HOW SHOULD MONETARY POLICY RESPOND TO CHANGES IN THE RELATIVE PRICE OF OIL? CONSIDERING SUPPLY AND DEMAND SHOCKS

Transcription

1 HOW SHOULD MONETARY POLICY RESPOND TO CHANGES IN THE RELATIVE PRICE OF OIL? CONSIDERING SUPPLY AND DEMAND SHOCKS MICHAEL PLANTE RESEARCH DEPARTMENT WORKING PAPER 1202 Federal Reserve Bank of Dallas

2 HOW SHOULD MONETARY POLICY RESPOND TO CHANGES IN THE RELATIVE PRICE OF OIL? CONSIDERING SUPPLY AND DEMAND SHOCKS. MICHAEL PLANTE Absrac. This paper examines opimal moneary policy in a New Keynesian model where he relaive price of oil is affeced by exogenous supply shocks and a produciviy-driven demand shock. When wages are flexible, sabilizing core inflaion is opimal and he nominal rae rises (falls) in response o a demand (supply) shock. When boh prices and wages are sicky, core inflaion falls (rises) in response o he demand (supply) shock. Sabilizing CPI inflaion generaes small welfare losses only if he demand shock is he main driver of oil prices. Based on a VAR esimaed using pos-1986 daa for he U.S., boh shocks have had minimal impacs on core inflaion. The federal funds rae rises in response o he demand shock bu falls in response o he supply shock, consisen wih he predicions of he heoreical model for a policy ha sabilizes core inflaion. JEL Classificaions: E31, E52, Q43 Keywords: oil prices, opimal moneary policy, inflaion Dae: January 10, This paper previously circulaed as a CAEPR working paper iled How Should Moneary Policy Respond o Exogenous Changes in he Relaive Price of Oil? For many helpful commens and suggesions I would like o hank he edior, wo anonymous referees, my hesis advisors Edward Buffie, Eric Leeper, Brian Peerson, and Todd Walker, as well as Anhony Landry, Mine Yucel and Anhony Murphy. In addiion, I am graeful for commens received from various people during my say a he Riksbank in he summer of 2008 and he Board of Governors in he fall of 2008, including Lars Svensson and Chrisopher Erceg. All errors remain my own. Federal Reserve Bank of Dallas, michael.plane@dal.frb.edu. As always, he resuls and my opinions regarding hese resuls are mine alone and do no necessarily reflec he official views of he Federal Reserve Bank of Dallas nor he Federal Reserve Sysem as a whole.

3 1. Inroducion A long radiion in he lieraure on moneary policy and oil prices has been o assume ha he relaive price of oil is exogenous o he model being considered. 1 One of he moivaions for his seup was he view ha exogenous supply shocks, paricularly due o OPEC, were he fundamenal driver of oil prices. Kilian (2009), however, has provided evidence ha demand shocks are also imporan in deermining he price of oil, and ha macroeconomic aggregaes may respond differenly o hese shocks even hough hey also cause he price of oil o increase. This raises an ineresing quesion abou wheher or no moneary policy should respond differenly o a rise in he price of oil driven by demand raher han supply. One way o answer his quesion is o solve for an opimal moneary policy and examine he impulse response funcions of ineres raes and inflaion variables o see if hey differ in imporan ways in response o supply and demand shocks. The approach aken in his paper is o consider he opimal responses ha come from a welfare maximizing policy done from he imeless perspecive wih a non-disored seady sae. For his ype of opimal policy, Bodensein, Erceg, and Guerrieri (2008) showed ha when wages and prices are sicky an exogenous supply shock brings abou a rise in core inflaion and a decrease in nominal wage inflaion. The supply shock reduces he marginal produc of labor so he real wage should fall, and higher core inflaion helps bring abou his adjusmen. Echoing he resuls provided in Aoki (2001), here is no explici aemp o sabilize he price of oil because i is a flexible price. As such, here is no disorion associaed wih changes in ha price and, herefore, no reason o sabilize he inflaion rae of ha price. As a consequence, here is also no explici aemp o sabilize CPI inflaion. In his paper, I show ha here are fundamenal differences in he opimal responses when he increase in he price of oil is due o a produciviy-driven demand shock insead of a supply shock. While core inflaion iniially rises in response o an exogenous oil supply shock, i falls in response o he demand shock. Even hough he produciviy shock drives up he price of oil, on ne i increases he marginal produc of labor, he opposie of wha occurs wih he supply shock. This calls for core inflaion o decrease so as o help push he real wage up. 1 Examples of his approach include Leduc and Sill (2004), Dhawan and Jeske (2007), Blanchard and Gali (2010), and he previous version of his paper, Plane (2009). Furher examples of he exogenous price assumpion can be found in lieraure ha explores how oil prices affec he macroeconomy, including, bu no limied o, Finn (2000), Roemberg and Woodford (1996), and Kim and Loungani (1992). Some recen work has begun o model endogenous oil prices, including Bodensein, Erceg, and Guerrieri (2008), Nakov and Pescaori (2010). 2

