Consumption and Real Exchange Rates with Incomplete Markets and Non-traded Goods *

Transcription

1 CENTRE FOR DYNAMIC MACROECONOMIC ANALYSIS CONFERENCE PAPERS 2004 CDMC04/05 Consumpton and Real Exchange Rates wth Incomplete Markets and Non-traded Goods * Ganluca Bengno London School of Economcs and CEPR Chrstoph Thoenssen Unversty of St Andrews SEPTEMBER 2004 ABSTRACT Ths paper addresses the consumpton-real exchange rate anomaly. Internatonal real busness cycle models based on complete fnancal markets predct a untary correlaton between the real exchange rate and the rato of home to foregn consumpton when subjected to supply sde shocks. In the data, ths correlaton s usually small and often negatve. Ths paper shows that ths anomaly can be successfully addressed by models that have an ncomplete fnancal market structure and a non-traded as well as traded goods producton sector. JEL Classfcaton: F31, F41. Keywords: Consumpton-real exchange rate anomaly, ncomplete fnancal markets, non-traded goods. * We would lke to thank Perpaolo Bengno, Gancarlo Corsett, Luca Dedola, Mchael Devereux, Charles Engel, Fabo Ghron, Andre Kurmann, Sylvan Leduc and Frank Smets for ther useful comments. We also thank semnar partcpants at the Bank of England, the Unversty of Lecester, Unversty of Strathclyde, EEA 2003, MMF 2003, 6th Conference of the Analyss of Internatonal Captal Market RTN, SED 2004 and the Inaugural CDMA conference for ther comments and dscussons. All remanng errors are ours. Department of Economcs and CEP, London School of Economcs and Poltcal Scence, Houghton Street, London, WC2A 2AE, Unted Kngdom. E-mal: g.bengno@lse.ac.uk Department of Economcs, Unversty of St Andrews, St Andrews, Ffe, KY16 9AL, Unted Kngdom. Emal: ct30@st-andrews.ac.uk CASTLECLIFFE, SCHOOL OF ECONOMICS & FINANCE, UNIVERSITY OF ST ANDREWS, KY16 9AL TEL: +44 (0) FAX: +44 (0) AWT2@ST-AND.AC.UK

2 1 Introducton One of the well known puzzles n nternatonal nance s the so called consumptonreal exchange rate anomaly (see Backus and Smth, 1993 for an early paper and Char, Kehoe and McGrattan, 2002 for a recent contrbuton). Most nternatonal busness cycle models predct that, under the assumpton of perfect nancal markets along wth supply dsturbances, consumpton across countres should be hgher n the country where ts prce, converted nto a common currency s lower. Ths models feature s n sharp contrast wth the emprcal evdence whch suggests that the consumpton d erental across countres does not move n any systematc pattern wth ts relatve prce (.e. the real exchange rate). The removal of the assumpton of perfect nancal markets s not su cent n replcatng the observed evdence: ndeed, n ther study, Char et al (2002) have shown that the same anomaly n the behavor of consumpton and the real exchange rate does contnue to hold. In ths work we explore the extent to whch the ntroducton of non-traded goods along wth a lmted nternatonal nancal market structure mght account for the aforementoned anomaly. Our results suggest that the combnaton of these two factors s a promsng avenue for understandng the behavor of consumpton across countres and the real exchange rate. Indeed, n our model, the calbrated moments are close to reproducng the observed behavor of the data for a wde range of plausble parameters values. There are two key features that are mportant n accountng for our results. By assumng that nternatonal asset trade s lmted to a rsk-less bond we break the lnk between the real exchange rate and relatve consumpton that would arse under perfect nancal markets. Whle by ntroducng non-traded goods we allow for the possblty that, dependng on the orgn of the shock (.e. traded versus non traded), the real exchange rate and relatve consumpton across countres can move n opposte drectons. In partcular, followng a postve shock to the traded goods sector n the home economy, home consumpton ncreases wth respect to consumpton abroad. On the other hand, the real exchange rate apprecates f the e ect comng from the relatve prce of non-traded to traded goods (the so-called Balassa-Samuelson e ect) outweghs the terms of trade e ect that would mply a deprecaton of the real exchange rate. The rst e ect wll be stronger the more domnant the shocks to the traded goods sector relatve to non-traded goods sector, whle the second e ect wll be stronger the hgher the degree of home bas n preferences. More generally, the structure of the dsturbance and the spec caton of preferences determne the overall cross-correlaton between real exchange rate and relatve consumpton. Fnally we check the performance of our baselne model n replcatng standard nternatonal busness cycle statstcs. Our model overcomes the problem of an unrealstcally hgh cross-correlaton between relatve consumpton and the real exchange rate and comes close to matchng the volatlty of other key varables lke, nvestment, the real exchange rate and the terms of trade. Our model follows closely the ones proposed by Char et al (2002) and Stockman and Tesar (1995): we construct a smple two-country stochastc dynamc open economy model n whch we allow households to trade nternatonally n only one rsk-less nomnal bond, prces are exble and households consume a nal non-traded good produced wth domestc as well as foregn-produced nter- 1

3 medate goods and a non-traded ntermedate component. We allow for captal accumulaton at the ntermedate goods level and devatons from purchasng power party are obtaned by allowng for home-bas toward home produced ntermedate goods at the producton level and because of the exstence of nontraded ntermedate nputs. The remander of the paper s structured as follows: n secton two, we dscuss the nature of the consumpton-real exchange rate anomaly and survey related contrbutons n the lterature. Secton three presents the basc structure of the model. The model s calbrated n secton four, and secton ve outlnes the basc mechansm behnd our results. The results of the calbrated model are dscussed n sectons sx and seven, respectvely. Secton eght concludes. 2 Data and Related Lterature Backus and Smth (1993) are the rst to document the lack of correlaton between relatve consumpton levels and the real exchange rate. Corsett, Dedola and Leduc (2004), whose calculatons we report n table 1, show that the crosscorrelatons obtaned from Hodrck-Prescott ltered as well as rst-d erence ltered data for a selecton of OECD countres appear to be small and often negatve. The medan s between 0:30 and 0:2. The data for consumpton and real exchange rates are annual seres from the OECD Man Economc Indcators dataset from 1973 to [Table 1 about here] Char, Kehoe and McGrattan (2002) report cross-correlatons for a sub-set of OECD economes from 1973 to 1994 at a quarterly frequency and nd a medan value of These results can be used to queston the assumpton of nancal market completeness, for that assumpton would mply a cross-correlaton between the real exchange rate and relatve consumpton of close to unty. 1 Other emprcal studes have smlarly questoned the assumpton of nancal market completeness: n partcular Ravn (2001) shows that there s no role for the real exchange rate n accountng for d erences n margnal utltes of consumpton n d erent countres. In hs study, he rules out non-separabltes n the utlty functon as possble canddates n testng for rsk-sharng. In another related study, Kollmann (1995) also rejects the complete market assumpton. Startng from these premses, recent theoretcal papers assume an ncomplete nancal market structure as a necessary condton for explanng the observed evdence. In Char et al (2002) domestc and foregn agents are only allowed to trade n a non-state contngent nomnal bond. Ther rch model wth stcky prces s unable to break the lnk between real exchange rate and margnal utltes of consumpton. Indeed, the cross correlaton between relatve consumpton and the real exchange rate for the ncomplete market case s stll perfect as n the complete market case. They conclude by sayng that the most wdely used forms of asset market ncompleteness does not elmnate - or even shrnk- the anomaly. 1 One would expect a cross-correlaton equal to 1.00 only f utlty s addtvely separable n consumpton. 2

