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in publicaions o Inernaional Finance Discussion Papers (oher han an acknowledgmen ha he wrier has had access o unpublished maerial) should be cleared wih he auhor or auhors.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. [email protected]. 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

21 fuures conrac of mauriy h as he h-period forecas of he price of oil. 17 In paricular, many cenral banks and he Inernaional Moneary Fund (IMF) use he price of NYMEX oil fuures as a proxy for he marke s expecaion of he spo price of crude oil. A widespread view is ha prices of NYMEX fuures conracs are no only good proxies for he expeced spo price of oil, bu also beer predicors of oil prices han economeric forecass. Forecass of he spo price of oil are used as inpus in he macroeconomic forecasing exercises ha hese insiuions produce. For example, he European Cenral Bank (ECB) employs oil fuures prices in consrucing he inflaion and oupu-gap forecass ha guide moneary policy (see Svensson 2005). Likewise he IMF relies on fuures prices as a predicor of fuure spo prices (see, e.g., Inernaional Moneary Fund 2005, p. 67; 2007, p. 42). Fuures-based forecass of he price of oil also play a role in policy discussions a he Federal Reserve Board. This is no o say ha forecasers do no recognize he poenial limiaions of fuures-based forecass of he price of oil. Neverheless, he percepion among many macroeconomiss, financial analyss and policymakers is ha oil fuures prices, imperfec as hey may be, are he bes available forecass of he spo price of oil. Such aiudes have persised nowihsanding recen empirical evidence o he conrary and nowihsanding he developmen of heoreical models aimed a explaining he lack of predicive abiliy of oil fuures prices and spreads (see, e.g., Knesch 2007; Alquis and Kilian 2010). Ineresingly, he convenional wisdom in macroeconomics and finance is a odds wih long-held views abou sorable commodiies in agriculural economics. For example, Peck (1985) emphasized ha expecaions are refleced nearly equally in curren and in fuures prices. In his sense cash prices will be nearly as good predicions of subsequen cash prices as fuures prices, echoing in urn he discussion in Working (1942) who was criical of he general opinion among economiss ha prices of commodiy fuures are he marke expression of consciously formed opinions on probable prices in he fuure whereas spo prices are no generally supposed o reflec anicipaion of he fuure in he same degree as fuures prices. Working specifically criicized he error of supposing ha he prices of fuures end o be 17 Fuures conracs are financial insrumens ha allow raders o lock in oday a price a which o buy or sell a fixed quaniy of he commodiy a a predeermined dae in he fuure. Fuures conracs can be reraded beween incepion and mauriy on a fuures exchange such as he New York Mercanile Exchange (NYMEX). The NYMEX offers insiuional feaures ha allow raders o ransac anonymously. These feaures reduce individual defaul risk and ensure homogeneiy of he raded commodiy, making he fuures marke a low-cos and liquid mechanism for hedging agains and for speculaing on oil price risks. The NYMEX ligh swee crude conrac is he mos liquid and larges volume marke for crude oil rading. 19

22 more srongly influenced by hese anicipaions han are spo prices. The nex secion invesigaes he empirical meris of hese compeing views in he conex of oil markes Forecasing Mehods Based on Monhly Oil Fuures Prices Alquis and Kilian (2010) recenly provided a comprehensive evaluaion of he forecas accuracy of models based on monhly oil fuures prices using daa ending in Below we updae heir analysis unil and expand he range of alernaive forecasing models under consideraion. 18 In his subsecion, aenion is limied o forecas horizons of up o one year. Le (h) F denoe he curren nominal price of he fuures conrac ha maures in h periods, S he curren nominal spo price of oil, and E ] he expeced fuure spo price a dae +h condiional on informaion available a. [ S h A naural benchmark for forecass based on he price of oil fuures is provided by he random walk model wihou drif. This model implies ha changes in he spo price are unpredicable, so he bes forecas of he spo price of crude oil is simply he curren spo price: S ˆ S h 1, 3, 6, 9, 12 (1) h This forecas is also known as he no-change forecas. In conras, he common view ha oil fuures prices are he bes available predicor of fuure oil prices implies he forecasing model: Sˆ ( h) h F 1, 3, 6, 9, 12 h. (2) A closely relaed approach o forecasing he spo price of oil is o use he spread beween he fuures price and he spo price as an indicaor of wheher he price of oil is likely o go up or down. If he fuures price equals he expeced spo price, he spread should be an indicaor of he expeced change in spo prices. The raionale for his approach is clear from dividing F E[ S ] by S, which resuls in E S S F S We explore he forecasing ( h) h ( h) [ h]. accuracy of he spread based on several alernaive forecasing models. The simples model is: ˆ ( h) h 1 / S S ln( F S ), h 1, 3, 6, 9, 12 (3) To allow for he possibiliy ha he spread may be a biased predicor, i is common o relax he 18 Because he Daasream daa for he daily WTI spo price of oil used in Alquis and Kilian (2010) were disconinued, we rely insead on daa from he Energy Informaion Adminisraion. As a resul he esimaion window for he forecas comparison is somewha shorer in some cases han in Alquis and Kilian (2010). 20

23 assumpion of a zero inercep: ˆ ( h) Sh S 1 ˆ ln( F / S), h 1, 3, 6, 9,12 (4) Alernaively, one can relax he proporionaliy resricion: ˆ ( ) 1 ˆ ln( h Sh S F / S ), h 1, 3, 6, 9,12 (5) Finally, we can relax boh he unbiasedness and proporionaliy resricions: ˆ ( ) 1 ˆ h ShS ˆ ln( F / S), h 1, 3, 6, 9,12. (6) Here ˆ and ˆ denoe leas-squares esimaes obained in real ime from recursive regressions. The objecive is o compare he real-ime forecas accuracy of models (1)-(6). Our empirical analysis is based on daily prices of crude oil fuures raded on he NYMEX from he commercial provider Price-Daa.com. The ime series begins in March 30, 1983, when crude oil fuures were firs raded on he NYMEX, and exends hrough December 31, Conracs are for delivery a Cushing, OK. Trading ends four days prior o he 25 h calendar day preceding he delivery monh. If he 25 h is no a business day, rading ends on he fourh business day prior o he las business day before he 25 h calendar day. A common problem in consrucing monhly fuures prices of a given mauriy is ha an h-monh conrac may no rade on a given day. We idenify he h-monh fuures conrac rading closes o he las rading day of he monh and use he price associaed wih ha conrac as he end-of-monh value. Our approach is moivaed by he objecive of compuing in a consisen manner end-of-monh ime series of oil fuures prices for differen mauriies. This allows us o mach up end-of-monh spo prices and fuures prices as closely as possible. The daily spo price daa are obained from he webpage of he Energy Informaion Adminisraion and refer o he price of Wes Texas Inermediae crude oil available for delivery a Cushing, OK. Tables 4 hrough 8 assess he predicive accuracy of various forecasing models agains he benchmark of a random walk wihou drif for horizons of 1, 3, 6, 9, and 12 monhs. The forecas evaluaion period is wih suiable adjusmens, as he forecas horizon is varied. The assessmen of which forecasing model is mos accurae may depend on he loss funcion of he forecaser (see Ellio and Timmermann 2008). We repor resuls for he MSPE and he relaive frequency wih which a forecasing model correcly predics he sign of he 21

24 change in he spo price based on he success raio saisic of Pesaran and Timmermann (2009). We formally es he null hypohesis ha a given candidae forecasing model is as accurae as he random walk wihou drif agains he alernaive ha he candidae model is more accurae han he no-change forecas. Suiably consruced p-values are shown in parenheses (as described in he noes o Table 4). I should be noed ha commonly used ess of equal predicive accuracy for nesed models (including he ess we rely on in his chaper) by consrucion are ess of he null of no predicabiliy in populaion raher han ess of equal ouof-sample MSPEs (see, e.g., Inoue and Kilian 2004a,b; Clark and McCracken 2010). This means ha hese ess will rejec he null of equal predicive accuracy more ofen han hey should under he null, suggesing cauion in inerpreing es resuls ha are only marginally saisically significan. We will discuss his poin in more deail furher below. This concern does no affec nonnesed forecas accuracy comparisons. Row (2) of Tables 4 hrough 8 shows ha he oil fuures price has lower MSPE han he no-change forecas a all horizons considered, bu he differences are mosly marginal and none of he differences is saisically significan. For all pracical purposes, he forecass are equally accurae. Nor do fuures forecass have imporan advanages when i comes o predicing he sign of he change in he nominal price of oil. Only a he 12-monh horizon is he success raio significan a he 10 percen level. The improvemen in his case is 5.7%. A he 1-monh and 3- monh horizon, he success raio of he fuures price forecas acually is inferior o ossing a coin. Similarly, rows (3)-(6) in Tables 4 hrough 8 show no sysemaic difference beween he MSPE of he spread-based forecass and ha of he random walk forecas. In no case is here a saisically significan reducion in he MSPE from using he spread model. In he rare cases in which one of he spread models significanly helps predic he direcion of change, he gains in accuracy are quie moderae. No spread model is uniformly superior o he ohers. We conclude ha here is no compelling evidence ha, over his sample period, monhly oil fuures prices were more accurae predicors of he nominal price of oil han simple nochange forecass. Pu differenly, a forecaser using he mos recen spo price would have done jus as well in forecasing he nominal price of oil. This finding is broadly consisen wih he empirical resuls in Alquis and Kilian (2010). To he exen ha some earlier sudies have repored evidence more favorable o oil fuures prices, he difference in resuls can be raced o 22

25 he use of shorer samples Oher Forecasing Mehods The preceding subsecion demonsraed ha simple no-change forecass of he price of oil end o be as accurae in he MSPE sense as forecass based on oil fuures prices, bu his does no rule ou ha here are alernaive predicors wih even lower MSPE. Nex we broaden he range of forecasing mehods o include some addiional predicors ha are of pracical ineres. One approach is he use of parsimonious regression-based forecasing models of he spo price of crude oil. Anoher approach is he use of survey daa. While economiss have used survey daa exensively in measuring he risk premium embedded in foreign exchange fuures, his approach has no been applied o oil fuures, wih he excepion of recen work by Wu and McCallum (2005). Ye anoher approach is o exploi he implicaion of he Hoelling (1931) model ha he price of oil should grow a he rae of ineres. Finally, we also consider forecasing models ha adjus he no-change forecas for inflaion expecaions and for recen percen changes in oher nominal prices Parsimonious Economeric Forecass One example of parsimonious economeric forecasing models is he random walk model wihou drif inroduced earlier. An alernaive is he double-differenced forecasing model proposed in Hendry (2006). Hendry observed ha when ime series are subjec o infrequen rend changes, he no-change forecas may be improved upon by exrapolaing oday s oil price a he mos recen growh rae: ˆ 1 h S S s h 1, 3, 6, 9, 12 (7) where h s denoes he percen growh rae beween 1 and. In oher words, we apply he nochange forecas o he growh rae raher han he level. Alhough here are no obvious indicaions of srucural change in our sample period, i is worh exploring his alernaive mehod, given he presence of occasional large flucuaions in he price of oil. Row (7) in Tables 4 hrough 8 shows ha he double-differenced specificaion does no work well in his case. 19 Alhough we have focused on he WTI price of oil, qualiaively similar resuls would also be obained on he basis of Bren spo and Bren fuures prices, which are available from he same daa sources. The evaluaion period for he Bren price series, however, is much shorer, casing doub on he reliabiliy of he resuls, which is why we focus on he WTI daa. 23

26 Especially a longer horizons, his forecasing mehod becomes erraic and suffers from very large MSPEs. Nor is his mehod paricularly adep a predicing he sign of he change in he nominal price of oil. Ye anoher sraegy is o exrapolae from longer-erm rends. Given ha oil prices have been persisenly rending upward (or downward) a imes, i is naural o consider a random walk model wih drif. One possibiliy is o esimae his drif recursively, resuling in he forecasing model: h Sˆ S 1 ˆ h 1, 3, 6, 9, 12 (8) Alernaively, a local drif erm may be esimaed using rolling regressions: ˆ (1 ( h) ) h S S s h 1, 3, 6, 9, 12, (9) where ˆ is he forecas of he spo price a +h; and S h ( h) s is he percen change in he spo price over he mos recen h monhs. This local drif model posulaes ha raders exrapolae from he spo price s recen behavior when hey form expecaions abou he fuure spo price. The local drif model is designed o capure shor-erm forecasabiliy ha arises from local rends in he oil price daa. Rows (8)-(9) in Tables 4 hrough 8 documen ha allowing for a drif ypically increases he MSPE and in no case significanly lowers he MSPE relaive o he no-change forecas, wheher he drif is esimaed based on rolling regressions or is esimaed recursively. Nor does allowing for a drif significanly improve he abiliy o predic he sign of he change in he nominal price of oil Forecass Based on he Hoelling Model Anoher forecasing mehod is moivaed by Hoelling s (1931) model, which predics ha he price of an exhausible resource such as oil appreciaes a he risk-free rae of ineres: Sˆ S (1 i ) h /12 h, h 3, 6, 12 h (10) where i h, refers o he annualized ineres rae a he relevan mauriy h. 20 Alhough he 20 Assuming perfec compeiion, no arbirage, and no uncerainy, oil companies exrac oil a a rae ha equaes: (1) he value oday of selling he oil less he coss of exracion; (2) and he presen value of owning he oil, which, 24

27 Hoelling model may seem oo sylized o generae realisic predicions, we include i in his forecas accuracy comparison. We employ he Treasury bill rae as a proxy for he risk free rae. 21 Row (10) in Tables 5, 6, and 8 shows no evidence ha adjusing he no-change forecas for he ineres rae significanly lowers he MSPE. The Hoelling model is beer a predicing he sign of he change in he nominal price of oil han he no-change forecas, alhough we canno assess he saisical significance of he improvemen, given ha here is no variabiliy a all in he sign forecas Survey Forecass Given he significance of crude oil o he inernaional economy, i is surprising ha here are few organizaions ha produce monhly forecass of spo prices. In he oil indusry, where he spo price of oil is criical o invesmen decisions, producers end o make annual forecass of spo prices for horizons as long as years, bu hese are no publicly available. The U.S. Deparmen of Energy s Energy Informaion Adminisraion (EIA) has published quarerly forecass of he nominal price of oil since The Economis Inelligence Uni has produced annual forecass since he 1990s for horizons of up o 5 years. None of hese sources provides monhly forecass. A source of monhly forecass of he price of crude oil is Consensus Economics Inc., a U.K.-based company ha compiles privae secor forecass in a variey of counries. Iniially, he sample consised of more han 100 privae firms; i now conains abou 70 firms. Of ineres o us are he survey expecaions for he 3- and 12-monh ahead spo price of Wes Texas Inermediae crude oil, which corresponds o he ype and grade delivered under he NYMEX fuures conrac. The survey provides he arihmeic average, he minimum, he maximum, and he sandard deviaion for each survey monh beginning in Ocober 1989 and ending in December We use he arihmeic mean a he relevan horizon: ˆ CF Sh S, h h 3, 12 (11) Row (11) in Tables 5 and 8 reveals ha his survey forecas does no significanly reduce he MSPE relaive o he no-change forecas and may increase he MSPE subsanially. The survey forecas is paricularly poor a he 3-monh horizon. A he 12-monh horizon he survey forecas given he model s assumpions, is discouned a he risk free rae. In compeiive equilibrium, oil companies exrac crude oil a he socially opimal rae. 21 Specifically, we use he 3-monh, 6-monh, and 12-monh consan-mauriy Treasury bill raes from he Federal Reserve Board s websie hp://federalreserve.gov/releases/h15/daa.hm 25

28 has a lower MSPE han he no-change forecas, bu he gain in accuracy is no saisically significan. There also is a saisically significan bu negligible gain in direcional accuracy. Furher analysis shows ha unil he consensus survey forecas had a much higher MSPE han he no-change forecas a boh he 3-monh and 12-monh horizons. This paern changes only oward he end of he sample. There is evidence ha he accuracy of he consensus survey forecass improves a he 12-monh horizon, especially in 2009 as he oil marke recovers from is collapse in he second half of I appears ha professional forecasers correcly prediced a long-erm price recovery in his insance, alhough hey were no successful a predicing he iming of he 2009 recovery. Nowihsanding hese caveas, here is no compelling evidence overall ha survey forecass ouperform he no-change forecas. We conclude ha he no-change forecass of he nominal price of oil no only are as accurae as forecass based on monhly fuures prices, bu end o be a leas as accurae as forecass based on simple economeric models or monhly survey forecass. This resul is consisen wih common views among oil expers. For example, Peer Davies, chief economis of Briish Peroleum, has noed ha we canno forecas oil prices wih any degree of accuracy over any period wheher shor or long (see Davies 2007) Predicors Based on Oher Nominal Prices The evidence on Granger causaliy in secion suggess ha some asse prices may have predicive power in real ime for he nominal price of oil. The las rows of Tables 4 hrough 8 explore ha quesion. One approach building on Chen, Rossi and Rogoff (2010) is o use recen percen changes in he bilaeral nominal dollar exchange rae of seleced commodiy exporers: Sˆ (1 i ) h hs e h 1,3, 6, 9,12, (12) where i Canada Ausralia Souh Africa,,. We do no include New Zealand given is poor showing in secion Tables 4 hrough 8 show ha his approach does no significanly reduce he ou-of-sample MSPE regardless of he exchange rae choice. There is some evidence ha he Ausralian exchange rae has significan predicive power for he sign of he change in he nominal price of oil, bu no a all horizons. For he oher exchange raes, he evidence is even weaker. We also considered he alernaive specificaion ˆ (1 i S ) h S e, h h 1,3, 6, 9,12, (13) 26

