Modeling Exchange Rate Passthrough After Large Devaluations

Transcription

1 Modeling Exchange Rae Passhrough Afer Large Devaluaions Ariel Bursein y, Marin Eichenbaum z and Sergio Rebelo x Sepember 2005 Absrac Large devaluaions are generally associaed wih large declines in real exchange raes. We develop a model which embodies wo complemenary forces ha accoun for he large declines in he real exchange rae ha occur in he afermah of large devaluaions. The rs force is sicky nonradablegoods prices. The second force is he impac of real shocks ha ofen accompany large devaluaions. We argue ha sicky nonradable goods prices generally play an imporan role in explaining pos-devaluaion movemens in real exchange raes. However, real shocks can someimes be primary drivers of real exchange-rae movemens. J.E.L. Classi caion: F31 Keywords: exchange rae, devaluaions, passhrough, sicky prices. We hank Miles Kimball and an anonymous referee for heir suggesions, and Pierpaolo Benigno, Mario Crucini, Andrew Levin, Carlos Vegh, Jessica Wacher, Ivan Werning, and Michael Woodford for heir commens. We graefully acknowledge nancial suppor from he Naional Science Foundaion and he Searle Foundaion. y UCLA. z Norhwesern Universiy, NBER and Federal Reserve of Chicago. x Norhwesern Universiy, NBER and CEPR.

2 1. Inroducion Large devaluaions are generally associaed wih large declines in he real exchange rae (RER). In an earlier paper (Bursein, Eichenbaum, and Rebelo (2005)) we argue ha he primary force causing hese declines is a slow adjusmen in he price of nonradable goods and services, no slow adjusmen in he price of goods ha are impored or expored. Our evidence suggess ha he key puzzle abou he pos-devaluaion behavior of in aion is, why do he prices of nonradable goods and services respond by so lile in he afermah of large devaluaions? We develop a model ha accouns for he negligible response of nonradable-goods prices in he afermah of large devaluaions. Our model highlighs wo complemenary forces ha produce his resul. The rs force is sicky nonradable-goods prices. Insead of assuming ha nonradablegoods prices are sicky, we develop condiions under which his phenomenon can emerge as an equilibrium oucome. The second force is he impac of real shocks associaed wih large devaluaions ha lead o a decline in he price of nonradable goods relaive o raded goods. We sudy he imporance of hese wo forces using hree examples moivaed by he devaluaions in Korea (1997), Uruguay (2002), and he U.K. (1992). In he Korean case, we nd ha o explain he large pos-devaluaion decline in he real exchange rae, we mus allow for sicky nonradable-goods prices. Moreover, we argue ha sicky nonradable-goods prices are susainable as an equilibrium phenomenon. In he UK case, we nd ha he pos-devaluaion behavior of he real exchange rae can be explained solely as a resul of sicky nonradable-goods prices. However, he Uruguayan case shows ha i can be very misleading o assume ha prices are sicky. In his case nonradable-goods prices canno be susained as an equilibrium phenomenon and real shocks alone 1

3 accoun for he pos-devaluaion real exchange-rae depreciaion. To model sicky nonradable-goods prices, we build on he many sudies ha analyze price sickiness in closed economies. The closed-economy lieraure ideni es a class of models in which he gains from adjusing prices in response o changes in moneary policy are very small. These gains can be so modes ha when here are small coss of changing prices, price sickiness is an equilibrium phenomenon. We incorporae ino our model he key feaure emphasized by Ball and Romer (1990), a relaively a marginal cos curve. In addiion, we adop Kimball s (1995) assumpion ha he elasiciy of demand for he oupu of a monopolisic producer is increasing in is price relaive o he prices of is compeiors goods. There are wo key di erences beween our analysis of sicky prices and he analogue closed-economy lieraure. Firs, we consider large changes in moneary policy insead of small changes. Second, we focus on open economies and idenify key feaures of he model economy ha play an imporan role in making sicky nonradable-goods prices susainable as an equilibrium phenomenon. To model he direc impac of real shocks on in aion and he real exchange rae, we build on he lieraure ha models he mechanisms hrough which large devaluaions lead o conracions in economic aciviy. 1 A common feaure of hese models is ha devaluaions are associaed wih negaive wealh e ecs. We capure hese e ecs by considering wo alernaive real shocks, a decline in expor demand and a reducion in ne foreign asses. The rs shock is drawn from he experience of counries like Uruguay, whose devaluaions were precipiaed by large declines in expor demand associaed wih recessions in counries wih whom hey rade. The second shock capures in a direc, albei in a brue force manner, he 1 See, for example, Aghion, Bachea, and Banerjee (2001); Burnside, Eichenbaum, and Rebelo (2001); Caballero and Krishnamury (2001); Chrisiano, Gus, and Roldos (2004); and Neumeyer and Perri (2005). 2

4 decline in real wealh ha is a hallmark of conracionary devaluaions. Arguably, we can hink of he fall in real wealh as a proxy for he balance-shee e ecs emphasized by some auhors. We suppose ha he model economy is iniially in a xed exchange-rae regime and ha here is hen a change in moneary policy ha leads o a large, permanen devaluaion. To simplify, we assume ha if here is a real shock, i occurs a he same ime as he devaluaion. To assess wheher or no sicky nonradable-goods prices are an equilibrium, we calculae he pos-devaluaion equilibrium assuming ha nonradable-goods prices are consan. We hen compue he bene s o a nonradable-goods producer of deviaing from a symmeric equilibrium by changing his price. In our model, he nonradable-goods secor is monopolisically compeiive. Firms in his secor se local currency prices as a mark-up on nominal marginal cos, which is proporional o he nominal wage rae. So he bene of deviaing from a symmeric sicky price equilibrium depends criically on he response of he mark-up and nominal wages o a devaluaion. Since we measure he bene s of deviaing relaive o an equilibrium in which prices are consan forever, we are adoping a conservaive sraegy for raionalizing sicky prices. Our model open economy incorporaes four assumpions ha mue his response. Firs, he share of radable goods in he consumer price index (CPI) is small. Second, here are domesic disribuion coss associaed wih he sale of raded goods. Third, here is a low elasiciy of he demand for expors. Fourh, here is a moderae elasiciy of subsiuion beween radable and nonradable goods. Secion 2 describes our model. Secion 3 presens our basic resuls. Secion 4 discusses he role played by di eren feaures of our model in accouning for sicky nonradable-goods prices. Secion 5 uses our model o discuss he possibiliy of an overvalued currency. Secion 6 concludes. 3

