Borders and Nominal Exchange Rates in Risk-Sharing

Transcription

1 Borders and Nominal Exchange Raes in Risk-Sharing Michael B. Devereux and Vikoria V. Hnakovska Sepember 25, 2018 Absrac Models of risk-sharing predic ha relaive consumpion growh raes are posiively relaed o changes in real exchange raes. We invesigae his hypohesis using a new muli-counry and muli-regional daa se. Wihin counries, we find evidence for risk-sharing: episodes of high relaive regional consumpion growh are associaed wih regional real exchange rae depreciaion. Across counries however, he associaion is reversed: relaive consumpion and real exchange raes are negaively correlaed. We define his reversal as a border effec. We find he border effec and show ha i accouns for over half of he deviaions from full risk-sharing. Since cross-border real exchange raes involve differen currencies, i is naural o ask how much of he border effec is accouned for by movemens in exchange raes. Our measures indicae ha a large par he border effec comes from nominal exchange rae flucuaions. We develop a simple open economy model ha is consisen wih he imporance of nominal exchange rae variabiliy in accouning for deviaions from cross-counry risk-sharing. JEL Classificaion: F3, F4 Keywords: Real exchange rae, risk sharing, border effec, inranaional economics 1 Inroducion Many sudies have documened he failure of naive models of consumpion risk-sharing. This is rue boh wihin counries (risk-sharing across provinces or saes) and across counries. Recognizing ha consumpion prices differ across ime and locaions leads o a more elaborae es for We are graeful o Margarida Duare, Charles Engel, and paricipans a various conferences and seminars for commens and suggesions. We also hank Marco del Negro for kindly sharing sae-level consumpion and price daa for he US wih us. Maias Cores provided excellen research assisance. Devereux hanks Social Sciences and Humaniies Research Council of Canada (SSHRC), he Bank of Canada, and he Royal Bank of Canada for financial suppor. Hnakovska hanks SSHRC for research suppor. The opinions expressed in his paper are hose of he auhors alone and canno be ascribed o he Bank of Canada. This is a compleely revised version of our earlier paper iled "Consumpion Risk Sharing and he Real Exchange Rae: Why Does he Nominal Exchange Rae Make Such a Difference?" and is an exension of our earlier working paper "Inernaional and Inra-naional Real Exchange Raes: Theory and Evidence". An online appendix o he paper is available from he auhors webpages. Deparmen of Economics, Universiy of Briish Columbia, 6000 Iona Drive, Vancouver, BC V6T 1L4, Canada; CEPR; NBER. address: devm@mail.ubc.ca. Deparmen of Economics, Universiy of Briish Columbia, 6000 Iona Drive, Vancouver, BC V6T 1L4, Canada. address: hnakovs@mail.ubc.ca. 1

2 consumpion risk-sharing, incorporaing boh wihin and beween-counry real exchange rae movemens. This exended model predics ha relaive consumpion growh raes (across regions or counries) are highly posiively correlaed wih movemens in real exchange raes. In inernaional daa, i is well known ha his predicion is srongly refued. This is essenially he well-known Backus-Smih puzzle (Backus and Smih, 1993). The evidence in fac seems o indicae ha relaive consumpion and real exchange raes are negaively correlaed across counries. Numerous recen sudies have aemped o raionalize he source of his failure of he basic model of inernaional risk-sharing. 1 To assess he failure of full inernaional risk-sharing in he daa i is criical o develop a benchmark for comparison. The degree of wihin-counry risk-sharing provides a simple and modelfree benchmark. In his paper we revisi he relaionship beween relaive consumpion and real exchange raes by focusing on he conras beween risk-sharing wihin counries and beween counries. Alhough previous sudies have noed he subsanial differences in measures of risksharing wihin and across counries (see Hess and Van Wincoop (2000) for an overview), here has been lile invesigaion of he predicions of risk-sharing for he consumpion-real exchange rae relaionship wihin counries. Our paper, o our knowledge, provides he firs comprehensive evidence on his wihin-counry relaionship. We use a new muli-counry and muli-regional daa se on consumpion and prices indices. We find a sharp dichoomy beween wihin-counry and across-counry comparisons. Across counries, as in previous sudies, we find ha relaive consumpion growh and real exchange raes are negaively correlaed. Wihin-counry, however, relaive consumpion growh and real exchange raes end o be posiively correlaed, as implied by sandard models of risk-sharing. Because our measures links a large number of bilaeral locaions wihin and beween counries, we can idenify a border effec in he consumpion-real exchange rae relaionship, similar o he border effec Engel and Rogers (1996). Our firs main resul is ha he border effec reverses he sign of he consumpion-real exchange rae relaionship. Wha accouns for he border effec? Cross-border real exchange raes involve differen currencies, so an obvious candidae explanaion is ha cross-counry real exchange raes behave in a differen way han wihin-counry real exchange raes due o flucuaions in he nominal exchange rae. 2 Following his logic, and using observed nominal exchange raes, we can decompose he border effec ino ha accouned for by he nominal exchange rae, and a residual, orhogonal o exchange rae movemens. We find ha movemens in he nominal exchange rae accoun for a large par of he consumpion-real exchange rae relaionship. 1 See, for insance, Obsfeld (2007), Chari, Kehoe, and McGraan (2002), Corsei, Dedola, and Leduc (2008), Benigno and Thoenissen (2008), Kollmann (2012) and ohers. 2 An exensive lieraure in open economy macroeconomics, going back a leas o Mussa (1986), has emphasized he large and puzzling behaviour of nominal exchange raes in accouning for real exchange rae variabiliy. Recen papers by Hadzi-Vaskov (2008) and Hess and Shin (2010) relae he anomalous findings on he consumpion-real exchange rae relaionship o he movemens of he nominal exchange rae. They show ha in OECD counries, he negaive correlaion beween relaive consumpion and real exchange raes is proximaely accouned for by movemens in nominal exchange raes. We discuss hese papers more exensively below. 2

