Trade Costs, Asset Market Frictions and Risk Sharing

Transcription

1 Trade Coss, Asse Marke Fricions and Risk Sharing Doireann Fizgerald July 2010 Absrac I use bilaeral impor daa o es for he role of rade coss and asse marke fricions in impeding inernaional consumpion risk sharing. Trade coss play a significan role. I do no rejec he null of opimal risk sharing wihin OECD counries, hough I do rejec for he world as a whole. I calculae he impac on ex-pos welfare of moving from hisorical asse marke fricions o opimal consumpion risk sharing, holding rade coss fixed. The gains o OECD counries are small while he gains o non-oecd counries are larger. These gains are dwarfed by hose from eliminaing rade coss. JEL Classificaion: F41 1 Inroducion In a world where here are no fricions in goods markes, and a full se of coningen claims can be raded, he growh rae of he marginal uiliy of consumpion should be perfecly correlaed across counries. This predicion is rejeced by he daa (e.g. Backus, Kehoe and Kydland [1992]). Popular explanaions for he failure of perfec consumpion risk sharing include coss of rading goods inernaionally and deviaions of inernaional asse markes I am graeful for financial suppor from he Universiy of California and he NSF under gran # Exper research assisance was provided by Daniel Belran. I hank wo anonymous referees, Manuel Amador, Jonahan Eaon, Pierre-Olivier Gourinchas, Sam Korum, Kenneh Rogoff, Iván Werning and seminar paricipans a Harvard, Sanford, he Spring meeings of he NBER ITI program, he NBER Summer Insiue and he Second Annual CEPR Workshop on Global Inerdependence for commens and suggesions. The usual disclaimer applies. Deparmen of Economics, Sanford Universiy, Sanford, CA 94305, dfizger a sanford.edu 1

2 from he Arrow-Debreu benchmark (e.g. Obsfeld and Rogoff [2000] and Heahcoe and Perri [2002]). Trade coss make risk sharing cosly, so i is opimal no o share consumpion risk fully. Asse marke fricions limi counries abiliy o wrie and honor he conracs necessary o implemen he opimal amoun of consumpion risk sharing condiional on rade coss. There is a subsanial body of evidence ha rade coss are large (Anderson and van Wincoop [2004]). There is also evidence ha fricions such as limied commimen affec asse rade bewen developed and developing counries. Bu somewha surprisingly, i appears ha fricions in asse markes also play an imporan role in impeding opimal consumpion risk sharing beween OECD counries (see Backus and Smih [1993], Kollmann [1995] and Ravn [2001]). In his paper, I es for and quanify he imporance of rade coss and asse marke fricions in explaining he failure of perfec consumpion risk sharing. In conras wih he previous lieraure, I find ha fricions in inernaional asse markes significanly impede opimal consumpion risk sharing beween OECD and non-oecd counries, bu no necessarily wihin OECD counries. Trade coss, in conras, significanly impede risk sharing for all counries. To moivae he ess and o provide a framework for he welfare calculaions, I firs presen a heoreical framework ha ness boh rade coss and asse marke fricions. In he way I inroduce rade coss, I borrow heavily from he lieraure on he heoreical foundaions of a graviy model of inra-emporal rade. Graviy models do a good job of maching he paern of bilaeral rade, and have become a workhorse for welfare analysis in he rade lieraure (see Arkolakis, Cosino and Rodriguez-Clare [2009]). Several differen saic models of specializaion and rade yield he same graviy srucure. For simpliciy, I follow Anderson and van Wincoop [2003] in assuming Armingon specializaion. Togeher wih CES demands and iceberg coss of rade, his assumpion yields predicions abou he marix of bilaeral rade which are observaionally equivalen o he predicions of he Ricardian model of Eaon and Korum [2002], or o hose which would resul from an increasing reurns sory as in Krugman [1980]. I nes he graviy model inside a sandard DSGE model, where counries produce oupu using elasically supplied labor, accumulable capial and sochasic produciviy. The srucure of inernaional asse markes deermines he exen o which counries can engage in rade across saes and over ime. Irrespecive of wha goes on in asse markes, all ypes of rade - wihin and across saes and periods - are limied by he presence of resource coss of rade. I do no ake a sand wha he asse marke looks like. Neverheless, exacly as in 2

3 a world wih no rade coss, a key implicaion of complee and fricionless asse markes is ha a counry s inverse marginal uiliy of wealh (relaive o oher counries) is consan over ime. Jus as in a world wihou rade coss, a naural meric for he salience of asse marke fricions in impeding consumpion risk sharing beween groups of counries is he degree o which he relaive inverse marginal uiliy of wealh moves around across saes of he world and over ime. The model provides a naural seing for esing for he role of rade coss and asse marke fricions in limiing consumpion risk sharing boh wihin and across saes and over ime. Empirical graviy models have long been used o infer he presence of rade coss from he rade-reducing effecs of disance. The key conribuion of his par of he paper is o show how bilaeral rade daa can also be used o es for he role of asse marke fricions in impeding perfec consumpion risk sharing. This relies on he appearance of he uiliy-consisen consumpion price, which is equal o he raio of he marginal uiliy of consumpion and he marginal uiliy of wealh, in he model-based graviy equaion. The es is hen based on comparing he abiliy of a resriced graviy model ha imposes a consan relaive inverse marginal uiliy of wealh across counries o explain he variaion in bilaeral rade daa wih ha of an unresriced graviy model. In addiion, I show how he same srucure can be used o es he null hypohesis of financial auarky agains he alernaive of some inernaional asse flows, by placing a differen resricion on he empirical graviy model. I implemen he ess using bilaeral rade daa for a sample of 88 developed and developing counries from Unsurprisingly, given wha we know from he lieraure on esimaed graviy models, he null hypohesis of no rade coss is overwhelmingly rejeced for all counries. The null hypohesis of financial auarky is rejeced, while he null hypohesis of opimal risk sharing beween OECD and non-oecd counries condiional on rade coss is also rejeced. However he resuls for OECD counries are srikingly differen from he previous lieraure: he es does no rejec he null hypohesis of opimal consumpion risk sharing wihin OECD counries. Nex, I use he model o provide a more coninuous meric of relaive disance from opimal consumpion risk sharing. More precisely, I reallocae he oupu hisorically devoed o consumpion consisen wih opimal risk sharing condiional on hisorical rade coss, and hen calculae he implied changes in rade and ex-pos welfare relaive o he hisorical benchmark. I do his separaely for opimal risk sharing wihin he OECD and opimal risk sharing in he world as a whole. I also examine he incremenal effec of moving from opimal 3

4 risk sharing in he world as a whole under hisorical rade coss o opimal risk sharing wih zero rade coss. These exercises require esimaes of hisorical rade coss and oupu. The obvious way o obain esimaes of rade coss is by esimaing a graviy model. To make everyhing inernally consisen, I also use he graviy model o obain esimaes of he oupu prices which I use o deflae nominal oupu. More precisely, I use he graviy model o esimae boh of hese variables up o he order of an exponen which depends on he elasiciy of subsiuion. In he esimaion, I make use of he full se of resricions implied by he srucural model. In paricular, I impose he resricion ha he prediced raio of ne expors o GDP for each counry exacly maches ha in he daa. The fied model does a good job of maching he paern of bilaeral rade and he evoluion of raios of rade o GDP. Based on he esimaes from he graviy model, and an assumpion abou he elasiciy of subsiuion from he previous lieraure, I can hen calculae boh he real oupu hisorically devoed o privae consumpion and he level of hisorical rade coss. The addiional assumpion of a value for risk aversion allows me o esimae he relaive inverse marginal uiliy of wealh for each counry in each year, and o calculae rade and welfare under counerfacual ime-invarian values for his variable. The esimaes of he hisorical inverse marginal uiliy of wealh are used o choose plausible poins on he Pareo fronier. Under opimal consumpion risk sharing wihin OECD counries alone, ex-pos welfare in he median OECD counry is almos unchanged from he benchmark. In conras, under opimal risk sharing in he world as a whole, he increase in ex-pos welfare in he median non-oecd counry is on he order of 3%, while here is a reducion of 1% in welfare in he median OECD counry. This suggess ha over he sample period, OECD counries were much closer o opimal risk sharing (wih each oher) han wih non-oecd counries. This is refleced in he behavior of rade and ne expors in he counerfacual exercises compared wih he fied model. Under opimal risk sharing wihin OECD counries alone, oal inra-oecd rade as a share of OECD GDP is 6% higher han in he fied model, while he median absolue value of he rade balance as a share of GDP for OECD counries widens from 2% o 4%. In conras, under opimal risk sharing in he world as a whole here are subsanial increases in rade beween OECD and non-oecd counries - his rade as a share of non-oecd GDP is 23% higher han in he fied model. This reflecs an increase in he median absolue value of he rade balance for non-oecd counries from 6% o 15%, and for OECD counries from 2% o 5%. Finally, he incremenal effec of eliminaing rade 4

