The Price Of Crude Oil On The Nymex

Explaining the real price of crude oil on the NYMEX

Will C. Hambly

December 2, 2005 Economics 272 Professor Studenmund

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Background Information Being the lifeblood of the world’s industrialized economies, crude oil is the most actively traded commodity. The world consumes roughly 80 million barrels of crude oil per day and uses petroleum products for a multitude of applications, including transportation, heating, and plastic production. Because oil is such an essential input in the production process, its price is closely followed and reported daily by the financial press. Also, most of the world’s heaviest consumers of petroleum rely on imports from Middle Eastern oil-producing nations. Since the formation of an international petroleum cartel, the Organization of Petroleum Exporting Countries (“OPEC”), the political importance of oil has escalated. In an effort to insulate the American economy from oil shocks, the U.S. government began stockpiling emergency oil reserves in 1977 as a national security policy. The question of whether the price of oil is high or low based on market fundamentals is a contentious debate. Currently, oil is trading at about $60 per barrel in 2005 dollars, a relatively high price compared to historical averages. Many justify this price and remain bullish, adhering to the idea that the supply of petroleum is fixed and that increased demand from developing countries will drive the price higher as they accelerate growth. Others dismiss the current price as being irrational and the result of increased speculative activity by large alternative investment funds. This paper seeks to explain what determines the price of oil. Several different types of crude oil are produced and receive different market prices. For instance, North Sea crude, generally known as Brent crude, commands about a $1 premium to the OPEC Basket Price, which includes various blends of Dubai, Saharan, and Venezuelan crudes. The price quoted on the New York Mercantile Exchange, however, is for light-sweet, or West Texas Intermediate (“WTI”) crude. WTI is the most easily and widely refined crude in

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U.S. refineries, making it the most frequently quoted type of oil in the world. Light-sweet WTI crude on the NYMEX trades at about a $2 premium to the OPEC Basket Crude. Changes in the price of crude oil have large affects on the U.S. economy and are difficult to explain and predict. The quoted price of crude oil on the NYMEX represents the cost of one 42-gallon barrel of crude oil before transaction and transportation costs. A Review of the Literature A careful review of the literature highlights many of the potential drivers behind the price of crude oil. Both scholarly, commercial, and professional sources described below provide insight into possible reasons for fluctuations in the price of crude on the NYMEX. 

In Robert S. Pindyck’s article, Volatility and Commodity Price Dynamics, published in the Journal of Futures Markets, Pindyck shows how short-run price volatility is affected by levels of inventories held. He also comments that price variation may be the result of speculation and “herd-behavior”. Pindyck uses a weekly model with price being the closing price of the nearest expiration futures contract.



Carlos Coimbra, Senior Economist at the Banco de Portugal, analyzes the demand for petroleum products in Oil Price Predictions in Macroeconomic Forecasts. He stresses that futures market prices reflect expectations for world economic activity. As economies and industrial output grow, demand for oil increases. Futures markets should, however, immediately adjust when actual output is less than what was expected. He notes that it is very difficult to explain systematic behavior in oil prices. Part of the “errors” in futures market prices may be related to errors in estimating world economic growth. He uses a monthly model of the price of nearest expiration futures contracts on the first trading day of the month.

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Much of the academic literature pertaining to the price of oil surrounds the impact of oil prices on the macroeconomy. Understanding the Impact of Oil Shocks, published by the Federal Reserve Bank of St. Louis, examines oil price shocks in the 1970’s and shows how they contributed to a drop in real GDP and an increase in the price level. This study, however, analyzes oil prices as an independent variable and does not describe how oil prices are set; nevertheless it confirms the correlation between economic growth and oil prices. Another scholarly article, The Cyclical Behavior of NYMEX Energy Prices, published in Energy Economics, explains that oil prices are procyclical. That is, an expansion of real GDP is usually accompanied by an increase in the price of crude.

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Besides a review of the scholarly literature, relevant commodities articles in both the Wall Street Journal and the Financial Times offer daily insight into what may be moving the market. Additionally, information provided by Phil Flynn, an oil trader with Alaron Trading Co., offered a perspective on fundamental evaluators, such as real GDP, housing starts, and industrial production. In the interview conducted, he stressed the importance of commercial crude oil stocks and economic growth.

A Theoretical Model A review of the literature pertaining to oil prices makes clear that as economic growth increases, demand for oil increases. The economic theory behind the relationship between economic growth and oil consumption is strong. In a model seeking to explain changes in price, there is no question that a measure of demand is necessary. Another important aspect of the oil market is the role of OPEC, the international petroleum cartel. While OPEC’s role in reducing petroleum production has diminished over time, the cartel is still likely to have a significant impact on the price of oil. Additionally, the role of stockpiles of crude oil should have an impact

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on the price of crude. As stocks are depleted, there may be a fear that the commodity is in short supply and traders will bid up the price. Also, a shock to the production of crude must have an impact on the price. If there is a significant decline in oil production in a specific area, the market will likely react to the prospect of reduced availability of oil by bidding up the price. Lastly, to reflect current trends in the market for crude oil, a time-series model with very frequent observations should be used. For practical reasons concerning the publishing of economic data, a monthly model from January of 2002 through June of 2005 will be used. Additionally, because crude oil on the NYMEX is measured in dollars, inflation must have an effect on the price of oil. To measure real impacts on the price, inflation must be filtered out of the dependent variable. The Independent Variables, Functional Form, and Expected Signs of Coefficients While it is clear that many variables affect the price of crude oil, determining the correct variables for an equation is difficult because there are several ways to measure a single phenomenon. Below are the independent variables and a detailed explanation of why each was chosen and what it means: 

Industrial Production Index: As the world’s economies grow, industrial production expands and global demand for oil increases. Because the United States economy consumes roughly 25% of the world’s crude oil, and meticulous monthly data is collected by the government, the Industrial Production Index was chosen to explain demand for oil in developed countries. The Industrial Production Index measures the monthly physical output of the manufacturing, mining, gas, and electricity industries. Other ways of measuring output, such as real GDP, are inferior to the Industrial Production Index for this model because real GDP measures output in the service and

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technology sectors, which consume less petroleum than heavy industries. Theory suggests that the relationship between industrial output and crude prices should be linear. Increases in industrial output should mean that oil demand has increased and that the price should rise. A positive (+) sign is expected. 