5 2. The Model Here we presen our model of a small open economy. The Represenaive Household The household values sreams of consumpion services (C ), hours worked (N ), and real balances. Consumpion services are produced by combining radable (C T ) and nonradable (C N ) goods according o he CES echnology C = i h 1 (C T ) 1 + (1 ) 1 (C N ) 1 1, 0. (2.1) The parameer governs he elasiciy of subsiuion beween C T price of consumpion services, P, is given by The variables P T h P = and P N denoe he local currency prices of radables and nonradable goods, respecively. P T Lifeime uiliy (U) is given by: and C N. The i (1 ) (P N ) 1 1. (2.2) U = 1X [u(c ; N ) + f(m =P )]; 0 < < 1. (2.3) =0 The variable M represens beginning-of-period nominal money balances, and f() is a sricly concave funcion. As in Greenwood, Hercowiz, and Hu man (1988), we assume ha u() akes he form u(c ; N ) = 1 1 C B N 1+ 1, (2.4) 1 + where B > 0. Given his speci caion of u(), here are no wealh e ecs on labor supply, so he uncompensaed labor-supply elasiciy, 1=, is equal o he Frisch elasiciy. 4

6 The household can borrow and lend in inernaional capial markes a a consan dollar ineres rae, r. For simpliciy, we assume ha in aion in he U.S. is equal o zero. To absrac from rends in he curren accoun, we also assume ha = 1=(1 + r). The household s ow budge consrain is given by P T C T + P N C N + S a +1 + M +1 M = (2.5) W N + + (1 + r)s a + T The variable a denoes he dollar value of household s ne foreign asses. The variables W and T represen he nominal wage rae and nominal governmen ransfers o he household, respecively. Toal nominal pro s in he economy are given by. The variable S denoes he exchange rae expressed in unis of local currency per dollar. We impose he no-ponzi game condiion The Impor Secor lim!1 a +1 = 0. (2.6) (1 + r) We assume ha he radable consumpion good is impored. The dollar price of his good, P, is se in inernaional markes and is invarian o he level of domesic consumpion. We assume ha purchasing power pariy (PPP) holds for prices a he dock, i.e., he price of impors exclusive of disribuion coss is For convenience, we normalize P P T = S P. o one. The variable P T denoes he domesic producer price of impors. In an earlier paper (Bursein, Eichenbaum, and Rebelo (2005)) argue ha relaive PPP is a reasonable approximaion for he behavior of impor prices a he dock afer large devaluaions. As in Bursein, Neves, and Rebelo (2003) and Erceg and Levin (1996), we assume ha selling a uni of a radable consumpion good requires unis of he 5

7 nal nonradable good. Perfec compeiion in he disribuion secor implies ha he reail price of impored goods is equal o P T = S + P N. (2.7) The domesic disribuion margin, which we de ne as he fracion of he nal price accouned for by disribuion coss, is equal o P N =P T. The Expor Secor Expors are produced by a coninuum of monopolisically compeiive producers indexed by i. The size of his secor has measure one. Firm i uses labor (N X i ) o produce X i unis of exporable good i using he echnology X i = A X N X i. For simpliciy, we assume ha he represenaive household does no consume he expor good. Demand for his good in he world marke is given by X i = (P i). (2.8) The variable P i denoes he dollar reail price of expor good i. The price elasiciy of demand for he expor good is given by > 1. As in Corsei and Dedola (2004), we assume ha o sell a uni of he expored good o foreign consumers, foreign reailers mus add unis of foreign disribuion services. We normalize he dollar price of hese services o one and assume ha he disribuion indusry is compeiive. I follows ha P i is given by The variable P X i P i = P X i =S +. (2.9) denoes he producer price of he expored good. Under hese assumpions, disribuion coss a ec he elasiciy of demand for expors wih respec o producer prices (d log(x i )=d log( P X i )). margin, he lower is he e ecive elasiciy of demand. 6 The higher he disribuion

8 Producer i maximizes pro s, given by X i = ( P X i W =A X )X i. The rs-order condiions for his problem imply ha all exporers charge he same price P X Toal pro s in he expor secor are given by The Final Nonradable Good =S = (W =S )=A X +. (2.10) 1 X = Z 1 0 X i di. The nal nonradable good (Y N ) is produced by compeiive rms using a coninuum of di ereniaed inpus, y N i, ha are produced by he inermediae nonradable-goods secor. As in Kimball (1995), we assume ha he producion echnology for Y N 1 = Z 1 0 is given by he implici funcion G(y N i =Y N )di. (2.11) The funcion G() sais es: G(1) = 1 and G 0 (1) = 1. The sandard Dixi-Sigliz speci caion corresponds o he following speci caion for G(), The represenaive rm maximizes pro s, G(yi N =Y N ) = (yi N =Y N ) ( 1)=. (2.12) N = P N Y N Z 1 subjec o he producion echnology (2.11). problem is p i = G 0 (yi N =Y N )(1=Y N ). 0 p i y N i di, (2.13) The rs-order condiion for his 7

