Monetary Policy and Dutch Disease: TheCaseofPriceandWageRigidity

Transcription

1 Federal Reserve Bank of Minneapolis Research Deparmen Moneary Policy and Duch Disease: TheCaseofPriceandWageRigidiy Consanino Hevia and Juan Pablo Nicolini Working Paper 726 June 25 ABSTRACT We sudy a model of a small open economy ha specializes in he producion of commodiies and ha exhibis exogenous fricions in he seing of boh prices and wages. We sudy he opimal response of moneary and exchange rae policy following a posiive (negaive) shock o he price of he exporable ha generaes an appreciaion (depreciaion) of he local currency. According o he calibraed version of he model, deviaions from full price sabiliy can generae welfare gains ha are equivalen o almos 5% of lifeime consumpion, as long as here is a significan degree of rigidiy in nominal wages. On he oher hand, if he rigidiy is concenraed in prices, he welfare gains can be a mos % of lifeime consumpion. We also show ha a rule formally definedinhe paper ha resembles a diry floaing regime can approximae he opimal policy remarkably well. Keywords: Duch disease; Inflaion argeing; Foreign exchange inervenion JEL classificaion: F3, F4 Hevia: Universidad Di Tella. Nicolini: Federal Reserve Bank of Minneapolis and Universidad Di Tella. This paper was prepared for he 8h annual conference of he Cenral Bank of Chile. We hank Cesar Calderon for he discussion and Rodrigo Capuo and Robero Chang for very deailed commens on an earlier draf. The views expressed herein are hose of he auhors and no necessarily hose of he Federal Reserve Bank of Minneapolis or he Federal Reserve Sysem.

2 . INTRODUCTION In his paper, we sudy opimal moneary and exchange rae policy in a small open economy wih boh price and wage rigidiy, following a shock o he price of an exporable commodiy. From a heoreical poin of view, and as we show in he paper, he presence of boh ypes of rigidiies implies ha, o he exen ha scal policy is unresponsive o shocks, full price sabiliy is no opimal. This paper is par of a research projec ha is moivaed by he experiences of many small open economies ha in he las wo decades became very e ecively! in aion argeers. Many of hese economies are commodiy producers, and he size of he commodiy secor o GDP is very high. For example, in he decade from 2 o 2, expors of copper and marine producs for Chile were, on average, around 7% of GDP, while oal expors of oil and marine producs in Norway accouned for 2% of GDP (Hevia and Nicolini, 23). During he same decade, he real price of copper and oil experienced changes of around 3%. The size of hese shocks is orders of magniude above any business cycle shock we have ever seen. These shocks have direc e ecs on he moneary side of hese economies. In e ec, he correlaion beween he HP- lered price of he exporable commodiy and he HP- lered nominal exchange rae o concenrae our analysis a he business cycle frequency ranges from 5% o 7% for boh counries, depending on wheher one includes he las hree periods of he decade in he sample. Tha period of ime winessed very large changes in commodiy prices, comoving wih he peso in Chile and he krone in Norway. In Figure, we plo he HP- lered daa for he nominal exchange rae and he relevan commodiy price for boh counries, where he correlaion is srikingly clear. Clearly, his correlaion canno be independen of he policy regime. In a currency board or xed exchange rae regime, ha correlaion is naurally zero. Thus, one should expec he The series are rs logged and hen HP- lered wih a smoohing parameer of 6.

3 6 Chile 6 Norway Exchange rae Price of copper Exchange rae Price of oil Fig.. Nominal exchange raes and main exporable commodiy price correlaion beween he price of copper and he exchange rae in Chile o be much closer o zero during he early nineies, during which ime in aion was driven down from close o 3% o below % using a managed exchange rae. Bu in a very successful in aion-argeing regime, like he ones followed by boh cenral banks during he period, he nominal exchange rae freely oas, so he correlaion is deermined by marke forces. According o he model ha follows, he negaive correlaion is a direc implicaion of he in aion-argeing regime. Indeed, in he model, following a large increase in he price of he exporable, and given price sabiliy, he nominal exchange rae and he real, given price sabiliy su ers a srong appreciaion, generaing he radiional Duch disease e ec, which is he opimal response of prices and quaniies o a relaive price shock. We are ineresed in sudying condiions under which he sric in aion-argeing regime is opimal. Pu di erenly, we wan o nd condiions under which hese Duch disease episodes are ine cien from he viewpoin of he allocaion of resources. In our view, his is one of he main policy quesions in counries like Chile. Indeed, during he successful in aion-argeing 2

4 period, he cenral bank deviaed from he sric rule wice: once in April 28 and again in January 2. On boh occasions, he jusi caion for he inervenion was essenially he same: he erms of rade were oo high and he nominal exchange rae oo low. In a previous paper (Hevia and Nicolini, 23), we sudied an economy wih only price fricions and showed ha even in a second bes environmen wih disoring axes, domesic price sabiliy is opimal as long as preferences are of he isoelasic ype (which is ypically used in he lieraure), even if scal policy canno respond o shocks. In oher words, resricions on price seing do no necessarily imply ha he large and persisen deviaions observed in nominal and real exchange raes in counries like Chile are subopimal, as long as moneary policy is execued so as o sabilize domesic prices. The model in ha paper hus fully jusi es a pure in aion argeing regime (a a zero rae of domesic price in aion). In oher words, he Duch disease is no really a disease, i is jus he opimal response of prices and quaniies o a relaive price shock. In he conclusion o our previous paper, we poined ou ha our resuls fall apar in he presence of boh price and wage fricions. Quaniaively exploring his quesion is he purpose of his paper. Exploring his policy problem in he conex of boh price and wage rigidiy seems o us a naural sep. Mos medium-scale models used for moneary policy evaluaion nowadays exhibi boh ypes of rigidiies, following he work of Chrisiano, Eichenbaum, and Evans (25) and Smes and Wouers (27). How far from pure price sabiliy is he opimal policy once boh ypes of fricions are presen? Wha implicaions do hey have for he diry oaing debae in counries ha experience large ucuaions in heir erms of rade? Answering hese quesions is he conribuion of his paper. As menioned, he heory is clear: he presence of boh fricions, coupled wih in exible ax insrumens, implies ha full price sabiliy is no opimal. For compleeness, we rs generalize he closed economy resuls of Correia e al. (23) and he small open economy resuls of Hevia and Nicolini (23) wih only price fricions o our small open economy model wih price and wage fricions and hen show ha, in general, full price sabiliy is no opimal when axes canno 3