Non-OECD Consumption of Petroleum: This variable is a measure of oil consumption in the developing world. As the developing world industrializes, the world economy’s demand for petroleum accelerates. Both China and India are two of the fastest growing nations and consume large amounts of oil. Almost all literature concerning the price of oil cites Chinese demand as a driver of prices. The relationship between non-OECD consumption and the price of oil should be linear as well. As the consumption of a non-renewable resource increases, price should rise, so the expected sign of this coefficient is positive (+).

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Change in Crude Stocks: Changes in the commercial stocks of crude oil are an important driver behind changes in price. Quantities of crude oil stocks are stocks of oil held at refineries, in pipelines, in bulk terminals, or any quantities in transit to the aforementioned destinations. If this variable were the absolute level of crude stocks, an inverse function form would be theoretically accurate, because the impact of the stock levels on price would diminish as they increased. Because it is the change in stocks, only linear is appropriate. An increase in crude stocks should ease the market’s fear of a shortage, so the expected sign of this coefficient is negative (-).

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Change in U.S. Field Production: A disruption in U.S. field production should have a large impact on prices. Because the U.S. consumes more petroleum than it produces, it is forced to import crude oil from abroad. As more oil is produced in the

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United States, fears of a shortage will diminish and the price should fall. The relationship between changes in field production and the price of oil should be linear. The expected sign of this coefficient is negative (-). 

Change in OPEC Output: By restricting output, OPEC has been able to raise the price of oil. OPEC’s share of world oil production has decreased since the 1970’s because new oil fields have come on-line and market power has eroded; nevertheless, OPEC’s pricing power still exists. Theory suggests that the relationship between changes in OPEC output and the price of oil is linear. The expected sign of this coefficient is negative (-) because as OPEC increases output, the price of oil should fall.

For this model it is reasonable to assume a functional form in which the equation is linear in both the coefficients and the variables. Theory does not suggest that the relationship between the variables described above and the price of oil should be anything other than linear. Discussion of the Data Below is a discussion of the dependent variable and each independent variable. A description of how the data is expressed, sources, and any irregularities found are offered. 

Real Price of NYMEX Crude: Daily data on the price of crude oil is available from the U.S. Energy Information Administration website. These prices are, however, in nominal prices. Because there has been persistent inflation throughout the last three years, prices quoted on the NYMEX were converted to January, 2002 dollars, when the Consumer Price Index, Less Energy was equal to 186. Each monthly observation is the real closing price (in January, 2002 dollars) of the contract of nearest expiration on the first trading day of the month.

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Industrial Production Index: Data was obtained from the Federal Reserve Bank of St. Louis’ Federal Reserve Economic Data website. This data is seasonally adjusted, of monthly frequency, and has a base year of 2002.

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Non-OECD Consumption of Petroleum: Monthly time series data concerning petroleum consumption and economic growth for countries not belonging to the Organisation for Economic Co-operation and Development is not accessible. Because data on oil consumption is not readily available, it was calculated as a residual. Non-OECD consumption was calculated as the difference between total world production per day per month of crude oil and OECD consumption per day per month. Because a portion of the oil produced could enter stockpiles, this variable may not be precise, however the theory behind the idea that developing countries consume large amounts of oil as they industrialize is very strong, so this variable must be included. It is expressed as the percentage change in consumption from the same month in the previous year to adjust for seasonality. Data was obtained from the U.S. Energy Information Administration website’s section on international petroleum.

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Change in Crude Stocks: Changes in the crude oil stocks are measured as a percentage change in the quantity of commercial crude oil stocks of the same month from the previous year to eliminate any seasonal trends. This data is available on the U.S. Energy Information Administration’s website in the supply and disposition section.

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Change in U.S. Field Production: Data on U.S. field production of crude oil is available at the U.S. Energy Information Administration’s website as well. This

Hambly variable is calculated as the percentage change in field production from the same month of the previous year to avoid seasonality. 

Change in OPEC Output: This variable is measured as the percentage change in output from the same month of the previous year to eliminate any seasonal patterns. Statistics on OPEC production are also available from the U.S. Energy Information Administration.

Estimation and Evaluation of the Equation Using Ordinary Least Squares and the variables discussed above to estimate an equation yields the following results (t-scores in parenthesis): Equation 1: NYMEX = -263.354 + 2.894 INDPROD + 0.061 NONOECD - 0.176 STOCKS (11.600)

(0.794)

(-2.210)

+ 0.212 FIELDPROD + 0.062 OPEC (0.9053) N = 42

(0.676)

Adjusted-R2 = 0.8795

DW = 1.400

INDPROD = the Industrial Production Index NONOECD = the percentage change in Non-OECD Consumption STOCKS = the percentage change in commercial stocks FIELDPROD = the percentage change in U.S. production OPEC = the percentage change in OPEC output Note: See Appendix Equation 1 for Regression Output, Correlation Matrix, Residuals, and Data. Hypothesis Tests for Each of the Coefficients in Equation 1: Degrees of Freedom = 36 5% One-Sided Test: tc = 1.697

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Hambly HO: βINDPROD ≤ 0

tINDPROD = 11.600

| tINDPROD| > tc

10

and the sign is in the correct direction. Reject HO.

HA: βINDPROD > 0

HO: βNONOECD ≤ 0

tNONOECD = 0.794

| tNONOECD| < tc

even thought the sign is in the correct direction.

