Forecasting the Price of Oil

Transcription

1 Board of Governors of he Federal Reserve Sysem Inernaional Finance Discussion Papers Number 1022 July 2011 Forecasing he Price of Oil Ron Alquis, Luz Kilian, and Rober J. Vigfusson NOTE: Inernaional Finance Discussion Papers are preliminary maerials circulaed o simulae discussion and criical commen. References in publicaions o Inernaional Finance Discussion Papers (oher han an acknowledgmen ha he wrier has had access o unpublished maerial) should be cleared wih he auhor or auhors. Recen IFDPs are available on he Web a This paper can be downloaded wihou charge from Social Science Research Nework elecronic library a hp://

2 Forecasing he Price of Oil Ron Alquis Luz Kilian Rober J. Vigfusson Bank of Canada Universiy of Michigan Federal Reserve Board CEPR Absrac: We address some of he key quesions ha arise in forecasing he price of crude oil. Wha do applied forecasers need o know abou he choice of sample period and abou he radeoffs beween alernaive oil price series and model specificaions? Are real or nominal oil prices predicable based on macroeconomic aggregaes? Does his predicabiliy ranslae ino gains in ou-of-sample forecas accuracy compared wih convenional no-change forecass? How useful are oil fuures markes in forecasing he price of oil? How useful are survey forecass? How does one evaluae he sensiiviy of a baseline oil price forecas o alernaive assumpions abou fuure demand and supply condiions? How does one quanify risks associaed wih oil price forecass? Can join forecass of he price of oil and of U.S. real GDP growh be improved upon by allowing for asymmeries? Acknowledgemens: We hank Chrisiane Baumeiser for providing access o he world and OECD indusrial producion daa and Ryan Kellogg for providing he Michigan survey daa on gasoline price expecaions. We hank Domenico Giannone for providing he code generaing he Bayesian VAR forecass. We have benefied from discussions wih Chrisiane Baumeiser, Mike McCracken, James Hamilon, Ana María Herrera, Ryan Kellogg, Simone Manganelli, and Keih Sill. We hank David Finer and William Wu for assising us in collecing some of he daa. The views in his paper are solely he responsibiliy of he auhors and should no be inerpreed as reflecing he views of he Board of Governors of he Federal Reserve Sysem or of he Bank of Canada or of any oher person associaed wih he Federal Reserve Sysem or wih he Bank of Canada. Correspondence o: Luz Kilian, Deparmen of Economics, 611 Tappan Sree, Ann Arbor, MI , USA. lkilian@umich.edu. 0

3 1. Inroducion There is widespread agreemen ha unexpeced large and persisen flucuaions in he real price of oil are derimenal o he welfare of boh oil-imporing and oil-producing economies. Reliable forecass of he price of oil are of ineres for a wide range of applicaions. For example, cenral banks and privae secor forecasers view he price of oil as one of he key variables in generaing macroeconomic projecions and in assessing macroeconomic risks. Of paricular ineres is he quesion of he exen o which he price of oil is helpful in predicing recessions. For example, Hamilon (2009), building on he analysis in Edelsein and Kilian (2009), provides evidence ha he recession of lae 2008 was amplified and preceded by an economic slowdown in he auomobile indusry and a deerioraion in consumer senimen. Thus, more accurae forecass of he price of oil have he poenial of improving forecas accuracy for a wide range of macroeconomic oucomes and of improving macroeconomic policy responses. In addiion, some secors of he economy depend direcly on forecass of he price of oil for heir business. For example, airlines rely on such forecass in seing airfares, auomobile companies decide heir produc menu and produc prices wih oil price forecass in mind, and uiliy companies use oil price forecass in deciding wheher o exend capaciy or o build new plans. Likewise, homeowners rely on oil price forecass in deciding he iming of heir heaing oil purchases or wheher o inves in energy-saving home improvemens. Finally, forecass of he price of oil (and he price of is derivaives such as gasoline or heaing oil) are imporan in modeling purchases of energy-inensive durables goods such as auomobiles or home heaing sysems. 1 They also play a role in generaing projecions of energy use, in modeling invesmen decisions in he energy secor, in predicing carbon emissions and climae change, and in designing regulaory policies such as auomoive fuel sandards or gasoline axes. 2 This paper provides a comprehensive analysis of he problem of forecasing he price of oil. In secion 2 we compare alernaive measures of he price of crude oil. In secion 3 we discuss he raionales of alernaive specificaions of he oil price variable in empirical work. Secion 4 sudies he exen o which he nominal price of oil and he real price of oil are predicable based on macroeconomic aggregaes. We documen srong evidence of predicabiliy 1 See, e.g., Kahn (1986), Davis and Kilian (2010). 2 See, e.g., Goldberg (1998), Allco and Wozny (2010), Busse, Kniel and Zeelmeyer (2010), Kellogg (2010). 1