5 be ime and sae dependen. Bu he main exploraion of his paper is a quaniaive one: on he one hand, we explore numerically how far apar from full in aion argeing he opimal policy is; on he oher, we compue he welfare di erence beween he opimal policy and full in aion argeing. For he calibraed version of our model, we nd ha he key facor is he degree of wage rigidiy. When wages are indeed highly rigid (he Calvo parameer is as high as :8) and here is enough price rigidiy (a Calvo parameer of a leas :25), he welfare e ec of full price sabiliy relaive o he opimal policy can be as high as :5% of lifeime consumpion. However, if he rigidiy is mosly concenraed in prices wih some wage rigidiy, he welfare e ec is bounded above by :% of lifeime consumpion. We also show ha a diry oaing regime approximaes he opimal policy remarkably well. The model we use is he one explored in Hevia and Nicolini (23), bu in his model, we allow for heerogeneous labor wih marke power and fricions in wage seing. A virue of he model is ha i is fully consisen wih he evidence presened in Figure, as we show in he paper. We presen he model in Secion 2. In Secion 3 we describe he calibraion and numerical soluions and discuss opimal policy. A nal secion concludes. 2. THE MODEL We sudy a discree ime model of a small open economy inhabied by households, he governmen, compeiive rms ha produce a radable commodiy, compeiive rms ha produce nal goods, and a coninuum of rms ha produce di ereniaed inermediae goods. There are wo di ereniaed raded nal goods: one produced a home and he oher produced in he res of he world. The small open economy faces a downward-sloping demand for he nal good i produces bu akes as given he inernaional price of he foreign nal good. There are also wo commodiies one produced a home, he oher impored used in he producion of inermediae goods. These inermediae goods are used o produce he nal domesic good. 4

6 Households A represenaive household has preferences over coningen sequences of wo nal consumpion goods, C h and C f, and leisure L. The uiliy funcion is weakly separable beween he nal consumpion goods and leisure and is represened by E X = U (C ; L ) ; () where < < is a discoun facor, C = H(C h ; C f ) is a funcion homogeneous of degree one and increasing in each argumen, and U (C; L) is concave and increasing in boh argumens. Sicky Wages. In order o allow for sicky wages, we assume he single household has a coninuum of members indexed by h 2 [; ], each supplying a di ereniaed labor inpu n h. Preferences of he household are described by (), where leisure is L = L Z n h dh; (2) and L is he oal amoun of ime available for work or for leisure. The di ereniaed labor varieies aggregae up o oal labor inpu N, used in producion, according o he Dixi-Sigliz aggregaor Z N = w n w w h w dh ; w > : (3) Each member of he household, which supplies a di ereniaed labor variey, behaves under monopolisic compeiion. The workers se wages as in Calvo (983), wih he probabiliy of being able o revise he wage w. This loery is i:i:d: across workers and over ime. The workers ha are no able o se wages in period all share he same wage w. Oher prices 5

7 are aken as given. There is a complee se of sae-coningen asses. We consider an addiional ax, a payroll ax on he wage bill paid by rms, p. Marke Srucure Financial markes are complee. We le B ;+ and B ;+ denoe oneperiod discoun bonds denominaed in domesic and foreign currency, respecively. These are bonds issued a period ha pay one uni of he corresponding currency a period + on a paricular sae of he world and zero oherwise. The household s budge consrain is given by P h C h + P f C f + E hq ;+ B ;+ + S Q ~ i ;+ B;+ (4) B ~ W ( n ; ) N + B ; + S ; + where S is he nominal exchange rae beween domesic and foreign currency, W is he nominal wage rae, n is a labor income ax, is a ax on he reurn of foreign-denominaed bonds (a ax on capial ows), and Q ;+ is he domesic currency price of he one-period coningen domesic bond normalized by he condiional probabiliy of he sae of he economy in period + condiional on he sae in period. Likewise, Q ;+ is he normalized foreign currency price of he foreign bond. 2 In his consrain, we assume ha dividends are fully axed and ha consumpion axes are zero (we explain hese choices laer). Using he budge consrain a periods and + and rearranging gives he no-arbirage condiion beween domesic and foreign bonds: Q ;+ = Q ;+ + + S S + : (5) Working wih he presen value budge consrain is convenien. To ha end, for any k >, we 2 We use he noaion ~ B ;+ insead of simply B ;+ o disinguish foreign bonds held by he household secor from foreign bonds held by he aggregae economy. 6

8 le Q ;+k = Q ;+ Q +;+2 :::Q +k ;+k be he price of one uni of domesic currency a a paricular hisory of shocks in period +k in erms of domesic currency in period ; an analogous de niion holds for Q ;+k. Ieraing forward on (4) and imposing he no-ponzi condiion lim! E [Q ; B + S Q ; ~ B ] gives E X = Q ; P h C h + P f C f W ( n ) N ; (6) where we have assumed ha iniial nancial wealh is zero, or B ; = ~ B ; =. The household maximizes () subjec o (6). The opimaliy condiions are given by H C h(c h ; C f ) H C f (C h ; C f ) = P h P f (7) U C (C ; L ) H C h(c h ; C f ) P h U C (C + ; L + ) H = Ch(C h ; C f ) ; (8) Q ;+ P+ h plus an opimal wage decision ha will be discussed laer. Governmen The governmen ses moneary and scal policy and raises axes o pay for exogenous consumpion of he home nal good, G h. 3 Moneary policy consiss of rules for eiher he nominal ineres rae R or he nominal exchange rae S. Fiscal policy consiss of labor axes n ; payroll axes n ; expor and impor axes on foreign goods, h and f, respecively; axes on reurns of foreign asses ; and dividend axes d. The wo sources of pure rens in he model are he dividends of inermediae good rms and he pro s of commodiy producers equivalenly, one can hink of he laer as a ax on he rens associaed wih a xed facor of producion. Throughou he paper, we assume ha all 3 I is sraighforward o also le he governmen consume foreign goods. 7