HA: βNONOECD > 0

Fail to Reject HO.

HO: βSTOCKS ≥ 0 tSTOCKS = -2.209

| tSTOCKS| > tc

and the sign is in the correct direction. Reject HO.

HA: βSTOCKS < 0

HO: βFIELDPROD ≥ 0

tFIELDPROD = 0.905

| tFIELDPROD| < tc and the sign is in the wrong direction. Fail to Reject HO.

HA: βFIELDPROD < 0

HO: βOPEC ≥ 0

tOPEC = 0.676

| tOPEC| < tc

and the sign is in the wrong direction. Fail to

Reject HO. HA: βOPEC < 0 Of the five coefficients, two are significant in the expected direction. βINDPROD and βSTOCKS were significant and in the hypothesized directions. βNONOECD had the expected positive sign, however it was not significant. βFIELDPROD and βOPEC were insignificant in the unexpected direction. Of the insignificant coefficients, the economic theory behind βOPEC and βNONOECD is indisputable.

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The impact of OPEC’s output and the developing world’s demand for crude oil is well documented and strongly supported by economic theory. By reducing output, OPEC is able to increase the price of oil. Also, as countries not in the OECD, or the world’s developing countries, industrialize they will increase demand for petroleum products and the price of oil will rise. Both OPEC and NONOECD belong in the equation. After rethinking the theory behind the regression, βFIELDPROD, which was insignificant in the wrong direction, could be an irrelevant variable. Although there is some theory behind the idea that as U.S. field production increases, the price of oil should fall, this variable may not belong because U.S. production is a small fraction of the world total. In fact, increases in field production may be highly correlated with increases in the price of oil. As the price rises, it becomes economically viable to drill in harsh environments, therefore increasing the production of crude oil. In other words, field production does not have a significant impact on the price of crude oil. The possibility of it being irrelevant must be investigated. It is now dropped from the model based on theory and the coefficients are re-estimated. The following is Equation 2 (t-scores in parenthesis): NYMEX = - 262.886 + 2.889 INDPROD + 0.057 NONOECD - 0.169 STOCKS (11.612)

(0.737)

+ 0.064 OPEC (0.702) N = 42

Adjusted-R2 = .8801

DW = 1.368

INDPROD = the Industrial Production Index NONOECD = the percentage change in Non-OECD Consumption STOCKS = the percentage change in commercial stocks OPEC = the percentage change in OPEC output

(-2.139)

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Note: See Appendix Equation 2 for Regression Output, Correlation Matrix, Residuals, and Data. Hypothesis Tests for Each of the Coefficients in Equation 2: Degrees of Freedom = 37 5% One-Sided Test: tc = 1.697 HO: βINDPROD ≤ 0

tINDPROD = 11.612

| tINDPROD| > tc

and the sign is in the correct direction. Reject HO.

HA: βINDPROD > 0

HO: βNONOECD ≤ 0

tNONOECD = 0.737

| tNONOECD| < tc

even thought the sign is in the correct direction. Fail to

HA: βNONOECD > 0

Reject HO.

HO: βSTOCKS ≥ 0 tSTOCKS = -2.139

| tSTOCKS| > tc

and the sign is in the correct direction. Reject HO.

HA: βSTOCKS < 0

HO: βOPEC ≥ 0

tOPEC = 0.702

| tOPEC| < tc

and the sign is in the wrong direction. Fail to

Reject HO. HA: βOPEC < 0 After re-estimating the equation excluding the suspected irrelevant variable, the four specification criteria must be applied to the results.

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Theory: The theory behind the idea that U.S. field production affects the price of crude oil is valid, however the United States only produces a small fraction of the world’s oil, so this variable may not be belong. Additionally, field production may not be affecting the price, but the price may be inducing producers to produce more. Also, U.S. oil supplies may be insulated from periodic disruptions in field production because of the Strategic Petroleum Reserves held by the government.

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T-test: The t-score for the coefficient of field production was insignificant in Equation 1. Two out of the four coefficients became more significant, but only one became more significant in the expected direction. This is a relatively weak sign that field production may be an irrelevant variable.

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Adjusted-R2: Adjusted-R2 increased from 0.8795 to 0.8801. This is a small change in adjusted-R2, nevertheless it increased. This is further evidence that field production was an irrelevant variable.

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Changes in the Coefficients: None of the coefficients changed significantly. This is evidence that that field production is an irrelevant variable and its exclusion is not causing any bias.

Based on the specification criteria, field production is removed from the model. Moving forward with Equation 2, the equation must be tested to determine if any econometric maladies afflict it. Omitted Variables The equation almost certainly has an omitted variable. A variable for political concern over future oil supply should be included, however, political tension is not easily quantified. A dummy variable for political events concerning the oil market would also be appropriate,

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however observations of this variable would indicate that in each month there was a political event, which would prove useless for the model. Also, since every month has a political event in the oil market, deciding which event should be considered important injects human error and the psychological phenomenon of confirmation bias into the equation. Another possible omitted variable is a gauge of the developing world’s economic growth. The Non-OECD Consumption of Petroleum variable contains imperfect data. Data on the developing world’s economic growth or expectations of growth would enhance the accuracy of the model and may result in a significant t-score for βNONOECD. Irrelevant Variables Based on the four specification criteria, the field production variable was eliminated from the model. The economic theory behind the existing variables is strong and in two of the four coefficients, it is supported by significant t-scores. Because the variables included are supported by strong theory, none is irrelevant. The regression results show that βNONOECD and βOPEC have a very small impact on the price of oil and the coefficients are insignificant. Despite this weakness, theory is strong and both variables must be included. Functional Form There is no reason to suspect that any functional form besides linear in the coefficients as well as in the variables is appropriate. Including an intercept dummy or slope dummy for political events may be theoretically appropriate, however, in every month there are several political events of importance involving oil supply, so determining which events to include would be of dangerously subjective nature. Multicollinearity

