Optimal Pass-Through of Oil Prices

Transcription

1 Opimal Pass-Through of Oil Prices Hafedh Bouakez HEC Monréal and CIRPÉE Nooman Rebei Inernaional Deparmen Bank of Canada Désiré Vencaachellum African Developmen Bank Ocober 2007 Preliminary and Incomplee Absrac In many developing and emerging marke economies, governmens inervene o limi he degree o which oil-price increases are passed hrough o domesic fuel prices. This paper invesigaes wheher, and o wha exen, his inervenion is warraned. I compues he welfare-maximizing level of pass-hrough of oil prices in an arificial oilimporing economy characerized by nominal price rigidiies. We find ha, o he exen ha moneary policy is capable of sabilizing he economy, governmen inervenion in he oil marke should be avoided. On he oher hand, when complee sabilizaion is no aainable, as is he case under CPI inflaion argeing, he governmen can improve social welfare by limiing he degree of pass-hrough of oil prices. We find, however, ha he welfare gain from pursuing such a policy is negligible. We hank Jean Boivin, Mick Devereux, Charles Engel, and Alok Johri for helpful discussions. Financial suppor from he FQRSC, IFM2, and SSHRC is graefully acknowledged. Address: 3000 chemin de la Côe-Saine-Caherine, Monréal, Québec, Canada H3T 2A7. Tel.: ; Fax: ; hafedh.bouakez@hec.ca. Address: Inernaional Deparmen, Bank of Canada, 234 Wellingon S., Oawa, Onario, Canada K1A OG9. Tel.: ; Fax: ; nrebei@bank-banque-canada.ca. Address: African Developmen Bank. BP , Tunis Belvedère,Tunisia. Tel.:

2 1. Inroducion How, if a all, should governmens respond o oil-price shocks? Ineres in his quesion has been revived by he recen episode of rapid and susained increase in inernaional oil prices, which sared owards he end of This episode has led several developing and emerging marke economies o adop a number of policies aimed a cushioning he adverse effecs of oil-price increases. Many of hese policies sough o avoid he full pass-hrough of oil-price increases o domesic consumers by conrolling reail fuel prices, providing explici fuel subsidies, lowering fuel axes, and reducing he profi margins of sae-owned oil companies. According o wo recen sudies by he World Bank (2006) and Baig e al. (2007), roughly half of he developing and emerging marke economies surveyed have no fully passed hrough he increase in inernaional fuel prices beween he end of 2003 and mid In conras, in mos indusrialized counries, governmens have absained from inervening in he oil marke, oping o mainain a full-pass-hrough policy. This behavior is consisen wih he convenional wisdom ha fuel prices ough o be compleely deregulaed. As is well known from he lieraure on regulaion, however, his view is valid in a fricionless environmen bu may no be jusified in he presence of marke failure. The objecive of his paper is o deermine wheher, and o wha exen, governmen inervenion in he oil marke is warraned in an economy characerized by nominal price rigidiies in he goods marke. More specifically, we invesigae wheher limiing he degree of pass-hrough of oil prices in such an environmen could be welfare improving relaive o a full-pass-hrough policy. For his purpose, we consider a heoreical small open economy ha uses oil as an inpu in he producion process. Oil is impored by he governmen a he world price and sold o domesic producers a a domesic price ha is deermined according o a specified rule. This assumpion is jusified by he fac ha in many oilimporing counries, he governmen ses domesic fuel prices according o ad hoc pricing formulae ha aim a smoohing oil-price changes. In our model, he governmen ses he domesic price of oil in a given period as a convex combinaion of he curren world price expressed in local currency and las period s domesic price. The coefficien aached o he world price is hen inerpreed as he degree of pass-hrough. Any value of his coefficien ha is sricly less han 1 implies incomplee pass-hrough of oil prices and he resuling wedge beween he world price of oil and is domesic counerpar, i.e., he subsidy, is 1

3 financed hrough lump sum axes. Imporanly, our analysis assumes ha he governmen can pre-commi o he announced pricing rule and ha agens are aware of boh he rule and he pre-commimen. In addiion o oil, domesic producers use non-oil inermediae goods as inpus. These goods have sicky prices, which means ha here is scope for moneary policy o affec real variables. We consider wo alernaive policy regimes, one in which he moneary auhoriy sricly arges CPI inflaion, and one in which i fixes he nominal exchange rae. We focus on hese wo specific cases because hey describe he conduc of moneary policy in a large number of developing and emerging marke economies. Our baseline resuls indicae ha, under CPI inflaion argeing, he opimal level of pass-hrough is abou 20 per cen. Tha is, aggressive sabilizaion of oil prices on he par of he governmen is desirable. On he oher hand, under a fixed exchange rae regime, complee pass-hrough is opimal. The inuiion for hese resuls is he following. Under CPI inflaion argeing and complee pass-hrough of oil prices, domesic prices are no compleely sabilized. This in urn induces inefficienly large movemens in he real exchange rae and causes oupu (and oher real variables) o over-reac o he oil-price shock and hus o deviae from he efficien allocaion. On he oher hand, a zero-pass-hrough policy sabilizes domesic prices, bu does so a he expense of sabilizing he real exchange rae, hereby leading o insufficien variaions in oupu. The deparure of he economy from he efficien allocaion in his case is simply a reflecion of he disorionary effecs of he subsidy involved. The opimal degree of pass-hrough, herefore, involves weighing he benefis of sabilizing domesic prices agains he coss of desabilizing oupu (or alernaively, he real exchange rae). Our analysis suggess ha he rade-off beween inflaion sabiliy and oupu sabiliy is resolved a a raher low degree of pass-hrough of oil prices. Under fixed exchange raes and complee pass-hrough of oil prices, he economy s response o an oil-price shock coincides wih he efficien allocaion, because he laer involves sabilizing he nominal marginal cos of domesic producers, which, given our marke srucure, is ied down by he nominal exchange rae. Any aemp o limi he pass-hrough of oil prices in his case would generae a welfare loss, which will be larger he lower he degree of pass-hrough. Nowihsanding ha under CPI inflaion argeing he opimal pricing rule deviaes 2

