The Relationship between Crude Oil and Natural Gas Prices

Transcription

1 Ene r g y F o ru m James A. Baker III Insiue for Public Policy Ri c e U n i v e r s i y Naural Gas in Norh America: Markes and Securiy The Relaionship beween Crude Oil and Naural Gas Prices Peer Harley, Ph.D., Kenneh B. Medlock III, Ph.D. and Jennifer Roshal

2 THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY RICE UNIVERSITY THE RELATIONSHIP BETWEEN CRUDE OIL AND NATURAL GAS PRICES By PETER HARTLEY, PH.D. GEORGE AND CYNTHIA MITCHELL CHAIR AND PROFESSOR OF ECONOMICS, RICE UNIVERSITY, RICE SCHOLAR, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY KENNETH B. MEDLOCK III, PH.D. FELLOW IN ENERGY STUDIES, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY, ADJUNCT ASSISTANT PROFESSOR OF ECONOMICS, RICE UNIVERSITY AND JENNIFER ROSTHAL GRADUATE FELLOW, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY, GRADUATE STUDENT, DEPARTMENT OF ECONOMICS, RICE UNIVERSITY PREPARED IN CONJUNCTION WITH AN ENERGY STUDY SPONSORED BY THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY AND MCKINSEY & COMPANY NOVEMBER 007

3 The Relaionship beween Crude Oil and Naural Gas Prices THIS PAPER WAS WRITTEN BY A RESEARCHER (OR RESEARCHERS) WHO PARTICIPATED IN A BAKER INSTITUTE STUDY, NATURAL GAS IN NORTH AMERICA: MARKETS AND SECURITY. WHEREVER FEASIBLE, THIS PAPER WAS REVIEWED BY OUTSIDE EXPERTS BEFORE THEY ARE RELEASED. HOWEVER, THE RESEARCH AND VIEWS EXPRESSED IN THESE PAPERS ARE THOSE OF THE INDIVIDUAL RESEARCHER(S) AND DO NOT NECESSARILY REPRESENT THE VIEWS OF THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY. 007 BY THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY OF RICE UNIVERSITY THIS MATERIAL MAY BE QUOTED OR REPRODUCED WITHOUT PRIOR PERMISSION, PROVIDED APPROPRIATE CREDIT IS GIVEN TO THE AUTHOR AND THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY.

4 The Relaionship beween Crude Oil and Naural Gas Prices ABOUT THE POLICY REPORT NATURAL GAS IN NORTH AMERICA: MARKETS AND SECURITY Prediced shorages in U.S. naural gas markes have promped concern abou he fuure of U.S. supply sources, boh domesically and from abroad. The Unied Saes has a premier energy resource base, bu i is a maure province ha has reached peak producion in many radiional producing regions. In recen years, environmenal and land-use consideraions have promped he Unied Saes o remove significan acreage ha was once available for exploraion and energy developmen. Tweny years ago, nearly 75 percen of federal lands were available for privae lease o oil and gas exploraion companies. Since hen, ha share has fallen o 17 percen. A he same ime, U.S. demand for naural gas is expeced o grow close o.0 percen per year over he nex wo decades. Wih growh in domesic supplies of naural gas producion in he lower 48 saes expeced o be consrained in he coming years, U.S. naural gas impors are expeced o rise significanly in he nex wo decades, raising concerns abou supply securiy and promping quesions abou wha is appropriae naional naural gas policy. The fuure developmen of he Norh American naural gas marke will be highly influenced by U.S. policy choices and changes in inernaional supply alernaives. The Baker Insiue Policy Repor on Naural Gas in Norh America: Markes and Securiy brings ogeher wo research projecs underaken by he Baker Insiue s Energy Forum. The firs sudy focuses on he fuure developmen of he Norh American naural gas marke and he facors ha will influence supply securiy and pricing. This sudy considers, in paricular, how access o domesic resources and he growh of inernaional rade in liquefied naural gas will impac U.S. energy securiy. The second sudy examines he price relaionship beween oil and naural gas, wih special aenion given o naural gas demand in he indusrial and power generaion secors secors in which naural gas can be displaced by compeiion from oher fuels. This policy repor is 3

5 The Relaionship beween Crude Oil and Naural Gas Prices designed o help boh marke paricipans and policymakers undersand he risks associaed wih various policy choices and marke scenarios. ACKNOWLEDGEMENTS The James A. Baker III Insiue for Public Policy would like o hank McKinsey & Company and he sponsors of he Baker Insiue Energy Forum for heir generous suppor in making his projec possible. The auhors of his paper would also like o acknowledge he seminar paricipans a Rice Universiy and he Unied Saes Associaion for Energy Economics annual meeings, 006, Ann Arbor, Michigan, for valuable commens. 4

6 The Relaionship beween Crude Oil and Naural Gas Prices ABOUT THE AUTHORS PETER HARTLEY, PH.D. GEORGE AND CYNTHIA MITCHELL CHAIR AND PROFESSOR OF ECONOMICS, RICE UNIVERSITY, RICE SCHOLAR, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY Peer Harley is he George and Cynhia Michell chair and a professor of economics a Rice Universiy. He is also a Rice scholar of energy economics for he James A. Baker III Insiue for Public Policy. He has worked for more han 5 years on energy economics issues, focusing originally on elecriciy, bu including also work on gas, oil, coal, nuclear and renewables. He wroe on reform of he elecriciy supply indusry in Ausralia hroughou he 1980s and early 1990s and advised he governmen of Vicoria when i compleed he acclaimed privaizaion and reform of he elecriciy indusry in ha sae in The Vicorian reforms became he core of he wider deregulaion and reform of he elecriciy and gas indusries in Ausralia. Apar from energy and environmenal economics, Harley has published research on heoreical and applied issues in money and banking, business cycles and inernaional finance. In 1974, he compleed an honors degree a he Ausralian Naional Universiy, majoring in mahemaics. He worked for he Prioriies Review Saff, and laer he Economic Division, of he Prime Miniser s Deparmen in he Ausralian governmen while compleing a maser s degree in economics a he Ausralian Naional Universiy in Harley obained a Ph.D. in economics a he Universiy of Chicago in KENNETH B. MEDLOCK III, PH.D. FELLOW IN ENERGY STUDIES, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY, ADJUNCT ASSISTANT PROFESSOR OF ECONOMICS, RICE UNIVERSITY Kenneh B. Medlock III is currenly research fellow in energy sudies a he James A. Baker III Insiue for Public Policy and adjunc assisan professor in he deparmen of economics a Rice Universiy. He is a principal in he developmen of he Rice World Naural Gas Trade Model, which is aimed a assessing he fuure of liquefied naural gas 5