9 rens are fully axed so ha d = for all. The reason for his assumpion is ha if pure rens are no fully axed, he Ramsey governmen will use oher insrumens o parially ax hose rens. We deliberaely absrac from hose e ecs in he opimal policy problem. Our descripion of scal policy is for compleeness. As is well known, 4 when scal policy can respond o shocks and here is a complee se of insrumens, price sabiliy is opimal. The axes described in his secion do represen a complee se of insrumens. The opimal moneary policy becomes nonrivial once scal insrumens are exogenously resriced o be unresponsive o shocks. Final good rms Perfecly compeiive rms produce he domesic nal good Y h by combining a coninuum of nonradable inermediae goods indexed by i 2 (; ) using he echnology Z Y h = y i di ; where > is he elasiciy of subsiuion beween each pair of inermediae goods. Taking as given he nal good price, P h, and he prices of each individual variey of inermediae goods, P h i for i 2 (; ), he rm s problem implies he cos minimizaion condiion y i = Y h P h (9) i P h for all i 2 (; ). Inegraing his condiion over all varieies and using he producion funcion gives a price index relaing he nal good price and he prices of he individual varieies, Z P h = P h i di : () 4 See Adao, Correia, and Teles (29), Correia, Nicolini, and Teles (28), Correia, Farhi, Nicolini, and Teles (23), Farhi, Gopinah, and Iskhoki (24), and Hevia and Nicolini (23). 8

10 Minimizaion of labor coss Before describing he echnologies of he secors ha demand labor, we believe i is useful o describe he labor cos minimizaion problem. Firms minimize R w hn h dh, where w h is he wage of he h-labor, for a given aggregae N, subjec o (3). The demand for n h is n h = w wh W N, () where W is he aggregae wage level, given by Z W = w h w w dh. (2) I follows ha R w hn h dh = W N. The opimal wage-seing condiions by he monopolisic compeiive workers are now w = w w E X j= w ;j U L ( + j) U C ( + j) ( + c +j)p +j ( n +j ) ; (3) wih w ;j = ( n +j) ( w ) j U C(+j) (W (+ c +j ) w N +j +j)p +j P E j= ( n +j ) : (4) (w ) j U C(+j) (W (+ c +j ) w N +j +j)p +j The wage level (2) can be wrien as W = ( w ) w w + w W w w. (5) Using (), we can wrie (2) as N = " Z w wh W dh# L L. (6) 9

11 From (2), i mus be ha R w h W w dh. This means ha for a given oal ime dedicaed o work, L L, he resources available for producion are maximized when here is no wage dispersion. In equilibrium X+ L L = N j= $ w j w w j W ; where $ w j is he share of household members ha have se wages j periods before, $ w j = ( w ) j ( w ), j = ; 2; :::;, and $ w + = ( w ) +, which is he share of workers ha have never se wages and charge he exogenous wage w. Primary commodiy secor Two radable commodiies, denoed by x and z, are used as inpus in he producion of inermediae goods. The home economy, however, is able o produce only he commodiy x; he commodiy z mus be impored. We denoe by P x commodiies. and P z he local currency prices of he Toal oupu of commodiy x; denoed as X ; is produced according o he echnology X = A (n x ) ; (7) where n x is labor, A is he level of produciviy, and <. Implici in his echnology is he assumpion of a xed facor of producion (when < ), which we broadly inerpre as land. Pro maximizaion implies P x A (n x ) = W ( + p ): (8)

12 Because he wo commodiies can be freely raded, he law of one price holds: P x = S P x (9) P z = S P z ; where P x and P z denoe he foreign currency prices of he x and z commodiies. 5 We can use (9) and (8) o obain S P x A (n x ) = W ( + p ); which, given values for he exogenous shocks and given an allocaion, resrics he feasible values for fs ; W ; p g: Inermediae good rms Each inermediae good i 2 (; ) is produced by a monopolisic compeiive rm ha uses labor and he wo radable commodiies wih he echnology y i = Z x i z 2 i (ny i ) 3 ; where x i and z i are he demand for commodiies, n y i is labor, Z denoes he level of produciviy, j for j = ; 2; 3, P 3 j= j =, and = The associaed nominal marginal cos funcion is common across inermediae good rms and given by MC = (P x ) (P z ) 2 W 3 ( + p ) 3 Z : Using (8) and (9), he nominal marginal cos can be wrien as MC = S MC, where MC, 5 We could also allow for ari s on he inermediae inpus. However, hese ari s are redundan insrumens in his environmen.

13 he marginal cos measured in foreign currency, is given by MC = (P x ) 2 (P z ) 2 (A (n x ) ( + p )) 3 Z : (2) Tha is, he marginal cos in foreign currency depends on he inernaional commodiy prices, on echnological facors, and on he equilibrium allocaion of labor in he commodiies secor. In addiion, cos minimizaion implies ha nal inermediae good rms choose he same raio of inpus, x i n y i z i n y i = A (n x ) ( + p ) (2) 3 = 2 P x A 3 P z (n x ) ( + p ) for all i 2 (; ) ; where we have used (8) in he second equaion. Inroducing (2) ino he producion funcion gives y i = n y Z i (A (n x ) ( + p )) 3 (P x 3 ) 2 (P z ) 2 : (22) Each monopolis i 2 (; ) faces he downward-sloping demand curve (9). We follow he sandard radiion in he New Keynesian lieraure and impose Calvo price rigidiy. Namely, in each period, inermediae good rms are able o reopimize nominal prices wih a consan probabiliy < p <. Those ha ge he chance o se a new price will se i according o p h = E X j= (P+j) x (P z +j ) 2 W+j ( + p +j ) 3 ;j ; (23) Z +j where ;j = pj Q ;+j (P+j) h Y+j h P E : (24) j= j Q ;+j (P+j h ) Y+j h 2

