Oil Price Shocks, Monetary Policy Rules and Welfare

Transcription

1 Oil Price Shocks, Moneary Policy Rules and Welfare Fiorella De Fiore Giovanni Lombardo Vikors Sebunovs July 5, 26 Work in progress) Absrac Sudden and proraced oil-price increases are generally accompanied by economic conracions and high inflaion. How should moneary policy reac o oil-price shocks in order o minimize heir adverse macroeconomic effecs? We build a DSGE model characerized by wo oil-imporing counries and one oil-exporing counry. Oil-imporing counries use oil for consumpion and as inpu in producion. The oil-exporing counry produces only oil and consumes impored goods. We calibrae he model and evaluae he performance of simple Taylor-ype ineres rae rules when he economy is hi by oil-price shocks, on he basis of a micro-founded welfare meric. We search for rules ha i) maximize welfare o a second order of approximaion, ii) saisfy he zero-lower-bound for he nominal ineres rae and iii) produce eiher a Nash or a cooperaive equilibrium. Under complee inernaional financial markes, we find ha he opimal ineres rae rule is inerial, i reacs srongly and posiively o headline inflaion and o oupu deviaions from he non-sochasic seady sae level, while i reacs negaively o oil-price inflaion. JEL classificaion: C68, E61, F41, F42. Keywords: oil prices, ineres-rae rules, welfare analysis. The views expressed in his paper are hose of he auhors and do no necessarily reflec he views of he ECB or he ESCB. Direcorae General Research, European Cenral Bank. fiorella.de fiore@ecb.in. Direcorae General Research, European Cenral Bank. giovanni.lombardo@ecb.in. Boson College. sebunov@bc.edu. 1

2 Conens 1 Inroducion 3 2 The model The EA and US economies Households Premia and UIP The energy-loaded capial secor Final goods secor Moneary policy Fiscal policy The Oil-exporing counry Marke clearing condiions Calibraion of he model Parameers and sochasic processes Size and preferences Oil shares Producion of final goods Price and wage seing Capial and invesmen Taxes and fiscal policy Inernaional capial marke and aggregae demand elasiciy Oil-producion Moneary policy Sochasic processes Daa and empirical fi The effec of an exogenous oil-price increase 23 5 Moneary policy and welfare The welfare measure Opimaliy crieria Resuls Complee markes Incomplee markes Conclusion 33 2

3 1 Inroducion Sudden and proraced oil-price increases are generally accompanied by economic conracions and high inflaion, as documened, e.g. by Hamilon 1983) and Hamilon 1996). The oil crises of he 7s provide one major example of he consequences of oil-price urbulence for he macroeconomy. No surprisingly, he surge in oil-prices experienced since 23 has raised concerns among analyss and policy makers. However, he macroeconomic effecs could be differen from hose observed in he pas. One reason is ha mos advanced economies experienced a seady reducion in oil dependence over he las decade. Anoher reason is ha boh demand and supply pressures have played a major role in he recen episode, as opposed o he dominan supply componen of he oil-price shock experienced in he 7s. Some auhors have aribued he adverse effecs of he oil-price increase in he 7s o he inappropriae response of moneary policy see, e.g., Bernanke e al. 1997) and Barsky and Kilian 22)) In his paper, we build a dynamic sochasic general equilibrium DSGE) model ha can capure he main feaures of he recen episode and ask how should moneary policy reac o oil price shocks. More specifically, we evaluae he welfare consequences of oil price shocks when he cenral bank commis o a feedback ineres rae rule. We compare he performance of opimized simple rules ha reac o differen macroeconomic variables such as he lagged ineres rae, real GDP, inflaion and energy price inflaion) according o a micro-founded welfare meric. We consider wo alernaive specificaions concerning he inernaional financial marke: a complee marke srucure conducive o consumpion-risk sharing across counries, and a non-coningen bonds srucure. Under complee inernaional financial markes, we find ha he opimal ineres rae rule is inerial, i reacs srongly and posiively o headline inflaion and o oupu deviaions from he non-sochasic seady sae level, while i reacs negaively o oil-price inflaion. As headline inflaion conains an oil-price inflaion componen, our rule amouns o a form of core price inflaion, alhough he weigh given o oil-prices is larger han he share of oil in oal households consumpion. Under incomplee markes [... o be compleed.] Our framework is a hree-counry DSGE model, which is characerized by wo oil-imporing counries he US and he euro area), and one oil exporing counry or a block of ne oilexporing counries). The wo oil-imporing counries are idenical in srucure. They are inhabied by infinielylived households consuming a baske of domesically produced goods, impored goods and oil. Each household supplies a differeniaed ype of labor o a union ha combines he differen ypes and offers his aggregae labor inpu o firms. Nominal wage conracs can be renegoiaed only a random inervals of ime and in a saggered fashion, alhough wages ha canno be changed are indexed o lagged and rend inflaion. Firms produce differeniaed goods using labor and capial and se prices opimally a random inervals, wih prices also being indexed o lagged and rend inflaion. Oil eners producion in wo ways. Firs, capial can only be used in producion if i is combined wih oil as in Kim and Loungani 1992)). Second, oil is needed o vary capial uilizaion and hence o produce capial services as in Finn 1995, 1996)). The fiscal auhoriies are consrained by a deb-o-gdp crierion. They can finance public expendiures by issuing deb cerificaes and by levying axes on labor, consumpion, oil and lump-sum axes. The cenral banks credibly commi o a feedback nominal ineres rae 3