29 based on he percen change in he exchange rae over he mos recen h monhs. Tha specificaion produces similar resuls for direcional accuracy. For he MSPE, here are significan MSPE gains of abou 13% up o horizon 3 for he Ausralian dollar and of abou 7% up o horizon 6 for he Canadian dollar. The Rand performs less well. The direcional accuracy resuls for all hree alernaive models are somewha erraic wih no model performing well consisenly. These resuls are no shown in he ables o conserve space. Anoher approach is o explore he forecasing value of recen percen changes in non-oil CRB commodiy prices. One such forecasing model is ˆ com h Sh S(1 p ) 1,3, 6, 9,12, com ind, me (14) h I can be shown ha model (14) does no produce saisically significan reducions in he MSPE, presumably because monh-o-monh changes in commodiy prices end o be noisy. In fac, model (14) ends o worsen he MSPE raio a long horizons, alhough i significanly improves direcional accuracy a horizons up o 9 monhs for meals prices and up o 12 monhs for prices of indusrial raw maerials. An alernaive model specificaion is based on he percen change in he CRB price index over he mos recen h monhs: ˆ (1 com S ) h S p, h 1,3, 6, 9,12, h com ind, me, (15) Model (15) is designed o capure persisen changes in commodiy prices in he recen pas. This specificaion is less successful a predicing he direcion of change a horizons beyond 6 monhs, bu can yield significan reducions in he MSPE a shor horizons. For example, he model using meals prices significanly lowers he MSPE a horizon 3 and he model using prices of indusrial raw maerials significanly reduces he MSPE a horizons 1 and 3. The MSPE reducions may be as large as 25% a horizon 3. Tha resul, of course, reflecs he imporance of global demand pressures across all indusrial commodiies during he forecas evaluaion period. To he exen ha he price of oil someimes is driven by oher shocks, one would expec he accuracy gains from using model (15) o be less favorable. Finally, in Table 8, we include resuls for forecass ha adjus he no-change forecas of he nominal price of oil for he 1-year inflaion expecaions in he Michigan Survey of Consumers. ˆ (1 MSC S ) h S, h h 12 (16) There are no similar survey expecaions for shorer horizons. This more direc approach does 27

30 no reduce he MSPE relaive o he no-change forecas. The same resul holds when using suiably scaled 10-year inflaion forecass from he Survey of Professional Forecasers. ˆ (1 SPF S ) h S, h h 12 (17) The fac ha hese resuls are weaker han hose obained using inflaion measures in Granger causaliy ess likely means ha here was no much variaion in inflaion expecaions in our sample period, bu considerable variaion hisorically. We conclude ha despie some success of he asse price approach in predicing he sign of he change in he nominal price of oil, only persisen changes in CRB indusrial commodiy prices significanly reduce he MSPE of he no-change forecas and even hose accuracy gains are limied o very shor horizons. Beyond he 3-monh horizon, based on he MSPE crierion, he no-change forecas for all pracical purposes remains he mos accurae model for forecasing he nominal price of oil in real ime Shor-Horizon Forecass Based on Daily Oil Fuures Prices Following he exan lieraure, our analysis so far has relied on monhly daa for oil fuures prices and spreads consruced from daily observaions. The consrucion of monhly daa allows one o compare he accuracy of hese forecass o ha of alernaive forecass based on daa only available a monhly frequency. A complemenary approach is o uilize all daily oil fuure prices and compare heir forecasing accuracy o he no-change forecas only. This alernaive approach makes use of all oil-fuures price daa and hence may have more accurae size and higher power. I is no wihou drawbacks, however. Ideally, one would like o compare he price of a fuures conrac for delivery in h monhs wih he price of delivery exacly h monhs laer, where one monh corresponds o 21 business days. Tha price, however, is no observed. The spo price quoed on he day of delivery insead will be he price for delivery someime in he monh following he dae on which he fuures conrac maures. In fac, he dae of delivery associaed wih a given spo price can never be made exac. We herefore follow he convenion of evaluaing fuures price forecass agains he spo price prevailing when he fuures conrac maures. A reasonable case can be made ha his is wha praciioners view as he relevan forecasing exercise. Noe ha he daily daa are sparse in ha here are many days for which no price quoes exis. We eliminae hese daes from he sample and sack he remaining observaions similar o 28

31 he approach aken in Kilian and Vega (2010) in he conex of modeling he impac of U.S. macroeconomic news on he nominal price of oil. Table 9 summarizes our findings. The MSPE raios in Table 9 indicae somewha larger gains in forecasing accuracy from using oil fuures prices han in Tables 4 hrough 8. There are a number of caveas, however. Firs, he h-monh oil fuures forecass are no forecass for a horizon of h monhs, as in Tables 4 hrough 8, bu raher for a horizon ha may vary arbirarily beween h and h+1 monhs. For example, an oil fuures conrac quoed on Augus 13 for delivery saring on Ocober 1 would be considered a 1-monh conrac for he purpose of Table 9, bu so would an oil-fuures conrac quoed on Augus 25 for delivery saring on Ocober 1. This is an inheren limiaion of working wih daily oil fuures price daa. This concern suggess cauion in inerpreing shor-horizon resuls, bu obviously becomes less imporan as h increases. A second concern is ha he sample period spanned by he daily daa exends back o January 1986, whereas he daa in Tables 4 hrough 8 sar in This difference is no driving he resuls in Table 9. I can be shown ha making he sample period compaible wih ha in he earlier Tables would yield subsanively idenical resuls. The hird and mos imporan concern is he saisical significance of he resuls in Table 9. Given ha he sample size in Table 9 is larger han in Tables 4 hrough 8 by a facor of abou 10, care mus be exercised in inerpreing he p-values. As is well known, for sufficienly large sample sizes, any null hypohesis is bound o be rejeced a convenional significance levels, making i inappropriae o apply he same significance level as in Tables 4 hrough 8. In recogniion of his problem, Leamer (1978, p ) proposes a rule for consrucing samplesize dependen criical values. For example, for he F-saisic, he appropriae level of saisical 1 ( 1) ( 1),1,. For 216, as in Table 4, his rule of humb (1/ ) significance is fcdf implies a hreshold for rejecing he null hypohesis of In conras, for 5968 he same rule implies a much higher hreshold of Applying his rule o he p-values in Table 9, none of he MSPE reducions are saisically significan excep a he 12-monh horizon. The MSPE raio a he 12-monh horizon of 0.93 is similar o he raio of 0.94 repored in Table 8 based on monhly daa. The saisical significance of hese MSPE gains in Table 9 is likely o be due o he larger sample size, illusraing he power gains from using daily daa. There also is evidence ha a horizons 6, 9 and 12, he oil fuures price has saisically significan direcional accuracy, bu he gains are quaniaively negligible excep perhaps a horizon

32 These resuls lead us o revise somewha our earlier findings. We conclude ha here is saisically significan evidence ha oil fuures prices improve on he accuracy of he no-change forecas of he nominal price of oil a he 1-year horizon, bu no a shorer horizons. The magniude of hese gains in accuracy is modes a leas by he sandards of he lieraure on forecasing macroeconomic aggregaes such as inflaion raes. Moreover, here are indicaions ha his resul is sensiive o changes in he sample period and may no be robus as more daa accumulae. Afer eliminaing he daa beyond March 2008, for example, he MSPE raio of he 12-monh fuures price exceeds 1 and only when exending he sample period beyond July 2008 is he MSPE reducion saisically significan. This resul, ogeher wih he lack of evidence for slighly shorer or slighly longer fuures conracs, suggess cauion in inerpreing he evidence for he 12-monh conrac in Table Long-Horizon Forecass of he Nominal Price of Oil For oil indusry managers facing invesmen decisions or for policymakers pondering he medium-erm economic oulook a horizon of one year is oo shor. Crude oil fuures may have mauriies as long as seven years. Nowihsanding he low liquidiy of oil fuures markes a such long horizons, documened in Alquis and Kilian (2010), i is precisely hese long horizons ha many policymakers focus on. For example, Greenspan (2004a) explicily referred o he 6-year oil fuures conrac in assessing effecive long-erm supply prices. For similar saemens also see Greenspan (2004b), Gramlich (2004) and Bernanke (2004). In his secion we focus on forecasing he nominal price of oil a horizons up o seven years. I can be shown ha he daily daa are oo sparse a horizons beyond one year o allow he consrucion of ime series of end-of-monh observaions for oil fuures prices. However, we can insead evaluae each daily fuures price quoe for conracs of any given mauriy agains he spo price ha is realized on he day he conrac expires. We already used his approach in Table 9 for horizons up o one year. One drawback of exending his approach o longer horizons is ha he evaluaion period for long-horizon conracs may exclude many of he paricularly informaive observaions a he end of our sample period. Anoher drawback is ha long-horizon fuures prices are sparsely quoed, grealy reducing he sample size as he horizon is lenghened. For ha reason, one would expec he resuls o be far less reliable han he earlier shor-horizon resuls. Neverheless, hey provide he only indicaion we have of he usefulness of oil fuures 30

33 prices a he horizons a which hey are employed by many policymakers. Table 10 shows he resuls for horizons of 2, 3, 4, 5, 6, and 7 years. In sharp conras wih Table 9 he MSPE raios are consisenly above 1, indicaing ha oil fuures prices are less accurae han he no-change forecas. In no case is here evidence of significan reducions in he MSPE. The es for direcional accuracy is saisically significan a he wo-year horizon, bu no a longer horizons. In fac, in many cases he success raios a longer horizons are disincly worse han ossing a coin. Table 10 provides no evidence in suppor of he common pracice a cenral banks of appealing o he price of long-horizon oil fuures conracs as an indicaion of fuure spo prices. In paricular, a a horizon of six years, which figures prominenly in policy saemens and speeches, cenral bankers would have been much beer off relying on he nochange forecas han on oil fuures prices. An ineresing quesion is wheher he poor accuracy of forecass from oil fuures prices beyond one year simply reflecs a sharp drop-off in he liquidiy of oil fuures markes a longer horizons. This does no appear o be he case. Figure 5 plos wo measures of he liquidiy of he oil fuures marke by horizon. Open ineres is he oal number of fuures conracs, eiher long or shor, ha have been enered ino for a given delivery monh and have no ye been offse by anoher ransacion or by physical delivery of oil. I measures he oal number of conracs ousanding for delivery in a specific monh. Volume is he oal number of conracs raded during a specific period of ime. Conracs are denoed in unis of 1,000 barrels of crude oil. Alhough boh average open ineres and average rading volume drop off quickly wih increasing mauriy, i is no he case ha average liquidiy a he daily frequency is disconinuously lower a horizons beyond one year han a he 12-monh horizon. Raher he decline in average liquidiy is smooh. One concern wih he resuls in Table 10 is ha he mos raded oil fuures conracs are he June and December conracs. This suggess focusing on he mos liquid daily conracs raher han averaging resuls across all daily conracs, as we did in Table 10. Below we repor sensiiviy analysis for his subse of daily oil fuures conracs. Because long-erm fuures conracs only became available in recen years and because heir use grealy reduces he effecive sample size, we focus on June and December conracs wih mauriies of one, wo and hree years. Based on he evaluaion period of , we find ha one-year conracs have an MSPE raio of 0.91 compared wih he no-change forecas, wo-year conracs an MSPE raio 31

34 of 1.01 and hree-year conracs an MSPE raio of These resuls are qualiaively similar o hose in Table 10 for he same mauriies, suggesing ha here are no gains in forecas accuracy from resricing he sample. Finally, we noe ha hese resuls may no have been apparen in he years when longererm oil fuures conracs were firs inroduced. As recenly as in he lae 1990s, a forecaser employing he same mehods ha we used in his secion, would have found ha he monhly price of oil fuures conracs wih one-year mauriy is much more accurae han he no-change forecas, alhough he MSPE reducions declined seadily hroughou he 1990s, as more informaion became available, and he raio has oscillaed abou 1 since hen. Even wo- and hree-year daily conracs, which were inroduced much more recenly, iniially seemed o forecas more accuraely han he no-change forecas, bu hese MSPE reducions have been reversed more recenly. Given ha he forecas errors become more highly serially correlaed, he higher he daa frequency, very long samples are required for reliable esimaes of relaive MSPEs. Clearly, an evaluaion period of fifeen years, for example, is insufficien o learn abou he forecasing abiliy of oil fuures prices, as illusraed by he repeaed sharp reversals in forecas rankings over ime. Even our resuls mus be considered enaive and could be reversed as more daa become available. One possible explanaion for he unexpecedly low ou-of-sample accuracy of oil fuuresbased forecass may be he presence of ransacion coss impeding arbirage. An alernaive forecasing sraegy in which one uses he fuures price only if he fuures spread exceeds 5% in absolue erms and uses he spo price oherwise, yields MSPE reducions beween 0% and 6% a shor horizons. Noably he MSPE reducions a horizons of 3 and 6 monhs are saisically significan in boh he daily and he monhly daa. A horizons beyond one year, his alernaive mehod is much less accurae han he no-change forecas, however. 7. Do Survey Expecaions Track Economeric Forecass of Nominal Energy Prices? Models of purchases of energy-inensive durables depend no on he price of crude oil, bu on he reail price of energy. A case in poin is he demand for auomobiles. Alhough here can be subsanial discrepancies beween he evoluion of he price of crude oil and he price of gasoline in he shor run, long-horizon forecass of he price of gasoline will rack long-horizon forecass of he price of crude oil (see Kilian 2010). In modeling auomobile purchases researchers ofen 32

35 need o ake a sand on consumers expecaions of gasoline prices. A variey of modeling sraegies has been explored, ofen wih widely differen resuls. Candidaes include ARIMA models, no-change forecass, oil fuures prices and gasoline fuures prices (see, e.g., Kahn 1986; Davis and Kilian 2010; Allco and Wozny 2010). The issue is no only one of finding a forecasing mehod ha achieves he smalles possible ou-of-sample forecas error, bu of undersanding how consumers form heir price expecaions. An obvious concern is ha acual consumer expecaions may differ from he predicions generaed by he forecasing mehods considered so far. Unforunaely, ime series daa on consumer expecaions of gasoline prices are rare, which has prevened a sysemaic invesigaion of his imporan quesion. Recenly, Anderson, Kellogg and Sallee (2010) obained a previously unused daa se from he Michigan Survey of Consumers on U.S. households expecaions of gasoline prices. The survey asks consumers abou how many cens per gallon hey hink gasoline prices will increase or decrease during he nex five years compared o now. Median responses are available for , bu here are gaps in he daa, prevening he consrucion of a coninuous monhly ime series. Expecaions daa may be consruced by adding he expeced change in he price of gasoline o he curren monhly U.S. ciy average reail price of gasoline (quoed in cens per gallon including axes), as repored by he Energy Informaion Adminisraion (EIA). The upper panel of Figure 6 shows ha he median 5-year survey forecas sysemaically exceeds he curren gasoline price. The magniude of he gap varies over ime. As Anderson e al. observe, a likely explanaion of his paern is ha households form heir expecaions by adding long-erm inflaion expecaions o he curren price of gasoline. If we adjus he survey gasoline price forecas for he 10-year inflaion forecas in he Survey of Professional Forecasers (suiably scaled o he 5-year horizon), he wo series line up raher well on average, implying ha households expecaions of gasoline prices closely resemble a random walk forecas for he real price of gasoline (see second panel of Figure 6). 22 Only on rare occasions such as immediaely before he peak of he nominal price of oil in mid-2008 and near he oil price rough of 2008/2009 do household expecaions depar from he no-change forecas. 22 The corresponding 5-year Michigan survey inflaion expecaions are only available back o mid-2004, making he Survey of Professional Forecasers (SPF) daa he bes available proxy for 5-year inflaion expecaions (afer suiable scaling). These daa were obained from he Federal Reserve Bank of Philadelphia. Alhough he SPF daa are quarerly, he daa evolve so smoohly ha assigning he same quarerly value o each monh in ha quarer is likely o provide a good approximaion. 33

36 In he firs insance, households prediced an even higher price of oil; in he second insance, hey did no expec he price of oil o drop as sharply as i did. The evidence in Figure 6 suppors he view ha he no-change forecas for he real price of gasoline is a beer proxy han alernaive forecasing models for modeling durables purchases. Tha evidence also is of ineres more generally, given he finding in Edelsein and Kilian (2009) ha flucuaions in reail energy prices are dominaed by flucuaions in gasoline prices. Finally, he absence of money illusion in households gasoline price forecass is of independen ineres. An ou-of-sample forecas accuracy comparison beween he survey forecas and he nochange forecas of he nominal price of gasoline shows ha survey daa are quie accurae wih an MSPE raio of only (see Table 11). The p-value for he null hypohesis of equal predicive accuracy is The success raio of is also exraordinarily high. 23 The reason for hese raher srong improvemens on he no-change forecas is ha a such long horizons he inflaion componen of he nominal price of gasoline becomes very large and canno be ignored. In oher words, i is a fairly safe be ha he price of gasoline mus increase in nominal erms over a five-year horizon. 24 The same logic applies o he nominal price of oil. As we showed in secion 4, predicing he price of oil a he one-year horizon based on expeced inflaion (much like households apparenly predic he price of gasoline), would no have been more successful han he nochange forecas. Repeaing ha exercise a he 5-year horizon, however, using he same SPF inflaion expecaions daa as in Figure 6, produces a highly significan MSPE raio of and a very high success raio of for he nominal price of oil as well (see Table 11). This simple forecasing rule is also much more accurae han he forecas implied by he 5-year oil fuures price. The las panel of Figure 6 shows ha, nowihsanding his improved long-horizon forecas accuracy, households commied sysemaic forecas errors during he mos recen oil price surge. Beween 1998 and 2004, households persisenly underesimaed he price of gasoline. This evidence may help explain he coninued populariy of SUVs, ligh rucks and oher energy-inefficien auomobiles during his period. Presumably, consumers would no have 23 The Pesaran-Timmermann es for direcional accuracy canno be applied because here is no variabiliy in he prediced sign, making i impossible o judge he saisical significance of he success raio. 24 A quesion of obvious ineres is how he survey predicor compares wih he price of gasoline fuures. Tha comparison is no feasible due o daa limiaions. The longes mauriy in he NYMEX gasoline fuures marke is 3 years, and he 3-year fuures conrac only became available in

37 chosen o buy as many SUVs, had hey foreseen he subsequen increase in gasoline prices a he ime of heir purchase decision. There are no household surveys of oil price expecaions, bu, as discussed earlier, here are monhly daa on he views of professional forecasers in he Consensus Economics forecas. Figure 7 highlighs some sysemaic differences beween hese professional forecass and he corresponding household gasoline price expecaions. Whereas households gasoline price forecas ends o exceed he curren gasoline price by he expeced inflaion rae, professional oil price forecass mos of he ime are below he curren price of oil. The upper panel of Figure 7 shows ha professional forecasers end o smooh he prediced pah relaive o he curren price. This smoohing is especially apparen during large oil price flucuaions such as hose in 1990/91, in 1999/2000, and in This endency conribues o he large and persisenly negaive forecas errors shown in he lower panel of Figure 7 and helps explain why he consensus forecas does no significanly improve on he no-change forecas (see Table 11). One possible explanaion of he less han saisfacory accuracy of hese survey forecass in secion 4 is ha professional macroeconomic forecasers may no be expers on he oil marke. Figure 8 herefore focuses on an alernaive ime series of 1-quarer and 4-quarers-ahead forecass of he U.S. nominal refiners acquisiion cos for impored crude oil. These daa were colleced from he EIA s Shor-erm Economic Oulook, which is published by he U.S. Deparmen of Energy. Given he difference in frequency and oil price definiion he resuls are no sricly speaking comparable wih our earlier analysis of he monhly WTI price. Neverheless, hese daa are illuminaing. Figure 8 illusraes ha even hese exper forecass generally underprediced he price of crude oil beween 2004 and mid-2008, especially a longer horizons, while overpredicing i following he collapse of he price of oil in mid-2008 and underpredicing i again more recenly. A naural quesion is how he EIA forecass compare o he no-change forecas on he basis of he EIA s preliminary daa releases for he curren refiners acquisiion cos for impored crude oil. The laer daa are provided by he same source. The DM es for equal predicive accuracy in Table 11 suggess ha he MSPE raio of 0.92 for he 1-quarer-ahead forecas is saisically significan a he 10% level, bu he MSPE raio of 0.97 for he 4-quarers-ahead forecas is no. We conclude ha even he EIA has had a bes modes success in forecasing he nominal price of oil in he shor run and none a longer horizons. 35