9 Here, is he Lagrange muliplier associaed wih equaion (2.11). Since he secor is compeiive, equilibrium pro s are zero and he price of he nal nonradable good is P N = R 1 p 0 iyi N di. Y N In a symmeric equilibrium where all inermediae good rms charge he same price, p i = p, he price of he nal nonradable good is P N = p. (2.14) The Inermediae Nonradable Good i is produced by monopolis i according o he echnology y N i = A N N N i. Monopolis i chooses a price p i o maximize pro s given by: i = p i y N i W y N i =A N, The nonradable inermediae good and commis o saisfy demand a his price. The rs-order condiion for he monopolis s problem implies ha Here, z i = y N i =Y N p i = "(zi ) W "(z i ) 1 A. N denoes he marke share of he ih producer and "(z i ) is he elasiciy of demand for inermediae nonradable good i "(z i ) = G 0 (z i ) z i G 00 (z i ). 8

10 We adop he following funcional form for "(z i ): 2 8 < " L, " (z i ) = " H, : (1 + z zi ) " H + (z i 1 + z) " L, 1 2z if z i 1 + z, if z i 1 z, if 1 z z i 1 + z. (2.15) This speci caion implies ha in a symmeric equilibrium (z i = 1), he elasiciy common o all he monopoliss is The opimal mark-up is " (1) = "H + " L. 2 = " (1) " (1) 1. Once z is speci ed, he parameers " L and " H joinly deermine he average markup and he local slope of he mark-up around he poin z i = 1. Given a value for " H, we choose " L so ha is equal o he calibraed seady-sae mark-up. Wih hese assumpions, he symmeric equilibrium is he same as he one in which G() akes he Dixi-Sigliz form, (2.12), so p i = p = W A N. (2.16) In pracice, we se z o a very small number (0:0001) so ha " (z i ) is close o a sep funcion. Therefore, a rm ha deviaes from a symmeric equilibrium by raising is price faces a discree increase in he elasiciy of demand for is produc. In he sandard Dixi-Sigliz case "(z i ) = and p i is a consan mark-up over marginal cos. Relaive o he Dixi-Sigliz case, rms in our model have less of an incenive o raise prices. 2 We hank Miles Kimball for suggesing his funcional form. 9

11 Governmen The governmen chooses a money supply sequence, fm s g 1 =1, and rebaes any seignorage revenue o he household via lump-sum ransfers: M s +1 M s = T. (2.17) Equilibrium and De niion of he RER A perfec-foresigh, compeiive equilibrium for his economy is a se of pahs for quaniies {X i ; N X i ; y N i ; Y N ; N N i,c,c N ; C T ; N ; a +1,M +1 } and prices {P i; P X i ; W ; S ; p i ; P N ; P T ; P T } such ha households maximize heir uiliy and rms maximize pro s; he governmen s budge consrain holds; and he goods, labor, money, and foreign exchange markes clear. We resric our aenion o symmeric equilibria in which all nonradable-goods producers choose he same price and quaniy. We de ne he RER as: Here, P P RER =. (2.18) S P denoes he foreign CPI. In our empirical measures of he RER, we compue boh S and P as rade-weighed averages of exchange raes and foreign CPIs. Wih he excepion of Uruguay, movemens in P he size of he devaluaion. So, o simplify, we normalize P 3. Basic Resuls are quie small relaive o o one in he model. Here we sudy he quaniaive properies of our model. We consider hree numerical examples moivaed by di eren devaluaion episodes: Korea (1997), Uruguay (2002), and he UK (1992). Korea and Uruguay experienced large devaluaions ha were followed by conracions in aggregae economic aciviy. In Korea, in aion remained sable afer he devaluaion. In conras, in Uruguay, in aion rose subsanially afer he devaluaion. The UK devaluaion was relaively small and was followed by a mild expansion and sable in aion. 10

12 In he Korean example, we generae a recession by assuming ha ne foreign asses, a 0, decline a he ime of he devaluaion. We calibrae he change in a 0 so ha our benchmark model generaes a fall in real consumpion consisen wih ha observed in Korea in he rs year afer he devaluaion. We assume ha he decline in a 0 coincides wih a 37 percen unanicipaed, permanen devaluaion. This devaluaion coincides wih he change in he rade-weighed exchange rae for he won in he rs year afer he devaluaion. For exposiional purposes we also consider he impac of a devaluaion in he Korean example when here is no coinciden decline in real wealh. The Uruguayan devaluaion coincided wih a large decline in he demand for heir expors, which semmed from he 2001 Argenina currency crisis. Drawing on his observaion, we assume in our Uruguayan example ha he devaluaion coincides wih a fall in, he level parameer in he expor demand equaion (2.8). We choose he devaluaion rae in our example, 42 percen, o coincide wih he cumulaive devaluaion in he rade-weighed peso exchange rae from January 2002 o June We noe ha he Uruguayan devaluaion occurred in June 2002, bu he rade-weighed nominal exchange rae changed subsanially before June 2002 due o he Argenina January 2002 devaluaion. For his reason we choose January 2002 as our reference poin. For our UK example, we absrac from real shocks and consider a pure devaluaion of 11 percen. This devaluaion coincides wih he rade-weighed change in he exchange rae for he pound serling in he rs year afer he UK devaluaion. In all of he examples, we assume ha prior o ime zero agens anicipae ha he exchange rae is xed a S = S and ha he economy is in a seady sae wih consan prices and quaniies. A ime zero, here is an unanicipaed change in moneary policy ha leads o a one-ime permanen exchange-rae devaluaion. Depending on he example, here can be a real shock ha coincides wih he 11

