THE RELATIONSHIPS AMONG PETROLEUM PRICES. Abstract

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1 Inernaional Conference On Applied Economics ICOAE THE RELATIONSHIPS AMONG PETROLEUM PRICES RAYMOND LI 1 Absrac This paper evaluaes in a mulivariae framework he relaionship among he spo prices for crude oil, gasoline, heaing oil, je fuel and diesel. Leading or lagging relaionships among he peroleum prices are examined wih a focus on assessing wheher or no he direcion of price informaion flow ha is be prediced from derived demand heory is observed. The economeric resuls provide srong evidence ha he price of crude oil and is refinery producs are coinegraed. In erms of long-run adjusmens, he crude oil price is found o be weakly exogenous and he refinery produc prices are responsible for he adjusmens owards he long-run equilibrium. JEL classificaions: Q400, C220 Keywords: Coinegraion, Granger causaliy, peroleum prices 1 Inroducion Since 2002, he world crude oil price has been rending upwards. The marke price of oil is an oucome of he ineracion of demand and supply. Some auhors (e.g. Amano and van Norden, 1998) recognize ha oil price shocks are supply-side shocks ha are hemselves he resuls of poliical conflics specific o evens in he Middle Eas. On he oher hand, he price of a commodiy should also respond o is demand o some exen, even under a monopolisic environmen. Crude oil is no excepion. For example, he srong and growing demand for crude oil from he developing Asian counries is widely perceived as an imporan facor for he high oil price in recen years. Apparenly, he prices of crude oil and is refined producs moved closely ogeher in he pas, suggesing ha some form of relaionship may exis among hese prices. However, are he movemens in crude oil price causing he peroleum produc prices o change or vice versa? Wha implicaions can be drawn from he underlying lead-lag relaionship? Using VAR and bivariae GARCH models, Adrangi e al. (2001) apply he concep of derived demand o explain he relaionship beween he price of diesel and crude oil in California. Where crude oil is he inermediae produc and diesel is he produc for final consumpion, he derived demand heory predics ha he price of crude oil should be deermined by is conribuion o he value of diesel, as refleced in he marke price. They found ha he Alaska Norh Slope crude oil price is he driving force in changes of L.A. diesel price and he derived demand heory of inpu pricing may no hold i heir case. The relaionships among peroleum prices have been sudied by various auhors. Serleis (1994) analyzes he daily spo-monh crude oil, heaing oil and unleaded gasoline fuures prices covering he period from 3 December 1984 o 30 April 1993 wih he Johansen maximum likelihood approach. The auhor found ha he hree fuures prices are coinegraed and followed a common sochasic rend. However, he focus of he sudy was he long-run relaionship and hence he shor-run dynamics and lead-lag relaionship were no explored. Gjolberg and Johnsen (1999) use a bivariae error correcion model o esimae he relaionships beween monhly spo prices of crude oil agains six of is refinery producs in he Norhwes European marke. The auhors found coinegraion in five ou of six price pairs and concluded ha pas deviaions from long-erm equilibrium are significan in an error correcion specificaion of shor-erm produc price changes. One main drawback of he sudy is ha useful informaion may be los in he bivariae sysem because he sysem does no consider he iner-relaionship among he prices of he refinery producs. Asche, Gjolberg and Völker (2003) perform a sudy similar o ha of Gjolberg and Johnsen (1999) bu in a mulivariae framework wih a slighly longer daase. The auhors found hree coinegraing vecors in he mulivariae sysem of five variables. From pairwise coinegraion ess he auhors hen found ha he heavy fuel oil price was found o be no coinegraed o he any of he oher prices. This paper invesigaes he price movemen dynamics among he monhly spo prices of crude oil and is refinery producs in he US marke. Compared o he previous sudies, his paper covers a wider range of producs compared o Serleis (1994). Also, he US focus of his paper complemens he sudies by Gjolberg and Johnsen (1999) and Asche e al. (2003) which focused on he European marke. Moreover, using a more up-o-dae daase, his paper provides a laes view of he price dynamics in he highly dynamic peroleum marke. The coinegraion and Granger causaliy ess are used for he empirical analysis. Examining he lead-lag relaionship among hese prices can help idenify he main cause of crude oil price flucuaions (i.e. supply driven or demand driven). If he simulan of price movemen is mainly produc demand driven, he price signal should flow from he refined producs o crude oil because crude oil demand is derived from he demand of is refined produc. If he price movemens are in general inpu supply driven, we would expec he price signal o flow from crude oil o he refined producs because a change in he supply of crude oil will affec he producion cos, hence supply, of he refined producs. The res of his paper is srucured as follows. Secion 2 briefly discusses he derived demand heory and is predicions. Secion 3 conains he empirical analysis. Secion 4 furher discusses he resuls and concludes he paper. 