38 8. Shor-Horizon Forecass of he Real Price of Oil Our analysis in secion 4 suggess ha we sand a beer chance of forecasing he real price of oil ou-of-sample using monhly daa, given he availabiliy of more appropriae predicors a he monhly frequency. A naural benchmark for all forecasing models of he real price of oil is again he no-change forecas. A shor horizons, inflaion is expeced o be a bes moderae and i may seem ha here is every reason o expec he high forecas accuracy of he random walk model wihou drif relaive o less parsimonious regression models o carry over o he real price of oil (see Kilian 2010). 25 On he oher hand, in forecasing he real price of oil we may rely on addiional economic srucure and on addiional predicors ha could poenially improve forecas accuracy. Secion 8 explores a number of such models. In addiion o focusing on he real WTI price, we also presen resuls for he real refiners acquisiion cos for oil impors Real U.S. Refiners Acquisiion Cos for Impored Crude Oil Unresriced AR, ARMA and VAR Models A useful saring poin is a forecas accuracy comparison of seleced monhly AR and ARMA models for he real price of oil in log levels and in log differences. Boh classes of models are evaluaed in erms of heir abiliy o predic he log level of he real price of oil in recursive seings. Below we consider wo alernaive measures of he real price of oil: The U.S. refiners acquisiion cos for impored crude oil, which may be hough of as a proxy for he price of oil in global oil markes, and he WTI price; in boh cases he deflaor is he U.S. CPI. Firs consider he refiners acquisiion cos. Esimaion sars in , and he evaluaion period is o faciliae direc comparisons wih VAR models of he global marke for crude oil in his and he nex secion. 26 All MSPE resuls are expressed as fracions of he MSPE of he nochange forecas. Some models are based on fixed lag orders of 12 or 24, whereas ohers rely on he Schwarz Informaion Crierion (SIC) or he Akaike Informaion Crierion (AIC) for lag order 25 Such a finding would no necessarily imply ha he real price of oil acually follows a random walk. I could merely reflec he fac ha he bias-variance radeoff favors parsimonious forecasing models in small samples. The local-o-zero asympoic approximaion of predicive models suggess ha using he no-change forecas may lower he asympoic MSPE even relaive o he correcly specified non-random walk model, provided he local drif parameer governing he predicive relaionship is close enough o zero (see, e.g., Inoue and Kilian (2004b), Clark and McCracken 2010). 26 The refiners acquisiion cos was exrapolaed back o as in Barsky and Kilian (2002). 36

39 selecion (see Inoue and Kilian 2006; Marcellino, Sock and Wason 2006). We search over p 0,...,12. The forecas accuracy resuls are robus o allowing for a larger upper bound. There are no heoreical resuls in he forecasing lieraure on how o assess he null of equal predicive accuracy when comparing ieraed AR or ARMA forecass o he no-change forecas. In paricular, he sandard ess discussed in Clark and McCracken (2001, 2005) or Clark and Wes (2007) are only designed for direc forecass. Below we assess he significance of he MSPE reducions based on boosrap p-values for he MSPE raio consruced under he null of a random walk model wihou drif. 27 The upper panel of Table 12 suggess ha AR and ARMA models in log levels have lower recursive MSPE han he no-change forecas a shor horizons. The accuracy gains may approach 17% in some cases and are highly saisically significan. Beyond he six-monh horizon, all gains in forecas accuracy evaporae. There also are saisically significan gains in direcional accuracy a horizons 1 and 3, and in some cases a horizon 6. There is lile o choose beween he AR(12), ARMA(1,1), AR(SIC) and AR(AIC) specificaions overall. The AR(24) model has slighly beer direcional accuracy a longer horizons, bu a he cos of a higher MSPE raio. The lower panel of Table 12 shows he corresponding forecasing models in log differences. Noe ha afer imposing he uni roo, he auoregressive lag order is reduced by one. For example, an ARMA(1,1) model in levels corresponds o an MA(1) model in differences. We find ha models in log differences generally are abou as accurae as models in log levels. There is robus evidence of saisically significan MSPE reducions a horizons 1 and 3 and here are saisically significan gains in direcional accuracy a horizons of up o 6 monhs in some cases. There is lile o choose beween he five forecasing models in log differences. We conclude (1) ha forecasing he real price of oil based on models in log levels is by no means inferior o forecasing based on models in log differences; (2) ha simple AR or ARMA models wih fixed lag orders perform quie well; and (3) ha he no-change forecas of he real price of oil can be improved upon a horizons of 1 monh and 3 monhs, bu generally no a horizons beyond half a year. All models in Table 12 have in common ha he informaion se is resriced o pas values of he real price of oil. The quesion we urn o nex is wheher suiably chosen 27 Because here is no reason o expec he limiing disribuion of he DM es saisic o be pivoal in his conex, we boosrap he average loss differenial insead. 37

40 macroeconomic predicors can be used o improve furher on he no-change forecas. Recenly, a number of srucural vecor auoregressive models of he global marke for crude oil have been proposed (see, e.g., Kilian 2009). These models produce empirically plausible esimaes of he impac of demand and supply shocks in he oil marke. A naural conjecure is ha such models may also have value for forecasing. Here we focus on he reduced-form represenaion of he VAR model in Kilian and Murphy (2010). The sample period is The variables in his model include he percen change in global crude oil producion, he global real aciviy measure we already discussed in secion 4, he log of he real price of oil, and a proxy for he change in global above-ground crude oil invenories. For furher discussion of he daa see Kilian and Murphy (2010). The VAR model may be consisenly esimaed wihou aking a sand on wheher he real price of oil is I(0) or I(1) (see Sims, Sock and Wason 1990). We focus on recursive raher han rolling regression forecass hroughou his secion. This approach makes sense in he absence of srucural change, given he greaer efficiency of recursive regressions and he small sample size. 28 A naural saring poin for he forecas accuracy comparison is he unresriced VAR model. An obvious concern wih forecasing from unresriced vecor auoregressions is ha hese highly parameerized models are subjec o considerable esimaion uncerainy which ends o inflae he ou-of-sample MSPE. For ha reason unresriced VAR models are rarely used in applied forecasing. They neverheless provide a useful poin of deparure. The upper panel of Table 13 shows resuls for unresriced VAR models wih 12 lags. Column (1) corresponds o he four-variable model used in Kilian and Murphy (2010). Table 13 shows ha his unresriced VAR forecas has lower recursive MSPE han he no-change forecas a all horizons bu one and nonrivial direcional accuracy. 29 Despie he lack of parsimony, he reducions in he MSPE are somewha larger han for he AR and ARMA models in Table 12. Boosrap p-values for he MSPE raio consruced under he null of a random walk model wihou drif indicae saisically significan reducions in he MSPE a horizons 1, 3, and 6. A longer horizons i becomes harder o bea he no-change forecas benchmark and here are no 28 Rolling regression forecass would no proec us from srucural change in any case. I has been shown ha he presence of srucural breaks a unknown poins in he fuure invalidaes he use of forecasing model rankings obained in forecas accuracy comparisons wheher one uses rolling or recursive regression forecass (see Inoue and Kilian 2006). 29 I also ouperforms he random walk model wih drif in boh of hese dimensions, wheher he drif is esimaed recursively or as he average growh rae over he mos recen h monhs. These resuls are no shown o conserve space. 38

41 saisically significan reducions in he MSPE. There also is evidence of saisically significan gains in direcional accuracy a horizons 1 and 3. The forecasing success of he VAR approach clearly depends on he choice of variables and of he lag lengh. The remaining columns of he upper panel of Table 13 show analogous resuls for five oher unresriced VAR(12) models obained by dropping one or more of he variables included in model (1). None of hese models performs as well as he original fourvariable model wih wo excepions. The bivariae model (4) which includes only he change in oil invenories and he real price of oil has slighly lower MSPE han he four-variable VAR(12) model and similar direcional accuracy, as does he rivariae model (6) specificaion ha drops oil producion from he baseline model. The lower panel of Table 13 suggess ha including 24 lags in he unresriced model ends o reduce he MSPE reducions. All VAR(24) models bu model (2) sill significanly improve on he MSPE of he no-change forecas a horizons 1 and 3, bu heir MSPE raio ends o exceed uniy a higher horizons. Likewise, all six VAR(24) models yield saisically significan gains in direcional accuracy a shor horizons. Only he four VAR(24) models ha include he global real aciviy variable in he model, however, reain heir superior direcional accuracy a all horizons. Unlike in he corresponding VAR(12) models, he gains in direcional accuracy are saisically significan a all horizons. We conclude ha here is imporan predicive informaion in he change in oil invenories and in global real aciviy in paricular, whereas he inclusion of oil producion growh appears less imporan for forecasing. Moreover, based on he MSPE meric, suiably chosen VAR models sysemaically ouperform he no-change forecas a shor horizons. A longer horizons, he no-change forecas remains unbeaen, excep based on he sign meric. This resul immediaely exends o longer horizons because none of he VAR forecasing models are suiable for exrapolaing o long horizons. I is imporan o keep in mind, however, ha Table 13 may oversae he rue saisical significance of he shor-horizon MSPE reducions. One indicaion of his problem is ha Table 13 someimes indicaes saisically significan rejecions of he no-change forecas benchmark even when he MSPE raio exceeds 1, indicaing ha he VAR has a sricly higher recursive MSPE. The reason for his counerinuiive resul is ha, as discussed earlier, sandard ess of equal predicive accuracy do no es he null of equal ou-of-sample MSPEs, bu acually es he 39

42 null of no predicabiliy in populaion much like he Granger causaliy ess we applied earlier as poined ou by Inoue and Kilian (2004a). This poin is readily apparen from he underlying proofs of asympoic validiy as well as he way in which criical values are simulaed. The disincion beween populaion predicabiliy and ou-of-sample predicabiliy does no maer asympoically under fixed parameer asympoics, bu fixed parameer asympoics ypically provide a poor approximaion o he finie-sample accuracy of forecasing models. Under more appropriae local asympoics (designed o mimic he weak predicive power of many regressors) i can be shown ha he null of no predicabiliy in populaion is disinc from he null of equal ou-of-sample MSPEs. I is always easier o rejec he former han he laer. In oher words, convenional ess of equal predicive accuracy es he wrong null hypohesis and may spuriously rejec he no-change forecas in favor of he alernaive. This is he deeper reason for he very low p-value obained, for example, for model (1) wih 24 lags a horizon 3. The inuiion for his rejecion is ha under he null ha he real price of oil is unpredicable one would expec much higher MSPE raios han 1.047, so he fac ha he MSPE of he VAR model is so close o 1 acually is evidence in favor of he VAR model being he populaion model. Which model is he populaion model, of course, is irrelevan for he quesion of which model generaes more accurae forecass in finie samples, so we have o inerpre his rejecion wih some cauion. This ype of insigh recenly has promped he developmen of alernaive ess of equal predicive accuracy based on local-o-zero asympoic approximaions o he predicive regression. Clark and McCracken (2010) for he firs ime proposed a correcly specified es of he null of equal ou-of-sample MSPEs. Their analysis is limied o direc forecass from much simpler forecasing models, however, and canno be applied in Table This cavea suggess ha we discoun only marginally saisically significan rejecions of he no predicabiliy null hypohesis in Table 13 and focus on he highly saisically significan es resuls. The ess for direcional accuracy are no affeced, of course. 30 The size problem of convenional ess of equal predicive accuracy ges worse, when he number of exra predicors under he alernaive grows large relaive o he sample size. This poin has also been discussed in a much simpler conex by Anaolyev (2007) who shows ha modifying convenional es saisics for equal predicive accuracy may remove hese size disorions. Relaed resuls can be found in Calhoun (2010) who shows ha sandard ess of equal predicive accuracy for nesed models such as Clark and McCracken (2001) or Clark and Wes (2007) will choose he larger model oo ofen when he smaller model is more accurae in ou-of-sample forecass and also proposes alernaive asympoic approximaions based on many predicors. None of he remedies is direcly applicable in he conex of Table 12, however. 40

43 Real-Time Forecass The resuls so far are encouraging in ha hey sugges ha VAR models (even more so han AR or ARMA models) may produce useful shor-horizon forecass of he real price of oil. An imporan cavea regarding he resuls in Tables 12 and 13 is ha he forecas accuracy comparison is no conduced in real ime. There are wo raher disinc concerns. One is ha no all useful predicors may be available o he forecaser in real ime. The oher concern is ha many predicors and indeed some measures of he price of oil are subjec o daa revisions. This cavea applies even o he no-change forecas. The reason is ha he refiners acquisiion cos daa become available only wih a delay of abou hree monhs and he CPI daa used o deflae he refiners acquisiion cos become available only wih a one-monh delay. Addiional caveas apply o he VAR evidence. Alhough he dry cargo shipping rae daa underlying he real aciviy index are available in real ime and no subjec o revisions, he consrucion of he real aciviy index involves real-ime CPI daa as well real-ime esimaes of he rend in real shipping raes. Moreover, he daa on global crude oil producion only become available wih a delay of 4 monhs and he daa used o approximae global crude oil invenories wih a delay of five monhs. This is less of a concern for he oil producion daa which end o evolve raher smoohly han for he more volaile daa on changes in crude oil invenories for which here is no good real ime proxy. How imposing hese real-ime daa consrains alers he relaive accuracy of no-change benchmark model compared wih VAR models is no clear a priori because boh he benchmark model and he alernaive model are affeced. The firs sudy o invesigae his quesion is Baumeiser and Kilian (2011) who recenly developed a real-ime daa se for he variables in quesion. They find (based on a daa se exending unil ) ha VAR forecasing models of he ype considered in his secion can generae subsanial improvemens in real-ime forecas accuracy. The MSPE reducion for unresriced VAR models may be as high as 25% a he one-monh horizon and as high as 9% a he hree-monh horizon. A longer horizons he MSPE reducions diminish even for he bes VAR models. Beyond one year, he no-change forecas usually has lower MSPE han he VAR model. Baumeiser and Kilian also show ha VAR forecasing models based on Kilian and Murphy (2010) exhibi significanly improved direcional accuracy. The improved direcional accuracy persiss even a horizons a which he MSPE gains have vanished. The success raios range from 0.51 o 0.60, depending on he model specificaion and horizon. 41

44 8.2. Real WTI Price Tables 14 and 15 show he corresponding resuls based on he real WTI price of oil insead of he real U.S. refiners acquisiion cos for impored crude oil. These resuls are no so much inended o validae hose in Tables 12 and 13, given he inheren differences in he definiion of he oil price daa, bu are of independen and complemenary ineres. The esimaion and evaluaion periods are unchanged o allow direc comparisons. The nominal WTI price is available wihou delay and is no subjec o revisions, reducing concerns over he real-ime availabiliy of he oil price daa. Table 14 provides robus evidence ha AR and ARMA models improve on he no-change forecas of he real WTI price of oil a horizons 1 and 3 wih he excepion of models wih 24 lags. The larges MSPE reducions are only 5%, however, and all such accuracy gains vanish a longer horizons. The VAR resuls in Table 15 pain a similar picure. None of he VAR(12) models has significanly lower MSPE han he no-change forecas beyond horizon 6. In general he reducions in MSPEs are smaller han in Table 13. The larges MSPE reducion is 16% a horizon 3. Likewise, he evidence ha forecass from VAR models wih 24 lags have direcional accuracy is weaker han in Table 13. By he MSPE meric, only in rare cases are he VAR(24) models more accurae han he no-change forecas of he real WTI price of oil. This finding highlighs ha he definiion of he real price of oil maers for he degree of forecasabiliy. Clearly, he real price of WTI crude oil is more difficul o forecas in he shor run han he real U.S. refiners acquisiion cos for impored crude oil. Broadly similar resuls would be obained wih real-ime daa (see Baumeiser and Kilian 2011). Unlike for he real refiners acquisiion cos, he differences beween real-ime forecass of he real WTI price and forecass based on ex-pos revised daa end o be small Resriced VAR Models Alhough he resuls for he unresriced VAR models in Tables 13 and 15 are encouraging, here is reason o believe ha alernaive esimaion mehods may reduce he MSPE of he VAR forecas even furher. One candidae is he use of Bayesian shrinkage esimaion mehods. In he VAR model a hand a naural saring poin would be o shrink all lagged parameers oward zero under he mainained assumpion of saionariy. This leaves open he quesion of how o deermine he weighs of he prior relaive o he informaion in he likelihood. Giannone, Lenza 42

45 and Primiceri (2010) recenly proposed a simple and heoreically founded daa-based mehod for he selecion of priors in recursively esimaed Bayesian VARs (BVARs). Their recommendaion is o selec priors using he marginal daa densiy (i.e., he likelihood funcion inegraed over he model parameers), which only depends on he hyperparameers ha characerize he relaive weigh of he prior and he informaion in he daa. They provide empirical examples in which he forecasing accuracy of ha model in recursive seings is no only superior o unresriced VAR models, bu is comparable o ha of single-equaion dynamic facor models (see Sock and Wason 1999). Table 16 compares he forecasing accuracy of his approach wih ha of he unresriced VAR models considered in Tables 13 and 15. In all cases, we shrink he model parameers oward a whie noise prior mean wih he desired degree of shrinkage being deermined by he daa-based procedure in Giannone e al. (2010). For models wih 12 lags, here is no srong evidence ha shrinkage esimaion reduces he MSPE. Alhough here are some cases in which imposing Bayesian priors reduces he MSPE slighly, in oher cases i increases he MSPE slighly. For models wih 24 lags, however, shrinkage esimaion ofen grealy reduces he MSPE raio and ypically produces forecass abou as accurae as forecass from he corresponding model wih 12 lags. As in Tables 12 and 14, here is evidence of MSPE reducions a horizons of up o 6 monhs. For example, model (1) wih 12 lags yields MSPE reducions of 20% a horizon 1, 12% a horizon 3, and 3% a horizon 6 wih no furher gains a longer horizons. Model (1) wih 24 lags yields gains of 20%, 12% and 1%, respecively. Again, i can be shown ha similar gains in accuracy are feasible even using real-ime daa (see Baumeiser and Kilian 2011). In addiion, such VAR models can also be useful for sudying how baseline forecass of he real price of oil mus be adjused under hypoheical forecasing scenarios, as illusraed in he nex secion. This does require he VAR model o be fully idenified, however. 9. Srucural VAR Forecass of he Real Price of Oil Recen research has shown ha hisorical flucuaions in he real price of oil can be decomposed ino he effecs of disinc oil demand and oil supply shocks associaed wih unpredicable shifs in global oil producion, real aciviy and a forward-looking or speculaive elemen in he real price of oil (see, e.g., Kilian and Murphy 2010). Changes in he composiion of hese shocks help explain why convenional regressions of macroeconomic aggregaes on he price of oil end o be 43