4 Some imporan differences remain even in he simpler case when wages are flexible. While core inflaion is perfecly sabilized regardless of he shock, he nominal ineres rae adjuss quie differenly. In response o he demand shock he rae rises, bu i falls in response o he exogenous supply shock. The welfare implicaions of some alernaive policy rules ha sabilize core inflaion, CPI inflaion, or nominal wage inflaion are also examined. Policy rules ha sabilize core or nominal wage inflaion produce relaively minor welfare losses in all of he cases considered, so long as he response o inflaion is no oo weak. The coss of sabilizing CPI inflaion, however, depend upon he relaive imporance of supply and demand shocks. When produciviy shocks are he sole driver of oil prices, sabilizing CPI inflaion performs relaively well. When exogenous oil supply shocks drive he relaive price of oil, however, his policy produces high losses compared o sabilizing core inflaion or nominal wage inflaion. The final conribuion of his paper is o ake he model s predicions abou moneary policy o he daa using a modified version of he VAR inroduced in Kilian (2009). The modified model can idenify exogenous oil supply shocks, demand shocks driven by global economic aciviy, and a demand shock driven by unexpecedly srong economic aciviy in he Unied Saes. Daa from he pos-1986 era is used o esimae he model. Impulse response funcions from he VAR show minimal movemens in core inflaion in response o boh he exogenous supply shock and he shock o U.S. real GDP. An oil supply shock causes a rise in core inflaion of abou 10 basis poins in he firs monh. In response o he demand shock, core inflaion iniially falls by a rivial amoun. Bu, he iniial responses and he ones following ha are no saisically differen from 0 for eiher shock. The federal funds rae adjuss differenly in response o he wo shocks. The monh o monh changes are small, bu he cumulaive impacs show he federal funds rae falling in response o he exogenous supply shock bu increasing in response o he demand shock. These resuls are similar o he findings in Kilian and Lewis (2011), which showed ha he federal funds rae had a endency o fall in response o a supply shock and increase in response o a demand shock driven by global economic aciviy. Ineresingly, he movemen in he funds rae is qualiaively similar o he response he heoreical model predics should occur when he cenral bank sabilizes core inflaion. This finding suggess ha moneary policy has effecively disinguished beween differen shocks ha affec he price of oil and successfully sabilized core inflaion. While his may no be he fully opimal policy in response o boh shocks, he losses prediced by he heoreical model under his policy are relaively small in naure. 3

5 The res of he paper is organized as follows. Secion wo oulines he model. Secion hree presens he resuls abou he opimal policy and he policy rules. Empirical resuls are presened in secion four. Secion five concludes. 2. The Model The model used is a New Keynesian model modified o incorporae firm and household demand for oil, capial accumulaion, and an exogenous oil supply. The following exposiion inroduces hose equaions necessary for undersanding he special feaures of he model or he resuls presened in laer secions. All oher equaions and derivaions are relegaed o he echnical appendix Producion. There is a coninuum of firms of measure 1 in he inermediae goods secor, wih firms being indexed by i. Each firm produces a specific good, denoed by y i, which is sold a price p i. The final good, Y, is produced using he inermediae goods under he sandard assumpions. The elasiciy of subsiuion beween he various inermediae goods is given by θ, wih θ > 1. In his model he price of he final good, P, is also he price of he final, non-oil consumpion good and is herefore referred o as he core CPI. The equaion for core inflaion is Π = P. (1) P 1 The final good is he numeraire so all nominal variables are deflaed by P and hese are referred o as real variables. In he inermediae goods secor, each firm i uses capial, k i, an aggregaed labor inpu, h i, and oil, o f i o produce y i. The real prices of capial, labor, and oil are denoed as R, W, and P o, respecively. Technology is CES and he funcional form is [ ] y i = A a 1 (z h i ) η 1 η + a 2 o f η 1 η η 1 η 1 η η + a 3 k, where η is he elasiciy of subsiuion beween he inpus, A a scaling parameer, and a 1, a 2, and a 3 are disribuion parameers. The variable z is a emporary produciviy shock. The firs order condiions for he inpus come from solving he usual cos-minimizaion problem. The real uni cos funcion for his echnology is [ φ = 1 A a η 1 ( W z i ) 1 η + a η 2P o 1 η + a η 3R 1 η 4 i ] 1 1 η. (2)

6 The assumpion ha here is no facor specificiy a he firm level implies ha he uni cos funcion is aken as given by firms in he inermediae goods secor. Price seing follows Calvo (1983) in ha only a se fracion of firms change heir prices each period, wih he probabiliy of a price remaining fixed given by ω. Firms ha are able o change heir price do so by solving he sandard profi maximizaion problem, given by [ ( ) 1 θ ( ) θ max Γ i = E ω j βj λ +j (1 + τ p pi pi ) Y +j φ p +jy +j], (3) i λ P +j P +j j=0 where β is he discoun facor of he represenaive household and λ is equal o he marginal uiliy of aggregae consumpion. In line wih Bodensein, Erceg, and Guerrieri (2008), I assume he exisence of a subsidy, τ p, which removes he disorion due o monopolisic compeiion in he seady sae The Labor Inpu. Following Schmi-Grohe and Uribe (2006) he labor inpu h i is an aggregae of a coninuum of labor ypes indexed by j. The labor ypes are imperfec subsiues for each oher wih he elasiciy of subsiuion given by θ n > 1. Demand by firm i for labor ype j is denoed as h j i. The seup for producing h i from h j i is analogous o he one used when producing Y from y i. Tha is, [ 1 ] θn h i = h j θn 1 θn 1 θn i dj. The demand for labor ype j by firm i is given by ( ) h j i = w j θn h i, 0 W where w j = wj P is jus he real wage of labor ype j. The variable W is an aggregae real wage index given by [ 1 ] 1 W = w j 1 θn 1 θn dj. Since W is he real wage, nominal wage inflaion is given by 0 Π w = W W 1 Π. (4) As wih prices, only a se fracion of nominal wages change each period, wih ω n being he probabiliy of a wage being fixed in he curren period. A firs order condiion for he rese wages comes direcly from he agen s opimizaion problem. As he job ypes are ex-ane idenical, all wages rese in he same period are equal in equilibrium. The opimal real wage 5

7 choice is denoed as w P while wages ha remain fixed are given by = w. Any real wage which is changed in period is given by w j = w, w j = wj 1 Π. Noe ha he unchanged wages are deflaed by core inflaion because hey are in real erms, no nominal, and over ime he real wage may rise or fall depending on wha happens wih core inflaion Aggregaion. Aggregaion is done linearly across firms and labor ypes. This inroduces wo sae variables, and w, which measure price and real wage dispersion, respecively. The equaion for he price dispersion variable is 1 ( ) θ pi = di (5) 0 while he equaion for real wage dispersion is ( ) 1 w w j θn = dj. (6) W 0 These variables are imporan because price and wage dispersion bring abou deadweigh losses hrough he inefficien use of he various goods and labor ypes. Opimal policy will, herefore, focus on minimizing hese disorions in order o reduce he welfare losses hey generae. This implies ha here will be an emphasis on sabilizing core and/or nominal wage inflaion in response o shocks. P 2.4. The Household. Uiliy from he final, non-oil consumpion good, C, and from oil producs, O h, is aggregaed wih a CES funcion ) (C ν 1 ν + κ 2 O h ν 1 ν ν 1 ν, where ν is he elasiciy of subsiuion beween non-oil and oil consumpion and κ 2 is a disribuion parameer. Per period uiliy is given by )( (C ν 1 ν + κ 2 O h ν 1 ν 1)(1 ν 1 τ ) ν 1 1 τ 1 µ N 1+ κ µ, where τ is he ineremporal elasiciy of subsiuion, µ is he wage elasiciy of labor supply, and N = 1 0 nj dj is aggregae labor supplied by he agen. 6