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Because the t-scores for βNONOECD and βOPEC are insignificant, and βOPEC has an unexpected sign, the equation could be afflicted with multicollinearity, which would result in high standard errors and low t-scores. The Equation 2 Correlation Matrix included in the Appendix shows the simple correlation coefficients between the independent variables. All simple correlation coefficients are below 0.80. This is evidence that the equation does not have multicollinearity. To further investigate multicollinearity in the equation, calculating the variance inflation factors is necessary. Computer output for each estimated auxiliary equation used to compute the VIF is included in the Appendix. Each VIF is presented below: R-squared VIF

INDPROD 0.5879 2.43

NONOECD 0.0147 1.01

STOCKS 0.4586 1.85

OPEC 0.4736 1.90

None of the variables have a variance inflation factor above the threshold of 5. This is further evidence that the equation does not have multicollinearity. Serial Correlation Being a time-series model, there is a high probability that the equation may have pure positive serial correlation. This would bias the estimates of the standard errors negative and increase the probability of a Type I error, making hypothesis testing unreliable. The Durbin-Watson statistic for the equation is 1.368. A 5% one-sided Durbin-Watson Test requires the appropriate critical values for an equation in which K = 4 and N = 42. These values are as follows: dL = 1.29, dU = 1.72. HO: ρ ≤ 0

(no positive serial correlation)

HA: ρ > 0

(positive serial correlation)

Because dL ≤ 1.368 ≤ dU, the results of the Durbin-Watson Test are inconclusive. The existence of positive impure serial correlation cannot be detected. Even though a time series

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model suggests serial correlation, because the Durbin-Watson test is inconclusive no remedy should be applied. Heteroskedasticity Because this is a time-series model and there are not huge differences in size of the dependent variable, heteroskedasticity is not extremely likely. Nevertheless, having heteroskedasticity could lead to unreliable hypothesis testing because standard errors will be biased negative, inflating the t-scores, and increasing the probability of a Type I error. The existence of heteroskedasticity should be investigated. Running a Park Test requires a proportionality factor, Z. It is reasonable to choose the Industrial Production Index as the proportionality factor for this equation. The Industrial Production Index measures the physical output of U.S. industry, and serves as a measure of the United States’ oil demand. As industrial output increases, it is reasonable to assume that there may be a higher variance in the price of crude oil. Thus, the Industrial Production Index is an appropriate proportionality factor. Running the Park Test requires the generation of three new variables: the squared residuals, the natural logarithm of the squared residuals, and the natural logarithm of the proportionality factor Z, which is the Industrial Production Index. These variables are included in the Appendix. An estimation of the regression to be used in the Park Test is as follows (t-scores in parenthesis): LNRESIDSQ = -78.974 + 17.255 LNZ (1.448) N = 42

Adjusted-R2 = 0.026

LNZ = the natural logarithm of the Industrial Production Index LNRESIDSQ = the natural logarithm of the residuals squared Note: Regression output is included in the Appendix.

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To run two-sided 1% t-test on the estimated coefficient of LNZ, the critical value of 2.704 is needed. HO: αlnZ = 0

tlnZ = 1.448

HA: αlnZ ≠ 0

Fail to Reject the Null Hypothesis.

| tlnZ| < tc

Because the Null Hypothesis cannot be rejected, there is no evidence of heteroskedasticity. Results Of the six major econometric diseases investigated, the only outstanding possibility of a problem with the equation is the existence of an omitted variable. The quality of the equation should not be judged by the adjusted-R2 statistic, but being able to explain approximately 88% of the variation in oil prices with the independent variables used is satisfying. Although βOPEC and βNONOECD have insignificant coefficients and the sign of βOPEC is in the unexpected direction, the theory behind these variables commands that they must be included. The tests performed above also show that the equation is not afflicted with multicollinearity or heteroskedasticity, however the existence of serial correlation is inconclusive. The final equation (Equation 2) is presented below: NYMEX = - 262.886 + 2.889 INDPROD + 0.057 NONOECD - 0.169 STOCKS (11.612)

(0.737)

(-2.139)

+ 0.064 OPEC (0.702) N = 42

Adjusted-R2 = .8801

DW = 1.368

INDPROD = the Industrial Production Index NONOECD = the percentage change in Non-OECD Consumption STOCKS = the percentage change in commercial stocks

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FIELDPROD = the percentage change in U.S. production OPEC = the percentage change in OPEC output Note: See Appendix Equation 2 for Data, Regression Output, Residuals, and Correlation Matrix Discussion and Conclusions The equation shows that industrial output and the change in crude stocks have significantly large impacts on the price of crude oil traded on the NYMEX. For each one-unit increase in the Industrial Production Index, the price of crude should rise almost $3, holding all other independent variables in the equation constant. Also, for each 1% increase in crude stocks compared to the same month of the previous year, the price of crude should fall nearly $0.17, holding constant all other variables in the equation. OPEC output and oil consumption in the developing countries are also likely to be important drivers behind the price of crude, but in this equation they are insignificant. The model can be used for judging the market’s response to changes in oil fundamentals, assessing the current price of oil, and creating an oil trading strategy. Because the financial press devotes thousands of pages each year to covering the price of oil, the equation above can be used to evaluate analysts’ interpretations of what moves the market. Further research on possible proxies for political tension should be examined because political concern is likely to have a positive impact on oil prices. Also, finding more accurate and extensive monthly data on the developing world’s economic growth would increase the precision of the model. As the developing world’s economic growth accelerates in the future and data becomes available, another estimation of the equation with an increased sample size should generate more robust results.