4 significanly from complee pass-hrough, he resuling welfare gain is negligible (less han 0.01 per cen of permanen consumpion). Our sensiiviy analysis reveals ha under sric CPI inflaion argeing, he opimal degree of pass-hrough increases wih he price-elasiciy of oil demand, decreases wih he share of oil in producion, and is essenially insensiive o he exen of financial fricions. In each of hese cases, he welfare gain associaed wih he opimal degree of pass-hrough remains very small. When impor prices are assumed o be sicky, however, he opimal degree of pass-hrough falls o roughly 10 per cen and he associaed welfare gain is significanly higher, exceeding 0.12 per cen of permanen consumpion. Of he vas lieraure on he macroeconomic effecs of oil-price shocks, one paricular sream is more closely relaed o our work. 1 I consiss of sudies ha examine he role of moneary policy in shaping he relaionship beween oil-price shocks and he macroeconomy. Some of hese conribuions are based on vecor auro-regressions (e.g., Bernanke, Gerler and Wason 1997, Hooker 2002, Hamilon and Herrera 2004), while ohers use dynamic general-equilibrium models (e.g., Leduc and Sill 2004, Medina and Soo 2005, and Blanchard and Galì 2007). 2 The main focus of his lieraure, however, is o deermine wheher he downurns ha follow large oil-price shocks are caused by he sysemaic (conracionary) response of moneary policy o he inflaionary pressure brough abou by hese shocks, raher han he shocks hemselves. 3 Our paper is also relaed o he recen lieraure on he welfare implicaions of macroeconomic policies in small open economies, as exemplified by he work of Kollmann (2002, 2006), Galì and Monacelli (2003), Ambler, Dib, and Rebei (2004), Monacelli (2005), and Devereux, Lane, and Xu (2006), among ohers. None of hese sudies, however, explicily examines he opimaliy of governmen inervenion in response o oil-price shocks. The res of he paper is srucured as follows. Secion 2 discusses he empirical evidence on pass-hrough of oil prices. Secion 3 describes he model. Secion 4 sudies he dynamic response of he economy o an oil-price shock. Secion 5 performs a welfare analysis. Secion 1 For comprehensive surveys of his lieraure, see Barsky and Kilian (2004) and Hamilon (2005). 2 Sudies based on dynamic general-equilibrium models build on earlier papers by Kim and Loungani (2002), Roemberg and Woodford (1996), Finn (2000), and Backus and Crucini (2000). These papers, however, consider real economies and absrac from money. 3 Blanchard and Galì (2007), on he oher hand, find ha moneary policy is one of he facors ha accoun for he fac ha oil-price shocks seem o have smaller effecs on economic aciviy in he 1990s han in he 1970s. 3

5 6 examines he sensiiviy of our resuls o alernaive modelling assumpions. Secion 7 concludes and discusses possible fuure exensions of he model. 2. Empirical Evidence on Pass-Through of Oil Prices Alhough i is well esablished ha several developing and emerging marke economies have aemped o limi he exen o which increases in he world price of oil are passed hrough o domesic fuel prices, lile empirical work has been done o formally measure and compare he degree of pass-hrough of oil prices across counries. The only wo sudies ha we are aware of hose by he World Bank (2006) and Baig e al. (2007), which use survey daa from, respecively, 38 and 44 developing and emerging marke counries o compue passhrough esimaes for gasoline and diesel beween January 2004 and mid In boh cases, pass-hrough is measured as he raio of he (absolue) change in domesic reail fuel prices (measured in local currency) o he (absolue) change in he inernaional price (convered o local currency). Their resuls are summarized in Table 1. For comparison, resuls for six indusrialized counries are also repored. Wih a few excepions, he wo sudies repor similar esimaes for counries ha are common o boh samples. Table 1 shows subsanial heerogeneiy in he degree of pass-hrough across counries. Esimaes range from 0 o 2.5 in he sudy by he World Bank and from 0.17 o 2.8 in he sudy by Baig e al. More imporanly, of he 38 counries surveyed by he World Bank, 19 (22) have no fully passed hrough he oil-price increase o domesic gasoline (diesel) prices. Baig e al. also documen incomplee pass-hrough o gasoline (diesel) prices in 21 (19) of he 44 counries in heir sample. Therefore, roughly half of he developing and emerging marke economies surveyed have no passed hrough he increase in he world price of oil. In a hird of hese counries, pass-hrough was less han 50 per cen. In conras, wih he excepion of Japan, mos indusrialized counries have allowed oil-price increases in he world marke o be fully passed hrough o domesic fuel prices. [To be compleed] 4

6 3. The Model 3.1 Overview of he Model The economy consiss of households, firms, a governmen, and a moneary auhoriy. There are four ypes of goods: a final good, a composie non-oil good, oil, and inermediae goods. The final good, which serves consumpion and invesmen purposes, is produced by perfecly compeiive firms using oil and a non-oil composie good as inpus. The non-oil composie good is produced by mixing domesically produced and impored inermediae goods. Domesic inermediae goods are produced by monopolisically compeiive firms ha use domesic labor and capial as inpus. Domesically produced inermediae goods are also expored o he res of he world. Expor prices are deermined a he world marke and are exogenous o he economy. Foreign inermediae goods are impored by monopolisically compeiive imporers a he world price. These goods are hen sold o local firms a domesic-currency prices. Prices se by monopolisic firms are cosly o change, and are hus sicky. Price sickiness inroduces a role for moneary policy in removing he disorions associaed wih he cosly adjusmen of nominal prices. I is assumed ha he moneary auhoriy ses he nominal ineres rae according o a Taylor-ype rule, which ness sric CPI inflaion argeing and fixed exchange raes as special cases. Oil used o produce he final good is impored by he governmen who plays he role of an inermediary, buying oil a he world price, P o, and reselling i o domesic firms a he domesic price P o. These wo prices need no be idenical even afer convering he world price o domesic currency. Depending on he way in which he governmen ses P o, pass-hrough from he world price o he local price of oil will be full or incomplee. In he model, he governmen follows a rule ha can yield any degree of pass-hrough beween zero and 100 per cen. Access o inernaional financial markes can be limied, depending on he severiy of credi consrains ha a given counry faces. Counries ha have only limied access o inernaional financial markes canno buffer shocks and smooh consumpion by resoring o inernaional borrowing. This feaure is capured in he model by assuming porfolioadjusmen coss. The res of his secion provides a deailed descripion of he model, derives he firs- 5

