NBER WORKING PAPER SERIES CONSUMPTION RISK-SHARING AND THE REAL EXCHANGE RATE: WHY DOES THE NOMINAL EXCHANGE RATE MAKE SUCH A DIFFERENCE?

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1 NBER WORKING PAPER SERIES CONSUMPTION RISK-SHARING AND THE REAL EXCHANGE RATE: WHY DOES THE NOMINAL EXCHANGE RATE MAKE SUCH A DIFFERENCE? Michael B. Devereux Vikoria Hnakovska Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA Augus 2011 We are graeful o Margarida Duare, Charles Engel, and paricipans a various conferences and insiuions 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. Hnakovska hanks SSHRC for research suppor. Devereux hanks SSRHC, he Bank of Canada, and he Royal Bank of Canada for financial suppor. The opinions expressed in his paper are hose of he auhors alone and canno be ascribed o he Bank of Canada. The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Naional Bureau of Economic Research by Michael B. Devereux and Vikoria Hnakovska. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Consumpion Risk-Sharing and he Real Exchange Rae: Why does he Nominal Exchange Rae Make Such a Difference? Michael B. Devereux and Vikoria Hnakovska NBER Working Paper No Augus 2011 JEL No. F3,F4 ABSTRACT A basic predicion of effcien risk-sharing is ha relaive consumpion growh raes across counries or regions should be posiively relaed o real exchange rae growh raes across he same areas. We invesigae his hypohesis, employing a newly consruced muli-counry and muli-regional daa se. Wihin counries, we find signifcan 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 idenify his failure of risk sharing as a border effec. We find ha he border effec is subsanially (bu no fully) accouned for by nominal exchange rae variabiliy. We hen ask wheher sandard open economy macro models can explain hese feaures of he daa. We argue ha hey canno. To explain he role of he nominal exchange rae in deviaions from cross counry consumpion risk sharing, i is necessary o combine muliple sources of shocks, ex-ane price seing, and incomplee financial markes. Michael B. Devereux Deparmen of Economics Universiy of Briish Columbia Eas Mall Vancouver, BC V6T 1Z1 CANADA and NBER mbdevereux@gmail.com Vikoria Hnakovska Deparmen of Economics Universiy of Briish Columbia Vancouver, BC V6T 1Z1 hnakovs@inerchange.ubc.ca

3 Consumpion Risk Sharing and he Real Exchange Rae: Why Does he Nominal Exchange Rae Make Such a Di erence? Michael B. Devereux y and Vikoria Hnakovska z Augus 2, 2011 Absrac A basic predicion of e cien risk-sharing is ha relaive consumpion growh raes across counries or regions should be posiively relaed o real exchange rae growh raes across he same areas. We invesigae his hypohesis, employing a newly consruced muli-counry and muli-regional daa se. Wihin counries, we nd signi can 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 idenify his failure of risk sharing as a border e ec. We nd ha he border e ec is subsanially (bu no fully) accouned for by nominal exchange rae variabiliy. We hen ask wheher sandard open economy macro models can explain hese feaures of he daa. We argue ha hey canno. To explain he role of he nominal exchange rae in deviaions from cross counry consumpion risk sharing, i is necessary o combine muliple sources of shocks, ex-ane price seing, and incomplee nancial markes. JEL Classi caion: F3, F4 Keywords: Real exchange rae, risk sharing, border e ec, inranaional economics 1 Inroducion Many sudies of aggregae consumpion behavior 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 relaive consumpion prices are ime-varying leads o a more elaborae es for consumpion risk-sharing, incorporaing boh wihin and beween counry We are graeful o Margarida Duare, Charles Engel, and paricipans a various conferences and insiuions 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. Hnakovska hanks SSHRC for research suppor. Devereux hanks SSRHC, he Bank of Canada, and he Royal Bank of Canada for nancial suppor. The opinions expressed in his paper are hose of he auhors alone and canno be ascribed o he Bank of Canada. y Deparmen of Economics, Universiy of Briish Columbia, Eas Mall, Vancouver, BC V6T 1Z1, Canada; CEPR; NBER. address: devm@inerchange.ubc.ca. z Deparmen of Economics, Universiy of Briish Columbia, Eas Mall, Vancouver, BC V6T 1Z1, Canada. address: hnakovs@inerchange.ubc.ca. 1