3 Since he negaive cross-border correlaion of consumpion and real exchange raes is o a large exen accouned for by he nominal exchange rae, could eliminaing nominal exchange rae variabiliy improve risk-sharing oucomes? This conclusion does no necessarily follow. Crossborder comparisons are almos always associaed wih some nominal exchange rae movemens. A negaive consumpion-real exchange rae correlaion may be an implicaion of naional borders, bu in fac independen of exchange rae policy. 3 One way o invesigae his is o ake cross-border pairs which exhibi lile exchange rae variabiliy, and compare heir properies wih hose cross-border pairs whose exchange rae is freely floaing. Our sample includes boh Germany and Spain, which since 1999 have had no bilaeral nominal exchange rae variabiliy, and in fac even before his, o he beginning of he sample (1995), had very small bilaeral nominal exchange rae volailiy. We find ha he consumpion-real exchange rae correlaion for Germany-Spain bilaeral pairs is posiive, while i remains negaive and significan beween all oher bilaeral pairs. We hen furher exend his exercise o a se of 12 Eurozone counries and conras he consumpion-real exchange rae correlaion among hem during he pre-euro period and euro-period. We show ha he average bilaeral correlaion is overwhelmingly negaive for all counries, excep Greece, in he pre-euro period of , equal o across all 12 counries. Imporanly, he correlaion urns posiive for he majoriy of counries afer he inroducion of he Euro. In wo ou of four counries where he correlaion remained negaive (France and Ialy), is value significanly increased relaive o he pre-euro period. Overall, he average pos-euro correlaion across counries is posiive This offers some evidence for he imporance of he nominal exchange rae regime iself, as opposed o indirec effecs of naional borders, in deermining he consumpion-real exchange rae correlaion. How much does he border conribue o he failure of consumpion risk-sharing, aking accoun of boh wihin and beween counry real exchange rae movemens? We address his quesion by compuing a cross-secion of deviaions from full risk-sharing beween all bilaeral locaions, over he whole sample. Our previous resuls sugges ha his should be posiively correlaed wih he presence of a naional border. Indeed we find ha he border accouns for 53 percen of he deviaion from full risk-sharing across regions. To evaluae he conribuion of he nominal exchange rae o he border effec we compue a proxy real exchange rae assuming ha he nominal exchange rae is equal o he sample average for all bilaeral pairs. We find ha in his case he border effec on he risk-sharing measure declines by one-hird, suggesing a non-rivial role for he nominal exchange rae in explaining he deviaions from full risk-sharing. Can hese findings be reconciled wih sandard models of real exchange rae deerminaion? A subsanial lieraure argues ha he presence of incomplee financial markes may explain why relaive consumpion growh and he real exchange rae co-vary negaively in he daa. See, for insance, Corsei, Dedola, and Leduc (2008) and Benigno and Thoenissen (2008). However, for he mos par, his lieraure offers no explici role for he nominal exchange rae regime in resolving 3 This is reminiscen of he Sockman (1987) argumen ha real exchange rae volailiy may be deermined by changes in real fundamenals which are only realized following changes in exchange rae regimes. 3

4 he puzzle. 4 Bu, if nominal goods prices are sicky, he correlaion of relaive consumpion and he real exchange rae may depend on he degree of nominal exchange rae flexibiliy. However, many sicky price models (e.g. Clarida, Gali, and Gerler, 2002; Devereux and Engel, 2003) exhibi volaile real and nominal exchange raes, bu sill have he implicaion ha he cross counry risk sharing condiion beween consumpion and real exchange raes holds exacly if financial markes are complee. Our model combines feaures of he previous lieraure on he Backus-Smih puzzle wih a wo counry New Keynesian model wih gradual price adjusmen. We also inroduce heerogeneous regions wih wo secors (radable and nonradable) wihin each counry o sudy inra-naional risk-sharing and is deerminans. Across counries he model admis flexible or fixed exchange rae regime. We hen posi wo key quesions o he model: (i) wheher his model exhibis he propery ha inra-naional risk-sharing is higher han inernaional risk-sharing; (ii) wheher he sign of he consumpion-real exchange rae correlaion across counries depends upon he exchange rae regime. We find ha when he model is calibraed using sandard parameers, and here exiss a degree of rule of humb pricing, as in Gali and Gerler (1999), he empirical findings above can be raionalized. Wihin counries, he model predics a consisenly posiive consumpion-real exchange rae correlaion, bu i is far from he complee markes implicaion of a uni correlaion. However, his correlaion rises in he presence of endogenous fiscal ransfers across regions wihin a counry and higher co-movemen beween produciviy shocks wihin counries. For he inernaional correlaion, he key insigh ha he model brings is ha when he exchange rae is flexible, raded goods produciviy shocks can lead boh he nominal and real exchange rae and relaive consumpion o move in differen direcions. Nonraded produciviy shocks produce a posiive correlaion beween relaive consumpion and he real exchange rae. Since he raded produciviy shocks are larger in he daa and in our calibraion, he uncondiional cross-counry consumpion-real exchange rae correlaion is negaive under he flexible exchange dae regime. When he exchange rae is fixed, he impac on he real exchange rae is significanly dampened, and more so following raded produciviy shocks. In our baseline model, he difference is enough o reverse he sign of he cross-counry consumpion-real exchange rae correlaion when nominal exchange raes are held fixed. Rule of humb behavior in price seing is criical however. The reason is ha he sandard model, specified according o he Calvo price seing mechanism wih full forward looking pricing, allows for oo much immediae price response. Even consequen upon fixing he exchange rae, in he Calvo model, prices respond suffi cienly flexibly ha he real exchange rae-relaive consumpion correlaion is lile changed when comparing floaing and fixed exchange raes. Wih rule of humb 4 Mos proposed resoluions emphasize he join role of incomplee markes and shocks which generae srong income effecs. The inuiion is ha a counry which has a faser growing consumpion experiences an appreciaing real exchange rae. Bu when we exend he anomaly o encompass boh regions wihin a counry, and he imporance of he nominal exchange rae, hese explanaions are no complee, since in hese models, he nominal exchange rae has no implicaion for he consumpion-real exchange rae correlaion. These models would predic ha consumpionreal exchange rae correlaion is he same across counries and across regions wihin counries. 4