4 On the other hand, the papers by Corsett, Dedola and Leduc (2004) and Selave and Tuesta (2003) ntroduce other frctons along wth asset market ncompleteness and are able to get closer n replcatng the emprcal facts. Corsett et al (2004) hghlght the role of dstrbutve trade along wth market ncompleteness. Assumng that brngng traded goods to the market requres non-traded dstrbuton servces can generate the low mport elastcty crucal for explanng the observed patterns n the nternatonal transmsson of productvty shocks and the hgh volatlty of the real exchange rate. Ther VAR analyss suggests that a postve productvty shock wll mprove the terms of trade, apprecate the real exchange rate and ncrease domestc consumpton relatve to the rest of the world: ths pattern of transmsson s compatble n ther model wth a relatvely low prce elastcty of mports. Selave and Tuesta (2003) consder a rcher structure n whch prces are stcky and monetary polcy s modelled through nterest-rate feedback rules. They emphasze the mportance of nancal frctons and the role of net foregn asset poston n breakng the lnk between real exchange rate dynamcs and relatve consumpton levels. Another related contrbuton s a recent work by Ghron and Meltz (2004). In ther work a non-traded sector arses endogenously because less productve rms decde not to export ther products. They nd that a Balassa-Samuelson e ect and a real exchange rate apprecaton s generated by aggregate productvty shocks rather than sector spec c ones to the traded sector. Our contrbuton d ers from the aforementoned works n some mportant aspects: d erently from Corsett et al (2004) there are no dstrbuton costs and the law of one prce always holds. In contrast to from Selave and Tuesta (2003) prces are perfectly exble. As n Char et al (2002), we assume that agents consume a nal consumpton good, whch s not traded nternatonally. Unlke Char et al we assume that ths nal good contans three types of ntermedate nputs: home and foregn-produced traded ntermedate nputs as well as nontraded domestcally produced ntermedate nput. We nd that our model, calbrated n a canoncal fashon, generates crosscorrelatons between the real exchange rate and relatve consumpton whch are not at odds wth the data. We attrbute ths to the combnaton of the presence of a non-traded producton sector together wth a smple form of ncomplete nancal markets. 3 A two-sector two-country model The structure of the model closely follows closely Char, Kehoe and McGrattan (2002) and Stockman and Tesar (1995). There are two key mod catons wth respect to ther baselne cases. Frstly we consder an ncomplete market structure at the nternatonal level. Secondly, unlke Char et al, but smlar to Stockman and Tesar, we ntroduce non-tradeable ntermedate nputs n the producton process. Moreover, we focus on a perfectly compettve settng whle Char et al analyze an mperfectly compettve framework wth staggered prce settng behavor. 3

5 3.1 Consumer Behavor We propose a two-country model wth n ntely lved consumers. The world economy s populated by a contnuum of agents on the nterval [0; 1]. The populaton on the segment [0; n) belongs to the country H (Home), whle the segment [n; 1] belongs to F (Foregn). Preferences for a generc Home-consumer are descrbed by the followng utlty functon: U j t = E t 1 X s=t s t U(C j s; (1 l j s)) (1) where E t denotes the expectaton condtonal on the nformaton set at date t, whle s the ntertemporal dscount factor, wth 0 < < 1. The Home consumer obtans utlty from consumpton, C j ; and receve ds-utlty from supplyng labor, l j. The asset market structure n the model s relatvely standard n the lterature. We assume that Home ndvduals are assumed to be able to trade two nomnal rsk-less bonds denomnated n the domestc and foregn currency. These bonds are ssued by resdents n both countres n order to nance ther consumpton expendture. On the other hand, foregn resdents can allocate ther wealth only n bonds denomnated n the foregn currency. 2 Home households face a cost (.e. transacton cost) when they take a poston n the foregn bond market. Ths cost depends on the net foregn asset poston of the home economy as n Bengno (2001). 3 Domestc rms are assumed to be wholly owned by domestc resdents, and pro ts are dstrbuted equally across households. Consumers face the followng budget constrant n each perod t: P t C j t + Bj H;t (1 + t ) + S t B j F;t (1 + t ) StB F;t P t = B j H;t 1 + S tb j F;t 1 + P tw t l j t + j t (2) where B j H;t and Bj F;t are the ndvdual s holdngs of domestc and foregn nomnal rsk-less bonds denomnated n the local currency. t s the Home country nomnal nterest rate and t s the Foregn country nomnal nterest rate. S t s the nomnal exchange rate expressed as unts of domestc currency needed to buy one unt of foregn currency, P t s the consumer prce level and w t s the real wage. j t are dvdends from holdng a share n the equty of domestc rms obtaned by agent j. All domestc rms are wholly owned by domestc agents and equty wthn these rms s evenly dvded between domestc agents. The cost functon (:) drves a wedge between the return on foregn-currency denomnated bonds receved by domestc and by foregn resdents. We follow Bengno (2001) n ratonalzng ths cost by assumng the exstence of foregnowned ntermedares n the foregn asset market who apply a spread over the rsk-free rate of nterest when borrowng or lendng to home agents n foregn currency. Ths spread depends on the net foregn asset poston of the home 2 We want to hghlght here the fact that ths asymmetry n the nancal market structure s made for smplcty. The results would not change f we allow home bonds to be traded nternatonally. We would need to consder a further arbtrage condton. 3 Further ways of closng open economy models are dscussed n Schmtt-Grohe and Urbe (2003). 4