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Bibliography Augilar-Conraria, Luis. “Understanding the Impact of Oil Shocks.” Federal Reserve Bank of St. Louis. Jun. 2005. Coimbra, Carlos. “Oil Price Assumptions in Macroeconomic Forecasts.” OPEC Review 28 (1976): 87-107. Farivar, Maswood. “Crude-Oil Futures Edge Higher As Inventories Post Sharp Drop.” Wall Street Journal, 1 Dec. 2005. Flynn, Phil. Alaron Trading Company. Personal Interview. 20 Oct. 2005. Goodman, Leah. “Crude Drops Below $57 a Barrel.” Wall Street Journal, 18 Nov. 2005. Hoyos, Carola. “IEA Urges Calm Over Energy Prices.” Financial Times, 10 Nov. 2005. McKay, Peter. “Energy Prices Finally Calm Down.” Wall Street Journal, 22 Nov. 2005. McNutty, Sheila. “US Grapples with The Age of Energy Insecurity.” Financial Times, 21 Nov. 2005. Padgett, Gary. Great Pacific Trading Company. Personal Interview. 3 Aug. 2005. “Petroleum.” Worldbook Encyclopedia. 2000. Pindyck, Robert. “Volatility and Commodity Price Dynamics.” Journal of Futures Markets 24 (1981): 1029-1047. Serletis, Apostolos. “The Cyclical Behavior of Monthly NYMEX Energy Prices.” Energy Economics 20 (1998): 265-270. Studenmund, A.H. Using Econometrics: A Practical Guide. New York: Addison Wesley, 2006. United States Energy Information Administration. Monthly Energy Review. Nov. 2005.

Hambly United States Energy Information Administration. This Week in Petroleum. Sept-Dec. 2005.

Appendix Equation 1. Regression Results for Equation 1. Dependent Variable: NYMEX Method: Least Squares Date: 11/30/05 Time: 20:41 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C -263.3541 INDPROD 2.894178 NONOECD 0.061189 STOCKS -0.176052 OPEC 0.061559 FIELDPROD 0.211721 R-squared 0.894220 Adjusted R-squared 0.879529 S.E. of regression 3.016061 Sum squared resid 327.4785 Log likelihood -102.7242 Durbin-Watson stat 1.400394

Std. Error t-Statistic 25.45925 -10.34414 0.249490 11.60038 0.077049 0.794155 0.079707 -2.208745 0.091025 0.676293 0.233857 0.905347 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

Prob. 0.0000 0.0000 0.4323 0.0336 0.5032 0.3713 33.83429 8.689565 5.177344 5.425583 60.86590 0.000000

Correlation Matrix for Equation 1. STOCKS OPEC NONOECD INDPROD FIELDPROD

STOCKS 1.000000 -0.153512 -0.100230 0.487337 0.111060

OPEC -0.153512 1.000000 0.083053 0.510144 -0.006444

NONOECD -0.100230 0.083053 1.000000 -0.006297 -0.076037

INDPROD 0.487337 0.510144 -0.006297 1.000000 0.046509

Residuals for Equation 1. obs 2002:01 2002:02 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10

Actual 21.0100 20.3400 22.3300 26.7400 26.5800 24.8900 26.5700 26.1600 27.4200 30.4000

Fitted 19.2563 18.0703 22.3629 24.7487 26.5426 27.7317 27.1877 28.4176 28.7411 28.0324

Residual 1.75370 2.26971 -0.03290 1.99125 0.03737 -2.84168 -0.61772 -2.25762 -1.32105 2.36763

| | | | | | | | | |

Residual Plot . |*. | . | *. | . * . | . | *. | . * . | * | . | . *| . | .* | . | .*| . | . | *. |

FIELDPROD 0.111060 -0.006444 -0.076037 0.046509 1.000000

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Hambly 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

26.7100 26.7900 31.2800 32.1200 35.1800 29.2000 25.4700 30.0200 29.6500 31.4600 28.6300 28.5500 28.0400 29.0100 32.6700 33.7800 35.4900 32.9200 36.6200 40.5000 37.0100 41.8400 41.9000 47.6100 47.5200 43.0800 39.8100 44.4700 48.6000 53.7700 47.7400 51.1600

29.6928 27.6288 31.1533 31.0965 31.6285 27.1463 27.5295 27.1727 27.5438 28.9880 28.4652 29.1924 32.5991 33.5845 35.0387 35.2113 34.7842 37.3893 40.0361 37.5816 40.9628 41.4789 41.1784 44.4186 44.2003 44.3408 45.9339 46.4533 46.7094 46.1458 46.7030 47.9609

-2.98283 -0.83877 0.12668 1.02351 3.55152 2.05366 -2.05954 2.84728 2.10619 2.47200 0.16475 -0.64236 -4.55914 -4.57450 -2.36866 -1.43131 0.70581 -4.46929 -3.41605 2.91837 -3.95281 0.36113 0.72161 3.19142 3.31972 -1.26079 -6.12389 -1.98332 1.89056 7.62417 1.03704 3.19914

| * | . | | . *| . | | . * . | | . |* . | | . | .* | | . | *. | | .* | . | | . | * | | . | *. | | . | *. | | . * . | | . *| . | | *. | . | | *. | . | | .* | . | | .*| . | | . |* . | | *. | . | | *. | . | | . | * | | *. | . | | . |* . | | . |* . | | . | * | | . | .* | | .*| . | | * . | . | | .* | . | | . | *. | | . | . * | . |* . | | . | * |

Data for Equation 1. obs 2002:01 2002:02 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07

FIELDPROD -0.677000 0.406000 0.206000 -0.421000 1.110000 -0.141000 -2.452000 0.709000 -6.880000 -0.889000 4.350000 1.834000 1.501000 0.100000 0.449000 -0.733000 -0.703000 -0.565000 -3.063000

NONOECD -4.470000 -2.408000 5.127000 1.528000 9.017000 -5.182000 -4.453000 0.852000 3.367000 3.549000 -3.619000 -12.92300 8.131000 -1.827000 17.59900 -1.495000 4.311000 -6.310000 -0.112000