5 pricing, as in Gali and Gerler (1999), prices show much less iniial response o shocks, and in he calibraed benchmark model, his leads o a subsanial difference in he consumpion-real exchange rae correlaion beween fixed and floaing exchange raes. 5 As menioned above, our analysis is relaed o an exensive recen lieraure on inernaional risk-sharing and he real exchange rae. The mos closely relaed papers are hose by Hadzi-Vaskov (2008) and Hess and Shin (2010) who invesigae he sources of he Backus-Smih puzzle in crosscounry daa. Hadzi-Vaskov (2008) shows ha movemens in he nominal exchange rae conribue significanly o he negaive consumpion-real exchange rae correlaion in a sample of Eurozone counries. Hess and Shin (2010) reach he same conclusion in a sample of OECD counries. Our paper builds on heirs, bu differs in several respecs. In paricular, by using inra-naional daa for numerous counries, we can define a border effec in he relaionship beween consumpion and real exchange raes. 6 In addiion, in our analysis we employ several decomposiion approaches ha allow us o robusly assess and quanify he role played by he border and he nominal exchange rae in he deviaion from risk-sharing. Finally, we provide an explici heoreical analysis of our resuls. The res of he paper is organized as follows. The nex secion presens he empirical evidence on he role of he nominal exchange rae in he consumpion-real exchange rae relaionship. In Secion 3 we develop models wih sicky prices o inerpre our empirical findings. Secion 4 concludes. 2 Esimaing he border effec 2.1 Key heoreical relaionship Consider a muli-jurisdicion (where a jurisdicion may be a counry or region) sochasic model. The uiliy of a represenaive household in jurisdicion j = 1,.., J is given by: E β s U(C j,+s ), β < 1 s=0 where β is he subjecive discoun facor, C j, denoes a composie consumpion good in counry j. 7 E is period- expecaion. Define P j, o be he price of a represenaive consumpion baske 5 This resul is very similar o he well known criique of he Calvo model ha i allows oo much variabiliy in inflaion in response o new informaion - see Gali and Gerler (1999), Gali, Gerler, and Lopez-Salido (2001), McAdam and Willman (2004), and Chrisiano, Eichenbaum, and Evans (2005). Alernaive approaches o inroducing sluggishness in inflaion response, such as Mankiw and Reis (2002), or Chrisiano, Eichenbaum, and Evans (2005), who assume ha prices mus be se before curren informaion on shocks is released, would produce very similar resuls o hose we find below. 6 Hess and Shin (2010) esimae he consumpion real exchange rae correlaion in inra naional daa for he US saes only. Therefore, hey can no conras heir findings direcly wih he inernaional evidence o isolae he role of he border. 7 I is possible ha he consumpion real exchange rae relaionship is affeced by counry or region-specific preference shocks which direcly aler he marginal uiliy of consumpion, apar from consumpion iself. As in mos of he lieraure, we absrac from such shocks, since hey are unobservable, and allow for a raionalizaion of a consumpion-real exchange rae correlaion of any sign or size. 5

6 in jurisdicion j in period. Also le S i,j be he exchange rae ha convers prices from counry j s currency o counry i s currency in period. If jurisdicions are wihin he same counry, hen S i,j = 1. Then he real exchange rae beween any wo regions i and j in differen counries is given = S i,j P j, /P i,, or RER j,i = P j, /P i, if i and j are wo regions in he same counry. Suppose ha here is a complee se of sae-coningen securiies available o households in all by RER j,i counries. In his case, he key opimaliy condiion is o equae marginal uiliies of consumpion across counries (or regions), adjused for differences in price levels, evaluaed in a common currency: U c (C i, )RER j,i = U c (C j, ). (2.1) This equaion mus hold in every dae and sae of he world, beween any wo counries or regions i and j. I says ha in equilibrium, consumpion beween households i and j mus be allocaed in a way ha marginal uiliy (convered ino he same unis using he real exchange rae) is equalized across counries. Then if uiliy is of a consan relaive risk aversion (CRRA) form, wih he coeffi cien of relaive risk aversion σ, equaion (2.1) becomes ( Ci, C j, ) σ = RER j,i, or equivalenly in logs σ (ln C i, ln C j, ) = ln RER j,i. Following Backus and Smih (1993) we wrie he expression above in growh raes: σ ( ln C i, ln C j, ) = ln RER j,i, (2.2) where ln X i, = ln X i, ln X i, 1. We should noe ha aking firs-differences provides a naural de-rending of he consumpion and real exchange rae variables. We also use he Hodrick-Presco (HP) filer o de-rend he variables, as in Corsei, Dedola, and Leduc (2008). This provides us wih a robusness check as i allows us o focus on variaions a business cycle frequency. We find ha all resuls remain robus o his alernaive de-rending, and herefore in wha follows we focus on he resuls in growh raes as hey correspond he closes o he approach in Backus and Smih (1993). 8 These expressions esablish he close relaionship beween he real exchange rae and relaive consumpion beween jurisdicions i and j. In paricular, equaion (2.2) implies ha consumpion growh beween 1 and should be relaively higher in jurisdicions whose real exchange raes depreciae during he same period. Therefore, if markes are complee, he correlaion, ρ e,cj /c i = corr( ln RER j,i, σ ln C j, C i, ), should be equal o 1, as poined ou by Backus and Smih (1993) and Kollmann (1995). A version of condiion (2.2), defined in erms of condiional expecaions, will also hold even under incomplee markes, so long as some financial asses can be raded across 8 The esimaion resuls wih HP-filered daa are provided in he online appendix. 6