6 economy. We assume that pro ts from ths actvty n the foregn asset market are dstrbuted equally among foregn resdents (see Bengno, P. 2001). 4 As n Bengno (2001), we assume that all ndvdual belongng to the same country have the same level of ntal wealth. Ths assumpton, along wth the fact that all ndvduals face the same labor demand and own an equal share of all rms, mples that wthn the same country all ndvduals face the same budget constrant. Thus they wll choose dentcal paths for consumpton. As a result, we can drop the j superscrpt and focus on a representatve ndvdual for each country. The maxmzaton problem of the Home ndvdual conssts of maxmzng 1 subject to 2 n determnng the optmal pro le of consumpton and bond holdngs and the labor supply schedule. Households equlbrum condtons (Home and Foregn) are descrbed by the followng equatons: P t U C (C t ; (1 l t )) = (1 + t )E t U C (C t+1 ; (1 l t+1 )) (3) U C (C t ; (1 P t+1 l t )) = (1 + t )E t U C C t+1; (1 l t+1) P t U C (C t ; (1 l t )) = (1+ St B F;t t ) E t U C (C t+1 ; (1 P t U l (C t ; (1 l t )) U C (C t ; (1 l t )) = w t 3.2 Producer Behavor P t+1 l t+1 )) S t+1p t S t P t+1 (4) (5) U l (C t ; (1 l t )) U C (C t ; (1 l t )) = w t (6) As n Char et al (2002), n our economy nal goods are obtaned by combnng ntermedate goods produced n the Home and n the Foregn economy. D erently from Char et al (2002) we now also consder the possblty that non-traded ntermedate nputs enter n the producton process for the nal goods. All trade between the two countres s n ntermedate goods. We let Y be the output of nal goods produced n the home country. Fnal goods producers combne home and foregn-produced ntermedate goods to produced Y n the followng manner: Y = h! 1 y 1 T + (1!) 1 1 y N 1 where y T and y N are the ntermedate traded and non-traded nputs and s the elastcty of ntratemporal substtuton between traded and non-traded ntermedate goods. The traded component s n turn produced usng home and foregn-produced traded goods n the followng manner: (7) y T = hv 1 y 1 H + (1 v) 1 1 y F 1 (8) 4 Here we follow Bengno (2001) n assumng that the cost functon (:) assumes the value of 1 only when the net foregn asset poston s at ts steady state level, e B F;t = B; and s a d erentable decreasng functon n the neghbourhood of B. Ths cost functon s convenent because t allows us to log-lnearse our economy properly snce n steady state the desred amount of net foregn assets s always a constant 2 B. The expresson 3 for pro ts from nancal ntermedaton s gven by K = B F;t P t (1+ t ) 4 RS t St 1 B F;t P t 5 : 5

7 where y H and y F are the ntermedate goods produced n the Home and Foregn countres respectvely. s the elastcty of ntratemporal substtuton between home and foregn-produced ntermedate goods. Fnal goods producers and producer of the composte traded goods are compettve and maxmze ther pro ts: max P Y P T y T P N y N (9) y N; y T max P T y T P H y H P F y F (10) y H; y F subject to 7 and 8 respectvely. Ths maxmzaton yelds the followng nput demand functons for the home economy (smlar condtons hold for Foregn producers) PN y N = (1!) Y; (11) y H =!v PH P T PT P P PF Y y F =!(1 v) P T PT P Y Correspondng to the prevous demand functon we have the followng prces ndexes: P 1 T = [vp 1 1 H + (1 v)pf ] (12) P 1 = [!P 1 T +!P 1 N ] (13) Intermedate goods sectors Frms n the traded ntermedate goods sector produce goods usng captal and labor servces. The typcal rm maxmzes the followng pro t functon: max P Ht y Ht + S t PH l H;t ;x t yh P t w t l H;t P t x H;t (14) H;t where l H;t s the total labor supply employed n the domestc traded ntermedate sector, x H;t denotes nvestment n the traded domestc sector. Snce we assume that the law of one prce holds for traded goods, we can rewrte the maxmzaton problem as: max l H;t ;x H;t P Ht (y Ht + y H) P t w t l H;t P t x H;t subject to: y Ht + yh t = F (k H;t 1; l H;t ) = (A t l H;t ) (k H;t 1 ) 1 (15) xht k H;t = (1 )k H;t 1 + x Ht k Ht 1 k Ht 1 where (:) s the cost for nstallng nvestment goods. 5 The rst-order condtons are gven by the followng equatons: P t w t = P H;t (A t ) ( k H;t 1 l H;t ) 1 (16) 5 The functon (:) has the followng form: xt k t 1 b( x t ) and 00 x t k t 1 k t 0 x t k t 1 = 0: 1 = b( x t k t 1 ) 2 2 so that 0 x t k t 1 = = b away from steady state and n steady state: x k = 6

8 E t U C (C t ; (1 l t )) = 1 0 xh;t EU C (C t+1 ; (1 k H;t x H;t k H;t x H;t+1 k H;t U C (C t+1 ; (1 l t+1 )) (1 ) xh;t+1 k H;t l t+1 )) w t+1 f kt+1 f lt+1 + (17) + 0 xh;t+1 k H;t where f kt s the margnal product of captal and f lt+1 the margnal product of labor and w t+1 s the real wage. A smlar problem holds for the non-traded goods sector: max P Nt y Nt P t w t l N;t P t x N;t (18) l N;t ;x N;t xh;t+1 k H;t y Nt = F (k t 1; l N;t ) = (A N;t l N;t ) (k N;t 1 ) 1 (19) xn;t k N;t = (1 )k N;t 1 + x t k N;t 1 (20) k N;t 1 And the correspondng rst order condtons are gven by: E t U C (C t ; (1 l t )) = 1 0 x N;t k N;t 1 P t w t = P N;t (A N;t ) ( k N;t 1 l N;t ) 1 (21) 1 0 xn;t EU C (C t+1 ; (1 k Nt x N;t+1 k N;t U C (C t+1 ; (1 l t+1 )) (1 ) xn:t+1 k N;t l t+1 )) w t+1 f kt+1 f lt+1 + (22) + 0 xn;t+1 k N;t where f kt s the margnal product of captal and f lt+1 the margnal product of labor and w t+1 s the real wage. 3.3 Current account One mportant mplcaton of the ncomplete market framework s that t allows us to characterze the dynamc of the current account. By aggregatng the ndvdual budget constrants n the home country, we obtan: P t C t + S tbt F (1 + t ) 1 ( StBF t P t ) = S tb F t 1 + P t w l l t + t (23) where we have appled the assumpton that home bonds are n zero net supply and only held by Home resdents. The aggregate pro ts n the home economy are gven by: t = P Ht y Ht + yh t P t w t l Ht P t x Ht + (24) P Nt y Nt P t w t l Nt P t x Nt xn;t+1 k N;t 7

