CEEPBIT WORKING PAPER SERIES. The crude oil market and the gold market: Evidence for cointegration, causality and price discovery


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1 CEEPBIT WORKING PAPER SERIES The crude oil marke and he gold marke: Evidence for coinegraion, causaliy and price discovery YueJun Zhang YiMing Wei Working Paper 5 hp:// Cener for Energy and Environmenal Policy Research Beijing Insiue of Technology No.5 Zhongguancun Souh Sree, Haidian Disric Beijing Ocober 009 This paper can be cied as: Zhang YJ, Wei YM The crude oil marke and he gold marke: Evidence for coinegraion, causaliy and price discovery. CEEPBIT Working Paper. This sudy is suppored by he Naional Naural Science Foundaion of China under gran Nos , , and he Humaniies and Social Science Research Foundaion from he Minisry of Educaion of China under he gran No.09YJC630011, and SRFDP under he granno The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Cener for Energy and Environmenal Policy Research. 009 by YueJun Zhang and YiMing Wei. All righs reserved.
2 The Cener for Energy and Environmenal Policy Research, Beijing Insiue of Technology (CEEPBIT), was esablished in 009. CEEPBIT conducs researches on energy economics, climae policy and environmenal managemen o provide scienific basis for public and privae decisions in sraegy planning and managemen. CEEPBIT serves as he plaform for he inernaional exchange in he area of energy and environmenal policy. Currenly, CEEPBIT Ranks 11, op10% insiuions in he field of Energy Economics a IDEAS(hp://ideas.repec.org/op/op.ene.hm), and Ranks 157, op10% insiuions in he field of Environmenal Economics a IDEAS (hp://ideas.repec.org/ op/op.env.hml). YiMing Wei Direcor of Cener for Energy and Environmenal Policy Research, Beijing Insiue of Technology For more informaion, please conac he office: Address: Direcor of Cener for Energy and Environmenal Policy Research Beijing Insiue of Technology No.5 Zhongguancun Souh Sree Haidian Disric, Beijing , P.R. China Access: Tel: Fax: Websie: hp://
3 The crude oil marke and he gold marke: Evidence from coinegraion, causaliy and price discovery YueJun Zhang a, b ; YiMing Wei a, b a Cener for Energy and Environmenal Policy Research, Beijing Insiue of Technology, Beijing, , China b School of Managemen and Economics, Beijing Insiue of Technology, Beijing, , China Absrac: Given ha he gold marke and he crude oil marke are he main represenaives of he large commodiy markes, i is of crucial pracical significance o analyze heir coinegraion relaionship and causaliy, and invesigae heir respecive conribuion, from he perspecive of price discovery, o he common price rend so as o inerpre he dynamics of he whole large commodiy marke and forecas he flucuaion of crude oil and gold prices. Empirical analysis indicaes ha, firsly, here are consisen rends beween he crude oil price and he gold price wih significan posiive correlaion coefficien during he sampling period, from January of 000 o March of 008. Secondly, here can be seen a longerm equilibrium beween he wo markes, and he crude oil price change linearly Granger causes he volailiy of gold price, bu no vice versa; moreover, he wo marke prices do no face a significan nonlinear Granger causaliy, which overall suggess heir fairly direc ineracive mechanism. Finally, wih regard o he common effecive price beween he wo markes, he conribuion of he crude oil price seems larger han ha of he gold price, wheher wih he Permanen Transiory (PT) model (86.50% versus 13.50%) or he Informaion Share (IS) model (50.8% versus 49.7%), which implies ha he influence of crude oil on global economic developmen proves more farreaching and exensive, and is role in he large commodiy markes has araced more aenion in recen years. Keywords: Crude oil marke; Gold marke; Granger causaliy; Permanen Transiory model; Informaion Share model; Price discovery Corresponding auhor: Y.M.Wei ( Tel/Fax: ) 1
4 Inroducion In recen years, he prices of crude oil and gold, as he wo main represenaives of he large commodiy markes, were no compleely driven by he basic marke supplydemand consideraions any more. In fac, a grea amoun of evidence has suggesed he financial feaures of he inernaional crude oil and gold markes, and a close ineracion beween he wo markes. Consequenly, from he evolving pah of he wo markes hese years, we migh see ha hey basically mainained a neighboring rend. For insance, in 00, caused by US dollar depreciaion, global inflaion, oil supply manipulaion by he OPEC and some sensaional geopoliical evens, boh he crude oil and gold prices enered ino a boom ime, and sared o soar approximaely a he same ime, and kep a almos consisen surging momenum ill he firs half of 008. In he second half of 008, due o he serious global financial and economic crisis, he large commodiy markes basically faced an ausere es. As a resul, he crude oil price coninually declined from 147 $ per barrel o nearly 30 a he end of 008; a he same ime, he gold also saw a sharp price collapse from over 1000 $ per ounce o 700 or so. However, ever since 009, wih he emergence of global economic recovery expecaion, he large commodiy marke demand began o rise again and boh he crude oil and gold prices changed heir saggering umble rends and sared a new surging sage. This paper aims o shed ligh upon he reasons for he consisen changes of he wo prices, as well as he ineracive mechanism of hem. I should be noed ha discussion on hese opics is of crucial imporance for risk managers so as o resis he large commodiy marke risk and forecas marke dynamics in he fuure. Addiionally, as we know, price is a concenraed carrier of marke informaion and price flucuaions can ofen reflec he comprehensive change of marke informaion. According o Sock and Wason (1988), marke informaion is comprised of wo pars, effecive informaion and noisy informaion. Therefore, he real marke price can be divided ino wo pars, effecive price and noisy price. In his paper, he common effecive price of he crude oil and gold markes embodies he common effecive informaion beween he wo markes, which can be viewed as an imporan reference of he overall rend of he large commodiy markes, due o he dominan