46 unsable. They also are poenially imporan in inerpreing oil price forecass. In secion 8 we showed ha recursive forecass of he real price of oil based on he ype of oil marke VAR model proposed in Kilian and Murphy (2010) for he purpose of srucural analysis are no necessarily inferior o simple no-change forecass. The case for he use of VAR models, however, does no res on heir predicive accuracy alone. Policymakers expec oil price forecass o be inerpreable in ligh of an economic model. They also expec forecasers o be able o generae projecions condiional on a variey of hypoheical economic scenarios. Quesions of ineres include, for example, wha effecs an unexpeced slowing of Asian growh would have on he forecas of he real price of oil; or wha he effec would be of an unexpeced decline in global oil producion associaed wih peak oil. Answering quesions of his ype is impossible using reduced-form ime series models. I requires a fully srucural VAR model (see Waggoner and Zha 1999). In his secion we illusrae how o generae such projecions from he srucural moving average represenaion of he VAR model of Kilian and Murphy (2010) esimaed on daa exending o The discussion closely follows Baumeiser and Kilian (2011). This model allows he idenificaion of hree srucural shocks: (1) a shock o he flow of he producion of crude oil ( flow supply shock), (2) a shock o he flow demand for crude oil and oher indusrial commodiies ( flow demand shock ) ha reflecs unexpeced flucuaions in he global business cycle, and (3) a shock o he demand for oil invenories arising from forward-looking behavior ( speculaive demand shock ). The srucural demand and supply shocks in his model are mainly idenified by a combinaion of sign resricions and bounds on impac price elasiciies. This model is se-idenified, bu he admissible models can be shown o be quie similar, allowing us o focus on one such model wih lile loss of generaliy. We focus on he same model ha Kilian and Murphy use as he basis for heir hisorical decomposiions. There is a sric correspondence beween sandard reduced-form VAR forecass and forecass from he srucural moving represenaion. The reduced-form forecas corresponds o he expeced change in he real price of oil condiional on all fuure shocks being zero. Deparures from his benchmark can be consruced by feeding pre-specified sequences of fuure srucural shocks ino he srucural moving-average represenaion. A forecas scenario is defined as a sequence of fuure srucural shocks. The implied movemens in he real price of oil relaive o he baseline forecas obained by seing all fuure srucural shocks o zero correspond 44

47 o he revision of he reduced-form forecas implied by his scenario. We consider hree scenarios of economic ineres. The forecas horizon is 24 monhs for illusraive purposes. The firs scenario involves a successful simulus o U.S. oil producion, as had been considered by he Obama adminisraion prior o he 2010 oil spill in he Gulf of Mexico. Here we consider he likely effecs of a 20% increase in U.S. crude oil oupu in , afer he esimaion sample of Kilian and Murphy (2010) ends. This is no o say ha such a dramaic and sudden increase would be feasible, bu ha i would be a bes-case scenario. Such a U.S. oil supply simulus would ranslae o a 1.5% increase in world oil producion, which is well wihin he variaion of hisorical daa. We simulae he effecs of such a simulus by calibraing a one-ime srucural oil supply shock such ha he impac response of global oil producion growh in is 1.5%. All oher fuure srucural shocks are se o zero. Figure 9 shows ha he resuling reducion in he real price of oil expressed in percen relaive o he baseline forecas is negligible. Even a much larger U.S. oil supply simulus would do lile o affec he forecas of he real price of oil, suggesing ha policies aimed a creaing such a simulus will be ineffecive a lowering he real price of oil. The second scenario involves a recovery of global demand for oil and oher indusrial commodiies. We ask how an unexpeced surge in he demand for oil similar o ha occurring during , bu saring in , would affec he real price of oil. This scenario involves feeding ino he srucural moving average represenaion fuure flow demand shocks corresponding o he sequence of flow demand shocks ha occurred in , while seing all oher fuure srucural shocks equal o heir expeced value of zero. Figure 9 shows a persisen increase in he real price of oil saring in early 2010 ha peaks in early 2011 abou 50% above he price of oil in Taking he no-change forecas as he baseline forecas, his means ha he peak occurs a a price of abou 100 dollars. Alernaively, one could express hese resuls relaive o he uncondiional VAR forecas. Finally, we consider he possibiliy of a speculaive frenzy such as occurred saring in mid-1979 afer he Iranian Revoluion (see Kilian and Murphy 2010). This scenario involves feeding ino he model fuure srucural shocks corresponding o he sequence of speculaive demand shocks ha occurred beween and and were a major conribuor o he 1979/80 oil price shock episode. Figure 9 shows ha his even would raise he baseline forecas emporarily by as much as 30%. Mos of he effecs would have dissipaed by mid

48 These resuls, while necessarily enaive, illusrae how srucural models of oil markes may be used o assess risks in oil price forecass and o invesigae he sensiiviy of reducedform forecass o specific economic evens, possibly in conjuncion wih he formal risk measures discussed in secion 12. Condiional projecions, of course, are only as good as he underlying srucural models. Our example highlighs he imporance of refining hese models and of improving srucural forecasing mehods, perhaps in conjuncion wih Bayesian mehods of esimaing VAR forecasing models. 10. Forecasing he Real Price of Oil in Oher Counries I is naural o focus on forecasing he real price of oil in dollars because crude oil is raded in dollars. This perspecive, however, is oo limied. From he poin of European oil imporers, for example, i is he real price of oil in Euros ha maers. Figure 10 shows he real price of oil beween and in he U.S., he Euro zone, Japan, he U.K. and Canada. These daa have been consruced from he U.S. refiners acquisiion cos for impored crude oil wih he help of daa on nominal exchange raes and consumer prices. For exposiory purposes all daa have been expressed in log deviaions from heir mean over his sample period. Alhough he overall picure is similar, Figure 10 illusraes ha here can be subsanial differences in he real price of oil across counries a imes. For example, he real exchange rae cushioned he increase in he real price of oil experienced by he Euro area in 2007/08, bu amplified i in 2000/01. These differences in he evoluion of he real price of oil across counries shown in Figure 10 sugges ha here is no a priori reason o expec he accuracy of alernaive forecasing models of he real price of oil o be he same across counries. A model ha works well for one counry need no work well for oher counries. Table 17 explores his quesion for Japan, he U.K. and Canada. We focus on he AR(12) model for illusraive purposes. The esimaion and evaluaion periods are he same as in Tables 12 and 14, allowing direc comparisons. The upper panel shows resuls based on he U.S. refiners acquisiion cos for impored crude oil and he lower panel resuls based on he WTI price. For each counry we fi an AR(12) model o he price of oil expressed in erms of domesic consumer goods. These prices are obained by muliplying he U.S. real price of crude oil by he appropriae monhly real exchange raes. The resuls in he upper panel are quie similar o hose in Table 12. For all hree counries he AR(12) model has significanly lower MSPE han he no-change forecas a horizons 1 and 3 and in some cases a 46

49 horizon 6 as well. A longer horizons, he no-change forecas is more accurae. The resuls in he lower panel are similar o hose in Table 14 in ha he evidence agains he no-change forecas is somewha weaker. For Japan and Canada he no-change forecas is rejeced a horizons 1 and 3, bu for he U.K. here is no rejecion a any horizon. The gains in accuracy, even if saisically significan, end o be smaller han in he upper panel. This example suggess ha subjec o he earlier caveas he forecas accuracy gains we documened for he U.S. real price of oil coninue o hold for oher counries. We defer o fuure work he quesion of wheher he relaive accuracy of alernaive AR and ARMA forecasing mehods is he same for oher counries as for he Unied Saes. Exending he VAR approach of secion 8 o oher counries raises addiional complicaions. One simple approach would be o augmen he baseline reduced-form forecasing model for he real price of oil in dollars by including he real exchange rae. This approach, however, may cos oo many degrees of freedom in pracice. A simple alernaive approach is o leave unchanged he VAR model, bu o conver all forecass of he real price of oil a he real exchange rae as of he dae from which he forecass are generaed. This amouns o imposing a no-change forecas for he real exchange rae. A shor horizons, he real exchange rae is dominaed by flucuaions in he nominal exchange rae. I is well known ha he change in he nominal exchange rae is unforecasable in real ime. This suggess ha he no-change forecas of he real exchange rae will provide a good approximaion a leas a shor horizons. The same approach may be used in consrucing he condiional predicions from srucural VAR models discussed in secion 9, which avoids having o reconsider he idenificaion of he srucural VAR shocks. 11. The Abiliy of Oil Prices o Forecas U.S. Real GDP One of he main reasons he price of oil is considered imporan by many macroeconomiss is is perceived predicive power for U.S. real GDP. Assessing ha predicive power requires a join forecasing model for he price of oil and for domesic real aciviy. In his secion we firs examine he forecasing accuracy of linear models and hen examine a variey of nonlinear forecasing models. The baseline resuls are for he U.S. refiners acquisiion cos for impored crude oil. Toward he end of he secion we discuss how hese resuls are affeced by oher oil price choices. Our discussion draws on resuls in Kilian and Vigfusson (2010c). 47

50 11.1. Linear Auoregressive Models A naural saring poin is a linear VAR(p) model for he real price of oil and for U.S. real GDP expressed in quarerly percen changes. The general srucure of he model is x BLx ( ) 1 e, where x [ r, y], r denoes he log of real price of oil, y he log of real GDP, is he difference operaor, e he regression error, and B L B B LB L B L The 2 p 1 ( ) p. benchmark model for real GDP growh is he AR(p) model obained wih BL ( ). 0 B22( L) The specificaion of he componens of B( L ) marked as is irrelevan for his forecasing model. We deermined he lag order of his benchmark model based on a forecas accuracy comparison involving all combinaions of horizons h 1,...,8 and lag orders p 48 1,..., 24. The AR(4) model for real GDP growh proved o have he lowes MSPE or abou he same MSPE as he mos accurae model a all horizons. The same AR(4) benchmark model has also been used by Hamilon (2003) and ohers, faciliaing comparisons wih exising resuls in he lieraure. We compare he benchmark model wih wo alernaive models. One model is he unresriced VAR(p) model obained wih BL The oher is a resriced VAR model of he form B ( L) B ( L) ( ). B21( L) B22 ( L) BL B ( L) 0 B21( L) B22 ( L) 11 ( ). The resricion B ( ) 0 12 L is implied by he hypohesis of exogenous oil prices. Alhough ha resricion is no lierally rue, in secion 4 we menioned ha in linear models he predicive conen of U.S. real GDP for he real price of oil, while no zero, appears o be weak. Thus, a naural conjecure is ha he added parsimony from imposing zero feedback from lagged real GDP o he real price of oil may help reduce he ou-of-sample MSPE of muli-sep ahead real GDP forecass. The real price of oil is obained by deflaing he refiners acquisiion cos for impored crude oil by he U.S. CPI. All hree models are esimaed recursively on daa saring in 1974.Q1.

51 The iniial esimaion period ends in 1990.Q1, righ before he invasion of Kuwai in Augus of The forecas evaluaion ends in 2010.Q2. The maximum lengh of he recursive sample is resriced by he end of he daa and he forecas horizon. We evaluae he MSPE of each model for he cumulaive growh raes a horizons h 1,...,8, corresponding o he horizons of ineres o policymakers. The firs column of Table 18 shows ha, a horizons of hree quarers and beyond, including he real price of oil in he auoregressive models may reduce he MSPE for real GDP growh by up o 8% relaive o he AR(4) model for real GDP growh. The unresriced VAR(4) model for he real price of oil is abou as accurae as he resriced VAR(4) model in he second column. Imposing exogeneiy marginally reduces he MSPE a some horizons, bu he differences are all negligible. This fac is remarkable given he greaer parsimony of he model wih exogenous oil prices. We conclude ha here are no significan gains from imposing exogeneiy in forecasing from linear models. Nex consider a similar analysis for he nominal price of oil. Alhough he use of he nominal price of oil in predicing real GDP is no suppored by sandard economic models, i is useful o explore his alernaive approach in ligh of he discussion in secion 3. Table 18 shows ha he unresriced VAR(4) model based on he real price of oil is consisenly a leas as accurae as he same model based on he nominal price of oil. We conclude ha in linear models here are no gains in forecas accuracy from replacing he real price of oil by he nominal price. Imposing exogeneiy, as shown in he las column, again makes lile difference. MSPE raios are informaive abou relaive forecasing accuracy, bu are no informaive abou how accurae hese models are in pracice. Figure 11 focuses on he abiliy of recursively esimaed AR(4) and VAR(4) models based on he real price of oil impors o predic he recessions of 1991, 2001, and 2007/8. The upper panel plos he one-quarer-ahead forecass agains he forecas realizaions. AR and VAR forecass are generally quie similar. Neiher model is able o forecas he large economic declines in 1990/91, 2001, and 2008/09. The forecas accuracy deerioraes furher a he one-year horizon, as shown in he lower panel. One possible explanaion is ha his forecas failure simply reflecs our inabiliy o forecas more accuraely he real price of oil. Pu differenly, he explanaion could be ha he real GDP forecass would be more accurae if only we had more accurae forecass of he real price of oil. Condiioning on realized values of he fuure price of oil, however, does no grealy 49

52 improve he forecas accuracy of he linear VAR model for cumulaive real GDP growh, so his explanaion can be ruled ou. An alernaive explanaion could be ha he predicive relaionship beween he price of oil and domesic macroeconomic aggregaes is ime-varying. One source of ime variaion is ha he share of energy in domesic expendiures has varied considerably over ime. This suggess ha we replace he percen change in he real price of oil in he linear VAR model by he percen change in he real price of oil weighed by he ime-varying share of oil in domesic expendiures, building on he analysis in Edelsein and Kilian (2009). Hamilon (2009) repored some success in employing a similar sraegy. 31 Anoher source of ime variaion may be changes in he composiion of he underlying oil demand and oil supply shocks, as discussed in Kilian (2009). Finally, ye anoher poenial explanaion invesigaed below is ha he linear forecasing model may be inherenly misspecified. Of paricular concern is he possibiliy ha nonlinear dynamic regression models may generae more accurae ou-of-sample forecass of cumulaive real GDP growh Nonlinear Dynamic Models In his regard, Hamilon (2003) suggesed ha he predicive relaionship beween oil prices and U.S. real GDP is nonlinear in ha (1) oil price increases maer only o he exen ha hey exceed he maximum oil price in recen years and ha (2) oil price decreases do no maer a all. This view was based on he in-sample fi of a single-equaion predicive model of he form: 4 4 ne,,3yr i i i i i1 i1, (18) y y s u where s denoes he log of he nominal price of oil and ne,,3yr s he corresponding 3-year ne increase in he nominal price of oil. Hamilon s line of reasoning has promped many researchers o consruc asymmeric responses o posiive and negaive oil price innovaions from censored oil price VAR models. ne,,3yr Censored oil price VAR models refer o linear VAR models for [ s, y ], possibly 31 In relaed work, Ramey and Vine (2010) propose an alernaive adjusmen o he price of gasoline ha reflecs he ime cos of queuing in gasoline markes during he 1970s. Tha adjusmen as well serves o remove a nonlineariy in he ransmission process. Boh he nonlineariy posulaed in Edelsein and Kilian (2009) and ha posulaed in Ramey and Vine (2010) is incompaible wih he specific nonlineariy embodied in he models of Mork (1989) and Hamilon (1996, 2003). In fac, he aforemenioned papers rely on linear regressions afer adjusing he energy price daa. 50

53 augmened by oher variables. Recenly, Kilian and Vigfusson (2010a) have shown ha impulse response esimaes from VAR models involving censored oil price variables are inconsisen even when equaion (18) is correcly specified. Specifically, ha paper demonsraed, firs, ha asymmeric models of he ransmission of oil price shocks canno be represened as censored oil price VAR models and are fundamenally misspecified wheher he daa generaing process is symmeric or asymmeric. This misspecificaion renders he parameer esimaes inconsisen and inference invalid. Second, sandard approaches o he consrucion of srucural impulse responses in his lieraure are invalid, even when applied o correcly specified models. Insead, Kilian and Vigfusson proposed a modificaion of he procedure discussed in Koop, Pesaran and Poer (1996). Third, sandard ess for asymmery based on he slope coefficiens of singleequaion predicive models are neiher necessary nor sufficien for judging he degree of asymmery in he srucural response funcions, which is he quesion of ulimae ineres o users of hese models. Kilian and Vigfusson proposed a direc es of he laer hypohesis and showed empirically ha here is no saisically significan evidence of asymmery in he response funcions for U.S. real GDP. Hamilon (2010) agrees wih Kilian and Vigfusson on he lack of validiy of impulse response analysis from censored oil price VAR models, bu suggess ha nonlinear predicive models such as model (18) may sill be useful for ou-of-sample forecasing. We explore his conjecure below. We consider boh one-quarer-ahead forecass of real GDP growh and forecass of he cumulaive real GDP growh rae several quarers ahead. The laer forecass require a generalizaion of he single-equaion forecasing approach proposed by Hamilon (2010). In implemening his approach, here are several poenially imporan modeling choices o be made. Firs, even graning he presence of asymmeries in he predicive model, one quesion is wheher he predicive model should be specified as 4 4 ne,,3yr i i i i i1 i1, (18) y y s u as in Hamilon (2003), or raher as: ne,,3yr i i i i i i i1 i1 i1 (19) y y s s u 51