4 rule ha responds o measures of he lagged ineres rae, inflaion, oupu and oil prices. The oil-exporing counry is modeled in a sylized way. I is inhabied by a represenaive household consuming a baske of goods ha can only be impored from he res of he world. Firms produce oil, which is expored and no used for inernal consumpion, and se prices opimally a each insan of ime. Governmen expendiures are se o zero, so ha he fiscal auhoriy has no need o raise axes or o issue deb. Finally, he moneary auhoriy is commied o a credible peg of he currency o he US dollar. A few feaures of our model are worh noice. Firs, we inroduce oil in an oherwise sandard medium-scale model such as he one presened in Smes and Wouers 23) or Chrisiano e al. 25)), where a number of fricions and economic disurbances are shown o be imporan o replicae some empirical sylized facs. The reason for choosing such an environmen is ha we aim a performing a welfare analysis based on a model ha closely mimic he daa. In his regard, our approach is similar o he one followed by Schmi-Grohé and Uribe 24a). 1 Second, our model can simulae oil-price shocks ha are eiher exogenous or endogenous o he world economy. Since oil eners boh consumpion and producion in he oil-imporing counries, demand and supply shocks in hose counries generae endogenous volailiy in he price of oil. On he conrary, a produciviy shock in he oil-exporing counry acs as an exogenous supply shock in he world economy. In he welfare analysis, we can modify he imporance of he exogenous supply-driven oil-price shock relaive o oher sources of economic disurbances and check he implicaions for he opimal moneary policy reacion. Third, we consider he effecs of fiscal policy on he propagaion of oil-price shocks o he macroeconomy. In paricular, we aim a capuring he asymmeric role of energy axes in differen counries. By imposing axes on labor, consumpion and energy, our model is able o measure he impac of fiscal asymmeries on he propagaion of oil-price shocks and on he desirable moneary policy response. Finally, we consider wo alernaive cases of inernaional asse rade: a complee marke srucure and a non-coningen bonds srucure. The reason is ha he degree of compleeness in inernaional financial marke can have imporan implicaions for he welfare analysis of moneary policy in he face of oil-price shocks. For insance, he exisence of inernaional rade in sae-coningen asses implies ha any domesic idiosyncraic risk no offse by a sub-opimal moneary policy can be insured. Thus, he welfare loss associaed o a sub-opimal rule migh be larger under incomplee markes. Our paper relaes o differen srands of he lieraure. One srand discusses he ransmission of oil-price shocks and heir macroeconomic effecs see e.g. Hamilon 1983, 1996), Bernanke e al. 1997), Barsky and Kilian 22), Dosey and Reid 1992) and Jimènez-Rodrìguez and Sanchèz 24) for an analysis based on VARs, or Backus and Crucini 2) and de Walque e al. 25) for an analysis based on calibraed or esimaed DSGE models). A second srand addresses he role of moneary policy in sabilizing or amplifying he macroeconomic effecs of oil-price shocks, as done e.g. by Bernanke e al. 1997), Barsky and Kilian 22) Kamps and Pierdzioch 22) and Leduc and Sill 24). Our paper differs from hese conribuions in he way we capure he ineracion beween energy and he macroeconomy, and in he use of a micro-founded welfare meric o compare sysemaically differen policy responses o 1 Examples of policy analysis based on more sylized models are provided by Leduc and Sill 24) and Kamps and Pierdzioch 22). 4

5 oil price shocks. A furher srand of he lieraure addresses opimal moneary and/or fiscal policy in models wih seady sae disorions, such as in Benigno and Woodford 24b), Benigno and Woodford 24a), Schmi-Grohé and Uribe 24b) and Schmi-Grohé and Uribe 24a, 25). Our model carries ou a similar analysis in a medium scale hree-counry open-economy model wih an explici role for oil. Finally, a number of conribuions propose alernaive algorihms o implemen second-order soluions o non-linear raional expecaions models, such as Schmi-Grohé and Uribe 24b) and Lombardo and Suherland 25). Our paper follows he soluion mehod o he second-order approximaion of he model proposed by Lombardo and Suherland 25). The paper proceeds as follows. In secion 2, we describe he main building blocks of he model. In secion 3, we presen he deails of he calibraion exercise and he empirical fi of he model wih he daa. In secion 4, we describe he effecs of an exogenous oil-price shock in our model. In secion 5, we presen he welfare analysis and discuss our main resuls. Finally, in secion 6, we conclude and indicae plans for fuure research. 2 The model Our world economy consiss of wo oil-imporing counries and one oil-exporing counry. We label he domesic oil-imporing counries as he euro area EA), he foreign oil-imporing counry as he Unied Saes US), and he oil-producing counry as he block of ne oilexporing counries O). The world populaion has measure 1 + ϑ. A fracion b lives in counry EA, a fracion 1 b lives in counry US and he remaining fracion ϑ lives in counry O. Counries EA and US share he same preferences, producion echnologies and rade srucures, and have access o he same se of domesic and cross-border financial asses. Differences beween he wo economies are refleced in he value of various srucural parameers. In each of he wo oil-imporing counries, households maximize he discouned sum of expeced fuure uiliies, defined over a consumpion baske, real money balances and leisure. Consumpion displays habi persisence. Households consume a baske of goods made of domesically produced final goods, impored final goods and impored oil. Labor is differeniaed over households, which implies some marke power in he wage seing decision and allows he inroducion of sicky wages à la Calvo. We allow for wage indexaion o an index of pas inflaion and rend inflaion. Households ren labor and capial services o firms, and hey decide he level of invesmen aking ino accoun he coss of adjusing he capial sock. Households also allocae nominal wealh among nominal money balances, one-period nominal governmen bonds, one-period inernaionally raded risk-free nominal asses denominaed in foreign currency and a porfolio of sae-coningen asses denominaed in domesic currency. We analyze wo polar specificaions on he inernaional capial markes and evaluae he imporance of his assumpion for he opimal response of moneary policy o oil shocks. Under he firs specificaion complee markes) a full se of sae-coningen one-period nominal asses denominaed in domesic currency is raded across counries. Under he second specificaion incomplee markes) only non-sae-coningen one-period nominal bonds denominaed in foreign currency can be raded inernaionally. Sae-coningen asses are raded only domesically. 2 2 The exisence of complee domesic markes guaranees equaliy of he households marginal income, despie 5