7 order condiions, and describes he equilibrium. Throughou he paper, variables ha originae in he res of he world are denoed by an aserisk, and variables ha do no have a ime subscrip refer o seady-sae values. 3.2 Households The represenaive household maximizes is lifeime uiliy given by U 0 = E 0 β u(c,h ), (1) =0 where β is he subjecive discoun facor (0 < β < 1), u is he insananeous uiliy funcion, c is consumpion, and h denoes hours worked by he household. 4 The insananeous uiliy funcion is assumed o be u( ) = γ γ 1 γ 1 c γ + log (1 h ), (2) where γ, η and are posiive parameers. The represenaive household eners period wih B 1 foreign-currency non-saeconingen bonds and a sock of capial, k. In period, he household pays a lump-sum ax, T, o he governmen and receives dividends, D, from monopolisic firms. I also receives oal facor paymens of W h + Q k from selling labor and rening capial o domesic inermediae-good producers, where W and Q denoe he nominal wage and renal raes, respecively. The household s income in period is allocaed o consumpion, invesmen, money holdings, and he purchase of nominal bonds. Acquiring foreign bonds enails paying (nominal) porfolio-adjusmen coss: 5 ψ b 2 e P (B B P where ψ b is a posiive parameer and e is he nominal exchange rae defined as he number of unis of domesic currency needed o purchase one uni of foreign currency. Invesmen, i, increases he household s sock of capial according o ) 2 k +1 = (1 δ)k + i, (3) 4 In each period, he household s oal endowmen of ime is normalized o uniy. 5 Wihou poroflio-adjusmen coss, he model would have a uni roo because he bond holdings process would follow a random walk. 6

8 where δ (0, 1) is he depreciaion rae of capial. Invesmen is subjec o quadraic adjusmen coss: ( ) ψ 2 k i δ k, 2 k where ψ k 0. The household s budge consrain is given by: P (c + i ) + e B W h + Q k + e R 1B 1 + D + T ψ k 2 P ( ) 2 i δ k ψ b k 2 e P ( B B ) 2, (4) where P he price of he final good, D D d +D m, wih D d being dividends received from domesic inermediae-good producers and D m P hose received from imporers of foreign inermediae goods, R denoes he gross domesic nominal ineres rae, and R denoes he gross world nominal ineres rae. The represenaive household chooses c, h, B, and k +1 o maximize is lifeime uiliy subjec o is budge consrain (4), he capial accumulaion equaion (3), and a no-ponzigame condiion on is holdings of asses. The household s firs-order condiions are λ = c 1 γ, (5) w = (1 h ) 1, (6) λ λ = βr (1 B B ) 1 ( ) λ+1 e +1 + ψ b E, (7) π +1 e P λ = βe {λ +1 [1 + q +1 δ + ψ( i +1 k +1 δ) + ψ 2 ( i ψ( i k δ) k +1 δ) 2 ]}, (8) where λ is he Lagrange muliplier associaed wih he budge consrain expressed in real erms; w W /P is he real wage; q Q /P is he real renal rae; and π P /P 1 is he gross inflaion rae beween 1 and. 3.3 Producion Final good Firms in he final-good secor are perfecly compeiive. They combine oil and a non-oil composie good o produce a single homogenous good using he following consan elasiciy of subsiuion (CES) echnology: y = [φ 1 ν (y o ) ν 1 ν ] + (1 φ) 1 ν (y no ) ν 1 ν ν 1 ν, (9) 7

9 where φ > 0 is he weigh of oil in he producion of he final good and ν > 0 is he elasiciy of subsiuion beween oil and non-oil inpus. Oil is impored by he governmen, who plays he role of an inermediary, buying oil a he world price, P o, and reselling i o domesic firms a he domesic price P o. In oil-exporing counries, i is assumed ha he oil indusry is owned by he governmen, which sells oil o he res of he world a he world price, P o, and o domesic firms a he domesic price, P o. The represenaive final-good producer solves max P y P o {y d,ym } y o P no y no, (10) where y is given by (9). Profi maximizaion implies ( ) P y o o ν = φ y. (11) P and ( P y no no) ν = (1 φ) y, (12) P Hence, he parameer ν also represens he price-elasiciy of oil demand. The zero-profi condiion implies ha he price of he final good, P, is given by Non-oil composie good P = [ φ(p o ) 1 ν + (1 φ) (P no ) 1 ν] 1 1 ν. (13) The non-oil composie good is produced by perfecly compeiive firms using he following Cobb-Douglas echnology y no = Γ(y d )σ (y m )1 σ, (14) ( where Γ σ σ (1 σ) σ 1 is a posiive parameer; y d 1 θ/(θ 1) 0 yd (i) di) (θ 1)/θ and ( y m 1 ϑ/(ϑ 1)are 0 ym di) (i)(ϑ 1)/ϑ aggregaes of domesic and impored inermediae goods, respecively; and θ (ϑ) > 1 is he elasiciy of subsiuion beween domesic (foreign) ( ) inermediae goods. Define P d 1 1/(1 θ) ( 0 P d(i)1 θ di and P m ) 1 1/(1 ϑ) 0 P m (i) 1 ϑ di as he price indexes associaed wih he aggregaors y d and y m. Then, demands for individual domesic and impored inermediae goods are, respecively, given by ( P y d d (i) = (i) P d ) θ y d, i (0,1), (15) 8

10 and where y d, y m, and P no ( P y m m (i) = (i) P m are given by, respecively ) ϑ y m, i (0,1). (16) ( P y d d ) 1 = σ P no y no, (17) and ( ) P y m m 1 = (1 σ) P no y no. (18) ( P no = P d ) σ (P m ) 1 σ. (19) Domesic inermediae goods Domesic inermediae-good producers have idenical Cobb-Douglas producion funcions given by z (i) y d (i) + yx (i) = A k (i) α h (i) 1 α, (20) where α (0,1); k (i) and h (i) are capial and labour inpus used by firm i; and A is an aggregae echnology shock. Le P d (i) denoe he price ha firm i chooses for is sales in he domesic marke. Changing he domesic price enails quadraic adjusmen coss à la Roemberg (1982): ψ d 2 ( ) 2 P d (i) π d P 1 d (i) 1, where ψ d 0; and π d is he seady-sae value of π d P d /P 1 d. On he oher hand, he domesic-currency expor price, P x (i), once convered o foreign currency, is equal o he world price, P. Tha is, P x (i) = e P. (21) This assumpion reflecs he fac ha he small open economy has no conrol over he world price of expored goods. In urn, i implies ha he law of one price holds for hese goods. Under hese assumpions, firm i solves he following dynamic problem: max {h (i),k (i),p d (i),yx (i)} E s=0 9 ( ) β s λ+s D d +s (i), (22) λ P +s