54 as in Balke, Brown and Yücel (2002) or Herrera, Lagalo and Wada (2010), for example. The laer specificaion encompasses he linear reduced-form model as a special case. Kilian and Vigfusson prove ha dropping he lagged percen changes from model (19) will cause an inconsisency of he OLS esimaes, excep in he heoreically implausible case ha here is no lagged feedback from percen changes in he price of oil o real GDP. Hamilon, in conras, argues in effec ha i 0 i, or, alernaively, ha he slopes i are close enough o zero for he misspecified (bu more parsimonious) nonlinear predicive model (18) o have lower ou-ofsample MSPE in finie samples han he unresriced encompassing model (19). This moivaion for he use of model (18) is new in ha hereofore he focus in he lieraure including Hamilon s own work has been on esablishing nonlinear predicabiliy in populaion raher han ou-of-sample. Hamilon (2010) is, of course, correc ha here is a radeoff beween esimaion variance and bias. Indeed, in many oher conexs parsimony has been shown o help reduce he ou-of-sample MSPE, bu no sysemaic evidence has been presened o make his case for his model. Below we explore he meris of imposing 0i no only in he conex of single-equaion models designed for one-sep ahead forecasing, bu for mulivariae nonlinear models as well. A second poin of conenion is wheher nonlinear forecasing models should be specified in erms of he nominal price of oil or he real price of oil. For linear models, a srong economic case can be made for using he real price of oil. For nonlinear models, he siuaion is less clear, as noed by Hamilon (2010). Because he argumen for using ne oil price increases is behavioral, one specificaion appears as reasonable as he oher. Below we herefore will consider models specified in real as well as in nominal oil prices. A hird issue ha arises only in consrucing ieraed forecass for higher horizons is how o specify he process governing he price of oil. The case can be made ha reaing his process as exogenous wih respec o real GDP migh help reduce he ou-of-sample MSPE, even if ha resricion is incorrec. Below we herefore consider specificaions wih and wihou imposing exogeneiy. In Table 19, we invesigae wheher here are MSPE reducions associaed wih he use of censored oil price variables a horizons h 1,...,8, drawing on he analysis in Kilian and Vigfusson (2010b, c). For compleeness, we also include resuls for he percen increase i 52

55 specificaion proposed in Mork (1989), he forecasing performance of which has no been invesigaed o dae. We consider nonlinear models based on he real price of oil as in Kilian and Vigfusson and nonlinear models based on he nominal price of oil as in Hamilon (2003). The unresriced mulivariae nonlinear forecasing model akes he form 4 4 ne,,3 yr ne,,1yr where r r r r r B r B y e 1 11, i i 12, i i 1, i1 i (20) y B r B y r e 2 21, i i 22, i i i i 2, i1 i1 i1,,, r ri( r 0) as in Mork (1989), and I( ) denoes he indicaor funcion. Analogous nonlinear forecasing models may be consruced based on he nominal price of oil, denoed in logs as s : ne,,3 yr ne,,1yr where s s s s , i i 12, i i 1, i1 i , i i 22, i i i i 2, i1 i1 i1 s B s B y e ( 20) y B s B y s e,,. In addiion, we consider a resriced version of models (20) and ( 20) which imposes he hypohesis ha he price of oil is exogenous such ha: , i i 1, i r B r e (21) y B r B y r e 2 21, i i 22, i i i i 2, i1 i1 i1 and 4 s B s e 1 11, i i 1, i1 (21) , i i 22, i i i i 2, i1 i1 i1 y B s B y s e Alernaively, we may resric he feedback from lagged percen changes in he price of oil, as suggesed by Hamilon (2003). Afer imposing B 21, 0 i, he baseline nonlinear forecasing model reduces o: 53 i

56 4 4 r B r B y e 1 11, i i 12, i i 1, i1 i1 (22) 4 4 y 2 B22, i yi ir i e2, i1 i1 and 4 4 s B s B y e 1 11, i i 12, i i 1, i1 i1 ( 22) , i i i i 2, i1 i1 y B y s e Finally, we can combine he resricions B12, 0 i and B21, 0 i, resuling in forecasing models (23) and ( 23 ): 4 r B r e i i 1 11, i i 1, i1 (23) 4 4 y 2 B22, i yi ir i e2, i1 i1 and , i i 1, i , i i i i 2, i1 i1 s B s e ( 23 ) y B y s e A he one-quarer horizon, real GDP growh forecass from model ( 22) and ( 23 ) only depend on he second equaion, which is equivalen o using Hamilon s model (1). All models are esimaed by leas squares, as is sandard in he lieraure. The forecass are consruced by Mone Carlo inegraion based on 10,000 draws. The esimaion and evaluaion periods are he same as in Table 18. Table 19 displays he MSPE raios for all eigh models by horizon. All resuls are normalized relaive o he AR(4) model for real GDP growh. No ess of saisical significance have been conduced, given he compuaional cos of such ess. The firs resul is ha no nonlinear model is more accurae han he AR(4) benchmark model a he one-quarer horizon excep for models (22) and (23). The reducion in MSPE is 9%. A longer horizons, model (23 ) which combines Hamilon s assumpions wih ha of exogenous oil prices and embeds all hese 54

57 assumpions in a mulivariae dynamic framework, yields even larger gains in accuracy relaive o he benchmark model. A he one-year horizon, he reducion in MSPE reaches 26% compared wih 15% for he unresriced nonlinear model (22). The use of nominal as opposed o real ne oil price increases (accouning for 11 percenage poins by iself) and he omission of lagged percen changes in he nominal price of oil (accouning for 4 percenage poins by iself) are mainly responsible for he addiional gain in accuracy; he imposiion of exogeneiy plays no role. Accuracy gains a slighly shorer or longer horizons are closer o 10%. Second, neiher he percen increase model based on Mork (1989) nor he one-year ne increase model moivaed by Hamilon (1996) is more accurae han he AR(4) benchmark a he one-quarer horizon. This is rue regardless of wheher he price of oil is specified in nominal or real erms and regardless of wha addiional resricions we impose. A longer horizons, here is weak evidence ha some of hese specificaions reduce he MSPE a some horizons, bu in no case as much as for he hree-year ne oil price increase. Third, here is no clear ranking beween forecasing models based on he real price of oil and models based on he nominal price of oil. For example, models (22) and (23) based on he real price of oil are more accurae a he one-quarer horizon han models (22 ) and (23 ) based on he nominal price, bu a longer horizons he ranking is reversed. An obvious quesion of ineres is o wha exen allowing for nonlineariies improves our abiliy o forecas major economic downurns in he U.S. The one-quarer ahead resuls in he upper panel of Figure 12 indicae ha he nominal ne increase model has considerable success in forecasing he 2008 recessions, abou half of which is forecas by he model, bu he model s performance during oher episodes is less impressive. For example, is performance during he oil price shock episode of 1990/91 is erraic. Alhough he model forecass a recession, he iming is off and he model forecass sharp subsequen oscillaions in economic growh ha did no maerialize. The corresponding lower panel in Figure 12 shows ha he ne increase model ( 23 ) is even more successful a forecasing he downurn of 2008 and he subsequen recovery four quarers ahead. If anyhing, his nonlinear model appears oo successful in ha i seems o leave lile independen role for he financial crisis. The forecasing success in 2008, however, comes a a price because model ( 23 ) on earlier occasions forecas a number of economic declines ha did no maerialize or were no nearly as severe as prediced by he model. For example, in panel 55

58 (b), he ne increase model incorrecly forecas pronounced declines in economic growh relaive o average growh in 2005/06 and he economic decline of 1990/91 began long before he forecased decline. Plos of he recursive MSPE of hese nonlinear models show ha much of he forecasing success of nonlinear models is driven by one episode, namely he economic collapse in 2008/09 following he financial crisis. This poin is illusraed in Figure 13. The lef panel of Figure 13 is based on he nominal PPI used in Hamilon s original analysis; he righ panel shows he corresponding resuls for he nominal refiners acquisiion cos for crude oil impors. The plo of he cumulaive recursive MSPE for he PPI model 23 reveals ha he overall gain in accuracy in his example is driven enirely by he 2008/09 recession. Excluding his episode, model 23 has higher MSPE han he linear AR model hroughou he evaluaion period. Given his evidence a srong case can be made ha few forecasers would have had he courage o sick wih he predicions of his nonlinear model given he susained failure of he model in he years leading up o he financial crisis. The corresponding resuls for he refiners acquisiion cos for impored crude oil in he righ panel are somewha more favorable, bu reveal he same endency of he ne oil price increase model o have a higher recursive MSPE han he AR(4) benchmark model for real GDP growh hroughou much of he pre-crisis period. Boh in 1990 and beween 1998 and 2008 he nonlinear forecasing model proved persisenly less accurae ou of sample han he AR(4) benchmark. Only in 2009 is ha ranking reversed again in favor of he nonlinear model. Given ha he financial crisis occurred immediaely afer a major surge in he price of oil, bu iself was presumably no caused by ha oil price surge, he obvious concern is ha he nonlinear model may have forecas he 2008 recession for he wrong reasons. I is usually hough ha ou-of-sample forecass proec agains overfiing. The example of 2008/09 illusraes ha his need no be he case. Under quadraic loss he abiliy of he nonlinear model o predic correcly he sharp economic decline associaed wih he financial crisis may more han offse he susained poor forecasing accuracy of his nonlinear model during earlier episodes no involving smaller forecasing errors. Only addiional daa will ulimaely resolve his quesion. If he near-simulaneous occurrence of he financial crisis and he oil price surge is coincidenal, hen he forecasing accuracy of he nonlinear model can be expeced o worsen, as he sample is exended. If he forecasing success of he nonlinear model 56

59 were o persis even afer he financial crisis is over, his would add credibiliy o he nonlinear real GDP growh forecass. The same concern regarding he financial crisis episode arises o varying degrees wih oher oil price series. Table 20 provides a sysemaic comparison of he performance of nonlinear forecasing models relaive o he AR(4) benchmark model for real GDP growh for differen oil price series and evaluaion periods. To conserve space, we focus on models (23) and (23 ) which end o be he mos accurae nonlinear forecasing models. Table 20 shows ha he relaive MSPE of nonlinear forecasing models can be highly sensiive o he choice of oil price series. The firs wo columns of Table 20 focus on he evaluaion period 1990.Q Q2. Column (1) shows ha, for eigh of en model specificaions, he one-quarer ahead nonlinear forecasing model proposed by Hamilon (2010) fails o ouperform he AR(4) benchmark model for real GDP. Only for he real refiners acquisiion cos for impored crude oil and for he nominal WTI specificaion are here any gains in forecas accuracy. In paricular, he nominal PPI specificaion favored by Hamilon (2010) on he basis of in-sample diagnosics is less accurae han he AR benchmark model. Much more favorable resuls are obained a he one-year horizon in column (2) of Table 20. All bu one nonlinear forecasing model yields reducions in he MSPE, alhough he exen of hese reducions grealy differs across models and can range from negligible o subsanial. However, all evidence of forecas accuracy gains vanishes if he financial crisis episode is excluded, as shown in columns (3) and (4) of Table 20. Some nonlinear forecasing models have more han wice he MSPE of he AR benchmark model. We conclude ha he evidence ha nonlinear oil price ransformaion help forecas cumulaive U.S. real GDP growh is mixed a bes. The resuls in Tables 19 and 20 were consruced from fully revised daa ha would no have been available o forecasers in real ime. As in our analysis of real oil price forecass, an obvious addiional quesion would be how he resuls of he forecas accuracy comparison for U.S. real GDP growh would have changed, had we only used daa ses acually available as of he ime he forecas is generaed. This remains an open quesion a his poin Some preliminary evidence on his quesion has been provided by Ravazzolo and Rohman (2010) and by Carlon (2010). I is no sraighforward o compare heir resuls o hose in Tables 19 and 20, however. No only is heir analysis based on one-sep-ahead real GDP growh forecass from single-equaion predicive models evaluaed a he relevan forecasing horizon (raher han ieraed forecass from mulivariae models), bu i is based on a sample period ha includes pre-1973 daa. 57

60 11.3. Nonparameric Approaches Our approach in his secion has been parameric. Alernaively, one could have used nonparameric economeric models o invesigae he forecasing abiliy of he price of oil for real GDP. In relaed work, Bachmeier, Li and Liu (2008) used he inegraed condiional momen es of Corradi and Swanson (2002, 2007) o invesigae wheher oil prices help forecas real GDP growh one-quarer ahead. The advanage of his approach is ha while imposing lineariy under he null i allows for general nonlinear models under he alernaive; he disadvanage is ha he es is less powerful han he parameric approach if he parameric srucure is known. Bachmeier e al. repor a p-value of 0.20 for he null ha nominal ne increases in he WTI price of oil do no help forecas U.S. real GDP. The p-value for percen changes in he WTI price of crude oil is Similar resuls are obained for real ne increases and for percen changes in he real WTI price. These findings are broadly consisen wih ours. Bachmeier e al. (2008) also repor qualiaively similar resuls using a number of fully nonparameric approaches. An obvious cavea is ha heir analysis is based on daa since 1949, which is no appropriae for he reasons discussed earlier, and ends before he 2008/09 recession. Using heir nonparameric echniques on our much shorer sample period does no seem advisable, however, because here is no way of conrolling he size of he es. 12. The Role of Oil Price Volailiy Poin forecass of he price of oil are imporan, bu hey fail o convey he uncerainy associaed wih oil price forecass. Tha uncerainy is capured by he predicive densiy. Figure 14 plos he 12-monh ahead predicive densiy for he real price of oil as of , generaed from he no-change forecasing model. Alhough i is obvious ha here is remendous uncerainy abou he fuure real price of oil, even when using he bes available forecasing mehods, i is less obvious how o convey and inerpre ha informaion. For example, sandard quesions in he financial press abou wheher he price of oil could increase o $200 a barrel, a he risk of being misundersood, ineviably and always mus be answered in he affirmaive because he predicive disribuion has infinie suppor. Tha answer, however, is vacuous because i does no convey how likely such an even is or by how much he price of oil is expeced o exceed he $200 hreshold in ha even. 58

61 12.1. Nominal Oil Price Volailiy One seemingly naural way of summarizing he informaion in he predicive disribuion is o repor he variabiliy of he forecass. Ineres in oil price volailiy measures arises, for example, from financial analyss ineresed in pricing opions and from porfolio managers ineresed in diversifying risks. Given ha a shor horizons CPI inflaion is negligible, i is cusomary in financial applicaions o focus on nominal oil price volailiy. One approach o measuring oil price volailiy is o rely on he implied volailiies of pu and call opions, which are available from January 1989 on. Implied volailiy measures are compued as he arihmeic average of he daily implied volailiies from he pu and call opions associaed wih a fuures conrac of a given mauriy. The upper panel of Figure 15 shows he 1-monh implied volailiy ime series for , compued from daily CRB daa, following he same procedure as for he spo and fuures prices in secion 5. Alernaively, we may use daily percen changes in he nominal WTI price of oil o consruc measures of realized volailiy, as shown in he second panel of Figure 15 (see, e.g., Bachmeier, Li and Liu 2008). Finally, ye anoher measure of volailiy can be consruced from parameric GARCH or sochasic volailiy models. The boom panel of Figure 15 shows he 1-monh-ahead condiional variance obained from recursively esimaed Gaussian GARCH(1,1) models. 33 The iniial esimaion period is The esimaes are based on he percen change in he nominal WTI price; he corresponding resuls for he real WTI price are almos indisinguishable a he 1-monh horizon. 34 Figure 15 plos all hree volailiy measures on he same scale. Alhough all hree measures agree ha by far he larges volailiy peak occurred near he end of 2008, here are imporan differences. For example, he implied volailiy measure increases seadily saring in early 2008 and peaks in December Realized volailiy also peaks in December 2008, bu does no increase subsanially he second half of Finally, GARCH volailiy is even 33 The sandard GARCH model is used for illusraive purposes. An alernaive would be a GARCH-in-Mean model. Given ha oil is only one of many asses handled by porfolio managers, however, i is no clear ha he GARCHin-Mean model for single-asse markes is appropriae in his conex, while more general mulivariae GARCH models are all bu impossible o esimae reliably on he small samples available for our purposes (see, e.g., Bollerslev, Chou and Kroner 1992). 34 We deliberaely focus on oil price volailiy a he 1-monh horizon. Alhough from an economic poin of view volailiy forecasing a longer horizons would be of grea ineres, he sparsiy of opions price daa makes i difficul o exend he implied volailiy approach o longer horizons. Likewise, GARCH volailiy esimaes quickly converge o he uncondiional variance a longer horizons. 59

62 slower o increase in 2008 and only peaks in January This ranking is consisen wih he view ha implied volailiy is he mos forward-looking volailiy measure and GARCH volailiy he mos backward-looking volailiy esimae (and hence he leas represenaive measure of real ime volailiy). Similarly, he implied volailiy and realized volailiy measures indicae subsanial secondary spikes in volailiy in 2001/02 and 2003, whereas he spikes in he GARCH volailiy esimae are much smaller and occur only wih a delay. I may seem ha flucuaions in oil price volailiy, defined in his manner, would be a good indicaor of changes in oil price risks. I is imporan no o equae risk and uncerainy, however. Whereas he laer may be capured by he volailiy of oil price forecass, he former canno. The sandard risk ha financial markes in oil-imporing economies are concerned wih is he risk of excessively high oil prices. Tha risk in general will be a bes weakly correlaed wih he volailiy of oil price forecass because any reducion in risk, as he price of oil falls, all else equal, will be associaed wih increased oil price volailiy. This is why in 1986, for example, oil price volailiy increased, as OPEC collapsed and he price of oil dropped sharply, whereas by all accouns consumers were pleased wih lower oil prices and he diminished risk of an OPEC induced supply disrupion. Hence, sandard volailiy measures are of limied use as summary saisics for he predicive disribuion of oil price forecass. We defer o secion 12.3 for a more deailed exposiion of how appropriae risk measures may be compued from he predicive disribuion of he price of oil Real Oil Price Volailiy Ineres in he volailiy of oil prices also has been promped by research aimed a esablishing a direc link from oil price volailiy o business cycle flucuaions in he real economy. For example, Bernanke (1983) and Pindyck (1991) showed ha he uncerainy of he price of oil (measured by he volailiy of he price of oil) maers for invesmen decisions if firms conemplae an irreversible invesmen, he cash flow of which depends on he price of oil. An analogous argumen holds for consumers considering he purchase of energy-inensive durables such as cars. Real opions heory implies ha, all else equal, an increase in expeced volailiy will cause marginal invesmen decisions o be posponed, causing a reducion in invesmen expendiures. Kellogg (2010) provides evidence ha such mechanisms are a work in he Texas oil indusry, for example. 60