5 coss on welfare and rade is enormous, which is no surprising given he esimaed size of rade coss. This paper is relaed o several differen lieraures. The es for he presence of fricions in inernaional asse markes is relaed o Lewis [1996] who ess for perfec consumpion risk sharing in a large sample of counries in a framework ha does no have rade coss. She does no rejec he null of risk sharing for counries classified as having more unresriced asse rade. I is also relaed o Backus and Smih [1993], Kollmann [1995] and Ravn [2001] among ohers, who es for opimal consumpion risk sharing among OECD counries, condiional on fricions in goods markes. Relaive o his laer lieraure, I innovae by giving a unified reamen o asse markes and rade coss, and by comparing OECD wih non-oecd counries. The role of rade coss in explaining inernaional macro puzzles has been previously explored by Backus, Kehoe and Kydland [1992], Dumas [1992], Obsfeld and Rogoff [2000], Dumas and Uppal [2001], Heahcoe and Perri [2004], Kose and Yi [2006], Mazzenga and Ravn [2004] and Fizgerald [2008] among ohers. I innovae relaive o much of his lieraure by underaking a quaniaive analysis for a large number of counries based on a srucural graviy model. Imporanly, in conras o much of his work, my analysis does no require me o ake a sand on wha exacly are he fricions in asse markes. The paper is also relaed o he subsanial lieraure on he specificaion and esimaion of srucurally-based saic graviy equaions of bilaeral rade, including Eaon and Korum [2002], Anderson and van Wincoop [2003] and Alvarez and Lucas [2007]. More recenly, a growing lieraure uses calibraed models of his ype for welfare analysis (see Arkolakis, Cosino and Rodriguez-Clare [2009] for ciaions), generally under he assumpion of balanced rade. An excepion is Dekle, Eaon and Korum [2008], who examine he effec on world rade and welfare of eliminaing rade balances in he conex of a calibraed graviy model. Of his laer lieraure, heirs is he mos closely relaed paper. Finally, his paper is relaed o he lieraure on measuring he poenial welfare gains from inernaional risk sharing, as summarized by van Wincoop [1999]. The nex secion lays ou he heoreical framework. The hird secion describes he es for he role of fricions. The fourh secion presens he daa and es resuls, and discusses heir inerpreaion. The fifh secion describes he welfare analysis and resuls. The final secion concludes. 5

6 2 Theoreical framework Summary There are N counries in he world, indexed i = 1,..., N. Each counry produces a disinc inermediae good (also indexed i) using capial, labor and maerials. Capial is accumulable. Labor is elasically supplied. Produciviy in he producion of each counry s inermediae good is sochasic. No resricions are placed on he join process for produciviy in all counries. The inermediae goods are radeable a some cos which akes an iceberg form. They are combined using a CES aggregaor, he same in all counries, o produce a nonradeable final good used for privae and public consumpion, invesmen and maerials. Asse markes are complee and fricionless wihin counries, bu here may be exogenous or endogenous limiaions on he conracs ha can be wrien beweeen agens from differen counries. Uncerainy In each period, he world economy experiences one even, s S. Denoe by s he hisory of evens from dae 0 o dae. The probabiliy of hisory s a dae is given by π (s ). Preferences and echnology For simpliciy, he problem is described as if counry i had a single agen wih expeced uiliy given by: U i = β π =0 s s C L i i (s ) u, Hi (s ) L i L i where L i is he (deerminisic) populaion of counry i, C i (s ) is oal consumpion and H i (s ) is he oal number of hours worked. Counry i produces inermediae good i by combining capial, labor and maerials using a consan reurns o scale producion funcion: (1) Y i s = F K i s 1, A i s H i s σ M i s 1 σ (2) where A i (s ) is he realizaion of produciviy, K i (s 1 ) is he (predeermined) capial sock available for use in producion in counry i a ime and M i (s ) is maerials used up in producion. 6

7 The producion funcion for he final good, X is: X i s = N k=1 Z ik η η 1 η 1 s η (3) where Z ik (s ) is absorpion in counry i of inermediae good k a s. If η, we are in he case of a one-good world. The resource consrain for he (non-raded) final good in i is: X i s = C i s + I i s + M i s (4) where I i (s ) is invesmen in counry i. Given he rae of depreciaion δ, capial in counry i accumulaes according o: K +1 i s = (1 δ) K i s 1 + I i s Resource coss of rade Inermediae goods rade may be cosly: in order for one uni of j s good o arrive in i, τ ij (s ) unis mus be shipped, wih τ ii is no in general required ha τ ij (s ) = τ ji (s ) = 1, τ ij mus ake accoun of he resource cos of rade: Y i s = (s ) 1 and τ ij (s ) τ jk (s ) τ ik (s ). I (s ). The inermediae goods resource consrains N k=1 τ ki s Z ki s (5) Goods marke Producers of inermediae goods are assumed o be aomisic price akers. Bu due o rade coss, inermediae goods prices differ across counries: Q ki i, s = τ ki s Q ii s (6) where Q ii (s ) is he spo price of inermediae i in counry i a s and Q ki (s ) is is spo price in counry k. In wha follows, Q ii (s ) is abbreviaed o Q i (s ), and Q ki (s ) is replaced by τ ki (s ) Q i (s ). Asse marke 7

8 A s, counry i eners wih a vecor of asse holdings B i (s 1 ) ha pays dividends wih value given by D (s ) B i (s 1 ). The vecor of asse prices, aken as given by each counry, is R (s ). The value of asse holdings is given by R (s ) B i (s 1 ). The counry can choose o re-opimize is holdings by spending R (s ) B i +1 (s ) o purchase a new vecor wih B i +1 (s ) B i (s, K (s 1 ), B (s 1 )). Asses are disinguished by heir dividend vecors, while he asse marke srucure deermines B i (s, K (s 1 ), B (s 1 )), he se of asses available o counry i a s. Asses are defined such ha hey are in zero ne supply: N B i s = 0 (7) i=1 This seup is general enough o encompass fricionless asse markes, financial auarky, and a variey of differen ypes of fricions ha allow for parial risk sharing hrough asse markes. 1 Sequenial compeiive equilibrium A each poin in ime, counry i chooses C i (s ), H i (s ), Z i (s ), M i (s ), K i +1 (s ) and B i +1 (s ) o maximize expeced uiliy (1) subjec o is aggregae good resource consrain: N k=1 Z ik η η 1 η 1 s η = C i s + K +1 i s (1 δ) K i s 1 + M i s (8) and is budge consrain, expressed in nominal erms: N k=1 τ ik s Q k s Z ik s Q i, s F K i s 1, A i s H i s σ M i s 1 σ = D s + R s B i s 1 R s B i +1 s (9) where he lef hand side is he difference bewen he value of expendiure and he value of oupu, and he righ hand side is he difference beween he value of wealh enering s, and he value of wealh sen forward o he fuure. R (s ), D (s ) and Q (s ), are aken as given, and B i +1 (s ) B i (s, K (s 1 ), B (s 1 )). A compeiive equilibrium is a vecor of prices (Q, R ) and a vecor of quaniies for each counry C i,h i, Z i, M i,k i, B i such ha each counry solves he above problem a every realized sae s and (5), (7) and (8) hold for all realized s (i.e. all markes clear). 1 For example, i ness he case where he only inernaionally raded asse is a risk-free bond. I also ness he cases of limied commimen wih endogenous and exogenous incompleeness. 8

9 Firs order condiions Assume he exisence of a compeiive equilibrium. Then a any s, given K and B, he firs order condiions wih respec o absorpion of each inermediae and aggregae consumpion are necessary for compeiive equilibrium (i.e. he problem of counry i a s is convex). 2 The firs order condiion wih respec o Z ik (s ) is: P i s X i s 1 η Z ik s 1 η The firs order condiion wih respec o C i (s ) is: λ i s C i u (s ) c, Hi (s ) L i L i = τ ik Q k s (10) = P i s (11) where λ i (s ) is he inverse of he marginal uiliy of curren per capia nominal wealh for counry i evaluaed a s (i.e. he inverse of he muliplier on he budge consrain), u c ( ) is he marginal uiliy of consumpion per capia, and P i (s ) is he nominal price of he consumpion aggregae in i a s, i.e.: P i s = N k=1 τ ik Q k s 1 η 1 1 η (12) As usual, he λ i (s ) s have an alernaive inerpreaion as he per capia Pareo weighs for each counry in a squence of inra-emporal planning problems. A useful normalizaion of he λ s, and consequenly, prices, suggesed by his inerpreaion is i λi (s ) = 1. Complee markes In general, he relaive marginal uiliy of nominal wealh, and hence is inverse, λ i (s ), varies across saes and over ime in a way ha depends joinly on he process for shocks, rade coss, and on he exac specificaion of he asse marke. The evoluion of λ i (s ) over ime is a convenien way of summarizing he combined impac of all of hese facors on ex-pos consumpion risk sharing. The value of his summary saisic lies in he fac ha i is sraighforward o characerize some aspecs of he behavior of λ i (s ) under complee and fricionless asse markes. When asse markes are complee and fricionless, he sequenial compeiive equilibrium of his economy is Pareo opimal. The compeiive equilibrium allocaion can herefore be recovered as he soluion o a planning problem where for appropriae λ 1,..., λ N he 2 I is no necessary o make use of he oher necessary condiions. 9

10 planner chooses sequences C, H, Z, M, and K o maximize he ex-ane weighed sum of expeced uiliies: N λ i U i = i=1 N i=1 β π =0 s s C λ i L i i (s ) u, Hi (s ) L i L i (13) subjec o (for all i and s ) he resource consrains (5) and (8). The firs order condiions for his problem wih respec o choices of C and Z are exacly (11) and (10), wih consan λ i. 3 A es for consumpion risk sharing I is naural o base ess for consumpion risk sharing on he firs order condiion for aggregae consumpion, (11). Given (11), he relaive marginal uiliy of consumpion is (dropping he sae-coningen noaion for he sake of breviy): u c C i L i, Hi L i C j u c, Hj L j L j λ i = λ j 1 P i P j This expression illusraes he fac ha he relaive marginal uiliy of consumpion can vary over ime and across saes for wo reasons. Firs, if asse markes are no fricionless, λ i /λ j need no be consan. In paricular, relaive wealh may respond o curren oupu. Of course, he converse is no rue, as depending on he exac naure of fricions, he process for shocks and he elasiciy of subsiuion η, λ i /λ j could be consan even if asse markes are no fricionless. (14) Second, in order for consumpion risk sharing o ake place, goods mus be shipped inernaionally. If shipping is cosly, agens will opimally choose no o smooh consumpion perfecly. The effec of rade coss is capured by he (consumpion) real exchange rae, P i /P j, which in general will vary wih curren oupu when rade is cosly. One srand of he lieraure on esing for inernaional consumpion risk sharing (e.g. Lewis [1996]) examines wheher relaive raded goods consumpion growh raes are correlaed wih relaive oupu growh raes. One disadvanage of his approach is ha if raded goods prices differ across counries, he es canno disinguish beween failures of risk sharing due o fricions in goods markes and failures of risk sharing due o fricions in asse markes. In conras, he lieraure on consumpion-real exchange rae correlaions (e.g. 10

