdom.

Recent studies have highlighted the role of oil price uncertainty. The results seem to favor the long-held conjecture that higher oil prices have a greater impact on the stock market than on the output market. This is supported in our model for the United States. Higher oil prices seem to have a lower impact on major economies such as those of the United States and Japan due to the presence of strategic oil reserve. A strategic oil reserve is essential to absorb the shocks from an excessive price hike. At the heart of the volatility analysis is the concept of oscillating price elasticity at the microeconomic foundation developed by Greenhut et al. The existence of unstable price elasticity indeed sows the seed of inherent volatile oil price changes, which can readily inflict shocks to the economy, especially a relatively small economy whose demand for oil depends solely on import. Our volatility model, employing the most recent data, supports this conclusion. The impacts on the interest rate and other monetary variables remain a challenging research avenue for the future.

Business Cycles and Energy Prices • Energy Futures and Options • Inflation and Energy Prices • Markets for Petroleum • Oil and Natural Gas: Economics of Exploration • Oil and Natural Gas Leasing • Oil Crises, Historical Perspective • Oil Industry, History of • Oil-Led Development: Social, Political, and Economic Consequences

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