5 posiions of crude oil and gold in he large commodiy markes. However, he conribuion of he wo markes o he common effecive price may be differen, and he goal of price discovery research is o examine heir respecive conribuion. In erms of no only he ousanding rading volume and value, bu also eviden marke influence and aracion among invesors, he crude oil and he gold play he main roles in he large commodiy markes, hence i is fairly imporan for relaed marke consulans and invesors o conduc an invesigaion of price coinegraion relaionship, leadandlag relaionship beween he wo markes and he conribuion of hem o price discovery. The res of he paper is organized as follows. The nex secion briefly summarizes he exising lieraure relaed wih he opics in his paper. Secion Mehodology presens he empirical mehodologies and daa definiion secion follows. Then, secion Empirical resuls and discussions provides he empirical sudy and policy implicaions of his paper, which mainly includes hree pars, i.e. he longerm equilibrium and shorerm adjusmen beween he crude oil and gold markes, he analysis of price informaion spillover across he wo markes, and he analysis of conribuion o price discovery beween he wo markes. Finally, some concluding remarks are pu forward in he las secion. Lieraure review Gold has been an imporan precious meal for many cenuries, and plays a special role as a sore of value especially in imes wih poliical and economic uncerainies (Aggarwal e al., 007). Hence, compared wih oher meals in he large commodiy marke, gold regisers an eviden advanage and ousanding posiion. In recen years, because of he nice profimaking siuaion and remarkable riskavoidance feaure, gold marke has seen a very acive picure. As a resul, he role of gold marke in he large commodiy marke even in he whole social economy has received increasing aenion by boh academia and indusrial cycles, and research concerned also can be found emerging. For insance, Xu e al. (005) used a bivariae asymmeric GARCH model o examine he informaion flow across he US and Japan markes for gold, plainum and silver fuures conracs, and found ha he volailiy spillover across he wo markes was srong bu US marke played he leading role. Sjaasad e al. (1996) and Sjaasad (008) sudied he relaionship 3
6 beween gold price and euro and US $ exchange rae respecively, and argued ha in erms of exchange rae, in he 1980s, gold price was dominaed by euros bu as of he 1990s, US $ gradually replaced he posiion of euros before. Tully e al. (007) developed an APGARCH model o invesigae he shocks of macroeconomy o gold spo and fuures markes and also found ha US $ was a major macroeconomic variable o influence he gold price volailiy. And Nakamura e al. (007) poined ou ha boh daily gold price and crude oil price daa were essenially random walk, and heir firs differences were independenly disribued random variables or imevarying random variables. I should also be noed ha research on crude oil price is a ho opic and a grea many of publicaions concerned have been found up o now (Zhang e al., 008). Overall, an array of research on he price dynamics in crude oil marke and gold marke respecively has been idenified and hisorical daa indicaed ha heir price movemen proved highly relaed, bu research on he ineracion of he wo markes appears sill scarce now (Yang, 007; Zhang, 007), and even some key opics have no been discussed by exising lieraure. For example, wheher here is srong influence beween he crude oil and gold markes, wha he influenial exen may be and wha heir relaive posiions may say in he large commodiy marke ec. However, hese opics are of crucial pracical significance for furher recognizing he feaures of commodiy markes and forecasing heir price volailiy. Therefore, more careful invesigaion should be carried ou. For his purpose, his paper aims o explore he ineracion beween he wo markes from hree perspecives, price coinegraion, price causaliy and price discovery. As for he price coinegraion discussion, he coinegraion heory and error correcion model provided by Engle and Granger (1987) are applied here. And hen his paper aemps o quaniaively sudy he leadandlag relaionship beween he crude oil price and he gold price. For his opic, i has been universally acknowledged ha one of he main mehods should be Granger causaliy es approach, especially he linear Granger causaliy es (Yang, 000; Jiao e al., 004; Jiao e al., 005; Tang, 008; Erdal e al., 008; Bekiros e al., 008; Henriques e al., 008; Zhang e al., 008;). Neverheless, he ineracion among economic variables ends o show some complexiy, and nonlinear characerisics can be found pervasive. Since Baek and Brock (199), Hiemsra and Jones (1994) pu forward he nonlinear Granger causaliy es approach, many auhors have found 4
7 i favorable and used i in many fields. For insance, Wang and Wu (005) used his approach o empirically sudy he nonlinear causaliy beween sock price and volume in Chinese Shanghai sock exchange and Shenzhen sock exchange. Fang e al. (006) made an empirical sudy on he relaionship beween Chinese sock markes and warran markes wih he help of his approach. Ma and Kanas (000) discussed he ineracion beween exchange rae and macroeconomic variables. Rashid (007) evaluaed he linear and nonlinear Granger causaliy beween sock price and volume in Pakisan. ChiouWei e al. (008) empirically researched he causaliy beween economic growh and energy consumpion. Despie so much lieraure abou he nonlinear Granger causaliy approach applicaion, here are few publicaions in an aemp o invesigae he nonlinear leadandlag relaionship beween he crude oil and gold markes. However, he previous applicaions of nonlinear causaliy es indeed provide favorable references for he sudy here. Besides, as far as he price discovery issue, here has been a large amoun of lieraure up o now, and mos of hem were focused on wo aspecs. One was based on he securiies of he same asse which is lised in differen exchanges, and he oher concenraed on he price discovery beween derivaive producs and heir corresponding subjec maers in he same marke. As for he empirical research mehodologies of price