4 in populaion. Predicabiliy in populaion, however, need no ranslae ino ou-of-sample forecasabiliy. The laer quesion is he main focus of secions 5 hrough 8. In secions 5, 6 and 7, we compare a wide range of ou-of-sample forecasing mehods for he nominal price of oil. For example, i is common among policymakers o rea he price of oil fuures conracs as he forecas of he nominal price of oil. We focus on he abiliy of daily and monhly oil fuures prices o forecas he nominal price of oil in real ime compared wih a range of simple ime series forecasing models. We find some evidence ha he price of oil fuures has addiional predicive conen compared wih he curren spo price a he 12-monh horizon; he magniude of he reducion in mean-squared predicion error (MSPE) is modes even a he 12- monh horizon, however, and here are indicaions ha his resul is sensiive o fairly small changes in he sample period and in he forecas horizon. There is no evidence of significan forecas accuracy gains a shorer horizons, and a he long horizons of ineres o policymakers, oil fuures prices are clearly inferior o he no-change forecas. Similarly, forecasing models based on he dollar exchange raes of major commodiy exporers, models based on he Hoelling (1931), and a variey of simple ime series regression models are no successful a significanly lowering he MSPE a shor horizons. There is evidence, however, ha recen percen changes in he nominal price of indusrial raw maerials oher han oil can be used o subsanially and significanly reduce he MSPE of he no-change forecas of he nominal price of oil a horizons of 1 and 3 monhs. The gains may be as large as 22% a he 3-monh horizon. The predicive success of exper survey forecass of he nominal price of oil proved disappoining. Only he one-quarer-ahead EIA forecas significanly improved on he no-change forecas and none of he survey forecass we sudied significanly improved on he MSPE of he no-change forecas a he one-year horizon. Finally, a horizons of several years, forecass based on adjusing he curren spo price for survey inflaion expecaions sysemaically ouperform he no-change forecas by a wide margin. A inermediae horizons, none of hese alernaive forecasing approaches ouperforms he no-change forecas of he nominal price of oil. The bes economeric forecas need no coincide wih he price expecaions of marke paricipans. The laer expecaions daa are rarely observed wih he excepion of daa in he Michigan consumer survey on gasoline price expecaions. We evaluae his survey forecas of he nominal reail price of gasoline agains he no-change forecas benchmark. We also conras 2

5 his survey forecas wih he price of he corresponding fuures conracs. Following Anderson, Kellogg and Sallee (2010), we documen ha, afer conrolling for inflaion, long-erm household gasoline price expecaions are well approximaed by a random walk. This finding has immediae implicaions for modeling purchases of energy-inensive consumer durables. Alhough he nominal price of crude oil receives much aenion in he press, he variable mos relevan for economic modeling is he real price of oil. Secion 8 compares alernaive forecasing models for he real price of oil. We provide evidence ha reduced-form auoregressive and vecor auoregressive models of he global oil marke are more accurae han he random walk forecas of he real price of oil a shor horizons. Even afer aking accoun of he consrains on he real-ime availabiliy of predicors, he MSPE reducions can be subsanial in he shor run. These gains end o diminish a longer horizons, however, and, beyond one or wo years, he no-change forecas of he real price of oil is he predicor wih he lowes MSPE in general. Moreover, he exen of hese MSPE reducions depends on he definiion of he oil price series. An imporan limiaion of reduced-form forecasing models from a policy poin of view is ha hey provide no insigh ino wha is driving he forecas and do no allow he policymaker o explore alernaive hypoheical forecas scenarios. In secion 9, we illusrae how recenly developed srucural vecor auoregressive models of he global oil marke may be used o generae condiional projecions of how he oil price forecas would deviae from he uncondiional forecas benchmark, given alernaive scenarios such as a surge in speculaive demand similar o previous hisorical episodes, a resurgence of he global business cycle, or increased U.S. oil producion. Much of he work on forecasing he price of oil has focused on he dollar price of oil. This is naural because crude oil is ypically raded in U.S. dollars, bu here also is considerable ineres in forecasing he real price of oil faced by oher oil-imporing counries such as he Euro area, Canada, or Japan. In secion 10, we discuss he changes required in forecasing he real price of oil in ha case and show ha accurae forecass may require differen forecasing models for differen counries, given he imporan role of exchange rae flucuaions. Secion 11 focuses on he problem of joinly forecasing U.S. macroeconomic aggregaes such as real GDP growh and he price of oil. Of paricular ineres is he forecasing abiliy of nonlinear ransformaions of he price of oil such as he nominal ne oil price increase or he real 3

6 ne oil price increase. The ne oil price increase is a censored predicor ha assigns zero weigh o ne oil price decreases. There is lile evidence ha his ype of asymmery is refleced in he responses of U.S. real GDP o innovaions in he real price of oil, as documened in Kilian and Vigfusson (2010a,b), bu Hamilon (2010) suggess ha he ne oil price increase specificaion is bes hough of as a parsimonious forecasing device. We provide a comprehensive analysis of his conjecure. Poin forecass of he price of oil are imporan, bu hey fail o convey he large uncerainy associaed wih oil price forecass. Tha uncerainy is capured by he predicive densiy. In secion 12 we discuss various approaches of conveying he informaion in he predicive densiy including measures of price volailiy and of ail condiional expecaions wih paricular emphasis on defining appropriae risk measures. Secion 13 conains a discussion of direcions for fuure research. The concluding remarks are in secion Alernaive Oil Price Measures Figure 1 plos alernaive measures of he nominal price of oil. The longes available series is he Wes Texas Inermediae (WTI) price of crude oil. Daa on U.S. refiners acquisiion cos for domesically produced oil, for impored crude oil and for a composie of hese series are available saring in Figure 1 highlighs sriking differences in he ime series process for he price of oil prior o 1973 and afer The WTI daa unil 1973 end o exhibi a paern resembling a sep-funcion. The price remains consan for exended periods, followed by discree adjusmens. The U.S. wholesale price of oil for used in Hamilon (1983) is numerically idenical wih his WTI series. As discussed in Hamilon (1983, 1985) he discree paern of crude oil price changes during his period is explained by he specific regulaory srucure of he oil indusry during Each monh he Texas Railroad Commission and oher U.S. sae regulaory agencies would forecas demand for oil for he subsequen monh and would se he allowable producion levels for wells in he sae o mee demand. As a resul, much of he cyclically endogenous componen of oil demand was refleced in shifs in quaniies raher han prices. The commission was generally unable or unwilling o accommodae sudden disrupions in oil producion, preferring insead o exploi hese evens o implemen someimes dramaic price increases (Hamilon 1983, p. 230). Whereas he WTI price is a good proxy for he U.S. price for oil during , when 4