7 The Relaionship beween Crude Oil and Naural Gas Prices (LNG) rade. Medlock s research covers a wide range of opics in energy economics, such as domesic and inernaional naural gas markes, choice in elecriciy generaion capaciy and he imporance of diversificaion, gasoline markes, emerging echnologies in he ransporaion secor, modeling naional oil company behavior, economic developmen and energy demand, forecasing energy demand, and energy use and he environmen. His research has been published in numerous academic journals, book chapers and indusry periodicals. For he deparmen of economics, Medlock eaches courses in energy economics. JENNIFER ROSTHAL GRADUATE FELLOW, JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY, GRADUATE STUDENT, DEPARTMENT OF ECONOMICS, RICE UNIVERSITY Jennifer Roshal is a graduae fellow a he James A. Baker III Insiue for Public Policy Energy Forum and a Ph.D. suden in he Rice Universiy economics deparmen. Roshal's research focuses on Unied Saes naural gas and elecriciy demand and gas and peroleum produc-price relaionships. Prior o coming o Rice Universiy, Roshal worked as a research assisan a Hobar and William Smih Colleges and co-auhored he book, Pahways o a Hydrogen Fuure (Elsevier Science, 007). She has presened her work a he Unied Saes Associaion of Energy Economics (USAEE) conferences and holds he suden represenaive posiion on he USAEE Council. Roshal has a B.A. in economics from William Smih College. 6

8 The Relaionship beween Crude Oil and Naural Gas Prices ABOUT THE ENERGY FORUM AT THE JAMES A. BAKER III INSTITUTE FOR PUBLIC POLICY The Baker Insiue Energy Forum is a mulifaceed cener ha promoes original, forward-looking discussion and research on he energy-relaed challenges facing our sociey in he 1s cenury. The mission of he Energy Forum is o promoe he developmen of informed and realisic public policy choices in he energy area by educaing policy makers and he public abou imporan rends boh regional and global ha shape he naure of global energy markes and influence he quaniy and securiy of vial supplies needed o fuel world economic growh and prosperiy. The forum is one of several major foreign policy programs a he James A. Baker III Insiue for Public Policy a Rice Universiy. The mission of he Baker Insiue is o help bridge he gap beween he heory and pracice of public policy by drawing ogeher expers from academia, governmen, he media, business, and nongovernmenal organizaions. By involving boh policymakers and scholars, he insiue seeks o improve he debae on seleced public policy issues and make a difference in he formulaion, implemenaion, and evaluaion of public policy. The James A. Baker III Insiue for Public Policy Rice Universiy MS 40 P.O. Box 189 Houson, TX hp:// bipp@rice.edu 7

9 The Relaionship beween Crude Oil and Naural Gas Prices I. Inroducion The relaionship beween naural gas and crude oil prices affecs energy consumers, producers and markeers. For example, energy prices for he wo fuels influence he incenives o inves in invenories or differen ypes of energy-using equipmen. Energy marke raders also are ineresed o know wheher here is a endency for he relaive prices of differen energy commodiies o reurn o a paricular value, since if such a endency exiss, i migh form he basis of a rading sraegy. Hisorically, i was hough ha he prices of Wes Texas Inermediae (WTI) crude oil and naural gas delivered a he Henry Hub, which are he mos widely quoed energy prices in he Unied Saes, mainained a 10-1 relaionship, so ha one barrel of WTI crude oil priced a roughly 10 imes 1 million Briish hermal unis (MMBu) of naural gas. More recenly, his appears o have declined by abou 40% o a 6-1 raio, which is close o hermal pariy. However, he observed variabiliy in he relaive price relaionship has led some o quesion wheher he naural gas price has decoupled from he crude oil price. In his paper, we invesigae he exisence of a long run sable relaionship beween crude oil and naural gas prices, idenify shocks ha cause deparures from ha relaionship, and esimae he lengh of he adjusmen process ha re-esablishes he long-erm relaionship beween he prices of he wo fuels. Imporanly, we conclude ha U.S. naural gas and crude oil prices remain linked in heir long-erm movemens. We demonsrae ha he narrowing in he relaive longerm price relaionship beween U.S. crude oil benchmark WTI and Henry Hub naural gas prices reflecs he widespread adopion of combined cycle gas urbines (CCGT), which has increased he efficiency of using naural gas o generae elecriciy in place of oil-based fuel. In addiion, we find ha he raio of he price of WTI crude o he price of naural gas a he Henry Hub will end o remain abou 40% lower han i would have been a decade ago, barring addiional echnological changes in user faciliies. One implicaion of his finding is ha, if inernaional crude oil prices remain high, U.S. naural gas prices are unlikely o collapse subsanially over he long erm. According o our analysis, a $70 per barrel WTI average price (expressed in real 000 prices) is likely o promoe a long run equilibrium naural gas price a he Henry 8

10 The Relaionship beween Crude Oil and Naural Gas Prices Hub of around $9.40 per MMBu. Furhermore, our analysis also shows ha facors such as weaher shocks and changes in sorage can lead o subsanial deviaions from his long run price raio. Moreover, our analysis shows ha he long run price raio iself will end o decline somewha as he oil price declines. I is also imporan o noe ha our analysis shows ha he long run relaionship beween crude oil price and naural gas price acs hrough residual fuel oil prices. Thus, if he spread beween residual fuel and crude oil prices increases, his will resul in he naural gas price falling relaive o crude oil. Finally, i was also found ha here ends o be a ime lag beween a significan change in U.S. crude oil prices and he adjusmen of naural gas markes o ha change. While here is srong evidence of his sable long run price relaionship beween oil and naural gas prices, as menioned above, we find ha seasonal flucuaions and oher facors such as abrup changes in weaher, supply disrupions and invenory rends can aler his price relaionship in he shor erm. In paricular, we find ha hisorical experience implies ha for every billion cubic fee of naural gas producion ha is shu in as a resul of a hurricane in he Gulf of Mexico, naural gas prices a he Henry Hub increase approximaely by $1.03 per MMBu (again expressed in real 000 prices). We begin from he premise ha elecriciy generaion plays a key role in influencing he relaive prices of differen energy commodiies. In a recen paper, Harley, Medlock and Roshal (007) show ha subsiuion beween naural gas and residual fuel oil is paricularly srong in a few Norh American Elecric Reliabiliy Council (NERC) regions where here is sufficien sysem-wide swiching capabiliy. 1 Even in regions where individual plans canno swich beween fuels, differen ypes of plans can be operaed for differen lenghs of ime as fuel prices change, amouning o grid-level (raher han plan-level) swiching, hus exending he swiching capabiliy of he sysem. Plan- and grid-level swiching beween differen fuel ypes by elecriciy generaors imposes srong pressure o limi deviaions in he relaive prices of compeing fuels. Specifically, when possible, generaors will arbirage he cos of producing 1 They also found limied subsiuabiliy beween naural gas- and disillae-fired peaking plans. Naural gas and heaing oil also compee in space heaing applicaions. We find in his paper, however, ha he relaionships beween disillae, naural gas and residual fuel oil were quie weak a he aggregae level. Eliminaing he few marginally significan disillae variables did no maerially affec any of he remaining coefficiens and hence he variables have been omied o simplify he exposiion. 9