2 Theoreical Consideraions According o he derived demand heory proposed by Marshall, he demand schedule for any facor of producion of a final produc can be derived from ha for he final produc. Assuming an unchanged demand schedule for a final produc and given supply prices for oher facors of producion, one may subrac he sum of he supply prices for corresponding amouns of he oher facors from he demand price of each separae amoun of he final produc o obain he derived demand price of he facor of producion. Therefore, wih he supply prices of oher facors held consan, an increase in he demand of he final good would lead o an increase in he (derived) demand of a given facor of producion. If he demand and supply schedules of crude oil and he refinery producs 1 Dr. Raymond Li, School of Accouning and Finance, Hong Kong Polyechnic Universiy. Tel:

2 460 Inernaional Conference On Applied Economics ICOAE 2010 ake he usual shape, a change in he demand of a refinery produc will provoke a price response in he produc iself and he change in he derived demand of crude oil will cause he oil price o change. Blomberg and Harris (1995) agree ha a higher demand for final goods increases he demand for commodiy inpus. Ye, hey argue ha if he price-deerminaion mechanism is more flexible in he commodiy inpu marke, he firs visible price movemen may be in he commodiy inpu marke even hough he impeus for a price response may sar in he final produc markes. As commodiy inpus are usually widely raded inernaionally, his price signal would readily occur when srong domesic demand is no offse by weak foreign demand. Blomberg and Harris (1995) also poin ou ha commodiy price shocks may simulae a price response in he final produc if he commodiy is an imporan inpu ino producion. They claim ha, all else being equal, an increase in commodiy prices should evenually be passed hrough o final goods prices. Supply shocks will lead o higher price impacs when he derived demand is inelasic. Marshall noes ha he derived demand of a facor will be more inelasic when (1) he facor is more essenial in he producion process of he final produc, (2) he more price inelasic is he demand for he final produc, (3) he smaller he fracion of oal cos ha is conribued by he facor, and (4) he more price inelasic is he supply of he oher facors. 3 Empirical Analysis 3.1 Daa Descripion and Uni Roo Tess Monhly spo prices of Wes Texas Inermediae Ligh Swee crude oil, New York Harbor convenional gasoline, No.2 heaing oil, kerosene-ype je fuel and Los Angeles No.2 diesel are used in he empirical analysis. The daase covers he period from June 1990 o May 2010, giving us 240 observaions. The daa are obained from he Energy Informaion Adminisraion (EIA). Figure 1 plos he prices used in his paper. Alhough each price has is own shor erm volailiy, he prices moved very closely ogeher and appear o be highly correlaed in he long erm. Figure 1. Spo Peroleum Prices a a The crude oil price is measured in US dollars per barrel, while he refined produc prices are measured in US cens per gallon Since his paper employs he coinegraion approach o es for long-run relaionship, we have o make sure ha he series conain uni roos (inegraed of order 1) before invesigaing he coinegraing relaionships. The lag lenghs for he augmened Dickey-Fuller (ADF) es are chosen so ha he error erms are serially uncorrelaed and he AIC crierion is minimized. The Phillips-Perron (PP) es uses a non-parameric correcion o he -es saisics o accoun for auocorrelaion in he regression model. In he PP es, he lag lengh is chosen using he formula 12(T/100)0.25. All he variables ener he regression in naural log form. I can be observed from Figure 1 ha he series exhibi rending behavior, so he uni roo ess are performed wih boh consan and rend erms. The es resuls are repored in Table 1. The null hypohesis is ha a uni roo exiss, while he alernaive hypohesis is ha he series is saionary. According o boh ADF and PP ess, he null hypohesis of uni roo is no rejeced for all series in levels a 10% significance. In firs differences, he uni roo hypohesis is rejeced a 1% significance. Therefore, we have srong evidence ha all series are inegraed of order one. 3.2 Coinegraion The Johansen and Juselius (1990) procedure is adoped o deec coinegraion in he daase. A disincive feaure of his procedure is ha i can be used o es for he number of coinegraing relaionships among a group of variables. The lag lengh (k) is chosen o ensure ha he error erms ( ) are normally disribued and do no exhibi auocorrelaion or ARCH effecs. The model o be esimaed is a reparameerized reduced form VAR model: X k 1 i 1 X i i ' X k D, X ' ( LWTI, LGAS, LHO, LJET, LDIE ) The choice of r (coinegraion rank) should be made in a correcly specified model. Before proceeding o he esimaion of coinegraion rank or relaionships, we need o es for misspecificaion of he reduced form VAR model. Table 2 repors he resuls of mulivariae Lagrange muliplier es for auocorrelaion, Lagrange muliplier es for ARCH effecs and Shenon-Bowman