9 From whch substtutng the economy-wde constrant on labor and nvestment (l = l H + l N and x = x H + x N ) we obtan: C t + S tbt F P t (1 + t ) 1 ( StBF t P t ) = S t B F t 1 P t + P H t P t y Ht + y H t + P Nt P t y Nt x t (25) or after substtutng n the nal goods sector constrant (Y = C + x): S t Bt F P t (1 + t ) 1 ( StBF t P t ) = S t B F t 1 P t + P H t P t a smlar equaton holds for the Foregn economy. 3.4 Monetary polcy y Ht + y H t + P Nt P t y Nt Y t (26) Snce we are characterzng a nomnal model we need to specfy a monetary polcy rule. In what follows we assume that the monetary authortes n both countres follow a strategy of settng producer prce n aton equal to zero. 3.5 Soluton technque Before solvng our model, we log-lnearze around the steady state to obtan a set of equatons descrbng the equlbrum uctuatons of the model. The loglnearzaton yelds a system of lnear d erence equatons whch we lst n the appendx and can be expressed as a sngular dynamc system of the followng form: AE t y(t + 1 j t) = By(t) + Cx(t) where y(t) s ordered so that the non-predetermned varables appear rst and the predetermned varables appear last, and x(t) s a martngale d erence sequence. There are four shocks n C: shocks to the Home traded and non-traded ntermedate goods sectors productvty and shocks to the Foregn traded and non-traded ntermedate goods sectors productvty. The varance-covarance as well as the autocorrelaton matrces assocated wth these shocks are descrbed n table 2. Gven the parameters of the model, whch we descrbe n the next secton, we solve ths system usng the Kng and Watson (1998) soluton algorthm. 4 Calbraton The calbraton of our model parameters as well as the process for technologcal nnovatons follows the calbraton suggested by Stockman and Tesar (1995) where applcable. 6 We assume that the Home and Foregn economy are of equal sze and are calbrated n a symmetrc fashon. Followng Stockman and Tesar we choose the followng functonal form for the utlty functon: U j t = E t 1 X s=t s t 1 1 (Cj s) 1 (1 l j s) ) (27) 6 We follow Stockman and Tesar (1995) because ther analyss uses a model smlar to ours, and s one of the very few publshed papers to provde estmated productvty shock processes for a symmetrc two-country two-sector model. 8

10 In choosng the parameters of utlty functon, we set to match a 4% annual dscount rate. The coe cent of constant relatve rsk averson, or the nverse of the ntertemporal elastcty of substtuton,, s set to 2, as n Stockman and Tesar. As n Stockman and Tesar we set the nverse of the ntertemporal elastcty of substtuton n lesure, to 3.17 and assume along wth most real busness cycle studes that agents devote around 80% of ther tme endowment to lesure and the remanng 20% to work. We calbrate the parameters pertanng to the nal goods producng sector n the followng way. The share of tradable ntermedate goods n the nal consumpton good,! s 0.4, whle the share of home-produced ntermedate nputs n the tradable ntermedate nput, v s 0.7. Ths calbraton suggests sgn cant home bas n consumpton, and s n lne wth other recent studes, see Corsett et al (2004). Followng Stockman and Tesar, we assume a untary elastcty of substtuton between home and foregn-produced traded goods,, and an elastcty of substtuton between traded and non-traded goods, of 0.44 n the producton of the nal consumpton good. We assume that the share of labor nput n ntermedate good producton, n our Cobb-Douglas producton functon, s the same across sectors. We choose the average of the shares reported for the traded and non-traded sectors as n Stockman and Tesar: = 0:585. We assume that captal stocks deprecate at a rate of 10% per annum. We choose the adjustment cost parameter n nvestment, d, so as to ensure a volatlty of nvestment relatve that of GDP n excess of 3. The two remanng parameters relate to our spec caton of ncomplete markets. We follow Bengno, P. (2001) n choosng a 10 bass pont spread (per quarter) of the domestc nterest rate on foregn assets over the foregn rate, such that on an annualzed bass " 0 ( b) Y = 0:004, whle the steady-state rato of net foregn assets to GDP, a = b Y s assumed to be equal to zero. The structure of our shock processes s also taken from Stockman and Tesar and s reproduced n table 2. The shocks to technology are assumed to follow a rst order autoregressve process: A t+1 = A t + t where A s a vector of shocks: [A H, A F, A N, A N ] and s a 4 4 matrx descrbng the autoregressve components of the shocks. The nnovatons to A are [ H, F, N, N ] and the varance-covarance matrx s V []. [Table 2 about here] In Stockman and Tesar s estmated shock processes the varance of traded goods sector shocks s about twce that of shocks to non-traded productvty. Shocks to the traded sector s supply sde are less persstent than shocks a ectng the non-traded sector. The cross-correlaton between shocks mpled by V [] can be summarzed as follows: Corr( ; j ) = :33 0:46 0:19 0:33 1 0:19 0:46 0:46 0:19 1 0:14 0:19 0:46 0:

11 5 Relatve consumpton and the real exchange rate: the role of ncomplete markets and sectoral shocks Before we analyze the characterstcs of our calbrated model n terms of second moments, ths secton looks at mpulse responses for the real exchange rate and relatve consumpton followng productvty shocks. Our mpulse responses are derved under the assumpton that all elements of the autocorrelaton matrx are set to zero and that the varance-covarance matrx V [] of the shocks takes the form of an dentty matrx. In ths secton we want to hghlght the roles of market ncompleteness, the mportance of the non-traded goods sector as well as the sectoral orgn of the dsturbance. Our two-country, two-sectors model wth no departures from the law of one prce, mples that the real exchange rate can be expressed as a combnaton of the terms of trade and relatve prces of traded versus non-traded goods n the home and the foregn economy. In log-lnear terms we have: crs t = (v v ) ^T t + (! 1) ^R t + (1! ) ^R t (28) As n Bengno and Thoenssen (2003), we can decompose movements n the real exchange rate nto two channels: the home-bas channel, (v v ) ^T t where ^T represents the terms of trade (.e. the relatve prce of foregn to home-produced traded goods) n devaton from ts steady state value and (v v ) s the d erence between the home and foregn share of home-produced ntermedate nput n the traded component h of nal output; and what we call the nternal real exchange rate (! 1) ^R t + (1! ) ^R t where ^R and ^R are devatons from steady state of the relatve prce of non-traded to traded goods (P N =P T ) at home and abroad, respectvely. Ths expresson shows that by allowng for home bas, v > v the terms of trade enters drectly nto the dynamcs of the real exchange rate va the home bas channel. We start by consderng a framework n whch markets are complete as n Stockman and Tesar (1995) (see Fgures 1 and 2). In the top panel we show the percentage devaton of the real exchange rate, the nternal real exchange rate as well as the home bas channel followng a postve productvty shock to the traded goods sector n the presence of Arrow-Debreu securtes. The bottom panel shows the response of the relatve consumpton measured as a d erence between the log-devatons of Home and Foregn consumpton from ther steady state levels. Snce markets are complete, the real exchange rate and relatve consumpton are lnked by the followng rsk sharng condton (here n log-lnear terms): crs t = ^U C (C t ; (1 l t )) ^UC (C t ; (1 l t )): (29) Rsk-sharng equates the rato of margnal utltes of consumpton wth the real exchange rate. For most types of preferences, ths rsk-sharng relatonshp mples a cross-correlaton between the real exchange rate and relatve consumpton close to unty no matter what s the source of the dsturbance. Ths theoretcal result s llustrated n our gures 1 and 2. Fgure 1, whch corresponds to our baselne calbraton except for the shock matrces, shows the response of our model to a one percent devaton to traded sector productvty. 10

12 The home country enjoys the productvty ncrease and domestc consumpton rses. Foregn consumpton also rses. One reason s the presence of statecontngent bonds, whch transfer resources from Home to Foregn n the case of a Home productvty ncrease. Moreover, because the terms of trade deprecate n response to a postve domestc supply shock, purchasng power s further transferred from Home to Foregn agents. The net e ect on relatve consumpton s that home consumpton rses by more than foregn consumpton, causng relatve consumpton to rse. Snce relatve consumpton and the real exchange rate are lnked through the above rsk sharng condton, the real exchange rate apprecates as relatve consumpton rses. In gure 2 we do the same experment for a home productvty shock to the non-traded goods sector: as n the prevous example, home consumpton ncreases (because of the ncrease n the non-traded goods component) and rsksharng operates va a deprecaton of the real exchange rate that mproves the purchasng power of foregn consumers. In both cases the dynamcs of relatve consumpton are lnked to that of the real exchange rate va the rsk-sharng mechansm assocated wth Arrow-Debreu securtes. In both of these cases, the model wth Arrow-Debreu securtes generates cross-correlatons between the real exchange rate and relatve consumpton close to unty (relatve consumpton and the real exchange rate move n the same drecton). Ths behavor, whch s at odds wth the evdence reported n secton 2, s referred to as the Backus-Smth puzzle or the consumpton-real exchange rate anomaly. In our next experments we examne to what extent the removal of the assumpton of market completeness wll break the lnk between relatve consumpton and the real exchange rate. One consequence of the ncomplete nancal market structure s presence of current account dynamcs. For llustratve purposes, we rewrte our loglnearzed current account equaton for the case n whch there are no nvestment dynamcs and the steady-state net foregn asset poston s zero: ^b t = ^b t 1 + (1 )(v 1)! ^T t (30) +! (1 v) RS c t +!(v 1) ^Ct ^C t + ( )(! 1)!(v 1) ^R t +( ) (! 1)! (1 v) ^R t where ^b s the devaton of foregn currency-denomnated bond holdngs from ther steady state, relatve to domestc GDP. In a bond economy there are only lmted opportuntes for sharng rsk between countres. Non-state contngent bonds o er one avenue for rsk dvers caton. The other way to share rsk s through changes n the terms of trade. Followng a postve supply sde shock to the home economy, home agents become rcher and demand more goods of all types. As a rsk-sharng mechansm the terms of trade deprecate mprovng the purchasng power of foregn consumers. In a two-sector economy, a postve supply shock a ects two relatve prces: the terms of trade and the relatve prce of non-traded goods. If the supply shock occurs n the traded goods sector, the relatve prce of non-traded goods tends to ncrease - ths e ect s sometmes called the Balassa-Samuelson e ect - whch contrbutes towards an apprecaton of the real exchange rate and swtches demand from home non-traded to traded goods. The terms of trade on the other 11