11 The Relaionship beween Crude Oil and Naural Gas Prices elecriciy in $/MWh (megawa hour) which equals he price of fuel in $/Bu muliplied by he hea rae in Bu/MWh. Hence, changes in he hea raes of he plans using he differen fuels will change heir relaive compeiiveness. We herefore argue ha he developmen of CCGTs has raised he araciveness of naural gas as a fuel for generaing elecriciy. The resul has been an increase in demand for naural gas relaive o residual fuel oil for elecriciy generaion, which has in urn conribued o an increase in he price of naural gas relaive o fuel oil, and hence also o crude oil. Figure 1: Real energy commodiy prices (February 1990 Augus 006) 000$/mmbu $11.00 $10.00 Henry Hub WTI Residual Fuel Oil $9.00 $8.00 $7.00 $6.00 $5.00 $4.00 $3.00 $.00 $1.00 $- Feb-90 Aug-90 Feb-91 Aug-91 Feb-9 Aug-9 Feb-93 Aug-93 Feb-94 Aug-94 Feb-95 Aug-95 Feb-96 Aug-96 Feb-97 Aug-97 Feb-98 Aug-98 Feb-99 Aug-99 Feb-00 Aug-00 Feb-01 Aug-01 Feb-0 Aug-0 Feb-03 Aug-03 Feb-04 Aug-04 Feb-05 Aug-05 Feb-06 Aug-06 Sources: Naural Gas Weekly and he Energy Informaion Adminisraion Figure 1 plos he real prices of hree energy commodiies expressed in real $000/MMBu (using an elecriciy price index as he deflaor). I shows ha naural gas prices have ended o flucuae around residual fuel oil prices wih alernaing periods of several monhs o a year where hey are persisenly above or below he residual fuel oil See he descripion of he daa series below for more deails on how hese variables were calculaed. 10

12 The Relaionship beween Crude Oil and Naural Gas Prices price. In some brief episodes, however, he naural gas price spikes subsanially above he residual fuel oil price, and even he WTI price, in energy-equivalen erms. In order o horoughly invesigae he relaionship beween he prices of naural gas, residual fuel oil, and WTI, and adjusmens o deviaions from ha relaionship, we develop and esimae an error correcion model (ECM). In general, Engle and Granger y 1 (1987) have shown ha if wo series, and, are coinegraed, hen here mus exis an error correcion represenaion of he dynamic sysem governing he join behavior of y y 1 and y over ime. This sysem can be wrien as p 1 Δy 1 = α 10 + α 11 Ω 1 + α 1,i Δy 1, i + α 13,i Δy, i + ε 1 i=1 p i=1 p 1 Δy = α 0 + α 1 Ω 1 + α,i Δy 1, i + α 3,i Δy, i + ε i=1 p i=1 where Ω 1 is an error correcion erm represening he deviaion from he equilibrium or coinegraing relaionship beween y 1, 1 on y, 1. The coefficiens on Ω 1 are speed of adjusmen parameers measuring how fas and rever o heir long run equilibrium relaionship. Noe ha since and are coinegraed, he esimaion of y 1 y 1 on y is superconsisen and he series Ω can be reaed in he esimaion of he ECM as if i were known. Each equaion in he sysem above has he desirable propery ha if we are a long run equilibrium ( Ω = 0 ) and here is no change in any of he oher 1 variables, here will be no change in and, provided he inercep erms y 1 ( α 10 and α 0 ) are equal o zero. In his paper, we focus on he long run coinegraing relaionships beween he naural gas price, he residual fuel oil price, and he WTI price. We hen exend he ECM represenaion o include some saionary exogenous variables, which allows us o idenify some of he shocks ha lead o deparures from he long run equilibrium beween prices. The esimaed ECM also allows us o idenify a causal ordering in price adjusmen, and how fas ha adjusmen occurs. y 1 y y y 11

13 The Relaionship beween Crude Oil and Naural Gas Prices II. Previous Research Oher auhors have considered he coinegraion of various energy prices. Of paricular ineres o us are papers ha examine he coinegraion of differen commodiies prices. 3 One paper in paricular considered he relaionship beween naural gas and residual fuel oil prices. Serleis and Herber (1999) es for he exisence of common rends in daily naural gas prices a he Henry Hub and Transco Zone 6, he price of power in PJM, and he price of residual fuel oil a New York Harbor from Ocober 1996 hrough November They find ha he hree fuel prices are coinegraed and ha Transco Zone 6 prices adjus significanly faser han do Henry Hub prices o deviaions in heir long run relaionship. Serleis and Herber also find ha residual fuel oil prices show no significan adjusmen o deviaions in he long run relaionship wih eiher Henry Hub or Transco Zone 6 naural gas prices. However, he Transco Zone 6 naural gas price does appear o adjus o movemens in he fuel oil price a New York Harbor. Their resuls hus suppor weak exogeneiy of residual fuel oil prices in he sysem of equaions. Similarly, he fac ha he Transco Zone 6 price adjuss mos quickly o boh long run price relaionships suggess ha i is in a sense he mos endogenous price of he hree. These findings are, o some exen, no very surprising. Transco Zone 6 is a he end of he Transco pipeline sysem, which delivers naural gas direcly from he Gulf Coas o Middle Alanic markes. Thus, coinegraion of he wo naural gas prices reflecs he arbirage possibiliies inheren in he physical link. In addiion, he Gulf Coas s high conneciviy o many regions implies ha naural gas prices a he Henry Hub will be influenced by shocks in many local markes and hus no paricularly responsive o he shocks in any one end-of-pipe marke like Transco Zone 6. The finding ha Transco Zone 6 naural gas prices also adjus o New York Harbor residual fuel oil prices indicaes regional compeiion beween hose fuels. 4 In addiion, he weak exogeneiy of he residual fuel oil price indicaes ha i may be responding o a differen driver, such as crude oil. 3 There is also a lieraure examining he coinegraion of a single commodiy across differen locaions (see, for example, DeVany and Walls (1993, 1999) and Siliversovs e al. (005)). 4 Harley, Medlock and Roshal (007) also found evidence for subsiuion in he New York NERC region. 1