11 Backus and Smih [1993], Kollmann [1995] and Ravn [2001]) infers he presence of fricions in inernaional asse markes from an examinaion of he relaionship beween real exchange raes (he inverse of relaive prices) and he relaive real consumpion implied by hose prices. This lieraure implicily condiions on (bu does no es for or esimae) fricions in goods markes. I finds ha for OECD counries, he correlaion beween relaive consumpion and real exchange raes is zero, or has he opposie sign o ha prediced under he null hypohesis of fricionless asse markes and concave uiliy. The conclusion drawn from his finding is ha here mus be fricions in asse markes impeding consumpion risk sharing beween OECD counries. 3.1 Tess based on bilaeral impor flows I now describe a unified framework for esing for he role of asse marke fricions and rade coss in impeding perfec consumpion risk sharing. The ess are based on esimaing resriced and unresriced graviy models of bilaeral impors. As such, he role of rade coss is idenified principally from he rade-reducing effec of disance. The es for opimal risk sharing (condiional on rade coss) is, like he ess described above, based on he firs order condiion for consumpion. Bu in conras wih he lieraure on consumpionreal exchange rae correlaions, which infers he presence of asse marke fricions from he correlaion beween relaive consumpion growh and he change in real exchange raes, he role of fricions in asse markes is inferred from he degree o which resricing he marginal uiliy of wealh o be consan over ime raher han allowing i o vary in an unresriced way reduces he abiliy of he graviy model o fi he bilaeral rade daa. Addiionally, he es uses he prices consisen wih he graviy model of rade (raher han measured prices) o decompose he value of consumpion ino price and quaniy erms. Finally, i is also possible o es he null hypohesis of financial auarky agains he alernaive of some asse rade wihin he conex of his framework. Because his es is based on he abiliy of a (differen) resriced graviy model o mach he same bilaeral rade daa, i provides a way of measuring wheher inernaional asse markes are furher from complee markes or from financial auarky. The model described above yields an expression for bilaeral impors ha akes he graviy form. Combining (10), he firs order condiion for inermediae goods, wih he 11

12 resource consrains for inermediae goods we ge: 3 IM ik EXP i OUT k = τ ik Q k Z ik P (P i X) i = Π k i Q k Y k τ ik η 1 (15) where Π k 1 η = N j=1 η 1 P j P j τ jk X j (16) and IM ik is he value of impors ino counry i from counry k, EXP i is he value of oal expendiure by counry i and OUT k is he value of gross oupu of counry k. This is a relaionship beween he value of impors ino i from k, he expendiure of he imporer, he oupu of he exporer, he iceberg rade cos beween he wo counries, and wo erms ha are known in he graviy lieraure as mulilaeral resisance erms. 4 This expression is valid for any asse marke srucure, and under he assumpion ha rade coss ake he iceberg form. 5 There are wo poins o be noed abou he appearance of P i in (15). Firs, since P i is relaed o λ i hrough (11), expresssion (15) can be used o es hypoheses abou he behavior of λ as well as τ. Second, while graviy equaions of he form (15) do a good job of fiing he daa on bilaeral impors (see Anderson and van Wincoop [2004] for exensive ciaions on he lieraure on esimaing graviy models), he relaive prices hey imply behave somewha differenly from measured real exchange raes. This can be a leas parially aribued o he fac ha he model-consisen prices implicily value variey in a way ha measured price indexes do no. The model-based approach o valuing variey is he basis for a subsanial lieraure ha measures he gains from inra-emporal rade (see he ciaions in Arkolakis, Cosino and Rodriguez-Clare [2009]), and he reamen of gains from iner-emporal rade here is consisen wih ha lieraure. To see he implicaions for (15) of assuming opimal risk sharing, subsiue in he firs order condiion for aggregae consumpion, (11), and impose λ i = λ i : IM ik EXP i OUT k = (λ i ) η 1 u c C i, Hi L i L i η 1 Π k η 1 τ ik η 1 (17) 3 See he online Appendix for he full derivaion. 4 This erminology is due o Anderson and van Wincoop [2003]. 5 Helpman, Meliz and Rubinsein [2008] develop a generalizaion of his expression under fixed and per uni coss of rade. This complicaes he graviy expression, bu does no affec he mehodological poin made here. 12

13 Of course, as already menioned, while he vecor λ is consan under complee and fricionless asse markes, his is no an if-and-only-if relaionship. A consan λ may be consisen wih fricions in asse markes under cerain circumsances. 6 For his reason, I say ha (17) holds under he null hypohesis of opimal risk sharing, raher han he null hypohesis of complee and fricionless asse markes. To see wha is implied by he assumpion of zero rade coss, noe ha he model predics ha in he absence of rade coss, he composiion of he expendiure baske is idenical across counries, wih expendiure shares given by exporer shares in world oupu. This does no depend on he naure of fricions in he asse marke, which dicae he size of he baske across periods and saes. This resricion on (15) can be easily imposed by seing τ ik = 1 i, k, P i = 1 i (a convenien normalizaion) and noing ha in his case, Π k = Π. IM ik EXP i OUT k = Π η 1 (18) Finally, as shown by Anderson and van Wincoop [2003], 7 under financial auarky and symmeric rade coss, (15) reduces o an expression where Π k = P k : IM ik EXP i OUT k P i = P k τ ik η 1 (19) Clearly he fac ha counries have non-zero rade balances indicaes ha hey are no in financial auarky. Bu he fi of his expression provides a meric of relaive disance from he polar opposies of opimal risk sharing and financial auarky. Since (15) ness (17), (18) and (19), I es he null hypoheses of (17), (18) and (19) in urn agains he alernaive of (15). 3.2 Implemenaion Marginal uiliy of consumpion Some assumpions mus be made abou he form of he marginal uiliy of consumpion in order o implemen he es of he null of opimal risk sharing agains he alernaive. I 6 For example, Cole and Obsfeld show how in an endowmen economy, risk sharing can be achieved hrough erms-of-rade movemens alone, if η = 1. 7 The derivaion is reproduced in he online Appendix. 13

14 assume ha marginal uiliy can be wrien: C u i i ρ c (, ) = H i ψ (20) L i Given ha a conribuion of he es I propose is o esimae P i raher han o use measured prices, o be inernally consisen, I do no wan o use any informaion on aggregae prices or real exchange raes in implemening i. The assumed form for marginal uiliy allows he firs order condiion for aggregae consumpion under he null o be rewrien as a funcion of he value of consumpion: L i P i = ρ λ i 1 1 ρ V C i L i 1 ρ H i L i ψ 1 ρ (21) where V C i = P i C i. Trade coss The sandard assumpion in he empirical graviy lieraure on he form of bilaeral rade coss is (see Anderson and van Wincoop [2004]): τ ik 1 η = J n=1 D ik γn n, D ik n = 1 if i = k, Dn ik 1 oherwise (22) Commonly used graviy variables (D ik n ) include bilaeral disance and indicaor variables for common language, colonial heriage ec. These areconsruced in such a way as o impose τ ii = 1. In general, he number of graviy variables J N 2, where N 2 is he number of bilaeral pairs included in he regressions. Ideally, non-resource coss of rade due o policy barriers should also be conrolled for (he form of he es would be unaffeced). However consrucing he required daa is beyond he scope of his paper. Given ha here is no ime variaion in he sandard se of graviy variables, I allow for ime variaion in rade coss by esimaing a differen vecor of coefficiens γ on he graviy variables for each year. Given he se of graviy variables used, symmery of rade coss is imposed by consrucion, i.e. τ ik = τ ki. Esimaing equaions Taking models (15), (17), (18) and (19), subsiuing in he expressions for P i and rade coss where appropriae, and aking logs yields he following four esimaing equaions: Esimaing Equaions 14

15 Asse marke Trade coss Esimaing equaion (a) General Yes w ik (b) Fricionless Yes w ik (c) General No w ik (d) Auarky Yes w ik Here, w ik = θ i + φ k + J n=1 γ nd ik n + ε ik = ψ i + φ k + β c vc i + β h h i + J n=1 γ nd ik n + ε ik = φ + ε ik = θ i + θ k + J n=1 γ nd ik n + ε ik = ln IM ik /EXP i OUT k, vc i = ln (V C/L i i ), h i = ln (H/L i i ) and d ik n = ln D ik n. θ i = (η 1) ln P i is an imporer-year fixed effec, while φ k = (η 1) ln Π k is an exporer-year fixed effec, ψ i = ((η 1) / (ρ 1)) ln λ i is an imporer fixed effec and φ = (η 1) ln (Π ) is a ime fixed effec in he case of zero rade coss. I do no impose resricion (16) on he relaionship beween θ i and φ k, because I do no have access o daa on he full universe of counries and i is no necessary o impose he resricion in order o perform he ess. Since (a) ness in urn (b), (c) and (d), an F-es can be used o es he null of (b), (c) or (d) agains he alernaive of (a). 4 Daa and es resuls All daa is annual. Populaion, he curren dollar value of GDP, he curren dollar value of oal impors and oal expors, and he curren dollar value of privae consumpion expendiures are aken from he World Bank s World Developmen Indicaors (WDI). The employmen rae is aken from he Penn World Tables, version 6.3 (PWT), a choice based on breadh of coverage raher han daa qualiy. Bilaeral merchandise impors in curren dollars from 1970 o 2000 are aken from he NBER-Unied Naions Trade Daa (NBER- UN) prepared by Feensra and Lipsey. 8 Bilaeral service rade flows are no available for he sample period. Addiional daa o fill in gaps for Taiwan and he former Wesern Germany are aken from he naional saisical agencies of hese counries. Deails are available on reques. To be consisen wih he model, I need daa on gross oupu o calculae he dependen variable for he es. Gross oupu is no generally available, bu for a given value for σ, a model-consisen esimae is given by OUT i = 1 1 σ GDP i 8 Bilaeral merchandise impors daa are available for laer years from he IMF s Direcion of Trade Saisics (DOTS). There are some inconsisencies across he NBER-UN and DOTS rade daa, as he laer have been less exensively cleaned, so I do no make use of DOTS in he baseline sample. 15