discovery, he permanen ransiory (PT) model (Gonzalo, Granger, 1995) and informaion share (IS) model (Hasbrouck, 1995) were ofen used, whose difference old he PT model emphasizes he decomposiion of he common facor (i.e. permanen impac), while he IS model disribued error erms ino differen markes. For example, Harris e al. (1995) sudied he price discovery of he IBM corporaion sock in hree exchanges which locaed in New York, Pacific region and Middle Eas, and resuls showed ha here could be found close relaionship among differen markes, which commonly deermined he price of IBM sock. Wang and Zhang (005) invesigaed he price discovery funcion of crude oil fuures marke and found ha, compared wih crude oil spo marke, he fuures ook he main conribuion wih he rae 54%. Aes and Wang (005) analyzed he conribuion of radiional index fuures rading and elecronic rading o fuures price discovery, and found ha he conribuion of elecronic rading ouweighed ha of radiional rading. Su and Chong (007) discussed he price discovery of some Chinese socks which were lised in he New York NYSE and Hong Kong SEHK simulaneously, and resuls indicaed ha some coinegraion relaionship could be idenified and Hong Kong sock price migh explain more informaion han New York 5
8 price. Li (007) analyzed he price discovery mechanism among Shanghai sock index, H sock index and H sock index fuures. Jiao and Liao (008) invesigaed he price discovery relaionship beween he Chinese Huangpu fuel spo price and Shanghai fuel fuures price. I also should be noed ha, besides he PT and IS models, Moosa (00) sill used he GS model o examine he price discovery opic in he crude oil marke, and argued ha he conribuion of crude oil fuures price appeared larger han ha of spo price. However, no lieraure has been found o sudy he price discovery mechanism beween he crude oil and gold markes. Anyway, hese previous applicaions presened helpful references for our research here. To sum up, i should be noed ha exising research relaed wih he crude oil and gold prices has some shorcomings in a leas hree folds. Firsly, given wo ypical large commodiy markes wih similar price rends, wheher here is saisical evidence showing long equilibrium relaionship beween he wo markes. Secondly, how abou he price leadandlag relaionship beween he wo markes? Pu i anoher way, wheher here exiss a siuaion ha one marke leads or lags anoher marke, and wheher heir relaionship akes on linear or nonlinear feaure. Finally, alhough an array of sudies on he wo markes respecively can be idenified, sudy on he ineracion beween he wo markes especially heir price discovery mechanism appears scarce. Overall, i is of grea pracical significance for marke dynamics forecasing o overcome hese shorcomings above. Therefore, hree folds of corresponding conribuion can be found in his paper. Mehodology I is of grea imporance for no only he crude oil marke and gold marke dynamic analysis bu also for he whole large commodiy marke forecas o es wheher here exiss a leadandlag price mechanism beween he crude oil price and gold price. For his purpose, a coinegraion es is invesigaed a firs, and hen boh linear and nonlinear Granger causaliy es approaches are used here so as o fully examine he price informaion ransfer mechanism. Addiionally, he PT and IS models are applied in order o find ou he respecive conribuion of he wo markes for heir common price. 6
9 Coinegraion es approach beween he crude oil marke and he gold marke In heory, he coinegraion relaionship indicaes ha neiher marke prices is saionary, bu here does exis some long equilibrium ineracion relaionship beween he wo markes. As for he crude oil and gold price, we may see ha neiher of hem follows a saionary dynamic, bu wheher here is long equilibrium relaionship beween hem should be furher sudied. To his end, we inroduce he wosep procedure provided by Engle and Granger (1987) o check he coinegraion beween oil price and gold price. And he coinegraion equaion is esablished as (1). P * P, O G P * P. (1) G O where O P and G P denoe he logarihmic crude oil price and gold price respecively, and boh 1 and are residuals. If ADF es for 1 or indicaes ha hey are saionary, hen we may say here is coinegraion relaionship beween he crude oil price and gold price. Linear Granger causaliy es procedure beween he crude oil marke and he gold marke Firsly, linear Granger causaliy relaionship beween he wo markes is esed. Based on he saionary marke reurns, a VAR model is developed as Equaion (). p p R _ OIL R _ OIL R _ GOLD, 10 11i i 1 j j 1 i 1 j 1 p p R _ GOLD R _ GOLD R _ OIL, () 0 1i i j j i 1 j 1 where R _ OIL sands for he oil price reurn, and R _ GOLD denoes he gold price reurn. Then a hypohesis es can be done for he firs equaion in Equaion (), in which he null hypohesis is =0 ( j 1,,..., p). When he null hypohesis is rejeced, hen i can be 1 j argued ha he change of gold price reurn linearly Granger causes he volailiy of inernaional crude oil price reurn; similarly, we also can es wheher he change of crude oil price reurn 7
10 linearly Granger causes he change of gold price reurn. In Equaion (), p represens he larges lag order, which is obained according o he principle of minimum AIC value. Nonlinear Granger causaliy es procedure beween he crude oil marke and he gold marke The complexiy of energy economic sysem deermines ha he relaionship among economic variables usually does no ake simple linear causaliy bu nonlinear causaliy can be seen exensively. In his way, based on he residual series removed linear predicive power wih a linear VAR model like Equaion (), he nonlinear Granger causaliy approach provided by Baek and Brock (199) and Hiemsra and Jones (1994) is employed here o invesigae he ineracion beween he crude oil marke and he gold marke. The specific idea of he approach can be briefly summarized as follows. Suppose X and Y denoe he residual series from Equaion () respecively, where X sands for he residual series when he crude oil price reurn acs as he dependen variable (i.e. 1 ), and Y implies he residual series when he gold price reurn is he dependen variable (i.e. ). And suppose X ( X, X,, X ), m 1,,, 1,, m 1 m 1 X ( X, X,, X ), L 1,,, L 1, L, Lx Lx Lx Lx 1 1 Ly Ly Ly Ly 1 1 x Y ( Y, Y,, Y ), L 1,,, L 1, L,. (3) m m Lx Lx y y If Pr( X X e X X e, Y Y e) y L L s Lx s Lx Ly s Ly m m Lx Lx = Pr( X X e X X e) holds, (4) s Lx s Lx hen we may say Y does no nonlinearly Granger cause X. Moreover, if suppose (,, ) Pr( m Lx m Lx, y y C ) 1 m Lx Ly e X L X s L e Y L Ys L e, x x y y (,, ) Pr( Lx Lx, y y C ) Lx Ly e X L X s L e Y L Ys L e, x x y y (, ) Pr( m Lx m Lx C ) 3 m Lx e X L X s L e, x x (, ) Pr( Lx Lx C ) 4 Lx e X L X s L e, (5) x x L L L y L x y x 8