14 The price level in () can be wrien as h P h = ( p ) p h + p P h i. (25) Foreign secor and feasibiliy We assume an isoelasic foreign demand for he home nal good of he form C h = (K ) P h ; (26) where >, P h is he foreign currency price of he home nal good, and K is a sochasic process ha ransforms unis of foreign currency ino domesic consumpion goods. 6 The governmen imposes a ax ( + h ) on nal goods expored o he res of he world and a ari ( + f ) o nal good impors. The law of one price on domesic and foreign nal goods hen requires P h ( + h ) = S P h (27) P f = S P f ( + f ); where P f is he foreign currency price of he foreign nal good. Ne expors measured in foreign currency are given by m = P h C h Z P f C f + P X x x i di P z Z z i di: (28) 6 We allow for he nal goods o be raded, so a paricular case of our model (he one wih A = and = 2 = ) wihou commodiies is he one ypically analyzed in he small open economy New Keynesian lieraure. 3

15 Thus, he ne foreign asses of he counry, denoed by B ;+, evolve according o B ; + m = E B ;+Q ;+: (29) Solving his equaion from period forward, and assuming zero iniial foreign asses, gives he economy foreign secor feasibiliy consrain measured in foreign currency a ime : E X = Q ;m = : (3) In addiion, marke clearing in domesic nal goods requires Y h = C h + C h + G h ; (3) and labor marke feasibiliy is given by N = Z n y i di + nx : (32) Fiscal and moneary policies We now show how a exible exchange rae sysem, coupled wih a exible payroll ax, can joinly sabilize domesic prices and wages. Firs, using he law of one price for he commodiies, P x = S P x P z = S P z ; 4

16 we can wrie he cos minimizaion condiion in he commodiy secor (8) and he marginal cos for he inermediae good rm as S P x A (n x ) = W ( + p ) MC = S (P x ) 2 (P z ) 2 (A (n x ) ) 3 Z : Because domesic prices are proporional o marginal coss, hey will be consan once marginal coss are consan, which implies MC = S (P x ) 2 (P z ) 2 (A (n x ) ) 3 Z ; so he nominal exchange rae moves o absorb produciviy and commodiy price shocks. Noe ha he negaive correlaion beween he nominal exchange rae and he prices of he exporable commodiy, presened in Figure, follows as a direc resul of price sabiliy. We can hen use his implied equilibrium relaionship o solve for he nominal exchange rae and use i on he cos minimizaion condiion of he commodiy secor o obain 3 P x 2 MC Z P z A (n x ) ( )( 3 ) = W ( + p ): So, o sabilize wages, he payroll ax mus move according o ( + p ) = W 3 P x 2 MC Z P z A (n x ) ( )( 3 ) : Clearly, o he exen ha scal policy canno be joinly used wih moneary policy, here is a rade-o beween eliminaing he disorion in prices and eliminaing he disorion in wages. The numerical analysis of ha quesion is addressed in he nex secion. 5

17 3. CALIBRATION AND NUMERICAL ANALYSIS OF MONETARY POLICY Before we sar, clarifying one issue is imporan. So far, we have been silen wih respec o he implemenaion of paricular equilibria hrough policy. Since he work of Sargen and Wallace (975), a vas lieraure has developed ha analyzed he problem of unique implemenaion using paricular policy arges. To brie y summarize ha lieraure, in general, when cenral banks use money or he ineres rae as he policy insrumen, ypically muliple equilibria are consisen wih a single policy rule. On he conrary, if he exchange rae is pegged, uniqueness ypically arises. Muliple soluions have been o ered. The mos popular, in he conex of ineres rae rules, is o only consider a bounded equilibrium and o assume rules ha saisfy he Taylor principle. We fully absain from he issue of implemenaion and simply assume ha policy can successfully arge a nominal variable (or a combinaion of wo of hem), such as prices of domesic goods, P h ; he nominal wage, W ; or he nominal exchange rae, S. We consider he following uiliy funcion: U (C; L) = C & L L + + ; where, &, and are posiive parameers. The subuiliy funcion beween domesic and foreign nal goods is of he consan elasiciy of subsiuion form, C = H C h ; C f = ( $) = C h + $ = C f ; where is he elasiciy of subsiuion beween home and foreign goods, and $ is he share parameer associaed wih he foreign good. As is common in he lieraure, $ can be inerpreed as he degree of openness of he economy. Each ime period in he model represens one quarer. Mos of he parameers ha we use for calibraing he model are sandard and repored in Table in he appendix. We choose 6

18 so ha he discoun facor is :95 on an annualized basis and se a sandard risk aversion parameer of = 2. The parameer is he reciprocal of he Frisch elasiciy of labor supply. We se =, which lies beween he micro and macro esimaes of his elasiciy (Chey e al., 2). Furhermore, his number is sandard in he lieraure (see, for example, Caao and Chang, 23). The parameers & and L de ne unis of measuremen and are no imporan for he quaniaive resuls of he paper; we se & = and choose L so ha in he seady sae, workers allocae one-hird of heir oal available ime o marke aciviies. The parameer measures he Armingon elasiciy of subsiuion beween home and foreign nal goods. Esimaes of he Armingon elasiciy using microeconomic daa end o be much higher han hose based on macroeconomic daa. We se = :5; which is a common number used in he inernaional business cycles lieraure (Backus, Kehoe, and Kydland, 994). This value is also consisen wih he macro esimaes of he Armingon elasiciy repored in Feensra e al. (24). We se he share parameer a $ = :2. This value is consisen wih he observed home bias in consumpion (Obsfeld and Rogo, 2) and is similar o ha used in Caao and Chang (23). 7 The producion funcion of he home inermediaes is characerized by he hree share parameers, ; 2, 3 ; and by he level of produciviy Z. We se he share parameers a = :, 2 = :4, and 3 = :5: A labor share of abou 5% is a sandard parameerizaion. We se = : o capure he observaion ha he home commodiy is no used inensively in he producion of home goods. The share of impored inermediae inpus 2 = :4 is no inended o capure he impor of a single commodiy, such as oil in he case of Chile, bu of a large array of inermediae inpus and commodiies used in he producion of goods in he small open economy. We normalize he long-run level of produciviy o Z =. Regarding he echnology o produce he home commodiy, we se a small labor share of 7 Galí and Monacelli (25) and de Paoli (29) use $ = :4: Quaniaive resuls are similar if we se $ o :4 insead of :2. 7