7 he U.S. was largely self-sufficien in oil, i becomes less represenaive afer 1973, when he share of U.S. impors of oil rapidly expanded. The price discrepancy beween unregulaed foreign oil and regulaed domesic oil creaed increasing pressure o deregulae he domesic marke. As regulaory conrol weakened in he mid-1970s, adjusmens o he WTI price became much more frequen and smaller in magniude, as shown in he righ panel of Figure 1. By he mid-1980s, he WTI had been deregulaed o he poin ha here was srong comovemen beween all hree oil price series mos of he ime. Figure 2 shows he corresponding oil price daa adjused for U.S. CPI inflaion. The lef panel reveals ha in real erms he price of oil had been falling considerably since he lae 1950s. Tha decline was correced only by he sharp rise in he real price of oil in 1973/74. There has been no pronounced rend in he real price of oil since 1974, bu considerable volailiy. The definiion of he real price of oil is of lesser imporance afer Prior o 1986, one key difference is ha he refiners acquisiion cos for impored crude oil fell in , whereas he real WTI price rose. A second key difference is ha he real WTI price spiked in 1980, whereas he real price of oil impors remained largely sable. Tha paern was only reversed wih he oubreak of he Iran-Iraq War in lae Figure 3 once more highlighs he sriking differences beween he pre- and pos-1973 period. I shows he percen growh rae of he real price of oil. A major srucural change in he disribuion of he price of oil in lae 1973 is readily apparen. 3 Whereas he pre-1973 period is characerized by long periods of low volailiy inerruped by infrequen large posiive price spikes, he pos-1973 period is characerized by high monh-o-monh volailiy. I has been suggesed ha perhaps his volailiy has increased sysemaically afer he collapse of OPEC in lae The answer is somewha sensiive o he exac choice of daes. If one were o dae he OPEC period as , for example, here is no evidence of an increase in he variance of he percen change in he real WTI price of oil. The volailiy in he OPEC period is virually idenical o ha in he pos-opec period of Shifing he saring dae of he OPEC period o , in conras, implies a considerable increase in volailiy afer Exending he ending dae of he OPEC period o include he price collapse in 1986 induced by 3 In relaed work, Dvir and Rogoff (2010) presen formal evidence of a srucural break in he process driving he annual real price of oil in Given his evidence of insabiliy, combining pre- and pos-1973 real oil price daa is no a valid opion. 5

8 OPEC acions, which seems reasonable, on he oher hand, renders he volailiy much more similar across subperiods. Finally, combining he earlier saring dae and he laer ending dae, here is evidence of a reducion in he real price volailiy afer he collapse of OPEC raher han an increase. Below we herefore rea he pos-1973 daa as homogeneous. Which price series is more appropriae for he analysis of pos-1973 daa depends in par on he purpose of he sudy. The WTI price daa (as well as oher measures of he domesic U.S. price of oil) are quesionable o he exen ha hese prices were regulaed unil he mid-1980s and do no reflec he rue scarciy of oil or he price acually paid by U.S. refiners. The refiners acquisiion cos for impored crude oil provides a good proxy for oil price flucuaions in global oil markes, bu may no be represenaive for he price ha U.S. refineries paid for crude oil. The laer price may be capured beer by a composie of he acquisiion cos of domesic and impored crude oil, neiher of which, however, is available before January The real price of oil impors, neverheless, is he price relevan for heories inerpreing oil price shocks as erms-of-rade shocks. Theories ha inerpre oil price shocks as allocaive disurbances, on he oher hand, require he use of reail energy prices, for which he composie refiners acquisiion cos may be a proxy. Below we will consider several alernaive oil price series Alernaive Oil Price Specificaions Alhough an increasing number of empirical sudies of he pos-1973 daa focuses on he real price of oil, many oher sudies have relied on he nominal price of oil. One argumen for he use of nominal oil prices has been ha he nominal price of oil unlike he real price of oil is exogenous wih respec o U.S. macroeconomic condiions and hence linearly unpredicable on he basis of lagged U.S. macroeconomic condiions. 5 This argumen may have some meri for he pre-1973 period, bu is implausible for he pos-1973 period. If he U.S. money supply unexpecedly doubles, for example, hen, according o sandard macroeconomic models, so will all nominal prices denominaed in dollars (including he nominal price of oil), leaving he relaive price or real price of crude oil unaffeced (see Gillman and Nakov 2009). Clearly, one would no wan o inerpre such an episode as an oil price shock involving a doubling of he 4 For furher discussion of he rade-offs beween alernaive oil price definiions from an economic poin of view see Kilian and Vigfusson (2010b). 5 For a review of he relaionship beween he conceps of (sric) exogeneiy and predicabiliy in linear models see Cooley and LeRoy (1985). 6