4 real exchange raes movemens. The predicion of his exended model is ha relaive consumpion growh raes (across regions or counries) are highly correlaed wih movemens in real exchange raes. We es his hypohesis using a novel muli-counry and muli-regional daa se. We show ha a sharp dichoomy arises beween wihin-counry and across-counry comparisons, paricularly for across-counry groups ha have exible bilaeral exchange raes. Wihin counries, movemens in real exchange raes end o suppor he hypohesis of some (imperfec) risk-sharing. Across counries however, he real exchange rae plays eiher no role or a negaive role in risk-sharing. This is essenially he well-known Backus Smih puzzle (Backus and Smih, 1993). This is paricularly rue of counries ha exhibi subsanial ucuaions in nominal exchange raes. 1 Thus, he failure of across-counry (as opposed o wihin-counry) risk sharing is proximaely due o movemens in nominal exchange raes. Counries (or regions) wih xed exchange raes end o exhibi relaive consumpion growh raes ha are posiively correlaed wih naional (or regional) real exchange raes. Bu in counries wih subsanial ucuaions in nominal exchange raes he correlaion ends o be negaive. Can his nding be reconciled wih sandard models of real exchange rae deerminaion? This paper is an aemp o resolve his quesion. We noe ha his is no quie he same as an aemp o resolve he Backus-Smih puzzle, or consumpion real exchange rae anomaly (see Chari, Kehoe, and McGraan, 2002). Sudies ha have o ered convincing resoluions of his anomaly (see below for a discussion) ypically do no make any predicions abou he behavior of he nominal exchange rae. Therefore, hese sudies imply ha he relaionship beween relaive consumpion and he real exchange rae should be una eced by he nominal exchange rae regime. We begin by providing a comprehensive empirical accoun of he role of he real exchange rae in regional and inernaional risk sharing in a large inra-naional and inernaional daase. daase conains consumpion and bilaeral consumpion prices (or real exchange raes) a he provincial or sae level for a group of counries. We show ha for all counries in he sample, here is evidence ha he real exchange rae plays a posiive role in wihin counry risk-sharing. The Tha is, consumpion growh di erences across provinces or saes are posiively correlaed wih bilaeral real exchange rae changes across he same geographical unis. Bu when we include a border dummy in he risk sharing regression, indicaing ha relaive consumpion growh involves comparisons across counries, he overall relaionship beween consumpion growh and real exchange rae changes falls dramaically, and in mos cases is negaive. Furher invesigaion reveals ha mos, (bu no all) of his border e ec can be aribued o nominal exchange rae volailiy. 2 We hen ask, are hese resuls consisen wih sandard models of inernaional risk sharing and real (and nominal) exchange rae volailiy? Mos proposed resoluions of he Backus-Smih anomaly have emphasized he join role of incomplee markes and shocks which generae srong income e ecs. The inuiion is ha a counry which has a faser growing consumpion experiences an appreciaing real exchange rae (e.g. Corsei, Dedola, and Leduc, 2008). Bu when we exend 1 See also Hess and Shin (2010) and Hadzi-Vaskov (2008). 2 Noe ha we refer o he "border" broadly de ned as a separaion beween any wo counries. 2

5 he anomaly o encompass boh regions wihin a counry, and he imporance of he nominal exchange rae, hese explanaions are no complee, since in he sandard models, hese shocks end o produce negaive consumpion real-exchange rae correlaions across regions wihin a counry, or across counries, independenly of how he nominal exchange rae is deermined. In order o adequaely explain he daa, i is necessary o allow for a non-rivial role for he nominal exchange rae regime in consumpion risk-sharing, since he evidence indicaes ha he failure of risk-sharing (or equivalenly, he large role played by he border) is srongly ied o movemens in he nominal exchange rae. We show ha he sandard sicky price inernaional macro model canno accoun for hese feaures of he daa. This is because, despie allowing for a non-rivial role for he nominal exchange rae regime, he model generically implies ha if here is a negaive correlaion beween relaive consumpion growh and he real exchange rae, i will occur equally under xed or exible exchange raes. In fac, o he exen ha saes (or provinces) are analogous o counries wihin a xed exchange rae area, he sandard model also predics a negaive correlaion beween relaive consumpion growh and real exchange raes beween saes; he presence of he nominal exchange rae in iself does no aler he implicaion of hese models. The essenial reason ha he sandard sicky price model canno accoun for he empirical regulariies in he daa is ha in fac, he (co)-variance properies of he real exchange rae in his model are only slighly a eced by he exchange rae regime iself. Essenially he reason is ha in hese models, alhough prices are nominally sicky, hey are forward looking, and price adjusmen may be subsanially enhanced by he absence of nominal exchange rae adjusmen, so ha he absence of nominal exchange rae adjusmen is compensaed for by addiional nominal price adjusmen. The criical requiremen in explaining he paern of correlaions in he daa is o allow for shocks which cause relaive consumpion growh o rise and he nominal exchange rae o simulaneously appreciae under exible exchange raes, bu which leave relaive in aion raes unchanged (or o increase) under xed exchange raes. The paper goes on o show one way ha his can be done in an amended form of he sandard sicky price open-economy framework. We do his by combining he basic model wih a number of elemens. In paricular, we employ he assumpions of a) incomplee nancial markes (limied by rade in non-coningen bonds), b) ex-ane saggered price seing in boh counries, and c) demand-ype shocks which simulaneously increase relaive consumpion while generaing a real exchange rae appreciaion. We show ha his combinaion leads o a model in which movemens in he nominal exchange rae may be dominaed by demand shocks, causing relaive consumpion and he real exchange rae o move in opposie direcions, while, conrolling for he nominal exchange rae, movemens in he real exchange rae aribuable o relaive in aion raes lead relaive consumpion and he real exchange rae o move in he same direcion. If demand shocks play a signi can enough role, hen he model predics ha under exible exchange raes, he correlaion beween relaive consumpion growh and he real exchange rae will be negaive. Bu xing he exchange rae produces a posiive correlaion. Thus, in principle, we can answer he quesion of he ile - he role of he border in cross 3