11 where D d (i) P d (i)y d (i) + P x (i)y x (i) W h (i) Q k (i) ψ d 2 Given he demand funcion (15), he firs-order condiions for firm i are ( ) 2 P d(i) π d P 1 d (i) 1 P d (i)y d (i). w = (1 α)ξ (i) z (i) h (i), (23) q = αξ (i) z (i) k (i), (24) [ θ ξ (i) p d = (1 θ) 1 ψ ( ) d π d 2 ] (i) (i) 2 π d 1 [ π d ( ) ( (i) π d ψ (i) λ +1 π d d π d π d 1 βe +1 (i) ) 2 ( ) ] π d (i) y d λ π +1 π d π d 1 +1 (i) y d(i), (25) p x (i) = ξ (i), where ξ (i) is he Lagrange muliplier associaed wih equaion (20) and is equal o he real marginal cos of firm i; p d (i) P d (i)/p ; p x (i) P x (i)/p, π d (i) P d (i)/p 1 d (i); and π P /P 1 is he gross inflaion rae in he res of he world, which is normalized o 1. Equaions (21) and (26) imply ha he marginal cos of he domesic inermediae-good producer is ied down by he exchange rae, boh in nominal and real erms. This resul will be imporan for undersanding he inuiion behind he paper s main findings Impored inermediae goods Foreign inermediae goods are impored by monopolisically compeiive firms a he world price, P. Imporing firms hen sell hose goods in domesic currency o final-good producers. Resale prices, P m (i) are also subjec o quadraic adjusmen coss: (26) ψ m 2 ( ) P m (i) 2 π m P 1 m (i) 1, where π m is he seady-sae value of π m following problem: max {P m (i)} E s=0 P m /P 1 m. The imporing firm i solves he ( ) β s λ+s D m +s (i), (27) λ P +s 10

12 where D m m (i) = (P (i) e P )ym (i) ψ ( ) m P m (i) 2 2 π m P 1 m (i) 1 P m (i)y m The firs-order condiion for his problem is (i). (28) ϑ s p m (i) = 1 + (1 ϑ) ψ ( ) m π m (i) 2 2 π m 1 [ π m ( ) (i) π m ψ (i) m π m π m 1 λ +1 βe λ ( π m +1 (i) ) 2 π +1 π m ( ) π m (i) y m π m 1 +1 (i) y m(i) ] (29), where p m (i) P m (i)/p and π m (i) P m (i)/p m 1 (i). 3.4 The governmen I is assumed ha he governmen ses he domesic price of oil in a given period as a convex combinaion of he curren world price expressed in local currency and las period s domesic price. Formally, P o = (1 χ)p o 1 + χe P o. (30) Thus, if χ = 1, here is complee pass-hrough from he world price of oil o he domesic price. If χ = 0, here is zero pass-hrough. The rule (30) is admiedly ad hoc inasmuch as i is no derived from an explici opimizaion problem of he governmen. This specificaion, however, is a convenien and parsimonious way o capure he fac ha, in many developing and emerging marke economies, domesic fuel prices are deermined according o ad-hoc pricing formulae, while allowing he degree of pass-hrough of oil prices o ake any value beween 0 and 1. The governmen s revenues include receips from selling oil o domesic firms and axes. The governmen s expendiures include he cos of acquiring oil. Hence, he governmen s budge consrain is given by e P o y o = P o y o + T. In wha follows, we will assume ha he real price of oil, p o he following process log p o P o P, evolves according o = (1 ρ o )log(p o ) + ρ o log(p o 1) + ǫ o, (31) 11

13 3.5 Moneary auhoriy I is assumed ha he cenral bank manages he shor-erm nominal ineres rae according o he following Taylor-ype policy rule: log(r /R) = π log(π /π) + e log(e /e). This rule encompasses wo polar moneary-policy/exchange-rae regimes. When π and e = 0, we obain a sric CPI inflaion argeing regime. Alernaively, when e and π = 0, he rule above represens a fixed exchange rae regime. 3.6 Symmeric equilibrium In a symmeric equilibrium, all inermediae-good producers make idenical decisions. Tha is, z (i) = z, k (i) = k, h (i) = h, P d (i) = P d, P m (i) = P m, and P x (i) = P x for all i (0, 1). Hence, a symmeric equilibrium for his economy is a collecion of 30 sequences (c, h, i, k +1, y, y d, y o, y no, y m, y x, z, w, q, ξ, λ, π, π d, π no, π m, π x, R, s, e, b, p d, p o, p no, p m, px, P ) =0 saisfying he privae agens firs-order condiions, he oil pricing rule, he moneary policy rule, marke-clearing condiions, and a balance of paymens equaion (he model s equaions are lised in he appendix). 6 The model is solved up o a second-order approximaion around a deerminisic seady sae in which all variables are consan. 3.7 Calibraion To sudy he behavior of he economy under differen degrees of pass-hrough of oil prices, we need o assign values o he model parameer and o seady-sae values of he variables. We sar by calibraing a baseline version of he model in which only domesic prices are rigid. Impor prices are fully flexible and obey he law of one price. Under his assumpion, he non-oil erms of rade are always consan (since boh impor and expor prices are equal o e P ) and he flexible-price allocaion, which is obained when boh domesic and impor prices are fully flexible and when here is complee pass-hrough of oil prices, is efficien. 7 The flexible-price allocaion, herefore, provides a benchmark for evaluaing and comparing alernaive pricing policies in his case. 6 The variable b denoes B /P. 7 Sricly speaking, he flexible-price allocaion is consrained-efficien (raher han Pareo efficien) because he exisence of monoplisic compeiion among inermediae-good producers leads o an ineffcienly low level of oupu. 12

