Hedonic prices for crude oil

Applied Economics Letters, 2003, 10, 857 861 Hedonic prices for crude oil Z. WANG Department of Economics, Monash University, PO Box 197, Caulfield East, Victoria 3145, Australia Email: Zhongmin.Wang@BusEco.monash.edu.au This article presents a hedonic analysis of crude oil, the price and quality of which varies considerably from one stream to another. Different from common hedonic applications in the literature, the estimated implicit prices for the physical characteristics of crude oil have a clear interpretation: it reflects the market s valuation, but not the production cost of the characteristics, for crude oil characteristics are determined by nature. Crude oil hedonic price equations are found to be non-linear in the major physical characteristics, indicating that a refiner s valuation of crude quality depends on its refining technology. The estimation results yield insights into the current pricing system of the world crude oil market. I. INTRODUCTION Since Griliches (1961) revival of the hedonic method pioneered by Waugh (1928), numerous empirical studies have estimated the implicit prices for characteristics of differentiated products. The estimated implicit prices, as shown by Rosen (1974), generally cannot be interpreted to directly reflect the market s valuation. A large implicit price of a particular characteristic may reflect the high cost of producing that characteristic rather than the high valuation of consumers. Using wine as an example, Nerlove (1995) highlighted the danger of drawing inferences about consumer preference directly from the standard hedonic equation. This article presents a unique hedonic application where the estimated implicit prices can be interpreted as directly reflecting the market s valuation. The hedonic method is used in this article to estimate the implicit prices of the quality characteristics of crude oil, perhaps the world s most important commodity. Crude oil characteristics, such as gravity and sulfur, are determined by the geological conditions under which the crude oil was formed: it does not cost more to extract crude oil of better quality, nor is it economical for crude oil producers to alter crude characteristics. Because of this special property, the implicit prices of crude oil characteristics can be interpreted as the refiners valuation, but not the production cost of those characteristics. For the many refineries and oil-exporting countries in the world, crude oil is a differentiated product. A hedonic analysis of crude oil yields useful insights into the market s valuation of crude quality and the current pricing system of the world crude oil market. Section II presents the industry background, a simple theoretical model and the empirical specification. Section III describes the data and presents the estimation results. Section IV concludes. II. INDUSTRY BACKGROUND AND MODEL Industry background A large number of crude oils are traded internationally, and they differ in quality and price. For example, the crude stream of Saudi Arabia Light is of lower quality (heavier and sourer) and cheaper than the UK Brent stream. See Table 1 for summary statistics of crude oil price and quality characteristics. Prices of virtually all crude oils are now linked to the spot prices of benchmark crude oils such as UK Brent, either through pricedifferential spot trading or according to some government pricing formulas that account for quality differences (Horsnell and Mabro, 1992). Quality differences, therefore, are expected to explain a large fraction of the price variations among the many streams of crude oils. The oil industry has long been using two different methods to evaluate crude oil quality. The first method is Applied Economics Letters ISSN 1350 4851 print/issn 1466 4291 online # 2003 Taylor & Francis Ltd http://www.tandf.co.uk/journals DOI: 10.1080/1350485032000148231 857

858 Z. Wang Table 1. Summary statistics of the variables in 1992 Variables Mean SD Maximum Minimum Price (US$/barrel) 18.16 1.87 20.98 13.23 Gravity (API degree) 33.98 7.00 63.30 20.30 Sulfur (%) 0.94 0.99 4.05 0.01 Viscosity index 22.48 66.02 488.50 0.70 Pour point ( C) 7.99 23.14 70.00 62.22 RVP (psi) 5.46 2.31 11.60 1.00 Residue share (%) 40.86 13.14 79.10 3.40 Notes: The statistics are for 55 streams of internationally traded crude oils. The definitions of the variables appear in Section III. measuring the physical characteristics of crude oil such as gravity and sulfur, and this is called the gravity and sulfurbased valuation method. Illustrations of this method in the trade literature simply regress the price of crude oil on gravity