6 counry consumpion risk sharing is crucially ied o he nominal exchange rae regime, and he exchange rae displays characerisics in he model which are akin o hose seen in he daa. 2 Esimaing he border e ec 2.1 Key heoreical relaionship In his secion, we presen a general model of risk-sharing wihou addiional feaures of producion, sicky prices, ec., ha are explored in secion (3) below. To obain key risk-sharing relaionships, 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: X 1 E s U(C j;+s ; j;+s ); < 1 s=0 where is he subjecive discoun facor, C j; denoes a composie consumpion good in counry j. Here j; represens a jurisdicion speci c facor which can a ec he marginal uiliy of consumpion, apar from consumpion iself. This could represen pure preference shocks, or movemens in workhours when households have non-separable uiliy. De ne P j; o be he price of a represenaive consumpion baske 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 di eren counries is given by RER j;i regions in he same counry. = S i;j P j; =P i; ; or RER j;i = P j; =P i; if i and j are wo Suppose ha here is a complee se of sae-coningen securiies available o households in all counries. In his case, he key opimaliy condiion is o equae marginal uiliies of consumpion across counries (or regions), adjused for di erences in price levels, evaluaed in a common currency: U c (C i; ; i; )RER j;i = U c (C j; ; 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. Say now ha j; = 1 for all : 3 Then if uiliy is of a consan relaive risk aversion (CRRA) form, wih he coe cien of relaive risk aversion ; equaion (2.1) becomes Ci; C j; = RER j;i ; or equivalenly in logs (ln C i; ln C j; ) = ln RER j;i : 3 In he simples version of he heoreical model below, we will re-inroduce preference shocks. 4

7 The expression above mus also hold in growh raes: ( ln C i; ln C j; ) = ln RER j;i ; (2.2) where ln X i; = ln X i; ln X i; 1. These expressions esablish he close relaionship beween he real exchange rae and relaive consumpion beween jurisdicions i and j: In paricular, i 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, e;cj =c i = corr( ln RER j;i ; 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), de ned in erms of condiional expecaions, will also hold even under incomplee markes, so long as some nancial asses can be raded across counries (see e.g. Obsfeld and Rogo (1996)). Noice ha if relaive purchasing power pariy (PPP) holds, so ha RER 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 Evidence from US saes and Canadian provinces 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. 4 We begin by focusing on jus he US and Canada. This allows us o invesigae he impac of he border on risk sharing in a similar manner o sudies of deviaions of he law of one price across regions wihin he US and Canada (Engel and Rogers (1996), Gorodnichenko and Tesar (2009)). In he nex sub-secion we invesigae he same quesion for all ve counries in our sample. We employ inra-naional daa on consumpion, oupu and prices in 50 US saes during and in 12 Canadian provinces and erriories during Using his daa we compue all possible unique bilaeral pairs of di erences beween log consumpion, price and oupu growh raes. The pairs of saes wihin he US we denoe by UU, he pairs of provinces wihin Canada by CC and sae-province pairs by UC. The summary saisics for our wo-counry daase are repored in Table 1. Noe ha, as o be expeced, wihin counry real exchange raes are much less volaile han across counry real exchange raes. Table 1 also reveals anoher ineresing characerisic of our inra-naional daa: Sandard deviaion of relaive consumpion growh wihin 4 These are he counries for which we found hisorical jurisdicion-level daa on consumpion and prices. Deails on daa sources are provided in he Appendix A.1. 5 For he US we use reail sales o proxy for privae consumpion; we consruc sae-level price indices using consumer price index (CPI) for main meropolian areas and rural/urban prices; and use Gross Sae Produc o measure oupu in he 50 saes. In all oher counries we use nal consumpion and oupu from regional accouns and regional consumer price indices. Daa deails are provided in he Appendix A.1. 5

8 he US and Canada is signi canly higher han he sandard deviaion of heir relaive price growh, while he opposie is rue for cross-border locaion pairs. Table 1: Sample summary saisics Variable Obs Mean Sd. Dev. Min Max (i) (ii) (iii) (iv) (v) Panel 1: US ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Panel 2: Canada ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Panel 3: US-Canada ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Noes: The able repors summary saisics of he presened variables for hree samples: all US-US sae pairs (Panel 1); all Canada-Canada province pairs (Panel 2); all US-Canada pairs (Panel 3). Obs. refer o he number of observaions in each sample; Mean - sample average; Sd. Dev. - sample sandard deviaion; Min-sample minimum; Max-sample maximum. To simplify our noaion we will use c i;j locaions i and j; so ha c i;j = ln C i; ln C j; ; and e j;i o denoe relaive consumpion growh beween wo 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 speci caion o link relaive consumpion growh and real exchange rae growh: c i;j = e j;i + 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. border i;j is he border dummy ha akes value of one for all UC locaion pairs, and a value of zero oherwise. This allows us o focus on he disincion beween cross counry risk sharing and cross region risk sharing. This speci caion resrics he relaionship beween he real exchange rae and relaive consumpion o be he same for any wo locaions in he US, in Canada or any wo locaions beween he US and Canada. However, i is plausible o posi ha he same change in he real exchange rae could be associaed wih di eren movemens in relaive consumpion depending on he paricular locaions observed. In he heoreical model below for insance, we allow for preference shocks which may di er beween any wo locaions. Bu more generally here may be di erences in he degree of openness in goods or nancial markes beween wo jurisdicions ha are no re eced 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 a ec 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 6