7 counries (see e.g. Obsfeld and Rogoff (1996)). Noice ha if relaive purchasing power pariy (PPP) holds, so ha real exchange rae is consan, hen ln RER j,i = 0. In his case we ge a sandard risk-sharing resul ha consumpion growh raes should be equal across jurisdicions. This simple implicaion has been esed exensively in he cross-counry conex in Asdrubali, Sørensen, and Yosha (1996), Ahanasoulis and van Wincoop (2001), Bayoumi and Klein (1997), Hess and Shin (1998), Del Negro (2002), Van Wincoop (1995), Crucini (1999), and ohers. 2.2 Empirical facs Equaion (2.2) gives us he key esable relaionship implied by he model. As is clear from (2.2), he condiion can be applied o any wo locaions of ineres: counries, regions, saes/ provinces/ prefecures, ec. We use his relaionship o sudy he exen of naional and regional risk-sharing beween he US, Canada, Germany, Japan and Spain. 9 We employ inra-naional daa on consumpion, oupu and prices in 50 US saes during , 12 Canadian provinces and erriories during , 47 Japanese prefecures over period, 16 German bundeslaender over period, and 18 auonomous communiies in Spain over period. 10 Using his daa we compue all possible unique bilaeral pairs of differences beween consumpion, price and oupu growh raes. The summary saisics for our daase are repored in Appendix A.2. To simplify noaion we will use c i,j o denoe relaive consumpion growh beween wo locaions i and j, so ha c i,j = ln C i, ln C j, ; and e j,i o denoe real exchange rae growh beween locaions i and j, so ha e j,i = ln RER j,i. Then based on equaion (2.2) we posi he following specificaion o link relaive consumpion growh and real exchange rae growh: c i,j = β 0 + β 1 e j,i + β 2 ( e j,i border i,j ) + v i,j, where v i,j is he error erm arising due o preference shocks, measuremen error, ec. 11 border i,j is he border dummy ha akes value of one for all cross-border locaion pairs, and zero oherwise. This allows us o disinguish beween cross counry risk sharing and wihin counry risk sharing. This specificaion resrics he relaionship beween he real exchange rae and relaive consumpion o be he same for any wo locaions wihin counries or any wo locaions across counries. However, i is plausible o posi ha he same change in he real exchange rae could be associaed wih differen movemens in relaive consumpion depending on he paricular locaions observed. For insance, here may be differences in he degree of openness in goods or financial markes 9 In he online appendix we also sudy he US and Canada separaely since hese wo counries are ofen he focus of he sudies of risk-sharing and he law of one price deviaions (see Engel and Rogers (1996), Gorodnichenko and Tesar (2009)). 10 These are he counries for which hisorical jurisdicion-level daa on consumpion and prices exis. For he US we use reail sales o proxy for privae consumpion. Consumpion and GDP are real and in per capia erms. Deails on daa sources and series consrucion are provided in he Appendix A Noe ha his equaion is no lierally a es of (2.2), since ha specificaion implies ha he relaionship holds exacly. Bu exending he model o incomplee markes (as shown in secion 3 below) implies ha he relaionship beween consumpion and he real exchange rae holds only in condiional expecaion. This can be used as more direc moivaion for he regression specificaion here. 7

8 beween wo jurisdicions ha are no refleced in changes in he real exchange rae. Disance represens a naural explanaory variable in he sudies of he deviaions from he law of one price beween locaion pairs. In erms of deviaions from risk sharing, disance may seem somewha less compelling, since a) i may already be incorporaed in he movemen in real exchange raes, and b) i is a consan, and may no affec he risk sharing relaionship when measured in growh raes. Neverheless, some sudies (e.g. Pores and Rey (2005), Okawa and van Wincoop (2010)) have documened he explanaory power of graviy ype variables in accouning for inernaional financial aciviy. To allow for his, we hus amend he basic relaionship so as o allow for a disance measure, as in he graviy lieraure. Our benchmark model specificaion hus becomes c i,j = β 0 + β 1 e j,i + β 2 ( e j,i border i,j ) + β 3 e j,i ln d i,j + v i,j, (2.3) where ln d i,j is he normalized log disance beween any wo locaions i and j, defined as ln d i,j = ln d i,j ln d i,j. Here d i,j is he disance beween locaions i and j, which we proxy using he disance beween he capial ciies of various jurisdicions; while ln d i,j is he average log disance beween all cross-border pairs. 12 This normalizaion implies ha ln d i,j is equal o zero a ln d i,j = ln d i,j, and simplifies inerpreaion of he β 2 coeffi cien, which now expresses he average effec of he border for he consumpion-real exchange rae relaionship beween any wo locaions ha are ln d i,j kilomeers away. The ineracion erm beween he real exchange rae and disance allows he relaionship beween c i,j and e j,i o change monoonically wih he disance. In all regressions sandard errors are clusered a he counry-pair level. Table 1: Esimaes of Border Effec Pooled Fixed effecs Pooled Fixed effecs (i) (ii) (iii) (iv) e j,i 0.349*** 0.373*** 0.275*** 0.298*** (0.085) (0.064) (0.062) (0.046) e j,i border i,j *** *** *** *** (0.081) (0.063) (0.060) (0.049) e j,i ln d i,j (0.013) (0.020) (0.013) (0.019) y i,j 0.169*** 0.161*** (0.024) (0.027) y i,j border i,j (0.036) (0.038) y i,j ln d i,j (0.028) (0.031) e j,i + ej,i border i,j (0.013) (0.016) (0.013) (0.017) N Noes: The dependen variable is relaive consumpion growh beween locaions i and j, c i,j. The esimaed specificaion in columns (i)-(ii) is equaion (2.3); while in columns (iii)-(iv) i is equaion (2.4). Sandard errors are clusered a he counry-pair level and are repored in parenheses. *,**, and *** indicae significance a 10%, 5%, and 1%, respecively. Our findings from he pooled OLS and fixed effecs esimaion of equaion (2.3) are presened in 12 We measure disance in kilomeers. 8