6 A perfecly compeiive inermediae secor produces an inpu for he producion of domesic final-goods by assembling ogeher he exising sock of capial wih impored energy à la Kim and Loungani 1992) and Backus and Crucini 2)). We call his produc energy-loaded capial. A coninuum of imperfecly compeiive firms produce differeniaed goods using labor and energy-loaded capial, aking facor prices as given. However, hey can reac o changes in he renal cos of capial by adjusing he inensiy of capial uilizaion. Varying capial uilizaion is cosly in erms of energy à la Finn 1995)). Firms producing differeniaed goods canno rese heir prices opimally a any insan of ime. Price seing occurs as in Calvo 1983) excep ha prices which canno be changed are linked o an index of pas and seady sae inflaion. In order o finance public expendiures, fiscal auhoriies levy axes on labor, consumpion, and oil, and issue deb cerificaes denominaed in local currency). The governmens can also make use of a lump-sum ax ransfer) o finance is defici. On he conrary, seigniorage is no used o finance he budge bu i is rebaed lump-sum o he households. We impose a deb-o-gdp crierion in seady sae. Moneary policy is characerized by a feedback ineres rae rule. We consider a class of simple rules ha respond o he lagged ineres rae, inflaion, oupu and is growh rae, oil prices and oil price inflaion. We model counry O in a sylized way. Households consume a baske of goods, which includes only goods impored from EA and US. They also inves in he inernaionally raded bonds denominaed in US dollars), under incomplee markes, or in Arrow-Debreu securiies denominaed in domesic currency), under complee markes. Firms only produce oil, which is expored and no used for inernal consumpion. Alhough hey operae in a monopolisically compeiive marke, firms can se prices opimally a each insan of ime. Governmen expendiures are se o zero, so ha he fiscal auhoriy has no need o raise axes or o issue deb. Finally, he moneary auhoriies implemen a peg of he currency o he US dollar. We assume ha he hree economies are hi by a se of shocks. In paricular, each of he oil-imporing counry faces a preference shock, a produciviy shock, a governmen expendiure shock, a moneary policy shock, a labor supply shock, and an invesmen shock. The oilexporing counry only faces a echnological shock ha affecs is produciviy in exracing oil. All exogenous sochasic processes are AR1). 2.1 The EA and US economies In his secion, we describe in some deails he EA economy. The US economy is modeled in a symmeric way. Unless differenly specified, we denoe EA variables wihou a counry label and US variables wih a sar Households There is a coninuum of households denoed by j,wih j [, b]. Each household j can allocae is beginning of period nominal wealh o nominal money balances, one-period nominal he presence of saggered wage seing. 6

7 governmen bonds, one-period inernaionally raded risk-free nominal asses denominaed in foreign currency and a porfolio of sae-coningen asses denominaed in domesic currency. Households also receive paymens of he facors hey ren o domesic firms, profis from owing shares of he domesic firms, and ransfers from he governmen. They use his income o finance consumpion and invesmen expendiures. Their budge consrains are given by B j, P = M j, P + S F j, P + E Q,+1 A j,+1 P + R 1B j, 1 P + A j, P + M j,+1 P + 1 τ l,)w j, P + C j,e, + P I I j, P [ 1 + Φ l j, + R K, K j, + Π j, P ε I I i, I i, 1 )] 1) + S R 1P F 1 ) F j, 1 + T P where C j,e, denoes consumpion of he final consumpion good, P is he consumer price index, l j, is labor, M j,+1 is end-of-period money, Π j, are oal profis ha accrue o he household by owning shares of domesic firms, B j, are domesically raded governmen bonds issued in domesic currency and paying wih cerainy R B j, unis of currency in period + 1, A j,+1 denoe a sae-coningen bond paying one uni of domesic currency in period + 1, Q,+1 is he price of such bond, F j, denoes an inernaionally raded one-period nominal bond in foreign currency delivering a reurn of R P F ) F j, unis of foreign currency in period + 1, P F ) is an ineres rae premium ha depends on he aggregae ne foreign-asse posiion, T is a real governmen ransfer o he households, S is he nominal exchange rae in domesic currency per uni of foreign currency) and τ l, is a labor income ax. The funcion Φ ) denoes he adjusmen coss incurred for each uni of invesmen, where Φ ) >, Φ ) > and Φ ) = Φ ) = in seady sae, ε I is a shock o he invesmen echnology. 3 Thus, I j,e, [1 + Φ )] is he amoun of invesmen devoed o nex period capial sock and P I, is he price of he invesmen good. The household s capial sock follows he law of moion K j,+1 = 1 δ) K j, + I j,, 2) where δ is he consan depreciaion rae of capial. Households maximize he discouned sum of expeced fuure uiliies, defined over he final consumpion good, real money balances and leisure max E β s ε C =s { C j,e, hc j,e, 1 ) 1 γ 1 γ φ Mj,+1 P P ) } 1 φ l 1+ς j, ζ, 3) 1 + ς where ε C is a preference shock and ζ is a labor supply shock. The final consumpion good C j,e, is a CES aggregaor of a baske of final goods, C j,, and of he demand of energy by domesic households, e j,h,. Neglecing he household index, we can wrie i as C e, = [1 o) 1ξ C ξ 1 ξ ] ξ + o 1 ξ eh, ) ξ 1 ξ ξ 1, 4) 3 In he numerical soluion of he model, we adop he funcional form Φ ε I e φ ɛ II 1) II 1) 2. ) I j, I j, 1 = e φ ɛ II II 1) 1) + 7

8 where o is he share of oil in he energy-loaded consumpion baske and ξ > is minus) he elasiciy of subsiuion. The bundle C is also a CES aggregaor of a bundle of domesically produced goods, C H,, and of foreign produced final goods, C F,, i.e. C = [n 1χ C χ 1 χ H, + 1 n) 1 χ 1 χ C χ F, ] χ χ 1, 5) where n measures he degree of home bias in consumpion and χ > is minus) he elasiciy of subsiuion. The bundles of domesic and impored consumpion goods are given respecively by C H, = { b 1 θ b } θ { cz) θ 1 θ 1 θ dz, C F, = 1 b) 1 θ 1 b } θ cz) ) θ 1 θ 1 θ dz, 6) where θ > 1 is he elasiciy of subsiuion. Finally, invesmen goods I are produced by combining domesic and impored consumpion goods in he same way as for he consumpion bundle 5). I follows ha he price index associaed o consumpion C and invesmen I are idenical, i.e. P c = P I. Households maximize heir preferences 3) subjec o he budge consrain 1), he law of moion for capial 2), he expressions for he baskes 4), 5), 6), and a ransversaliy condiions. Our assumpion ha households can hold a se of sae-coningen securiies raded across counries in he case of inernaionally complee markes or jus domesically in he case of incomplee markes) ensures hem agains household-specific variaions in labor income due he presence of wage seing rigidiies. Since he marginal uiliy of wealh is idenical for all households, he opimaliy condiions are also idenical across households. Up o he choice of labor supply, he opimaliy condiions are given by he households firs-order condiions, repored in Appendix A, ogeher wih he demand funcions ) 1 + τc, )P c ξ C = 1 o) C e, 7a) C H, = n cz) = 1 b I H, = n Iz) = 1 b I = 1 o) P c P P ) ξ C e, 7b) ) 1 + τe, ) S P e ξ + ϖ) e h, = o C e, 7c) P H P c pz) P H P H P c pz) P H P ) χ C, C F, = 1 n) S P F ) θ C H,, cz) = 1 1 b P c ) χ I, I F, = 1 n) S P F pz) P F P c ) θ I H,, Iz) = 1 1 b 8 ) χ C ) χ I pz) P F ) θ C F, ) θ I F,.