3 Inernaional Conference On Applied Economics ICOAE normaliy ess. The number of lags (k) in he Vecor Error Correcion Model (VECM) is chosen such ha auocorrelaion is absen in he elemens of he vecor while he informaion crieria (SC or HQ) are minimized. The resuls indicae ha wih 5 lags, a 5% significance, he residuals are normally disribued and do no exhibi auocorrelaion and ARCH (5). We proceed wih his specificaion of he VECM and es for coinegraion. Table 3 presens he resuls of he Trace es of coinegraion rank. The Trace es saisics indicae ha here are four coinegraing vecors (r = 4) a he 5% significance level. I means ha here is only one sochasic rend in he sysem and all prices are linked ogeher by his rend in he long-run. Table 1. Augmened Dickey-Fuller and Phillips-Perron Tess a Augmened Dickey-Fuller Phillips-Perron Level 1s Difference Level 1s Difference Crude Oil *** *** Gasoline *** *** Heaing Oil *** *** Je Fuel *** *** Diesel *** *** a *** denoes significance a 1% Table 2. Residual Diagnosic Tess Sample Period: 1990:6 2010:5 k = 5 Auocorrelaion Tes Saisics p-value LM (1) LM (12) ARCH p-value Normaliy p-value Crude Oil Gasoline Heaing Oil Je Fuel Diesel Table 3. Mulivariae Coinegraion Tes Rank (r) Eigenvalue Trace Saisic Criical Value (5%) p-value r = r r r r A long-run exclusion es is performed o provide informaion abou wheher or no any variable can be omied from all coinegraion relaions. The null hypohesis for he es is: H 0 : ij = 0 (j = 1,,r) The es is performed for i = 1,,p and r = 1,,p-1, where p is he number of variables and r is he coinegraing rank. The es saisic is asympoically disribued as 2 wih r degrees of freedom. From he resuls in Table 4, we can see ha when r = 4, none of he variables can be excluded from he coinegraion relaions. There exis a long-run relaionship beween he price of crude oil, gasoline, heaing oil, je fuel and diesel under he period sudied in his paper. Having confirmed ha none of he variables can be excluded from he coinegraing relaions, we nex proceed o es for weak exogeneiy of he prices. The es is used o invesigae if any of he variables can be considered weakly exogenous wih respec o he long-run parameers. The null hypohesis is: H 0 : ij = 0 (j = 1,,r) The es procedure is similar o ha for long-run exclusion and he resuls are repored in Table 4. When r = 4, he null hypohesis canno be rejeced for he crude oil price a 10% significance bu he same null can be (srongly) rejeced for all he oher prices a 1% significance. There is srong evidence ha he crude oil price is weakly exogenous in he sysem and so i does no adjus o deviaions from he long-run equilibrium. Also, he resuls imply ha he refinery produc prices will adjus o he crude oil price in he long-run and crude oil price is he driving force behind he co-movemen of he peroleum prices. Table 4. Long-run Exclusion and Weak Exogeneiy Tess (r = 4) Long-run Exclusion Weak Exogeneiy Variable Tes Saisic p-value Tes Saisic p-value Crude Oil Gasoline

4 462 Inernaional Conference On Applied Economics ICOAE 2010 Heaing Oil Je Fuel Causaliy Diesel To es for Granger causaliy in he VECM, a heoreically simple procedure proposed by Toda and Yamamoo (1995) is adoped in his paper. Toda and Yamamoo (1995) show ha one can esimae models in VAR-level represenaion and es for resricions of parameer marices using a Wald-ype es, even if he series are inegraed or coinegraed. The es saisics are shown o follow an asympoic 2 disribuion when a VAR (k + d max ) is esimaed, where d max is he maximum order of inegraion. A Mone Carlo experimen conduced by Zapaa and Rambaldi (1997) provides evidence ha his simple procedure performs reasonably well when he sample size is greaer han 50. Following he procedures proposed by Toda and Yamamoo (1995), he VECM is re-parameerized ino an augmened VAR model wih 6 lags in levels and he usual Wald es is applied o es for Granger causaliy. The resuls are presened in Table 5. There are hree poins ha deserve aenion. Firs, he crude oil price responds o boh is pas values and heaing oil price. I means ha none of he prices in he sysem can be considered srongly exogenous. Bu more imporanly, his resul suggess ha he derived demand heory