11 hen according o he definiion of condiional probabiliy, i.e. Pr( E F) Pr( EF) / Pr( F), Equaion (4) can be rewrien as C1 ( m Lx, Ly, e) C3( m Lx, e). (6) C ( L, L, e) C ( L, e) x y 4 x Furhermore, Correlaion Inegral 1 is inroduced o express he join probabiliy as Equaion (7). m Lx m L Ly L x y C1 ( m Lx, Ly, e, n) I( X L,, ) (,, ) s X x s L e I Y x L Y y s L e y nn ( 1), Lx L Ly L x y C( Lx, Ly, e, n) I( X L,, ) (,, ) s X x s L e I Y x L Y y s L e y nn ( 1), m Lx m Lx C3( m Lx, e, n) I( X L, X, ) s x s L e x nn ( 1), Lx Lx C4( Lx, e, n) I( X L, X, ) s x s L e x nn ( 1), (7) where, s max( L, L ) 1,, T m 1, n T max( L, L ) m 1. I( X, Y, e ) is x y a kernelbased funcion, and is value is 1 when he maximum norm of vecor X and Y proves wihin he given parameer e, oherwise 0. Given m, L, L 1, e 0, and saionary and dependen residual series X and Y, if x y Equaion (8) holds, which means he saisic W follows he asympoical normal disribuion, hen we may say he change of Y does no nonlinearly Granger cause he change of X. x y C1 ( m L,, ) 3(, ) a x Ly e C m Lx e W n ~ N(0, ( m, Lx, Ly, e)) C( Lx, Ly, e) C4( Lx, e) (8) PTIS models for price discovery beween he crude oil marke and he gold marke In his paper, he PT and IS models are used in order o explore he price discovery issue. Specifically, he IS model is based on he PT model while he PT model is based on he vecor error correcion model (VECM). Suppose O P and G P denoe he logarihmic crude oil price 1 Briefly, Correlaion Inegral Ce () is defined as he rae of he number of pairs of poins X, X ) whose disance is wihin e o he number of all possible pairs of poins for he vecor, given any e. ( i j 9
12 and gold price respecively. If here can be ascerained coinegraion relaionship beween hem, according o Engle and Granger (1987), a vecor error correcion model can be specified as: P * P A P, (9) 1 i i i 1 q where P P P O G ' (, ) is he price vecor, 1 (, )' is he error correcion coefficien vecor, is he coinegraing coefficien vecor, and ( 1, )' refers o he random error and ~ N(0, ). I should be poined ou ha here is no erm wih 1 ~ N(0, 1) auocorrelaion feaure wih respec o he wo error erms and heir covariance marix is saed as: where and correlaion coefficien., (10) are he variance of 1 and series respecively, and is heir Based on he hisorical rading daa of he wo ypical commodiies, here exis a clear common rend beween he crude oil price and he gold price. According o Sock and Wason (1988) and Su and Chong (007), he price vecor P may be divided ino wo pars, he common effecive price (i.e. common facor) of he wo markes and noisy price of each marke. This means: P f, (11) where f is he common effecive price, which denoes he common changing rend of crude oil marke and gold marke, and ( 1, )' is he noisy price vecor, which means he specific O G change of each marke. Hence, P f 1 and P f can be specified. According o Gonzalo and Granger (1995), here he common facor f may be defined as a linear combinaion of O P and O G P, i.e. f 1P P ; pu i anoher way, he common G facor can be viewed as a porfolio consising of he crude oil price and he gold price. And (, ) denoes he coefficien vecor of common facor, which can be considered as he 1 10
13 weighs of crude oil price and gold price in he porfolio, and 1 1. As proved by Gonzalo and Granger (1995), he vecor is orhogonal o vecor of he error correc model, which implies ha Therefore, 1 and, which sand for he conribuion of he wo markes o price discovery, can be worked ou using he wo equaions above. This process is he main idea of he PT model, which sresses he decomposiion of common facor (i.e. permanen influence). Based on he resuls above, he IS model (Hasbrouck, 1995) can be developed so as o find ou he conribuion of he crude oil price and he gold price o price discovery. Differen from he PT model, he IS model emphasizes he variance decomposiion of innovaions o he common facor and defines he price discovery in erms of he conribuion of each marke o he variance. According o Baillie e al. (00), when here does no exis significan correlaion beween he wo residual erms arising from he coinegraion regression equaions for he crude oil price and gold price, he IS model can be specified as: IS i i i 1 1, i 1,. (1) Bu when he wo error erms are highly correlaed, Equaion (1) does no hold. In his way, Cholesky facorizaion mehod is used o ransform he covariance of error erms of he vecor error correcion model as ' MM, where m M 1 m 1 m (1 ). (13) As a resul, he IS model can be figured ou as Equaion (14), and we can see IS1 IS 1. IS ( m m ) ( 1m11 m1) ( m ), IS ( m ) ( 1m11 m1) ( m ) (14) I should be noed ha, Cholesky facorizaion mehod imposes a greaer informaion share on he firs marke in he equaion; herefore, i needs o change he order of variables in he facorizaion procedure so as o ge he upper and lower limis of heir informaion shares. For 11
14 Oil price (USD/bbl) Gold price (USD/Ounce) example, when he crude oil price works as he firs variable, hen he calculaed informaion share is is upper limi, whereas i lies as he second variable, hen corresponding informaion share should be is lower limi. As presened by Baillie e al. (00), he average of upper and lower limis for each variable here can be a reasonable esimae of is conribuion o price discovery. Daa definiion In his paper, we use daily daa from January 4 h 000 o March 31 s 008, wih oal 064 price samples and heir rends in Figure 1. The crude oil price daa are derived using Bren spo price from he US Energy Informaion Agency (EIA) and quoed in US dollars per barrel, while he gold price daa come from he Global Insigh and are based on he London PM fix, which are also spo price and quoed in US dollars per ounce. Roughly, i can be seen ha he wo markes ake very consisen price rends even hough here exiss some inconsisen volailiy in some shor periods. And our calculaion resuls show ha he wo prices are highly correlaed wih he correlaion coefficien in he sampling period, which indicaes ha hey do ake some common informaion Bren Gold Fig. 1. Crude oil price and gold price. The research in his paper mainly comprises hree pars, price coinegraion, causaliy and price discovery. As for he daa, he empirical research abou linear and nonlinear causaliy 1