8 For convenience, I re-wrie per period uiliy in erms of real aggregae consumpion expendiure, X = C + P o O h. This can be done by seing up he indirec uiliy version of he aggregaor funcion. 2 In his form per period uiliy is equal o The P CP I erm is simply he CPI, equaion for his erm is ( P CP I X P CP I 1 1 τ ) 1 1 τ 1 µ N 1+ κ (7) µ CP I P, deflaed by P. As he aggregaor is CES he exac = ( ) 1 + κ ν 2P o1 ν 1 1 ν. (8) CPI inflaion is herefore [ 1 + κ Π CP I ν = Π 2 P o 1 ν ] 1 1 ν. (9) 1 + κ ν 2P 1 o 1 ν As expeced, CPI inflaion consiss of a core inflaion componen as well as a erm ha represens, in a slighly complicaed manner, changes in he relaive price of oil. This is clearer in he special case when he aggregaor is Cobb-Douglas, in which case CPI inflaion is equal o ( ) P Π CP I o γo = Π, P 1 o where γ o is he weigh of oil producs in he Cobb-Douglas aggregaor. In addiion o a shor-erm nominal bond, I assume he exisence of wo oher bonds: a real bond indexed o he core CPI and a real bond indexed o he CPI. The firs-order condiions for hese bonds provide he equaions ha link up he nominal ineres rae wih he wo real ineres raes. These bonds are in ne-zero supply and do no affec he resuls, bu heir firs-order condiions will be necessary o discuss he resuls in secions 3 and 4. The agen s budge consrain is X + B + B CORE + P CP I B CP I + I k = (1 + τ w ) 1 0 w j n j dj + R K + T +Γ + I 1 B 1 + R 1 CORE Π B CORE 1 +P CP I R 1 CP I B 1 CP I + P o O s. (10) As in Bodensein, Erceg, and Guerrieri (2008), I assume he exisence of a subsidy, 1 + τ w, which removes he disorion in he seady sae due o monopolisic compeiion in labor markes. 2 This is done for exposiional purposes only and has no impac on he resuls. Nor does he fac ha he non-oil consumpion good is he numeraire. 7

9 In he budge consrain B is real holdings of he nominal bond, I 1 is he nominal reurn on ha bond, I k is aggregae invesmen spending on capial goods, Γ is aggregaed real profis, T is lump sum ransfers, and I 1 is he nominal reurn on he bond. Holdings of he bond indexed o core inflaion are denoed as B CORE R CORE. The bond indexed o he CPI is denoed as B CP I and is real reurn denoed as and is real reurn is denoed as R CP I. Noe ha since he numeraire is he non-oil consumpion good, here is a P CP I muliplying holdings of he CPI-indexed bond. 3 The law of moion for capial is given by erm K +1 K = I k δ k K. (11) 2.5. Ineres Raes on Bonds in he Model. The fac ha he relaive price of he wo consumpion goods is no necessarily equal o 1 implies here are wo ways o index bonds o inflaion in he model, and hence wo differen real ineres raes. One is linked o core inflaion and he oher linked o CPI inflaion. This is differen from he basic New Keynesian model, where here is simply one real ineres rae linked o he price of he final good. In he sandard New Keynesian model wih log preferences (τ = 1), he log-linearized firs order condiions for consumpion, C, he nominal bond, and a real bond indexed o P are given by Ĉ = ˆλ, Î = ˆλ E ˆλ+1 + E ˆΠ+1, ˆR CORE = ˆλ E ˆλ+1 where λ is he muliplier on he household s budge consrain, equal o he marginal uiliy of consumpion. Variables in has are log-deviaions of variables from heir seady sae values. The firs order condiion for he nominal bond and he real bond can be combined o provide he usual (log-linearized) Fisher equaion which says ha deviaions in he nominal ineres rae are equal o deviaions in he real ineres rae and expeced inflaion. Deviaions in he real ineres rae are driven by he growh rae of consumpion. For he model used here, assuming log preferences for simpliciy, he firs order condiions for aggregae consumpion expendiure, he nominal bond, he bond indexed o he core 3 The echnical appendix describes how o go from he nominal budge consrain o he real budge consrain, denominaed in erms of he final good / non-oil consumpion good. 8

10 CPI, and he bond indexed o he CPI are, respecively, The log-linearized versions of hese equaions are X 1 = λ, (12) ˆX = ˆλ, λ = βe I λ +1 Π +1, (13) λ = βe R CORE λ +1, (14) Π CP +1 I λ = βe R CP I λ +1. (15) Π +1 Î = ˆλ E ˆλ+1 + E ˆΠ+1, ˆR CORE = ˆλ E ˆλ+1, ˆR CP I = ˆλ E ˆλ+1 + E (ˆΠ+1 ) CP I ˆΠ +1. As in he sandard model, he firs order condiion for he nominal bond and he bond linked o he core CPI can be combined again o give he usual log-linearized Fisher equaion, Î = ˆR CORE + E ˆΠ+1. (16) There is also a Fisher equaion linking up he nominal ineres rae and he real reurn on he bond indexed o he CPI, Î = ˆR CP I + E ˆΠCP I +1. (17) Equaions (16) and (17) imply ha he model is sill Wicksellian in ha sabilizing inflaion requires he nominal ineres rae o rack he real rae. Bu, he paricular real ineres rae ha needs o be racked depends upon he inflaion rae being sabilized. If core inflaion is being sabilized hen he nominal ineres rae should rack R CORE, whereas if CPI inflaion is being sabilized hen he nominal ineres rae should rack R CP I. One imporan difference beween he model in his paper and he basic model is ha i is no he growh rae of consumpion iself which drives R CORE bu insead he growh rae in aggregae consumpion denominaed in erms of he non-oil consumpion good. The growh rae of he aggregae consumpion baske, denominaed in erms of he CPI, is linked o R CP I. This suggess ha inuiion abou consumpion smoohing and he behavior i implies for he real ineres rae should apply o R CP I of his will become clearer in secion 3. bu may no apply o R CORE. The imporance 9