13 hand stll deprecates thereby swtchng demand from foregn to home-produced traded goods. Fgures 3 and 4 show the response of our key varables followng a productvty shock to the Home traded ( gure 3) and Home non-traded ( gure 4) sectors. In our model and for our calbraton, the terms of trade deprecates (rses) followng a postve productvty shock to home-produced traded goods. Whereas an ncrease n productvty rases domestc output and consumpton, part of the ncrease n consumpton s shared wth foregn agents va the terms of trade deprecaton. In our model and calbraton, ths e ect s outweghed by an ncrease n the relatve prce of non-traded to traded goods, so that the real exchange rate apprecates n response to an ncrease n home traded sector productvty. Because rsk-sharng opportuntes are lmted, consumpton ncreases by more at Home than n Foregn. However, consumpton and the real exchange rate move n opposte drectons ndcatng a negatve cross-correlaton between the two varables. Both the rse n relatve consumpton, and the apprecaton of the real exchange rate contrbute towards an ntal current account de ct. When the source of the dsturbance arses n the non-traded goods sector the relatve prce of non-traded to traded goods and the terms of trade wll ncrease causng the real exchange rate to deprecate. For ths shock and calbraton, the current account mproves. In general, the response of the current account depends on both the response of relatve output and relatve prces. Fgure 4 suggests that predomnance of non-traded shocks wll result n large and postve cross-correlatons between relatve consumpton and the real exchange rate. In gure 5 we revew Char et al s (2002) ndngs: by settng! to 1 (.e. absence of non-traded goods) and = 0:984 as n ther calbraton. In ths case the only determnant of the real exchange rate s gven by the terms of trade (see equaton 28). On mpact a postve productvty shock n the Home economy wll mply a real exchange rate deprecaton caused by a relatve decrease n the prce of home produced goods. Because rsk-sharng opportuntes are lmted under ncomplete nancal markets, home consumpton rses by more than foregn consumpton. The mpled cross-correlaton between the real exchange rate and relatve consumpton s large and postve. [Fgures 1-5 about here] 6 Characterstcs of the calbrated model Havng analyzed the mpulse responses for = 0 and V [] = I, n ths secton, we analyze the second moments generated by our model usng the calbraton n table 2 for model parameters as well as shock processes. Table 3 summarzes a selecton of second moments from the data and compares these wth moments generated by the art cal model economes under d erent calbratons. Both the actual data, taken from Corsett, Dedola and Leduc (2004) as well as the art cal model economy data are of annual frequency, and logged as well as Hodrck-Prescott ltered. [Table 3 about here] The column headed baselne model n table 3 shows a selecton of second moments generated by our model under the calbraton proposed n table 2. The 12

14 numbers n the bottom rows of table 3 show that for our baselne calbraton our model generates a negatve correlaton between the real exchange rate and relatve consumpton. We also nd a large postve correlaton between the real exchange rate and the terms of trade, as suggested by the data. As ponted out above, our chosen calbraton s close to that proposed by Stockman and Tesar. The only parameter not usually determned n the lterature and one whch does not appear to have a counterpart n Stockman and Tesar s model s d the adjustment cost parameter n nvestment. The choce of d determnes, amongst other thngs, the volatlty of nvestment relatve to GDP. We chose a low value of d (1.00) to generate a relatvely volatle seres for aggregate nvestment. In the baselne model the standard devaton of nvestment s 3.08 tmes that of GDP. Ths value s slghtly above the one reported n the data by Stockman and Tesar (2.18) but below the one reported by Corsett et al (4.25). If nvestment s volatle, then so s GDP. As a result consumpton, employment, and to an lesser extent the real exchange rate, are all too smooth relatve to GDP as the rst ve reported statstcs of table 3 show. 7 8 Where our calbrated model fares better are the relatve volatltes of the real exchange rate and the terms of trade, as well as the cross-correlatons between GDP and net exports and as mentoned above, the cross-correlaton between the real exchange rate and, respectvely, relatve consumpton and the terms of trade. Two broadly accepted stylzed facts of nternatonal real busness cycles are that the trade balance s counter-cyclcal and that the correlaton between the real exchange rate and relatve consumpton s sgn cantly below unty, as evdence reported n table 1 suggests. Our model generates a correlaton between GDP and net exports of 0:30 and a correlaton between the real exchange rate and relatve consumpton of 0:65. Compared to the data, net exports are not qute as counter-cyclcal as n the data, whereas the model s predcton of the correlaton between relatve consumpton and the real exchange rate s towards the hgher end of evdence suggested n table 1. The correlaton between the real exchange rate and the terms of trade s 0:92. As n Stockman and Tesar consumpton s more hghly correlated wth ts foregn counterpart than s output, whch s n contrast to what s found n the data. Ths ndng s sometmes called the quantty anomaly. As n the data, we nd that employment s more correlated across borders than nvestment, but our generated correlatons are hgher than the data suggests. 7 Senstvty analyss In ths secton we examne how the propertes of our reported moments change when we alter some to the key parameters of the model. The column of table 7 For our symmetrc calbraton, the standard devaton of foregn varables are the same as that of home country varables. Hence we do not report statstcs for the foregn economy n table 3. 8 An alternatve calbraton strategy, followed by Char et al (2002) s to choose d so as to match the relatve volatlty of consumpton. As n Char et al, ths yelds an nvestment seres that s too smooth at around 1.5 tme the volatlty of GDP. The real exchange rate and the terms of trade, on the other hand, are more volatle than n our baselne calbraton. The cross-correlaton between the real exchange rate and relatve consumpton s stll negatve, the trade balance s stll counter-cyclcal and the terms of trade are postvely correlated wth the real exchange rate. 13

15 3 headed Arrow-Debreu reports the selecton of second moments for an economy wth a full set of state-contngent Arrow-Debreu securtes. We nclude ths spec caton to show that whereas ncomplete markets help to address the consumpton-real exchange rate anomaly, they do not do so at the expense of other moments of the model. Indeed, the real exchange rate s even less volatle under complete nancal markets than n our baselne model tmes as volatle as GDP as opposed to 2.91 tmes for the baselne model. As expected the correlaton between the real exchange rate and relatve consumpton s close to unty (0.94). 9 Next, we consder economes wth market ncompleteness. Consumpton home-bas s a well documented phenomenon whereby the share of home-produced traded goods n consumpton s greater at home than abroad. By assumng zero home-bas the real exchange rate can only devate from purchasng power party (PPP) through the presence of non-traded goods (see equaton 28). Equaton 28 shows that by allowng for home bas, v > v the terms of trade enters drectly nto the dynamcs of the real exchange rate. Assume the domestc economy s ht by a postve shock to ts traded ntermedate goods sector. Such a shock causes the domestc relatve prce of non-traded to traded goods to ncrease relatve to the foregn non-traded to traded prce rato,.e. h(! 1) ^R t + (1! ) ^R t < 0. Ths causes the real exchange rate to apprecate. At the same tme, such a shock lowers the prce of the domestcally produced ntermedate traded goods relatve to the prce of the foregn-produced ntermedate traded good, causng the terms of trade to deprecate. Ths deprecaton of the terms of trade partly o -sets the apprecaton of the real exchange rate. Thus for a gven supply shock to the traded goods sector, the real exchange rate apprecates less n the presence of consumpton home-bas, whch should lead to a hgher correlaton between the real exchange rate and relatve consumpton. The column headed Home-bas reports selected second moments for a calbraton assumng a hgher degree of home bas where v = 0:85 and v = 0:15. Ths calbraton s suggested by Char et al (2002). As our ntuton suggests the cross-correlaton between the real exchange rate and relatve consumpton rses - from 0:65 to 0:09: Because of the greater weght attached to the home bas channel n the determnaton of real exchange rate dynamcs, we observe that the real exchange rate s both more volatle and more hghly correlated wth the terms of trade. Next, we examne the role of the ntratemporal elastcty of substtuton between home and foregn produced goods,. Ths parameter determnes the degree to whch the terms of trade respond to supply shocks. The greater s, the more substtutable are home and foregn-produced traded ntermedate goods n the producton of nal goods. In the lmt, as becomes very large, the two types of tradable ntermedate goods wll be perfect substtutes wth a constant terms of trade. In the column headed = 0 :5 ( = 1 :5 ) we examne the consequences of changng form ts baselne value of 1.00 to 0.5 and 1.5 (values n brackets). As noted above, the volatlty of the terms of trade relatve to the volatlty of GDP vares nversely wth. The real exchange rate becomes more (less) volatle the hgher (lower) s relatve to the baselne case. For the lower value of, the correlaton of the real exchange rate and relatve consumpton s 9 Only when preferences are addtvely separable n consumpton and lesure or when labour supply s completely nelastc, does the correlaton equals