9 nominal price of oil. Indeed, economic models of he impac of he price of oil on he U.S. economy correcly predic ha such a nominal oil price shock should have no effec on he U.S. economy because heoreical models ineviably are specified in erms of he real price of oil, which has no changed in his example. Anoher argumen in he lieraure has been ha he nominal price of oil can be considered exogenous afer 1973 because i is se by OPEC. This inerpreaion is wihou basis. Firs, here is lile evidence o suppor he noion ha OPEC has been successfully acing as a carel in he 1970s and early 1980s, and he role of OPEC has diminished furher since 1986 (see, e.g., Skee 1988; Smih 2005; Almoguera, Douglas and Herrera 2010). Second, even if we were o accep he noion ha an OPEC carel ses he nominal price of oil, economic heory predics ha his carel price will endogenously respond o U.S. macroeconomic condiions. This heoreical predicion is consisen wih anecdoal evidence of OPEC oil producers raising he price of oil (or equivalenly lowering oil producion) in response o unanicipaed U.S. inflaion, low U.S. ineres raes and he depreciaion of he dollar. Moreover, as observed by Barsky and Kilian (2002), economic heory predics ha he srengh of he oil carel iself (measured by he exen o which individual carel members choose o deviae from carel guidelines) will be posiively relaed o he sae of he global business cycle (see Green and Porer 1984). Thus, boh nominal and real oil prices mus be considered endogenous wih respec o he global economy, unless proven oherwise. A hird and disinc argumen has been ha consumers of refined oil producs choose o respond o changes in he nominal price of oil raher han he real price of oil, perhaps because he nominal price of oil is more visible. In oher words, consumers suffer from money illusion. There is no direc empirical evidence in favor of his behavioral argumen a he micro level. Raher he case for his specificaion, if here is one, has o be based on he predicive success of such models; a success ha, however, has ye o be demonsraed empirically. We will address his quesion in secion 11. Even proponens of using he nominal price in empirical models of he ransmission of oil price shocks have concluded ha here is no sable dynamic relaionship beween percen changes in he nominal price of oil and in U.S. macroeconomic aggregaes. There is evidence from in-sample fiing exercises, however, of a predicive relaionship beween suiable nonlinear ransformaions of he nominal price of oil and U.S. real oupu, in paricular. The mos 7

10 successful of hese ransformaions is he ne oil price increase measure of Hamilon (1996, 2003). Le s denoe he nominal price of oil in logs and he difference operaor. Then he ne oil price increase is defined as:, ne * s max 0, s s, where s * is he highes oil price in he preceding 12 monhs or, alernaively, he preceding 36 monhs. This ransformaion involves wo disinc ideas. One is ha consumers in oil-imporing economies respond o increases in he price of oil only if he increase is large relaive o he recen pas. If correc, he same logic by consrucion should apply o decreases in he price of oil, suggesing a ne change ransformaion ha is symmeric in increases and decreases. The second idea implici in Hamilon s definiion is ha consumers do no respond o ne decreases in he price of oil, allowing us o omi he ne decreases from he model. In oher words, consumers respond asymmerically o ne oil price increases and ne oil price decreases and hey do so in a very specific fashion. Alhough here are heoreical models ha imply he exisence of an asymmery in he response of he economy o oil price increases and decreases, hese models do no imply he specific nonlinear srucure embodied in he ne increase measure nor do hey imply ha he ne decrease measure should receive zero weigh. Neverheless, Hamilon s nominal ne oil price increase variable has become one of he leading specificaions in he lieraure on predicive relaionships beween he price of oil and he U.S. economy. Hamilon (2010), for example, inerpres his specificaion as capuring nonlinear changes in consumer senimen in response o nominal oil price increases. 6 As wih oher oil price specificaions here is reason o expec lagged feedback from global macroeconomic aggregaes o he ne oil price increase. Whereas Hamilon (2003) made he case ha ne oil price increases in he 1970s, 1980s and 1990s were capuring exogenous evens in he Middle Eas, Hamilon (2009) concedes ha he ne oil price increase of was driven in large par by a surge in he demand for oil. Kilian (2009a,b; 2010), on he oher hand, provides evidence based on srucural VAR models ha in fac mos ne oil price increases have conained a large demand componen driven by global macroeconomic condiions, even 6 Ineresingly, he behavioral raionale for he ne oil price increase measure applies equally o he nominal price of oil and he real price of oil. Alhough Hamilon (2003) applied his ransformaion o he nominal price of oil, several oher sudies have recenly explored models ha apply he same ransformaion o he real price of oil (see, e.g., Kilian and Vigfusson 2010a; Herrera, Lagalo and Wada 2010). 8

11 prior o This finding is also consisen wih he empirical resuls in Baumeiser and Peersman (2010). For now we se aside all nonlinear ransformaions of he price of oil and focus on linear forecasing models for he nominal price of oil and for he real price of oil. Nonlinear join forecasing models for U.S. real GDP and he price of oil based on ne oil price increases are discussed in secion Granger Causaliy Tess Much of he exising work on predicing he price of oil has focused on esing for he exisence of a predicive relaionship from macroeconomic aggregaes o he price of oil. The exisence of predicabiliy in populaion is a necessary precondiion for ou-of-sample forecasabiliy (see Inoue and Kilian 2004a). Wihin he linear VAR framework he absence of predicabiliy from one variable o anoher in populaion may be esed using Granger non-causaliy ess Nominal Oil Price Predicabiliy The Pre-1973 Evidence Granger causaliy from macroeconomic aggregaes o he price of oil has received aenion in par because Granger non-causaliy is one of he esable implicaions of sric exogeneiy. The noion ha he percen change in he nominal price of oil may be considered exogenous wih respec o he U.S. economy was bolsered by evidence in Hamilon (1983), who observed ha here is no apparen Granger causaliy from U.S. domesic macroeconomic aggregaes o he percen change in he nominal price of oil during Of course, he absence of Granger causaliy is merely a necessary condiion for sric exogeneiy. Moreover, a failure o rejec he null of no Granger causaliy is a bes suggesive; i does no esablish he validiy of he null hypohesis. Hamilon s case for he exogeneiy of he nominal price of oil wih respec o he U.S. economy herefore resed primarily on he unique insiuional feaures of he oil marke during his period, discussed in secion 2, and on hisorical evidence ha unexpeced supply disrupions under his insiuional regime appear o be associaed wih exogenous poliical evens in he Middle Eas, allowing us o rea he resuling price spikes as exogenous wih respec o he U.S. economy. For a more nuanced view of hese hisorical episodes see Kilian (2008b; 2009a,b; 2010). Even if we accep Hamilon s inerpreaion of he pre-1973 period, he 9