9 columns (i) and (ii) of Table The resuls in column (i) indicae ha he condiional correlaion beween he growh raes of real exchange rae and relaive consumpion wihin our sample of counries is posiive and significan, equal o 0.35 on average. Hence, wihin counries, he risk-sharing relaionship beween relaive consumpion and real exchange raes (which are cross jurisdicional differences in raes of CPI inflaion) holds quie srongly regions wih higher relaive consumpion growh exhibi depreciaing relaive cross-jurisdicional real exchange raes. Bu when we inerac real exchange rae changes wih he border, he esimaed border coeffi cien is negaive. I is also large and economically significan. In fac, due o his effec, he consumpion-real exchange rae correlaion across counries urns negaive, equal o on average, alhough his correlaion is no significanly differen from zero. Taking equaion (2.2) as our basic heory of risk-sharing, hese resuls sugges ha relaive prices faciliae risk-sharing wihin counries, bu impede risk-sharing across counries. The esimaes in column (ii) obained from he fixed effecs regression confirm his finding. 14 How sensiive are hese resuls o he assumpion of complee access o capial markes? Many sudies of risk-sharing, boh inra-naional and inernaional, have relaxed his assumpion and posied he alernaive specificaion in which a leas a fracion of consumers do no make consumpion plans based solely on ineremporal opimizaion, bu may alernaively follow rules of humb, or in fac have no abiliy o borrow and lend a all. 15 To allow for his, we exend our framework o encompass limied capial marke paricipaion. Say ha a fracion of households are hand-o-mouh consumers ha is hey are resriced o consume only heir curren income. The esable implicaion of such a modified model is ha relaive consumpion growh of hese hand-o-mouh consumers living in any wo locaions follows heir relaive income growh. Le y i,j = ln Y i, ln Y j, denoe he relaive income growh beween locaions i and j a ime. Then he relaionship in equaion (2.3) mus be modified o accoun for he limied paricipaion as follows: c i,j = β 0 + β 1 e j,i + β 4 y i,j + β 2 ( e j,i + β 5 ( y i,j border i,j ) + β 3 e j,i border i,j ) + β 6 y i,j ln d i,j ln d i,j + v i,j (2.4) This specificaion allows for he border o affec he consumpion-income relaionship, and also for he he relaionship beween c i,j and y i,j o change monoonically wih disance. The resuls from his esimaion are presened in columns (iii) and (iv) of Table 1. We find ha here is significan posiive associaion beween c i,j and y i,j in boh pooled and fixed effecs specificaions. Allowing for limied paricipaion also affecs he wihin-counry correlaion beween c i,j and e j,i as i declines o abou A he same ime, he border effec in he consumpion- 13 In he fixed effecs regression he fixed effecs capure he ime-invarian, bilaeral pair specific jurisdicion effecs. 14 Noe ha he coeffi cien on he ineracive erm beween RER and log disance indicaes ha he consumpion- RER correlaion increases slighly for he jurisdicions ha are locaed furher away from each oher. 15 See for insance, Crucini (1999), Hess and Shin (2000), Hess and Shin (2010), Kollmann (2009) and Devereux, Smih, and Yeman (2009). 9

10 real exchange rae relaionship remains negaive and significan. As before, wih he addiion of he border coeffi cien, he relaionship beween c i,j and e j,i becomes slighly negaive. Overall, our esimaed border effec in he consumpion-real exchange rae risk-sharing remains robus o possibiliy of limied paricipaion in domesic and inernaional capial markes. 2.3 Wha drives he border effec? Wha explains he large drop in he consumpion-real exchange rae correlaion associaed wih crossing borders? An obvious fac is ha wihin-counry real exchange raes compare only relaive inflaion differenials beween regions, while across-counry real exchange raes involve comparisons across currencies and so involve nominal exchange rae changes. For his purpose we decompose he real exchange rae ino is componens as follows. Recall he definiion of he real exchange rae: RER j,i = P j, S i,j /P i,. Taking logs and firs-differencing we ge ln RER j,i = ln(p j, /P i, ) + ln S i,j, (2.5) where he firs erm on he righ-hand-side capures movemens in he he real exchange rae due o local raes of goods price inflaion, while he second erm is due o he movemens in he nominal exchange rae. Using his decomposiion, we amend he specificaion in equaions (2.3) and (2.4) o include he growh rae in nominal exchange raes. The resuls from fixed effecs regressions are presened in columns (i) and (ii) of Table 2. Columns (i) provides esimaes of specificaion (2.3), while column (ii) allows for marke segmenaion and hus summarizes he esimaes of specificaion (2.4), boh amended o include he nominal exchange rae growh rae beween jurisdicions i and j. The key resul ha sands ou from Table 2 is he coeffi cien on he nominal exchange rae growh is negaive and significan. Furhermore, he negaive coeffi cien on he border effec is subsanially reduced when we conrol for nominal exchange rae movemens. This suggess ha a sizeable componen of he border effec from Table 1 can be accouned for by nominal exchange rae movemens. Thus, wihou a his sage suggesing causaion, he finding indicaes ha counry pairs wih higher nominal exchange rae volailiy will deviae more from he benchmark model of full risk sharing. Our resuls do no imply ha he enire border effec is accouned for by he nominal exchange rae. The negaive effec of he border is reduced when he nominal exchange rae is added o he regression specificaion, bu i is no eliminaed. There are many possible reasons for why he border effec may remain imporan. Risk sharing wihin counries may be greaer han ha across counries due o deeper financial inegraion; common language, culure and insiuions; lower formal and informal rade barriers; greaer labor and capial mobiliy; presence of fiscal insurance mechanisms; greaer synchronizaion of shock processes wihin counries; differences in demand elasiciies across counries (pricing-o-marke); ec. We invesigae he quaniaive role played by some of hese facors below, using he model. Our resuls here, however, poin o he nominal exchange rae as an imporan new driver of he border effec in risk-sharing. 10