14 The baseline model is calibraed a a quarerly frequency. The subjecive discoun facor, β, is se o 0.99, which implies ha he annual real ineres rae is equal o 4 per cen in he deerminisic seady sae. The elasiciy of ineremporal subsiuion is se o 0.5. The preference parameer is chosen so ha he fracion of hours worked in he deerminisic seady sae is equal o 0.3. The capial s share in producion, α, is se o 0.36, while he depreciaion rae, δ, is chosen o be These values, which have become quie sandard in he lieraure, were used, for example, by Backus and Crucini Following Bouakez and Rebei (2006), we se he capial adjusmen cos parameer, ψ k o 30, which implies an elasiciy of invesmen wih respec o he price of capial of The parameer governing porfolio-adjusmen coss is se o , he value suggesed by Schmi-Grohé and Uribe (2004). The share of domesic inermediae goods in he non-oil composie good, σ, is chosen o be The elasiciy of subsiuion beween domesic inermediae goods, θ, and is analogous for impored goods, ϑ, are se o 10, implying a markup of 11 per cen in he deerminisic seady sae. The price-adjusmen-cos parameer ψ d is calibraed so ha, up o a firs-order approximaion, he resuling nominal rigidiy is equivalen o ha implied by a Calvo-ype saggered price seing wih an average duraion of price conracs of 4 quarers. The parameers ha describe he way in which he producion echnology depends on oil are crucially imporan o our analysis. We se he price-elasiciy of oil demand (which is also he elasiciy of subsiuion beween oil and non-oil inpus), ν, o This value is consisen wih he evidence ha oil demand is highly insensiive o price changes. For example, Gaely and Huningon (2002) esimae he shor-run elasiciy of demand for crude oil o be 0.05 for OECD counries and beween 0.02 and 0.03 for a group of non- OECD counries. Cooper (2003) provides individual esimaes for 23 counries ha range beween 0 and These sudies indicae, however, ha he shor-run price elasiciy of oil demand is significanly lower han he long-run elasiciy. 8 Given ha he specificaion of he producion funcion (9) does no allow us o disinguish beween he shor-run and he long run elasiciy of oil demand, our calibraion reflecs he fac ha we mainly focus on he shor-run raher han he secular effecs of oil-price shocks. The seady-sae oil share in producion is given by he parameer φ. Because he model 8 Gaely and Huningon (2002) esimae he long-run elasiciy o be 0.64 for OECD counries and 0.18 for he non-oecd group, while Cooper (2003) repor esimaes ranging beween 0 and

15 economy does no produce oil, φ is also he seady-sae raio of oil impors o oupu. In he daa, his raio differs subsanially across counries, bu i is generally much lower in indusrialized counries han in developing and emerging marke economies. Since he end of 2001, however, here has been a widespread increase in he oil impor bill as a resul of rising oil prices and he inelasic demand for oil. For example, he average raio of oil impors o GDP in African counries rose from abou 4 per cen in 2001 o roughly 6 per cen by he end of A similar paern has also been observed in a number of Asian and Lain American counries: In 2003, he share of oil impors in GDP reached 3.8 per cen in India, 5 per cen or more in Singapore, Korea, Thailand, Taiwan and he Philippines, and 4.9 per cen on average for Cosa Rica, El Salvador, Guaemala, Honduras, Nicaragua and Panama. 9 These numbers are likely o have increased since hen given ha oil prices coninued o rise. Based on hese consideraions, we se he parameer φ o To obain values for he parameers ρ o and σ ǫo, we esimae an AR(1) process using daa on he real price of oil over he period 1974Q1 2006Q4. The real price of oil is measured by he average spo price of Wes Texas Inermediae crude oil, divided by he U.S. GDP deflaor and expressed in logarihm. Boh series are aken from he Federal Reserve Bank of Sain-Louis daabase. Our esimaion yields ρ o = and σ ǫo = Table 2 summarizes our baseline calibraion. In Secion 5, we consider alernaive values of he elasiciy of oil demand, he share of oil in producion, and he porfolio-adjusmencos parameer, as well as he case wih sicky impor prices (ha is, ψ m 0). 4. Impulse Response Analysis The purpose of his secion is o conras he dynamic response of he economy o an oil-price increase under complee and zero pass-hrough. The comparison is made under wo alernaive scenarios abou moneary policy: sric CPI inflaion argeing and a fixed exchange rae regime. We focus on hese wo paricular cases because hey represen he sance of moneary policy in a wide range of oil-imporing small open economies. As a benchmark, we also compue he efficien response of he economy, which is obained when he following wo condiions are me: (i) domesic prices are compleely sabilized and (ii) here is complee pass-hrough of oil prices. Indeed, under hese condiions, he equilibrium 9 Unied Naions Conference On Trade And Developmen (2005). 14

16 allocaion coincides wih he flexible-price allocaion, which, as argued in Secion 3.7, is efficien. 4.1 Sric CPI inflaion argeing Figure 1 depics he impulse response of oupu, consumpion, invesmen, domesic and CPI inflaion, he nominal and real ineres rae, and he nominal and real exchange rae o a sandard-deviaion (0.137) increase in he world price of oil under CPI inflaion argeing. Consider firs he case wih complee pass-hrough (χ = 1). The shock riggers a persisen decline in oupu, consumpion and invesmen, which hen converge o heir seady-sae levels from below. This oucome is aribued o a combinaion of wo effecs of he higher oil price: a direc income effec, hrough he balance of paymens, and an indirec effec on producion, hrough higher coss of inpus. The former decreases consumpion and increases labor supply. The laer decreases demand for non-oil inpus and, by exension, demand for labor and capial. The ne effec on hours worked is, in principle, ambiguous and depends on he model parameers, bu labor income unambiguously falls due o a subsanial decrease in he real wage. Moreover, he lower reurn on capial leads households o cu invesmen. Because he domesic price of oil eners he composiion of he CPI, he rise in he world price of oil ends, under full pass-hrough, o increase CPI inflaion. To eliminae he upward pressure on inflaion, he nominal ineres rae rises subsanially, and given ha expeced inflaion is zero, he real ineres rae rises by he same amoun. The large increase in he real ineres rae leads o a sharp appreciaion of he nominal and he real exchange rae. 10 This appreciaion is needed o (parially) offse he increase in he world price of oil, i.e., o limi he degree of pass-hrough of he oil-price increase o CPI inflaion. Figure 1 shows ha he iniial fall in oupu is significanly larger under sric inflaion argeing han under he efficien allocaion of resources (0.8 versus 0.4 percen), and ha he wedge persiss for more han four quarers. This discrepancy is due o he inabiliy of he moneary auhoriy o sabilize he economy under CPI inflaion argeing. Indeed, in he baseline version of he model, only domesic prices are rigid. The opimal policy, herefore, involves argeing domesic-price inflaion. As explained above, such a policy susains he flexible-price allocaion. A regime ha arges CPI inflaion, on he oher 10 The nominal and and he real exchange rae exhibi idenical responses because he laer is compued using he CPI, which is compleely sabilized under sric CPI inflaion argeing. 15