12 insiuional condiions ha Hamilon (1983) appeals o ceased o exis in he early 1970s, and Hamilon s resuls for he period are mainly of hisorical ineres. The real quesion for our purposes is o wha exen here is evidence ha oil prices can be prediced from macroeconomic aggregaes in he pos-1973 period The Pos-1973 Evidence There is widespread agreemen among oil economiss ha, saring in 1973, nominal oil prices mus be considered endogenous wih respec o U.S. macroeconomic variables (see Kilian 2008a). Wheher his endogeneiy makes he nominal price of oil predicable on he basis of lagged U.S. macroeconomic aggregaes depends on wheher he price of oil behaves like a ypical asse price or no. In he former case, one would expec he nominal price of oil o incorporae informaion abou expeced U.S. macroeconomic condiions immediaely, rendering he nominal price of oil linearly unpredicable on he basis of lagged U.S. macroeconomic aggregaes. This line of reasoning is familiar from he analysis of sock and bond prices as well as exchange raes. 7 In he laer case, he endogeneiy of he nominal price of oil wih respec o he U.S. economy implies ha lagged changes in U.S. macroeconomic aggregaes have predicive power for he nominal price of oil in he pos-1973 daa (see, e.g., Cooley and LeRoy 1985). A recen sudy by Kilian and Vega (2010) helps resolve he quesion of which inerpreaion is more appropriae. Kilian and Vega find no evidence of sysemaic feedback from news abou a wide range of U.S. macroeconomic aggregaes o he nominal price of oil wihin a monh. This lack of evidence is in sharp conras o he evidence for ypical asse prices, so lack of power canno explain he absence of significan feedback from U.S. macroeconomic news o he nominal price of oil. These wo resuls in conjuncion allow us o rule ou he pure asse price inerpreaion of he nominal price of oil. We conclude ha, if he nominal price of oil is endogenous wih respec o lagged U.S. macroeconomic aggregaes, hen hese macroeconomic aggregaes mus have predicive power a leas in populaion. Predicabiliy in he conex of linear vecor auoregressions may be esed using Granger causaliy ess. Table 1a invesigaes he evidence of Granger causaliy from seleced nominal U.S. macroeconomic variables o he nominal price of oil. All resuls are based on pairwise vecor auoregressions. The lag order is fixed a 12. Similar resuls would have been obained 7 Hamilon (1994, p. 306) illusraes his poin in he conex of a model of sock prices and expeced dividends. 10

13 wih 24 lags. We consider four alernaive nominal oil price series. The evaluaion period is alernaively or I is no clear a priori which oil price series is bes suied for finding predicabiliy. On he one hand, one would expec he evidence of predicabiliy o be sronger for oil price series ha are unregulaed (such as he refiners acquisiion cos for impored crude oil) han for parially regulaed domesic price series. On he oher hand, o he exen ha he 1973/74 oil price shock episode was driven by moneary facors, as proposed by Barsky and Kilian (2002), one would expec sronger evidence in favor of such feedback from he WTI price series ha includes his episode. There are several reasons o expec he dollar-denominaed nominal price of oil o respond o changes in nominal U.S. macroeconomic aggregaes. One channel of ransmission is purely moneary and operaes hrough U.S. inflaion. For example, Gillman and Nakov (2009) sress ha changes in he nominal price of oil mus occur in equilibrium jus o offse persisen shifs in U.S. inflaion, given ha he price of oil is denominaed in dollars. Indeed, he Granger causaliy ess in Table 1a indicae highly significan lagged feedback from U.S. headline CPI inflaion o he percen change in he nominal WTI price of oil for he full sample, consisen wih he findings in Gillman and Nakov (2009). The evidence for he oher oil price series is somewha weaker wih he excepion of he refiners acquisiion cos for impored crude oil, bu ha resul may simply reflec a loss of power when he sample size is shorened. 9 Gillman and Nakov view changes in inflaion in he pos-1973 period as rooed in persisen changes in he growh rae of money. 10 Thus, an alernaive approach of esing he hypohesis of Gillman and Nakov (2009) is o focus on Granger causaliy from moneary aggregaes o he nominal price of oil. Given he general insabiliy in he link from changes in moneary aggregaes o inflaion, one would no necessarily expec changes in moneary aggregaes o have much predicive power for he price of oil, excep perhaps in he 1970s (see Barsky and Kilian 2002). Table 1a neverheless shows ha here is considerable lagged feedback 8 In he former case, he pre observaions are only used as pre-sample observaions. 9 I can be shown ha similar resuls hold for he CPI excluding energy, albei no for he CPI excluding food and energy. 10 For an earlier exposiion of he role of moneary facors in deermining he price of oil see Barsky and Kilian (2002). Boh Barsky and Kilian (2002) and Gillman and Nakov (2009) view he shifs in U.S. inflaion in he early 1970s as caused by persisen changes in he growh rae of he money supply, bu here are imporan differences in emphasis. Whereas Barsky and Kilian sress he real effecs of unanicipaed moneary expansions on real domesic oupu, on he demand for oil and hence on he real price of oil, Gillman and Nakov sress ha he relaive price of oil mus no decline in response o a moneary expansion, necessiaing a higher nominal price of oil, consisen wih anecdoal evidence on OPEC price decisions (see, e.g., Kilian 2008b). These wo explanaions are complemenary. 11