and sulfur, the two most important physical characteristics. The second method is measuring the shares and properties of the various oil products refined from a barrel of crude oil, such as petrol, diesel and fuel oil. The shares and properties of the refined oil products depend on the physical characteristics of the crude and the technology used to refine it. For a given technology, crude oil of better physical characteristics yields larger shares of high-value products such as petrol. The crude assays reported by the oil industry include the shares and properties of the refined products from the simplest refining technology, atmospheric distillation. Crude oil is heated in this process at high pressures, and the vaporized hydrocarbon components are separated at different boiling points into various oil products. The components that do not vaporize are called residue, usually used as fuel oil, the cheapest oil product. As residue accounts for, on average, about 41% of the oil products from distillation, the share of residue is an important indicator of crude quality. More complicated upgrading technologies, such as cracking and reforming, can be used to turn low-value products into high-value products. The roughly 700 refineries in the world differ significantly in the complexity of their technologies. For instance, the upgrading capacity as a percentage of total crude refining capacity is 61% on average in North America, but is only 35% in Western Europe (Worldwide Refining Report, 1997). Model and empirical specification In the short run, a refiner s technology is fixed, so it needs to decide the type of crude to buy and the mix of products to produce. Below is a simple one-period model that shows how a refiner makes the optimal decisions and how the hedonic price function is determined. The basic assumption is that crude oil quality characteristics are direct inputs to the refining process. Assume crude oil has k quality characteristics, Z ¼ ðz 1, z 2,..., z k Þ, with z i measuring the quantity of characteristic i. The price of a barrel of crude oil with characteristics Z is given by p(z), the hedonic price function. It is exogenous as far as an individual refiner is concerned. Assume crude oil can be refined into n oil products, Q ¼ðq 1, q 2,..., q n Þ 0, with q j measuring the quantity of product j. The prices of these products are given exogenously by W ¼ðw 1, w 2,..., w n Þ 0. Assume the cost of refining M barrels of crude oil of type Z can be separated into two parts: the cost of buying the crude oils, Mp(Z), and the cost of all the other inputs, C(M, Z, Q; ). The parameter reflects the refining technology a refiner has installed. The optimal choices of Z, Q, and M can be found by maximizing profit ¼ W 0 Q ½MpðZÞþ CðM, Z, Q; ÞŠ. Rosen (1974) showed how the hedonic price function p(z) is determined in a competitive market. The highest price a refiner is willing to pay for a barrel of crude oil of quality Z at constant profit is given by its bid function ðz;, Þ. The lowest price a seller is willing to accept for a barrel of crude oil of certain quality is given by its offer curves. Since crude oil characteristics are determined by nature, the supply of crude characteristics is perfectly price inelastic. Thus, the offer curves degenerate into points in the price-characteristic s space. In equilibrium, the hedonic price function p(z) traces out an envelope of refiner bid functions. Since the value of a crude characteristic to a refiner depends on its technology, it is expected that the hedonic function is nonlinear, or the implicit price, p i ðzþ ¼ @pðzþ=@z i, depends on the level of characteristics chosen by the refiner. A linear hedonic price function would imply that the implicit characteristic prices are constant, so that every refiner s valuation of crude quality is the same. Write the hedonic price equation as: p ¼ pðzþ þ ðhedonic price equationþ This model assumes that the physical characteristics of crude oil, given the refining technology, determine the refined oil products. To test this assumption, we can regress the share of residue from distillation, s, on crude physical characteristics: s ¼ sðzþ þ" ðresidue share equationþ These two equations are first estimated separately by ordinary least squares (OLS). Given that any crude quality characteristics omitted from the hedonic regression are also absent in the residue share equation, the error terms in these two equations, " and, are likely to be correlated if the omitted characteristics are important. To account for this error covariance structure, we estimate the two equations together by seemingly unrelated regression (SUR).