17 hand, sabilizes a combinaion of domesic and impor prices. As Figure 1 shows, however, domesic prices are no compleely sabilized under his policy, which in urn causes oupu o depar from is efficien response. The reason for his deparure is he exaggeraed (and, hence, inefficien) response of he real exchange rae, which appreciaes by more han i would have under he efficien allocaion. Nex, consider he case wih zero pass-hrough of he oil-price increase (χ = 0). Following he shock, oupu and consumpion decrease for several periods before reurning o heir pre-shock levels, whereas invesmen rises on impac and converges o is seady-sae level from above. In all cases, however, he magniude of he response is subsanially smaller han under complee pass-hrough. The reason is obvious: a zero-pass-hrough policy implies ha he firms real cos of acquiring oil is unaffeced by he oil-price increase if no for changes in he real exchange rae. As a resul, inpu demand and producion fall only slighly in he shor run relaive o he case wih complee pass-hrough case. 11 Given ha he oil-price increase is no passed hrough o CPI inflaion, he nominal (and he real) ineres rae need no increase by as much as in he complee-pass-hrough case. In fac, he nominal ineres rae remains virually unchanged in his case, leading o roughly consan nominal and real exchange raes. The figure shows ha he zero-pass-hrough policy goes a long way oward sabilizing domesic prices. Ye, he response of oupu deviaes markedly from he efficien one. In oher words, argeing CPI inflaion sabilizes domesic prices bu desabilizes oupu. The reason for his resul is ha he flexible-price allocaion is no aainable when here is incomplee pass-hrough of oil prices, due o he disorionary effecs of he subsidy involved. Higher degrees of pass-hrough (ha is, higher values of χ) have wo offseing effecs on oupu. On he one hand, higher pass-hrough enails smaller disorions o he economy, and his effec ends o bring oupu closer o is efficien level. On he oher hand, when pass-hrough is high, argeing CPI inflaion leads o inefficienly large swings in he real exchange rae, which ends o desabilize oupu. This discussion suggess ha o deermine 11 I is worh emphasizing, however, ha he effecs of an oil-price increase are no permanenly smaller (in absolue value) under zero han under complee pass-hrough. Because he governmen mus raise axes o finance any oil-price subsidy given o firms, deviaing from complee pass-hrough amouns o ransferring he higher cos of oil from firms o households. The mued effecs under zero pass-hrough herefore simply reflec he households abiliy o smooh consumpion over ime via borrowing and lending. Evenually, for sufficienly long horizons, he effecs of he oil-price shock will be larger under incomplee han under complee pass-hrough. 16

18 he opimal degree of pass-hrough, he sabilizing benefis of he governmen s inervenion have o be weighed agains he disorionary coss of he implied subsidy. Given ha, under CPI inflaion argeing, boh zero and complee pass-hrough lead o significan deparures from he efficien allocaion, i is likely ha he opimal pricing rule involves a parial degree of pass-hrough in his case. This conjecure will be formally verified in Secion Fixed exchange rae regime Figure 2 shows he dynamic responses o an oil-price shock under a fixed exchange rae regime. Under complee pass-hrough, he economy s response coincide wih he efficien allocaion. In order o undersand his resul, i is useful o recall ha he efficien allocaion requires ha he markup of domesic inermediae good producers be consan in each period. In order o achieve his oucome, he moneary auhoriy needs o compleely sabilize domesic prices, or alernaively, he nominal marginal cos of domesic good producers. Because hose firms also sell abroad and ake expor prices as given, heir marginal cos is ied down by he nominal exchange rae (assuming ha he world price, P, remains consan). Hence, he efficien allocaion involves sabilizing he nominal exchange rae. 12 Noe, however, ha efficiency requires ha he real exchange rae appreciaes despie he fixiy of he nominal exchange rae. Under he efficien allocaion, he CPI does move, which allows he nominal and he real exchange rae o have disinc dynamics. Under zero pass-hrough, boh domesic prices and he CPI are sabilized. Domesic prices are sabilized because he moneary auhoriy fixes he nominal exchange rae and hus he nominal marginal cos of domesic inermediae-good producers. The sabilizaion of he CPI originaes from wo sources: he zero-pass-hrough of he oil-price increase and he fixiy of he nominal exchange rae, which implies ha boh componens of he price of he non-oil inpu are sabilized. The consancy of he CPI in urn implies ha he real 12 This discussion suggess ha, from a welfare sandpoin, a fixed exchange rae regime dominaes sric CPI inflaion argeing. This resul seems o conradic he conclusion reached by Devereux, Lane, and Xu (2006) who show ha fixing he nominal exchange rae grealy desabilizes he economy in response o exernal shocks. This differen conclusion sems from differences in he modelling assumpions. In he model developed by Devereux, Lane and Xu, here is a raded and a non-raded good, which are produced by disinc producion unis. A crucial assumpion in heir seing is ha he raded good is no sold on he domesic marke, which implies ha he nominal marginal cos (and herefore he price of he non-raded good) is no pinned down by he nominal exchange rae. Under hese condiions, a peg prevens he real exchange rae from playing is role of a shock absorber, so ha he full impac of he shocks is passed hrough o domesic oupu. 17

