Trade Costs, Asset Market Frictions and Risk Sharing


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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 expos 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 nonoecd 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, PierreOlivier 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 ArrowDebreu 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 nonoecd 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 inraemporal 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 RodriguezClare [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 radereducing 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 uiliyconsisen consumpion price, which is equal o he raio of he marginal uiliy of consumpion and he marginal uiliy of wealh, in he modelbased 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 nonoecd 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 expos 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 imeinvarian 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, expos 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 expos welfare in he median nonoecd 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 nonoecd 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 inraoecd 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 nonoecd counries  his rade as a share of nonoecd GDP is 23% higher han in he fied model. This reflecs an increase in he median absolue value of he rade balance for nonoecd 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 nonoecd 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 srucurallybased 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 RodriguezClare [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 onegood world. The resource consrain for he (nonraded) 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 reopimize 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 riskfree 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 inraemporal 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 expos 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 exane 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 saeconingen 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 consumpionreal 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 radereducing 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 modelconsisen prices implicily value variey in a way ha measured price indexes do no. The modelbased approach o valuing variey is he basis for a subsanial lieraure ha measures he gains from inraemporal rade (see he ciaions in Arkolakis, Cosino and RodriguezClare [2009]), and he reamen of gains from ineremporal 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 ifandonlyif 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 nonzero 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 ermsofrade 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, nonresource 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 imporeryear fixed effec, while φ k = (η 1) ln Π k is an exporeryear 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 Fes 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 NBERUnied 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 modelconsisen 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 NBERUN 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 NBERUN 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. Wihinsample 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 88counry 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 Fes saisics and pvalues 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 Fes saisics and associaed pvalues for he OECD subsample. 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 Fes saisics and associaed pvalues for he wo subsamples. 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 Fes 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 Fes 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 fiveyear 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 firssage 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 subsample, 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 pvalue 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 risksharing 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 nonsandard 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 88counry 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 consumpionreal exchange rae correlaions. The es I presen infers he salience of asse marke fricions from he relaive abiliy of consan versus imevarying relaive marginal uiliies of wealh o explain he variaion in bilaeral impor daa. conras, he lieraure on consumpionreal 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 consumpionrealexchangerae 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 expos 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 backofheenvelope 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 imeseries 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 counrypair he coefficien of variaion of log changes in λ i /λ US over he sample period. The disribuion of his measure of volailiy for nonoecd 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 nonoecd 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 nonoecd 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 expos welfare for OECD and nonoecd 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 expos welfare raher han changes in exane 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 nonoecd 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 expos 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 (imeinvarian) 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 insample 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 radereducing 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
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