9 Here τ c, denoes a value-added ax on final goods, τ e, a value-added ax on final purchases of energy, ϖ an excise ax on energy, P H is he producer-price index in he EA, P F is he producer-price index in he US, P c is he domesic core consumer price index, P e is he price of energy in US dollars), pz) is he price in EA of he differeniaed good z, and pz) is he price of he differeniaed good z in dollars. We assume ha he law of one price holds, implying ha pz) = S pz). Noice, from 7a) and 7b), ha invesmen purchases are no subjec o VAT axes. The absence of arbirage opporuniies requires he exisence of a discoun facor Q,+1 such ha he price of any porfolio of financial asses wih random value A +1 in he following period is given by E [Q,+1 A +1 ]. Opimaliy requires ha he riskless nominal ineres rae solves he equaion R 1 = E [Q,+1 ]. Subsiuing he demand funcions 7a) and 7c) ino he CES funcion 4), we obain he expression for he consumer price index P = [ 1 o) [1 + τ c, )P c ] 1 ξ + o [1 + τ e, ) S P e + ϖ)] 1 ξ] 1 1 ξ. Similarly, we obain he following expressions for he core consumer price index and for he EA and US producer-price index, [ 1 P H = b b [ P c = n P H ) 1 χ ) ] n) S P F 1 χ 1 χ, ] 1 [ p z, ) 1 θ 1 θ 1 dz, P F = 1 b 1 b p z, ) 1 θ dz ] 1 1 θ. Wage seing Each household supplies is labor services o a rade union. Labor services are only parially subsiuable so ha households have wage-seing power. Each household in each period has a probabiliy 1 ξ w ) of re-opimizing he posed wage. When he wage is no re-opimized, he household updaes he las period wage according o an index of las period inflaion and seady-sae inflaion. The oal labor supplied by he union o firms a ime s, L s, is an aggregaor of each differeniaed labor ype j, [ b ] ω L s = b 1 ω l ω 1 ω 1 ω j,s dj. where ω > 1 is he elasiciy of subsiuion beween labor ypes. An agen seing he wage opimally a ime faces he following demand for labor a ime s, W π s ) 1 κ ) κ ) ω π 1 s 1 L s 12) l j,s = 1 b W s where W s is he aggregae nominal wage, W is he opimal nominal wage se a ime, π 1 s 1 is he gross cumulaive inflaion rae beween period 1 and s 1, π is he seady-sae P s 1 P 1 9

10 inflaion rae and κ, 1) is he degree of indexaion o pas-quarer inflaion relaive o oal indexaion. Each household chooses he opimal wage by maximizing he discouned sream of fuure uiliies subjec o he budge consrain, aking ino accoun he probabiliy of being able o renegoiae opimally her wage a ime s, condiional on being he las ime he wage was se opimally. Denoe as λ c s he marginal uiliy of income.using he problem s firs-order condiions, ogeher wih equaion 12), we obain he following condiion for he opimal wage and W 1, = γ w ε C ζ Ls b W 2, = γ w λ c 1 τ l ) Ls b w ) 1+ως w = ) ς+1 π ωκς+1) π ωςκ ) π κ1 ω) π κ ω ω 1) π ) κ1+ως) W1,, π W 2, [ ] ω1 κ)ς+1) E π +1 ) w+1 + βξ w π w [ ] 1 κ)1 ω) E π +1 ) w+1 + βξ w π w ) ως+1) W1,+1, ) ω W2,+1, where w W W is he opimal wage se by he household relaive o he conemporaneous aggregae nominal wage and where γ w 1 βξ w ) /π ωκ. The domesic real wage index can hen be wrien as ) 1 w = 1 ξ w ) w 1 ω π) 1 κ π 1 ) κ 1 ω 1 ω + ξ w w 1. In order o measure welfare, we need o express he aggregae supply of differeniaed labor. Using equaion 12), we obain 1 b ) 1+ς 1 l 1+ς j,s = b b L s ŵs, where ŵs denoe a wage dispersion wedge. The wedge, derived in Appendix B, is given by ) ω1+ς) ) ω1+ς) ŵ = 1 ξ w ) w ω1+ς) π w + ξ w ŵ π 1 κ) π 1 κ w Premia and UIP Combining he household s firs-order condiion wih respec o governmen bonds equaion 28c) in Appendix A) wih he corresponding equaion derived for he US economy, given by λ c, π = βe λ c, +1R P F ) P P+1, 15) and equaing he reurn of he inernaionally raded bond o ha of he domesic risk-free bond, we obain he uncovered ineres pariy UIP) condiion R = R P F ) E S +1 S. 1