19 exchange rae inheris he fixiy of he nominal exchange rae. As is apparen in Figure 2, he lack of flexibiliy of he real exchange rae leads oupu o deviae subsanially from is efficien level. Given ha he equilibrium allocaion under a fixed exchange rae regime and complee pass-hrough replicaes he efficien allocaion, any policy ha seeks o limi he degree of pass-hrough of oil prices will necessarily be welfare deerioraing. Formal welfare evaluaion, performed in Secion 5 will confirm his inuiion. 5. Welfare Analysis In his secion, we sudy he welfare implicaions of he governmen s inervenion o limi he degree of pass-hrough of oil prices. Tha is, we seek o (i) deermine wheher, and under which circumsances, such a policy is opimal, and (ii) evaluae he welfare gain associaed wih he opimal policy relaive o full pass-hrough. The opimal policy will be defined as he one ha maximizes welfare wihin he class of pricing rules given by (30). Finding he opimal policy, herefore, amouns o selecing he value of χ ha maximizes he mean of he represenaive household s lifeime uiliy. Formally, his problem is wrien as follows: max χ E {u(c,h )}. (32) To solve his problem, we compue a second-order approximaion of he model s equilibrium condiions and he uiliy funcion. Figure 3 depics our welfare meric for differen values of χ under CPI inflaion argeing and a fixed exchange rae regime. Firs, consider he case wih CPI inflaion argeing. The upper panel of Figure 3 shows ha welfare is a non-monoonic funcion of pass-hrough, reaching is maximum when χ = Hence, boh complee and zero pass-hrough are sub-opimal. Insead, he welfare-maximizing policy involves parially sabilizing he domesic price of oil. By assigning a relaively large weigh o he lagged domesic price of oil, he opimal pricing rule implies a significan amoun of ineria in oil prices. How large is he welfare gain associaed wih he opimal pricing rule relaive o a complee-pass-hrough policy? As is sandard in he lieraure, we measure he welfare gain by means of he compensaing variaion in consumpion, ha is, he percenage change in consumpion under complee pass-hrough ha would give households he same uncondiional expeced uiliy as under he opimal pricing rule. The compensaing variaion is 18

20 defined as follows: { E {u(c (1 + ζ),h )} = E u( c, h } ), (33) where variables wihou ildes refer o variables under complee pass-hrough, and variables wih a ilde refer o variables under he opimal pricing rule. The fourh column of Table 3 shows ha he fracion of permanen consumpion ha mus be offered o households o make hem as well of under complee pass-hrough as under he opimal pass-hrough policy is less han 0.01 per cen. This gain is clearly very small by any convenional sandard. Therefore, oping for complee pass-hrough of oil prices, albei sub-opimal, does no enail imporan welfare coss in he baseline model. The boom panel of Figure 3 shows ha under a peg, welfare increases unambiguously wih χ, alhough i flaens significanly for large value of χ. Tha is, he higher he degree of pass-hrough, he beer off he economy. Hence, he opimal policy is o le changes in he world price of oil be fully passed hrough o domesic prices. This resul should no come as a surprise: he impulse-response analysis in Secion 4.2 shows ha, condiional on oil-price shocks, he fixed exchange rae regime replicaes he efficien allocaion under complee pass-hrough. Therefore, any aemp o limi he degree of pass-hrough mus be welfare deerioraing in his case. Because complee pass-hrough is opimal, he compensaing variaion in consumpion is obviously nil, as shown in he las column of Table 3. In sum, our analysis suggess ha, o he exen ha moneary policy is capable of sabilizing he economy, governmen inervenion in he oil marke should be avoided. On he oher hand, when complee sabilizaion is no aainable, as is he case under CPI inflaion argeing, he governmen can improve social welfare by limiing he degree of pass-hrough of oil prices. We find, however, ha he welfare gain from pursuing such a policy is negligible. 6. Sensiiviy Analysis We now discuss he sensiiviy of our resuls o changes in he assumpions underlying he baseline model. More specifically, we consider (i) alernaive values of he price-elasiciy of oil demand, (ii) alernaive shares of oil in producion, and (iii) differen degrees of financial fricions, and (iv) he case of sicky impor prices, 19

21 6.1 Price-elasiciy of oil demand We begin our sensiiviy analysis by sudying he effec of varying he price-elasiciy of oil demand, ν. Figure 4 depics he opimal degree of pass-hrough as a funcion of his elasiciy. The op panel of he figure shows ha, under sric CPI inflaion argeing, he opimal degree of pass-hrough increases wih he elasiciy of demand for oil. This resul is quie inuiive: higher values of ν imply a larger drop in he quaniy of impored oil following he oil-price increase, inducing firms o subsiue non-oil inpus for oil. 13 Greaer subsiuabiliy ends o miigae he adverse effecs of he oil-price shock. A he same ime, i implies ha, everyhing else being equal, he welfare cos of a given subsidy is larger, which in urn weakens he argumen for a price-based sabilizaion policy. The op panel of Figure 4 shows ha as he elasiciy of demand approaches 0.5, he opimal degree of pass-hrough ends owards 100 per cen. Such a high elasiciy, however, is more in line wih he long-run esimaes repored by exising empirical sudies. Values of ν ha fall in he range of available shor-run esimaes imply ha he welfare-maximizing exen of pass-hrough is less han 30 per cen. The welfare gain associaed wih such a policy, however, is even smaller han in he baseline case, as indicaed by he value of he compensaing variaion in consumpion of per cen. The boom panel of Figure 4 shows ha, under a fixed exchange rae regime, complee pass-hrough of oil prices is always opimal regardless of he degree of responsiveness of oil demand o oil-price increases. This is because he fixed exchange regime allows o replicae he efficien allocaion for any value of he elasiciy of demand. As a resul, he compensaing variaion in consumpion associaed wih he complee-pass-hrough policy is always zero, as shown in Table Share of oil in producion Nex, consider he impac of varying he share of oil in producion. As saed above, in ne oil-imporing indusrialized counries, oil impors represen a smaller percenage of GDP han in he median developing or emerging marke economy. Indeed, he average share of oil impors in GDP in major indusrialized counries was less han 2 per cen in 2004, alhough i is likely o have increased laely. On he oher hand, several developing counries 13 Noe ha ν is also he elasiciy of subsiuion beween oil and non-oil inpus. 20