16 I assume a value of σ = 0.5, based on he fac ha he average raio of gross oupu o GDP in he OECD Inersecoral Daabase is approximaely equal o 2. A counry s absorpion of is own oupu (IM ii ) is hen calculaed as gross oupu less oal expors. Toal expendiure including expendiure on maerials (i.e. EXP i ) is calculaed as gross oupu less oal expors plus oal impors. In he absence of daa on bilaeral service flows, I assume hey follow he same paern as bilaeral merchandise flows. IM ik is consruced by calculaing bilaeral merchandise impors as a share of he imporer s oal merchandise impors (using NBER-UN daa), and muliplying his by oal impors a he counry level from he WDI. For somehing over one hird of he counry pairs in he sample, bilaeral impors are recorded as zero. The lieraure on esimaing graviy equaions has aken a variey of differen approaches o dealing wih his issue. As a baseline, I add one o bilaeral impors (i.e. consruc he dependen variable as w ik = ln 1 + IM ik /EXP i OUT k ). In secion 4.2, I describe ess of he robusness of he resuls o alernaive approaches o his issue. For he purpose of esimaing he graviy equaions, variables ha are correlaed wih rade coss are required. The baseline se of variables consiss of bilaeral disance in kilomeers from larges populaion cener o larges populaion cener, and indicaor variables for coniguiy, common language and former colonial hisory. These are aken from he daase made available by CEPII. A dummy variable indicaing common legal origin (Briish, French, German, Scandinavian or Socialis) is consruced based on he caegorizaion provided by la Pora e al [1999]. The disance variable in he regression is calculaed as ln 1 + dis ik, where dis ii = 0. The indicaor variables are normalized such ha hey equal zero for he case when a counry rades wih iself. wihin a counry are zero. This imposes he normalizaion ha rade coss The larges possible sample given he requiremen ha all of he above variables be available for all years consiss of 88 developed and developing counries. These are lised in he Appendix. Over he sample period, hese counries cover beween 90% and 94% of world GDP. Wihin-sample rade (i.e. rade ha does no involve a parner no in he sample) accouns for beween 72% and 83% of world rade, assuming ha he bilaeral paern of service rade is he same as ha for merchandise. 4.1 Resuls Baseline bilaeral ess The resuls from esimaing he four models described above using he full 88-counry sample are repored in he online Appendix. The esimaed coefficiens on he graviy variables are 16

17 fairly sandard. They differ somewha beween he opimal risk sharing specificaion and he unresriced and auarky specificaions, bu no markedly so, and he implied fied values of rade coss are very similar. The R 2 s are 0.55, 0.52, 0.04 and 0.52 for he unresriced, opimal risk sharing, zero rade cos and auarky models respecively. Table 1 repors he F-es saisics and p-values for he hree hypohesis ess. The null hypohesis of opimal consumpion risk sharing condiional on rade coss is rejeced a all significance levels in favor of he alernaive of some fricion in asse markes ha impedes risk sharing. The null hypohesis of no rade coss is rejeced a all significance levels in favor of he alernaive of rade coss. The null hypohesis of financial auarky is rejeced a all significance levels in favor of he alernaive of some inernaional asse rade or ransfers. Do developed and developing counries face differen fricions? To es he hypohesis ha developed counries are closer o opimal risk sharing wih each oher han are developed and developing counries, I repea he exercise jus described, using only observaions on bilaeral impors beween 22 OECD counries. 9 This amouns o esing wheher here is opimal consumpion risk sharing beween hese 22 counries, condiional on esimaed rade coss. A he same ime, I also implemen he oher wo ess on he OECD subsample. The resuls from esimaing he four models are repored in he online Appendix. The magniude of he coefficiens on he graviy variables in he models wih rade coss are differen from hose in he full sample, and he implied rade coss are subsanially smaller. The R 2 s of he hree models wih rade coss are higher when esimaed on he OECD subsample han when esimaed on he full sample - hey range from 0.81 o 0.83 insead of from 0.52 o Table 1 repors he F-es saisics and associaed p-values for he OECD sub-sample. The null hypohesis of opimal consumpion risk sharing condiional on rade coss canno be rejeced for his sample. The null hypohesis of no rade coss is rejeced a all levels of significance, despie he fac ha he implied rade coss are smaller han in he full sample. The null hypohesis of financial auarky is rejeced a all levels of significance. Implemenaion of he same ess for randomly seleced samples of 22 counries indicaes ha he failure o rejec he opimal risk sharing null for developed counries bu no he world as a whole is no driven by he difference in sample size. Resuls from his exercise are repored in he online Appendix. Are fricions declining in imporance over ime? 9 These are he 22 founding OECD economies, less Turkey. The full lis is in he online Appendix. 17

18 I also esimae he four models separaely on he period and he period Table 1 repors he F-es saisics and associaed p-values for he wo sub-samples. In boh he earlier period and he laer period, he null hypohesis of opimal risk sharing and cosly rade is rejeced agains he alernaive of fricions in boh goods and asse markes, hough he F-es saisic is lower in he laer period. Similarly, he null hypohesis of no rade coss is srongly rejeced in boh periods, and he null hypohesis of financial auarky is rejeced in favor of he alernaive of some asse rade or ransfers. The fac ha he F-es saisic falls over ime is suggesive of some weakening in asse marke fricions. 4.2 Robusness I examine he robusness of hese resuls along several dimensions. provided in he online Appendix. Deailed resuls are I use four alernaive approaches o dealing wih zeros in he dependen variable. Firs, I repea he same ess wih an alernaive dependen variable, consruced as: w ik = ln min j IM ij + IM ik /EXP i OUT k Second, I esimae using he baseline sample, bu dropping observaions where here are zeros in he dependen variable. Third, I esimae using daa aggregaed over five-year inervals o reduce he number of zeros. Finally, I implemen a version of he sraegy suggesed by Helpman, Meliz and Rubinsein [2008], which involves a correcion for selecion based on a firs-sage probi or logi. In all cases, he resuls are qualiaively unchanged. Nex, I es he robusness of he resuls o dropping he employmen variable. resuls are no affeced. I also es robusness o using differen ses of graviy variables. In paricular, since he esimaed coefficien on disance differs beween he full sample and he OECD sub-sample, I allow for a full se of main effecs and ineracions wih disance for wo dummy variables, one indicaing ha only one counry of he bilaeral pair is in he OECD, and he oher ha neiher counry in he pair is in he OECD. The resuls are qualiaively unchanged. I also check he robusness of he resuls o including Turkey (he excluded founder member of he OECD) in he OECD sample. The p-value rises, and he null of opimal risk sharing in he group including Turkey is (jus) rejeced a he 5% level, hough no a he 10% level. The oher resuls are unchanged. However if in addiion Korea is included in he OECD group, he null of opimal risk-sharing wihin he OECD is overwhelmingly rejeced (23) The 18

19 in favor of he alernaive. I also check wheher spliing he sample by de jure financial openness yields similar resuls o he baseline spli. The measure of financial openness I use is ha consruced by Chinn and Io [2008]. I rank counries wihin years by his measure, and pick groups of counries ha are on average mos financially open. There is considerable overlap beween his sample and he OECD sample. For comparable sample sizes, he null hypohesis of opimal risk sharing is no rejeced for he financially open sample, hough I also canno rejec he null hypohesis of financial auarky for his sample. 4.3 Discussion and inerpreaion The mos surprising aspec of he es resuls is ha hey are considerably more favorable o he null hypohesis of opimal consumpion risk sharing beween OECD counries han he ess previously used in he lieraure, so i is worh explaining how and why hey are differen. There are wo key differences beween he es I implemen and hose used in he previous lieraure. I discuss each in urn. Firs, he es is implicily based on a decomposiion of he value of consumpion ino price and real quaniy erms ha relies no on measured prices, bu on he prices consisen wih fiing a srucural graviy model of bilaeral rade o he daa. To undersand how hese non-sandard prices conribue o a differen view of consumpion risk sharing, I do he following. Firs, I use sandard daa on CPIs and nominal exchange raes (aken from World Developmen Indicaors) o decompose he value of consumpion ino price and real quaniy erms, and use hese o calculae he correlaion beween changes in log relaive real consumpion and log relaive prices (wih he US as numeraire) similar o he pas lieraure. I hen perform he decomposiion using insead he esimaed prices (his requires an assumpion abou η, since he graviy equaions idenify (η 1) ln P i, no P i ), and calculae he same correlaions. I repea he exercise for a range of values of η. Using measured prices, he correlaion beween he wo variables for he median OECD counry is posiive and close o zero, similar o wha is found by Backus and Smih [1993]. 10 For he full 88-counry sample, he correlaion for he median counry is negaive and close o zero. This conrass wih he fac ha using he esimaed prices, he correlaion is sysemaically and srongly negaive, boh for OECD counries and for he world as a whole. This goes a leas some way owards explaining why he resuls I presen above for he OECD are differen from he sandard lieraure. Full resuls, and resuls from regressing changes in log relaive real consumpion on log relaive prices are repored in he online Appendix. 10 They work wih real exchange raes, he inverse of relaive prices. 19