11 2.1.3 The energy-loaded capial secor Each oil-imporing counry has a compeiive secor producing energy-loaded capial and a monopolisically compeiive inermediae goods secor. As in Kim and Loungani 1992) and Backus and Crucini 2), he exising capial sock mus be combined wih oil in order o be used in he producion of differeniaed goods. This is done by a compeiive secor ha rens capial from households, purchases energy from he oil-exporing counry and assembles he wo o sell a capial-energy bundle o firms. We assume an equal number of firms as households in he wo oil-imporing counries. The energy-loaded capial secor solves he following problem min R K K + S P e + ϖ) e p, K,e p, s.. K e, = [ϕ 1η K η 1 η + 1 ϕ) 1 η 1 η η ep, ] η η 1 16a) 16b) where K denoes he physical capial sock, e p, he demand of energy used in producion, R K he renal cos of capial, η > is minus) he elasiciy of he demand for oil wih respec o is relaive price and ϕ, 1) deermines he weigh of capial in he capial aggregaion funcion. Equaion 16b) describes he echnology used o produce energy-loaded capial using capial and energy as inpus. Using he opimaliy condiions, we can express he demand by he represenaive producer of energy-loaded capial as ) R K η K = ϕ K e, 17) P Ke S P e e p, = 1 ϕ) + ϖ P Ke ) η K e,, 18) where P Ke is he Lagrangian associaed wih he consrain 16b). Replacing hese condiions in equaion 16b), we obain he deflaor of he energy-loaded capial, Final goods secor [ P Ke = ϕ R K ) 1 η + 1 ϕ) S P e + ϖ) 1 η] 1 1 η. Firms ha produce differeniaed radable goods operae in monopolisically compeiive markes and se prices only a random inervals of ime à la Calvo 1983). In each counry here are as many final goods producers as households. In he following, we firs describe he cos minimizaion problem of he firm and, second, he price seing problem. Each firm produces using labor and energy-loaded capial services according o he producion funcion y = ɛ L 1 α u K e, ) α. where we have omied he firm-specific sub-index. Here u denoes he degree of uilizaion of he energy-loaded capial and ɛ an exogenous saionary echnology shock. We follow Finn 11

12 1995) and Leduc and Sill 24) by assuming ha capial uilizaion is cosly in erms of energy. The oal amoun of energy used direcly in producion, e u,, saisfies he following relaionship e u, = a u ) K e,. 19) In paricular, we assume ha au ) ξ e u ν u ν ). The firm chooses he capial-energy bundle, is degree of uilizaion and is demand for labor, L, by solving he following problem min W L + P Ke K e, + S P e + ϖ) e u, 2) L,K e.,u s.. y = ɛ L 1 α u K e, ) α 21) e u, = a u ) K e,. 22) Using he firs order condiions, we obain an expression for marginal coss mc, mc = 1 W 1 α P Ke ɛ + S P e + ϖ) au ) ) α u α 1 α) 1 α α α and one for he degree of capial uilizaion as a funcion of he relaive cos of energy-loaded capial and he price of energy, u u = P Ke S P e + ϖ) ν 1) ξ e where u denoes he seady sae level of uilizaion. Firms producing final goods se prices only a random inervals of ime. In each quarer a fracion ξ p of firms sells goods a he price posed in he previous quarer, afer updaing i in par o he inflaion observed in he pas quarer and in par o rend inflaion. The remaining firms are able o pos he opimal price. Firms are owned by he domesic households. Therefore, each firm chooses he opimal price in order o maximize he expeced discouned dividends accruing o households [ ξ p ) s p π s ) 1 ψ ) ψ ] π 1 s 1 Rs, max E p s= where T C denoes oal coss of producion and R s, β s λ c s λ c facor beween period s and s. The soluion o his problem yields a relaive price P s pi) = µ f π ψ Q1, π ψ Q 2, ) 1 ν, y s T C s P s is he household nominal discoun where Q 1, = γ ψ mc π ψ ) θ P H C W [ ]θ1 ψ) π+1 + ξ p E R +1, Q1,+1, π 12

13 π Q ψθ 1) ) )θ 1)1 ψ) 2, = γ ψ P H θ π ψ C W π+1 + ξ p E R+1, Q2,+1, π µ f = θ is he firm s mark-up and γ θ 1 ψ 1 ξpβ ). Here C W π θψ denoes he demand for EA goods for consumpion, invesmen and governmen expendiures from residens of counries EA, US and O respecively, i.e. C W = C H, + I H, + G H, + CH, + I H, + G H, + Co H,. The producer price index in erms of he domesic CPI can be wrien as P H P H = 1 ξ p ) p ) 1 θ π) 1 ψ π 1 ) ψ + ξ p P π P H 1 ) 1 θ 1 1 θ Moneary policy We assume ha he cenral bank commis iself o a feedback ineres rae rule. We sudy he performance of a simple class of linear feed-back rules, of he form [ π ) ) ) R = λ R R λ R ) λ π π 1 Y + λ Y Y 1 Y + λ Y 1 Y ) ) ] 1 Pe, Pe, +λ P e 1 + λ P e ε R 23) P e, 1 P e where variables wihou a subscrip denoe seady-sae values. Here Y denoes real GDP a curren prices Fiscal policy Governmens are assumed o purchase a baske of goods wih he same composiion as he one purchased by he households. 4 Governmens expendiures do no conribue direcly o households welfare. In order o finance expendiures, he fiscal auhoriies can levy lump-sum axes on households T ), axes on domesic labor income τ l ), axes on domesic purchases of final goods τ c ) and axes on oil purchases. The laer axes are of wo ypes: a value added ax τ e ) and an excise ax ϖ). Furhermore, governmens can issue bonds denominaed in domesic currency. The consrain of he governmen in per capia erms) is herefore given by B G = τw l L + τ ) c P H C H, + S P F C F, + τ e S P e + ϖ) e h, + e G, ) + 24) ϖ e u, + e h, + e G, + e p, ) P G + R 1 B 1 G + P T. 2.2 The Oil-exporing counry The O counry is populaed by a fracion ϑ of he world populaion. The represenaive household produces and expors oil and consumes exclusively goods impored from he US and 4 Given he parameer values used in he calibraion, his assumpion amouns o a srong home bias in governmen spending. 13