14 The Relaionship beween Crude Oil and Naural Gas Prices Building on his analysis, Serleis and Rangel-Ruiz (00) examine he exisence of common price cycles in Norh American energy commodiies using he daily prices of naural gas a he Henry Hub and WTI from 1991 hrough 001. In addiion, hey sudied coinegraion of U.S. and Canadian naural gas prices. They concluded ha naural gas prices a Henry Hub and AECO (a liquid pricing poin in Albera) demonsrae common cycles. While naural gas does no flow direcly beween he Henry Hub and AECO, i flows from boh of hose areas o common markes in he Middle Alanic and he Midwes. Hence, hese prices, like he Henry Hub and Transco Zone 6 prices, also appear o be linked via ransporaion differenials. Serleis and Rangel-Ruiz also found, however, ha Henry Hub and WTI do no have common price cycles. They claim his decoupling of U.S. energy prices is a resul of deregulaion. Villar and Jouz (006) examine he apparen decoupling of he prices of WTI crude oil and Henry Hub naural gas in more deail, finding a coinegraing relaionship beween he wo prices ha exhibis a posiive ime rend. This indicaes ha he prices have a long run relaionship ha is slowly evolving raher han consan. Villar and Jouz esimae an error correcion model ha includes exogenous variables such as naural gas sorage levels, seasonal dummy variables, and dummy variables for a few oher ransiory shocks. Their analysis suppors he findings of Serliis and Rangel-Ruiz (00) ha he price of WTI is weakly exogenous o he price of naural gas a he Henry Hub. Specifically, Villar and Jouz find ha he price of naural gas adjuss o deviaions in he long run evolving relaionship, bu hese deviaions do no affec he price of WTI. They also found ha changes in naural gas prices end o lag behind changes in crude oil prices. Brown (003) and Brown and Yücel (006) observed ha naural gas and crude oil prices had apparenly decoupled on several occasions in he immediae pas: once beginning in 000 wih naural gas prices becoming relaively high compared o crude oil prices, and again in 005 wih he relaionship moving in he opposie direcion. Brown argued in he 003 paper ha he fuures markes suppored he hypohesis ha he movemen away from he previous long run relaionship in 000 was likely o coninue. Brown and Yücel (006) used an ECM o analyze weekly prices from January 1994 hrough July 006. They found ha he price series are coinegraed over his 13

15 The Relaionship beween Crude Oil and Naural Gas Prices period, indicaing a sable long run relaionship. However, hey also found ha a coinegraing relaionship does no exis if hey consider he shorer ime period of June 1997 hrough July 006. Proceeding wih he esimaed coinegraing relaionship from he longer ime series, hey found ha shor run deviaions from he esimaed long run relaionship could be explained by marke fundamenals such as sorage levels, weaher (measured by he normal degree days for he week of he year and deviaions from ha norm), and he quaniy of producion shu-in due o hurricanes. They repor ha he price of naural gas a he Henry Hub responds significanly o he deviaion from he long run relaionship, changes in he prices of naural gas for he preceding wo weeks, and he change in he price of oil one week earlier. Furhermore, hey repor ha weaher and sorage levels boh have significan effecs on he price of naural gas by moving i emporarily away from he long run relaionship o crude oil prices. Similar o previous sudies, Brown and Yücel found he direcion of causaliy is from he price of WTI o he price of Henry Hub, bu no he oher direcion. Bachmeir and Griffin (006) also examine he evidence for coinegraion wihin as well as across various commodiy markes. Specifically, hey find ha various global crude oils are srongly coinegraed, bu ha he coinegraing relaionship beween he prices of differen coals in he Unied Saes is no srong. Moreover, hey repor ha cross-commodiy coinegraion in he Unied Saes is weak, and conclude ha he marke for energy can only be considered a single marke for primary energy in he very long run. By conras, Asche, Osmundsen and Sandsmark (006), using daa for he Unied Kingdom, repor ha he prices of crude oil, naural gas and elecriciy are coinegraed. Moreover, hey find ha here is a single marke for primary energy in he Unied Kingdom in which price is deermined exogenously by he global marke for crude oil. In addiion, hey conclude ha changes in regulaory srucures and capaciy consrains can make prices appear o be more or less coinegraed. Neiher of hese sudies, however, considers he influence of exogenous variables, such as weaher and invenories, on shor run price adjusmen. In addiion, none of he sudies we reviewed considered he influence of echnology for he long run price relaionships. We also examine he relaionship beween oil and naural gas prices. Like Villar and Jouz, we use monhly daa and aemp o find a sable coinegraing relaionship 14