15 Oil price change (USD per barrel) Gold price change (USD per ounce) beween he crude oil and gold markes is based on price reurns (logarihmic difference of original price series) muliplied by 100, in which R _ OIL and R _ GOLD sand for he crude oil and he gold price reurn a ime respecively. And he price coninegraion and price discovery research use he logarihmic values of original price series; specifically, O P and G P denoe logarihmic crude oil price and gold price a ime respecively. In order o derive a general image of he crude oil price and gold price, we furher calculae he frequency disribuion and basic saisics of logarihmic crude oil and gold prices, and find ha neiher of oil price and gold price follows a normal disribuion because of heir significan JB saisics a 1% level, righ kuroses and posiive skewnesses. Addiionally, he volailiy magniude of he crude oil price appears abou imes larger han ha of he gold price, which is validaed from he coefficiens of variances (CV in brief, i.e. he sample mean divided by he sample sandard deviaion) during he sampling period. The CV of crude oil price is while ha of gold price is , which is less han a half of he former. Moreover, if he whole sampling period is divided ino wo segmens, i.e and , hen we may find ha afer 004, boh he crude oil marke and gold marke have more dramaic volailiy (see Figure for he firs difference of he crude oil price and gold price series); specifically, boh he coefficiens of variances for he crude oil price and he gold price have increased abou 100%. As for he reasons behind, we argue ha afer 004, a large sum of inernaional speculaing money especially some huge index funds has been fas swarming ino he crude oil fuures marke and he gold marke for profimaking and riskavoidance. And heir fasgrowing scale and frequen speculaing aciviies caused boh he crude oil marke and gold marke winessed coninual sharp flucuaions and marke risk soared rapidly
16 (a) Crude oil price (b) Gold price Fig.. Firs differences of he crude oil price and gold price. Empirical resuls and discussions The empirical resuls are repored from hree pars, i.e. he longerm equilibrium and shorerm adjusmen, he price informaion spillover and he conribuion o price discovery beween he crude oil marke and he gold marke. Longerm equilibrium and shorerm adjusmen beween he crude oil marke and he gold marke Before we es he long equilibrium, according o he coinegraion heory, saionary properies of price series should be examined. ADF approach is used and resuls are shown in Table 1. We may find ha from he p values, a 1% level, boh of he crude oil price and he gold price are I(1) series, which are up o he precondiions of coinegraion relaionship es. Table 1 T saisic values of ADF es for he crude oil price and he gold price O P G P Level price series Firsorder difference price series Noe: pvalues are repored in parenheses (0.551) (0.0001) (0.431) (0.0001) Because he crude oil price O P and he gold price G P are I(1) series, according o Equaion (1), he coinegraion es resuls can be seen from Table, which indicae ha boh he 14
17 variables and equaions are significan a 1% level, and boh residual series 1 and are saionary, hence we may say here exiss a significan coinegraion relaionship beween he crude oil price and gold price. Pu i anoher way, hey have longerm equilibrium ineracion for each oher. Table Coinegraion resuls of he crude oil price and he gold price Dependen variables F saisic T saisic of ADF es for O P (0.0000) (0.0000) (0.0000) (0.0001) G P (0.0000) (0.0000) (0.0000) (0.0001) Noe: pvalues are repored in parenheses. As for he reasons for he coinegraion relaionship beween he crude oil marke and gold marke, in our opinions, his arises from he fac ha boh markes are influenced by several similar even he same conribuing facors. Firsly, boh of inernaional crude oil and gold rading are quoed and invoiced in US dollars, as a resul, he volailiy of US dollars ends o cause he flucuaions of he crude oil price and he gold price o he same direcion. For insance, he US $ coninuous depreciaion in he sampling period has become an imporan force o commonly suppor he volaile boos of he crude oil price and gold price. Based on he Nominal Broad US Dollar Index and simple calculaion, we find ha he correlaion coefficien beween he US dollar exchange rae and he crude oil price is , while ha beween he US dollar exchange rae and he gold price appears in he sampling period, which suggess he high correlaions beween he US dollar exchange rae and he wo prices. Furhermore, we find ha he US dollar index may Granger cause he change of boh he crude oil price and he gold price. Quaniaively, we find ha when he US dollar index The broad index is a weighed average of he foreign exchange values of he U.S. dollar agains he currencies of a large group of major U.S. rading parners. The index weighs, which change over ime, are derived from U.S. expor shares and from U.S. and foreign impor shares. For deails on he consrucion of he weighs, see he aricle in he Winer 005 Federal Reserve Bullein. 15