11 2.6. Oil Supply. The supply of oil is given by an exogenous process, ln O s = (1 ρ o )O s + ρ o O s 1 + ɛ o, (18) where ɛ o is a mean zero, i.i.d. shock wih a sandard deviaion of σ o. The assumpion of an exogenous supply of oil follows Bodensein, Erceg, and Guerrieri (2008). Unlike ha model, here is jus a emporary shock o he supply insead of a emporary and a (near) permanen componen. The relaive price of oil is deermined endogenously by he marke clearing condiion, O f + O h = O s. (19) 2.7. Moneary Policy. Moneary policy is given by he Ramsey opimal soluion or by a simple Taylor-ype rule. The Ramsey problem maximizes he expeced sum of discouned uiliy subjec o all of he equilibrium equaions in he model, such as he agen s firs order condiions, he resource consrain, and he law of moions for he exogenous processes. The opimal policy is done under full commimen from he imeless perspecive. This problem produces is own se of firs order condiions which, along wih he original equilibrium condiions, provide a se of non-linear equaions ha can hen be solved using sandard echniques. For cases where he Ramsey soluion is no used, moneary policy follows a simple Taylor ype rule of he form ln( I I ) = α π ln( Π Π ) (20) where he parameers I, and Π are he seady sae values of he nominal ineres rae and core inflaion, respecively. Rules ha replace Π wih Π w or Π CP I are also considered. As shown in he previous version of his paper, here was an inverse relaionship beween he volailiy of he variable in he rule and he calibraion of α π. This coninues o hold in he model used here. Consequenly, hese policy rules can be considered as alernaive policies ha focus on sabilizing he paricular inflaion variable in he rule Calculaion of he Welfare Losses and Soluion Mehod. Welfare losses are calculaed as he amoun of aggregae real consumpion required o produce he same welfare in a model wih sub-opimal policy as he Ramsey opimal policy. To make his clearer, define per period uiliy under he Ramsey opimal soluion as U( Xr soluion as U( Xn E P CP I =0 P CP I, N r ) and in a non-opimal, N n ). Then he condiional welfare losses, λ c, are implicily given by [ X β {U n, N n P CP I ]} = E β {U 10 =0 [ (1 λ c ) Xr P CP I, N r ]}.

12 As shown in Schmi-Grohe and Uribe (2006) i is possible o derive an equaion for λ c. In order o be able o disinguish he welfare implicaions of differen policies i is necessary o solve a second order approximaion of he model. I use he mehod of Schmi-Grohe and Uribe (2004) and he code wrien by he auhors in conjuncion wih ha paper o solve he model. Furher deails can be found in ha paper Calibraion. The model is calibraed o an iniial seady sae using a calibraion ha follows Bodensein, Erceg, and Guerrieri (2008) in mos regards. Table 1 shows he values for he model s parameers. The elasiciy of subsiuion beween inermediae goods, θ, and he elasiciy of subsiuion beween various labor ypes, θ n, are boh se o 6. Boh he probabiliy of a price and a wage being fixed in any given period, ω and ω n, are se o.75. Log preferences are used so τ is se o 1. The seady sae inflaion rae is he Ramsey opimal seady sae inflaion rae. As his paper absracs from money demand he he opimal seady sae gross inflaion rae is 1. Real GDP is calibraed o uniy and seady sae real aggregae consumpion expendiure, invesmen spending, household demand for oil, and firm demand for oil are se as percenage shares of GDP. Household and firm demand for oil producs are se o 5 percen of GDP and 2 percen of GDP, respecively. These roughly mach he averages found in NIPA daa for energy usage by firms and households from 1987 o The one significan deparure in he calibraion is he elasiciy of subsiuion parameers, ν and η. In Bodensein, Erceg, and Guerrieri (2008) hese are se o 1. Here, he elasiciy of subsiuion beween C and O h, ν, is se o.25. This makes C and O h Edgeworh complimens and ensures ha he price elasiciy of demand for oil producs is fairly low. The elasiciy of subsiuion in producion, η, is calibraed o se he compensaed price elasiciy of demand for oil. Empirical sudies end o find fairly small sizes, in absolue erms, for boh his elasiciy and oher closely relaed elasiciies. I calibrae he value of η o.25 which ses he own price elasiciy of oil o abou.25. The moivaion for hese choices comes from he calibraion of he shock processes. The law of moion for he echnology shock is ln z = ρ z ln z 1 + ɛ z, (21) where ɛ z is an i.i.d whie noise shocks wih sandard deviaion σ z. The parameers for he oil supply process also need o be calibraed. The parameers ρ z and ρ o are se o.80. The sandard deviaions of he shocks are se so ha volailiy of real GDP and he relaive 11