13 devaluaion. We summarize he parameer values for our benchmark model in Table 1. Our resuls are independen of he funcion f(:), which conrols he uiliy of real balances (see equaion (2.3)). We se he elasiciy of subsiuion beween radables and nonradables () o 0:40. This value is consisen wih esimaes in he lieraure. 3 For each counry, we se, he share parameer in he CES consumpion aggregaor in equaion (2.1), so ha given, he pre-devaluaion share of impor goods in consumpion, exclusive of disribuion coss, coincides wih he daa repored in Bursein, Eichenbaum, and Rebelo (2005). We assume ha = 0:25. This value implies a labor supply elasiciy of four which coincides wih he sandard value of he Frisch labor supply elasiciy used in he realbusiness-cycle lieraure (see Chrisiano and Eichenbaum (1992) and King and Rebelo (2000)). We choose B, he level parameer ha conrols he disuiliy of labor, so ha he price of nonradables in he pre-devaluaion seady sae is equal o one. We se and so ha he pre-devaluaion disribuion margin is 50 percen in boh he domesic and foreign markes. This value is consisen wih he evidence in Bursein, Neves, and Rebelo (2003). We se he level parameer in he demand for expors,, o one. The elasiciy of demand for expors,, conrols how much he expor secor expands in he wake of he devaluaion. For every counry, we se so ha he model replicaes he expansion in expors ha occurs in he year afer he devaluaion (see Table 1). We require a relaively inelasic demand so ha he model yields a plausible pos-devaluaion expansion of he expor secor. This low elasiciy is a simple 3 See, for example, Sockman and Tesar (1995); Lorenzo, Aboal, and Osimani (2003); and Gonzalez-Rozada and Neumeyer (2003). 12

14 way o mimic he fricions ha limi in pracice he expansion of he expor secor, e.g. capaciy consrains, nancing consrains, or fricions o secoral employmen reallocaion. For every counry, we se he level parameer in he producion funcion of he expor secor, A X, and he iniial level of ne foreign asses (a 0 ) so ha he share of expors in GDP in he model s seady sae is equal o is value in he year prior o he devaluaion. We choose he inermediae demand aggregaor parameers, " L and " H, so ha he model has wo properies. Firs, he seady-sae mark-up is 20 percen. Second, he parameers are consisen wih he calibraion used by Kimball (1995) o generae sicky prices in a closed economy. This calibraion has he propery ha when he relaive marke share (z i ) decreases, he elasiciy of demand increases from six o nine. Given how lile informaion is available o calibrae he Kimball aggregaor, we repor he sensiiviy of our resuls o alernaive calibraions. We consider a calibraion such ha i is opimal for he deviaor o change his price by 50 percen of he increase in marginal cos. This calibraion is consisen wih he symmeric ranslog speci caion of Bergin and Feensra (2000). These wo speci caions of he demand aggregaor encompass he calibraion used by Dosey and King (2005), which lies in beween he Kimball and Bergin-Feensra speci caions. Finally, we also consider he sandard Dixi-Sigliz speci caion of demand in which he elasiciy of demand is consan. The Korean Example The rs wo columns of Table 2 repor he response of he benchmark model o a single shock: a 37 percen devaluaion. Columns 1 and 2 correspond o he case of exible and sicky nonradable-goods prices, respecively, when here is no real shock. Columns 3 and 4 repor he impac of wo simulaneous shocks: a 37 percen devaluaion and a negaive wealh shock 13

15 for he exible and sicky price case, respecively. 4 We sar wih he case in which here is no real shock o build inuiion ha is useful for undersanding he empirically relevan case of when here is a negaive real shock. No Real Shock Column 1 of Table 2 indicaes ha when prices are exible, he devaluaion has no impac on quaniies, whereas all prices, including he nominal wage, increase by 37 percen. Column 2 of Table 2 shows ha when nonradable-goods prices are sicky, he devaluaion induces a low rae of CPI in aion (8:7 percen). Even hough PPP holds for impor prices a he dock, he presence of disribuion coss implies ha he reail price of impored goods rises by only 20:4 percen. When nonradable-goods prices are sicky, he devaluaion leads o a rise in hours worked (9:9 percen). To undersand he expansion in hours worked we brie y discuss he response of oupu in he expor and nonradable secors. The devaluaion induces a fall in he dollar wage rae (W=S), which reduces he marginal cos of producing expor goods. This reducion leads o a 8.4 percen decline in he dollar price of expors ( P X =S) and a 10:4 percen rise in he volume of expors (see Table 2). To undersand he behavior of P X =S and W=S, we noe ha he opimal response of expor goods producers o a decline in marginal cos is o lower heir dollar price and sell more unis. Consisen wih equaion (2.10), absen foreign disribuion coss ( = 0), he percenage declines in P X =S and W=S would be he same. However, as emphasized by Corsei and Dedola (2004), when > 0, a one percen decline in he dollar price of expors ( P X =S) induces a less han one percen decline in he reail dollar price of expors. Consequenly, 4 We also analyze he Korean example by assuming ha he real shock is a decline in he demand for expors. Our resuls are similar hose obained wih he ne foreign asse shock. The only di erence is ha expors rise by less when here is a negaive shock o expor demand. 14

16 he price reducion induces a smaller rise in he demand for he produc. Pu di erenly, a posiive value of reduces he e ecive elasiciy of demand wih respec o P X =S. Therefore, he opimal response of he monopolis is o lower P X =S by less han when = 0. According o Table 2 consumpion of radable goods rises by 3:7 percen. To undersand his e ec noe ha in equilibrium he following condiion mus hold: ra = ra 0 = C T ( P X =S )X. (3.1) To derive his equaion we sar wih (2.5) and rewrie pro s as sales revenue minus labor coss. We hen use equaions (2.17), (2.6), he marke clearing condiion for nonradable goods, and he ineremporal Euler equaion for radable consumpion. The assumpions ha = 1=(1 + r) and shocks are permanen imply ha a is consan (a = a 0 ). I follows from (3.1) ha impors (C T ) mus rise o mach expor revenues. To explain he response of hours worked in he nonradable-goods secor we noe ha he consumer s rs-order condiions for C T and C N imply ha C N C T = 1 P T. (3.2) P N We noe ha P T =P N rises, since P N remains consan and P T o he devaluaion (see equaion (2.7)). Since boh C T equaion (3.2) rise, i follows ha C N rises in response and he righ-hand side of mus also rise. By assumpion, nonradablegoods rms mus saisfy demand a xed prices, so hours worked in he nonradable secor rise. Since hours worked in boh he expor and nonradable-goods secors increase so do he overall hours worked. The wage rae ha is relevan for labor supply decisions is he CPI-de aed real wage, W =P. Given our assumpions abou preferences W =P mus rise, because 15