9 ype variables in accouning for nancial marke inegraion. 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 speci caion hus becomes c i;j = e j;i + 2 (e j;i border i;j ) + 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; de ned 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 he US saes and Canadian provinces; while ln d i;j = 7:69 is he average log disance beween all UC pairs. 6 This normalizaion implies ha ln ~ d i;j is equal o zero a ln d i;j = ln d i;j ; and simpli es inerpreaion of he 2 coe cien, which now expresses he average e ec of he border for he consumpion-rer 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. Table 2: Esimaes of Border E ec: US-Canada Pooled Fixed e ecs Pooled Fixed e ecs (i) (ii) (iii) (iv) e j;i 0.429*** 0.424*** 0.319*** 0.317*** (0.023) (0.026) (0.023) (0.027) e j;i border i;j *** *** *** *** (0.024) (0.027) (0.024) (0.027) e j;i ln ~ d i;j *** *** *** *** (0.011) (0.012) (0.011) (0.011) y i;j 0.157*** 0.153*** (0.007) (0.007) y i;j border i;j (0.011) (0.014) y i;j ln ~ d i;j (0.008) (0.010) e j;i + e j;i border i;j *** *** *** *** (0.007) (0.007) (0.007) (0.007) N R Noes: The dependen variable is relaive consumpion growh beween locaions i and j; c i;j : The esimaed speci caion in columns (i)-(ii) is equaion (2.3); while in columns (iii)-(iv) i is equaion (2.4). Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively. Our ndings from he OLS and xed e ecs esimaion of equaion (2.3) are presened in columns (i) and (ii) of Table 2. 7 The resuls in column (i) indicae ha he condiional correlaion beween he growh raes of RER and relaive consumpion wihin US and Canada is posiive and signi can, equal o 0.43 on average. We can also see ha he esimaed border e ec is large and economically signi can. In fac, due o his e ec, he consumpion-rer correlaion across counries urns negaive, equal o on average. Taking (2.2) as our basic heory of risk-sharing, hese resuls sugges ha relaive prices faciliae risk-sharing wihin counries, bu 6 We measure disance in kilomeers. 7 In he xed e ecs regression he xed e ecs capure he ime-invarian, bilaeral pair speci c e ecs. 7

10 impede risk-sharing across counries. The esimaes in column (ii) obained from he xed e ecs regression con rm his nding. 8 How sensiive are hese ndings 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 speci caion in which a leas a fracion of consumers do no make consumpion plans based on ineremporal opimizaion, bu raher follow rules of humb, or equivalenly, have no abiliy o borrow and lend a all. 9 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. These households do no have access o capial markes, and herefore canno paricipae in inernaional risk-sharing. The esable implicaion of such a modi ed 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 (2.3) mus be modi ed o accoun for he limied paricipaion as follows: c i;j = e j;i + 4 y i;j + 2 (e j;i + 5 (y i;j border i;j ) + 3 e j;i border i;j ) + 6 y i;j ln ~ d i;j ln ~ d i;j + v i;j (2.4) Noe ha he equaion speci caion in (2.4) allows for he border e ec in he consumpion-income relaionship, and for he ineracion erm beween y i;j and he normalized disance measure o allow he relaionship beween c i;j and y i;j o change monoonically wih he disance. The resuls from his esimaion are presened in columns (iii) and (iv) of Table 2. We nd ha here is signi can posiive associaion beween c i;j and y i;j in boh pooled and xed e ecs speci caions. Allowing for limied paricipaion also a ecs he wihin-counry correlaion beween c i;j and e j;i as i declines o abou A he same ime, he border e ec in he consumpionreal exchange rae relaionship remains negaive and signi can. In fac, his e ec urns he correlaion beween c i;j and e j;i for he UC pairs negaive and signi can, as before. Overall, our esimaed border e ec in he consumpion-real exchange rae risk-sharing remains robus o he inclusion of income Wha drives he border e ec? We now invesigae he source of he negaive border e ec. Tha is, wha explains he negaive relaionship beween consumpion and he real exchange rae across borders? For his purpose we decompose he real exchange rae ino is componens as follows. Recall he de niion of he real 8 Noe ha he coe cien on he ineracive erm beween RER and log disance indicaes ha he consumpion- RER correlaion declines for he jurisdicions ha are locaed furher away from each oher. 9 See for insance, Crucini (1999), Hess and Shin (2000), Hess and Shin (2010), Kollmann (2009a) and Devereux, Smih, and Yeman (2009). 8