NYMEX 21.01000 20.34000 22.33000 26.74000 26.58000 24.89000 26.57000 26.16000 27.42000 30.40000 26.71000 26.79000 31.28000 32.12000 35.18000 29.20000 25.47000 30.02000 29.65000

OPEC -11.20200 -10.01400 -11.19300 -13.02000 -9.268000 -5.321000 -7.312000 -9.498000 -3.703000 -0.538000 0.526000 -2.691000 2.508000 7.787000 9.162000 10.80600 7.320000 5.339000 3.430000

STOCKS 8.825000 15.89200 8.090000 -1.793000 -0.407000 3.019000 -2.752000 -3.805000 -12.49300 -6.948000 -7.727000 -11.01500 -14.44200 -17.18900 -15.56700 -10.24900 -12.69200 -10.37900 -6.360000

21

Hambly 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

1.244000 1.579000 -0.858000 -1.316000 0.327000 -0.150000 -0.258000 0.928000 -1.444000 0.389000 -2.698000 1.099000 -2.283000 -5.078000 1.861000 4.648000 0.321000 -0.359000 1.383000 0.530000 -0.175000 0.118000 -1.214000

4.409000 -1.316000 1.179000 5.370000 -6.411000 7.504000 -5.883000 1.212000 7.039000 7.190000 -0.989000 -0.059000 -2.749000 0.778000 1.878000 -4.525000 -8.431000 11.11200 -5.102000 4.556000 8.464000 5.156000 -9.968000

31.46000 28.63000 28.55000 28.04000 29.01000 32.67000 33.78000 35.49000 32.92000 36.62000 40.50000 37.01000 41.84000 41.90000 47.61000 47.52000 43.08000 39.81000 44.47000 48.60000 53.77000 47.74000 51.16000

6.149000 4.132000 3.248000 2.745000 12.30400 10.35300 4.832000 2.306000 5.407000 4.500000 11.93300 13.00700 10.15000 10.56100 8.388000 6.528000 5.099000 4.242000 4.881000 5.843000 6.379000 6.631000 2.897000

-5.645000 5.915000 1.089000 -2.375000 -3.148000 -0.890000 4.880000 5.597000 4.093000 6.649000 7.116000 3.335000 -0.304000 -4.781000 -2.708000 2.493000 6.273000 6.269000 6.791000 7.198000 8.993000 9.229000 7.992000

Sources: Energy Information Administration website, Federal Reserve Economic Data website Equation 2. Regression Results for Equation 2. Dependent Variable: NYMEX Method: Least Squares Date: 11/30/05 Time: 21:43 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C -262.8857 INDPROD 2.889269 NONOECD 0.056550 STOCKS -0.169321 OPEC 0.063705 R-squared 0.891812 Adjusted R-squared 0.880116 S.E. of regression 3.008702 Sum squared resid 334.9346 Log likelihood -103.1970 Durbin-Watson stat 1.367571

Std. Error t-Statistic 25.39188 -10.35314 0.248822 11.61177 0.076691 0.737384 0.079166 -2.138824 0.090772 0.701815 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

Prob. 0.0000 0.0000 0.4655 0.0391 0.4872 33.83429 8.689565 5.152238 5.359103 76.24912 0.000000

Correlation Matrix for Equation 2. STOCKS OPEC NONOECD

STOCKS 1.000000 -0.153512 -0.100230

OPEC -0.153512 1.000000 0.083053

NONOECD -0.100230 0.083053 1.000000

INDPROD 0.487337 0.510144 -0.006297

22

Hambly INDPROD

0.487337

0.510144

-0.006297

23

1.000000

Residuals for Equation 2. obs 2002:01 2002:02 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

Actual 21.0100 20.3400 22.3300 26.7400 26.5800 24.8900 26.5700 26.1600 27.4200 30.4000 26.7100 26.7900 31.2800 32.1200 35.1800 29.2000 25.4700 30.0200 29.6500 31.4600 28.6300 28.5500 28.0400 29.0100 32.6700 33.7800 35.4900 32.9200 36.6200 40.5000 37.0100 41.8400 41.9000 47.6100 47.5200 43.0800 39.8100 44.4700 48.6000 53.7700 47.7400 51.1600

Fitted 19.4402 18.0661 22.3067 24.7696 26.2203 27.7670 27.6676 28.1915 30.0642 28.1324 28.7126 27.1976 30.6808 30.9595 31.3423 27.2420 27.5684 27.2416 28.1335 28.6551 28.1582 29.3548 32.8102 33.5166 35.0161 35.2967 34.5864 37.6593 39.9279 38.1869 40.7337 41.9461 42.1930 43.9645 43.2158 44.3094 45.9530 46.1817 46.5786 46.1600 46.6714 48.2609

Residual 1.56979 2.27392 0.02332 1.97035 0.35970 -2.87704 -1.09756 -2.03151 -2.64418 2.26762 -2.00259 -0.40762 0.59923 1.16049 3.83772 1.95795 -2.09838 2.77843 1.51653 2.80491 0.47181 -0.80482 -4.77021 -4.50658 -2.34613 -1.51671 0.90361 -4.73931 -3.30787 2.31310 -3.72368 -0.10606 -0.29298 3.64551 4.30421 -1.22944 -6.14299 -1.71167 2.02137 7.60998 1.06864 2.89912

Residual Plot | . |*. | | . | *. | | . * . | | . | *. | | . |* . | | * | . | | .*| . | | .* | . | | * | . | | . | *. | | .* | . | | . *| . | | . |* . | | . |*. | | . | .* | | . | *. | | .* | . | | . | * | | . |*. | | . | * | | . |* . | | . *| . | | * . | . | | *. | . | | .* | . | | .*| . | | . |* . | | * . | . | | *. | . | | . | *. | | *. | . | | . * . | | . * . | | . | .* | | . | .* | | .*| . | | * . | . | | .*| . | | . | *. | | . | . * | . |* . | | . | * |