19 = :, o capure ha he producion of commodiies is eiher land or capial inensive, and se he seady-sae level of echnology, A, a :2. Wih his calibraion, he seady-sae share of labor in he commodiies secor is abou.5. This is he arge number used in Hevia, Neumeyer, and Nicolini (23) using a broad de niion of he commodiy secor and an inpu-oupu marix for Chile (see he discussion in ha paper for more deails). For he parameerizaion of he foreign demand of he home nal good in equaion (26), we assume an elasiciy of = :5 and se K o a consan value of :. The foreign demand does no play an imporan role in he simulaions ha we discuss laer and, hus, hese parameers are almos irrelevan. The parameers p and w deermine he average number of periods beween price and wage adjusmens. We follow Chrisiano, Eichenbaum, and Rebelo (2) and se w = :85. The parameer p is se a :5, which implies an expeced price duraion of wo quarers. This is consisen wih he evidence in Klenow and Malin (2). 8 Finally, as is common in he lieraure, we consider an e cien seady sae. This amouns o imposing a consan labor subsidy ha eliminaes he monopolisic disorions, and a consan ari ha exracs he monopolisic rens in he rade of he home nal good. This follows because he small open economy faces a downward-sloping foreign demand for he nal good. We now consider he calibraion of he sochasic processes for he di eren shocks. We assume ha boh produciviy parameers, A and Z, follow auoregressive processes of he form log A = A = A log A = A + " A log Z = Z = Z log Z = Z + " Z ; where " A and " Z are independen mean zero shocks wih a sandard deviaion of A and Z, 8 The value used in Chrisiano, Eichenbaum, and Rebelo (2) is P = :85: As we show, he resuls change very lile if we use ha value. 8

20 respecively. We values of hese parameers are se a A = Z = :95 and A = Z = :3: These are he sandard values used in he lieraure of business cycles in small open economies (Neumeyer and Perri, 25). I remains o calibrae he price processes. Commodiy prices end o be correlaed among hem. One possibiliy is o calibrae he price processes by running a vecor auoregression (VAR) wih he exporable and imporable commodiy prices. The problem wih his approach, however, is ha i is no obvious how o idenify he imporable commodiy. Indeed, while exporable commodiies are easily ideni ed, imporable commodiies are no concenraed in a few goods. We hus proceed as follows. We calibrae he price process of he home commodiy by running a rs-order auoregression using HP- lered world prices of copper de aed by he U.S. consumer price index over he period 2 24: log P x = P x = x log P x = P x + " x ; where " x N (; 2 x) : The esimaion delivers x = :72 and x = :6. We nex impose a VAR srucure of he form x log P = P x log P z = P z = x z x log P = P x log P z = P z " x " z ; where z = x, so ha he imporable commodiy is as persisen as he home commodiy, bu z = x =2, re ecing ha shocks o a bundle of commodiies will be less volaile han shocks o a single commodiy. Finally, we se he free parameer so ha he model is able o replicae he correlaion beween he home commodiy price and he nominal exchange observed in Chile over he sample period discussed earlier. Seing = :8 implies a correlaion beween he nominal exchange rae and he commodiy price of :63 under a policy of price sabiliy. As a reference, if we se = ; he laer correlaion drops o :2. 9

21 In wha follows, and given he policy rule we now discuss, we simulae he model by shuing down all shocks excep he commodiy price P x : To approximae he soluion of he model, we use he quadraic perurbaion mehod around he seady sae developed by Schmi-Grohé and Uribe (24). The policy rule In order o capure our inerpreaion of he recen Chilean experience, one could consider a regime in which price sabiliy is he main saed objecive, bu wih some inervenions o reduce he volailiy of he nominal exchange rae (similar o he inervenions in 28 and 2). Noe ha from he soluion for he marginal cos, we can wrie MC = S MC ; where MC = (P x ) 2 (P z ) 2 (A (n x ) ) 3 Z : Clearly, MC he marginal cos in foreign currency is a funcion of he underlying shocks. As we menioned earlier, full price sabiliy implies consan marginal coss in local currency, so S = MC : MC We hen allow for a general rule in which he deviaions of he log of he nominal exchange rae adjus a fracion of he deviaions in he log of he marginal coss in foreign currency, or d ln S = d ln MC : (33) Thus, when = ; we have pure in aion argeing, when = we have a currency peg, and 2

22 by leing 2 (; ) we can have all inermediae cases: he lower he value for, he lower he volailiy of he nominal exchange rae and he larger he volailiy of domesic in aion. Wih he policy rule so speci ed, he model can be solved numerically. The policy rade-o implied by he previous rule may re ec he one implied by diry oaing regimes, in which some inervenion in foreign exchange markes is allowed. According o he heory, dampening he movemens in he nominal exchange rae implies increasing he volailiy of marginal coss and herefore he volailiy of he price level. However, wha seems a more naural rade-o, given he naure of he wo disorions, is sabilizing prices versus sabilizing nominal wages. In he heory secion, we showed how a payroll ax can be used ogeher wih he nominal exchange rae o sabilize boh prices and wages. Once he payroll ax canno be used, he nominal exchange rae can be used o sabilize eiher of hem bu no boh. Thus, le w h W : P h Then, we can de ne a policy where d ln W = d ln w h : (34) Thus, if = ; nominal wages are fully sabilized, whereas = implies full price sabiliy. The opimal policy is given by he value of ha maximizes welfare, given he process for he exogenous shock he price of he exporable commodiy in his case. The earlier discussion suggess ha he opimal policy will indeed have 2 (; ): This conjecure will be veri ed numerically laer. In he appendix we discuss how we perform he welfare comparisons across he di eren rules. In view of he preceding discussion, we rs consider he case in which he policy rades o price sabiliy wih nominal wage sabiliy, which is he rade-o ha will deliver he opimal 2