16 about zero. For the hgher value of the correlaton decreases relatve to the baselne to 0:87. The remanng moments are not greatly a ected by varyng. The column headed = 0 :74 explores an alternatve calbraton of the ntratemporal elastcty of substtuton between traded and non-traded goods. The value we use n our baselne calbraton s that estmated by Stockman and Teasar (1995). Ther estmate s based on a sample of developed as well as developng countres. Mendoza (1991) provdes an estmate of ths elastcty for a sample of ndustralzed countres, whch s somewhat hgher at = 0:74. Our analyss suggests that a hgher ntratemporal elastcty of substtuton between traded and non-traded goods results n a lower relatve volatlty of the real exchange rate and the terms of trade, but leaves most of the other varables of nterest relatvely unchanged. Indeed, the correlaton between the real exchange rate and relatve consumpton s even more negatve under ths calbraton. The column headed! = 0 :5 explores an alternatve calbraton of the share of traded ntermedate goods n the nal good. Equaton (28) shows that! and! determne the weght attached to devatons from steady state of the nternal real exchange rate, h(! 1) ^R t + (1! ) ^R t, n the dynamcs of the real exchange rate. A pror one would expect that a larger! reduces the n uence of ths real exchange rate channel thereby reducng the overall volatlty of the real exchange rate. Table 3 con rms ths presumpton. For the hgher value of! we observe a declne n the volatlty of the real exchange rate and the terms of trade. The cross-correlatons between the real exchange rate and relatve consumpton on the one hand, and the terms of trade on the other, do not change sgn cantly under ths calbraton, compared to the baselne. We argue n the ntroducton that one of the reasons Char, Kehoe and McGrattan (2002) nd such a hgh cross-correlaton between the real exchange rate and relatve consumpton n ther bond economy model s the omsson of non-traded goods. The column headed Char et al tests ths proposton. We present a calbraton that approxmates that of Char et al. Frst, Char et al s model does not have a non-traded ntermedate goods sector. To capture ths n our model we set the share of traded ntermedate nputs n nal goods producton equal to unty,.e.! =! = 1: Next, we rewrte the shock processes n such a way that the varance and autocorrelaton of non-traded shocks s zero and any spll overs only take place between the home and foregn traded goods sectors. 10 We also set the degree of home-bas as n Char et al, v = 1 v = 0:984. Ths calbraton produces a cross-correlaton between the real exchange rate and GDP of 0:81. The most of the remander of the moments are close to those of our baselne model, except for the relatve volatlty of the real exchange rate and the terms of trade whch are now substantally less volatle than GDP : The autocorrelaton matrx becomes: = 6 0 0: and the varance covarance matrx: V [] = 6 4 3:62 1: :21 3:

17 8 Concluson In ths paper, we address the consumpton-real exchange rate anomaly. Ths anomaly refers to the propensty of nternatonal busness cycle models based on complete nancal markets to generate cross-correlatons between the real exchange rate and relatve consumpton close to unty. In the data, ths correlaton s close to zero or even negatve. We show that f a canoncal nternatonal busness cycle model, smlar to the one proposed by Char et al (2002) ncludes both an ncomplete nancal markets structure as well as a non-traded goods sector, then such a model, calbrated n a standard way wll generate crosscorrelatons between the real exchange rate and relatve consumpton close to those n the data. The presence of a non-traded goods sector allows the real exchange rate to apprecate (decrease) n response to a productvty shock to the domestc traded goods sector - the famlar Balassa-Samuelson e ect - whle lmted rsksharng opportuntes cause consumpton n the domestc economy to ncreases by more than consumpton n the foregn economy followng such a shock. The result s a negatve cross-correlaton between the real exchange rate and relatve consumpton. References [1] Backus, D. K. and Smth, G. W. (1993). Consumpton and real exchange rates n dynamc economes wth non-traded goods. Journal of Internatonal Economcs, Vol. 35, pages [2] Bengno, G. and Thoenssen, C. (2003). Equlbrum exchange rates and supply sde performance. Economc Journal, Vol. 113, no. 486, pages C [3] Bengno, P. (2001). Prce stablty wth mperfect nancal ntegraton. New York Unversty, mmeo. [4] Char, V. V., Kehoe, P. J. and McGrattan, E. R. (2002). Can stcky prce models generate volatle and persstent real exchange rates? Revew of Economc Studes, Vol 69, pages [5] Corsett, G., Dedola, L. and Leduc, S. (2004). Internatonal rsk sharng and the transmsson of productvty shocks. ECB workng paper seres, No [6] Engel, C. (1999). Accountng for US real exchange rate changes. Journal of Poltcal Economy, Vol. 107, No. 3, pages [7] Ghron, F. and Meltz, M.J. (2004). Internatonal trade and macroeconomc dynamcs wth heterogeneous rms. Mmeo, Boston College and Harvard Unversty. 16