17 hours worked (N ) increase. Since N rises by 9:9 percen and he elasiciy of labor supply is four, W =P mus rise by roughly 9:9=4 percen. 5 The dollar-denominaed wage falls by 26:4 percen, bu his wage is no relevan for labor-supply decisions. Mos of he worker s consumpion baske is composed of nonradable goods whose prices have no changed. As a resul, CPI and dollar-de aed real wages respond very di erenly o he devaluaion. The real-wage rae is consan in he exible-price case and rises when prices are sicky. The increase in he nominal wage, W, is smaller in he sicky-price case because CPI in aion is much lower han in he exible-price case. Table 2 repors ha he mark-up of nonradable-goods producers falls o 7:6 percen afer he devaluaion. A key quesion is, how grea is he incenive of an individual nonradable-goods rm o deviae from he symmeric sicky price equilibrium? According o Table 2, he opimal mark-up for he deviaor is 12:5 percen and he percenage increase in his pro s is 9:9 percen. Consequenly, he loss from keeping prices consan for a long period of ime would be very grea. We conclude ha absen any real shocks, a large devaluaion would lead rms o change prices and he economy would go o he exible-price equilibrium. Negaive Real Shock Column 3 of Table 2 shows ha when prices are exible, a devaluaion of 37 percen leads o a 23:1 percen rise in he CPI. A devaluaion also induces a fall in he dollar price of expors, an expansion of hours worked in he expor secor, and an even greaer drop in hours worked in he nonradable-goods secor. In addiion, here is a decline in he dollar price of nonradable goods and in he dollar and CPI-de aed real wages. 5 The nominal wage rae repored in Table 2 rises by somewha less han 9.9/4 because we compue he CPI repored in our ables as an arihmeic average of radable and nonradable prices. The rae of change in he arihmeically averaged CPI is similar o he rae of change he heoreical price index ha corresponds o he household s uiliy funcion (see equaion (2.2)). 16

18 These e ecs happen because when here is a negaive real shock, he devaluaion coincides wih a decline in ne foreign asses. According o equaion (3.1) a decline in a mus be accompanied by an improvemen in he rade balance (C T ( P X =S )X ). In principle, his reducion can be accomplished by increasing expors or reducing impors. Expors can be increased eiher by raising aggregae hours worked or by reallocaing workers from he nonradable-goods secor o he expor secor. Given our preference speci caion, i is no opimal o respond o a decline in a 0 solely hrough a fall in C T, so ha X mus rise. For expors o rise, he dollar price of expors mus fall. Equaion (2.10) implies ha he dollar wage mus also fall. Under exible prices (bu no under sicky prices) whenever he dollar wage declines he CPI-de aed real wage also declines. To see his we noe ha he CPI-de aed real wage is h W =P = W = P T i (1 ) (P N ) 1 1 : (3.3) Using equaions (2.14), (2.16), and (2.7) his expression can be rewrien as W =P = 1= h S =W + =A N i (1 ) (=A N ) 1 1 : (3.4) Our preference speci caion implies ha aggregae hours worked depend only on he wage rae. Therefore aggregae hours worked fall. I follows ha here mus be a subsanial decline in nonradable consumpion o allow for a rise in he producion of expors. Since nonradable-goods prices are a mark-up on wages, he drop in dollar wages leads o a decline in he dollar price of nonradable goods. This decline creaes a wedge beween he devaluaion rae (37 percen) and he CPI in aion rae (23 percen). However, even hough he CPI in aion is lower han he change in he exchange rae, i is much higher ha he acual rae of in aion in Korea (6:6 percen). 17

19 Column 4 of Table 2 shows ha when nonradable-goods prices are sicky, he CPI in aion in he model (8:7 percen) is much closer o he acual rae of in aion (6:6 percen). Thus, he model does well in accouning for he posdevaluaion decline in he RER. Viewed as a whole, our resuls indicae ha when nonradable-goods prices are sicky, he model successfully accouns for low pos-devaluaion raes of in aion. This resul begs he quesion, is i reasonable o assume ha nonradable-goods prices are sicky? To answer his quesion, we calculae he incenive of an individual nonradable-goods monopolis o deviae from a symmeric sicky-price equilibrium. The percenage change in pro s of a deviaor is equal o zero (see column 4 of Table 2). If here are any coss of changing prices, nonradable-goods producers will keep heir prices consan, hus raionalizing he sicky-price equilibrium. 6 The gains o deviaing from a sicky-price equilibrium are very small, when here is a negaive real shock bu large oherwise. This di erence re ecs he fac ha nominal wages rise by much less when here is a negaive real shock. The Uruguay Example Table 3 repors he resuls of a 42 percen devaluaion ha coincides wih a fall in, he level parameer in he demand for expors (2.8), from one o 0:69. When nonradable-goods prices are exible, he CPI in aion in he model (26 percen) is close o he acual rae of in aion (29 percen). This resul suggess ha sicky prices did no play a signi can role in he Uruguayan case. Even hough he model does well in accouning for he pos-devaluaion rae of in aion, i undersaes he pos-devaluaion decline in he RER (15.5 compared o 30.6). This shorcoming is due o he fac ha he model absracs from changes in he inernaional price of radable goods, P. In he year afer 6 There is, of course, anoher equilibrium in which all nonradable goods producers change heir prices. The exisence of wo equilibria, one in which prices are sicky and one in which all rms change prices, is a generic propery of models ha emphasize coss of changing prices. 18