13 price of oil in he model mach ha found in U.S. daa from 1987 o he presen. 4 For he model wih sicky wages and prices, his led o a calibraion of σ o o and σ z o Wihou low price elasiciies of demand hese volailiies would have o unrealisically large o generae sufficien volailiy in he price of oil. 3. Theoreical Resuls This secion presens resuls for he opimal policy and he policy rules for he cases where only prices are sicky and where boh wages and prices are sicky. Comparing he resuls from he wo provides srong inuiion abou wha drives he opimal policy in a very general manner. I also gives a broader se of heoreical resuls o ake o he daa Opimal Policy wih Flexible Wages. I is well known ha when sicky prices are he only disorion ha here is no radeoff beween sabilizing inflaion and he oupu gap. I has also been shown ha a policy ha fully sabilizes inflaion makes he equilibrium nominal ineres rae change one-for-one wih changes in he real ineres rae. 5 These resuls also hold in he model used here. As discussed in Bodensein, Erceg, and Guerrieri (2008), and presened in a more general form in Aoki (2001), he inclusion of he oil secor does no add any disorions o his model since he price of ha good is flexible. Since his price is flexible here is no reason o sabilize is inflaion rae. This holds rue regardless if supply or demand shocks are driving he price of oil. The analysis, however, is complicaed by he fac ha here are muliple inflaion raes ha could be sabilized and muliple real ineres raes in he model. Since wages are flexible, he relevan inflaion variable o be sabilized is core inflaion. This is because deviaions in core inflaion from is arge level generae price dispersion, which will lead o welfare losses. inflaion is sabilized perfecly in response o all shocks. As policy is done from he imeless perspecive, core Given ha he opimal policy sabilizes core inflaion, from equaion (16) we can see ha he relevan real ineres rae ha needs o be racked is R CORE, no R CP I. In equilibrium, herefore, he log-deviaions of he nominal ineres rae will be given by Î = ˆR CORE. 4 The model is simulaed and he simulaed daa is hen logged and HP filered. A differen mehod would lead o differen calibraions for he volailiies bu changing he volailiies does no impac he qualiaive feaures of he impulse response funcions. 5 See Woodford (2003) and he numerous references herein for more discussion on his feaure of he model. 12

14 The ineresing quesion is wheher or no R CORE responds differenly o supply and demand shocks. Figure 1, which plos he responses of he nominal ineres rae and he wo real ineres raes o a negaive oil supply shock and a posiive produciviy shock, shows ha his is indeed he case. The op panel shows he deviaions of I, he middle panel R CORE, and he boom panel R CP I. The shocks are one-sandard deviaion in size. The responses have been annualized. In response o a negaive supply shock, he nominal ineres rae is iniially lowered and remains below average for around wo years. Bu, in response o he produciviy shock he rae is increased and remains above average for almos wo years. The movemen in he nominal rae is being driven by he response of R CORE. To see wha drives R CORE more explicily, noe ha he firs order condiions for aggregae consumpion is given by λ = 1 X, where X = C +P o O h. This variable measures aggregae consumpion expendiure, in erms of he non-oil good. In response o a negaive oil supply shock, X iniially rises and hen falls overime. This occurs because oil is demanded inelasically by he household, so ha spending by households, denominaed in erms of he non-oil consumpion good, rises. 6 As such, he muliplier falls iniially and hen rises over ime, bringing abou he behavior of R CORE seen in figure 1. This may seem a odds wih he usual inuiion ha he agen would wan o smooh consumpion over ime in response o a shock like he supply shock. Such smoohing should cause he real ineres rae o increase. Bu, he key poin o remember is ha he ineres rae linked o he overall consumpion baske is given by R CP I, no R CORE. As shown in figure 1, R CP I rises in response o boh shocks, as expeced Policy Rules wih Flexible Wages. Given ha sabilizing core inflaion is he opimal policy, how cosly would i be o pursue a differen policy, say of sabilizing CPI inflaion, and would he resuls differ significanly if one shock or he oher was more imporan in driving oil prices? To answer hese quesions, he welfare losses for he hree simple policy rules inroduced earlier are calculaed. This is done for hree cases: one where boh shocks hi he economy, one where only oil supply shocks hi he economy (σ z se o 0), and one where only produciviy shocks hi he economy (σ o se o 0). 6 This does no imply ha uiliy is higher for he household, since uiliy is given by X 13 P CP I.

15 Figure 2 plos he losses as a funcion of α π. The op panel shows he case wih boh shocks, he middle panel he case wih only supply shocks, and he boom panel he case wih only he produciviy shock. Under all hree cases, he rules ha sabilize core inflaion or nominal wage inflaion produce essenially zero welfare losses, so long as α π is away from he lower bound of 1. 7 The rule ha sabilizes CPI inflaion, however, only performs well when produciviy shocks are he sole shock o hi he economy. Why is his so? Theoreically speaking, sabilizing CPI inflaion always produces welfare losses in his model since his policy forces he core CPI o adjus in response o movemens in he relaive price of oil. How large hese losses are, hough, depends upon how big he movemens in he relaive price of oil are. When produciviy shocks are he sole shock in he model, hese price movemens are minue because firms use a fairly small amoun of oil. Given his, he coss of sabilizing CPI inflaion are small. The cos of sabilizing CPI inflaion, however, would rise if he produciviy shocks were more volaile, or if he firms used more oil o produce goods and services Opimal Policy wih Sicky Wages. As shown in Bodensein, Erceg, and Guerrieri (2008), sicky wages inroduce a radeoff beween sabilizing inflaion and he oupu gap in his model. This radeoff exiss because a shock which affecs he marginal produc of labor requires he real wage o adjus. When wages are flexible, i is cosless o have nominal wages adjus o ensure he real wage is a is opimal level. Wih sicky wages, however, nominal wage movemens generae heir own welfare losses. These losses can be miigaed, parially, hrough movemens in core inflaion. For example, any shock which requires he real wage o fall opimally brings abou a rise in core inflaion. Figure 3 shows he imporance of his for he case of an oil supply shock. The black line is for he case wih flexible wages while he dashed line is for he case wih sicky wages. When wages are flexible, here is a sharp drop in wage inflaion in he iniial period of he shock and no movemen in core inflaion. As prediced, wih sicky wages core inflaion rises and here is a more mued response in nominal wage inflaion. An imporan finding in his paper is ha he response o he produciviy-driven demand shock is no he same as he response o he supply shock. This can be seen in figure 4, where he op panel plos he response of core inflaion o he wo shocks while he boom panel 7 In a previous version of his paper, Plane (2009), I showed ha he volailiy of he inflaion variable (around is arge value) in he rule is inversely relaed o he value of α π, wih he volailiy becoming essenially zero for larger values of α π. This holds in his model, as well, and explains why values of α π closer o 1 cause larger welfare losses. 14