18 [8] Kng, R. and Watson, M. (1998). The soluton of sngular lnear d erence systems under ratonal expectatons. Internatonal Economc Revew, Vol. 39, No. 4, pages [9] Kollmann, R. (1995). Consumpton, real exchange rates, and the structure of nternatonal captal markets. Journal of Internatonal Money and Fnance, Vol. 14, pages [10] Mendoza, E. (1991). Real busness cycles n a small open economy. Amercan Economc Revew, Vol. 81, no. 4, pages [11] Ravn, M. O. (2001). Consumpton dynamcs and real exchange rates. CEPR Dscusson Paper, No [12] Schmtt-Grohé, S. and Urbe, M. (2003). Closng small open economy models. Journal of Internatonal Economcs, Vol. 61, pages [13] Selave, J. D. and Tuesta, V. (2003). Net foregn assets and mperfect passthrough: the consumpton-real exchange rate anomaly. Board of Governors of the Federal Reserve System, Internatonal Fnance Dscusson Papers, No [14] Stockman, A. C. and Tesar, L. L. (1995). Tastes and technology n a twocountry model of the busness cycle: explanng nternatoanl comovements. Amercan Economc Revew, Vol. 85, No.1, pages A Summary of equatons In ths appendx, we lst all the equatons of the model n the order n whch they appear n our code. Home and foregn euler equatons, the UIP condton, home and foregn consumpton-labor e ort trade-o and current account: l E t ^Ct+1 + E t 1 l ^l t+1 = ^C l t + 1 l ^l t + ^{ t E t t+1 (A1) l E t ^C t+1 + E t 1 l ^l t+1 = ^C t l + 1 l ^l t + ^{ t E t t+1 (A2) E t ^s t+1 = ^{ t ^{ t + "^b t (A3) l ^C t + ^w t = 1 l ^l t (A4) ^C t + ^w t l = 1 l ^l t (A5) 17

19 (1 + a")^b t = ^b t 1 + a ( t + s t t ) + (1 )(v 1) ^T t (A6) + ( v!) c RS t +!(v 1) ^Y t + [ v!] ^Y t +(! 1) ((1 )!(v 1) + (1 ) [ v!]) ^R t +( ) (! 1) [ v!] ^R t The rms optmalty condtons for nvestment, captal and labor nput n traded and non-traded sectors home... l E t ^Ct+1 + E t 1 l ^l t+1 = ^C l t + 1 l ^l t (A7) h +(1 + ( 1)) ^w t+1 + ^l Ht+1 ^kht b h^x Ht ^kht 1 + b h^x Ht+1 ^kht l E t ^Ct+1 + E t 1 l ^l t+1 = ^C l t + 1 l ^l t (A8) h +(1 + ( 1)) ^w t+1 + ^l Nt+1 ^knt b h^x Nt ^knt 1 + b h^x Nt+1 ^knt b kht = (1 ) b k Ht 1 + bx Ht (A9) b knt = (1 ) b k Nt 1 + bx Nt (A10) ^w t = (v 1) ^T t + (! 1) ^R t + ^A Ht + ( 1)^l Ht + (1 )k Ht 1 (A11)...and foregn ^w t =! ^R t + ^A Nt + ( 1)^l Nt + (1 )k Nt 1 (A12) l E t ^C t+1 + E t 1 l ^l t+1 = ^C t l + 1 l ^l t (A13) h +(1 + ( 1)) ^w t+1 + ^l Ft+1 ^k Ft b h^x Ft ^k Ft 1 + b h^x Ft+1 ^k Ft l E t ^C t+1 + E t 1 l ^l t+1 = ^C t l + 1 l ^l t (A14) h +(1 + ( 1)) ^w t+1 + ^l Nt+1 ^k Nt b h^x Nt ^k Nt 1 + b h^x Nt+1 ^k Nt 18

20 ^k F t = (1 )^k Ft 1 + ^x Ft (A15) ^k N t = (1 )^k N t 1 + ^x N t (A16) ^w t = v ^T t c RSt + (! 1) ^R t + ^A Ft + ( 1)^l Ft + (1 )^k Ft 1 (A17) ^w t =! ^R t + ^A N t + ( 1)^l N t + (1 )^k N t 1 (A18) Producton constrants - home... (v 1) T b t +!v Y b v! h t + RS c t + Y b t!v v! + (1!) + (1!) ^R t v! + ( )(! 1) ^R t = (1 ) b k Ht 1 + b l Ht + A b Ht! ^R t + ^Y t = (1 ) b k Nt 1 + b l Nt + A b Nt (A19) (A20) and foregn v ^T (1 v)v! h t +!(1 v)v + (1 v ) [ v!] " (1 v ) [ v!] +!(1 v)v + (1 v ) [ v!] = (1 ) k c F t (! 1) ^R t + ^Y t ( )(! 1) ^R t (! 1) ^R t + RS c t + ^Y t + b 1 lf + b t A Ft! ^R t + ^Y t = (1 ) b k N t 1 + b l N + b A t N t # (A21) (A22) Economy wde constrants where x NY ^Y t = C Y ^C t + x H Y ^x Ht + x H Y ^x Nt x HY = = 1 1= (1 ) 1 1= (1 ) (1!) (A23) 19

21 where ^Y t C = Y ^C t + x F Y ^x F t + x N Y ^x N t x F Y = 1!(1 v)! v +! (1 v )( v!) 1= (1 ) ( v!) x N Y = 1 (1! ) 1= (1 ) (A24) where ^lt = l Hl ^lht + l Nl ^lnt lnl = lhl = 1! 1 + a( 1)! + a( 1) 1 + a( 1) (A25) where l Nl = l Fl = 1 ^l t = l F l ^lht + l N l ^l Nt (1! ) [(1 v)! + a( 1)] (1! v ) [(1 v)! + a( 1)] +!(1 v)v! (1! ) [(1 v)! + a( 1)] (1! v ) [(1 v)! + a( 1)] +!(1 v)v! The real exchange rate and the terms of trade (A26) crs t = (v v ) ^T t + (! 1) ^R t + (1! ) ^R t (A27) ^T t = ^T t 1 + s t + F t H t (A28) In aton when monetary authortes n both countres set producer n aton to zero: t =!(1 v) F t +!(1 v)s t (A29) t =! v H t! v s t (A30) where H t = F t = 1! h ^AH;t ^A N;t!v + (1!) (1! ) h ^AF;t! (1 v ) + 1! ^A N;t (A31) (A32) A31 and A32 are derved by settng equatons (16) and (21) from the text equal to one another, dvdng by the lagged value of the resultng expresson and lnearsng. We make use of the fact that f the two sectors have the same labour ntensty, they wll have the same captal - e ectve labor rato. 20