14 from narrow measures of money such as M1 for he refiners acquisiion cos and he WTI price of oil based on he evaluaion period. The much weaker evidence for he full WTI series may reflec he sronger effec of regulaory policies on he WTI price during he early 1970s. The evidence for broader moneary aggregaes such as M2 having predicive power for he nominal price of oil is much weaker, wih only one es saisically significan. A hird approach o esing for a role for U.S. moneary condiions relies on he fac ha rising dollar-denominaed non-oil commodiy prices are hough o presage rising U.S. inflaion. To he exen ha oil price adjusmens are more sluggish han adjusmens in oher indusrial commodiy prices, one would expec changes in nominal Commodiy Research Bureau (CRB) spo prices o Granger cause changes in he nominal price of oil. Indeed, Table 1a indicaes highly saisically significan lagged feedback from CRB sub-indices for indusrial raw maerials and for meals. In conras, neiher shor-erm ineres raes nor rade-weighed exchange raes have significan predicive power for he nominal price of oil. According o he Hoelling model, one would expec he nominal price of oil o grow a he nominal rae of ineres, providing ye anoher link from U.S. macroeconomic aggregaes o he nominal price of oil. Table 1a, however, shows no evidence of saisically significan feedback from he 3-monh T-Bill rae o he price of oil. This finding is no surprising as he price of oil clearly was no growing a he rae of ineres even approximaely (see Figure 1). Nor is here evidence of significan feedback from lagged changes in he rade-weighed nominal U.S. exchange rae. This does no mean ha all bilaeral exchange raes lack predicive power. In relaed work, Chen, Rossi and Rogoff (2010) show ha he floaing exchange raes of small commodiy exporers (including Ausralia, Canada, New Zealand, Souh Africa and Chile) wih respec o he dollar have remarkably robus forecasing power for global prices of heir commodiy expors. The explanaion is ha hese exchange raes are forward looking and embody informaion abou fuure movemens in commodiy expor markes ha canno easily be capured by oher means. Alhough Chen e al. s analysis canno be exended o oil exporers such as Saudi Arabia because Saudi Arabia s exchange rae has no been floaing freely, he bilaeral dollar exchange raes of Ausralia, Canada, New Zealand and Souh Africa may serve as a proxy for expeced broad-based movemens in indusrial commodiy prices ha may also be helpful in predicing changes in he nominal price of oil. According o Chen e al., he share of nonagriculural 12

15 commodiy expors is larges in Souh Africa, followed by Ausralia, Canada and New Zealand. In general, he larger he share of nonagriculural expors, he higher one would expec he predicive power for indusrial commodiies o be. For he price of oil, he share of energy expors such as crude oil, coal and naural gas may be an even beer indicaor of predicive power, suggesing ha Canada should have he highes predicive power for he price of oil, followed by Ausralia, Souh Africa, and New Zealand. Table 1b shows srong evidence of predicabiliy for all bilaeral exchange raes bu ha of New Zealand, consisen wih his inuiion. Moreover, when using he dollar exchange rae of he Japanese Yen and of he Briish Pound as a conrol group, here is no significan evidence of Granger causaliy from exchange raes o he price of oil. 11 The resuls in Table 1b are also very much in line wih he direc evidence of predicive power from nonagriculural commodiy price indices in Table 1a Reconciling he Pre- and Pos-1973 Evidence on Predicabiliy Tables 1a and 1b sugges ha indicaors of U.S. inflaion have significan predicive power for he nominal price of oil. This resul is in sriking conras o he pre-1973 period. As shown in Hamilon (1983) using quarerly daa and in Gillman and Nakov (2009) using monhly daa, here is no significan Granger causaliy from U.S. inflaion o he percen change in he nominal price of oil in he 1950s and 1960s. This difference in resuls is suggesive of a srucural break in lae 1973 in he predicive relaionship beween he price of oil and he U.S. economy. One reason ha he pre-1973 predicive regressions differ from he pos-1973 regressions is ha prior o 1973 he nominal price of oil was adjused only a discree inervals (see Figure 1). Because he nominal oil price daa was generaed by a discree-coninuous choice model, convenional vecor auoregressions by consrucion are no appropriae for esing predicabiliy. One way of illusraing his problem is by fiing a random walk model wih drif o hese daa and ploing randomly generaed draws from he fied model agains he acual daa. Figure 4 shows one such sequence. Wihou loss of generaliy, Figure 4 illusraes ha he fied ime series model model like any convenional ime series model is unable o replicae he disconinuous adjusmen process underlying he pre-1973 WTI daa. This is rue even allowing for lepokuric error disribuions. In oher words, auoregressive or moving average ime series processes are inappropriae for hese daa and ess based on such models have o be viewed wih 11 Alhough he U.K. has been exporing crude oil saring in he lae 1970s, is share of peroleum expors is oo low o consider he U.K. a commodiy exporer (see Kilian, Rebucci and Spaafora 2009). 13

16 cauion. This problem wih he pre-1973 daa may be amelioraed by deflaing he nominal price of oil, which renders he oil price daa coninuous and more amenable o VAR analysis (see Figure 2). Addiional problems arise, however, when combining oil price daa generaed by a discree-coninuous choice process wih daa from he pos-texas Railroad Commission era ha are fully coninuous. Concern over low power has promped many applied researchers o combine oil price daa for he pre-1973 and pos-1973 period in he same model when sudying he predicive relaionship from macroeconomic aggregaes o he price of oil. This approach is obviously inadvisable when dealing wih nominal oil price daa, as already discussed. Perhaps less obviously, his approach is equally unappealing when dealing wih vecor auoregressions involving he real price of oil. The problem ha he naure and speed of he feedback from U.S. macroeconomic aggregaes o he real price of oil differs by consrucion, depending on wheher he nominal price of oil is emporarily fixed or no. This insabiliy manifess iself in a srucural break in he predicive regressions commonly used o es for lagged poenially nonlinear feedback from he real of price of oil o real GDP growh (see, e.g., Balke, Brown and Yücel 2002). The p-value for he null hypohesis ha here is no break in 1973.Q4 in he coefficiens of his predicive regression is (see Kilian and Vigfusson 2010b). 12 For ha reason, regression esimaes of he relaionship beween he real price of oil and domesic macroeconomic aggregaes obained from he enire pos-war period are no informaive abou he srengh of hese relaionships in pos-1973 daa. 13 In he analysis of he real price of oil below we herefore resric he evaluaion period o sar no earlier han Real Oil Price Predicabiliy in he Pos-1973 Period I is well esablished in naural resource heory ha he real price of oil increases in response o low expeced real ineres raes and in response o high real aggregae oupu. 14 Any analysis of he role of expeced real ineres raes is complicaed by he fac ha inflaion expecaions are 12 Even allowing for he possibiliy of daa mining, his break remains saisically significan a he 5% level. 13 This siuaion is analogous o ha of combining real exchange rae daa for he pre- and pos-breon Woods periods in sudying he speed of mean reversion oward purchasing power pariy. Clearly, he speed of adjusmen oward purchasing power pariy will differ if one of he adjusmen channels is shu down, as was he case under he fixed exchange rae sysem, han when boh prices and exchange raes are free o adjus as was he case under he floaing rae sysem. Thus, regressions on long ime spans of real exchange rae daa produce average esimaes ha by consrucion are no informaive abou he speed of adjusmen in he Breon Woods sysem. 14 For a review of his lieraure see Barsky and Kilian (2002). 14