23 policy. Then, we discuss how he rule ha rades o price sabiliy wih nominal exchange rae sabiliy behaves, paricularly compared wih he opimal policy. We believe exploring his a priori subopimal rule is ineresing for wo reasons. Firs, i is he one ha bes approximaes, in our view, he diry oaing policy debae, as our discussion of he recen Chilean experience suggess. Second, while sabilizing wages in his simple model is rivial, i is much less so in a real economy wih so many secors and so many di eren ypes of labor. I does seem o us ha focusing he policy debae on a single, exremely visible price is much more aracive. The price/wage rade-o We will rs discuss he resuls using he general policy rule (34). To begin, we presen simulaions for he model wih he baseline calibraion, excep ha we se he rigidiy in wages o be zero. The advanage of his case is ha when prices are fully sabilized ( = ), we obain he opimal allocaion, which we use as a benchmark. In Figure 2 we show he impulse responses for oupu, he real wage, he real exchange rae, and labor following a one-sandard-deviaion posiive shock o he price of he exporable, for several values of. Throughou he paper, oupu (GDP) is compued as he sum of he value added evaluaed a he seady-sae prices. As expeced, a he e cien allocaion ( = ), here is a redisribuion of labor oward he exporable secor (labor increases by 4% in he commodiy secor and drops by :8% in he home good secor). Consumpion of he home good becomes very expensive, so i goes down, increasing oal labor supply. This lowers he real wage and rms hire more labor overall, so GDP goes up by almos :35%. Since prices are sable, as he nominal exchange rae goes down, so does he real exchange rae. When nominal wages are sabilized ( = ), he same equilibria would obain by increases in he price level, if prices were fully exible. Bu hey are no, so he drop in he real wage is lower in his case. Because he price of nal goods does no go up as much, demand for he nal consumpion good is relaively higher, so he drop in labor a he 22

24 Perc. dev. from seady sae Perc. dev. from seady sae ν = ν =.25 ν =.5 ν =.75 ν = Fig. 2. Economy wih no wage rigidiies home good secor is smaller and he increase in GDP is higher (alhough he e ec is small). Because he price level does no increase enough, he real exchange rae does no drop very much. An ineresing feaure ha arises from Figure 2 is ha he e ec of he policy regime (from a xed exchange rae o a fully oaing one in which prices are sabilized) does no have a very big impac on he ransmission mechanism of a commodiy price shock, even wih a relaively high value for he Calvo parameer ( p = :5). The larger di erences are in he movemens of he real wage and he real exchange rae, bu no on he real allocaion, which is wha maers for welfare. The e ec of he policy regime is much more dramaic for he benchmark calibraion (wih w = :85), in which he opimal allocaion canno be implemened because of he presence of boh price and wage rigidiy. We show he relevan impulse responses in Figure 3. When policy fully sabilizes nominal wages, he behavior of labor and oupu is relaively similar o 23

25 Perc. dev. from seady sae Perc. dev. from seady sae he e cien allocaion: oal oupu goes up by abou :35%; oal labor goes up by abou :7%; and he labor reallocaion is very similar. Noe, however, ha fully sabilizing nominal prices delivers a very di eren oucome: GDP falls by :3% and oal labor by :2% ν = ν =.25 ν =.5 ν =.75 ν = Fig. 3. Baseline economy We also solved he model by seing he share of foreign goods o : and :4 (he benchmark is :2) and he degree of price sickiness o :25 and :85 (he benchmark is :5). The resuls, presened in he appendix, are roughly similar. Finally, we swiched he degree of rigidiy beween prices and wages, relaive o he benchmark. Tha is, we increased he degree of price rigidiy o p = :85 and reduced he degree of wage rigidiy o w = :5: Resuls are depiced in Figure 4. Now, he choice of he policy regime is much less relevan han in he benchmark case. As can be seen, full price sabiliy delivers oucomes ha are very similar o he opimal allocaion: an increase in oupu a bi below :35%, an increase in oal labor close o :6%, and a very similar labor reallocaion. This is naural, 24

26 Perc. dev. from seady sae Perc. dev. from seady sae ν = ν =.25 ν =.5 ν =.75 ν = Fig. 4. Economy wih higher price and lower wage rigidiy given ha i is in he seing of prices where we have he larges fricion. However, noice ha he e ecs of a regime ha fully sabilizes nominal wages do no a ec he allocaion very much: i generaes an ine cienly larger expansion, bu i is small noneheless (:4% insead of :35%). For a beer visual comparison, in Figure 5 we plo he impulse responses of oupu, he real wage, and labor in he nal good secor for he benchmark case ( p = :5 and w = :85) and for his las case analyzed, in which he degrees of rigidiy beween prices and wages have been swiched ( p = :85 and w = :5) using he same scales. The di erence is remarkable. The welfare analysis is in line wih he previous discussion. We show in Figure 6 he welfare gain, in unis of lifeime consumpion, of alernaive values of 2 [; ], relaive o he regime = ; which is equivalen o full wage sabiliy. Naurally, for he case in which w = ; full price sabiliy is opimal, which is re eced in he fac ha he line wih circles is always increasing. Noe, however, ha he opposie policy, he one ha fully sabilizes wages ( = ), enails a cos 25

27 Perc. dev. from seady sae Perc. dev. from seady sae ν = ν =.25 ν =.5 ν =.75 ν = Fig. 5. Comparison of di eren degrees of price and wage rigidiies under he wage rule of only :% of lifeime consumpion. On he oher hand, for our baseline parameerizaion, he opimal policy is slighly below = :; which amouns o almos full nominal wage sabiliy. Noice ha in his case, which exhibis a high degree of wage rigidiy, he welfare cos of full price sabiliy is over :45% of lifeime consumpion, almos ve imes more. This is in line wih our previous discussion: when here is a high degree of wage rigidiy and some degree of price rigidiy, he choice of he policy regime becomes more relevan. Noice ha lowering he degree of price rigidiy o p = :25 makes he opimal policy be even closer o full nominal wage sabiliy. Sill, he e ec of he policy regime (he value for ) is very relevan. Finally, when he wage rigidiy is lowered o w = :5; he opimal regime becomes close o = :5, and he e ec of full price sabiliy becomes lower han :% of lifeime consumpion. Overall, our resuls imply ha he policy regime is much more relevan when here is a subsanial degree of wage rigidiy, coupled wih some rigidiy in he seing of prices. On he oher hand, if here is a high degree of price sickiness, coupled wih some degree of wage rigidiy, he 26