11 Table 2: Esimaes of he Border Effec: RER Decomposiion (i) (ii) (iii) (iv) e j,i 0.384*** 0.308*** 0.387*** 0.311*** (0.060) (0.043) (0.059) (0.042) e j,i border i,j (0.122) (0.082) (0.123) (0.083) e j,i ln d i,j 0.038* ** 0.037* (0.020) (0.021) (0.020) (0.020) y i,j 0.159*** 0.160*** (0.026) (0.026) y i,j border i,j (0.038) (0.040) y i,j ln d i,j (0.029) (0.030) ln S i,j ** *** ** *** (0.110) (0.076) (0.111) (0.077) e j,i A GER bordersp i,j 0.481*** 0.375*** (0.043) (0.048) e j,i + ej,i border i,j 0.257** 0.248*** 0.250** 0.242*** (0.106) (0.072) (0.107) (0.073) e j,i + ej,i border i,j+ ln S i,j * ** * e j,i + ej,i border i,j+ ln S i,j + e j,i (0.019) (0.020) (0.018) (0.019) SP A GER borderi,j 0.441*** 0.342*** (0.041) (0.052) N Noes: The dependen variable is relaive consumpion growh beween locaions i and j, c i,j. The esimaed specificaion in columns (i) and (iii) is equaion (2.3), while in column (ii) and (iv) is equaion (2.4). All are modified o include he growh rae of he nominal exchange rae. All regressions are esimaed wih bilaeral jurisdicion pair-specific fixed effecs. Sandard errors are clusered a he counry-pair level and are repored in parenheses. *,**, and *** indicae significance a 10%, 5%, and 1%, respecively. 2.4 Disenangling he border from he nominal exchange rae The resuls show ha he consumpion-real exchange rae correlaion drops significanly when comparing across borders, and ha he nominal exchange rae accouns for a significan par of his decrease. Does his mean ha eliminaing nominal exchange rae flexibiliy would lead o an increase in he consumpion-real exchange rae correlaion? The problem wih his inerpreaion is ha all our cross-border comparisons also involve nominal exchange raes. If here are aribues of cross-border relaionships ha are correlaed wih he nominal exchange rae, we may misakenly ascribe he significan fall in he consumpion-real exchange rae correlaion o he nominal exchange rae, while i is in fac independen of exchange rae policy Spain-Germany case One way o disenangle he effecs of he nominal exchange rae from he border is by focusing on cross-border pairs wihin he sample ha exhibi lile nominal exchange rae volailiy. Our sample includes Germany and Spain. These wo counries have had eiher very low or zero bilaeral nominal exchange rae variabiliy during our sample period. To furher isolae he role of he nominal exchange rae, we can herefore compare he properies of all regional pairs across he Spain-Germany border wih he cross-border pairs whose exchange rae is freely floaing. 11

12 Table 3 shows he mean sandard deviaion of monhly exchange rae changes beween all cross-border pairs of counries for our sample. Table 3: Nominal Exchange Rae Variabiliy US Japan Germany Spain Canada US Japan Germany Noes: Sandard deviaions of changes in monhly bilaeral nominal exchange raes over samples maching hose in our bilaeral consumpion and real exchange rae daase. I is apparen ha he oulier is Germany and Spain. The cross-border sample for Germany and Spain covers he period from 1995 o For he firs four years, Germany and Spain had separae currencies, bu very low bilaeral exchange rae movemens. From 1999 onward, hey had zero bilaeral nominal exchange rae movemens. Over he whole sample, he mean monhly sandard deviaion of nominal exchange rae changes is only 0.6 percen. This conrass wih much higher nominal exchange rae volailiy for all oher cross-border pairs. If i is he nominal exchange rae iself raher han some aspec of he border (which may be correlaed wih nominal exchange raes) ha is causing he drop in he consumpion-real exchange rae correlaion for across-counry pairs, we should expec ha including a separae conrol for Germany-Spain comparisons in he basic regressions would reverse some of he negaive border effec. Wih his in mind, we exend he specificaions in columns (i) and (ii) of Table 2 o include an ineracive erm beween e j,i and a Germany-Spain border dummy ha akes a value of one for all jurisdicion pairs locaed across he border beween Germany and Spain, and zero oherwise. 16 The resuls are presened in column (iii) of Table 2 for he benchmark specificaion, and in column (iv) for he specificaion wih hand-o-mouh consumers. We find ha he coeffi cien on e j,i borderger SP i,j A is posiive and significan, and, imporanly, i is large enough o urn he border effec beween Germany and Spain posiive, equal o 0.44 in he benchmark specificaion and 0.34 in he specificaion wih hand-o-mouh consumers. This is in sharp conras o he average border effec in he full sample of counries equal o in he benchmark specificaion and in he specificaion wih hand-o-mouh consumers As noed, since he nominal exchange rae beween Germany and Spain is fixed from 2000 onwards we canno idenify he conribuion of he nominal exchange rae o he border effec beween hese wo counries. Insead, we esimae how he border effec beween Germany and Spain differs from he average border effec esimaed in he full sample of counries. 17 As an addiional check, we allowed for ineracion erm beween he real exchange rae and he border for Spain paired wih all oher counries (bu Germany) and Germany paired wih all oher counries (bu Spain) in our sample. The esimaes of he border effec for hese pairs are negaive and significan, similar in magniude o he average border effec. This suggess ha our findings for he Germany-Spain pairs are no driven by facors specific o hese wo counries, bu raher by he aribues specific o Spain-Germany bilaeral pairs. See Table S1 in he online appendix for deailed resuls. 12