17 difficul o pin down, especially a longer horizons, and ha he relevan horizon for resource exracion is no clear. We herefore focus on he predicive power of flucuaions in real aggregae oupu. Table 2 repors p-values for ess of he hypohesis of Granger non-causaliy from seleced measures of real aggregae oupu o he real price of oil. A naural saring poin is U.S. real GDP. Economic heory implies ha U.S. real GDP and he real price of oil are muually endogenous and deermined joinly. For example, one would expec an unexpeced increase in U.S. real GDP, all else equal, o increase he flow demand for crude oil and hence he real price of oil. Unless he real price of oil is forward looking and already embodies all informaion abou fuure U.S. real GDP, a reasonable conjecure herefore is ha lagged U.S. real GDP should help predic he real price of oil. Recen research by Kilian and Murphy (2010) has shown ha he real price of oil indeed conains an asse price componen, bu ha his componen mos of he ime explains only a small fracion of he hisorical variaion in he real price of oil. Thus, we would expec flucuaions in U.S. real GDP o predic he real price of oil a leas in populaion. Under he assumpion ha he join process can be approximaed by a linear vecor auoregression, his implies he exisence of Granger causaliy from U.S. real GDP o he real price of oil Nowihsanding his presumpion, Table 2 indicaes no evidence of Granger causaliy from U.S. real GDP growh o he real price of oil. This finding is robus o alernaive mehods of derending and alernaive lag orders. In he absence of insananeous feedback from U.S. real GDP o he real price of oil, a finding of Granger noncausaliy from U.S. real GDP o he real price of oil in conjuncion wih evidence ha he real price of oil Granger causes U.S. real GDP would be consisen wih he real price of oil being sricly exogenous wih respec o U.S. real GDP. I can be shown, however, ha he evidence of Granger causaliy from he real price of oil o U.S. real GDP is no much sronger. When linear derending (LT), Hodrick-Presco-filering (HP) and log-differencing (DIF) he daa, which each ransformaion applied symmerically o boh ime series in a bivariae VAR(4) model, here is only one marginal rejecion a he 10% level. This rejecion occurs for he real WTI price in differences when evaluaed on he 1973.I IV period. There are no rejecions using oher daa ransformaions or shorer evaluaion periods. The fac ha here are few rejecions, if any, in eiher direcion suggess ha he Granger noncausaliy es may simply lack power for samples of his lengh. In fac, his is precisely he argumen ha promped some researchers o combine daa from he pre-1973 and pos

18 period a sraegy ha we do no recommend for he reasons discussed in secion Anoher likely explanaion of he failure o rejec he null of no predicabiliy is model misspecificaion. I is well known ha Granger causaliy in a bivariae model may be due o an omied hird variable, bu equally relevan is he possibiliy of Granger noncausaliy in a bivariae model arising from omied variables (see Lükepohl 1982). This possibiliy is more han a heoreical curiosiy in our conex. Recen models of he deerminaion of he real price of oil afer 1973 have sressed ha his price is deermined in global markes (see, e.g., Kilian 2009a; Kilian and Murphy 2010). In paricular, he demand for oil depends no merely on U.S. demand, bu on global demand. The bivariae model for he real price of oil and U.S. real GDP by consrucion omis flucuaions in real GDP in he res of he world. The relevance of his poin is ha offseing movemens in real GDP abroad can easily offse he effec of changes in U.S. real GDP, obscuring he dynamic relaionship of ineres and lowering he power of he Granger causaliy es. Only when real GDP flucuaions are highly correlaed across counries would we expec U.S. real GDP o be a good proxy for world real GDP. 15 In addiion, as he U.S. share in world GDP evolves, by consrucion so do he predicive correlaions underlying Table 2. In his regard, Kilian and Hicks (2010) have documened dramaic changes in he PPPadjused share in GDP of he major indusrialized economies and of he main emerging economies in recen years ha cas furher doub on he U.S. real GDP resuls in Table 2. For example, oday, China and India combined have almos as high a share in world GDP as he Unied Saes. A closely relaed hird poin is ha flucuaions in real GDP are a poor proxy for business-cycle driven flucuaions in he demand for oil. I is well known, for example, ha in recen decades he share of services in U.S. real GDP has grealy expanded a he cos of manufacuring and oher secors. Clearly, real GDP growh driven by he non-service secor will be associaed wih disproporionaely higher demand for oil and oher indusrial commodiies han real GDP growh in he service secor. This provides one more reason why one would no expec a srong or sable predicive relaionship beween U.S. real GDP and he real price of oil. 15 For example, he conjuncion of rising growh in emerging Asia wih unchanged growh in he U.S. all else equal would cause world GDP growh and hence he real price of oil o increase, bu would imply a zero correlaion beween U.S. real GDP growh and changes in he real price of oil. Alernaively, slowing growh in Japan and Europe may offse rising growh in he U.S., keeping he real price of oil sable and implying a zero correlaion of U.S. growh wih changes in he real price of oil. This does no mean ha here is no feedback from lagged U.S. real GDP. Indeed, wih lower U.S. growh he increase in he real price of oil would have slowed in he firs example and wihou offseing U.S. growh he real price of oil would have dropped in he second example. 16