16 The Relaionship beween Crude Oil and Naural Gas Prices beween naural gas and oil prices by adding an addiional variable, bu we consider echnology raher han a ime rend. More specifically, we assume ha an elecriciy producer chooses among alernaive fuels o minimize coss in dollars per MWh given as he fuel price muliplied by he hea rae. The subsanial increase in combined-cycle power generaing capaciy over he pas decade has lowered he capaciy-weighed average hea rae for naural gas plans, effecively lowering he cos of producing elecriciy wih naural gas relaive o oher fuels. Since a subsanial amoun of fuel compeiion occurs in he power secor, we would expec his echnological change o have affeced he long run relaionship beween naural gas and crude oil prices. Thus, we hypohesize ha he increased efficiency of producing elecriciy wih naural gas is responsible for he increasing price differenial observed by Villar and Jouz. We also follow boh Villar and Jouz and Brown and Yücel by allowing marke fundamenals such as sorage levels and weaher o influence he shor run dynamic relaionship beween he prices. Finally, we follow he earlier papers by Serleis e al. in relaing naural gas prices no o he price of crude oil bu raher o he prices of he main compeiive oil produc, namely residual fuel oil. I is clear from Figure 1 ha naural gas prices have ended o relae more closely o residual fuel oil han o crude prices. Neverheless, we also allow crude prices o ener a sysem of equaions ha we esimae and hus o influence boh of he oher prices. III. Daa As we noed in he previous secion, much of he recen lieraure focuses on he relaionship beween he prices of crude oil and naural gas. Like Serleis and Herber, we insead focus on he relaionship beween he prices of naural gas and residual fuel oil, alhough we also es for direc effecs of crude oil prices on boh end-user prices. Thus, we examine a sysem of hree fuel prices: he price of naural gas a he Henry Hub (compiled from Naural Gas Weekly), he wholesale price of residual fuel oil and he price of WTI crude (he laer wo series were obained from he U.S. Energy Informaion Agency (EIA) web sie). We examine he price of Henry Hub raher han naural gas prices in oher regions because variaions in basis differenials primarily reflec 15

17 The Relaionship beween Crude Oil and Naural Gas Prices ransporaion consrains, and hence he shadow value of scarce ransporaion capaciy, raher han changes in he value of energy as such. Consisen wih our heoreical framework, fuel prices are expressed in real $000/MMBu, 5 and are deflaed using indusrial elecriciy reail prices, which mos closely resemble a wholesale oupu price for he elecriciy secor. 6 The hea rae daa were consruced from wo sources. The Environmenal Proecion Agency s (EPA) NEEDS 004 daa provides he hea raes for many generaing plans in he Unied Saes, bu very few capaciies and no informaion abou monh of firs use. To obain he addiional informaion, he EPA daa were mached o he faciliies lised in he Energy Informaion Agency (EIA) Form-860 (Annual Elecric Generaor Repor) in four seps. Sep 1: Boh he EIA and EPA daases lis plans by Faciliy ID and Generaor number. For any plan where hese mached exacly, he repored hea rae was mached o he EIA daa. Sep : If a plan did no have an exac mach, bu had he same Faciliy ID number, year of firs use, prime mover, and fuel ype, ha plan from he EIA daabase was mached o he analogous plan in he EPA daabase. Sep 3: For he remaining plans, a plan in he EIA daabase was assigned he average hea rae of faciliies in he EPA daabase having he same year of firs use, prime mover, and fuel ype. Sep 4: Finally, if a plan in he EIA daabase wih a paricular prime mover and fuel ype had a year of firs use ha did no mach he year of firs use of any plans of ha ype in he EPA daabase, hen i was assigned he average hea rae of plans in he EPA daabase wih he same prime mover and fuel ype and year 5 The conversion facors for energy conen, obained from he EIA web sie, were 1.03 MMBu per housand cubic foo for naural gas, 6.87 MMBu per barrel for residual fuel oil, and MMBu per barrel for WTI crude oil. 6 We relaed real, raher han nominal prices since general inflaion could make any nominal price nonsaionary and he general inflaion rae would need o be included in he coinegraing relaionship. This may obscure he real relaionship beween he differen energy commodiies. From he perspecive of a cos-minimizing elecriciy producer, he relevan real inpu price for each fuel is he nominal price imes he hea rae divided by he price of elecriciy. Taking logs, we hen obain he coinegraing relaionship as esimaed. 16

18 The Relaionship beween Crude Oil and Naural Gas Prices of firs use closes o he acual year of firs use, wih a preference for using more modern plans where closes is ambiguous. 7 The formula used for calculaing he capaciy-weighed hea rae for plans using fuel of ype f in monh ( HR f ) is hen given as HR f = i f (Capaciy i, i f * HeaRae i, ) f Capaciy i, for all plans i using fuel f ha were available for use a any ime during monh. The EIA daabase provides as many as six energy sources for any one generaor. Only he primary energy source was considered for he hea rae calculaions. The use of he hea rae variable in our analysis resrics us o using daa a he monhly frequency. One advanage of using monhly daa, however, is ha we can cover quie a long ime series from February 1990 o Ocober 006. Oher variables included in he dynamic adjusmen process include beginning of period invenory levels, variables reflecing weaher condiions, and a variable o capure disrupions o Gulf of Mexico producion as a resul of hurricanes. The invenory variables allow for shor-erm supply availabiliy o eiher miigae or exacerbae he effecs of shocks on price movemens. The weaher variables are included o capure he effecs ha weaher has on demand and hence price, and he hurricane variable is included o capure he price impacs of shor-erm supply disrupions. Invenory daa was obained from he EIA web sie. For naural gas, we used working naural gas in sorage a he end of he previous monh (beginning of he curren monh), and, for residual fuel oil, we used monhly socks a he end of he previous monh measured in housands of barrels. 8 The weaher variables were calculaed using daa on heaing and cooling degreedays ( HDD and CDD ) from he Naional Oceanic and Amospheric Adminisraion 7 For example, suppose he year of firs use for an EIA plan was 1999 and plans of ha ype appear in he EPA daabase wih years of firs use of 1998 and 001, bu no Then he average hea rae for he 1998 plans would be assigned. If plans in he EPA daabase had a year of firs use of 1998 and 000, bu no 1999, he average hea rae for he 000 plans would be assigned. 8 Naural gas invenories are measured in unis of rillion cubic fee. We convered he residual fuel oil socks o rillions of barrels prior o he regression analysis. 17