16 plos nominal wage inflaion. Core inflaion immediaely rises in response o he supply shock, while in response o he demand shock i falls. Similarly, he immediae impac of wage inflaion o he supply shock is down, bu for he demand shock i is up. The difference is because of he opposie impac he wo shocks have on he marginal produc of labor, which deermines he opimal response of he real wage and core inflaion. An exogenous supply shock reduces he marginal produc of labor. This calls for a fall in he real wage and higher core inflaion. While he produciviy shock raises he price of oil, is ne effec on he marginal produc of labor is posiive. This makes i opimal for he real wage o increase in response o he demand shock and hen evenually decline over ime. In order o accomplish his, he opimal policy calls for core inflaion o decrease a firs, and hen evenually rise for some lengh of ime Policy Rules wih Sicky Wages. Given ha he opimal policy allows for non-zero core inflaion when wages are sicky, does his significanly change which policy rules perform well? To answer his, I re-calculae he welfare losses generaed by he hree policy rules and plo he losses as a funcion of α π in figure 5. A visual inspecion shows ha he qualiaive resuls are exacly he same as in figure 2. When supply shocks drive he price of oil, a rule ha sabilizes CPI inflaion performs poorly. When hese shocks are shu down and he demand shock drives oil prices, his rule performs jus as well as he oher rules. The reason for his finding, however, is slighly more nuanced han he previous case. Under flexible wages, sabilizing CPI inflaion performs poorly because i generaes price dispersion. Under sicky wages, he opimal policy iself generaes some price dispersion, so his explanaion may no hold. Indeed, i urns ou ha wha drives he resuls is he impac ha sabilizing CPI inflaion has on he real wage, no on price dispersion. More specifically, when oil supply shocks affec he relaive price of oil, sabilizing CPI inflaion pushes he real wage in he wrong direcion. One way o see his is o re-examine he equaion for CPI inflaion under he Cobb-Douglas assumpion, Π CP I ( ) P o γo = Π. P 1 o Under he exreme case where CPI inflaion is perfecly sabilized a is seady sae level, any rise in he relaive price of oil forces he core CPI o adjus down. The cach is ha pushing he core CPI downwards pushes he real wage up, which is he wrong direcion in response o an exogenous oil supply shock. Nominal wages compensae for his by adjusing more han hey would under he opimal policy, leading o unnecessary welfare losses. The 15

17 sickier wages are relaive o prices, he worse his policy will fare when supply shocks are he main driver of oil prices. Pushing he real wage up, however, is he correc choice when produciviy shocks are he sole driver of oil prices. In ha case, rising oil prices require rising real wages. Consequenly, if produciviy shocks drive he price of oil hen a policy rule which sabilizes CPI inflaion performs jus as well as he oher wo rules Sensiiviy Analysis. In his secion I conduc a sensiiviy analysis by considering wo special cases of he model. In he firs, household demand for oil producs is shu down so as o highligh he role ha firm demand has on he opimal policy. This is followed by a scenario where firm demand for oil is shu down so as o shed ligh on he role of household demand on he opimal policy. All resuls are for he model wih sicky wages and sicky prices, and for breviy s sake he impulse response funcions are omied No Household Demand. Compared o he baseline model, he opimal policy resuls are qualiaively similar when household demand for oil is absraced from. As before, he effec of boh shocks on he marginal produc of labor is in he opposie direcion. The oil supply shock drives up he relaive price of oil, essenially reducing he demand for labor by firms. The produciviy shock, on he oher hand, increases he demand for labor. Consequenly, in response o he supply shock core inflaion rises and wage inflaion falls while a demand shock causes he opposie o occur No Firm Demand. The resuls for he produciviy shock are he same wih or wihou firm demand for oil, as i increases he marginal produc of labor. Therefore core inflaion falls and wage inflaion rises. An oil supply shock now impacs he marginal produc of labor enirely hrough he decisions of he household, and hese are driven by wheher or no oil and he non-oil consumpion good are complemens or subsiues. I can be shown ha he wo goods are Edgeworh complemens when τ > σ c and subsiues when τ < σ c. The baseline calibraion herefore leads hem o be complemens, as τ is equal o 1 and σ c equal o For he baseline calibraion, an oil supply shock leads o he opposie responses in core inflaion and wage inflaion compared o he model wih boh household and firm demand. The supply shock forces consumpion of he oil good o fall. Since he wo goods are complemens, non-oil consumpion mus also fall. In equilibrium, his implies a fall in he producion of he final good and, consequenly, a fall in he equilibrium quaniy of labor. 8 The impulse response funcions are available upon reques. Resuls for he model wih flexible wages or for oher experimens are also available upon reques. 16

18 The opimal way o do his is o push up he real wage, which can be accomplished hrough a drop in core inflaion. In an alernaive calibraion where τ is 1 and σ c is 1.25, so ha he wo consumpions goods are subsiues, he resuls are he opposie wih core inflaion rising and nominal wage inflaion falling. 4. Empirical Resuls The heoreical model makes predicions abou he responses of several policy relevan variables, including he nominal ineres rae and he rae of inflaion. To summarize, when wages are flexible core inflaion is sabilized a is arge value and he nominal ineres rae falls in response o an exogenous supply shock bu rises in response o a demand shock. Wih sicky wages, core inflaion rises in response o an exogenous supply shock bu falls in response o he produciviy shock. An ineresing quesion o ask is o wha exen hese predicions migh be found in he daa. This has been considered, indirecly, in wo recen and imporan papers. Kilian (2009) inroduced an empirical model ha allows one o idenify an exogenous oil supply shock, a global demand shock (essenially a demand shock for all commodiies driven by global economic aciviy), and an oil specific-demand shock. An exension of his model, which incorporaed he federal funds rae as a fourh variable, was used in Kilian and Lewis (2011). There are many ineresing findings in boh publicaions bu here I focus on hose resuls specifically relaed o he federal funds rae and he rae of inflaion. The findings of hese papers was ha he federal funds rae responds differenly depending upon he underlying shock driving he price of oil. The federal funds rae has a endency o fall when a supply shock his, while a demand shock driven by global economic aciviy or by some oil specific-demand shock causes he federal funds rae o rise. I was also shown ha he CPI was more affeced by he demand shocks, because hey appeared o have more persisen affecs on he price of oil han he supply shocks. Several ineresing quesions, however, remain unaddressed. Firs, here are no resuls for how core inflaion responds o he differen shocks. This is imporan because, in heory, i is he behavior of core inflaion ha is relevan for discussing opimal policy. Second, he empirical resuls do no, by hemselves, provide an explanaion for he differen responses seen in he federal funds rae. The heoreical model migh provide a coheren sory abou he empirical resuls. Finally, here is a quesion abou wheher or no he Federal Reserve responds differenly if he demand shock originaes from unexpecedly srong economic aciviy in he U.S. as opposed o a globally driven demand shock. 17