20 he Uruguayan devaluaion here was a large rise in he CPI of Uruguay s major rading parners. This rise was associaed primarily wih a high rae of in aion in Uruguay s main rading parner, Argenina. The CPI in aion is lower ha he rae of devaluaion because, oher hings equal, a negaive shock o expor demand induces a decline in expor revenues. Given agens preferences, i is no opimal o mach his decline wih only a fall in C T, herefore P X =S mus fall o miigae he decline in X. I follows from (2.10) ha he dollar wage mus fall, so ha nominal wages mus rise by less han he rae of devaluaion. Since nonradable-goods prices are a mark-up on nominal wages hey also rise by less han he rae of devaluaion. This resul in urn implies ha he rae of CPI in aion is lower han he rae of devaluaion. The previous resuls sugges ha he exible-price version of he model can accoun for pos-devaluaion in aion raes in Uruguay. This conclusion leads us o ask wheher or no he sicky price equilibrium was susainable in Uruguay. To answer his quesion, we compue he equilibrium of he model under he assumpion ha nonradable-goods prices are sicky. We hen assess he gains o a nonradable rm from deviaing from ha equilibrium. According o column 2 of Table 3, he gains are equal o roughly one percen of a deviaor s pro s. These calculaions indicae ha a sicky-price equilibrium would no have been susainable in Uruguay. The UK Example Column 1 of Table 4 repors he response of our model economy o a permanen 11 percen devaluaion when prices are exible. In his case, here is no impac on real quaniies, and prices increase by he rae of devaluaion. This version of he model clearly canno accoun for he low posdevaluaion rae of in aion and mild expansion observed in he UK. Column 2 of Table 4 repors resuls for he sicky-price case. The inuiion 19

21 behind hese resuls is similar o ha underlying he Korean case when here is no real shock. The key resul here is ha he CPI in aion is only 2:4 percen, which is roughly consisen wih he CPI in aion in he daa (1:7 percen). Also, consisen wih he daa, he model generaes a mild expansion afer he devaluaion. We infer ha he sicky nonradable-goods price model capures he salien feaures of he UK devaluaion episode. As above, he key quesion is wheher sicky prices are susainable as an equilibrium phenomenon. Table 4 indicaes ha he answer o his quesion is yes. The gain o a nonradable-goods producer of deviaing from a symmeric sicky price equilibrium is equal o zero under he Kimball (1995) speci caion of he nonradable-goods demand aggregaor.. 4. Isolaing he Key Margins Here, we use he UK example o discuss he mechanisms ha enable our model o accoun for sicky nonradable-goods prices. We conduc his analysis by absracing from real shocks, because he inuiion is easier o convey when he only shock is a change in he exchange rae. As noed, he opimal price for a nonradable-goods producer who chooses o deviae from a symmeric sicky nonradable-goods price equilibrium is given by p i = W A N. The only way in which di eren speci caions of he demand for nonradable goods a ec p i is hrough heir impac on he gross mark-up,. Oher feaures of he model in uence p i because hey a ec he response of nominal wages o shocks. To discuss he sensiiviy of our resuls o our benchmark speci caion of he nonradable-goods demand aggregaor, we consider wo alernaives. Firs, we choose he parameers of he nonradable-goods demand aggregaor (2.15) 20

22 o be consisen wih he speci caion proposed by Bergin and Feensra (2000). Second, we consider he sandard Dixi-Sigliz demand speci caion. In boh cases, we calibrae he demand aggregaors so ha he pre-devaluaion values of all quaniies and prices are he same as in our benchmark speci caion. Thus, di eren speci caions of he aggregaor only a ec he bene o a nonradablegoods producer of deviaing from a symmeric sicky-price equilibrium. Column 2 of Table 4 summarizes he bene o a deviaor for di eren speci- caions of he demand aggregaor. As we have noed, he bene is roughly zero for he Kimball case. Wih he Bergin-Feensra calibraion, he bene is roughly 0:5 percen of pro s. The presen value of his gain is sill moderae relaive o he coss of changing prices esimaed by Levy, Bergen, Dua, and Venable (1997) and Zbaracki, Rison, Levy, Dua, and Bergen (2004). Wih he Dixi-Sigliz speci caion, he bene o a deviaor rises o 1:7 percen of pro s. We conclude ha our resuls are reasonably robus o modi caions of he demand aggregaor, as long as we do no go o he exreme of he Dixi-Sigliz speci caion. We also wish o explore he impac of oher key parameers on he response of he nominal wage o he devaluaion and on rm s incenives o deviae from he sicky price equilibrium. For every change in a model parameer, we recalibrae he value of a 0 so ha he pre-devaluaion share of expors in GDP remains consan. We use his procedure o faciliae comparisons across he di eren speci caions. For a small devaluaion, such as ha of he UK, he bene s from deviaing from he sicky-price equilibrium for he Kimball speci caion are always close o zero. Therefore we focus our sensiiviy analysis on he Bergin-Feensra speci caion. Firs, we consider he impac of foreign disribuion coss. Column 2 of Table 5 repors resuls for he case in which he foreign disribuion margin is zero insead of 50 percen. In his case, here is a smaller rise in he local currency price of expors (5:7 percen compared o 8:1 percen) and a larger fall in P X =S ( 5:6 21