18 depreciaes 1%, on average, he crude oil price and gold price may increase 5.6% and 4.4% respecively. Secondly, generally, he high crude oil price aggravaes he inflaion, while he gold has an excellen naure o resis inflaion and mainain is value so as o become an effecive ool o hedge inflaion, hence high inflaion causes he surge of gold invesmen demand and hus seps up he gold price. Thirdly, dominan crude oil exporing counries make use of high oil revenue and increase gold invesmen so as o cause heir volailiy o he same direcion. Afer heir oil revenue fas expands, hey buy a large amoun of gold in order o disperse marke risk and mainain commodiy value, as a resul, he gold marke invesmen appears enhanced and gold price sees an ascending. Las bu no he leas, he crude oil price and he gold price are influenced by some geopoliical evens simulaneously. Acually, boh he crude oil marke and he gold marke are very sensiive o he urmoil of inernaional poliical siuaion, and as soon as he geopoliical deerioraion occurs, ciizens ofen rush o buy gold like he sheepflock effec in he financial marke; consequenly, he gold price sees a skyrockeing. Moreover, some key inernaional poliical evens direcly influence he global economy and he US dollar exchange rae hus simulae he gold price. Meanwhile, in he sampling period, many key evens ended o have a bearing wih he crude oil, which consequenly affeced he regular producion and supply of crude oil hus raised he crude oil price. Besides he longerm equilibrium across he crude oil marke and he gold marke, based on Equaion (9), we furher inroduce he error correcion model (Granger, 1988) o sudy he shorerm ineracion across he wo markes. And esimaed resuls can be seen in Table 3. 16
19 Table 3 Esimaed resuls of he error correcion model Dependen: D_GOLD Dependen: D_OIL Coefficien P value Coefficien P value C D_OIL D_OIL(1) D_OIL() D_GOLD D_GOLD(1) D_GOLD() ecm(1) F saisic and p value (0.0000) (0.0000) Adjused R squared Noe: C denoes he consan erm. D_OIL sands for he firs difference of he oil price, while D_OIL(1) is he 1order lagged series of D_OIL, and oher relaed series have similar implicaion. Ecm represens he error correcion erm. Resuls in Table 3 ell ha from he shorerm perspecive, he ineracion across he crude oil marke and he gold marke appears srong in erms of heir price change on he same day a 1% level, and he shock magniude of he gold price o he crude oil price is abou 5 imes larger han ha of he crude oil price o he gold price. Specifically, when he crude oil price changes 1%, he gold price changes 0.07% o he same direcion; whereas he gold price changes 1%, he crude oil price changes 0.37%, which seems much sronger han he shock of he crude oil price o he gold price. Furhermore, we may find some differences as for heir ineracion wih 1day lagged price series. A 5% level, he influence of 1day lagged crude oil price change on he gold price proves significan bu he 1day lagged gold price change does no exer significan shock o he crude oil price. And neiher of heir influence in erms of day lagged price series is significan saisically. Therefore, i should be noed ha alhough he influence of he crude oil price change on he gold 17
20 price is considered o be relaively smaller, i can las for a longer ime; ha is, 1 day. And he influence of gold price change on oil price is found much sronger, ye i can jus coninue for a shorer ime, exacly, only on he same day. Addiionally, according o he value of ecm erm in Table 3, i can be found ha alhough he longerm equilibrium beween he crude oil marke and he gold marke may significanly adjus he shorerm changes of he crude oil and he gold prices and cause ha heir shorerm changes do no deviae from heir longerm equilibrium pah very far, he adjusing exen appears quie limied. Specifically, he adjusing exen o he crude oil price shorerm change is 0.94%, which is abou 4 imes larger han ha o he gold price change (0.4%). Analysis of price informaion spillover across he crude oil marke and he gold marke In order o have a profound inerpreaion of he price dynamics of he crude oil and gold markes, i is essenial o invesigae he spillover effec beween he crude oil marke and gold marke. And price or reurn informaion is he concenraed reflecion of a marke, so i should be aached grea imporance o examine he price or reurn leadandlag relaionship beween he wo markes, o forecas he crude oil and gold prices and analyze he dynamics of he large commodiy marke. Therefore, linear and nonlinear Granger causaliy approaches are adoped here o check he price ineracion beween he wo markes. Because he VAR model, linear and nonlinear Granger causaliy es all require relaed ime series be saionary, hence logarihmic crude oil and gold reurns R _ OIL and R _ GOLD are used, boh of which are significanly saionary a 1% level based on he ADF es resuls 3. (1) Linear causaliy beween he crude oil marke and he gold marke Boh he R _ OIL and R _ GOLD series are saionary, which comply wih he precondiion of he VAR models, so a VAR model like Equaion (1) is developed, and according o he principle of minimum AIC value, he opimum lag order proves 1. And hen linear Granger 3 Deailed ADF es resuls can be obained from he auhors upon reques. 18
21 causaliy es is done whose deailed resuls are shown in Table 4. Meanwhile, we also carry ou he linear Granger causaliy es wih oher lag orders in order o examine he robusness of he linear Granger causaliy beween he wo markes (see Table 4). Table 4 Linear Granger causaliy es resuls Null Hypohesis Lag F saisic Probabiliy R _ GOLD R _ OIL R _ OIL R _ GOLD R _ GOLD R _ OIL R _ OIL R _ GOLD R _ GOLD R _ OIL R _ OIL R _ GOLD R _ GOLD R _ OIL R _ OIL R _ GOLD Noe: R _ OIL denoes he logarihmic crude oil price reurns, and R _ GOLD denoes he logarihmic gold price reurns, while means here does no exis linear Granger causaliy from he lef marke o he righ marke. According o Table 4, i should be noed ha no maer wha lag orders are adoped, he es resuls prove very similar, ha is, here exiss a significan unilaeral linear Granger causaliy beween he crude oil marke and he gold marke. Specifically, in he sampling period, he crude oil price reurn change significanly linearly Granger causes he change of he gold price reurns; pu i anoher way, he crude oil price soaring causes he gold price moving o he same direcion based on he fac ha he wo prices have very similar rends. However, he gold price reurn change does no significanly linearly Granger cause he volailiy of he crude oil price reurns. To our knowledge, hese resuls are closely relaed wih he naural properies of he crude oil and he gold. Crude oil is an imporan raw maerial of indusrial producion and oil price 19