22 are heavily dependen on oil, wih an oil-impor bill ha was already above 6 per cen of GDP in 2004 (e.g., Kenya, Seychelles, and Sierra Leone). In order o accoun for his heerogeneiy across counries, we consider values of φ ranging from 0.02 o Obviously, he more oil-inensive he producion process, he larger he impac of an oil-price increase on economic aciviy. This saemen does no imply, however, ha here is greaer scope for sabilizaion. Such would be he case only if he economy deviaes furher from he efficien allocaion as he share of oil in producion becomes larger. Figure 5 shows ha his is indeed he case under sric CPI inflaion argeing. The op panel of he figure indicaes ha opimal degree of pass-hrough of oil prices is a decreasing funcion of he oil share. The model implies, however, ha he opimal pass-hrough falls by only 10 percenage poins as he oil share increases from 0.02 o More imporanly, he welfare gain associaed wih he opimal pricing rule is sill iny regardless of he oil share in producion: Even when his share is as high as 0.06, consumpion would have o permanenly increase by less hen 0.03 per cen in he model wih complee pass-hrough in order for consumers o be as well off as wih he opimal pricing rule. Again, under a fixed exchange rae regime, he abiliy of he moneary auhoriy o replicae he efficien allocaion is independen of he weigh of oil in producion. Therefore, complee pass-hrough coninues o be opimal under alernaive values of he oil share, as illusraed in he boom Panel of Figure 5, while he corresponding compensaing variaion in consumpion coninues o be zero. 6.3 Financial fricions In he hird sensiiviy experimen, we sudy he effec of varying he degree of financial fricions, as measured by he porfolio-adjusmen-cos parameer, ψ b. Financial fricions impede access o inernaional financial markes, hus prevening agens from smoohing flucuaions in heir income as much as hey would like in response o he oil-price shock. This siuaion characerizes a number of heavily indebed poor counries, which are plagued by heir lack of solvency. Larger porfolio-adjusmen coss obviously enail larger welfare losses a any given level of pass-hrough of oil prices. The direcion in which hese coss aler he opimal degree of pass-hrough, however, is ambiguous and depends on he way in which hey affec he rade-off beween he sabilizing benefi of governmen s inervenion 21

23 and he inheren welfare loss. The op panel of Figure 6 shows ha he relaionship linking he opimal degree of pass-hrough o he degree of financial fricions is raher fla. Even very large (and even implausible) values of he parameer ψ b yield an opimal pass-hrough of roughly 15 per cen, jus 5 percenage poins below he opimal level of pass-hrough in he baseline model. Furhermore, he welfare gain associaed wih he opimal pricing rule is almos unchanged as one moves from almos zero o prohibiive porfolio-adjusmen coss. On he oher hand, he degree of financial fricions does no aler he mechanism whereby he fixed exchange rae regime yields he efficien allocaion of resources, which implies ha complee pass-hrough of oil prices is opimal irrespecive of he value of ψ b. 6.4 Sicky impor prices When impor prices are sluggish (ha is, when ψ m is sricly posiive), exchange rae passhrough o impor prices becomes incomplee and, as a resul, he law of one price no longer holds for impored goods. Impor-price sickiness also means ha he non-oil erms of rade vary endogenously in response o oil-price shocks. This in urn implies ha, excep in special cases, he flexible-price allocaion is no longer opimal, because he moneary auhoriy can sraegically affec he erms of rade in a way ha improves welfare. 14 To inroduce sickiness in impor prices, we se ψ m = 100. Figure 7 shows welfare as a funcion of pass-hrough in his case. Our resuls indicae ha under sric CPI inflaion argeing, he opimal degree of pass-hrough is abou 10 per cen. Hence, wih sicky impor prices, he opimal pricing rule involves a higher degree of sabilizaion of he domesic price of oil compared wih he case of flexible impor prices. As he op panel of Figure 7 shows, welfare decreases rapidly as pass-hrough increases. This is refleced in he size of he variaion in consumpion required o leave agens indifferen beween complee pass-hrough and he opimal pricing rule, which is more han 12 imes larger han in he baseline case. These resuls can be explained as follows. Under sicky impor prices, he appreciaion of he real exchange rae does no ranslae ino cheaper foreign inermediae goods for he producers of he non-oil good (as would be he case under flexible impor prices). As a resul, he negaive impac of he oil-price increase is much larger han in he 14 See, for example, Corsei and Peseni (2001), Benigno and Benigno (2003) and Monacelli (2005). 22

24 baseline model a any given level of pass-hrough. In he case of a fixed exchange rae regime, on he oher hand, welfare under sicky impor prices is exacly idenical, a any value of χ, o wha is obained under flexible impor prices. This resul, which can be verified by comparing he boom panels of Figures 3 and 7, emanaes from he fac ha under fixed exchange raes, he nominal marginal cos of imporing firms is consan, which also means ha nominal impor prices are consan. Therefore, he magniude of he price-adjusmen-cos parameer, ψ m, is irrelevan o he dynamics of he economy. In urn, his implies ha our resuls regarding he opimal degree of pass-hrough and he associaed welfare gain are idenical o hose peraining o he baseline model. 7. Conclusion This paper has shown ha, o he exen ha moneary policy is unable o sabilize he economy in he wake of an oil-price shock, he governmen of an oil-imporing counry can find i opimal o limi he degree of pass-hrough of oil prices o domesic consumers. This would be he case of economies where he moneary auhoriy sricly arges CPI inflaion. On he oher hand, counries where he nominal exchange rae is pegged (o he currency in which oil prices are denominaed) have no incenive o deviae from he full-pass-hrough policy. Whenever he opimal pricing rule requires deviaing from full pass-hrough, we find, however, ha he resuling welfare gain is negligible. Our framework lends iself o a number of poenially ineresing exensions. One would be o add wage sickiness o he model. Real wage rigidiy would render he adjusmen of he economy o oil-price shocks more painful han wih a perfecly compeiive labor marke, because he households unwillingness o accep wage cus would imply a larger drop in labor demand, employmen and producion, hus amplifying he welfare loss associaed wih subopimal pricing policies. Second, i would be worhwhile o depar from he Ricardian environmen assumed in his paper, and o allow for he possibiliy ha he governmen relies on deb raher han axes o finance fuel subsidies. This assumpion is cerainly more realisic in counries where he ax base is narrow. Escalaing oil prices would in his case require increasingly large subsidies, leading o poenially unsusainable fiscal imbalances and increasing he likelihood ha he governmen s borrowing consrain becomes binding. 23