14 he EA. Governmen expendiures are se o zero, so ha he fiscal auhoriy has no need o raise axes or issue deb. The moneary auhoriies implemen an irrevocable one-o-one) peg of he O currency wih he dollar. Each household produces one paricular ype of oil in monopolisic compeiion wih he oher households. As prices are flexible and all households face he same echnology, equilibrium prices and quaniy will be idenical across agens. We denoe wih he superscrip o he variables of he represenaive agen in he O counry. The problem of he household is given by subjec o F o P o max E β s + E Q o,+1a o +1 S P o =s { + C o + M o +1 P o C o1 γ 1 γ φ M o +1 P o + R 1P ) F 1 o ) } 1 φ l o ) ζo+1 ϕ o ζ o a) = M o F o P o P o 1 + Ao P + P e e o o P o + T o e o = ν e l o ) ι 25b) where e o is oal supply of oil, T o amouns o seigniorage ransfers, ν e is a produciviy shock, and ι, 1) measures he degree of reurn o labor in producion. 5 Firs-order condiions, demand funcions and price indexes repored in Appendix A) can be derived similarly o he case of he represenaive household of each oil-imporing counries. Since households can adjus he price of heir oil produc e each insan in ime, and given he absence of asymmery among households, he opimal price is given by where µ o denoes he mark-up. P e = µ o P o 2.3 Marke clearing condiions ϕ o ν e ι e o ν e ) ζo ι+1 ι The following condiions ensure clearing in he EA counry for he following markes corresponding condiions hold for he US counry). run. Energy-loaded capial: b K e = b mc α yz) dz. P Ke Goods: Recall ha oal demand for firm i good is given by pz) y z) = P H, ) θ C W. 5 This amouns o assuming ha here is a firm-specific facor, e.g. oil wells, ha is consan in he shor 14

15 Now, aggregaing over firms in per-capia erms), we can equae aggregae supply Y s o aggregae demand o obain Y s = 1 b b yz) s dz = P H ) θ C W s 1 b b pz) ) θ dz = P H ) θ C W P H, 26) where P H denoes a price dispersion wedge which can be derived similarly o he wage dispersion wedge and is given by P H = 1 ξ p ) p θ + ξ p Labor: equaing demand and supply, we ge L = [ b 1 ω b ] ω l ω 1 ω 1 ω j, dj π) 1 ψ π 1 ) ψ π = mc 1 α) 1 b ) θ P H 1. b yz) W dz. Domesic asse marke: Sae-coningen bonds if domesically raded) mus be in zero ne supply. Also, marke clearing for governmen bonds implies ha B G = b B i,di. The following condiions ensure clearing for he following markes in counry O. Energy: e o = b e h, + e G, + e p, + e u, ) + 1 where e G, denoes he demand for energy of he governmen. b ) e h + e G, + e p, + e u,, Labor: e l o o = ν e ) 1 ι. Finally, he following condiion ensures clearing for he inernaionally raded asses. Inernaionally raded asses: he sum of he ne foreign asse posiion of he hree counries obained by inegraing he budge consrain of he households in each counry) has o add up o zero. 3 Calibraion of he model In order o calibrae he model we solve i o a firs order of approximaion. We compue variances and cross correlaions on he basis of simulaed series afer using he Hodrik-Presco filer for quarerly daa. 6 6 We solve and simulae he model using DYNARE. For compuaional convenience we hen HP filer he series using a separae code. Furhermore we comupe he variance decomposiion using SYMBSOLVE available from he auhors on reques). 15

16 We se he sochasic properies of he shocks and he parameer values of he model in order o mach hree crieria: i) replicae he volailiy and correlaions of some relevan macroeconomic variables, such as oupu, consumpion, labor, invesmen, he ne rade and he erms of rade defined as he price of impored goods over he price of expored goods); ii) reproduce he oil inensiy in producion and consumpion observed in he daa; iii) generae a conribuion of he oil-price shocks o he overall variance of GDP as obained in relaed empirical work e.g., Dosey and Reid 1992) Jiménez-Rodríguez and Sánchez 24), de Walque e al. 25)). Our benchmark calibraion exercise is performed using he incomplee markes version of he model. We obain similar calibraion resuls no repored) under complee markes. We adop he following procedure: firs, we evaluae he model according o he hree crieria repored above using available esimaes of he parameer values e.g. using he values repored in de Walque e al. 25)); second, we marginally modify he sochasic properies of he shocks and parameer values in order o improve he mach of sample momens and o replicae he observed conribuion of he oil price shock o he variance of GDP and inflaion. The lis of all parameer values is given in Appendix C. Here we briefly commen on some of hese parameers. 3.1 Parameers and sochasic processes Size and preferences We se he size of he EA relaive o he US a 75% and he size of he oil-exporing block relaive o he US a 2%. The parameer measuring consumpion habi for he EA and US is close o he values used in he relaed lieraure.7 for EA and.45 for US), alhough i is in he low range for he US. 7 The elasiciy of labor supply is se a.4, symmerically for US and EA. This number is lower han he values used in he real business cycle lieraure, bu closer o he values found in models wih wage sickiness. I is also similar o he poserior mode esimaed by de Walque e al. 25). 8 Finally, we se he elasiciy of iner-emporal subsiuion in consumpion a 2.5 in he EA and 2 in he US. These values are also close o hose esimaed by de Walque e al. 25) Oil shares The seady-sae shares of oil in consumpion and producion are measured as he raio beween he value of energy expendiures and he value of oal consumpion and nominal GDP, respecively. In he model, we rea energy as oil and naural gas. Concerning he share of energy in consumpion, he oal weigh of gas, fuel and car fuels in he euro-area HICP amouns o For insance, Chrisiano e al. 25) se i a.65 for he US. The poserior mode repored in de Walque e al. 25) is beween.72 and.74 for he EA depending on he model specificaion) and beween.71 and.72 for he US. 8 The poserior mode repored in de Walque e al. 25) is beween.42 and.53 for he EA depending on he model specificaion) and beween.34 and.37 for he US. 16