Hedonic prices for crude oil 859 III. DATA AND RESULTS Data The data on crude oil prices and characteristics are drawn from the International Crude Oil Market Handbook, published by the Energy Intelligence Group in various years. This article presents the estimation results for 1992, and the results for 1993 1998 are qualitatively similar. The data sample consists of 55 streams of crude oils for which complete data are available. These 55 crude oils account for over 80% of the total volume of global crude oil production. Crude oil prices are in US dollars per barrel free on board (FOB) at the port of loading. The crude assays reported by the Handbook for most crude oils contain five crude oil quality characteristics: gravity, sulfur content, viscosity, pour point and volatility. Gravity is measured by the grading system set by the American Petroleum Institute (API), in which a lighter crude oil is given a higher API degree. Sulfur content is measured in percent by weight. Pour point is the lowest temperature (in Celsius) at which crude oil pours easily. Viscosity measures how well crude oil flows above pour point. The viscosity index used in this study is the kinematical scale. Crude oil volatility is measured in terms of Reid Vapor Pressure (RVP), the unit of which is pounds per square inch (psi). These five quality characteristics are all included in the regressions. Table 1 summarizes the basic statistics of the crude oil price, characteristics and the share of residue from simple distillation. Residue share equation Only the first-order terms of quality characteristics appear in the residue share equation (Equation 1 in Table 2), as no second-order terms were found statistically significant. While gravity and RVP have negative coefficients, sulfur, viscosity and pour point have positive coefficients. While RVP is only significant at the 10% level, all the other four variables are significant at or above the 5% level. As residue is the cheapest oil product, it is expected that gravity and RVP have positive implicit prices, and sulfur, viscosity and pour point have negative implicit prices. Hedonic price equations The natural logarithm of crude oil price is the dependent variable in the hedonic price equation. Three specifications of the hedonic equation are estimated. In the first Table 2. Estimates of the hedonic and residue share equations Residue Hedonic Hedonic Residue Implicit Equation number: 1 2 3 4 5 6 Prices Estimation method: OLS OLS OLS OLS SUR (US$) Constant 66.47 (7.11) 2.81 (0.041) 2.93 (0.040) 3.00 (0.10) 2.96 (0.085) 66.47 (6.71) Gravity 0.74 (0.21) 0.0046 (0.0011) 0.0011 (0.0012) 0.00059 (0.0050) 0.0023 (0.0041) 0.74 (0.20) Sulfur 4.48 0.080 0.095 0.45 0.42 4.48 (1.32) (0.0076) (0.0074) (0.058) (0.048) (1.25) Viscosity 0.055 0.0004 0.00042 0.00040 0.055 (0.016) (0.00009) (0.00008) (0.00007) (0.015) Pour Point 0.11 0.00060 0.00069 0.00071 0.11 (0.049) (0.00028) (0.00022) (0.00020) (0.046) RVP 0.94 0.0046 0.0013 0.0013 0.94 (0.52) (0.0029) (0.0021) (0.0019) (0.49) Gravity 2 0.00002 0.00004 (0.00006) (0.00005) Sulfur 2 0.038 0.033 (0.0064) (0.0053) Gravity sulfur 0.0087 0.0081 (0.0015) (0.0012) Number of 55 55 55 55 55 55 Observations Adjusted R 2 0.70 0.81 0.87 0.93 0.93 0.70 0.132 (0.019) 1.46 (0.12) 0.007 (0.001) 0.013 (0.004) Notes: Numbers in parenthesis are standard errors. The share of residue is the independent variable in Equations 1 and 6. The natural logarithm of crude price is the independent variable in Equations 2 5. SUR refers to seemingly unrelated regression. All implicit prices are computed at the mean price of crude oil in 1992, and the implicit gravity and sulfur prices are computed at the mean levels of gravity and sulfur.