19 The Relaionship beween Crude Oil and Naural Gas Prices (NOAA). To begin wih, we calculaed he 15-year average degree-days for each monh ( HDDavg and CDDavg ) over he period Since we also included monhly indicaor variables in he dynamic adjusmen equaions, we did no include hese normal seasonal variaions in weaher as explanaory variables. 9 However, we did include deviaions in heaing and cooling degree-days in each monh, measured as he acual values minus he 15-year average: HDDdev = HDD HDDavg CDDdev = CDD CDDavg We also included a measure of exreme winer weaher evens calculaed as he op decile of he HDD disribuion: 10 HDDex = 0 if HDDdev is no in he op 10% of values HDDdev if HDDdev is in he op 10% of values We derived he hurricane variable by regressing federal offshore Gulf of Mexico naural gas producion on a cubic ime rend and a se of dummy variables represening periods when major hurricanes, as repored by NOAA, affeced Gulf producing areas NG Gulf = α 0 + α 1 + α + α δ j D j + ε j. (1) In equaion (1), j indexes he hurricanes ha racked hrough producing areas in he Gulf j j of Mexico wihin he sample period, j indexes monhs for which hurricane j had a saisically significanly negaive effec on producion (relaive o rend), and D j = 1 for = j and 0 oherwise. The measure of producion shu-in as a resul of hurricanes is hen aken o be HurrShuIn = δ j D j. j j j 9 An argumen for including monhly effecs raher han normal weaher variables is ha seasonal facors oher han weaher, such as he disribuion of holidays or variaions in he number of working days in a monh, could influence demands for differen ypes of energy commodiies and hence prices. 10 A similar exreme cooling-degree day variable was neiher numerically nor saisically significanly differen from zero in any equaion. 18

20 The Relaionship beween Crude Oil and Naural Gas Prices There are several moivaions for our approach. Firs, a number of hurricanes over his period were believed o have had a lingering effec on producion beyond he monh in which hey occurred. We sough a mehod ha could deec he number of monhs affeced and allowed he effecs o moderae over ime. Second, we waned o allow for he possibiliy ha differen hurricanes affeced producion by differen amouns. A simple dummy variable for he monhs of major hurricane srikes would rea all hurricanes idenically. Third, he effecs of hurricanes may be difficul o idenify in he presence of changes in Gulf producion for oher reasons, such as depleion or new discoveries. We implicily assume ha hese oher influences are slow moving and hus can be approximaed by a smooh polynomial ime rend. The producion shu-ins aribued o major hurricanes were hen measured as saisically significan deviaions from he smooh ime rend coinciding wih hurricane evens in he Gulf producing areas. The mehod indicaes ha producion was los due o hurricanes during he following ime periods: Augus-Sepember 199, Ocober 1995, Sepember 1998, Sepember- Ocober 00, Sepember-Ocober 004, and Sepember-December We also included an indicaor variable (Chicago) for February The firs week of ha monh was very cold in many pars of he Unied Saes and produced exremely high demand. In paricular, when coupled wih low sorage levels, he period winessed unprecedened prices of naural gas in he Chicago marke area, bu hose price increases were reversed quickly when he weaher reurned o normal in he following weeks. Alhough we have included variables o capure he effec of exreme weaher on high prices, he 1996 inciden had a peculiarly large effec on prices. This migh be relaed o he hen relaively new emergence of major marke hubs and he offering of hub services such as parks and loans, which were no widely used a major hubs a ha ime. 1 In any case, he February 1996 even is an oulier in analysis. The high prices in 11 We examined he effec of using simple dummy-variables in place of our measure of los producion. The coefficien on he hurricane shu-in variable became less significan bu none of he remaining coefficiens was maerially affeced. 1 The February 1996 episode is discussed in Naural Gas 1996: Issues and Trends which is available a The EIA noes on page 1 ha some indusrial gas consumers paid more han $45.00 per MMBu in Chicago in order o avoid pipeline imbalance penalies of over $60.00 per MMBu. On page 78 i claimed, Oher evidence ha marke ceners are no being fully uilized is he size of he daily price spikes experienced his pas winer. Parks (shor-erm gas sorage) and loans (an advance of gas) can miigae he impac of such combinaions of severe weaher and low sorage levels because hey allow 19

21 The Relaionship beween Crude Oil and Naural Gas Prices he Chicago area were ransmied back o Henry Hub due o he direc pipeline linkages beween he Gulf Coas and he Chicago marke area. Finally, we allowed for seasonaliy in he adjusmen process by including a se of monhly dummy variables. The naural gas price has a pronounced seasonal paern, and alhough invenories rise and fall in an effor o parly miigae seasonal price movemens, hey do no eliminae hem compleely. Invenory build is a funcion of curren marke condiions and expeced fuure marke condiions. If expecaions are accurae, we migh expec ha conrolling for invenory levels and normal weaher condiions could explain seasonal movemens in price. However, oher facors such as he number of days in a monh, and normal seasonal demand paerns in fuel consumpion may no necessarily be capured by seasonal changes in invenories and heaing or cooling degree days. 13 IV. Analysis and Resuls The premise of he ECM is ha, alhough naural gas and residual fuel oil prices are each nonsaionary (or more specifically inegraed of order 1), here exiss a sable long run relaionship beween hem. Saisically, if wo nonsaionary variables are coinegraed, he residual afer esimaing heir coinegraing relaionship will be saionary. Phillips-Perron ess indicae ha he levels of he logs of he hree price variables and he relaive hea rae variable are nonsaionary and inegraed of order one, I(1). The remaining variables are all saionary, I(0). 14 consumers o mee conracual obligaions and a he same ime smooh he profile of capaciy uilizaion on marke area pipelines. Brownfield and greenfield expansions of pipeline infrasrucure (i.e. Norhern Border and Alliance) occurred afer he winer of These also increased access o Canadian supplies and sorage and helped cope wih similar problems in subsequen years. 13 We also invesigaed he use of acual weaher raher han deviaions from normal, bu he monhly dummies remain significan. Thus, we adop he approach aken here. 14 For NG ln(pp ), he ess saisics are Z(ρ) = 8.75 and Z(τ) =.08 compared wih Z(ρ) = and Z(τ) = for ln(p NG P ). For ln(pprfo ), he ess saisics are Z(ρ) = and Z(τ) = compared wih Z(ρ) = and Z(τ) = for ln(p rfo P ). For ln(ppwti ), he ess saisics are Z(ρ) = and Z(τ) = compared wih Z(ρ) = and Z(τ) = for ln(p WTI P ). For ln(hrrel), he ess saisics are Z(ρ) = and Z(τ) = compared wih Z(ρ) = and Z(τ) = for ln(hrrel). The inerpolaed 10% criical value for Z(ρ) is , and for Z(τ) is.573. The saisics for he levels of he weaher and sorage variables are Z(ρ) = and Z(τ) = for HDDdev, Z(ρ) = and Z(τ) = for CDDdev, Z(ρ) = and Z(τ) = 5.46 for ngsor, and Z(ρ) = and Z(τ) = for rfosor. 0