11 exchange rae: RER j;i = P j; S i;j =P i; : Taking logs and rs-di erencing we ge ln RER j;i = ln(p j; =P i; ) + ln S i;j ; (2.5) where he rs erm on he righ-hand-side capures movemens in he he real exchange rae due o changes in he relaive prices, while he second erm is due o he movemens in he nominal exchange rae. Table 3 repors he summary saisics for he hree erms above. Table 3: Decomposing RER movemens for UC locaion pairs Variable Obs Mean Sd. Dev. Min Max (i) (ii) (iii) (iv) (v) ln RER j;i ln(p j; =P i; ) ln S i;j Noes: The able repors summary saisics of he presened variables for a sample of all US-Canada pairs. Obs. refer o he number of observaions in each sample; Mean - sample average; Sd. Dev. - sample sandard deviaion; Min-sample minimum; Max-sample maximum. As can be seen from column (iii) he real exchange rae across borders is very volaile and he majoriy of his volailiy comes from nominal exchange rae movemens. A he same ime, relaive prices across counries exhibi more volailiy han heir inra-naional counerpars repored in Table 1: compare he volailiy of 1.77% for UC locaion pairs wih 1.17% for UU locaion pairs and 0.95% for CC locaion pairs. Nex we amend our speci caion in equaions (2.3) and (2.4) o include he growh rae in nominal exchange raes. This allows us o assess he relaive conribuion of real exchange rae componens relaive prices and nominal exchange rae o he consumpionreal exchange rae relaionship. The resuls are presened in Table 4. Columns (i) and (ii) provide esimaes of speci caion (2.3), while columns (iii) and (iv) allow for marke segmenaion and hus summarize he esimaes of speci caion (2.4), boh amended o include he nominal exchange rae growh rae beween regions i and j. The key resul ha sands ou from Table 4 is ha border e ec urns posiive when we conrol for nominal exchange rae movemens. The coe cien on he nominal exchange rae growh, in urn, is negaive and signi can. This suggess ha he negaive border e ec esimaed in Table 2 is primarily due o he nominal exchange rae movemens. This suppors he ndings of Hess and Shin (2010) and Hadzi-Vaskov (2008) who look a cross counry regressions in which di eren bilaeral pairs of counries have di erences in heir exchange rae volailiy. Thus, wihou a his sage suggesing causaion, he nding seems o indicae ha counry pairs wih higher nominal exchange rae volailiy will deviae more from he benchmark model of full risk sharing. To sum up so far, our ndings seem o sugges ha he relaive price movemens faciliae consumpion risk-sharing across Canadian provinces, and across he U.S. saes; while hey obsruc consumpion risk-sharing across he Canada-US border. Moreover, mos of his border e ec can be aribued o nominal exchange rae variabiliy. 9

12 Table 4: Esimaes of he Border E ec: RER Decomposiion Pooled Fixed e ecs Pooled Fixed e ecs (i) (ii) (iii) (iv) e j;i 0.429*** 0.424*** 0.320*** 0.318*** (0.023) (0.026) (0.023) (0.027) e j;i border i;j *** 0.125*** (0.031) (0.035) (0.030) (0.034) e j;i ln ~ d i;j *** *** *** *** (0.011) (0.012) (0.011) (0.011) y i;j 0.156*** 0.152*** (0.007) (0.007) y i;j border i;j *** * (0.010) (0.013) y i;j ln ~ d i;j (0.007) (0.009) ln S i;j *** *** *** *** (0.021) (0.024) (0.021) (0.022) N R Noes: The dependen variable is relaive consumpion growh beween locaions i and j; c i;j : The esimaed speci caion in columns (i)-(ii) is equaion (2.3); while in columns (iii)-(iv) i is equaion (2.4). Boh are modi ed o include he growh rae of he nominal exchange rae. Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively. 2.3 Robusness Exended sample We nex expand our sample of counries o include Japanese prefecures, Spanish communiies and German bundeslaender. Our daa for Germany covers 16 bundeslaender over period; for Japan our daase covers 47 prefecures over period; while for Spain we have daa for 18 auonomous communiies over period. For each counry our daase includes informaion on consumpion, price indices and oupu in each regional uni. Summary saisics for he exended sample are presened in Table 5. As before, we repor he mean, sandard deviaion, minimum and maximum for he key variables of ineres. These saisics are repored for he wihin-counry pairs in Germany (Panel 1), Spain (Panel 2), and Japan (Panel 3); as well as for all cross-counry pairs beween Canada, US, Germany, Spain and Japan (Panel 4). Panel 4 also includes summary saisics on he componens of he RER growh rae as shown in equaion (2.5). The numbers ell a sory similar o ha for he US and Canada: Inernaional RER are signi canly more volaile han RER for wihin-counry pairs and are more volaile han inernaional consumpion di erenials. Wihin-counry RER are much smooher and in fac are less volaile han relaive consumpion wihin our group of counries. Furhermore, as eviden from Panel 4, majoriy of cross border RER ucuaions is due o movemens in he nominal exchange rae. Nex, we urn o he regression analysis. Table 6 presens our esimaes of he border e ec for he ve counries comprising our full sample. Columns (i) and (ii) repor our esimaes of equaions (2.3), while columns (iii) and (iv) repor he esimaes for equaion (2.4). 10