63 Unlike in empirical finance, he relevan volailiy measure in hese models is he volailiy of he real price of oil a horizons relevan o purchase and invesmen decisions, which is ypically measured in years or even decades raher han days or monhs, making sandard measures of shor-erm nominal price volailiy inappropriae. Measuring he volailiy of he real price of oil a such long forecas horizons is inherenly difficul given how shor he available ime series are, and indeed researchers in pracice have ypically assered raher han measured hese shifs in real price volailiy or hey have reaed shor-horizon volailiy as a proxy for longer-horizon volailiy (see, e.g., Elder and Serleis 2010). 35 This approach is unlikely o work. Sandard monhly or quarerly GARCH model canno be used o quanify changes in he longerrun expeced volailiy of he real price of oil because GARCH forecass of he condiional variance quickly rever o heir ime invarian uncondiional expecaion, as he forecasing horizon increases. If volailiy a he economically relevan horizon is consan by consrucion, i canno explain variaion in real aciviy over ime, suggesing ha survey daa may be beer suied for characerizing changes in forecas uncerainy over ime. Some progress in his direcion may be expeced from ongoing work conduced by Anderson, Kellogg and Sallee (2010) based on he disribuion of Michigan consumer expecaions of 5-year-ahead gasoline prices. For furher discussion of his poin also see Kilian and Vigfusson (2010b) Quanifying Oil Price Risks Alhough oil price volailiy shifs play an imporan role in discussions of he impac of oil price shocks, i is imporan o keep in mind ha volailiy measures are no in general useful measures of he price risks faced by eiher producers or consumers of crude oil (or of refined producs). Consider an oil producer capable of producing crude oil from exising wells as long as he price of oil exceeds his marginal cos of $25 a barrel. One risk faced by ha oil producer is ha he will go ou of business if he price of oil falls below ha hreshold. Excessively high oil prices, in conras, are of no concern unil hey reach he poin of making replacemen echnologies economically viable. Tha migh be he case a a hreshold of $120 a barrel, for example, a 35 In rare cases, he relevan forecas horizon may be shor enough for empirical analysis. For example, Kellogg (2010) makes he case ha for he purpose of drilling oil wells in Texas, as opposed o Saudi Arabia, a forecas horizon of only 18 monhs is adequae. Even a ha horizon, however, here are no oil-fuures opions price daa ha would allow he consrucion of implied volailiy measures. Kellogg (2010) herefore convers he one-monh volailiy o 18-monh volailiies based on he erm srucure of oil fuures. Tha approach relies on he assumpion ha oil fuures prices are reliable predicors of fuure oil prices. 61

64 which price major oil producers risk inducing he large-scale use of alernaive echnologies wih adverse consequences for he long-run price of crude oil. 36 Thus, he oil producer will care abou he risk of he price of oil no being conained in he range beween $25 and $120, and he exen o which he is concerned wih violaions of ha range depends on his risk aversion, which need no be symmeric in eiher direcion. 37 There is no reason why oil producers should necessarily be concerned wih a measure of he variabiliy of he real price of oil. In fac, i can be shown ha risk measures are no only quaniaively differen from volailiy measures, bu in pracice may move in he opposie direcion. Likewise, a consumer of reail moor gasoline (and hence indirecly of crude oil) is likely o be concerned wih he price of gasoline exceeding wha he can afford o spend each monh (see Edelsein and Kilian 2009). The hreshold a which consumers migh rade in heir SUV for a more energy-efficien car is near $3 a gallon perhaps. The hreshold a which commuers may decide o relocae closer o heir place of work migh be a a price near $5 a gallon. The possibiliy ha he price of gasoline could fall below $2, in conras, is of comparaively lile consequence o consumers economic choices, making he volailiy of oil prices and relaed saisics such as he value a risk irrelevan o he ypical consumer. In boh examples above, he appropriae specificaion of hese agens decision problem is in erms of upside and downside price risks. The lieraure on risk managemen posulaes ha risk measures mus saisfy wo basic requiremens. One requiremen is ha he measure of risk mus be relaed o he probabiliy disribuion F() of he random variable of ineres; he oher requiremen is ha i mus be linked o he preferences of he user, ypically parameerized by a loss funcion (see Machina and Rohschild 1987). Excep in special cases hese requiremens rule ou commonly used measures of risk based on he predicive disribuion alone such as he sample momens, sample quaniles or he value a risk. In deriving appropriae risk measures ha characerize he predicive disribuion for he real price of oil, i is useful o sar wih he loss funcion. A reasonably general class of loss funcions l() ha encompasses he wo empirical examples above is: 36 A similar irreversible shif in OECD demand occurred afer he oil price shocks of he 1970s when fuel oil was increasingly replaced by naural gas. The fuel oil marke never recovered, even as he price of his fuel fell dramaically in he 1980s and 1990s (see Dargay and Gaely 2010). 37 The hreshold of $120 in his example follows from adjusing he cos esimaes for shale oil producion in Farrell and Brand (2006) for he cumulaive inflaion rae since

65 ar ( Rh) ifrh R lr ( h) 0 ifr Rh R (1 a)( Rh R) if Rh R where R hdenoes he real price of oil in dollars h periods from dae, 0a 1is he weigh aached o downside risks, and 0 and 0 measure he user s degree of risk aversion. Risks are associaed wih he even of R hexceeding an upper hreshold of R or falling below he lower hreshold of R. I can be shown ha under his loss funcion, he expeced loss is a weighed average of upside and downside risks of he form where El () adr (1 aur ), R DR ( R R ) df( R ), 0 h h UR ( R R) df( R ), 0 R h are he downside risk and upside risk, respecively. This definiion encompasses a variey of risk definiions familiar from he finance lieraure. For example, for he special case of 0 hese expressions reduce o he (arge) probabiliies DR0 Pr( R R) and UR0 Pr( R R) and for he special case of 1 hey reduce o he ail condiional h expecaions DR1 E( R R R R)Pr( R R) and UR1 E( R R R R) h h h Pr( R h R). Noe ha he laer definiion no only is concerned wih he likelihood of a ail even, bu also wih how far he real price of oil is expeced o be in he ail. The laer erm is also known as he expeced shorfall (or expeced excess). The expecaions and probabiliies in quesion in pracice can be esimaed by heir sample equivalen. 38 This digression highlighs ha he volailiy of he real price of oil in general is no he relevan saisic for he analysis of risks. In paricular, if and only if he loss funcion is quadraic and symmeric abou zero, he variance of he price of oil abou zero provides an adequae summary saisic for he risk in oil price forecass. Even ha arge variance, however, is disinc h h h h 38 Measures of risk of his ype were firs inroduced by Fishburn (1977), Holhausen (1981), Arzner, Delbaen, Eber and Heah (1999), and Basak and Shapiro (2001) in he conex of porfolio risk managemen and have become a sandard ool in recen years (see, e.g., Engle and Brownlees 2010). For a general exposiion of risk measures and risk managemen in a differen conex see Kilian and Manganelli (2007, 2008). 63

66 from convenionally used measures of oil price volailiy, defined as he variance abou he sample mean of he predicive disribuion. The laer measure under no circumsances can be inerpreed as a risk measure because i depends enirely on he predicive disribuion of he price of oil and no a all on he user s preferences. Risk measures can be compued for any predicive disribuion. The consrucion of he predicive disribuion from regression forecasing models ypically relies on boosrap mehods applied o he sequence of forecas errors obained from fiing he forecasing model o hisorical daa. This requires he forecas errors o be serially uncorrelaed, as would ypically be he case in forecasing models a horizon h = 1. For example, when fiing a random walk model of he form s 1 s 1, he forecas errors a horizon 1 may be resampled using sandard boosrap mehods for homoskedasic or condiionally heeroskedasic daa (see, e.g., Gonçalves and Kilian 2004). A longer horizons, one opion is o fi he forecasing model on nonoverlapping observaions and proceed as for h = 1. This approach is simple, bu may involve a considerable reducion in esimaion precision. For example, in consrucing he predicive disribuion of oneyear-ahead no-change forecass from monhly daa, one would consruc for he curren monh he sequence of year-on-year percen changes relaive o he same monh in he preceding year and approximae he predicive disribuion by resampling his sequence of year-on-year forecas errors. The oher opion is o consruc forecas errors from overlapping observaions and o recover he underlying whie noise errors by fiing an MA(h-1) process o he sequence of h- sep- ahead forecas errors. This allows he consrucion of boosrap approximaions of he predicive densiy by firs resampling he serially uncorrelaed whie noise residuals using suiable boosrap mehods such as he wild boosrap and hen consrucing boosrap replicaes of he h-monh-ahead forecas errors from he implied moving averages. The risk measures are consruced direcly from he boosrap esimae of he predicive disribuion, as discussed above. Below we implemen his approach in he conex of a 12-monh-ahead no-change forecas of he real WTI price of oil. Figure 16 plos he risk ha he price of oil (expressed in dollars) exceeds $80 one year laer ( R 80) and he risk ha i drops below $45 one year laer ( R 45). These hresholds have been chosen for illusraive purposes. The upper panel of Figure 16 plos he upside and downside risks for 0, whereas he lower panel plos he corresponding resuls 64

67 for 1. Noe ha by convenion he downside risks have been defined as a negaive number o improve he readabiliy of he plos. Alhough he upside risks and downside risks respond o susained changes in he condiional mean forecas by consrucion, he relaionship is no one-for-one. Figure 16 shows ha he ex ane probabiliy of he real price of oil exceeding $80 one year laer was small excep during and afer mid-2009; high probabiliies of he real price of oil falling below $45 occurred only in and The lower panel shows he corresponding ail condiional expecaions. Allowing for some risk aversion in he form of 1, he upside risks in become disproporionaely larger relaive o earlier upside risks and relaive o he downside risks. Regardless of he choice of and, he balance of risks since mid-2009 has been iled in he upside direcion. Recen upside risks are comparable o hose in I is immediaely eviden ha he hree sandard volailiy measures in Figure 15 are no good proxies for eiher of he wo risks shown in Figure 16. For example, in he second half of 2008 volailiy skyrockes while he upside risk plummes. The upside risk peaks in mid-2008, when he real price of oil peaked, bu volailiy only peaks in December 2008 or January 2009, when he real price of oil had reached a rough, much o he relief of oil consumers. Moreover, he spikes in volailiy in 2001/02 and 2003 are no mirrored by increases in upside risk, while he susained increase in upside risk afer 2004 is no mirrored by a susained increase in volailiy. Nor is volailiy sysemaically relaed o downside oil price risks. Alhough boh downside risks and volailiy peak in 2001/02, he susained increase in volailiy in early and mid-2008 is no mirrored by an increase in downside risk. Furhermore, he decline in downside risks during 2004 and 2005 is no refleced in sysemaic changes in volailiy. I is worh emphasizing ha none of hese 12-monh-ahead risk forecass provided any warning of he collapse of he real price of oil in lae To he exen ha he collapse in he real price of oil was unpredicable based on pas daa, his is no surprising. The problem is no wih he risk measures bu raher wih he underlying predicive disribuion ha hese risk measures have been applied o. Alhough he predicive disribuion based on he no-change forecas is among he bes available approaches o forecasing he real price of oil, his is a useful reminder ha even he bes available approach need no be very accurae in pracice. 65

68 13. Avenues for Fuure Research There are a number of direcions for fuure research on forecasing oil prices. One relaes o he use of addiional indusry-level predicors no commonly considered by economiss. Alhough crude oil is one of he more homogeneous commodiies raded in global markes, no all refineries may process all grades of crude oil. Moreover, differen grades of crude oil yield differen mixes of refined producs. Hence, shifs in he demand for one ype of refined produc, say, diesel fuel, have implicaions for he produc mix of refined producs (diesel, gasoline, kerosene, heaing oil, ec.) and hence for he demand for differen grades of crude oil, depending on he capaciy uilizaion raes of differen refineries. Siuaions can arise in which excess demand for one grade of crude oil may resul in rising prices, while excess supply of anoher grade of crude oil is associaed wih falling prices. Models ha incorporae informaion abou such spreads or abou he underlying deerminans of demand have he poenial of improving forecass of he price of a given grade of crude oil. A second issue of ineres is he role played by heerogenous oil price and gasoline price expecaions in modeling he demand for energy-inensive durables (see Anderson, Kellogg and Sallee 2010). There is srong evidence ha no all households share he same expecaions, casing doub on sandard raional expecaions models wih homogeneous agens. This also calls ino quesion he use of a single price forecas in modeling purchasing decisions in he aggregae. This problem is compounded o he exen ha differen marke paricipans (households, refiners, oil producers) in he same model may have very differen risk assessmens based on he same predicive oil price disribuion. Boh of hese effecs may undermine he predicive power of he price of oil for macroeconomic aggregaes as well as he explanaory power of heoreical models based on oil price forecass. Third, we have deliberaely refrained from exploring he use of facor models for forecasing he price of oil. In relaed work, Zagaglia (2010) repors some success in using a facor model in forecasing he nominal price of oil a shor horizons, alhough his evaluaion period is limied o early 2003 o early 2008, given he daa limiaions, and i is unclear how sensiive he resuls would be o exending he evaluaion period. An obvious concern is ha here are no price reversals over he evaluaion period, so any predicor experiencing susained growh is likely o have some forecasing power. Moreover, we have shown in secion 5 ha much simpler forecasing models appear capable of generaing equally subsanial reducions in 66

69 he MSPE of he nominal price of oil a shor horizons and do so for exended periods. The more imporan problem from an economic poin of view, in any case, is forecasing he real price of oil. I seems unlikely ha approximae facor models could be used o forecas he real price of oil. The variables ha maer mos for he deerminaion of he real price of oil are global. Shor of developing a comprehensive worldwide daa se of real aggregaes a monhly frequency, i is no clear wheher here are enough predicors available for reliable real-ime esimaion of he facors. For example, drawing excessively on U.S. real aggregaes as in Zagaglia (2010) is unlikely o be useful for forecasing he global price of oil for he reasons discussed in secion 4. Using a cross-secion of daa on energy prices, quaniies, and oher oil-marke relaed indicaors may be more promising, bu almos half of he series used by Zagaglia are specific o he Unied Saes and unlikely o be represenaive of global markes. 14. Conclusions Alhough here are a fair number of papers dealing wih he problem of predicing he price of oil, i is difficul o reconcile he seemingly conflicing resuls in his lieraure. The problem is no only he precise definiion of he oil price variable, bu wheher he price of oil is expressed in nominal or in real erms, wha esimaion and evaluaion periods are chosen, how forecas accuracy is evaluaed, wheher he condiional mean, condiional variance or condiional densiy is being forecas, wheher he analysis is conduced in-sample or ou-of-sample, wheher he mehods are parameric or nonparameric, and wheher ess of saisical significance are provided or no. The mos common problem in he lieraure is ha resuls are sensiive o he choice of sample period and vanish when he sample period is exended. In his chaper, our objecive has been o provide a benchmark based on daa ha include he recen collapse of he price of oil in 2008 and is subsequen recovery. We sared by discussing problems wih combining daa from he pre-1973 and pos-1973 period, highlighing he need o discard he pre-1973 daa because hese daa canno be represened by sandard ime series models. We documened a srucural break in he ime series process of boh he nominal and he real price of oil in lae We also noed he presence of a srucural break in he dynamic correlaions beween changes in he real price of oil and U.S. real GDP growh. Tha srucural break invalidaes predicive regressions based on daa exending back furher han

70 A naural saring poin for our analysis was he quesion of wheher he price of oil is inherenly unpredicable, as is someimes claimed. We provided srong evidence ha afer 1973 he nominal price of oil is predicable in populaion, consisen wih economic heory. The mos successful predicors are recen percen changes in U.S. consumer prices and moneary aggregaes as well as global non-oil indusrial commodiy prices. An even beer predicor is he recen percen change in he bilaeral dollar exchange rae of major commodiy exporers. We also found srong evidence ha afer 1973 he real price of oil is predicable in populaion based on flucuaions in global real oupu, as suggesed by sandard economic heory. We illusraed how problems of omied variables and of mismeasuremen can obscure his predicive relaionship. We emphasized he imporance of accouning for srucural changes in he composiion of real oupu, of using measures wih broad geographic coverage, and of using mehods of derending ha can capure long swings in he demand for indusrial commodiies. These resuls demonsrae ha neiher he nominal nor he real price of oil follows a random walk. Predicabiliy in populaion need no ranslae ino ou-of-sample forecas accuracy, however. One concern is ha in small samples simple parsimonious forecasing models such as he no-change forecas ofen have lower MSPE han forecass from largerdimensional models suggesed by economic heory. This may occur even if he largedimensional model is correcly specified, provided he increase in he forecas variance from esimaing he unknown parameers of he correcly specified model exceeds he reducion in he (squared) forecas bias from eliminaing he model misspecificaion. We provided evidence ha a horizons up o six monhs suiably designed unresriced vecor auoregressive models esimaed recursively on ex-pos revised daa end o be more accurae ou of sample han he no-change forecas of he real price of oil. There also is srong evidence ha recursively esimaed AR and ARMA models have lower MSPE han he nochange forecas, especially a horizons of 1 and 3 monhs. A longer horizons, he no-change forecas of he real price of oil ypically is he predicor wih he lowes MSPE. These resuls are robus o he use of real ime daa. Forecasing he nominal price of oil is a comparaively easier ask. There is srong evidence of saisically significan MSPE reducions in forecasing he nominal price of oil a horizons of 1 and 3 monhs based on recen percen changes in he price of non-oil indusrial raw maerials, for example. The gains in accuracy a he 3-monh horizon are 22%. There also is 68