19 An alernaive quarerly predicor ha parially addresses hese las wo concerns is quarerly world indusrial producion from he U.N. Monhly Bullein of Saisics. This series has recenly been inroduced by Baumeiser and Peersman (2010) in he conex of modeling he demand for oil. Alhough here are serious mehodological concerns regarding he consrucion of any such index, as discussed in Beyer, Doornik and Hendry (2001), one would expec his series o be a beer proxy for global flucuaions in he demand for crude oil han U.S. real GDP. Indeed, Table 2 shows srong evidence of Granger causaliy from world indusrial producion o he real WTI price in he full sample period for he LT model. For he four shorer series here are hree addiional rejecions for he LT model; he oher p-value is no much higher han 0.1. The reducion in p-values compared wih U.S. real GDP is dramaic. The fac ha here is evidence of predicabiliy only for he linearly derended series makes sense. As discussed in Kilian (2009b), he demand for indusrial commodiies such as crude oil is subjec o long swings. Derending mehods such as HP filering (and even more so firs differencing) eliminae much of his low frequency covariaion in he daa, removing he feaure of he daa we are ineresed in esing. Addiional insighs may be gained by focusing on monhly raher han quarerly predicors. The firs conender in Table 3 is he Chicago Fed Naional Aciviy Index (CFNAI). This is a broad measure of monhly real economic aciviy in he Unied Saes obained from applying principal componen analysis o a wide range of monhly indicaors of real aciviy expressed in growh raes (see Sock and Wason 1999). As in he case of quarerly U.S. real GDP, here is no evidence of Granger causaliy. If we rely on U.S. indusrial producion as he predicor, here is weak evidence of feedback o he domesic price of oil for he LT model. For oher measures of he real price of oil, none of he es saisics is significan, alhough we again noe he sharp drop in p-values as we replace he CFNAI by indusrial producion. There are no monhly daa on world indusrial producion, bu he OECD provides an indusrial producion index for OECD economies and six seleced non-oecd counries. As expeced, he rejecions of Granger noncausaliy become much sronger when we focus on OECD+6 indusrial producion. Table 3 indicaes srong and sysemaic Granger causaliy, especially for he LT specificaion. Even OECD+6 indusrial producion, however, is an imperfec proxy for business-cycle driven flucuaions in he global demand for indusrial commodiies such as crude oil. 17

20 One alernaive is he index of global real aciviy recenly proposed in Kilian (2009a). This index does no rely on any counry weighs and has ruly global coverage. I has been consruced wih he explici purpose of measuring flucuaions in he broad-based demand for indusrial commodiies associaed wih he global business cycle. 16 As expeced, he las row of Table 3 indicaes even sronger evidence of Granger causaliy from his index o he real price of oil, regardless of he definiion of he real price of oil. I also highlighs a fourh issue. There is evidence ha allowing for wo years worh of lags raher han one year ofen srenghens he significance of he rejecions. This finding mirrors he poin made in Hamilon and Herrera (2004) ha i is essenial o allow for a rich lag srucure in sudying he dynamic relaionship beween he economy and he price of oil. Alhough none of he proxies for global flucuaions in demand is wihou limiaions, we conclude ha here is a robus paern of Granger causaliy, as we correc for problems of model misspecificaion and of daa mismeasuremen ha undermine he power of he es. This conclusion is furher srenghened by evidence in Kilian and Hicks (2010) based on disribued lag models ha revisions o professional real GDP growh forecass have significan predicive power for he real price of oil during afer weighing each counry s forecas revision by is PPP-GDP share. Predicabiliy in populaion, of course, does no necessarily imply ou-of-sample forecasabiliy (see Inoue and Kilian 2004a). The nex wo secions herefore examine alernaive approaches o forecasing he nominal and he real price of oil ouof-sample. 5. Shor-Horizon Forecass of he Nominal Price of Oil The mos common approach o forecasing he nominal price of oil is o rea he price of he oil 16 This index is consruced from ocean shipping freigh raes. The idea of using flucuaions in shipping freigh raes as indicaors of shifs in he global real aciviy daes back o Isserlis (1938) and Tinbergen (1959). The panel of monhly freigh-rae daa underlying he global real aciviy index was colleced manually from Drewry s Shipping Monhly using various issues since The daa se is resriced o dry cargo raes. The earlies raw daa are indices of iron ore, coal and grain shipping raes compiled by Drewry s. The remaining series are differeniaed by cargo, roue and ship size and may include in addiion shipping raes for oilseeds, ferilizer and scrap meal. In he 1980s, here are abou 15 differen raes for each monh; by 2000 ha number rises o abou 25; more recenly ha number has dropped o abou 15. The index was consruced by exracing he common componen in he nominal spo raes. The resuling nominal index is expressed in dollars per meric on, deflaed using he U.S. CPI and derended o accoun for he secular decline in shipping raes. For his paper, his series has been exended based on he Balic Exchange Dry Index, which is available from Bloomberg. The laer index, which is commonly discussed in he financial press, is essenially idenical o he nominal index in Kilian (2009a), bu only available since