860 Z. Wang specification (Equation 2 in Table 2), only two linear terms, gravity and sulfur, are included as the explanatory variables. This equation may represent the gravity and sulfurbased evaluation method often used by the oil industry. In this specification, both gravity and sulfur have the expected sign and are statistically significant. After controlling the effects of viscosity, pour point and RVP in the second specification (Equation 3 in Table 2), gravity is no longer significant. This seemingly contradicts the finding that gravity has a significant negative effect on the share of residue. Recall that the value of gravity to a refiner depends on the refiner technology, so that the price of gravity is likely to depend on the level of characteristics the refiner chooses to buy. To see this, three second-order terms, gravity squared, sulfur squared and gravity sulfur, are added in the third specification (Equation 4 in Table 2). Other second-order terms were also tried in preliminary analyses, but none of them were found to be statistically significant. The first and secondorder terms of gravity are still not significant, but the interaction term is positive and significant at the 1% level. Gravity does have a significant effect on crude price, but only through its interaction term with sulfur. Sulfur has a negative coefficient and sulfur squared has a positive coefficient, and both are strongly significant. Therefore, the marginal price of sulfur depends on the levels of both sulfur and gravity. Both viscosity and pour point have the expected negative coefficients, and both are strongly significant. RVP has the expected positive sign, but is not significant. Notice that the adjusted R-squares for the hedonic regressions are high (0.93 for the third specification), indicating that the price differentials among the many streams of crude oils sold by different countries are primarily determined by their quality differences. A dummy variable indicating whether a stream of crude oil is produced by the member states of the Organization of Petroleum Exporting Countries was considered in preliminary analyses, but it has no effect on crude oil relative price. SUR estimates and implicit prices The Breusch-Pagan Lagrange multiplier test is used to discover whether the error terms of the hedonic equation (the third specification) and the residual share equation are correlated. The test statistic is 9.1, so the null of no correlation is rejected at the 1% level. The SUR estimates of the two equations appear as Equations 5 and 6 in Table 2. The standard errors for all coefficients become smaller, indicating that the SUR estimates are more precise. The estimated implicit prices for those significant characteristics appear in the last column of Table 2. All imputed prices are computed from the SUR estimates at the mean crude oil price in 1992, and the implicit prices of gravity and sulfur are computed at their mean levels too. The estimated implicit price of gravity is 13.2 cents per barrel per degree of API gravity, and the estimated sulfur price is (negative) 1.46 dollars per barrel per percentage point. Danielsen (1982: 65), the only relevant reference in the literature that the author is aware of, reported that: The sulfur differential amounts to about 4 cents per barrel per percentage point of sulfur content, and is seldom more than 10 cents per barrel. The gravity differential is about 10 cents per barrel per degree of API gravity. Danielsen does not state how he computed his numbers, but does say that the numbers were based on data in February 1978. The estimated gravity price in this article is consistent with that of Danielsen s, but the sulfur price is over 10 times larger. Wang (2002) showed this huge increase in sulfur price is likely to be caused by the environmental regulations aimed at abating sulfur emissions. The implicit prices of viscosity and pour point are small, but statistically significant. IV. CONCLUSION The estimated hedonic prices for characteristics of differentiated products usually do not have a clear interpretation in terms of either the market valuation or the production cost. The estimated implicit prices for crude oil quality characteristics, however, can be interpreted as reflecting directly the market s valuation, but not the production cost of those characteristics, because crude oil characteristics are determined by nature. This article showed that the simple gravity and sulfur-based valuation method used by the oil industry can be improved significantly in terms of specification and estimation. The crude oil hedonic price function is found to be nonlinear in gravity and sulfur, which is consistent with the fact that a refiner s valuation of crude quality depends on its refining technology. The estimation results also confirm that the price differentials among the many streams of crude oils in the world market are primarily determined by their quality differences. REFERENCES Danielsen, A. L. (1982) The Evolution of OPEC, Harcourt Brace Jovanovich, New York. The International Crude Oil Market Handbook (various years), Energy Intelligence Group, New York. Horsnell, P. and Mabro, R. (1993) Oil Markets and Prices: The Brent Market and the Formation of World Oil Prices, Oxford University Press, Oxford. Griliches, Z. (1961) Hedonic price indexes for automobiles: an econometric analysis of quality change, in The Price Statistics of the Federal Government, General Series, No.

Hedonic prices for crude oil 861 73. National Bureau of Economic Research, New York, pp. 137 96. Nerlove, M. (1995) Hedonic price functions and the measurement of preferences: the case of Swedish wine consumers, European Economic Review, 39, 1697 716. Rosen, S. (1974) Hedonic prices and implicit markets: product differentiation in pure competition, Journal of Political Economy, 82, 34 55. Wang, Z. (2002) A hedonic analysis of crude oil: have environmental regulations changed refiners valuation of sulfur content? Department of Economics Discussion Papers, No. 22/02, Monash University. Waugh, F. V. (1928) Quality factors influencing vegetable prices, Journal of Farm Economics, 10, 185 96. Worldwide Refining Report (1997) Oil and Gas Journal, December, 36.