Data for Equation 2. obs 2002:01 2002:02

FIELDPROD -0.677000 0.406000

INDPROD 98.56700 98.43900

NONOECD -4.470000 -2.408000

NYMEX 21.01000 20.34000

OPEC -11.20200 -10.01400

STOCKS 8.825000 15.89200

Hambly 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

0.206000 -0.421000 1.110000 -0.141000 -2.452000 0.709000 -6.880000 -0.889000 4.350000 1.834000 1.501000 0.100000 0.449000 -0.733000 -0.703000 -0.565000 -3.063000 1.244000 1.579000 -0.858000 -1.316000 0.327000 -0.150000 -0.258000 0.928000 -1.444000 0.389000 -2.698000 1.099000 -2.283000 -5.078000 1.861000 4.648000 0.321000 -0.359000 1.383000 0.530000 -0.175000 0.118000 -1.214000

99.32800 99.71200 100.0660 100.9930 100.6500 100.7140 100.6760 100.2590 100.5310 100.0670 100.5450 100.5590 100.3760 99.60600 99.53900 99.81300 100.2780 100.3520 101.0140 101.1160 102.0380 102.2570 102.6790 103.4980 103.2110 104.0040 104.9560 104.3770 104.9950 105.3170 105.0620 105.8230 106.0350 106.7430 106.9480 107.3610 107.3120 107.1840 107.4340 108.2900

5.127000 1.528000 9.017000 -5.182000 -4.453000 0.852000 3.367000 3.549000 -3.619000 -12.92300 8.131000 -1.827000 17.59900 -1.495000 4.311000 -6.310000 -0.112000 4.409000 -1.316000 1.179000 5.370000 -6.411000 7.504000 -5.883000 1.212000 7.039000 7.190000 -0.989000 -0.059000 -2.749000 0.778000 1.878000 -4.525000 -8.431000 11.11200 -5.102000 4.556000 8.464000 5.156000 -9.968000

22.33000 26.74000 26.58000 24.89000 26.57000 26.16000 27.42000 30.40000 26.71000 26.79000 31.28000 32.12000 35.18000 29.20000 25.47000 30.02000 29.65000 31.46000 28.63000 28.55000 28.04000 29.01000 32.67000 33.78000 35.49000 32.92000 36.62000 40.50000 37.01000 41.84000 41.90000 47.61000 47.52000 43.08000 39.81000 44.47000 48.60000 53.77000 47.74000 51.16000

-11.19300 -13.02000 -9.268000 -5.321000 -7.312000 -9.498000 -3.703000 -0.538000 0.526000 -2.691000 2.508000 7.787000 9.162000 10.80600 7.320000 5.339000 3.430000 6.149000 4.132000 3.248000 2.745000 12.30400 10.35300 4.832000 2.306000 5.407000 4.500000 11.93300 13.00700 10.15000 10.56100 8.388000 6.528000 5.099000 4.242000 4.881000 5.843000 6.379000 6.631000 2.897000

8.090000 -1.793000 -0.407000 3.019000 -2.752000 -3.805000 -12.49300 -6.948000 -7.727000 -11.01500 -14.44200 -17.18900 -15.56700 -10.24900 -12.69200 -10.37900 -6.360000 -5.645000 5.915000 1.089000 -2.375000 -3.148000 -0.890000 4.880000 5.597000 4.093000 6.649000 7.116000 3.335000 -0.304000 -4.781000 -2.708000 2.493000 6.273000 6.269000 6.791000 7.198000 8.993000 9.229000 7.992000

Sources: Energy Information Administration website, Federal Reserve Economic Data website Auxiliary Equations Used in Calculating VIFs. Dependent Variable: INDPROD Method: Least Squares Date: 11/30/05 Time: 22:27 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C 102.0284 NONOECD 0.000973 STOCKS 0.211323

Std. Error 0.326063 0.049999 0.038583

t-Statistic 312.9100 0.019461 5.477105

Prob. 0.0000 0.9846 0.0000

24

Hambly OPEC R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.246962 0.587933 0.555401 1.961543 146.2108 -85.79040 0.472237

0.043557 5.669907 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

0.0000 102.5887 2.941805 4.275733 4.441225 18.07268 0.000000

Dependent Variable: NONOECD Method: Least Squares Date: 11/30/05 Time: 22:28 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient Std. Error t-Statistic C -0.508813 53.71062 -0.009473 INDPROD 0.010243 0.526324 0.019461 STOCKS -0.070717 0.167063 -0.423296 OPEC 0.057427 0.191781 0.299439 R-squared 0.014745 Mean dependent var Adjusted R-squared -0.063038 S.D. dependent var S.E. of regression 6.364216 Akaike info criterion Sum squared resid 1539.123 Schwarz criterion Log likelihood -135.2227 F-statistic Durbin-Watson stat 2.432060 Prob(F-statistic)

Prob. 0.9925 0.9846 0.6745 0.7662 0.740381 6.172633 6.629652 6.795144 0.189566 0.902852

Dependent Variable: STOCKS Method: Least Squares Date: 11/30/05 Time: 22:29 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C -213.0143 INDPROD 2.087632 NONOECD -0.066365 OPEC -0.607943 R-squared 0.458641 Adjusted R-squared 0.415903 S.E. of regression 6.165256 Sum squared resid 1444.394 Log likelihood -133.8887 Durbin-Watson stat 0.619896

Std. Error t-Statistic 38.89989 -5.475960 0.381156 5.477105 0.156781 -0.423296 0.157707 -3.854900 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

Prob. 0.0000 0.0000 0.6745 0.0004 -0.569786 8.066933 6.566129 6.731621 10.73125 0.000030