28 Fig. 6. Welfare comparisons of di eren wage rules choice of he policy regime is relaively less imporan. The reason lies behind he logic of he mechanism a he opimal allocaion discussed earlier: he drop in he real wage, which increases oal labor and generaes an expansion. When prices are sabilized, he nominal wage mus fall. If nominal wages are very rigid, real wages do no fall and rms do no hire much labor, which creaes he usual recession observed in models wih wage rigidiy. On he oher hand, when prices are very rigid bu wages are no, if wages are sabilized, he adjusmen mus be realized by an increase in prices. As before, if prices are very rigid, hey do no increase and he real wage does no fall, creaing a recession as before. Bu conrary o he previous case, since prices do no increase, consumpion is relaively cheaper, and demand goes up. This demand e ec, also common in models wih price rigidiy, parially compensaes for he lack of adjusmen in he real wage. Thus, he more rigid he prices, he lower he adjusmen in he real wage, bu he larger he demand e ec. Therefore, he price rigidiy is less relevan han he wage rigidiy. 27

29 Perc. dev. from seady sae Perc. dev. from seady sae Exchange rae rule: impulse responses o commodiy price shock (baseline calibraion) ν = ν =.25 ν =.5 ν =.75 ν = Fig. 7. Baseline economy under he exchange rae rule The price/exchange rae rade-o Admiedly, he noion of nominal wage sabiliy is much simpler in he model han in acual economies. Thus, we now consider a resriced opimal policy problem in which we choose he bes value for bu use he rule (33) ha rades o price versus nominal exchange rae sabiliy. Figure 7 shows impulse responses following a one-sandard-deviaion increase in he price of he exporable commodiy for he baseline calibraion. In Figure 8, we compare he impulse responses of he benchmark case for oupu, he real wage, and labor in he nal good secor wih he case in which we reverse he degree of rigidiy ( p = :85 and w = :5). As before, he policy regime maers more when wages are more rigid han prices. In Figure 9, we show he welfare e ec, in unis of lifeime consumpion, of alernaive values of 2 [; ], relaive o he regime = ; which is equivalen o full exchange rae sabiliy. Noice ha for he baseline calibraion, he opimal value for is close o :5; which means a subsanial degree of diry oaing. Figure 9 reveals hree ineresing feaures. The rs is 28

30 Perc. dev. from seady sae Perc. dev. from seady sae ν = ν =.25 ν =.5 ν =.75 ν = Fig. 8. Comparison of di eren degrees of price and wage rigidiies under he exchange rae rule ha, as before, he welfare cos of implemening he wrong regime is higher when he fricion is concenraed in wages raher han prices (alhough he di erence is no as big as before). The second is ha he bes policy for he baseline calibraion is abou :45% percen of lifeime consumpion, relaive o price sabiliy. This is very ineresing, since i is very similar o he welfare gain of using he opimal policy, as described in he previous subsecion, again relaive o full price sabiliy. This means ha welfare a he bes diry oaing regime is very close o welfare a he opimal policy. To he exen ha a policy aimed a sabilizing nominal wages is hard o implemen in pracice, his resul suggess ha he bes diry oaing regime may be almos as good in erms of implemening good allocaions. The hird feaure is unrelaed o he discussion so far bu is sill very ineresing. A recen paper (Schmi-Grohé and Uribe, 22) argues ha he cos of a xed exchange rae regime can be very high relaive o a full in aion-argeing one. Our resuls provide an uninended example in which he resul is exacly he opposie: when he wage rigidiy is larger han he price rigidiy, a policy ha fully sabilizes prices is worse han one ha xes he nominal exchange rae. In 29

31 Fig. 9. Welfare comparisons of di eren exchange rae rules our case, he di erence can be up o :4% of lifeime consumpion. Exploring he robusness of his resul and using he di eren experiences of Chile (which arges low in aion) and Ecuador (which dollarizes) in he las 5 years is lef for furher research. CONCLUSIONS From a heoreical viewpoin, he presence of price and wage rigidiy implies ha full in aion argeing is no he opimal policy. In commodiy expor counries, which are subjec o very large changes in commodiy prices ha generae very large swings in he real exchange rae, his could be a serious concern. Thus, he quesion of real exchange rae sabilizaion has become a cenral issue in policy debaes. In his paper, we sudied a small open economy model ha is able o reproduce he large swings in nominal and real exchange raes and which exhibis price and wage fricions. We rs showed ha if scal policy insrumens (payroll axes, for insance) can be made as exible as 3

32 moneary policy, hen price sabiliy is he opimal policy. Bu if scal insrumens canno, a rade-o beween sabilizing domesic prices or nominal wages is involved. We showed ha his rade-o is paricularly imporan for policy design when here is a high degree of nominal wages (Calvo parameer higher han :8) and some degree of price rigidiy (Calvo parameer higher han :25). In his case, he wrong regime can cos as much as :45% of lifeime consumpion, relaive o he opimal rule. On he oher hand, if he rigidiy in prices is he mos severe, he wrong regime can cos a mos :% of lifeime consumpion. In our benchmark calibraion, based on models for he Unied Saes, wage rigidiy is indeed he one ha is he mos severe. To he exen ha his is a reasonable calibraion for small open economies, his means ha exible in aion-argeing regimes ha le domesic prices move somewha may be beer han pure price sabilizaion regimes. Alhough implemening a rule ha rades o price versus wage sabiliy is very simple in he model, given he heerogeneiy of wages in acual economies, he discussion in erms of in aion and exchange rae sabilizaion seems much more useful. Thus, we also considered such a rule and showed ha i can approximae he opimal policy remarkably well. Our paper herefore suggess ha srong wage rigidiy, coupled wih some price rigidiy, can jusify a diry oaing regime, where policy parially sabilizes he nominal (and real) exchange rae. 3