17 while he same weigh in he US CPI is Concerning he share of energy in producion, i is beween 1% and 1.5% in he EA. Moreover, energy inensiy in 23 was abou 3% higher in he US han in he EA. 1 Hence, we ake he share of oil in producion o be below 2% in he US. We se he elasiciies of subsiuion in he CES aggregaors of oil a he values used by Backus and Crucini 2) and he oher relevan parameers of he model o replicae he evidence repored above. The model produce he following shares. 11 Table 1: Oil shares Consumpion Producion EA 6.3% 1.56% US 6.89% 1.96% Producion of final goods The share of labor in producion is se o.64 for boh he oil-imporing counries. The degree of capial uilizaion is normalized o uniy in he seady sae. In order o mach he share of energy in producion, he cos of capial uilizaion in erms of energy is assumed o be very elasic o he level of uilizaion. The elasiciy is se o 28 in he EA and o 2 in he US Price and wage seing The elasiciy of he demand for final goods is assumed o be he same in boh counry implying profi margins of 2%). As for he Calvo-probabiliy of no adjusing he price in a paricular quarer, we se hem o.8 for he EA and.6 for he US, as from he esimaes of de Walque e al. 25). As for wages, he mark-up over marginal disuiliy of labor is 1.5. The Calvoprobabiliy of no readjusing wages is se o.83 for he EA and.73 for he US. We assume insead an equal degree of price and wage indexaion in boh he EA and US.4 for prices and.7 for wages) Capial and invesmen The adjusmen cos of invesmen is se o 7 for EA and 5 for US, close o he esimaes obained by de Walque e al. 25). The capial depreciaion rae is Source: ECB calculaions. Noice ha he oal weigh of oil and gas in he euro area HICP canno be compared o he weigh of he same aggregae in he US CPI, as he baske underlying he laer index includes a larger number of iems. A comparable baske would produce a weigh larger han 5.6 for he US. 1 Source: ECB calculaions. 11 Par of he value of oil and gas used in consumpion and producion has a domesic value-added componen. For example, in he US, he Energy Informaion Adminisraion for he year 1999 aribues o refining and disribuion coss and profis abou 26% of he final price of perol. In he EA his share would probably be somewha smaller due o a larger share of axes. To his exen our calibraion migh oversae he share of oil in final consumpion. 17

18 3.1.6 Taxes and fiscal policy The labor income ax rae and he VAT and sales axes are aken from Coenen e al. 25). As for he axes on oil, we disinguish beween VAT or sales axes and excise axes. The former are assumed o be he same as he VAT axes on oher final consumpion goods. 12 Excise axes are measured in unis of domesic currency per uni of energy. Transforming hese values in relaive erms requires fixing a baseline price of oil. For example, if he price of oil is aken o be he 1999 price abou $17.5 per barrel) he Federal and Sae axes in he US would amoun o abou 36% of he reail price of regular grade gasoline. A 2 prices abou $28.4 per barrel) he ax burden is only 28%. 13 We se he excise ax a 2% of he seady-sae price of oil for he US, corresponding o he case when he price of oil is a abou $3 per barrel. A his prevailing price, he excise ax on oil would be a 7% for he EA Inernaional capial marke and aggregae demand elasiciy The calibraion of he model is no paricularly sensiive o he assumpion concerning he inernaional financial marke. The same se of parameers delivers saisfacory resuls boh under complee markes and under incomplee markes. Under he assumpion of incomplee markes, our benchmark case assumes an ineres rae premium on foreign liabiliies such ha a 1% increase in ne foreign liabiliies relaive o seadysae GDP, ceeris paribus, increases he domesic ineres rae by abou 2 basis poins. A key parameer in an open economy model is he elasiciy of subsiuion beween impored goods and domesically produced goods. We se his parameer o a raher low number,.7 boh for he US and he EA, as limied subsiuabiliy conribues o produce a posiive cross-counry correlaion of oupu and a negaive correlaion of ne-expor and oupu Oil-producion The calibraion of he oil-exporing counry is key for he model o replicae he shares of oil in consumpion and producion of he oil-exporing counries, as well as o reproduce he volailiy of he price of oil and he conribuion of oil-shocks o he forecas-error variance decomposiion. We se he parial elasiciy of he price of oil o is demand equal o 9. Given he small share of oil in global demand his is a relaively small number. The producion funcion is furher scaled by a produciviy coefficien of one housand and a mark-up of 1. These numbers are needed o generae a price of oil relaive o he CPI ha is compaible wih he observed shares of oil in consumpion and GDP. Their exreme value reflec he highly simplified srucure of he oil-exporing counry. 12 No all he Saes in he US impose sales axes on oil derivaives. As a consequence, he sale ax on oil for he US migh be overesimaed. 13 Source: Energy Informaion Adminisraion 21). 18

19 3.1.9 Moneary policy For he calibraion of our model we choose he parameers repored in Table 2 for he ineres rae rule 23). Table 2: Ineres rules parameers Counry λ R λ π λ y λ y λ P e λ P e EA US These values are aken from de Walque e al. 25), alhough heir rule differs from ours in wo imporan respecs. Firs, heir rule implies ha he ineres rae responds o aggregae demand while our rule respond o domesic value added a curren prices). Second, in heir rule he ineres rae responds o deviaions of he arge variables from heir value in he flexible price equilibrium, while in our rule he policy insrumen responds o deviaions of he arge variables from heir value in he non-sochasic seady sae. Noice ha he sochasic properies of our model remain virually unchanged if we alernaively use he rule esimaed by Chrisiano e al. 26) for he euro area and he US in a closed economy seing Sochasic processes We choose o add o he model a large number of sochasic disurbances for wo reasons. Firs, we wan o base our normaive analysis on a model ha provides a reasonable fi wih he daa. Second, we aim a capuring he main channels linking oil prices o he macroeconomy bu we also aim a maching he relaive imporance of he oil price shock relaive o oher relevan economic disurbances. In paricular, we ry o obain a share of oil-shocks in he oal forecas-error variance ha is of he same magniude of he one obained in empirical sudies. 3.2 Daa and empirical fi The sample period we consider in he calibraion is 1987:1 o 22:4. We sar he sample jus afer he oil-price collapse of 1986 as his marked he end of he high oil-price period sared 13 years earlier. We neglec mos recen observaions 23:1 onwards) as hey coincide wih he sharp escalaion in oil-prices We ake he following values from Chrisiano e al. 26) Counry λ R λ π λ y λ y λ P e λ P e EA US According o Backus and Crucini 2), he paern of co-movemens and volailiy in major macroeconomic variables during he period of high oil-price volailiy wha hey call he OPEC period) is considerably differen from he paern observed before and afer ha period. Furher below we will discuss he implicaions for moneary policy of differen degrees of oil-price volailiy. 19