22 Percen of GDP (%) skyrockeing ends o bring abou some inflaion. Differen from he crude oil, he gold naurally plays a nice role in hedging inflaion, which is rooed in gold's abiliies o ensure agains uncerainy and insabiliy and proec agains risk. In he sampling period, he inernaional crude oil price broke hrough hisoric records ime and ime again, which augmened he aracion of gold for hedging inflaion and spurred on a grea deal of gold rading for resising marke risk; as a resul, he gold price saw a fas soaring. On he oher hand, he dramaically surging crude oil price booss he oil revenue of dominan oil exporing counries, i.e. oil dollars, which can be confirmed from Figure 3. Specifically, since he saring year 00 of he crude oil price surge, oil expor value relaive o GDP of Middle Eas and Norh Africa has coninuously risen, nearly up 59% from 00 o 005, which largely refleces he increase of oil price (IMF, 008); so in order o reduce he marke risk and enrich invesmen variey, hose counries end o increase he gold invesmen demand, which leads o he gold price rise. According o a repor of he World Gold Council, since 00, gold invesmen in Middle Eas has shown a coninuous rise; by he end of 007, gold invesmen had increased abou 50% compared wih ha in 00. Especially in Saudi Arabia, is gold consumpion had a yearonyear 15% srong growh in 007, and is gold invesmen value reached.9 billion US dollars, which surpassed for he firs ime he previous value peak of.7 billion US dollars in 1997 (World Gold Council, 008). So i can be seen hose oil dollars from Middle Eas mus be an imporan impeus o promoe he gold invesmen demand and rigger he gold price soaring in a large scale hese years Fig. 3. Percen of he fuel expor value o GDP in Middle Eas and Norh Africa. 0
23 () Nonlinear causaliy beween he crude oil marke and he gold marke Besides linear causaliy, here can ofen be idenified complex nonlinear relaionship among economic variables, which adds difficulies for recognizing and judging he marke siuaion. Anyway, i is crucial for beer appreciaing he crude oil and he gold marke dynamics o sudy wheher here is some nonlinear relaionship beween he wo prices. Therefore, based on he wo residual series removed linear influence from a VAR model above, he nonlinear Granger causaliy approach provided by Baek and Brock (199) and Hiemsra and Jones (1994) is used o invesigae he nonlinear ineracion beween he wo markes. According o Hiemsra and Jones (1994), ChiouWei e al. (008) and oher auhors, we specify m 1, L L ( 1,,,8), and e 1.5, and he resuls of nonlinear Granger causaliy x y es for he crude oil and he gold markes can be seen from Table 5, which demonsraes ha a 10% level, all null hypoheses can no be rejeced. Hence here does no exis significan nonlinear Granger causaliy beween he crude oil marke and he gold marke in he sampling period. To summarize he linear and nonlinear causaliy beween he wo markes, i should be noed ha heir ineracion shows more linear feaures and appears relaively direc, concise and swif bu no very complicaed. 1
24 Table 5 Nonlinear Granger causaliy es resuls Null Hypohesis Lx=Ly W saisic Probabiliy Y X X Y Y X X Y Y X X Y Y X X Y Y X X Y Y X X Y Y X X Y Y X X Y Noe: X denoes he residual series when he oil price reurn acs as he dependen variable in he VAR model, and Y denoes he residual series when he gold price reurn acs as he dependen variable in he VAR model, while means here does no exis nonlinear Granger causaliy from he lef marke o he righ marke. And W saisic is he saisic in Equaion (8). Analysis of he conribuion o price discovery beween he crude oil marke and he gold marke
25 As saed above, he crude oil and gold are supposed o be he represenaives of he large commodiy markes, and heir price movemen basically can reflec and guide he price rends of he whole large commodiy marke. In his way, quaniaively invesigaing heir conribuion o price discovery helps o judge he influence exen of he crude oil marke and he gold marke respecively, which may provide some reference informaion for forecasing he crude oil price, he gold price and he movemen of he whole large commodiy marke, such as he CRB index. Due o he coinegraion relaionship beween he crude oil price and he gold price, a vecor error correcion model can be developed as Equaion (15). q q O O G 1 1 i * i 1 i * i 1 * 1( 1) 1 i 1 i 1, P P P vecm q q G G O i * i i * i * ( 1) i 1 i 1. (15) P P P vecm From he regression equaions above, he vecor error correcion coefficien ( 1, )' can be aained (see Table 6). And hen according o he PT model, a join equaion group is esablished o figure ou 1 and. Furhermore, he common facor of he crude oil marke O G and gold marke can be goen hrough he equaion f 1P P (see Figure 4), from which i can be roughly seen ha he crude oil price accouns for a larger par in he common facor, i.e. he common effecive price. 3
26 Logarihmic price Bren Gold Common facor Fig. 4. Oil price, gold price and heir common effecive price. Then based on he Equaion (14) of he IS model, informaion share coefficiens can be obained (see Table 6). From he esimaed resuls, i can be noed ha as for he price discovery using he PT model and he IS model, he conribuion of he crude oil price and he gold price proves (86.50% versus 13.50%) and (50.8% versus 49.7%) respecively. Therefore, we may see wheher wih he PT or IS models, he conribuion of he crude oil price is greaer han ha of he gold price, which implies ha he influence of he crude oil on he whole large commodiy marke may be larger han ha of he gold. Table 6 Esimaed resuls of price discovery models Parameers Markes Crude oil marke Gold marke Vecor error correcion coefficien ( ) (.3179) coefficien in he PT model Informaion share coefficiens in he IS model Noe: saisic values are repored in parenheses. 4