13 Table 5: Sample summary saisics, exended sample Variable Obs Mean Sd. Dev. Min Max (i) (ii) (iii) (iv) (v) Panel 1: Germany ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Panel 2: Spain ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Panel 3: Japan ln C i; ln C j; ln Y i; ln Y j; ln RER j;i Panel 4: All cross-counry ln C i; ln C j; ln Y i; ln Y j; ln RER j;i ln(p j; =P i; ) ln S i;j Noes: The able repors summary saisics of he presened variables for several samples: all Germany bundeslaender pairs (Panel 1); all Spain auonomous communiies pairs (Panel 2); all Japan prefecure pairs (Panel 3); and all cross-counry pairs for he ve counries in our exended sample (Panel 4). Obs. refer o he number of observaions in each sample; Mean - sample average; Sd. Dev. - sample sandard deviaion; Min-sample minimum; Max-sample maximum. Consisen wih our ndings for he US and Canada, he inra-naional consumpion-real exchange rae correlaion for our sample of counries is posiive and signi can, equal o abou 0.35 in a benchmark speci caion, and o abou 0.28 when we conrol for he e ec of oupu on consumpion. This correlaion declines dramaically when we accoun for he border. In paricular, he cross-counry consumpion-real exchange rae correlaion is 0.02 when esimaed from a pooled regression, and increases o 0.01 in he xed e ecs speci caion (robus o he inclusion of oupu). Boh correlaions are highly signi can. Table 7 con rms ha he majoriy of his drop in he correlaion is due o nominal exchange rae movemens he coe cien on he variable ( ln S i;j ) is negaive and signi can. I is also worhwhile o noe ha he coe cien on he e j;i border i;j variable is negaive and signi can, implying ha he movemens of cross-border relaive prices (conrolling for he nominal exchange rae) also reduce inernaional risk-sharing in our full sample of counries. Overall, our empirical analysis provides us wih several insighs ino he consumpion-rer relaionship: (i) Wihin counries his correlaion is posiive and signi can, implying some amoun of inra-naional risk-sharing. This risk-sharing, however, is far from perfec; (ii) Across counries, he consumpion-real exchange rae correlaion is signi canly smaller han wihin counries. I is in fac negaive beween US and Canada, and in he full sample of counries; (iii) The majoriy of he decline in inernaional risk-sharing relaive o he inra-naional risk-sharing is due o nominal exchange rae co-moving negaively wih relaive consumpion; (iv) Inernaional relaive price movemens (conrolling for nominal exchange rae changes) hinder inernaional risk-sharing. 11

14 Table 6: Esimaes of Border E ec, all counries Pooled Fixed e ecs Pooled Fixed e ecs (i) (ii) (iii) (iv) e j;i 0.349*** 0.373*** 0.275*** 0.298*** (0.019) (0.023) (0.019) (0.022) e j;i border i;j *** *** *** *** (0.020) (0.024) (0.020) (0.023) e j;i ln ~ d i;j 0.021*** 0.026*** 0.019*** 0.022*** (0.003) (0.004) (0.003) (0.004) y i;j 0.169*** 0.161*** (0.006) (0.008) y i;j border i;j *** *** (0.008) (0.012) y i;j ln ~ d i;j 0.040*** 0.039*** (0.004) (0.005) e j;i +ej;i border i;j *** *** *** ** (0.004) (0.004) (0.004) (0.004) N R Noes: The dependen variable is relaive consumpion growh beween locaions i and j; c i;j : The esimaed speci caion in columns (i)-(ii) is equaion (2.3); while in columns (iii)-(iv) i is equaion (2.4). Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively Counry heerogeneiy In he regression speci caions (2.3) and (2.4) he e ec of he border on C-RER correlaion, as capured by he ineracive erm on he RER wih he border dummy, is measured relaive o he average C-RER 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 di erenials and consumpion di erenials, such benchmark is arbirary and can lead o misleading resuls. In paricular, in his case, he border coe cien may capure he join e ec of he border and cross-counry heerogeneiy in C-RER correlaion. We nex address his issue by allowing he inra-naional correlaion beween c i;j and e j;i o be counry-speci c. In paricular, we amend he regression speci caion in equaion (2.4) wih he produc erms of e j;i wih a se of dummy variables, each idenifying wihin-counry jurisdicion pairs in each counry in our sample. In all cases we use wihin US sae pairs as he benchmark. For insance, for US-Canada case, we include in he regression (2.4) an ineracive erm of e j;i wih a dummy variable ha equals one for all province pairs wihin Canada. The coe cien on his ineracive erm will give us he change in he inra-naional C-RER when ransiioning from US sae pairs o Canadian province pairs. The coe cien on he ineracive erm beween e j;i and border dummy, as before, will give us he e ec of he border on C-RER correlaion, excep now we can esimae he e ec of he border crossing from he perspecive of each individual counry in our sample. Table 8 repors our resuls for he US-Canada sample and for he exended sample of 5 counries. 10 For compleeness, panel (a) summarizes our earlier resuls from he xed e ecs regressions 10 Deailed esimaion resuls are available from he auhors upon reques. 12