20 We follow he relaed lieraure e.g. Backus and Crucini 2)) and HP-filer he daa in per capia real erms 16. Neverheless, some correlaions are srongly affeced by he filering while for ohers he HP-filer looks raher inappropriae e.g. for oil prices). The laer problem is paricularly severe when periods of persisen deviaions from he hisorical mean are included e.g. he 197s). In our calibraion, we have aimed a obaining shares of he oil-shock in he oal forecaserror variance of GDP ha are close o hose repored in he lieraure. The exising lieraure finds a raher wide range of values. For example, Dosey and Reid 1992) argue for a 5 o 6% conribuion of oil-price shocks o he 12-quarer horizon) variance of US real GNP. Jimènez- Rodrìguez and Sanchèz 24) esimae larger values for he 12-quarer) share of variance induced by oil-price shocks, i.e. 7.5% for he EA and 1.9% for he US. de Walque e al. 25) repor smaller values in he order of 1.% EA) and 1.5% US) a 1-quarer horizon. In our calibraion we obain a share of oil-price shocks in he variance of he forecas error of real GDP of 1.9% EA) and 4.37% US) a 12-quarer horizon. 17 Table 3 compares a selecion of simulaed momens wih he empirical counerpars. The sandard deviaions and cross-correlaions of mos of he macroeconomic variables described by he model are broadly in line wih hose observed in he daa. In paricular, he model is able o reproduce qualiaively he evidence of a correlaion of oupu ha is greaer han ha of consumpion and of invesmen. We reproduce almos exacly he sample evidence on he cross-counry oupu correlaion while our model predics a correlaion of consumpion ha is oo low and of invesmen ha is oo large. As for he correlaion beween he real exchange rae denoed as RER) and he consumpion differenial, in he daa his correlaion is ypically small and ofen negaive, implying a low degree of risk sharing. In our sample, he HP-filered series only produce a very small, hough posiive, correlaion. If we don filer he real exchange rae he correlaion remains very small, hough in his case negaive. Quaniaively, our model is no far from our sample evidence. Anoher imporan sylized fac in he inernaional macroeconomics lieraure is he negaive correlaion beween ne-expors relaive o GDP denoed as NX) and GDP and beween he erms of rade denoed as o) and GDP. Backus and Crucini 2) argue ha oil price shocks help in explain his negaive correlaion. In heir model, oil price increases lead o a fall in he relaive price of he domesic goods and o lower oupu, while produciviy shocks lead o a fall in he relaive price of he domesic goods bu o an increase in oupu. Our model is able o reproduce he sign of he correlaion and is also quaniaively close o he daa as for he EA. For he US he model predics a correlaion ha is wice as large as ha in he daa. The model fails o mach he correlaion of invesmen and ne expor for he US. Alogeher, he model has limied abiliy in predicing he correlaion of consumpion and invesmen wih ne expor. As for he sandard deviaions, he major failure of he model concerns he erms of rade 16 Daa are HP-filered using he longer sample 197:1 o he laes available observaions 25:2 for mos US series and 23:4 for mos EA series). Mos of he US series are aken from he S. Louis Fed daa se FRED) and from Global Insigh. Mos of he EA series are aken from he daa se consruced by Fagan e al. 21). The daa se used in he paper is available from he auhors on reques. 17 The model-based real GDP is compued a seady-sae prices. The conribuion of oil-shocks o he real GDP a curren prices is more han hree imes as large. 2

21 and inflaion oo volaile in he model). The sandard deviaion of he real) price of oil denoed as Pe) is smaller han in he daa boh for he US and he EA. Noice ha increases in he variance of he oil-price could be obained a he cos of furher increasing he volailiy of he erms of rade. The correlaion beween he price of oil and ne expor, and beween he erms of rade and he real exchange rae is of he correc sign and magniude. On he conrary, he correlaion of he real exchange rae and US ne expor is of he wrong sign. Neverheless, if we compue he empirical measure wihou filering he daa or filering only ne expor) he sign of he correlaion becomes negaive and of he order of magniude of -.1). 21

22 Table 3: Empirical momens US model EA model Sandard deviaions in pp GDP C I NX o RER π R Pe x-correlaions GDP, N X) C, N X) I, N X) P e, N X) o, N X) P e, o) RER, N X) REX, P e) Cross-counry correlaions daa model C, C ) I, I ) GDP, GDP ) R, R ) π, π ) C C ), RER) Noice ha if measure he correlaion beween he consumpion differenial and he non-filered RER obain a correlaion of abou

23 Dollar Real Price of Oil Toal Consumpion ea) GDP us) Core Inflaion us) * Policy Rae us) * Headline inflaion ea) * Toal Consumpion us) Headline inflaion us) * Producer Price inflaion ea) Producer Price * inflaion us) *.2 Ex Ane Real Rae ea) * Ex Ane Real Rae us) * GDP ea) Core Inflaion ea) * Policy Rae ea) * LR Real Rae ea) * Figure 1: Response o one sandard deviaion innovaion o he produciviy of he oil secor. 4 The effec of an exogenous oil-price increase We model he oil-price shock as a negaive ransiory one-sandard-deviaion innovaion o he level of produciviy of he oil-producing secor. Figures 1 and 2 show he impulse-response diagrams of a selecion of variables afer he shock, which generaes on impac a 7.8% increase in he real price of oil i.e. he raio of he nominal price of oil o he US CPI). The shock is persisen auo-correlaion coefficien of.95) so ha he half-life of he oil-price change is abou 12 quarers. A robus finding in he VAR lieraure is ha ransiory oil-price shocks drive up inflaion CPI as well as GDP-deflaor) and down real GDP. 19 Bernanke e al. 24) using a fivevariable quarerly VAR find ha a 1% increase in he price of oil implies a change of GDP of abou -.7% a he rough four quarers afer he innovaion). 2 Bernanke e al. 1997), using a seven-variable monhly VAR, find ha a 1% increase in he price of oil produce a fall in GDP of around -.25% 24 monhs afer he shock. As for prices, he monhly VAR used in Bernanke e al. 1997) yields an increase in he CPI of abou.2% wo years afer he oil-price shock. The quarerly VAR used in Bernanke e al. 24) produces a milder increase abou.1%). 19 See for example Bernanke, Gerler and Wason e al. 1997, 24), Hamilon and Herrera 24) and Jiménez-Rodríguez and Sànchez 24). 2 The oil-price shock is consruced as in Hamilon 1996), i.e. i is he amoun by which he log oil price in monh exceeds is maximum value over he previous 12 monhs; if oil prices are lower han hey have been a some poin during he pas year, no oil shock is said o have occurred. 23