20 Of course, while a negaive correlaion beween relaive prices and relaive real consumpion is cerainly less inconsisen wih opimal risk sharing han a zero or posiive correlaion, i is by no means conclusive evidence of opimal risk sharing. Even ignoring oher poenial deerminans of marginal uiliy besides consumpion, he sign of he reduced form correlaion beween relaive prices and relaive consumpion need no be reversed by fricions in asse markes. Indeed, he es I presen rejecs he null hypohesis of no asse marke fricions for he full sample of counries, despie he negaive correlaion beween relaive prices and relaive consumpion implied by he prices used in he es. This brings me o he second key difference beween he es I presen and he approach of he lieraure on consumpion-real exchange rae correlaions. The es I presen infers he salience of asse marke fricions from he relaive abiliy of consan versus ime-varying relaive marginal uiliies of wealh o explain he variaion in bilaeral impor daa. conras, he lieraure on consumpion-real exchange rae correlaions infers he presence of fricions from he fac ha he join behavior of relaive prices and relaive real consumpion deviaes from ha prediced by he null hypohesis of opimal risk sharing. I is possible o nes a version of his approach in mine, as follows. In Under he null hypohesis of opimal risk sharing, following equaion (21) he coefficien on he log of he value of consumpion is equal o ρ (η 1). The esimaed value of his coefficien for he 1 ρ OECD sample is negaive (equal o wih sandard error 0.6). This is only possible if (a) ρ < 1, i.e. he represenaive agen is less risk averse han log uiliy, or (b), η < 1, implying ha rade coss are lower for counries ha are far away han for counries ha are close. Clearly (b) does no make sense, and (a) violaes he priors of many macroeconomiss. Moreover, reasonable values of η imply values of ρ ha, hough posiive, are very close o zero. I is sraighforward o implemen a es of he join null of opimal risk sharing and a paricular value for ρ ρ (η 1) by subracing (η 1 ρ 1 ρ 1)vci from he dependen variable in he opimal risk sharing model. In resuls repored in he online Appendix, I do his for a variey of values of ρ (η 1). I rejec he join null hypohesis for a range of pairs {η, ρ} 1 ρ considered sandard by he lieraure. In his sense, my findings are consisen wih hose of he consumpion-real-exchange-rae lieraure, even hough I use differen prices. Obviously, his raises quesions abou how o inerpre he es resuls presened above. If a more sringen es rejecs he null of opimal risk sharing for boh OECD counries and he world as a whole, can he baseline resuls be inerpreed as implying OECD counries are a leas closer o opimal risk sharing han he res of he world? A disadvanage of he esing framework is ha i is no clear if his is he case. In he nex secion, I address 20

21 his issue by explicily measuring he changes in ex-pos welfare from moving o opimal risk sharing, holding rade coss fixed a heir hisorical levels. Before going o he full counerfacual exercise, i is ineresing o perform he following back-of-he-envelope calculaion. Assume ha he marginal uiliy of per capia consumpion akes he form (C i /L i ) ρ, for a paricular value of ρ. Given daa on real consumpion per capia and he consumer price index, he firs order condiion for aggregae consumpion can hen be used o back ou ime-series of λ i /λ j for pairs of counries i and j. I assume ρ = 2 and consruc λ i /λ US for all he counries in he daa se. I hen calculae for each counry-pair he coefficien of variaion of log changes in λ i /λ US over he sample period. The disribuion of his measure of volailiy for non-oecd counries has significan mass well o he righ of he disribuion for OECD counries - he median for OECD counries is 0.22, while he median for non-oecd counries is 0.42 (deails are repored in he online Appendix). This is consisen wih OECD counries being on average closer o opimal risk sharing wih he US (he bigges OECD counry) han mos non-oecd counries are wih he US. Obviously his is jus suggesive evidence. Bu wih his in mind, I move on o he full counerfacual exercise. 5 Trade and welfare under counerfacual risk sharing In his secion, I calculae he changes in rade and ex-pos welfare for OECD and non-oecd counries from moving from hisorical fricions in asse markes o opimal consumpion risk sharing, holding rade coss fixed a heir hisorical levels. I also examine he incremenal effec of moving from opimal risk sharing wih hisorical rade coss o opimal risk sharing wih zero rade coss. The exercises focuses on consumpion risk sharing raher han he full impac of moving o fricionless asse markes. 11 Moreover, I focus on changes in ex-pos welfare raher han changes in ex-ane welfare. I resric he exercises in his way because I do no wan o have o ake a sand on counry wealh in 1970, he hisorical srucure of asse markes, or he underlying process for shocks. My sraegy makes use of he fac ha esimaes of he marginal uiliy of wealh provide a convenien summary saisic for he hisorical impac of asse marke fricions on consumpion risk sharing, wihou having o characerize hose fricions. The exercises have he disadvanage ha hey demand ha he model be aken more lierally han in previous secion. Bu relaive o esing he null 11 Gourinchas and Jeanne [2006] address precisely he quesion of he welfare effecs of financial inegraion in a world where all he poenial gains come hrough he effec on invesmen, and find ha he effecs are on he order of a 1% permanen increase in domesic consumpion for he ypical non-oecd counry. 21

22 hypohesis of one model agains he alernaive of anoher, hey have he disinc advanage ha hey more direcly address he quesion of how far differen groups of counries are from opimal risk sharing. I proceed in wo sages. In he firs sage I consruc esimaes of hisorical rade coss and oupu prices, and use hese o consruc esimaes of he oupu hisorically devoed o consumpion. To do his, I firs choose funcions of rade coss and oupu prices o mach daa on bilaeral impors, while imposing ha he prediced raio of ne expors o GDP for each counry exacly maches ha in he daa. This makes use of he informaion on he exen of asse rade conained in ne expors in a way ha he reduced form esimaion sraegy in he previous secion does no. The esimaed model does a good job of maching he paern of bilaeral impors and he evoluion over ime of raios of rade o GDP. The esimaion does no ie down values for he elasiciy of subsiuion η, or for he parameers of he period uiliy funcion, u ( ). I choose values for hese based on he previous lieraure, and combine hem wih he esimaed funcions of rade coss and oupu prices o calculae rade coss, real oupu, real consumpion and ex-pos welfare for boh OECD and non- OECD counries. In he process, I also obain esimaes of he hisorical inverse marginal uiliy of wealh. In he second sage, I reallocae he oupu devoed o real consumpion across counries, firs, consisen wih opimal consumpion risk sharing wihin OECD counries alone, and second, consisen wih opimal consumpion risk sharing across he world as a whole, while holding rade coss fixed a heir calibraed hisorical levels. The esimaes of he hisorical inverse marginal uiliy of wealh are used o choose plausible poins on he Pareo fronier. Finally, I reallocae consumpion consisen wih opimal risk sharing and zero rade coss. I hen calculae a measure of compensaing variaion for each counry under each counerfacual. I also compare rade and ne expors as a share of GDP under he fied model and under he counerfacuals. I now describe he procedure in more deail, followed by he resuls. 5.1 Esimaion sraegy In order o perform an inernally consisen counerfacual exercise, i is necessary o assume ha one has daa on he universe of counries. Having made his assumpion, i makes sense o exploi he full srucure of he model in esimaing rade coss and prices, somehing I do no do in he previous secion. For echnical reasons, i is more convenien o esimae 22

23 oupu prices raher han consumpion prices. 12 The esimaing equaion is based on: IM ik = τ ik 1 η Q k 1 η N j=1 τ ij 1 η Q j 1 η EXP i (24) which is obained by rearranging he firs order condiion for Z ik. I divide across by oal expendiure, ake logs and include an error erm: 13 IM ik N ln = d ik γ EXP i + α k ln exp d ij γ + α j + ε ik (25) j=1 where α i = (1 η) ln (Q i ), d ik γ = (1 η)ln τ ik, and d ik is a vecor of (ime-invarian) graviy variables, consruced such ha exp (d ii γ ) = 1. This imposes ha he esimaed Q s and τ s are posiive, and ha τ ii weighed sum of squared errors: = 1. I hen choose he vecors γ and α o minimize he N i=1 N j=1 ω ij ε ij 2 (26) subjec o he resricion ha he fied value of he raio of ne expors o GDP for each counry is exacly equal o he raio in he daa, i.e.: OUT i = N j=1 exp (d ji γ + α) i N k=1 exp EXP j d jk γ + α k (27) I se he weighs ω ij equal o EXP i OUT j (he prediced size of IM ik in a zero rade cos world). Upweighing large flows relaive o small flows ensures ha he prediced values of rade as a share of GDP mach world aggregaes. The procedure is repeaed for each period independenly. The daa is exacly he daa used in he secion on esing, reformulaed in erms of in-sample shares. The exac ransformaion is described in he online Appendix. I use a parsimonious vecor d ij of graviy variables ha includes ln 1 + dis ik and main effecs and ineracions of ln 1 + dis ik wih indicaors for one of he rading parners being in he OECD and he oher ouside he OECD, and for boh rading parners being ouside he OECD. 14 Allowing he rade-reducing effec of disance o differ depending on he naure 12 This guaranees ha boh oupu prices and consumpion prices are posiive. 13 In he baseline esimaion I drop observaions where IM ik = 0. The resuls are robus o his. 14 These are se equal o zero when a counry rades wih iself 23