19 To address hese issues, I modify he empirical model firs developed in Kilian (2009), and laer used in Kilian and Lewis (2011). In wha follows, he main poins of he original VAR are summarized, followed by a discussion of he modificaions made o he model and he reasons for he modificaions. The impulse response funcions from his model are hen examined and discussed in ligh of he resuls from he heoreical model The Original Model. The VAR used in Kilian (2009) is wrien in he following form, 24 A 0 z = α + A i z i + ɛ. (22) i=1 The daa is monhly, from 1973:1 o 2007:12, and given by z = ( prod, rea, rpo ) where prod is he monhly percenage change in world oil producion, rea is a measure of global economic aciviy consruced by Kilian, and rpo is he refiner s acquisiion cos of oil deflaed by he CPI. The daa for world oil producion comes from he Deparmen of Energy and measures producion in housands of barrels per day. In Kilian and Lewis (2011) his model was exended by adding he federal funds rae (differenced) as a fourh variable in he sysem. The hree srucural shocks in he vecor ɛ are defined, in order, as oil supply shock ɛ, aggregae demand shock ɛ, oil specific-demand shock ɛ. A Cholesky decomposiion is used o back ou he srucural shocks using he residuals. The variables are ordered as lised in z. This implies ha world oil producion responds o boh demand shocks wih a one-monh lag, and ha world economic aciviy responds o oil specific-demand shocks wih a lag. The assumpion ha he oil supply responds wih a lag is grounded in he fac ha changing producion levels in he oil indusry is very difficul o do wihin a one monh window. Kilian (2009) argues ha he assumpion ha economic aciviy responds wih a lag o he oil-specific demand shock is jusified due he sluggish response of economic aciviy seen in he daa o changes in oil prices, in general. Noe ha his ordering also implies ha oil prices can respond in one monhs ime o he oher shocks, a quie reasonable assumpion The Modified Model. Any aemp o mach up he predicions of he heoreical model wih he daa needs o ake ino accoun ha he global demand shock in he original empirical model does no direcly map ino he demand shock in heoreical model. Taking his ino accoun is imporan for a leas hree reasons. Firs, a demand shock originaing 18

20 in he Unied Saes need no always be associaed wih a demand shock driven by global economic aciviy. Second, i would be a srong assumpion o claim a priori ha he Federal Reserve responds equivalenly o hose wo demand shocks. Finally, any demand shock originaing in he U.S. which, for whaever reason, is orhogonal o he global demand shock would, in he original empirical model, ge shuffled ino he oil-specific demand shock. My soluion is o modify he model in several ways which should allow for a beer mach beween he empirical model and he heoreical model. Le z = ( prod, rea, lrgdp, rpo, F F, π core ), where prod is he monhly percenage change in world oil producion, rea is Kilian s measure of global economic aciviy, lrgdp is he log of Sock and Wason s monhly real GDP for he U.S., firs differenced, rpo is he log of he refiner acquisiion cos of oil deflaed by he core CPI, firs differenced, F F is he monhly change in he effecive Federal Funds rae, and π core rae of he CPI excluding energy prices. 9 is he inflaion The model is esimaed wih monhly daa spanning from 1987:1 o 2008:6. This sample is chosen for wo reasons. Firs, here was a change in US moneary policy in he early 1980s. Second, here were also imporan changes in he oil marke in he mid-1980s, wih one example being he collapse of OPEC. Saring in 1987 avoids having o deal wih he poenial problems ha migh occur if here are significan breaks in he daa generaing process due o one or boh of hose issues. Daa from he recen crisis is excluded given he aypical moneary policy ha has been in place since hen. The form of he VAR is given by A 0 z = α + 5 A i z i + ɛ. (23) i=1 Only 5 lags are included insead of he original 24. This is done for wo reasons. Firs, he sample is smaller while he number of variables included larger, so here are fewer degrees of freedom available. Second, he LR es and he AIC es picked an opimal lag lengh of 5 lags while he Schwarz crierion chose 1 lag as opimal. In he ineres of capuring a richer se of dynamics, 5 lags were chosen. Daa from he end of 1986 is used in he esimaion process so useable observaions run from 1987:1 o 2008:6, leading o a oal of 258 observaions. 9 The model was also esimaed using Sock and Wason s measure of monhly real GDI, logged and firs differenced, insead of real GDP. The responses were similar in boh cases. As an addiional check he model was also esimaed using he monhly GDP series from Macroeconomic Advisers, available saring in 1992:04. The error bands were wider in his case due o he smaller sample, bu qualiaively he responses of core inflaion and he federal funds rae remained similar. 19