33 REFERENCES [] Adao, Bernardino, Isabel Correia, and Pedro Teles. 29. On he Relevance of Exchange Rae Regimes for Sabilizaion Policy. Journal of Economic Theory 44 (4): [2] Backus, David K., Parick J. Kehoe, and Finn E. Kydland Dynamics of he Trade Balance and he Terms of Trade: The J-Curve? American Economic Review 84 (): [3] Calvo, Guillermo A Saggered Prices in a Uiliy-Maximizing Framework. Journal of Moneary Economics 2 (3): [4] Caão, Luis, and Robero Chang. 23. Moneary Rules for Commodiy Traders. IMF Economic Review 6 (): [5] Chey, Raj, Adam Guren, Day Manoli, and Andrea Weber. 2. Are Micro and Macro Labor Supply Elasiciies Consisen? A Review of Evidence on he Inensive and Exensive Margins. American Economic Review: Papers and Proceedings (3): [6] Chrisiano, Lawrence J., Marin Eichenbaum, and Charles L. Evans. 25. Nominal Rigidiies and he Dynamic E ecs of a Shock o Moneary Policy. Journal of Poliical Economy 3 (): 45. [7] Chrisiano, Lawrence, Marin Eichenbaum, and Sergio Rebelo. 2. When Is he Governmen Spending Muliplier Large? Journal of Poliical Economy 9 (): [8] Correia, Isabel, Emmanuel Farhi, Juan Pablo Nicolini, and Pedro Teles. 23. Unconvenional Fiscal Policy a he Zero Bound. American Economic Review 3 (4): [9] Correia, Isabel, Juan Pablo Nicolini, and Pedro Teles. 28. Opimal Fiscal and Moneary Policy: Equivalence Resuls. Journal of Poliical Economy 6 (): 4 7. [] De Paoli, Bianca. 29. Moneary Policy and Welfare in a Small Open Economy. Journal of Inernaional Economics 77 (): 22. [] Farhi, Emmanuel, Gia Gopinah, and Oleg Iskhoki. 24. Fiscal Devaluaions. Review of Economic Sudies 8 (2): [2] Feensra, Rober C., Philip Luck, Maurice Obsfeld, and Kaheryn N. Russ. 24. In Search of he Armingon Elasiciy. NBER Working Paper No [3] Galí, Jordi, and Tommaso Monacelli. 25. Moneary Policy and Exchange Rae Volailiy in a Small Open Economy. Review of Economic Sudies 72 (252): [4] Hevia, Consanino, and Juan Pablo Nicolini. 23. Opimal Devaluaions. IMF Economic Review 6 ():

34 [5] Hevia, Consanino, Pablo Andrés Neumeyer, and Juan Pablo Nicolini. 23. Opimal Moneary and Fiscal Policy in a New Keynesian Model wih a Duch Disease: The Case of Complee Markes. Universidad di Tella Working Paper. [6] Klenow, Peer J., and Benjamin A. Malin. 2. Microeconomic Evidence on Price-Seing. In Benjamin M. Friedman and Michael Woodford, eds., Handbook of Moneary Economics, Vol. 3, Chaper 6, Amserdam: Elsevier. [7] Neumeyer, Pablo A., and Fabrizio Perri. 25. Business Cycles in Emerging Economies: The Role of Ineres Raes. Journal of Moneary Economics 52 (2): [8] Obsfeld, Maurice, and Kenneh Rogo. 2. The Six Major Puzzles in Inernaional Macroeconomics: Is There a Common Cause? In Ben S. Bernanke and Kenneh Rogo, eds., NBER Macroeconomics Annual 2, Vol. 5, Cambridge, MA: MIT Press. [9] Sargen, Thomas J., and Neil Wallace Raional Expecaions, he Opimal Moneary Insrumen, and he Opimal Money Supply Rule. Journal of Poliical Economy 83 (2): [2] Schmi-Grohé, Sephanie, and Marín Uribe. 24. Solving Dynamic General Equilibrium Models Using a Second-Order Approximaion o he Policy Funcion. Journal of Economic Dynamics and Conrol 28 (4): [2] Smes, Frank, and Rafael Wouers. 27. Shocks and Fricions in US Business Cycles: A Bayesian DSGE Approach. American Economic Review 97 (3): [22] Yun, Tack. 25. Opimal Moneary Policy wih Relaive Price Disorions. American Economic Review 95 ():

35 Appendix Welfare comparisons This appendix elaboraes on he welfare comparisons discussed in he ex. Suppose ha here is a baseline policy, denoed by b, associaed n wih an o equilibrium allocaion of consumpion, aggregae labor, and labor disorions C b ; N b ; w;b +j. The proposed policy delivers he level welfare V b a ime, given he sae of he economy, which we denoe by x, where V b = E V C;b V N;b X U j= C+j; b w;b +j N +j b V C;b " X C b # = E j +j j= 2 6 X w;b = E 4 j +j N +j b & + j= + 3 V N;b ; 7 5 : Now consider an alernaive policy, a, wih associaed allocaion C a ; N a ; w;a +j and uiliy level V a = V C;a V N;a : Our objecive is o measure he welfare gain of policy a relaive o policy b in erms of consumpion unis. For his, we ask by wha fracion he consumpion pah associaed wih policy b should be increased (or decreased) forever o achieve he same level of uiliy as under he alernaive policy a. In paricular, we nd he value ha sais es V a = E X U j= ( + ) C+j; b w;b +j N +j b = ( + ) V C;b V N;b : Solving for gives = V C;a V N;a V C;b + V N;b! : The recursive srucure of he model implies ha he values V C;j and V N;j for j = a; b are 34

36 ime-invarian funcions of he sae x, V C;j = V C;j (x ) V N;j = V N;j (x ) ; which, in urn, implies ha he welfare gain is also a ime-invarian funcion of x, = (x ). We hus can wrie V C;a (x ) V N;a (x ) + V N;b (x ) (x ) = V C;b (x ) : We repor he average value of (x ) under he ime-invarian disribuion of sae x. This average value is obained by compuing a simulaion of,2 periods in he model saring from he seady-sae condiion, dropping he rs 2 simulaed values, and hen compuing he average along he simulaed sample pah. For he welfare comparisons, i is crucial o perform an approximaion of he policy funcions of degree higher han one (second order in our case); oherwise, all policies deliver he same level of uiliy. 35