24 of he bilaeral pair is necessary o simulaneously mach rade-gdp raios for OECD and non-oecd counries. The esimaed parameers on he graviy variables are repored in he online Appendix. 5.2 Model fi The firs panel of Figure 1 is a scaer plo of he fied values of bilaeral impors agains he daa, for all bilaeral pairs and all years in he sample (bilaeral impors are expressed as a share of oal in-sample world expendiure so ha all years can be presened in he same figure). The second panel is a scaer plo of he log of he fied values agains he log of he acual values. These figures illusrae he fac ha paricularly for large flows (which are imporan in maching world aggregaes) he fi is excellen. The relaive fi of large and small flows is conrolled by he weighing of he error erm in he bilaeral rade equaions. The cross-secional correlaions beween fied and acual values are sysemaically high for all ypes of bilaeral pair, excep for rade beween wo (differen) non-oecd counries. This is illusraed in he online Appendix. The relaively poor fi for rade beween non-oecd counries is consisen wih he view ha measuremen error is a paricular problem for flows beween developing counries. I also examine he fi of he model in erms of maching he evoluion of rade-gdp raios. This depends heavily on how well he model maches he share of a counry s impors from iself in oal expendiure. I focus on five differen raios. Firs is he raio of world impors o world GDP. I hen look a he raio of wihin-oecd impors o OECD GDP, he raio of rade beween OECD and non-oecd counries o OECD GDP and o non-oecd GDP respecively, and finally, he raio of wihin-non-oecd impors o non-oecd GDP. The four panels of Figure 2 plo he fied and acual values of he laer four raios respecively, wih he fied and acual values for he world raios also repored in each panel. The model slighly overpredics wihin-oecd rade and slighly underpredics wihin-non-oecd rade. However he order of magniude is corrrec, and in erms of ime-series evoluion, he fied values closely follow acual values. By consrucion, he fied model exacly maches he raio of ne expors o GDP from he daa, so I do no repor saisics on fi along his dimension. 24

25 5.3 Parameers, rade coss and Pareo weighs To back ou an esimae of real consumpion, and of he Pareo weighs, I require a value for η, he elasiciy of subsiuion, an assumpion abou he funcional form for marginal uiliy, and values for he parameers of his funcion. Anderson and van Wincoop [2004] sugges a range of values beween 5 and 8 for η, while Eaon and Korum [2002] sugges a value for he corresponding parameer in heir model beween 3 and 12. The macro lieraure has radiionally ended o choose values on he lower end of he specrum. I choose a benchmark value of 6, and check he robusness of he resuls o his choice. I assume ha marginal uiliy of per capia consumpion akes he form u c ( ) = (C/L) ρ. For ρ, I choose a benchmark value of 2, and again check he robusness of he resuls o his choice. Then, using he esimaes ˆγ and ˆα, and daa on populaion and he share of expendiure devoed o consumpion, I recover fied values of ˆτ ij i, ˆQi, ˆP, Ĉ, i ˆλ i, Ŷ i, and Ŷ ic, he real oupu devoed o consumpion purposes. The deails of hese calculaions are described in he online Appendix. The relaionship beween oupu in one period and he nex (and he ime-series behavior of all oher variables) is pinned down by he evoluion of real GDP in he US, aken from he WDI. This choice affecs he welfare calculaions, bu no predicions on counerfacual rade-o-gdp raios or ne expor-o-gdp raios. Trade coss Figure 3 plos median rade coss for rade wihin OECD counries, rade beween OECD and non-oecd counries and rade wihin non-oecd counries under he assumpion ha η = 6. Trade coss are expressed as a percenage of he sales price, so τ = 3 implies a rade cos of 200%. These rade coss are large. 15 However, as Figure 4 illusraes, rade coss on his order of magniude do a good job of maching rade-gdp raios. 16 Moreover, while observed rade coss for goods and services ha are acually raded are no his high, observed rade coss are no represenaive of hose ha apply o oupu as a whole, as in equilibrium, only he goods and services wih he lowes rade coss are acually raded. Pareo weighs I is also ineresing o examine he behavior of he esimaed Pareo weighs (normalized such ha N i=1 ˆλ i = 1). For each counry, I calculae he coefficien of variaion based on he ime series of ha counry s esimaed Pareo weigh from 1970 o Figure 4 plos he hisogram of he disribuion of hese coefficiens of variaion for OECD and non-oecd 15 Anderson and van Wincoop [2004] summarize he evidence on he size of rade coss. 16 This saemen is of course condiional on a value for η, as he fi of he model depends only on ˆγ. 25

26 counries separaely. The median for OECD counries is 0.26, while he median for non- OECD counries is The disribuion for non-oecd counries is shifed o he righ and is much more spread ou han for OECD counries. This greaer volailiy is consisen wih non-oecd counries being furher from opimal risk sharing han OECD counries. Figure 5 illusraes he ime-series behavior of he esimaed Pareo weighs for a seleced se of counries. This figure demonsraes ha here is subsanial co-movemen wihin OECD counries, and o some exen, wihin groups of non-oecd counries. However, he volailiy of he esimaed weighs is much more subsanial for non-oecd counries. Moreover, heir evoluion reflecs episodes such as he 1980s deb crisis and he Eas Asian financial crisis. 5.4 Counerfacual exercises The firs wo counerfacual exercises are designed o measure he disance from opimal risk sharing for boh OECD counries and non-oecd counries. This is no exacly he same as measuring he disance from fricionless asse markes. To calculae he decenralized equilibrium ha would have obained if various groups of counries had had access o fricionless asse markes from 1970, i is no sufficien o hold relaive Pareo weighs consan a he esimaed levels for I would insead have o characerize each counry s lifeime budge consrain under fricionless asse markes in This is beyond he scope of he paper, so I pick a poin on he Pareo fronier ha seems o be a reasonable benchmark. The baseline poin is chosen by averaging he esimaed relaive Pareo weighs over ime wihin he risk-sharing group, I presenly examine he robusness of he resuls o his choice. Firs, I impose opimal risk sharing wihin he OECD only, while keeping rade coss fixed a heir esimaed hisorical levels. I do his by imposing ha he weighs of OECD counries relaive o each oher are consan over ime, equal o he ime-series average of heir esimaed relaive weighs. The weigh of he OECD as a whole relaive o ha of he res of he world is held fixed a is esimaed level (remember N i=1 ˆλ i = 1): λ i,oecd (1) = 2000 ˆλ =1970 i j OECD 2000 =1970 ˆλ j j OECD The ime-series of Pareo weighs for non-oecd counries are also fixed a heir esimaed i,noecd i,noecd levels, i.e. λ (1) = ˆλ. Second, I impose opimal risk sharing for he full sample of counries. I do his by ˆλ j (28) 26

27 imposing ha he weigh of each counry relaive o each oher is held consan over ime, wih each counry s weigh calculaed as he ime-series average of is esimaed weigh: λ i (2) = 2000 =1970 ˆλ i N j= =1970 ˆλ j (29) The hird counerfacual exercise eliminaes rade coss in addiion o imposing opimal risk sharing (i.e. λ (2)) for he full sample of counries. The eliminaion of rade coss is achieved by seing τ ij = 1 for all bilaeral pairs in all periods. Given daa on populaion, L, and τ, ŶC, λ ; η, ρ, I calculae he consumpion allocaion ha solves he problem of a social planner who maximizes he weighed sum of counry uiliies each period, wih weighs given by λ (1) or λ (2) where appropriae, subjec o he aggregae good and inermediae good resource consrains (which depend on rade coss). The numerical algorihm for finding he soluion is based on aonnemen as in Alvarez and Lucas [2007] (See he online Appendix for deails). Since I do no characerize eiher he baseline asse marke, or he process for shocks, I canno calculae a measure of compensaing variaion based on ex-ane welfare. Insead, I calculae compensaing variaion based on averaging ex-pos welfare across all sample years: W i = 1 T T (C/N i i ) 1 ρ =1 1 ρ (30) The compensaing variaion, δ, is hen such ha: 1 T T δĉi /L i =1 1 ρ 1 ρ = 1 T T =1 1 ρ Ci /L i 1 ρ (31) This measure of welfare weighs all periods equally, consisen wih how he poin on he wihin-group Pareo fronier is chosen. In he online Appendix, I describe an alernaive baseline poin on he Pareo fronier and corresponding welfare measure ha apply discouning from he perspecive of 1970, and which yield resuls ha are very similar o he baseline. 5.5 Resuls Table 2 repors summary saisics on he disribuion of he compensaing variaion measure δ for he world as a whole, for he OECD, and for non-oecd counries, for all hree 27

28 counerfacual exercises. Opimal risk sharing Given he poin I choose on he wihin-oecd Pareo fronier, opimal risk sharing wihin he OECD alone does no increase ex-pos welfare for he median OECD counry. 17 I leads o a reducion in he welfare of he median non-oecd counry on he order of 2%. conras, opimal risk sharing for he world as a whole leads o a reducion in he welfare of he median OECD counry on he order of 1%, while i leads o an increase in welfare for he median non-oecd counry of 3%. In he online Appendix I repor saisics on he disribuion of compensaing variaion weighed by average populaion share over he period. The implicaions are qualiaively similar. These resuls sugges ha he poenial gains from relaxing fricions in asse markes beween OECD counries may be relaively small. On he oher hand, he gains from relaxing fricions in asse markes beween OECD and non-oecd counries could be considerably larger. In Of course, his is no he same as saying here are no fricions in asse markes beween OECD counries; i could be ha shocks are much more correlaed wihin OECD counries han across OECD and non-oecd counries. Given he relaive size of OECD and non-oecd counries, his would imply small gains o he OECD from greaer financial inegraion, bu large gains o non-oecd counries from greaer inegraion wih he OECD. In addiion, I examine he effecs of opimal risk sharing wihin hese wo ses of counry groups on rade-o-gdp raios and ne expor-gdp raios. Here, I calculae he value of boh GDP and impors by adding consumpion-relaed flows o he real oupu and real rade flows necessary o mainain real absorpion devoed o invesmen, governmen consumpion and maerials a heir esimaed levels (hese laer are no changed from esimaed model o counerfacual). These oal real flows are valued a he esimaed and counerfacual prices as appropriae. Figure 6 plos he following fied and counerfacual rade-o-gdp raios for he opimal risk sharing exercises: OECD rade as a share of OECD GDP, rade beween OECD and non- OECD counries as a share of OECD GDP, rade beween OECD and non-oecd counries as a share of non-oecd GDP, and rade beween non-oecd counries as a share of non- OECD GDP. Opimal risk sharing wihin OECD counries alone leads on average o a small increase in wihin-oecd rade and rade beween OECD and non-oecd counries. Opimal risk sharing for he world as a whole, on he oher hand, leads o similarly small 17 This is as expeced. Even if he poin chosen on he Pareo fronier is a Pareo improvemen from he perspecive of (unobserved) hisorical ex-ane welfare, here is no guaranee ha opimal consumpion risk sharing wihin a group of counries will increase ex-pos welfare for all counries. 28