22 The Relaionship beween Crude Oil and Naural Gas Prices To obain a beer undersanding of he relaionship among he prices and he relaive hea rae variable, we esimaed a vecor auo-regression (VAR) on a vecor Y of naural gas price, residual fuel oil price, WTI, and he relaive hea rae using Johansen's maximum likelihood mehod. 15 Since he elemens of are each I(1), he changes in he variables a ime, ΔY, are esimaed as a funcion of and n lags of ΔY, where he opimal n is deermined using he Akaike Informaion Crierion (AIC). Y Y 1 The rank of he marix muliplying Y 1 is he number of coinegraing relaionships in he sysem. The errors from he esimaed coinegraing relaionships are hen used o consruc an error correcion model similar o ha used in he Engle-Granger mehod. The Johansen ess imply ha here are wo coinegraing relaionships, and he AIC indicaes ha he opimal number of lags n is one. The wo normalized coinegraing relaionships are given as: 16 ce 1 = ln P NG ln P rfo ln HR (0.61) (1.7855) ce = ln P rfo ln P WTI. (0.0708) NG HR rfo Table 1 gives he corresponding esimaed vecor error correcion model (VECM). The coefficiens on he wo coinegraing equaions imply ha only naural gas prices respond o divergences in he firs long run relaionship and only residual fuel oil prices adjus in response o deviaions in ce. Furhermore, he negaive coefficiens imply ha he subsequen adjusmens will end o resore he long run relaionships. ce 1 15 For more informaion on maximum likelihood esimaion in his conex see Hamilon (1994). 16 The likelihood raio es of he over idenifying resricions in his normalizaion yields a saisic χ 1 = wih a p-value of

23 The Relaionship beween Crude Oil and Naural Gas Prices Table 1: Esimaed VECM model (wihou exogenous variables) Variable Δ ln P NG Δ ln P rfo Δ ln P WTI Δ ln HRrel ce *** , 1 (0.0455) (0.059) ce, (0.100) (0.063) (0.0004) 0.15*** (0.0570) (0.0580) (0.0008) NG Δ ln P * *** (0.0780) (0.0444) (0.0451) (0.0007) rfo Δ ln P (0.1835) WTI Δ ln P (0.189) Δ ln HRrel (6.575) consan (0.0113) (0.1044) (0.1077) (3.714) (0.0064) * (0.106) ** * (0.0015) *** 0.375*** (0.1096) (0.0016) *** (3.7801) (0.0545) (0.0065) *** (0.0001) R join significance χ 7 = 7.40 χ 7 = 6.03 χ 7 = 1.81 χ 7 = ***- saisically significanly differen from zero a he 1% level;**- saisically significanly differen from zero a he 5% level;*- saisically significanly differen from zero a he 10% level The fac ha neiher changes in he WTI price nor changes in he relaive hea rae variable respond o deviaions in he wo coinegraing relaionships implies ha boh of hese variables are weakly exogenous. 17 The VECM also implies ha he WTI price influences he remaining prices mainly hrough is effec on he residual fuel oil price. However, he esimaed dynamic adjusmen process in he VECM needs o be reaed wih some cauion since he AIC es for lag lengh only considers uniform incremens of all lags in all equaions. In addiion, he sysem may omi imporan exogenous variables 17 A join es ha he coefficiens on ce1, and ce 1, are zero excep for ce 1 1, in he naural gas price 1 adjusmen equaion and ce, 1 in he residual fuel oil price adjusmen equaion yields a es saisic χ = 5.35 wih a p-value of A es only ha he coefficiens on ce 6 1, and ce are boh zero in he 1, 1 WTI equaion yields a es saisic χ = 0.38 wih a p-value of 0.857, while a es ha boh coefficiens on ce and are zero in he relaive hea rae equaion yields a es saisic wih a p-value of 1, ce 1, 1 χ = While his laer es is jus significan a he 10% level, neiher coefficien individually is significanly differen from zero (he corresponding z-saisics have p-values of 0.73 and 0.199). Finally, a join es ha he coefficien on ce is zero in he residual fuel oil equaion and he coefficien on 1, ce 1, 1 is zero in he naural gas equaion yields a es saisic χ = wih a p-value of

24 The Relaionship beween Crude Oil and Naural Gas Prices such as he weaher and sorage variables, and his could bias he esimaed coefficiens. To invesigae more flexible dynamic adjusmen models, we used he Engle-Granger wo-sep mehodology. Engle-Granger Mehodology The Engle-Granger mehod esimaes each coinegraing relaionship individually using ordinary leas squares (OLS). Then, he errors from hose coinegraing equaions are included, along wih he exogenous variables, in shor run dynamic adjusmen equaions o explain adjusmen o he long run equilibrium. Following he Johansen mehod resuls, we esimaed equaions () and (3) below by OLS: 18. ln P NG = (0.0913) (0.0849) ln P rfo (0.5785) ln HR NG rfo HR ln P rfo = ln P WTI rfo + ε (0.0339) (0.034) + ε NG () (3) Since he Phillips-Perron es indicaes boh residuals are saionary, in each case here is a sable long run relaionship and he parameer esimaes will be superconsisen. 19 The srong and saisically significan negaive coefficien on he relaive hea rae in () indicaes ha improvemen in he hea rae of a naural gas-fired relaive o an oil-fired generaing plan has raised he price of naural gas relaive o residual fuel oil as hypohesized. Furhermore, if we omi he relaive hea rae from () he residual is closer o being nonsaionary. In addiion, if we use WTI raher han he residual fuel oil price in (), he residual is nonsaionary a he 1% level. By subsiuing equaion (4) ino equaion () we can express he relaionship beween WTI and naural gas as lnp NG = lnP WTI 3.003ln HR NG HR rfo Solving his for a range of prices of WTI and relaive hea raes can yield some insigh ino he behavior of he raio of WTI o naural gas price. In paricular, given he hea rae raio in 1990, if he price of crude oil is $0 per barrel, he price of naural gas would be 18 The esimaed sandard errors are in parenheses below each esimaed coefficien. 19 NG For ε, he es saisics are Z(ρ) = (10% criical value ) and Z(τ) = 4.033, which has a MacKinnon approximae p-value of For Z(τ) = 3.719, which has a MacKinnon approximae p-value of ε rfo, he es saisics are Z(ρ) = and. 3