23 percen compared o 3:2 percen). As noed, a fall in raises he e ecive demand elasiciy faced by expor-goods producers. This fall makes i opimal for producers o lower P X =S by more han hey do when is posiive. Relaive o he benchmark case, he associaed increase in demand leads o a larger expansion in hours worked in he expor secor and a greaer rise in he nominal wage (5:7 percen compared o 3:1 percen). Consequenly, he percenage increase in pro s from deviaing from he symmeric sicky-goods price equilibrium rises from 0:5 percen o 3:7 percen. We infer ha he presence of foreign disribuion coss helps raionalize he sicky-price equilibrium. Column 3 repors he impac of changing he parameer so ha he share of raded goods (inclusive of disribuion) in he CPI bundle falls from 40 percen o 25 percen. The devaluaion now leads o a lower rae of CPI in aion (1:5 percen compared o 2:4 percen) and o smaller rise in nominal wages (2:6 percen compared o 3:1 percen). The bene o he deviaor falls from 0:5 o 0:2 percen of pro s. We conclude ha a small share of raded goods in he CPI bundle plays a posiive role in raionalizing sicky nonradable-goods prices. Column 4 repors he resuls we obain by increasing he elasiciy of subsiuion beween radables and nonradables from 0:4 o one. This change implies ha he demand for nonradable goods is more responsive o a change in he price of impored consumpion goods relaive o nonradable-goods. Relaive o he benchmark speci caion, he devaluaion induces larger rises in he demand for nonradable-goods, hours worked in he nonradable-goods secor, and nominal wages. 7 The percenage change in pro s for a deviaor rises from 0:5 percen o 0:9 percen of pro s. We conclude ha a low degree of subsiuion beween nonradable goods and impored goods helps raionalize sicky nonradable-goods 7 An o seing e ec resuls from he fac ha he heoreical consumpion de aor changes by less since he wo goods are more subsiuable. Oher hings equal, his e ec leads o a smaller increase in he nominal wage. 22

24 prices. Column 5 repors he resuls we obain by eliminaing domesic disribuion coss. Seing equal o zero increases he e ecive share of pure radable goods in consumpion and he e ecive elasiciy of subsiuion beween radables and nonradables. For he reasons discussed above, boh hese e ecs imply ha, afer he devaluaion, nominal wages rise by more han hey do in he benchmark model. The incenive for nonradable goods rms o change heir price is 3:9 percen compared o 0:5 percen of pro s in he benchmark model. We conclude ha sicky nonradable goods prices are easier o raionalize in he presence of domesic disribuion coss. Column 6 repors resuls of increasing he elasiciy of demand for expors,, from 2:7 o 3:7. This change in increases he response of expors for wo reasons. Firs, for a given drop in P X =S, here is a larger increase in expors. Second, he equilibrium fall in P X =S is acually larger. Raising has he same e ec as lowering on he elasiciy of P X =S wih respec o W=S. For he reasons discussed above, P X =S becomes more responsive o he drop in W=S. Therefore, he decline in P X =S is greaer han in he benchmark model, which leads o a larger expansion in he expor secor. There is also a larger increase in he nominal wage. The bene of changing he price of nonradable goods increases from 0:5 o 1:2 percen of pro s. A low elasiciy of demand for expors helps o raionalize sicky prices in our model. Column 7 summarizes he impac of lowering he share of expors in GDP from 23 percen o 10 percen. This value is closer o he pre-devaluaion expor shares in Argenina (10.9 percen) and Brazil (10.6 percen). In our model, a smaller expor secor reduces he absolue value of he pos-devaluaion rise in hours worked in he expor secor. 8 Consequenly, here is a smaller rise in nominal 8 This is consisen wih evidence in Gupa, Mishra and Sahay (2001) ha suggess ha he 23

25 wages. The percenage change in pro s for a deviaor falls from 0:5 percen o 0:4 percen of pro s. We conclude ha a smaller share of expors in GDP helps raionalize he sicky-price equilibrium. Column 8 repors he impac of lowering he labor supply elasiciy from four o one. Relaive o he benchmark model, here is a greaer rise in he nominal wage and he CPI-de aed real wage. The greaer impac on wages is a direc consequence of he lower labor-supply elasiciy. These gains from deviaing from he symmeric sicky nonradable-goods price equilibrium rise from 0:5 percen o 2:7 percen of pro s. A high elasiciy of labor supply is clearly criical in accouning for sicky prices. 5. An Overvaluaion Experimen A sandard way of formalizing he noion ha an exchange rae is overvalued is o assume ha raded goods prices are sicky in domesic currency. Here, we discuss an alernaive, complemenary mechanism hrough which exchange raes can become overvalued. We show ha if nonradable-goods prices do no change afer a real shock, he exchange rae becomes overvalued. By his we mean ha he real exchange rae is higher han i would be under exible prices. We consider an economy ha is in he seady sae of a xed exchange rae regime. For convenience, we normalize he foreign price level o one and de ne he real exchange rae as RER = P =S. For exposiional purposes we consider he Korean example, where he economy su ers a decline in is ne foreign asses, a. Qualiaively similar resuls obain if here is a negaive shock o expor demand, as in our Uruguay example. Table 6 repors he response of he economy o a decline in ne foreign asses, he negaive real shock considered in Table 2, under di eren scenarios. The expansionary e ec of a devaluaion is sronger when he radable secor is larger. 24

26 numbers we repor are raes of change relaive o he pre-shock seady sae. Column 1 repors resuls for he case of exible prices wih no devaluaion. Equaion (3.1) implies ha a decline in ne foreign asses requires an improvemen in he rade balance. Given our assumpions abou preferences, his improvemen occurs via boh a decline in impors and an increase in expors. The decline in impors is achieved hrough an increase in he reail price of impors relaive o nonradables, P T =P N in P T =P N = S =P N + (see equaion (3.2)). Since S is xed, a rise requires a drop in P N, which in urn induces a decline in he P (see equaions (2.7) and (2.2)) and in he RER. Wha are he consequences for wages and hours worked? Since he price of nonradables falls, he nominal wage, W, also falls (see equaion (2.16)). The response of aggregae hours depends on he behavior of he CPI-de aed real wage, W =P. To see wha happens o W =P we recall ha o achieve an improvemen in he rade balance, he quaniy of expors mus rise. This rise requires a fall in he dollar price of expors, P X =S. The drop in P X =S induces a decline in boh he dollar-denominaed wage, W =S and W =P (see equaions (2.10), (3.3), and (3.4)). The drop in W =P leads o a decrease in aggregae hours worked. Column 2 repors he response of he economy o he negaive real shock when nonradable-goods prices are sicky and here is no devaluaion. The rae of he CPI in aion is zero and he RER remains consan. When we compare columns one and wo we see ha he RER is 14:2 percen higher when nonradable-goods prices are sicky. In his sense, sicky nonradable-goods prices lead o an overvalued exchange rae afer a negaive real shock. In he sicky-price equilibrium, he nominal wage falls by less han i does when nonradable-goods prices are exible. This smaller wage decline implies ha he dollar price of expors falls by less han when prices are exible ( 1:7 percen compared o 5:9 percen). As a resul, here is a smaller expansion in 25