13 2.4.2 Cross-counry evidence To furher assess he role of he exchange rae in consumpion-real exchange rae correlaions, we urn o cross-counry evidence. In paricular, we sudy a cohor of he 12 European Union member saes during period. 18 ino pre-euro period ( ) and euro period ( ). 19 To evaluae he role of he exchange rae, we spli he sample For each subsample we compue all bilaeral correlaions of relaive consumpion growh wih he growh rae in he real exchange rae for each counry. The average correlaions for each counry and each sub-period are repored in Table 4. A clear conras arises beween he wo periods: In he pre-euro period, he relaive consumpion-real exchange rae correlaion is negaive, on average, across counries, equal o The same correlaion urns posiive in he euro period and is equal o correlaions across he wo sub-periods is also saisically significan a 1 percen level. 20 Table 4: Inernaional C-RER correlaion: Fixed vs flexible regime Pre-euro period Euro period (i) (ii) Ausria Belgium Finland France Germany Greece Ireland Ialy Luxembourg Neherlands Porugal Spain Average The difference in Overall, hese resuls suppor our earlier findings on he role of exchange rae flucuaions for he finding of negaive correlaion beween relaive consumpion growh and real exchange rae growh. 21 Vaskov (2008). 22 Furhermore, our resuls in his subsecion are in line wih recen findings in Hadzi- To summarize, our findings sugges ha he relaive price movemens faciliae consumpion risk-sharing wihin counries; while hey obsruc consumpion risk-sharing across counry borders. Imporanly, mos of his border effec can be aribued o nominal exchange rae variabiliy. In Table 2, he inclusion of he bilaeral nominal exchange rae reduces he coeffi cien on he border 18 Daa deails and sources are provided in he Appendix A Greece adoped euro on January 1, We adjus our calculaions accordingly. 20 The es of significance is obained using Fisher s variance sabilizing ransformaion of correlaion coeffi ciens. 21 We recognize ha besides he exchange rae regime, oher facors could have also conribued o he increase in he consumpion-rer correlaion in he second sub-period. For insance, he degree of financial inegraion could have risen, or policy coordinaion could have increased in he laer period beween he EU members. However, he evidence in his subsecion, ogeher wih inra-naional comparisons sugges o us ha he exchange rae is an imporan par of he sory. 22 Our analysis in his subsecion differs from Hadzi-Vaskov (2008) in ha we use annual daa and an exra year of he daa. 13

14 by 67 percen and 80 percen in he case wih and wihou hand-o-mouh consumers, respecively. In he nex sub-secion we show he robusness of our findings using alernaive regression specificaions and differen decomposiion approaches. 2.5 Robusness Counry heerogeneiy In he regression specificaions (2.3) and (2.4) he effec of he border on he consumpion-real exchange rae correlaion as capured by he ineracive erm on he real exchange rae wih he border dummy, is measured relaive o he average correlaion in he inra-counry pairs. Gorodnichenko and Tesar (2009) argue ha in he presence of cross-counry heerogeneiy in he disribuion of wihin-counry price differenials, such an average benchmark is arbirary and can lead o misleading resuls. In paricular, in his case, he border coeffi cien may capure he join effec of he border and counry heerogeneiy in he consumpion-real exchange rae correlaion. We can address his issue by allowing he inra-naional correlaion beween c i,j and e j,i o be counry-specific. In paricular, we amend he regression specificaion in equaion (2.4) wih he produc erms of e j,i wih a se of dummy variables, each idenifying jurisdicion pairs wihin each counry in our sample. In all cases we use wihin US saes pairs as he benchmark. The coeffi cien on his ineracive erm will give us he change in he inra-naional consumpion-real exchange rae correlaion when ransiioning from US sae pairs o oher counry pairs. The coeffi cien on he ineracive erm beween e j,i and he border dummy, as before, will give us he effec of he border on he correlaion, excep now we can esimae he effec of he border crossing from he perspecive of each individual counry in our sample. Table 5 repors our findings. 23 For compleeness, panel (a) summarizes our earlier resuls from he fixed effecs regressions where we used he average correlaion in he inra-counry pairs as he benchmark for gauging he border effec (see columns (ii) and (iv) in Table 1). Panel (b) presens he esimaion resuls ha allow for counry heerogeneiy. We also repor he resuls from he specificaion wih hand-o-mouh consumers (columns labelled wih y i,j ) and wih homogeneous consumers (columns labelled no y i,j ). 24 All regressions include jurisdicion-pairs fixed effecs. Our resuls reveal some amoun of heerogeneiy across our sample of counries. However, some common paerns emerge. Firs, he inra-naional consumpion-real exchange rae correlaions are consisenly posiive, wih he US and Spain showing he highes numbers in our sample, while Germany is characerized by he lowes correlaion. 25 Second, inernaional correlaions are negaive for all counries, excep Spain. Noe however ha even for Spain, inernaional correlaions are 23 Deailed esimaion resuls are available from he auhors upon reques. 24 The specificaion wih he hand-o-mouh consumers also includes he ineracive erms beween oupu growh and dummy variables ha idenify wihin-counry jurisdicion pairs for each counry in our sample. This allows he consumpion-oupu growh correlaion o be counry-specific as well. 25 The only excepion is Germany in he specificaion wih no hand-o-mouh consumers, who exhibis negaive inra-naional consumpion-rer correlaion. 14

15 Table 5: Esimaes of he Border Effec: Accouning for counry heerogeneiy no y i,j wih y i,j Panel (a). Homogeneous benchmark Inra-naional 0.373*** 0.298*** (0.064) (0.046) Inernaional (0.016) (0.017) Panel (b). Heerogeneous benchmarks Inra-naional correlaions US 0.433*** 0.329*** (0.011) (0.007) Canada 0.214*** 0.159*** (0.009) (0.006) Germany *** 0.135** (0.048) (0.050) Japan 0.360*** 0.227*** (0.043) (0.042) Spain 0.925*** 1.151*** (0.032) (0.053) Inernaional correlaions US (0.017) (0.019) Canada *** *** (0.019) (0.022) Germany *** *** (0.029) (0.033) Japan *** *** (0.025) (0.025) Spain 0.485*** 0.817*** (0.017) (0.041) Noes: The dependen variable is relaive consumpion growh beween locaions i and j, c i,j. Panel (a) summarizes he resuls from columns (ii) and (iv) in Table 1. Panel (b) repors he resuls from a regression specificaion in equaion (2.3) column labelled "no y i,j ", and specificaion in equaion (2.4) column labelled "wih y i,j ", boh modified o include produc erms beween e j,i and dummies ha idenify all wihin counry pairs for Canada, Germany, Japan and Spain. Wihin US sae pairs are used as he benchmark. All regressions include jurisdicion pairs fixed effecs. Sandard errors are clusered a he counry-pair level and are repored in parenheses. *,**, and *** indicae significance a 10%, 5%, and 1%, respecively. sill considerably lower han naional correlaions. The correlaions are he lowes (mos negaive) in Germany Oher conrols One poenial criicism of our benchmark specificaion derived in equaion (2.2) is he fac ha i assumes a separable uiliy funcion. A number of variables can poenially affec he marginal uiliy of consumpion, such as leisure, governmen consumpion, real money balances, ec. Ravn (2001) invesigaes he imporance of hese variables for he consumpion-real exchange rae correlaion in cross-counry daa. He finds ha he negaive correlaion beween relaive consumpion and he real exchange rae remains robus o relaxing he separabiliy assumpion. Unforunaely, a similar exercise can no be conduced wih our daa because inra-jurisdicion informaion for hese variables is no available. One way o accoun for he omied variables for which daa or proxies are no available is o use a lagged dependen variable (i.e. relaive consumpion growh) in specificaions (2.3)-(2.4). Such 15