21 Wih he changes in z, he srucural shocks are now defined as oil supply shock ɛ, global demand shock ɛ, U.S. specific-demand shock ɛ, oil specific-demand shock ɛ, ɛ fed funds shock, ɛ shock o core inflaion. A Cholesky decomposiion, where he variables are ordered in he same way as hey are found in z, is used o idenify he srucural shocks. The jusificaion for he ordering of he firs wo variables follows from he argumens given in Kilian (2009). Ordering U.S. real GDP afer global economic aciviy is done for wo reasons. Firs, his allows economic aciviy in he U.S. o endogenously respond o shocks ha affec he world economy, which by definiion should include he U.S. I also ensures ha he srucural shock o U.S. real GDP is due o unexpecedly higher aciviy originaing in he U.S., and no simply a spill over from world economic aciviy. Second, his ordering ensures ha a demand shock due o U.S. economic aciviy does no ge shuffled ino he oil specific-demand shock. Wih oil prices ordered afer he economic aciviy variables, he shock o he price of oil can again be inerpreed as an oil specific-demand shock, as in Kilian (2009). The one difference is ha U.S. specific-demand shocks are specifically parceled ou of his. The wo oher shocks in he model are unimporan for he resuls of his paper and no discussed furher. The resuls presened are insensiive o he ordering of he federal funds rae or core inflaion Resuls. The impulse response funcions for he oil supply shock and U.S. demand shock are shown in figures The responses are ploed over a 24 monh period. In all of he graphs he solid line is he poin esimae, he dashed lines he one-sandard error bands, and he dos are he wo-sandard error bands. A response is defined as marginally significan if 0 is ouside of he one-sandard error band and significan if 0 is ouside of he wo-sandard error band. Figure 6 shows he responses due o a one-sandard deviaion shock o he supply of oil. The unexpeced decrease in he supply of oil causes several monhs of rising oil prices. Core inflaion iniially rises, on an annualized basis, by abou 10 basis poins. This movemen, 10 Resuls for he oher shocks are available upon reques. 20

22 however, is jus marginally significan and all oher oher movemens afer i are no saisically differen from 0. While he federal funds rae declines, his movemen is only significan saring abou 5 monhs afer he shock. Some of he responses are choppy and he monh o monh movemens can mask he longer run implicaions of he responses. Figure 7, herefore, plos he cumulaive responses of he variables o he supply shock. From his viewpoin, here is a marginally significan reducion in economic aciviy in he U.S. due o higher oil prices, similar o he findings in Kilian (2009). The cumulaive impac on core inflaion is essenially 0. In figure 6, he federal funds rae declined over a number of monhs. The cumulaive effec of hese declines is a reducion in he rae ha is marginally significan afer 5 monhs, and very close o being significan over he course of wo years. Figure 8 plos he responses o a posiive shock o U.S. real GDP growh. Unexpecedly srong growh in he U.S. brings abou several rounds of increases in he real price of oil, which are marginally significan in he firs wo monhs. While he poin esimae of core inflaion shows some variaion, none of he movemens are saisically significan a any horizon. The response of he federal funds rae o his shock is very differen from he exogenous oil supply shock. Insead of falling, here are a series of small increases over ime, some of which are saisically significan. As wih he supply shock, looking a he cumulaive responses gives a beer view of wha happens over ime. Two resuls are saisically significan: he increases in he federal funds rae and he higher growh in real GDP. The cumulaive impac on he price of oil is upwards, and his is marginally significan. The response of core inflaion, while posiive according o he poin esimae, is no saisically differen from 0 a any poin in ime. Quaniaively, he impulse response funcions for core inflaion are similar bu here are very differen responses in he federal funds rae. Can he heoreical model provide a reasonable sory for hese resuls? In he case of he demand shock, he answer is very much yes. In response o he demand shock, he federal funds rae rises over ime while core inflaion shows no saisically significan movemens. This is exacly wha he model predics should happen when moneary policy sabilizes core inflaion in response o his ype of shock. 11 Analyzing he supply shock is slighly more difficul. inflaion, alhough his is barely significan. There is an iniial rise in core This is he response ha would be opimal if one believes wages need o be adjused downwards hrough higher core inflaion. Bu, 11 The responses in figure 1 are from he model wih flexible wages. The responses from he model wih sicky wages are qualiaively quie similar when core inflaion is sabilized. The nominal rae rises in response o he demand shock bu is lowered in response o he supply shock. 21

23 all movemens in core inflaion afer he iniial rise are no significanly differen from 0. Furhermore, he federal funds rae is, cumulaively, lower over he firs wo years. The sory behind hese responses would be generally consisen wih wha he heoreical model says moneary policy should do o sabilize core inflaion. Taken ogeher hen, afer 1986 he Federal Reserve seems o have placed a srong emphasis on sabilizing core inflaion in response o boh oil supply shocks and a demand shock ha is driven by unexpecedly srong economic aciviy in he U.S. Movemens in he federal funds rae show ha he Federal Reserve has responded differenly in response o he wo differen shocks. This is despie he fac ha boh drive up he price of oil, and herefore migh naively be lumped ogeher as an oil price shock. There is one final issue regarding he empirical resuls worh addressing. Given he large degree of wage and price sickiness ofen found a an aggregae level, sabilizing core inflaion in response o hese wo shocks is echnically sub-opimal. Is his somehing o be concerned abou? The resuls from figure 5 show ha his policy is fairly innocuous in welfare erms. Even wih sicky wages and prices, a policy rule ha sabilized core inflaion would produce rivial losses for values of α π ha have been found in he lieraure for U.S. moneary policy afer Conclusions This paper has examined opimal moneary policy in a New Keynesian model where he relaive price of oil is driven by boh an exogenous supply shock and a produciviy-driven demand shock. When wages are flexible, he opimal policy keeps core inflaion on arge regardless of which shock drives oil prices. The nominal ineres rae falls in response o he supply shock and rises in response o he demand shock. When here is a radeoff beween sabilizing inflaion and oupu, here are imporan qualiaive differences in he response of core inflaion. This variable iniially rises in response o he supply shock bu falls in response o he demand shock. This occurs because he supply shock reduces he marginal produc of labor while he produciviy shock, while raising he price of oil, on ne raises he marginal produc of labor. The opimal policy, since i uses variaions in core inflaion o affec he real wage, consequenly generaes higher inflaion in response o he supply shock bu lower inflaion in response o he demand shock. These predicions are aken o he daa using a VAR ha ha can idenify exogenous oil supply shocks and a demand shock driven by unexpecedly srong economic aciviy in he U.S. The impulse response funcions show ha he federal funds rae responds quie differen in response o he wo differen shocks. The federal funds rae is lowered in response o he 22