15 Table 7: Esimaes of he Border E ec: RER Decomposiion, all counries Fixed e ecs Fixed e ecs (i) (ii) e j;i 0.384*** 0.308*** (0.023) (0.022) e j;i border i;j *** *** (0.026) (0.025) e j;i ln ~ d i;j 0.038*** 0.034*** (0.004) (0.004) y i;j 0.159*** (0.008) y i;j border i;j *** (0.012) y i;j ln ~ d i;j 0.037*** (0.005) ln S i;j *** *** (0.011) (0.010) N R Noes: The dependen variable is relaive consumpion growh beween locaions i and j; c i;j : The esimaed speci caion in column (i) is equaion (2.3), while in column (ii) is equaion (2.4). Boh are modi ed o include he growh rae of he nominal exchange rae. Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively. where we used he average correlaion in he inra-counry pairs as he benchmark for gauging he border e ec (see columns (ii) and (iv) in Tables 2 and 6). Panel (b) presens he esimaion resuls ha allow for counry heerogeneiy. We repor he resuls from he speci caion wih hando-mouh consumers (columns labelled "wih y i;j ") and wih homogeneous consumers (columns labelled "no y i;j "). 11 All regressions include jurisdicion-pairs xed e ecs. Our resuls reveal some amoun of heerogeneiy across our sample of counries. However, some common paerns emerge. Firs, inra-naional C-RER correlaions are consisenly posiive, wih he US and Spain showing he highes numbers in our sample, while Germany is characerized by he lowes correlaion. 12 Second, inernaional correlaions are negaive for all counries, excep Spain. The correlaions are he lowes (mos negaive) in Germany Exchange rae regime To furher assess he role of he exchange rae in C-RER correlaions, we urn o inernaional evidence. In paricular, we sudy a cohor of he 12 European Union member saes during period. 13 To evaluae he role of he exchange rae, we spli he sample ino pre-euro period ( ) and euro period ( ). 14 For each subsample we compue all bilaeral correlaions 11 Speci caion 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 correlaions o be counry-speci c as well. 12 The only excepion is Germany in he speci caion wih no hand-o-mouh consumers, who exhibis negaive inra-naional C-RER correlaion. 13 Daa deails and sources are provided in he Appendix A Greece adoped euro on January 1, We adjus our calculaions accordingly. 13

16 Table 8: Inernaional C-RER correlaion: Accouning for counry heerogeneiy no y i;j US-Canada wih y i;j no y i;j Exended sample wih y i;j Panel (a). Homogeneous benchmark Inra-naional 0.424*** 0.317*** 0.373*** 0.298*** (0.026) (0.027) (0.023) (0.022) Inernaional *** *** *** *** (0.007) (0.007) (0.004) (0.004) Panel (b). Heerogeneous benchmarks Inra-naional correlaions US 0.413*** 0.305*** 0.433*** 0.329*** (0.027) (0.027) (0.027) (0.027) Canada 0.203*** 0.140*** 0.214*** 0.159*** (0.056) (0.057) (0.042) (0.045) Germany *** 0.135*** (0.021) (0.029) Japan 0.360*** 0.227*** (0.034) (0.035) Spain 0.925*** 1.151*** (0.144) (0.113) Inernaional correlaions US *** *** ** (0.007) (0.006) (0.004) (0.004) Canada *** *** *** *** (0.050) (0.051) (0.050) (0.053) Germany *** *** (0.033) (0.039) Japan * *** (0.043) (0.043) Spain 0.485*** 0.817*** (0.147) (0.116) 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 Tables 2 and 6. Panel (b) repors he resuls from a regression speci caion in equaion (2.3) column labelled "no y i;j ", and speci caion in equaion (2.4) column labelled "wih y i;j ", boh modi ed 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 benchmark. All regressions include jurisdicion pairs xed e ecs. Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively. of relaive consumpion growh wih he growh rae in he RER for each counry. The average correlaions for each counry and each sub-period are repored in Table 9. A clear conras arises beween he wo periods: In he pre-euro period, he C-RER correlaion is negaive, on average, across counries, equal o The same correlaion urns posiive in he euro period and is equal o These resuls suppor our earlier ndings on he role of exchange rae ucuaions for he nding of negaive correlaion beween relaive consumpion growh and RER growh We recognize ha besides he exchange rae regime, oher facors could have also conribued o he increase in he C-RER correlaion in he second sub-period. For insance, he degree of nancial 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. 14

17 Table 9: Inernaional C-RER correlaion: Fixed vs exible regime Pre-euro period Euro period presen (i) (ii) Ausria Belgium Finland France Germany Greece Ireland Ialy Luxembourg Neherlands Porugal Spain Average An alernaive measure of risk-sharing and he role of he nominal exchange rae Up o now, we have assumed ha he benchmark for e 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 meric for he degree o which risk-sharing fails in he daa, nor he exen o which he border (or he nominal exchange rae) conribues o his failure. Here we follow in he spiri of (Engel and Rogers (1996)) in consrucing a measure of he degree o which he border accouns for he failure of risk-sharing. 16 We reurn o equaion (2.2) and for each regional pair, for a choice of, we compue c i;j (1=)e j;i and obain is sandard deviaion in he ime-series. 17 This gives us a cross-secion of such sandard deviaions. If our choice of is correc, hen wih full risk-sharing his saisic would be zero for each bilaeral pair. 18 repored in panel (i) of Table 10. The summary saisics of his measure are Table 10: Alernaive meaure of risk-sharing: Summary saisics Variable Obs Mean Sd. Dev. Min Max h (i) sd:dev: c i;j h (ii) sd:dev: c i;j i (1=)e j;i i (1=)~e 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. 16 Engel and Rogers (1996) measure he exen of he failure of he law of one price using he sandard deviaion of he price di erenials of similar goods across ciies in he US and Canada. 17 We also conduc he analysis of his secion using he mean of he squared di erence, mean c i;j (1=)~e j;i 2 ; and nd ha he resuls are robus o his alernaive measure of risk-sharing. 18 We se = 2, so ha he elasiciy of ineremporal subsiuion is equal o 0.5 a sandard value in he lieraure. 15