29 changes in wihin-oecd rade, bu quie subsanial increases in rade beween OECD and non-oecd counries and wihin non-oecd counries. Table 3 provides summary saisics on ime-series averages of he cross-secion disribuion of he absolue value of ne expors over GDP. Opimal risk sharing wihin he OECD alone is accompanied by a doubling of he median rade balance for OECD counries from 2% o 4% of GDP in absolue value. Median rade balances for non-oecd counries fall from 6% o 5% of GDP. In conras, opimal risk sharing in he world as a whole is accompanied by an increase in median rade balances for OECD counries from 2% o 5%, and for non-oecd counries from 6% o 15%. This is consisen wih a large porion of consumpion smoohing for non-oecd counries being provided by OECD counries. 18 An addiional ineresing poin o noe is ha opimal consumpion risk sharing does no imply perfec consumpion risk sharing. While he sandard deviaion of differences beween counry-level consumpion growh raes and he (unweighed) cross-counry average is dramaically lower under opimal risk sharing han in he baseline model (2.8 percenage poins compared wih 14.1 percenage poins), non-rivial cross-counry dispersion in consumpion growh raes persiss. More deails are provided in he online Appendix. Relaionship o pas lieraure The lieraure on he welfare gains o inernaional risk sharing has ypically focused only on OECD counries, and has found a very wide range of poenial gains, including some ha are very large. 19 In he online Appendix, I documen ha he esimaed baseline prices imply considerably more volaile consumpion han is implied by daa on prices and nominal exchange raes. This is rue boh for OECD and non-oecd counries. I migh appear ha he scope for gains from consumpion risk sharing in his conex is very large relaive o wha one would calculae based on using real consumpion series derived from daa on prices. However unlike he previous lieraure on inernaional risk sharing, I focus on opimal consumpion risk sharing condiional on rade coss. Since I esimae ha rade coss are large, his subsanially limis he opimal degree of risk sharing relaive o a world wihou rade coss. The difference in welfare gains beween OECD and non-oecd counries arises because OECD counries are large, so heir flucuaions are srongly correlaed wih aggregae risk, and here is lile scope for addiional consumpion smoohing, while his is no he case for non-oecd counries. Relaive o he lieraure on he welfare coss of business cycles, he esimaed gains 18 The resuls on he raios of rade and ne expors o GDP are independen of he values chosen for η and ρ. 19 See van Wincoop [1999]. 29

30 o non-oecd counries from opimal risk sharing are big. The choice of consan Pareo weighs means ha he exercise I perform does no jus smooh ou shor-run flucuaions in consumpion growh, bu also medium-run deviaions of growh from long-run rends, or differences in growh rends over differen pars of he 31-year sample. Of course, opimal ex-ane consumpion risk sharing may no be a reasonable benchmark, in he sense ha inernaional asse markes migh be unlikely ever o allow counries o insure agains longrun growh differenials. I consider an alernaive where he counerfacual Pareo weighs are calculaed o smooh deviaions (of he esimaed Pareo weighs) from rend, raher han o eliminae rends. The resuls of his exercise (presened in he online Appendix) are qualiaively similar o hose from he baseline exercise: he median OECD counry gains from his exercise, bu less han he median non-oecd counry gains. Zero rade coss Eliminaing rade coss in addiion o moving o opimal risk sharing in he world as a whole leads o esimaed increases in welfare ha dwarf hose from opimal risk sharing alone. This is no surprising, given he esimaed size of rade coss. While clearly of firs order imporance for undersanding he failure of perfec consumpion risk sharing, he policy relevance of his finding is less clear, as he esimaed rade coss are very subsanial relaive o policy barriers o rade (e.g. ariffs). Robusness I examine he robusness of he resuls along he following dimensions. Deails of hese resuls are repored in he online Appendix. Firs, I look a how he resuls change when differen values are chosen for η and ρ. The effec of changing hese parameers on he magniude of welfare changes is no sraighforward, because changing each parameer affecs he baseline consumpion allocaion and Pareo weigh esimaes, he counerfacual poin on he Pareo fronier, and he price and welfare effecs of consumpion reallocaion. However he comparaive saic resul ha he welfare gains o he median OECD counry from opimal risk sharing wihin he OECD are smaller han hose o he median non-oecd counry from opimal risk sharing in he world as a whole is unaffeced by choosing differen parameer values. The gains o all counries from eliminaing rade coss are always sarkly greaer han hose from opimal risk sharing alone. Second, I perform he same hree counerfacual exercises a baseline parameer values, bu for an alernaive baseline poin on he Pareo fronier ha applies discouning from he perspecive of 1970 o calculae weighed averages over ime of relaive Pareo weighs wihin risk-sharing groups. Corresponding o his, I apply a differen welfare measure ha discouns 30

31 uiliy from he perspecive of The resuls from his exercise are boh qualiaively and quaniaively very similar o hose from he baseline exercise. Finally, I perform he same hree counerfacual exercises a baseline parameer values, bu holding relaive Pareo weighs wihin risk-sharing groups consan a heir esimaed levels for Once again, hese are no necessarily hose ha would have obained had he world shifed o fricionless asse markes in 1970, because he ineremporal budge consrain acually faced by counries in 1970 was differen from wha hey would have faced under fricionless asse markes. The resuls of his exercise imply ha he median OECD counry loses subsanially from risk sharing among OECD counries, while he median non- OECD counry gains subsanially from risk sharing in he world as a whole. 6 Conclusion Why does perfec inernaional consumpion risk sharing fail? The previous lieraure has suggesed boh rade coss and asse marke fricions as imporan candidae explanaions. There has been some debae over he relaive imporance of hese explanaions, and he relevance of each for developed and developing counries. I show ha a graviy model wih an ineremporal dimension provides a naural framework for examining hese issues. I use he model boh o es for he presence of he wo fricions, and o esimae he ex-pos gains relaive o hisorical welfare from eliminaing hem. The resuls from boh exercises sugges ha OECD counries are relaively closer o opimal risk sharing han non-oecd counries, and by some measures, are very close indeed o opimal risk sharing condiional on rade coss. In conras, rade coss are of firs order imporance in welfare erms, principally because hey affec consumpion of variey wihin daes and saes, bu also because hey affec counries abiliy o smooh consumpion across daes and saes. The resuls on rade coss are in line wih he findings of he previous lieraure (hough an explici comparison of he welfare losses associaed wih rade coss and asse marke fricions is new). The resuls on opimal risk sharing conras wih he previous lieraure, in ha hey sugges ha for OECD counries, he scope for welfare gains from opimal risk sharing condiional on rade coss is small. However i is ineresing ha his is no he case for he world as a whole, as under he very same parameer values, he resuls indicae ha many developing counries gain significanly from being able o opimally smooh consumpion wih he res of he world. There is a subsanial body of ineresing research devoed o undersanding he exac naure of hese fricions. By clarifying heir relaive imporance for 31

32 differen groups of counries, his paper hopes o conribue o direcing ha lieraure. References [1] Alvarez, F. and R. Lucas, [2007], General equilibrium analysis of he Eaon-Korum model of inernaional rade, Journal of Moneary Economics, 54(6), [2] Anderson, J. and E. van Wincoop, [2003], Graviy wih Gravias: A Soluion o he Border Puzzle, American Economic Review 93, [3] Anderson, J. and E. van Wincoop, [2004], Trade Coss, Journal of Economic Lieraure 42, [4] Arkolakis, C., A. Cosino and A. Rodriguez-Clare, [2009], New Trade Models, Same Old Gains?, NBER Working Papers [5] Backus, D., P. Kehoe and F. Kydland, [1992], Inernaional Real Business Cycles, Journal of Poliical Economy 100 (4), [6] Chinn, M. and H. Io, [2008], A New Measure of Financial Openness Journal of Comparaive Policy Analysis, 10(3), [7] Cole, H. and M. Obsfeld, [1991], Commodiy Trade and Inernaional Risk Sharing, Journal of Moneary Economics 28, [8] Dekle, R., J. Eaon and S. Korum, [2008], Global Rebalancing wih Graviy: Measuring he Burden of Adjusmen, IMF Saff Papers, 55(3), [9] Dumas, B., [1992], Dynamic Equilibrium and he Real Exchange Rae in a Spaially Separaed World, Review of Financial Sudies 5 (2), [10] Dumas, B. and R. Uppal, [2001], Global Diversificaion, Growh and Welfare wih Imperfecly Inegraed Markes for Goods, Review of Financial Sudies 14 (1), [11] Eaon, J. and S. Korum, [2002], Technology, Geography and Trade, Economerica 70 (5), [12] Fizgerald, D., [2008], Can Trade Coss Explain Why Exchange Rae Volailiy Doesn Feed Ino Consumer Prices? Journal of Moneary Economics, 55(3),