27 expors when nonradadable-goods prices are sicky (2:2 percen compared o 7:3 percen). Equaion (3.1) implies ha consumpion of impored goods mus fall by more in he sicky-price equilibrium. To explain he response of hours worked in he nonradable-goods secor we noe ha wih a xed exchange rae and sicky nonradable prices, he righ-hand side of (3.2) is xed. Consequenly, he percenage declines in C N and C T are he same (23:6 percen). In conras, under exible prices, he negaive real shock leads o a decline in P N =P T and a rise in C N =C T. This rise, ogeher wih he fac ha C T drops by less under exible prices, implies ha C N also falls by less under exible prices. Since he hours worked in he expor secor rise by more in he exible-price case, he previous argumen esablishes ha he recession induced by he real shock is miigaed by exible prices. Given ha nonradable-goods prices remain consan and he wage falls, he mark-up of nonradable-goods producers rises (from 20 percen o 26:3 percen). An individual producer could raise his pro by lowering his price relaive o he symmeric sicky-price equilibrium. As Table 6 shows, he resuling rise in pro s is zero if we assume a Kimball demand aggregaor. This rise in pro s is very modes (0:7 percen of pro s) for he Bergin-Feensra aggregaor. The previous resuls show ha if nonradable-goods prices are sicky, hen he impac of a real shock o he economy leads o a smaller decline in he real exchange rae and a larger conracion han would be he case under exible prices. In his sense, he negaive real shock resuls in he exchange rae being overvalued. Under hese circumsances, a devaluaion leads o an expansion in economic aciviy and helps realign he real exchange rae. Our model is consisen wih he convenional wisdom ha prices do no increase afer a large devaluaion, because hey were oo high before he devaluaion. If we suppose ha he exchange is overvalued in he sense jus described above, 26

28 hen a devaluaion ha preserves he sicky nonradable-goods price equilibrium leads o a decline in he real exchange rae wihou a subsanial amoun of in aion (see column 3 of Table 6). 6. Conclusion We propose an open economy, general equilibrium model ha can accoun for he subsanial drop in real exchange raes ha occurs in he afermah of large devaluaions. Our model embodies several elemens ha dampen wage pressures in he wake of a devaluaion. If he nominal wage remains relaively sable in he afermah of a large devaluaion, his sabiliy can eliminae he incenive for nonradable-goods producers o change heir prices. If nonradable-goods prices remain sable, in aion is low, which is compaible wih a sable nominal wage rae. We conclude by noing an imporan shorcoming of our paper. To simplify our analysis, we focus on raionalizing a pos-devaluaion equilibrium in which nonradable-goods prices do no change a all. In realiy, hese prices do change, albei by far less han he exchange rae, he price of impors and exporables, or he reail price of radable goods. Modeling he deailed dynamics of nonradablegoods prices is a ask ha we leave for fuure research. 27

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30 [9] Chrisiano, Lawrence, Chrisopher Gus, and Jorge Roldos, Moneary Policy in a Financial Crisis, Journal of Economic Theory, 119: , [10] Corsei, Giancarlo and Luca Dedola, Macroeconomics of Inernaional Price Discriminaion, forhcoming Journal of Inernaional Economics, [11] Dosey, Michael and Rober G. King, Implicaions of Sae-dependen Pricing for Dynamic Macroeconomic Models, Journal of Moneary Economics, 52: , [12] Erceg, Chrisopher and Andrew Levin, Srucures and he Dynamic Behavior of he Real Exchange Rae, mimeo, Board of Governors of he Federal Reserve Sysem, [13] Gonzalez-Rozada, Marín and Pablo Andrés Neumeyer The Elasiciy of Subsiuion in Demand for Non-radable Goods in Lain America Case Sudy: Argenina, mimeo, Universidad T. Di Tella, [14] Gordon, Rober, The Afermah of he 1992 ERM Breakup: Was There a Macroeconomic Free Lunch? in Paul Krugman (ed.) Currency Crises, Universiy of Chicago Press, , [15] Greenwood, Jeremy, Zvi Hercowiz and Gregory Hu man, Invesmen, Capaciy Uilizaion, and he Real Business Cycle, American Economic Review 78: , [16] Gupa, Poonam, Deepak Mishra and Rana Sahay, Oupu Response o Currency Crises, mimeo, Inernaional Moneary Fund, [17] Kimball, Miles S., The Quaniaive Analyics of he Basic Neomonearis Model, Journal of Money, Credi and Banking, 27: ,

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32 Table 1: Benchmark Calibraion, Parameer Values Common Parameers Disribuion Margin, percen Elasiciy of labor supply Elasiciy of subs. in consump. beween radables and nonradables Pre-devaluaion markup 50, 1 4, , , 1. 2 Counry Specific Parameers Korea Uruguay UK Share of radable goods in CPI (inclusive of disribuion coss), percen Foreign disribuion margin, percen Elasiciy of demand for expors Share of expors in GDP, percen Level parameer, expor producion funcion Level parameer, desuiliy of labor 40, , , 1 r a A X B , , , , , 1 r a , 1 r a A X A X B B 0. 41