Dependent Variable: OPEC Method: Least Squares Date: 11/30/05 Time: 22:30 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C -187.9143 INDPROD 1.855699 NONOECD 0.040992 STOCKS -0.462417 R-squared 0.473559 Adjusted R-squared 0.431997

Std. Error t-Statistic 33.61505 -5.590184 0.327289 5.669907 0.136895 0.299439 0.119956 -3.854900 Mean dependent var S.D. dependent var

Prob. 0.0000 0.0000 0.7662 0.0004 2.753167 7.134466

25

Hambly S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

5.376958 1098.644 -128.1428 0.571854

Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

Park Test Data. obs 2002:01 2002:02 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

RESIDSQ 2.464240 5.170714 0.000544 3.882282 0.129385 8.277362 1.204643 4.127040 6.991669 5.142083 4.010386 0.166152 0.359080 1.346734 14.72810 3.833571 4.403182 7.719650 2.299865 7.867526 0.222607 0.647728 22.75490 20.30926 5.504349 2.300400 0.816511 22.46104 10.94198 5.350435 13.86581 0.011249 0.085839 13.28975 18.52621 1.511521 37.73628 2.929806 4.085945 57.91187 1.141997 8.404904

LNZ 4.590737 4.589437 4.598428 4.602286 4.605830 4.615051 4.611649 4.612285 4.611907 4.607757 4.610466 4.605840 4.610605 4.610745 4.608923 4.601222 4.600550 4.603298 4.607946 4.608684 4.615259 4.616268 4.625345 4.627489 4.631608 4.639552 4.636775 4.644429 4.653541 4.648009 4.653913 4.656975 4.654551 4.661768 4.663769 4.670424 4.672343 4.676197 4.675740 4.674547 4.676877 4.684813

LNRESIDSQ 0.901883 1.643011 -7.517133 1.356423 -2.044962 2.113524 0.186183 1.417560 1.944719 1.637458 1.388887 -1.794850 -1.024210 0.297682 2.689757 1.343797 1.482328 2.043769 0.832851 2.062744 -1.502350 -0.434284 3.124780 3.011077 1.705538 0.833083 -0.202715 3.111782 2.392606 1.677178 2.629426 -4.487494 -2.455276 2.586993 2.919187 0.413116 3.630622 1.074936 1.407553 4.058922 0.132779 2.128815

6.292515 6.458008 11.39425 0.000018

26

Hambly

Regression Results for Park Test Dependent Variable: LNRESIDSQ Method: Least Squares Date: 12/05/05 Time: 11:06 Sample: 2002:01 2005:06 Included observations: 42 Variable Coefficient C -78.97407 LNZ 17.25491 R-squared 0.049818 Adjusted R-squared 0.026063 S.E. of regression 2.173788 Sum squared resid 189.0142 Log likelihood -91.18262 Durbin-Watson stat 2.081217

Std. Error t-Statistic 55.17128 -1.431435 11.91497 1.448170 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

Prob. 0.1601 0.1554 0.921850 2.202682 4.437268 4.520014 2.097197 0.155363

Park Test Residuals obs 2002:01 2002:02 2002:03 2002:04 2002:05 2002:06 2002:07 2002:08 2002:09 2002:10 2002:11 2002:12 2003:01 2003:02 2003:03 2003:04 2003:05 2003:06 2003:07 2003:08 2003:09 2003:10 2003:11 2003:12 2004:01 2004:02 2004:03 2004:04 2004:05 2004:06 2004:07 2004:08

Actual 0.90188 1.64301 -7.51713 1.35642 -2.04496 2.11352 0.18618 1.41756 1.94472 1.63746 1.38889 -1.79485 -1.02421 0.29768 2.68976 1.34380 1.48233 2.04377 0.83285 2.06274 -1.50235 -0.43428 3.12478 3.01108 1.70554 0.83308 -0.20272 3.11178 2.39261 1.67718 2.62943 -4.48749

Fitted 0.23868 0.21625 0.37138 0.43796 0.49911 0.65822 0.59952 0.61049 0.60398 0.53236 0.57911 0.49928 0.58151 0.58391 0.55248 0.41961 0.40800 0.45543 0.53563 0.54836 0.66181 0.67923 0.83585 0.87284 0.94390 1.08099 1.03307 1.16514 1.32237 1.22691 1.32878 1.38161

Residual 0.66321 1.42676 -7.88852 0.91846 -2.54407 1.45530 -0.41334 0.80707 1.34074 1.10510 0.80978 -2.29414 -1.60572 -0.28623 2.13727 0.92419 1.07433 1.58834 0.29722 1.51439 -2.16416 -1.11351 2.28893 2.13824 0.76164 -0.24790 -1.23579 1.94664 1.07024 0.45026 1.30065 -5.86911

Residual Plot | . |* . | | . | *. | |* . | . | | . |* . | | * | . | | . | *. | | . *| . | | . |* . | | . | *. | | . |* . | | . |* . | | * | . | | .* | . | | . * . | | . | * | | . |* . | | . |* . | | . | *. | | . * . | | . | *. | | * | . | | . *| . | | . | * | | . | * | | . |* . | | . * . | | .* | . | | . | * | | . |* . | | . |* . | | . | *. | | * . | . |

27

Hambly 2004:09 2004:10 2004:11 2004:12 2005:01 2005:02 2005:03 2005:04 2005:05 2005:06

-2.45528 2.58699 2.91919 0.41312 3.63062 1.07494 1.40755 4.05892 0.13278 2.12882

1.33978 1.46432 1.49885 1.61368 1.64678 1.71329 1.70541 1.68482 1.72502 1.86195

-3.79506 1.12268 1.42034 -1.20056 1.98384 -0.63835 -0.29786 2.37410 -1.59224 0.26686

| | | | | | | | | |

*. | . . | *. . | *. .* | . . | * . *| . . * . . | * .* | . . * .

| | | | | | | | | |

28