33 [13] Gourinchas, P. and O. Jeanne, [2006], The Elusive Gains from Inernaional Financial Inegraion, Review of Economic Sudies 73, [14] Heahcoe, J. and F. Perri, [2000], Financial Auarky and Inernaional Business Cycles, Journal of Moneary Economics 49 (3), [15] Heahcoe, J. and F. Perri, [2004], Financial Globalizaion and Real Regionalizaion, Journal of Economic Theory 119, [16] Helpman, E., M. Meliz and Y. Rubinsein, [2008], Esimaing Trade Flows: Trading Parners and Trading Volumes, Quarerly Journal of Economics, 123(2), [17] Kollmann, R. [1995], Consumpion, Real Exchange Raes and he Srucure of Inernaional Asse Markes, Journal of Inernaional Money and Finance 14 (2), [18] Kose, M. and K.-M. Yi, [2006], Can he Sandard Inernaional Business Cycle Model Explain he Relaion Beween Trade and Comovemen? Journal of Inernaional Economics, 68(2), [19] Krugman, P., [1980], Scale Economies, Produc Differeniaion, and he Paern of Trade, American Economic Review, 70(5), [20] la Pora, R., F. Lopez-de-Silanes, A. Shleifer and R. Vishny, [1999], The Qualiy of Governmen, Journal of Law, Economics and Organizaion 15 (1), [21] Lewis, K., [1996], Wha Can Explain he Apparen Lack of Inernaional Consumpion Risk Sharing? Journal of Poliical Economy 104 (2), [22] Mazzenga, E. and M. Ravn, [2004], Inernaional Business Cycles: The Quaniaive Role of Trade Coss, Journal of Inernaional Money and Finance 23 (4), [23] Obsfeld, M. and K. Rogoff, [2000], The Six Major Puzzles in Inernaional Macroeconomics: Is There a Common Cause, in Ben Bernanke and K. Rogoff (eds.), NBER Macroeconomics Annual 2000 (Cambridge: MIT Press), [24] Ravn, M., [2001], Consumpion Dynamics and Real Exchange Raes, mimeo. [25] van Wincoop, E., [1999], How Big Are Poenial Welfare Gains From Inernaional Risksharing, Journal of Inernaional Economics, 47,

34 Table 1: Baseline es resuls Null Alernaive F-sa # res d.f. p-val Full sample Opimal risk sharing Trade coss, asse mk fricion No rade coss Trade coss, asse mk fricion Financial auarky Trade coss, asse mk fricion OECD only Opimal risk sharing Trade coss, asse mk fricion No rade coss Trade coss, asse mk fricion Financial auarky Trade coss, asse mk fricion , Full sample Opimal risk sharing Trade coss, asse mk fricion No rade coss Trade coss, asse mk fricion Financial auarky Trade coss, asse mk fricion , Full sample Opimal risk sharing Trade coss, asse mk fricion No rade coss Trade coss, asse mk fricion Financial auarky Trade coss, asse mk fricion Noes: This able repors resuls from F-ess of null hypohesis agains alernaive. Tess are based on esimaing resriced and unresriced log-linear graviy models of rade, as described in he ex. Baseline sample includes 88 counries as lised in he Appendix, annual daa All bilaeral pairs including rade wih self are included. Zeros in bilaeral rade are replaced by 1 o generae he dependen variable, which is bilaeral impors normalized by imporer s expendiure and exporer s gross oupu. Baseline graviy variables include log disance and six indicaor variables consruced o normalize rade coss o zero wihin counries. Table 2: Summary saisics on compensaing variaion avg min p25 p50 p75 max Opimal risk sharing in OECD only All OECD non-oecd Opimal risk sharing in full sample All OECD non-oecd Opimal risk sharing for all, no rade coss All OECD non-oecd Noes: This able repors summary saisics on he disribuion of δ, he measure of compensaing variaion based on a measure of ex-pos welfare ha is a simple average of per-period welfare. These disribuions are repored for he hree counerfacual exercises described in he ex relaive o he baseline esimaed disribuion of real consumpion, and for he full sample as well as he OECD and non-oecd subsamples. The hree counerfacual exercises are firs, he imposiion of opimal risk sharing beween OECD counries, second, he imposiion of opimal risk sharing in he world as a whole, and hird, opimal risk sharing and zero rade coss in he world as a whole. The poin on wihin-risk-sharing-group Pareo fronier is chosen based on he simple ime-series average of he wihin-risk-sharing group esimaed Pareo weighs. Pareo weighs are held fixed a heir esimaed levels for counries ouside he risk-sharing group, while he weigh of he risk-sharing group as a whole varies wih respec o he weighs of counries ouside he group as esimaed. The baseline in each case is based on he srucural esimaion of he nonlinear graviy equaion. For boh fied and counerfacual exercises, {η, ρ} = {6, 2}. 34

35 Table 3: Ne expors over GDP: Acual and counerfacual avg min p50 max Acual All OECD non-oecd Opimal risk sharing, OECD only All OECD non-oecd Opimal risk sharing, All All OECD non-oecd Opimal risk sharing, no rade cos All OECD non-oecd Noes: This able repors he average across ime of summary saisics of he cross-secion disribuion of ne expors over GDP. These are repored for he whole sample, and for OECD and non-oecd counries only. The acual values (equal o he prediced values from he srucural esimaion of he nonlinear graviy equaion by consrucion) are subjec o a renormalizaion ha imposes a zero aggregae rade balance for he sample. Saisics are repored for hree differen counerfacual exercises. The hree counerfacual exercises are firs, he imposiion of opimal risk sharing beween OECD counries, second, he imposiion of opimal risk sharing in he world as a whole, and hird, opimal risk sharing and zero rade coss in he world as a whole. In each chase, {η, ρ} = {6, 2}. 35

36 Figure 1: Prediced and acual bilaeral rade flows Noes: This figure shows wo scaer plos of prediced agains acual bilaeral rade flows. The predicions are aken from he srucural esimaion of he nonlinear graviy equaion. Acual bilaeral impors in his case are he bilaeral impors renormalized as in-sample shares, which are used o consruc he dependen variable in he esimaion. The firs figure shows he scaer plo for bilaeral impors in levels, where each bilaeral flow is expressed as a share of world oupu. The second figure shows he scaer plo for he same variables, bu in logs. Figure 2: Prediced and acual rade-o-gdp raios Inra OECD rade / OECD GDP OECD non OECD rade / OECD GDP OECD non OECD rade / non OECD GDP Inra non OECD rade / non OECD GDP Acual Fied Acual, World Fied, World Noes: The panels of his figure plo he evoluion over ime of prediced and acual rade-o-gdp raios for rade beween differen groups of parners, and normalized by he GDP of differen groups of counries. The predicions are aken from he srucural esimaion of he nonlinear graviy equaion. By consrucion, prediced and acual GDP are equal. The firs panel shows he raio of wihin-oecd rade (excluding a counry s impors from iself) o OECD GDP. The second panel shows he raio of rade beween OECD and non-oecd counries o OECD GDP. The hird panel shows he raio of rade beween OECD and non-oecd counries o non-oecd GDP. The final panel shows he raio of wihin-non-oecd rade (excluding a counry s impors from iself) o non-oecd GDP. All panels show he raio of world rade (excluding a counry s impors from iself) o world GDP. 36

37 Figure 3: Median rade coss for differen ypes of rade All Inra OECD OECD non OECD inra non OECD Noes: This figure plos he ime-series evoluion of he median across rade beween specific groups of parners of he fied values of rade coss based on he srucural esimaion of he nonlinear graviy equaion, and he assumpion ha η = 6. The ypes of bilaeral rade are inra-oecd rade, rade beween OECD and non-oecd counries, and inra-non-oecd counry rade. Also repored is he median rade cos for all rade. Trade coss are expressed as a percenage of he sales price, so τ = 3 implies a rade cos of 200%. Figure 4: Coefficien of variaion of Pareo weighs from srucural esimaion Noes: This figure plos he disribuion of he wihin-counry coefficien of variaion (sandard deviaion/mean) of esimaed Pareo weighs expressed relaive o he res of he world. The Pareo weigh esimaes are based on he srucural esimaion of he nonlinear graviy equaion, combined wih he assumpion ha {η, ρ} = {6, 2}. The disribuions for OECD and non-oecd counries are ploed separaely. 37

38 Figure 5: Normalized Pareo weigh esimaes for selec counries 4 3 USA CAN US and Canada 4 3 Four European counries DEU FRA GBR ITA Four Eas Asian counries IDN KOR MYS THA 4 3 Four Lain American counries BRA CHL MEX URY Noes: This figure plos he ime-series evoluion of esimaed Pareo weighs for selec groups of counries. The Pareo weigh esimaes are based on he srucural esimaion of he nonlinear graviy equaion, combined wih he assumpion ha {η, ρ} = {6, 2}. Weighs are normalized by he wihin-counry cross-ime mean so differen counries can be ploed on he same axes. Figure 6: Prediced and counerfacual rade-o-gdp raios Inra OECD rade / OECD GDP OE CD non OECD rade / OECD GDP OECD non OECD rade / non OECD GDP Inra non OECD rade / non OECD GDP Fied CF: OECD risk sharing CF: world risk sharing Noes: The panels of his figure plo he evoluion over ime of prediced and counerfacual rade-o-gdp raios for rade beween differen groups of parners, and normalized by he GDP of differen groups of counries. The predicions are aken from he srucural esimaion of he nonlinear graviy equaion. By consrucion, prediced and acual GDP are equal. The wo counerfacual exercises for which rade-o-gdp raios are repored are firs, he case of opimal risk sharing for he OECD alone, and second, opimal risk sharing in he world as a whole. The firs panel shows he raio of wihin-oecd rade (excluding a counry s impors from iself) o OECD GDP. The second panel shows he raio of rade beween OECD and non-oecd counries o OECD GDP. The hird panel shows he raio of rade beween OECD and non-oecd counries o non-oecd GDP. The final panel shows he raio of wihin-non-oecd rade (excluding a counry s impors from iself) o non-oecd GDP. All panels show he raio of world rade (excluding a counry s impors from iself) o world GDP. 38