is no compleely refued in he peroleum marke. Crude oil price is affeced by heaing oil price a leas in he shorrun. Second, he prices of refinery producs all respond o he crude oil price, so hey are affeced by he crude oil price in boh he shor and long run. Third, he gasoline price is Granger-caused by heaing oil and je fuel. One possible explanaion of his resul relaes o chemical processing of crude oil refineries. Since only approximaely 35% of disilled crude oil is gasoline, i is common for oil refineries o increase he yield of gasoline by chemically processing oher fracions of he disillaion column. Heaing oil and je fuel are amongs he poenial candidaes. However, when he demand for heaing oil and je fuel is high, he scope for he conversion is limied. Consequenly, he demand driven price change in heaing oil and je fuel may be ransmied o a supply driven price change in gasoline. Table 5. Granger Causaliy Tess To: From: Crude Oil Gasoline Heaing Oil Je Fuel Diesel Crude Oil Gasoline Heaing Oil Je Fuel Diesel p-values are shown. H 0 : no Granger causaliy 4 Discussions and Conclusions Using he mulivariae Johansen es, he coinegraion findings of his paper are consisen wih he findings in Serleis (1994), Gjolberg and Johnsen (1999) and Asche e al. (2003) ha he price of crude oil and is refinery producs are found o be coinegraed. The weak exogeneiy es suggess ha crude oil price ransmis exogenous shocks o he sysem in he long-run. Gasoline, heaing oil, je fuel and diesel prices bear he responsibiliy o he adjusmens owards he long-run equilibrium sae. In oher words, changes in oil price will be passed hrough o he refined produc prices in he long-run. Apparenly, he general resuls indicae ha he derived demand predicion does no hold for he peroleum prices. Price informaion does no appear o flow from he end producs o he facor inpu. However, he mere observaion ha price signal flows from crude oil o he refinery producs does no necessarily rejecs he derived demand heory. I may mean ha he price changes are supply-side driven he simulus occurs in he crude oil marke and he price change ransmis o he end-produc marke because oil is an essenial inpu o he refinery produc. Shocks in he crude oil marke can be in he form of supply, derived demand and speculaive demand shocks. In paricular, perurbaions in he speculaive demand for crude oil can be frequen and hese can cause large and immediae effec on he price of oil which can hen be ransmied o he refinery produc markes. Also, since he marke for crude oil is more liquid and inernaional in scope han he refinery producs considered in his paper, when he demands for refinery producs change, he price of crude oil may firs adjus. Anoher possible explanaion is ha he supply of crude oil ends o be elasic, so ha changes in is derived demand do no cause any significan movemen in price. If he demands for he refinery producs are price inelasic, he derived demand for crude oil will also end o be inelasic. Consequenly, a small disrupion in supply may lead o a very significan change in he oil price. High supply elasiciy combined wih low derived demand elasiciy concepually favors he flow of price signal from crude oil o he refinery producs. However, his explanaion relies on empirical esimaes of he elasiciies and his may be a direcion for furher research. 5 References Adrangi, B., Charah, A., Raffiee, K. & Ripple, R.D. (2001), Alaska Norh Slope crude oil price and he behaviour of diesel prices in California, Energy Economics, 23:29-42.

5 Inernaional Conference On Applied Economics ICOAE Amano, R.A. & van Norden, S. (1998), Oil prices and he rise and fall of he US real exchange rae, Journal of Inernaional Money and Finance, 17: Asche, F., Gjolberg, O. & Völker, T. (2003), Price relaionships in he peroleum marke: an analysis of crude oil and refined produc prices, Energy Economics, 25: Blomberg, S.B. & Harris, E.S. (1995), The commodiy-consumer price connecion: fac or Fable? FRBNY Economic Policy Review, Ocober, Gjolberg, O. & Johnsen, T. (1999), Risk managemen in he oil indusry: can informaion on long-run equilibrium prices be uilized?, Energy Economics, 21: Johansen, S. & Juselius, K. (1990), Maximum likelihood esimaion and inference on coinegraion - wih applicaions o he demand for money, Oxford Bullein of Economics and Saisics, 52: Naka, A. & Tufe, D. (1997), Examining impulse response funcions in coinegraed sysems, Applied Economics, 29: Serleis, A. (1994), A coinegraion analysis of peroleum fuures prices, Energy Economics, 16: Toda, H.Y. & Yamamoo, T. (1995), Saisical inference in vecor auoregressions wih possibly inegraed processes, Journal of Economerics, 66: Zapaa, H.O. & Rambaldi, A.N. (1997), Mone Carlo evidence on coinegraion and causaion, Oxford Bullein of Economics and Saisics, 59:

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