16 Table 6: Esimaes of Border Effec: Lagged consumpion growh (i) (ii) e j,i 0.161*** 0.062** (0.043) (0.032) e j,i border i,j *** *** (0.060) (0.038) e j,i ln d i,j 0.063*** 0.053*** (0.018) (0.017) y i,j 0.184*** (0.028) y i,j border i,j (0.091) y i,j ln d i,j (0.091) c i,j (0.010) (0.015) e j,i + ej,i border i,j ** (0.023) (0.021) N Noes: The dependen variable is relaive consumpion growh beween locaions i and j, c i,j. The esimaed specificaion in columns (i) is equaion (2.3); while in columns (ii) i is equaion (2.4). Each regression also includes one lag of he dependen variable. All equaions are esimaed wih Arellano and Bond (1991) GMM mehod. Sandard errors are clusered a he counry-pair level and are repored in parenheses. *,**, and *** indicae significance a 10%, 5%, and 1%, respecively. an exension would also arise from a model wih exogenous habi persisence, as in Abel (1990). In dynamic panels, however, he unobserved panel-level effecs are correlaed wih he lagged dependen variables, making sandard esimaors inconsisen. To obain consisen esimaes for model parameers we use Arellano and Bond (1991) generalized mehod of momens (GMM) approach. The mehod uses he firs difference of all he exogenous variables and second and higher lags of he dependen variable and all oher variables as insrumens. Sandard errors are clusered a he counry-pair level. The resuls from he esimaion are presened in Table 6. The lagged consumpion variable is negaive and generally saisically significan. A he same ime, our resuls for he consumpion-real exchange rae correlaion remain largely robus. If anyhing, he inroducion of a lagged relaive consumpion growh ino our esimaion, worsens he inernaional evidence on consumpion-real exchange rae risk-sharing by producing a more negaive correlaion beween he wo variables. The inra-naional correlaion remains posiive and significan. Imporanly, our resuls also remain robus when we include he nominal exchange rae explicily in he regressions. The nominal exchange rae sill accouns for a large share of he border effec in risk-sharing An alernaive decomposiion and he role of he nominal exchange rae Up o now, we have assumed ha he benchmark for effi cien risk-sharing in he daa is ha relaive consumpion growh raes across any wo locaions should be posiively associaed wih he real exchange rae, independen of oher variables. Bu hese ess do no give a clear meric for he 26 These resuls can be found in he online appendix o he paper. 16

17 degree o which risk-sharing fails in he daa, nor he exen o which he border and he nominal exchange rae conribue o his failure. Here we follow in he spiri of Engel and Rogers (1996) in consrucing a welfare-relevan measure of he failure of risk-sharing. We hen ask how much he border and he nominal exchange rae can accoun for his measure. 27 We reurn o equaion (2.2) and for each jurisdicion pair in our sample, for a choice of σ, we compue c i,j (1/σ) e j,i and obain is sandard deviaion in he ime-series. 28 This gives us a cross-secion of such sandard deviaions. If our choice of σ is correc, hen wih full risk-sharing his saisic would be zero for each bilaeral pair. We se σ = 2, so ha he elasiciy of ineremporal subsiuion is equal o 0.5 a sandard value in he lieraure. The summary saisics of his measure are repored in row (i) of Table 7. Table 7: Alernaive meaure of risk-sharing: Summary saisics Variable Obs Mean Sd. Dev. Min Max [ (i) sd.dev. (ii) sd.dev. c i,j [ c i,j ] (1/σ) e j,i ] (1/σ) ẽ j,i Noes: The able repors summary saisics of he presened variables. Obs. refer o he number of observaions in each sample; Mean - sample average; Sd. Dev. - sample sandard deviaion; Min-sample minimum; Max-sample maximum. Using his measure of he deparure from full risk-sharing, we esimae he following regression: [ sd.dev. c i,j ] (1/σ) e j,i = β 1 border i,j + 5 α m D mm + ε i,j, (2.6) where border i,j, is as before a dummy variable ha akes on a value of one if locaions i and j are in separae counries, and zero oherwise, while ε i,j is he regression error erm. We also consider a specificaion in which we include he log of he disance beween locaions i and j. To accoun for poenial heerogeneiy across counries in he average volailiy of deviaions from perfec risk-sharing, we also include a se of dummies, idenifying wihin-counry pairs, D mm. 29 Table 8 repors he resuls. Panel (i) presens he resuls wihou he log disance variable in he specificaion, while panel (ii) - includes he log disance variable. The effec of he border is posiive and significan. I means ha conrolling for counry-specific volailiy in he risk-sharing measure, here is a greaer deviaion from effi cien risk-sharing when comparing across counries relaive o comparing wihin counries. This resul holds wheher we conrol for disance in our esimaion or no. How imporan is he border? The average volailiy of our risk-sharing measure is 5.14 percen, while he border coeffi cien is 2.74 percen, so he border accouns for 53 percen of he oal, conrolling for disance. Wihou he disance conrol, he conribuion of he border is even 27 Engel and Rogers (1996) measure he exen of he failure of he law of one price using he sandard deviaion of he price differenials of similar goods across ciies in he US and Canada. 28 We also conduc he analysis of his secion using he mean of he squared difference, mean [ ] c i,j (1/σ) e j,i 2, and find ha he resuls are robus o his alernaive measure of risk-sharing. 29 Noe ha his is a cross-secional regression. m=1 17