18 Using his measure of he deparure from risk-sharing, we esimae he following regression: h sd:dev: c i;j i (1=)e j;i = 1 border i;j + 5X m D mm + " i;j ; (2.6) m=1 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 " i;j is he regression error erm. We also consider a speci caion in which we include 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 : 19 Table 11 repors he resuls. Panel (i) presens he resuls wihou he log disance variable in he speci caion, while panel (ii) - includes he log disance variable. The e ec of he border is posiive and signi can. I means ha conrolling for counry-speci c volailiy in risk-sharing measure, here is a greaer deviaion from e 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 coe cien is 2.74 percen, so he border accouns for 53 percen of he oal, afer conrolling for disance. Table 11: Alernaive meaure of risk-sharing: The role of he border Variable border ln(disance) N R 2 explained h i by border (i) sd:dev: c i;j (1=)e j;i *** h (ii) sd:dev: c i;j h (iii) sd:dev: c i;j h (iv) sd:dev: c i;j i (1=)e j;i i (1=)~e j;i i (1=)~e j;i (0.0008) *** *** (0.0009) (0.0003) *** (0.0008) *** *** (0.0008) (0.0002) Noes: This Table presens resuls from esimaing regression speci caion (2.6). The dependen variable is noed in he rs column of he able. Robus sandard errors are in parenheses. *,**, and *** indicae signi cance a 10%, 5%, and 1%, respecively. Can his border e ec be aribued o movemens in he nominal exchange rae, as argued previously? In his example, he es is purely a cross-secion one, so we canno include he nominal exchange rae as a righ-hand side variable. Bu we can again follow Engel and Rogers (1996) in using an alernaive measure of real exchange raes as he relaive real price. To conrol for he volailiy of he nominal exchange we obain a measure of he real exchange rae as he relaive foreign o home real price, so ha nominal exchange rae does no appear in he calculaions. De ne P i =P o be he raio of he price level in jurisdicion i o he aggregae price in he foreign counry. Similarly, le he home real price be de ned as P j =P, where P is he aggregae 19 Noe ha his is a cross-secional regression. 16

19 price index a home. Then he relaive real price beween locaions i and j is given by ]RER j;i = Pj;=P = (Pi; =P ) : Noe ha for any wo locaions wihin he same counry, ]RER j;i = P j; =P i; as before. Bu for any wo locaions in di eren counries, his alernaive measure of he real exchange rae does no conain he nominal exchange rae. Engel and Rogers (1996) used his measure of he real exchange rae o es he degree o which he border e ec could be aribued o nominal price sickiness, since if all nominal prices wihin counries were xed and real exchange raes were fully accouned for by nominal exchange rae variaion, hen his measure of he real exchange rae would be consan, and he border e ec would be insigni can. In he same spiri, his alernaive real exchange rae de niion gives us a way in which o assess he degree o which he presence of he nominal exchange rae accouns for he size of he border in deviaions from e cien risk-sharing. Afer compuing ]RER j;i ; we repea he sepsh above o consrucihe volailiy of our risk-sharing measure for every jurisdicion pair as sd:dev: c i;j (1=)~e j;i ; where ~e j;i = ln( ]RER j;i ) ln( ]RER j;i 1): Panel (ii) of Table 10 presens he summary saisics on his adjused measure. Clearly, his measure is less volaile han he original measure based on unadjused real exchange rae. 20 We hen esimae he regression speci caion in (2.6) using his adjused measure of deviaions from he perfec risk-sharing. The resuls are repored in panels (iii) and (iv) of Table 11. We nd ha he coe cien on he border dummy is sill posiive and signi can. Bu i is subsanially smaller han before. How much does he border maer afer we conrol for he nominal exchange rae in he calculaion of relaive prices? From panel (iv), he coe cien on he border dummy is 1.16 percen, while he average volailiy of he adjused risk-sharing measure as repored in Table 10 is 3.35 percen. So he border accouns for 35 percen of he sandard deviaion. Thus, when he nominal exchange rae is dropped from he calculaion of he relaive prices, he conribuion of he border o he average volailiy of he risk-sharing measure declines from 53 percen o 35 percen. We nex develop a heoreical framework o shed some ligh on our empirical ndings. 3 Consumpion Risk-Sharing wih Sicky Prices From he previous secion, i is apparen ha he presence of he nominal exchange rae plays a key role in empirical ess of he risk sharing relaionship beween bilaeral consumpion di erences and real exchange rae changes. Wha can accoun for his? One obvious suggesion is ha goods prices are sicky, and so subsanial real exchange rae adjusmen, in he shor run, can be 20 Engel (1999) shows ha if preferences are idenical across counries and he law of one price holds for raded goods, hen he real exchange rae can be exacly wrien as a relaive-relaive price, expressing he relaive price of non-raded o raded goods for one counry relaive o he oher counry. If we subsiued he price index for raded goods for he aggregae price index for each counry, hen our measure of he real exchange rae would be exac under he same condiions as Engel (1999). 17