27 In order o check he robusness of price discovery resuls above, we also inroduce he GS model by Moosa (00) o examine he conribuion o price discovery beween he crude oil marke and he gold marke. The GS model is developed as follows. P c (1 d ) P d P O O G G G 1 G 1 1 P c d P (1 d ) P (16) G O G O O 1 O 1 Then le d /( d d ), which is used o explain he imporance exen of he crude oil G O G marke and he gold marke in price discovery. Specifically, if is larger han 0.5, he role of he gold price in price discovery ouweighs ha of he crude oil price; oherwise, we may argue he role of he crude oil price proves more imporan. Afer implemening he OLS approach in Equaion (16), esimaed resuls can be found in Table 7. Table 7 Esimaed resuls of he GS model Coefficien R squared DW d G d O (0.0574) (0.0611) Noe: pvalues are repored in parenheses. DW means he DurbinWason saisic. According o he esimaed values of d O and d G, we may ge he value of, which is and less han 0.5. Therefore, we may say he role of he crude oil price in commodiy marke seems more imporan han ha of he gold price, which means he imporance of he crude oil price movemen should be aached more aenion. This validaes he resuls from he PT and IS model above, and also keeps in line wih he aforemenioned empirical research saemen ha he crude oil price volailiy Granger causes he change of he gold price bu no vice versa. This may arise from he fac ha crude oil is considered o be an essenial raw maerial of indusrial producion. As a resul, compared wih he gold, he influence of crude oil on global 5
28 economic developmen appears more direc and exensive, hence is price change urns ou o be more aracive and imporan o invesors concerned. Indeed, in he wake of global indusrializaion and markeoriened process, crude oil fuures, as he larges commodiy fuures in he world, has a profound influence on oher fuures. For insance, due o he rapid developmen of alernaive energy, America uses a grea deal of corn and whie sugar o produce bioehanol and employs soybean o generae biodiesel oil; as a resul, here can be seen a close relaion beween he crude oil price and he prices of grease producs, soybean and corns. Addiionally, given he exensive usage, he crude oil has become one of he mos imporan and fundamenal lifelines of global economy, and is price is supposed o be of grea significance o he prices of oher commodiies. In brief, here has been some growing evidence ha he influence of crude oil price has become increasingly crucial for world economic developmen, and he flucuaion of he whole large commodiy marke prices, for he mos par, depends on he riseandfall of he crude oil price. Concluding remarks and fuure work This paper conducs a comprehensive empirical sudy on he ineracion beween he crude oil marke and he gold marke from hree perspecives, i.e. price coinegraion, price causaliy and price discovery, so as o provide some rewarding suppor for recognizing and analyzing he dynamics of he crude oil marke, gold marke and even he whole large commodiy marke. To recap wha we have done above, several main conclusions and policy implicaions can be obained as follows. (1) Overall, he crude oil price volailiy magniude proves greaer han ha of he gold price in he sampling period. From he value of Coefficien of Variance (CV), i can be found ha he flucuaion of crude oil price is imes sronger han ha of gold price. Moreover, due o he rampan speculaing aciviies of index funds, from 004 o 008, he volailiy magniude of boh crude oil price and gold price has almos doubled. I also should be noed ha here is a high posiive correlaion beween he crude oil price and he gold price wih he correlaion coefficien in he sampling period, which implies he wo markes ake very similar price rends and conain some common effecive price informaion. 6
29 () Significan coinegraion relaionship can be idenified beween he crude oil price and he gold price. Pu i anoher way, here exiss longerm equilibrium relaionship beween he wo markes, which resuls from he fac ha he wo markes end o be influenced by some common facors, such as he US dollars exchange rae, economic fundamenals, geopoliical evens. Besides, as for heir shorerm ineracion, we find ha heir muual influence appears saisically significan a 1% level on he same day, and he influence of he gold price on he crude oil price is abou 5 imes sronger han ha of he crude oil price on he gold price. However, he sronger influence of he gold price on he crude oil price can exis only on he same day, bu he smaller influence of he crude oil price on he gold price can las unill he nex day. Furhermore, we find ha he longerm equilibrium across he crude oil and he gold markes can only adjus heir shorerm change in a fairly limied manner. Therefore, when we analyze he main facors driving he crude oil price shorerm change, he volailiy of he gold marke is necessary o be considered as a dominan facor and can only provide a supplemenary reference. (3) There can be found significan unilaeral linear Granger causaliy beween he crude oil marke and he gold marke. Specifically, he crude oil price reurn change linearly Granger causes he movemen of he gold price reurn, bu no vice versa, which means in he firs few years of he 1 s cenury, he surging crude oil price has driven up he gold price, bu i is no he case in he opposie direcion. Addiionally, hey do no have any significan nonlinear Granger causaliy. Therefore, i can be argued ha he ineracion beween he crude oil marke and he gold marke proves fairly direc and concise. (4) Based on he common effecive price informaion beween he crude oil price and he gold price, we find ha he conribuion of he crude oil price appears larger han ha of he gold price, which implies ha among he price rends of he large commodiy marke, he role of crude oil ouweighs ha of he gold. This displays ha, in he sampling period, he crude oil, as an imporan raw maerial of indusrial producion, has gained a remarkable soaring marke posiion and exensive acknowledgemen of invesors. As for he fuure work, wih respec o he relaionship beween he crude oil and he gold markes, a leas wo hings have o be conduced furher. For one hing, in his paper, we are focused on heir overall relaionship, so he resuls here are relaively saic wih an average meaning; in he fuure, aenion can be paid o heir dynamic and imevarying ineracion. For 7
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