71 evidence ha simply adjusing he no-change forecas for he real price of oil for expeced inflaion yields much more accurae forecass of he nominal price of oil han he no-change forecas a horizons of several years. There is no evidence agains he no-change forecas for he nominal price of oil a inermediae horizons, however. More commonly used mehods of forecasing he nominal price of oil based on he price of oil fuures or he spread of he oil fuures price relaive o he spo price canno be recommended. There is no reliable evidence ha oil fuures prices significanly lower he MSPE relaive o he no-change forecas a shor horizons, and long-erm fuures prices ofen cied by policymakers are disincly less accurae han he no-change forecas. One possible explanaion for he unexpecedly low ou-of-sample accuracy of oil fuures-based forecass may be he presence of ransacion coss impeding arbirage. An alernaive forecasing sraegy in which one uses he fuures price only if he fuures spread exceeds 5% in absolue erms and uses he spo price oherwise, yields MSPE reducions beween 0% and 6% a shor horizons (some of which are saisically significan), bu performs much worse han he no-change forecas a longer horizons. Likewise professional and governmen forecass of he nominal price of oil do no significanly improve on he no-change forecas, excep in some cases in he very shor run, and can be much less accurae. One of he main reasons for he imporance ha many macroeconomiss aach o he price of oil is is perceived predicive power for U.S. real GDP. Assessing ha predicive power requires a join forecasing model for he price of oil and for domesic real aciviy. We showed ha here are only small gains in using he price of oil in forecasing cumulaive real GDP growh from VAR models. This finding is robus o wheher he price of oil is specified in nominal or in real erms and wheher i is reaed as exogenous or endogenous. More imporanly, linear auoregressive models fail o predic major economic downurns. One possible explanaion of his forecas failure is ha he predicive relaionship is nonlinear. We herefore evaluaed and compared a wide range of nonlinear join forecasing models for he price of oil and real GDP growh. Excep for he hree-year ne oil price increase specificaion, we found no evidence a all of subsanially improved forecas accuracy for real GDP growh. Even for he hree-year ne increase model, he evidence was mixed a bes. For example, we found no evidence ha he nominal PPI hree-year ne increase model is more accurae han linear models for real GDP growh a he one-quarer horizon. A mulivariae generalizaion of 69

72 he model proposed by Hamilon (2003, 2010) ended o provide MSPE gains of up o 12% relaive o he AR(4) benchmark model a longer horizons. Even more accurae resuls were obained wih some alernaive oil price series. All hese forecasing successes, however, were driven enirely by he 2008/09 recession. Excluding ha episode from he evaluaion period, even he mos accurae nonlinear model was less accurae han he benchmark AR(4) model for real GDP growh. We showed ha here is reason o be skepical of he seeming forecasing success of many nonlinear models during he recen financial crisis. In paricular, if he one-year forecass are o be believed, he financial crisis played almos no role in he economic decline of 2008/09, which does no seem economically plausible. An alernaive explanaion is ha he evaluaion sample is oo shor for reliable inference and ha hese resuls reflec overfiing. We observed ha ne oil price increase models have a endency o predic major economic declines anyime he price of oil has increased subsanially. Alhough such predicions repeaedly proved incorrec, mos noably in 2005/06, he abiliy of some hree-year ne increase models o forecas he exreme decline of 2008/09 under quadraic loss more han compensaes for earlier forecasing errors and accouns for he higher average ou-of-sample forecas accuracy of hese models for U.S. real GDP growh. We also discussed he use of srucural forecasing models for he real price of oil. An imporan limiaion of reduced-form forecasing models of he real price of oil 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 forecasing scenarios. We illusraed how recenly developed srucural vecor auoregressive models of he global oil marke no only generae quie accurae ou-of-sample forecass, bu may be used o generae projecions of how he oil price forecas would deviae from he uncondiional baseline forecas, condiional on alernaive economic 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. The proposed mehod allows users o assess he risks associaed wih reduced-form oil price forecass. Finally, we showed ha oil price volailiy measures commonly used o characerize predicive densiies for he price of oil are no adequae measures of he risks faced by marke paricipans. We demonsraed how appropriae risk measures can be consruced. Those risk 70

73 measures, however, are only as good as he underlying forecasing models and would no have provided any advance warning of he collapse of he real price of oil in lae 2008, for example. 71

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82 Figure 1: The Nominal Price of Oil 4.5 Nominal Price of Oil: Nominal Price of Oil: WTI 120 WTI RAC Domesic RAC Impored U.S. Dollars/Barrel U.S. Dollars/Barrel NOTES: WTI sands for he Wes Texas Inermediae price of crude oil and RAC for he U.S. refiners acquisiion cos. 80

83 Figure 2: The Real Price of Oil -2.1 Real Price of Oil: Real Price of Oil: WTI -0.5 WTI RAC Domesic RAC Impored U.S. Dollars/Barrel U.S. Dollars/Barrel NOTES: Log scale. See Figure 1. 81

84 Figure 3: Percen Changes in he Real Price of Oil 50 Real Price of Oil: Real Price of Oil: WTI 40 WTI RAC Domesic RAC Impored Percen Change Percen Change NOTES: See Figure 1. 82

85 Figure 4: The Impossibiliy of Modeling Pre-1973 WTI Daa as an ARMA Process 4.5 Nominal Price of Oil: Acual WTI Random Draw from Fied Model 4 U.S. Dollars/Barrel NOTES: The fied model is a random walk wih drif in logs. The fied values have been exponeniaed. The figure illusraes ha unlike he original daa he daa generaed a random from he fied model will never remain unchanged for exended periods of ime. Hence, he class of ARMA processes is no suiable for modeling his daa se. 83

86 Ave. Number of Open Conracs Figure 5: Measures of Liquidiy in he Oil Fuures Marke (by Mauriy) Average Open Ineres 14 x M 3M 6M 9M 12M 2Y 3Y 4Y 5Y 6Y 7Y Ave. Number of Conracs Traded 7 x 104 Average Volume M 3M 6M 9M 12M 2Y 3Y 4Y 5Y 6Y 7Y NOTES: Compuaions by he auhors based on CRB daa. 84

87 Figure 6: Household Expecaions of U.S. Reail Gasoline Prices (Cens/Gallon) Expeced price 5 years from now Curren price Expeced real price 5 years from now Curren price Expeced price 5 years from now Acual price 5 years from now NOTES: Compuaions by he auhors based on Michigan Consumer Survey Expecaions, SPF 10-year CPI inflaion forecass, and EIA daa for he ciy average of reail moor gasoline prices. This analysis draws on Anderson, Kellogg and Sallee (2010). 85

88 Figure 7: Consensus Economics Expecaions of Nominal Price of Oil (Dollars/Barrel) Expeced price 1 year from now Curren price Expeced price 1 year from now Acual price 1 year from now NOTES: Compuaions by he auhors based on daa from Consensus Economics Inc. 86

89 Dollar per Barrel Figure 8: EIA Forecass of he U.S. Refiners Acquisiion Cos for Impored Crude Oil 1983.Q Q4 EIA Forecas Realizaion One Quarer Ahead Dollar per Barrel EIA Forecas Realizaion Four Quarers Ahead NOTES: The quarerly price forecass were colleced manually from he EIA s Shor-Term Economic Oulook and compared wih he ex-pos realizaions of he average quarerly nominal refiners acquisiion cos for impored crude oil. The plo shows he price realizaions ogeher wih he EIA forecass made for he same poin in ime one and four quarers earlier. 87

90 Figure 9: Forecasing Scenarios for he Real Price of Oil based on he Srucural VAR Model of Kilian and Murphy (2010) Condiional Projecions Expressed Relaive o Baseline Forecas 100 Forecas Adjusmen Based on U.S. Oil Producion Simulus Scenario Percen Forecas Adjusmen Based on World Recovery Scenario Percen Forecas Adjusmen Based on Iran 1979 Speculaion Scenario Percen NOTES: All resuls are based on he srucural oil marke model of Kilian and Murphy (2010). The U.S. oil producion simulus involves a 20% increase in U.S. oil producion in , which ranslaes o a 1.5% increase in world oil producion. For his purpose, a one-ime srucural oil supply shock is calibraed such ha he impac response of global oil producion is 1.5%. The world recovery scenario involves feeding in as fuure shocks he sequence of flow demand shocks ha occurred in The Iran 1979 speculaion scenario involves feeding in as fuure shocks he speculaive demand shocks ha occurred beween and and were a major conribuor o he 1979/80 oil price shock episode. 88

91 Figure 10: Real Price of Oil in Differen Currencies US Euro Japan UK Canada Log Deviaions from Mean NOTES: Compuaions by he auhors based on he U.S. refiners acquisiion cos for impored crude oil. 89

92 Percen a Annual Raes Figure 11: Auoregressive Forecass of Cumulaive Real GDP Growh based on he Real Price of Oil U.S. Refiners Acquisiion Cos for Impors Realizaions AR Forecas Linear VAR Forecas (a) One Quarer Ahead Percen a Annual Raes Realizaions AR Forecas Linear VAR Forecas (b) Four Quarers Ahead NOTES: The benchmark model is an AR(4) for real GDP growh. The alernaive is an unresriced linear VAR(4) model for real GDP growh and he percen change in he real price of oil. The price of oil is defined as he U.S. refiners acquisiion cos for impors. 90

93 Figure 12: Nonlinear Forecass of Cumulaive Real GDP Growh from Models (23) and ( 23 ) U.S. Refiners Acquisiion Cos for Impors Percen a Annual Raes Realizaions 3-Year Nominal Ne Increase Forecas 3-Year Real Ne Increase Forecas (a) One Quarer Ahead Percen a Annual Raes Realizaions 3-Year Nominal Ne Increase Forecas 3-Year Real Ne Increase Forecas (b) Four Quarers Ahead NOTES: One forecasing model is a suiably resriced VAR(4) model for real GDP growh and he percen change in he real price of oil augmened by four lags of he 3-year real ne oil price increase. The oher model is a similarly resriced VAR(4) model for real GDP growh and he percen change in he nominal price of oil augmened by four lags of he 3-year nominal ne oil price increase. 91

94 Figure 13: Nonlinear Forecass of Cumulaive Real GDP Growh from Model (23 ) U.S. Producer Price Index for Crude Oil: U.S. Refiners Acquisiion Cos for Impors: 10 Recursive Forecass and Realizaions 10 Recursive Forecass and Realizaions Percen (Annual Raes) Acual Forecas Based on 3-Year Ne Oil Price Increase Percen (Annual Raes) Acual Forecas Based on 3-Year Ne Oil Price Increase Relaive o AR(4) Benchmark 2 Relaive o AR(4) Benchmark Recursive MSPE Raio Recursive MSPE Raio NOTES: The nonlinear forecasing model is a suiably resriced VAR(4) model for real GDP growh and he percen change in he nominal price of crude oil augmened by four lags of he corresponding 3-year nominal ne oil price increase. 92

95 Figure 14: 12-Monh Ahead Predicive Densiy of he Real WTI Price of Oil as of Based on No-Change Forecas Dollars/Barrel 93

96 40 Figure 15: Alernaive Measures of Nominal Oil Price Volailiy 1-Monh Implied Volailiy Percen Realized Volailiy Percen Recursive GARCH Volailiy Percen NOTES: The GARCH volailiy esimae is for he percen change in he nominal WTI price. The realized volailiy was obained from daily WTI prices. The implied volailiy measure refers o he arihmeic average of he daily implied volailiies from a-hemoney pu and call opions associaed wih 1-monh oil fuures conracs and was consruced by he auhors from CRB daa. All volailiy esimaes are monhly and expressed as sandard deviaions, following he convenion in he lieraure. 94

97 1 0.5 UR(0)>80 DR(0)<45 Figure 16: 12-Monh Ahead Upside and Downside Risks in he Real WTI Price Based on No-Change Forecas Targe Probabiliies UR(1)>80 DR(1)<45 Tail Condiional Expecaions NOTES: Risks are defined in erms of he even ha he price of oil (in dollars) exceeds 80 dollars or falls below 45 dollars. For furher discussion of hese risk measures see Kilian and Manganelli (2007). 95

98 Table 1a: Predicabiliy from Seleced Nominal U.S. Aggregaes o he Nominal Price of Oil (p-values of he Wald es saisic for Granger Non-Causaliy) Evaluaion Period: WTI WTI RAC RAC Oil Impors Domesic Oil Monhly Predicors: CPI RAC Composie M M CRB Indusrial Raw Maerials Index CRB Meals Index Monh T-Bill Rae Trade-Weighed Exchange Rae NOTES: Boldface indicaes significance a he 10% level. RAC sands for U.S. refiners acquisiion cos and CRB for he Commodiy Research Bureau. All variables bu he ineres rae are expressed in percen changes. In some cases, one needs o consider he possibiliy of coinegraion in levels. All rejecions above remain significan if we follow Dolado and Lükepohl (1996) in conducing a lag-augmened Granger non-causaliy es. All es resuls are based on bivariae VAR(12) models. Similar resuls are obained wih bivariae VAR(24) models. 96

99 Table 1b: Predicabiliy from Seleced Bilaeral Nominal Dollar Exchange Raes o he Nominal Price of Oil (p-values of he Wald es saisic for Granger Non-Causaliy) Evaluaion Period: Monhly Predicors: WTI WTI RAC Oil Impors RAC Domesic Oil RAC Composie Ausralia Canada New Zealand Souh Africa NOTES: Boldface indicaes significance a he 10% level. RAC sands for U.S. refiners acquisiion cos. All variables are expressed in percen changes. All es resuls are based on bivariae VAR(12) models. 97

100 Table 2: Predicabiliy from Seleced Real Aggregaes o he Real Price of Oil (p-values of he Wald es saisic for Granger Non-Causaliy) 1973.I-2009.IV Evaluaion Period: 1975.II-2009.IV Quarerly Predicors: WTI WTI RAC Oil Impors RAC Domesic Oil U.S. Real GDP LT HP DIF World Indusrial Producion 1 LT HP DIF RAC Composie NOTES: Boldface indicaes significance a he 10% level. LT denoes linear derending, HP denoes HP filering wih smoohing parameer 1600, and DIF denoes firs differencing. RAC sands for U.S. refiners acquisiion cos. All es resuls are based on bivariae VAR(4) models. Similar resuls are obained wih bivariae VAR(8) models. In he baseline specificaion he real price of oil is expressed in log levels. Similar resuls are obained when boh variables are derended by he same mehod. 1 Daa source: U.N. Monhly Bullein of Saisics. These daa end in 2008.III because he U.N. has emporarily suspended updaes of his series, resuling in a shorer evaluaion period. 98

101 Monhly Predicors: 12 Chicago Fed Naional Aciviy Index (CFNAI) Table 3: Predicabiliy from Seleced Real Aggregaes o he Real Price of Oil (p-values of he Wald es saisic for Granger Non-Causaliy) Evaluaion Period: WTI WTI RAC RAC Oil Impors Domesic Oil RAC Composie p p 24 p 12 p 24 p 12 p 24 p 12 p 24 p 12 p U.S. Indusrial Producion LT HP DIF OECD+6 Indusrial Producion 1 LT HP DIF Global Real Aciviy Index NOTES: Boldface indicaes significance a he 10% level. LT denoes linear derending, HP denoes HP filering wih smoohing parameer (see Ravn and Uhlig 2002), and DIF denoes firs differencing. The CFNAI and he global real aciviy index are consruced o be saionary. RAC sands for U.S. refiners acquisiion cos. All es resuls are based on bivariae VAR(p) models. In he baseline specificaion he real price of oil is expressed in log levels. Similar resuls are obained when boh variables are derended by he same mehod. 1 Daa source: OECD Main Economic Indicaors. 2 Daa source: Updaed version of he index developed in Kilian (2009a). 99

102 Table 4: 1-Monh Ahead Forecas Error Diagnosics for Nominal WTI Price of Oil S MSPE Success Raio ˆ 1 (p-value) (p-value) S N.A. (1) F (0.108) (0.780) (1) S ˆ ˆ 1 lnf S (0.326) (0.209) (1) S ˆ 1 lnf S (0.125) (0.090) (1) S ˆ 1 lnf S (0.408) (0.576) (1) S1 lnf S (0.108) (0.780) S1 s (0.945) (0.488) S 1 ˆ (0.513) (0.428) (1) S1 s (0.518) (0.488) AUS S(1 e ) (0.212) (0.394) CAN S(1 e ) (0.163) (0.739) RSA S(1 e ) (0.425) (0.626) CRB, ind S(1 p ) (0.266) (0.008) CRB, me S(1 p ) (0.566) (0.017) CRB, ind,(1) S(1 p ) (0.008) (0.008) CRB, me,(1) S(1 p ) (0.404) (0.017) NOTES: All MSPE resuls are presened as raios relaive o he benchmark no-change forecas model, for which we repor he level of he MSPE. The forecas evaluaion period is The iniial esimaion window is For regressions based on 6-monh fuures prices he esimaion window begins in ; for he 9- monh fuures price in ; for he 12-monh fuures price in is he fuures price ha maures in h periods; i m, is he m monh ineres rae; s is he percen change in S in he mos recen monh; and percen change in he spo price over he mos recen h monhs. All p-values refer o pairwise ess of he null of equal predicive accuracy wih he no-change forecas. Comparisons of nonnesed models wihou esimaed parameers are based on he DM-es of Diebold and Mariano (1995) using N(0,1) criical values; p-values for oher nonnesed comparisons are obained by boosrapping he loss differenial. Nesed model comparisons wih esimaed parameers are obained by boosrapping he DM-es saisic as in Clark and McCracken (2005) and Clark and Wes (2006, 2007). The success raio is defined as he fracion of forecass ha correcly predic he sign of he change in he price of oil. The sign es in he las column is based on Pesaran and Timmermann (2009). This es canno be applied when here is no variabiliy in he prediced sign. In such cases he p-value is repored as N.A. 100 ( h) F ( h) s is he

103 Table 5: 3-Monh Ahead Forecas Error Diagnosics for Nominal WTI Price of Oil S MSPE Success Raio ˆ 3 (p-value) (p-value) S N.A. (3) F (0.467) (0.727) (3) S ˆ ˆ 1 lnf S (0.490) (0.493) (3) S ˆ 1 lnf S (0.215) (0.668) (3) S ˆ 1 lnf S (0.323) (0.727) (3) S1 lnf S (0.478) (0.727) S 1 3 s (0.997) (0.168) S 1 ˆ (0.570) (N.A.) (3) S1 s (0.656) (0.219) S 1 1/4 i ,3 (0.507) (N.A.) S ˆCF ,3 (0.994) (0.760) AUS 3 S(1 e ) (0.173) (0.071) CAN 3 S(1 e ) (0.207) (0.570) RSA 3 S(1 e ) (0.851) (0.231) CRB, ind 3 S(1 p ) (0.143) (0.001) CRB, me 3 S(1 p ) (0.422) (0.000) CRB, ind,(3) S(1 p ) (0.013) (0.012) CRB, me,(3) S(1 p ) (0.004) (0.018) NOTES: See Table