25 The Relaionship beween Crude Oil and Naural Gas Prices $.08/MMBu, yielding a raio. If he price of crude oil is $70, however, he price of naural gas would be $6.01/MMBu, yielding a raio. Alernaively, if we change he hea rae raio o reflec curren condiions, a $0 per barrel and a $70 per barrel price of crude oil implies a price of naural gas of $3.7/MMBu and $9.43, respecively, yielding a and raios in each case. I is imporan o noe ha hese are long run relaionships. Nex, we esimae he shor run dynamic adjusmen o he long run relaionships including saionary variables X, such as sorage levels and weaher, which affec shor run price adjusmens. Using ˆ ε NG o denoe he prediced residual from (), he ECM for he change in naural gas prices can be wrien as ( L) ( ) ( ) ( ) Δ ln P = β + β ˆ ε + α L X + γ L Δ ln P + δ L Δln P NG NG rfo NG φ Δ ln P + ω WTI 0 1 NG NG Equaion (5) reveals ha if we are a long run equilibrium, so ha ˆ ε = 0, and all oher variables remain unchanged, hen he price of naural gas will remain unchanged. NG Oherwise, if ˆ ε > 0 ( ˆ ε NG < 0 ), he price of naural gas is above (below) is long run (5) equilibrium value, and if β 01 < 0 subsequen movemens in he naural gas price will end o resore he long run equilibrium relaionship beween fuel prices. The erms γ 0 (L), δ 0 (L) and φ 0 (L) in (5) are polynomials in he lag operaor while, since X is a vecor, α 0 (L) is a marix of polynomials in he lag operaor. An equaion similar o (5) can be wrien for he dynamic price adjusmen of residual fuel oil as ( L) ( ) ( ) ( ) Δ ln P = β + β ˆ ε + α L X + γ L Δ ln P + δ L Δln P rfo rfo NG rfo WTI + φ Δ ln P + ω 1 rfo where ˆrfo ε, he prediced residual from (3), represens deviaions from he long run equilibrium beween he residual fuel oil price and WTI. The inerpreaion of he variables in (5) is analogous o ha for (4). (6) 4

26 The Relaionship beween Crude Oil and Naural Gas Prices Figure : Implied long run relaionship beween he WTI and Henry Hub naural gas price (boh in $000) as a funcion of he WTI price per barrel To provide a baseline for our subsequen analysis, we esimaed (5) and (6) using OLS. Variables ha proved individually and joinly insignifican a he 10% level, apar from he full se of monhly dummy variables and he change in WTI prices, have been eliminaed from he equaions. The resuls are repored in Table. The monhly dummy variables are no repored, bu are available upon reques. 5

27 The Relaionship beween Crude Oil and Naural Gas Prices Table : Error Correcion Model Esimaion Resuls Variable ˆ j Δ ln P NG OLS Δ ln P rfo ε (0.047) NG Δ ln P (0.071) NG Δ ln P 1 NG Δ ln P Δ ln P rfo rfo Δ ln P 1 Δ ln P WTI (0.0660) (0.0594) *** (0.0407) *** (0.066) Δ ln P NG IV Δ ln P rfo *** 0.313*** *** (0.047) (0.043) *** (0.0818) ** 0.51 (0.0656) * * (0.0593) *** *** (0.1415) (0.116) (0.1019) (0.1465) WTI Δ ln P (0.0485) ngsor (0.0349) rfosor (1.030) * * (0.104) *** ** (0.070) *** *** (0.0474) (0.0568) *** 0.05*** (0.0486) *** *** (0.0349) *.0584** (1.055) HDDdev *** *** (0.0004) (0.0004) HDDdev ( ) *** *** ( ) CDDdev *** *** ( ) (0.0004) CDDdev (0.0004) HDDex ( ) HurrShuIn ( ) * * (0.0004) ** ( ) *** ( ) *** *** ( ) Chicago *** 0.674*** (0.1073) (0.1060) Chicago (0.1164) *** *** (0.1149) * ** ( ) N R Join significance F 6,170 = F 18,179 = 9.10 F 5,171 = F 18,178 = 8.6 Q-saisic (1 lags) χ 1 = χ 1 = χ 1 = χ 1 = Breusch-Pagan es χ 1 = 0.60 χ 1 = 0.00 Hausman es χ 19 = 0.06 χ 17 = 1.10 ***- significan a he 1% level; **- significan a he 5% level; *- significan a he 10% level 6

28 The Relaionship beween Crude Oil and Naural Gas Prices Several feaures of hese esimaed equaions are of ineres. Firs, all variables have he expeced signs, and diagnosic ess indicae he models fi he daa reasonably well while leaving uncorrelaed and homoskedasic residuals. Second, he change in he residual fuel oil price has a much larger effec in he naural gas price equaion han vice versa. Third, while he conemporaneous (and lagged) change in WTI has a large effec in he residual fuel oil equaion, is coefficien in he naural gas equaion is much smaller and no saisically very differen from zero. This suggess ha crude oil prices influence naural gas prices mainly via compeiion wih residual fuel oil as hypohesized. A poenial problem wih he OLS esimaes, however, is ha he prices of residual fuel oil and naural gas may be joinly deermined. To examine his possibiliy, we re-esimaed he equaions using insrumenal variables (IV). In order o esimae (4) and (5) using IV we need a suiable se of insrumens. Such variables should be exogenous or predeermined variables ha are direcly correlaed wih one of he price changes bu no wih he oher so ha hey would influence he dependen variable only via heir effec on he included endogenous variable. As insrumens in each equaion, we used he weaher variables, own invenories, lagged values of own price, and curren and lagged values of WTI. The weaher variables are exogenous, and on he basis of he OLS resuls, i would appear ha only he mos exreme weaher in winer direcly affecs he change in residual fuel oil prices (holding oher variables in (5) fixed). We herefore used he conemporaneous and lagged heaing and cooling degree-day deviaions, as well as he hurricane shu-in variable, as insrumens for he change in naural gas prices in (5). We also used beginning-of-monh invenories as an insrumenal variable in each equaion. Beginning-of-monh invenories should signal he availabiliy of supply enering ha monh, and hus influence he change in price over he res of he monh. However, invenories a he beginning of he monh should no be influenced by he change in price ha subsequenly occurs over he following monh. The OLS resuls also indicae ha he change in naural gas prices from wo monhs ago (ha is, he wice-lagged change) does no direcly affec he conemporaneous change in residual fuel oil price, bu does affec he conemporaneous change in he naural gas price. Hence, he wice-lagged change in naural gas price is 7