104 Table 6: 6-Monh Ahead Forecas Error Diagnosics for Nominal WTI Price of Oil S MSPE Success Raio ˆ 6 (p-value) (p-value) S N.A. (6) F (0.411) (0.322) (6) S ˆ ˆ 1 lnf S (0.422) (0.431) (6) S ˆ 1 lnf S (0.140) (0.151) (6) S ˆ 1 lnf S (0.269) (0.398) (6) S1 lnf S (0.445) (0.322) S 1 6 s (0.992) (0.153) S 1 ˆ (0.563) (N.A.) (6) S1 s (0.734) (0.547) S 1 1/2 i ,6 (0.533) (N.A.) AUS 6 S(1 e ) (0.745) (0.048) CAN 6 S(1 e ) (0.351) (0.225) RSA 6 S(1 e ) (0.985) (0.080) CRB, ind 6 S(1 p ) (0.433) (0.001) CRB, me 6 S(1 p ) (0.899) (0.005) CRB, ind,(6) S(1 p ) (0.660) (0.054) CRB, me,(6) S(1 p ) (0.673) (0.007) NOTES: See Table

105 Table 7: 9-Monh Ahead Forecas Error Diagnosics for Nominal WTI Price of Oil S MSPE Success Raio ˆ 9 (p-value) (p-value) S N.A. (9) F (0.328) (0.121) (9) S ˆ ˆ 1 lnf S (0.355) (0.120) (9) S ˆ 1 lnf S (0.192) (0.070) (9) S ˆ 1 lnf S (0.242) (0.202) (9) S1 lnf S (0.378) (0.121) S 1 9 s (0.940) (0.430) S 1 ˆ (0.500) (0.980) (9) S1 s (0.743) (0.658) AUS 9 S(1 e ) (0.965) (0.011) CAN 9 S(1 e ) (0.455) (0.080) RSA 9 S(1 e ) (0.986) (0.102) CRB, ind 9 S(1 p ) (0.887) (0.042) CRB, me 9 S(1 p ) (0.964) (0.054) CRB, ind,(9) S(1 p ) (0.679) (0.212) CRB, me,(9) S(1 p ) (0.683) (0.113) NOTES: See Table

106 Table 8: 12-Monh Ahead Forecas Error Diagnosics for Nominal WTI Price of Oil S MSPE Success Raio ˆ 12 (p-value) (p-value) S N.A. (12) F (0.139) (0.064) (12) S ˆ ˆ 1 lnf S (0.461) (0.396) (12) S ˆ 1 lnf S (0.706) (0.152) (12) S ˆ 1 lnf S (0.391) (0.442) (12) S1 lnf S (0.177) (0.064) S 1 12 s (0.886) (0.584) S 1 ˆ (0.478) (0.999) (12) S1 s (0.765) (0.934) S1 i, (0.482) (N.A.) S ˆCF ,12 (0.382) (0.081) AUS 12 S(1 e ) (0.969) (0.010) CAN 12 S(1 e ) (0.795) (0.443) RSA 12 S(1 e ) (0.997) (0.489) CRB, ind 12 S(1 p ) (0.906) (0.048) CRB, me 12 S(1 p ) (0.966) (0.112) CRB, ind,(12) S(1 p ) (0.594) (0.190) CRB, me,(12) S(1 p ) (0.655) (0.254) ˆ MSC Sh S(1, h ) (0.764) (N.A.) ˆ SPF Sh S(1, h ) (0.667) (N.A.) NOTES: See Table

107 Table 9: Shor-Horizon Forecass of he Nominal WTI Price of Oil from Daily Oil Fuures Prices since January 1986 Sar of evaluaion period: January 1986 h 1 h 3 h 6 h 9 h 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR ( ) F (0.009) (0.040) (0.053) (0.072) (0.077) (0.002) (0.063) (0.001) (0.001) (0.000) NOTES: There are 5968, 5926, 5861, 5744, and 5028 daily observaions a horizons of 1 hrough 12 monhs, respecively. Following Leamer s (1978) rule for adjusing he hreshold for saisical significance wih changes in he sample size, p-values below abou are considered saisically significan and are shown in boldface. Table 10: Long-Horizon Forecass of he Nominal WTI Price of Oil from Daily Oil Fuures Prices h( in years ) Saring dae Sample size MSPE 2 11/20/ (1.000) 3 05/29/ (0.996) 4 11/01/ (1.000) 5 11/03/ (1.000) 6 11/03/ (0.999) 7 11/21/ (0.957) SR (0.000) (0.281) (N.A.) (N.A.) (N.A.) (N.A.) NOTES: Following Leamer s (1978) rule for adjusing he hreshold for saisical significance wih changes in he sample size, p-values below for a horizon of wo years are considered saisically significan and are shown in boldface. 105

108 Table 11: Accuracy of Survey Forecass Relaive o No-Change Forecas h 3 h 12 h 60 MSPE Raio Success Raio MSPE Raio Success Raio MSPE Raio Success Raio ˆ CE Sh S, h ˆ EIA Sh S, h ˆ gasoline gasoline, MSC Ph P, h ˆ MSC Sh S(1, h ) ˆ SPF S S (1, ) h h NOTES: Boldface indicaes saisical significance a he 10% level. 1 No significance es possible due o lack of variaion in success raio. MSC denoes he Michigan Survey of Consumers, SPF he Survey of Professional Forecasers, EIA he Energy Informaion Adminisraion and CE denoes Consensus Economics Inc. h, sands for he expeced inflaion rae beween and h. 106

109 Table 12: Recursive Forecas Error Diagnosics for he Real Price of Oil from Seleced AR and ARMA Models U.S. Refiners Acquisiion Cos for Impored Crude Oil Evaluaion period: h 1 h 3 h 6 h 9 h 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR AR(12) (0.000) (0.001) (0.000) (0.081) (0.042) (0.370) (0.374) (0.915) (0.279) (0.472) AR(24) (0.000) (0.023) (0.010) (0.062) (0.133) (0.073) (0.373) (0.871) (0.344) (0.859) AR(SIC) (0.000) (0.001) (0.000) (0.130) (0.374) (0.796) (0.483) (0.602) (0.257) (0.519) AR(AIC) (0.000) (0.001) (0.001) (0.090) (0.082) (0.826) (0.273) (0.690) (0.170) (0.549) ARMA(1,1) (0.001) (0.009) (0.000) (0.560) (0.094) (0.767) (0.266) (0.644) (0.201) (0.572) ARI(11) (0.000) (0.000) (0.003) (0.024) (0.224) (0.243) (0.969) (0.671) (0.937) (0.279) ARI(23) (0.000) (0.037) (0.015) (0.139) (0.183) (0.027) (0.694) (0.248) (0.654) (0.120) ARI(SIC) (0.000) (0.003) (0.002) (0.001) (0.951) (0.101) (0.908) (0.570) (0.423) (0.377) ARI(AIC) (0.000) (0.002) (0.006) (0.002) (0.366) (0.050) (0.806) (0.610) (0.375) (0.346) ARIMA(0,1) (0.001) (0.001) (0.000) (0.004) (0.464) (0.093) (0.767) (0.463) (0.410) (0.575) NOTES: ARI and ARIMA, respecively, denoe AR and ARMA models in log differences. The SIC and AIC are implemened wih an upper bound of 12 lags. MSPE is expressed as a fracion of he MSPE of he no-change forecas. SR sands for success raio. The p- values for he sign es are compued following Pesaran and Timmermann (2009); hose for he es of equal MSPEs are compued by boosrapping he VAR model under he null, adaping he boosrap algorihm in Kilian (1999). 107

110 Table 13: Recursive Forecas Error Diagnosics for he Real Price of Oil from Seleced Unresriced VAR Models U.S. Refiners Acquisiion Cos for Impored Crude Oil Evaluaion period: Model: (1) (2) (3) (4) (5) (6) p h MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR (0.000) (0.030) (0.000) (0.004) (0.000) (0.000) (0.000) (0.000) (0.000) (0.017) (0.000) (0.006) (0.000) (0.080) (0.008) (0.078) (0.003) (0.040) (0.000) (0.005) (0.003) (0.267) (0.000) (0.033) (0.011) (0.173) (0.184) (0.523) (0.086) (0.294) (0.006) (0.148) (0.123) (0.329) (0.007) (0.161) (0.314) (0.125) (0.596) (0.339) (0.470) (0.314) (0.148) (0.231) (0.555) (0.781) (0.130) (0.111) (0.111) (0.004) (0.391) (0.154) (0.313) (0.132) (0.059) (0.012) (0.397) (0.593) (0.039) (0.002) (0.000) (0.033) (0.000) (0.086) (0.000) (0.010) (0.000) (0.034) (0.000) (0.052) (0.000) (0.046) (0.073) (0.006) (0.708) (0.024) (0.186) (0.002) (0.000) (0.012) (0.038) (0.100) (0.004) (0.019) (0.852) (0.023) (0.945) (0.081) (0.431) (0.038) (0.237) (0.163) (0.523) (0.261) (0.467) (0.081) (0.925) (0.820) (0.080) (0.013) (0.962) (0.919) (0.085) (0.049) (0.656) (0.515) (0.015) (0.010) (0.614) (0.505) (0.900) (0.782) (0.765) (0.700) (0.881) (0.718) (0.747) (0.565) (0.086) (0.044) NOTES: MSPE is expressed as a fracion of he MSPE of he no-change forecas. SR sands for success raio. The p-values for he sign es are compued following Pesaran and Timmermann (2009); hose for he es of equal MSPEs are compued by boosrapping he VAR model under he null, adaping he boosrap algorihm in Kilian (1999). Model (1) includes all four variables used in he VAR model of Kilian and Murphy (2010); model (2) excludes oil invenories; model (3) excludes boh oil invenories and oil producion; model (4) excludes real aciviy and oil producion; model (5) excludes real aciviy and oil invenories; and model (6) excludes oil producion. 108

111 Table 14: Recursive Forecas Error Diagnosics for he Real Price of Oil from Seleced AR and ARMA Models WTI Evaluaion period: h 1 h 3 h 6 h 9 h 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR AR(12) (0.015) (0.525) (0.032) (0.813) (0.279) (0.813) (0.461) (0.920) (0.403) (0.747) AR(24) (0.130) (0.666) (0.048) (0.474) (0.090) (0.503) (0.173) (0.806) (0.230) (0.720) AR(SIC) (0.002) (0.667) (0.047) (0.813) (0.418) (0.896) (0.519) (0.844) (0.488) (0.610) AR(AIC) (0.002) (0.656) (0.050) (0.813) (0.375) (0.896) (0.463) (0.844) (0.420) (0.610) ARMA(1,1) (0.008) (0.774) (0.058) (0.815) (0.302) (0.857) (0.420) (0.420) (0.402) (0.610) ARI(11) (0.024) (0.436) (0.069) (0.234) (0.704) (0.278) (0.924) (0.703) (0.875) (0.848) ARI(23) (0.150) (0.216) (0.039) (0.127) (0.088) (0.006) (0.275) (0.100) (0.345) (0.177) ARI(SIC) (0.001) (0.267) (0.020) (0.060) (0.529) (0.305) (0.556) (0.836) (0.403) (0.743) ARI(AIC) (0.003) (0.333) (0.036) (0.180) (0.584) (0.761) (0.619) (1.000) (0.469) (0.996) ARIMA(0,1) (0.006) (0.301) (0.028) (0.006) (0.390) (0.574) (0.513) (0.927) (0.382) (0.817) NOTES: See Table

112 Table 15: Recursive Forecas Error Diagnosics for he Real Price of Oil from Seleced Unresriced VAR Models WTI Evaluaion period: Model: (1) (2) (3) (4) (5) (6) p h MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR (0.000) (0.279) (0.017) (0.885) (0.014) (0.810) (0.000) (0.056) (0.024) (0.461) (0.000) (0.053) (0.000) (0.208) (0.034) (0.336) (0.022) (0.181) (0.000) (0.119) (0.092) (0.266) (0.000) (0.165) (0.063) (0.331) (0.353) (0.279) (0.209) (0.226) (0.070) (0.206) (0.520) (0.785) (0.043) (0.207) (0.334) (0.230) (0.587) (0.688) (0.436) (0.507) (0.257) (0.132) (0.639) (0.919) (0.184) (0.216) (0.178) (0.125) (0.450) (0.557) (0.363) (0.578) (0.152) (0.045) (0.518) (0.909) (0.098) (0.053) (0.006) (0.419) (0.127) (0.672) (0.060) (0.192) (0.003) (0.037) (0.182) (0.487) (0.002) (0.451) (0.072) (0.037) (0.701) (0.191) (0.055) (0.134) (0.005) (0.060) (0.265) (0.663) (0.002) (0.003) (0.843) (0.074) (0.938) (0.306) (0.147) (0.062) (0.475) (0.605) (0.515) (0.541) (0.317) (0.043) (0.854) (0.691) NOTES: See Table 13. (0.134) (0.190) (0.938) (0.870) (0.484) (0.572) (0.261) (0.249) (0.115) (0.084) (0.602) (0.570) (0.815) (0.649) (0.586) (0.568) (0.484) (0.599) (0.373) (0.214) (0.084) (0.056) 110

113 Table 16: Recursive MSPE Raios for he Real Price of Oil from Seleced Bayesian VAR Models Evaluaion period: Model: (1) (2) (3) (4) (5) (6) p h RAC WTI RAC WTI RAC WTI RAC WTI RAC WTI RAC WTI NOTES: The Bayesian VAR forecas relies on he daa-based procedure proposed in Giannone, Lenza and Primiceri (2010) for selecing he opimal degree of shrinkage in real ime. MSPE is expressed as a fracion of he MSPE of he no-change forecas. Boldface indicaes MSPE raios lower han for he corresponding unresriced VAR forecasing model in Tables 12 and 14. RAC refers o he U.S. refiners acquisiion cos for impored crude oil and WTI o he price of Wes Texas Inermediae crude oil. Model (1) includes all four variables used in he VAR model of Kilian and Murphy (2010); model (2) excludes oil invenories; model (3) excludes boh oil invenories and oil producion; model (4) excludes real aciviy and oil producion; model (5) excludes real aciviy and oil invenories; and model (6) excludes oil producion. 111

114 Table 17: Recursive Forecas Error Diagnosics for he Real Price of Oil (by Counry) Evaluaion period: U.S. Refiners Acquisiion Cos for Impored Crude Oil h 1 h 3 h 6 h 9 h 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR Japan AR(12) (0.000) (0.005) (0.001) (0.112) (0.100) (0.741) (0.445) (0.429) (0.355) (0.714) U.K. AR(12) (0.000) (0.010) (0.009) (0.042) (0.097) (0.042) (0.394) (0.856) (0.370) (0.233) Canada AR(12) (0.000) (0.004) (0.002) (0.207) (0.019) (0.266) (0.210) (0.808) (0.159) (0.534) WTI h 1 h 3 h 6 h 9 h 12 MSPE SR MSPE SR MSPE SR MSPE SR MSPE SR Japan AR(12) (0.003) (0.197) (0.011) (0.567) (0.276) (0.998) (0.417) (0.957) (0.431) (0.964) U.K. AR(12) (0.358) (0.110) (0.262) (0.760) (0.392) (0.720) (0.440) (0.828) (0.416) (0.626) Canada AR(12) (0.030) (0.297) (0.053) (0.414) (0.122) (0.633) (0.257) (0.767) (0.213) (0.444) NOTES: All MSPE resuls have been normalized relaive o he no-change forecas of he counry in quesion. The sample period is he same as in Tables 11 and 13. The foreign real price is obained by convering he U.S. real price a he real exchange rae. 112

115 Table 18: MSPE Raios of Linear Auoregressive Models Relaive o he AR(4) Benchmark Model Cumulaive U.S. Real GDP Growh Raes Real RAC Price of Impors Nominal RAC Price of Impors Horizon Oil Price Endogenous Oil Price Exogenous Oil Price Endogenous Oil Price Exogenous NOTES: The benchmark model is an AR(4) for U.S. real GDP growh. The firs alernaive is a VAR(4) model for real GDP growh and he percen change in he price of oil ha allows for unresriced feedback from U.S. real GDP growh o he price of oil. The second alernaive is a resriced VAR(4) model ha reas he price of oil as exogenous. Boldface indicaes gains in accuracy relaive o he benchmark model. No ess of saisical significance have been conduced, given ha hese models are economically indisinguishable. 113

116 Table 19a: MSPE Raios of Nonlinear Dynamic Models Relaive o he AR(4) Benchmark Model Cumulaive U.S. Real GDP Growh Raes Real Refiners Acquisiion Cos for Impored Crude Oil Unresriced Model (20) Exogenous Model (21) Horizon Mork Increase Hamilon Ne Increase Mork Increase Hamilon Ne Increase 1 Year 3 Year 1 Year 3 Year Nominal Refiners Acquisiion Cos for Impored Crude Oil Unresriced Model ( 20) Exogenous Model ( 21) Horizon Mork Increase Hamilon Ne Increase Mork Increase Hamilon Ne Increase 1 Year 3 Year 1 Year 3 Year NOTES: The benchmark model is an AR(4) for U.S. real GDP growh. The nonlinear dynamic models are described in he ex. Boldface indicaes gains in accuracy relaive o benchmark model. The exogenous model suppresses feedback from lagged real GDP growh o he curren price of oil. 114

117 Table 19b: MSPE Raios of Nonlinear Dynamic Models Relaive o he AR(4) Benchmark Model Cumulaive U.S. Real GDP Growh Raes Real Refiners Acquisiion Cos for Impored Crude Oil Resriced Model (22) Resriced Exogenous Model (23) Horizon Mork Increase Hamilon Ne Increase Mork Increase Hamilon Ne Increase 1 Year 3 Year 1 Year 3 Year Nominal Refiners Acquisiion Cos for Impored Crude Oil Resriced Model ( 22) Resriced Exogenous Model ( 23 ) Horizon Mork Increase Hamilon Ne Increase Mork Increase Hamilon Ne Increase 1 Year 3 Year 1 Year 3 Year NOTES: The benchmark model is an AR(4) for U.S. real GDP growh. The nonlinear dynamic models are described in he ex. Boldface indicaes gains in accuracy relaive o benchmark model. The resriced model suppresses feedback from lagged percen changes in he price of oil o curren real GDP growh, as proposed by Hamilon (2003, 2010). The resriced exogenous model combines his resricion wih ha of exogenous oil prices, furher increasing he parsimony of he model. 115

118 Table 20: MSPE Raios for Cumulaive U.S. Real GDP Growh Rae Relaive o AR(4) Benchmark Model: Models (23) and ( 23 ) for Alernaive Oil Price Specificaions and Evaluaion Periods Oil Price Series 1990.Q Q Q Q4 Horizon Horizon h 1 h 4 h 1 h 4 Real RAC impors RAC composie RAC domesic WTI PPI Nominal RAC impors RAC composie RAC domesic WTI PPI NOTES: To conserve space, we focus on he mos accurae nonlinear forecasing models. The models are described in he ex. Boldface indicaes gains in accuracy relaive o AR(4) benchmark model for real GDP growh. 116