Hedging Against the Government: A Solution to the Home Asset Bias Puzzle *

Transcription

1 Federal Reserve Bank of Dallas Globalizaion and Moneary Policy Insiue Working Paper No. 3 hp:// edging Agains he Governmen: A Soluion o he ome Asse Bias Puzzle * Tiago C. Berriel EPGE RGV-Rio Saroj Bhaarai Pennsylvania Sae Universiy April 202 Absrac This paper explains wo puzzling facs: inernaional nominal bonds and equiy porfolios are biased domesically. In our wo-counry model, holding domesic governmen nominal deb provides a hedge agains shocks o bond reurns and he impac on axes hey induce. For his resul, only wo feaures are essenial: some nominal risk and axes falling only on domesic agens. A hird feaure explains why agens choose o hold primarily domesic equiy: governmen spending falls on domesic goods. Then, an increase in governmen spending raises he reurns on domesic equiy, providing a hedge agains he subsequen increase in axes. These conclusions are robus o a wide range of preference parameer values and he incompleeness of financial markes. A calibraed version of he model predics asse holdings ha quaniaively mach he daa. JEL codes: F30, F4, G * Tiago Berriel, Praia de Boafogo 90, 0, Rio de Janeiro, Brazil Tiago.berriel@fgv.br. Saroj Bhaarai, 65 Kern Building, Pennsylvania Sae Universiy, Universiy Park, PA Sub3@psu.edu. We hank wihou implicaing Arpia Chaerjee, Nicolas Coeurdacier, John Duca, Chris Erceg, Luca Guerrieri, Jonahan eahcoe, Oleg Iskhoki, Nobu Kiyoaki, Fernanda Nechio, seminar paricipans a Princeon Universiy, Far Eas Meeing of he Economeric Sociey, he Fed Board, Cornell-Penn Sae Macro Workshop, Ipea, IBMEC-Rio, PUC-Rio, Fed New York, Universiy of Arkansas, EEA/ESEM, and especially, Ricardo Reis and Chris Sims for helpful suggesions and commens. Firs Circulaed Draf: Aug This Draf: March 202. The views in his paper are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem.

2 Inroducion While inernaional rade in bonds and equiy has increased grealy in he las wo decades, counry porfolios sill show a sizeable bias owards domesic asses. For example, Burger and Warnock 2003 find ha foreign bonds comprised abou 6% of U.S. invesors bond porfolios in 997 and 4% in 200 and Kyrychenko 2005 finds ha around 95% of U.S. bond holders choose o hold only domesic bonds. Moreover, Nechio 2009 shows ha in he U.S., only around 2 % of governmen bond holders hold any kind of foreign bonds, including indirec holdings hrough muual funds. Corroboraing his evidence furher, Fidora e al 2003 show ha here is subsanial home bias in bond holdings for several advanced counries. 2 Such evidence poins owards significan domesic bias in inernaional bond porfolios. Similarly, able, reproduced from Coeurdacier e al 2007, shows ha inernaional equiy porfolios are heavily biased domesically as counries hold a significanly higher fracion of heir porfolios in domesic equiy as compared o he world marke capializaion share of heir sock markes. From he perspecive of sandard inernaional macroeconomic models, he degree of home asse bias observed in he daa is a long-sanding puzzle, as i implies a lack of inernaional risk sharing among counries. For equiy holdings, Lucas 982 showed in a wo-counry economy wih rade in claims o domesic and foreign endowmens ha perfec risk sharing agains endowmen shocks can be suppored by each agen owning half he claims o he home endowmen and half o he foreign endowmen. 3 For deb holdings, if here are idiosyncraic risk o reurns on bonds, one would similarly expec agens o diversify heir porfolio holdings. Our baseline model ha yields exac analyical soluions is a sandard wocounry wo-good wo-period endowmen economy model wih rade in equiies and one-period governmen nominal bonds. The governmen issues deb and axes domesic agens o finance is expendiure on he domesic good. Burger and Warnock 2003 use he 997 and 200 benchmark surveys of U.S. oldings of Foreign Securiies while Kyrychenko 2005 and Nechio 2009 use he Survey of Consumer Finances. 2 In paricular, hey compue home bias for bonds in Japan, U.K., Germany, Ialy, and France using IMF daa. They also show ha in fac, home bias in bonds is sronger han home bias in equiies. 3 Moreover, in a producion economy model, Baxer and Jermann 997 show ha opimal porfolio holdings involve shoring domesic asses. This implies ha he daa is highly a odds wih he heory. 2

3 In his fricionless se-up wih complee markes, we show ha equilibrium porfolio holdings are biased compleely owards domesic deb and equiy. To our knowledge, his is he firs paper o generae join home bias in boh nominal governmen deb and equiy in a sandard fricionless inernaional macroeconomic model. Wha drives our resuls? olding domesic bonds offers insurance agains shocks ha lead o a revaluaion of governmen deb, such as innovaions o he price level. For example, in he case of bonds wih nominal reurns known one period in advance, he risk ha agens face is in he form of he price level nex period. If he price level is higher han expeced a home, hen agens will realize a lower real reurn on domesic bonds. Wih a higher price level a home however, he expeced value of fuure axes on domesic agens is lower since he real value of deb ousanding has decreased and he ineremporal governmen budge consrain has o be saisfied. Therefore, real reurn on domesic bonds and axes co-move posiively and, since he governmen axes only domesic agens, holding only domesic bonds achieves opimal risk-sharing. olding only domesic equiy is an opimal porfolio decision because governmen spending falls on domesic goods. 4 Then, a posiive domesic governmen spending shock will increase he relaive price of he domesic good. This means ha he relaive reurn of claims on he domesic good is higher compared o he claims on he foreign good. Since governmen spending has increased, in order o fulfill he ineremporal governmen budge consrain, domesic axes have o increase. Therefore, o hedge agains his risk, agens will wan o hold an asse ha offers a relaively higher reurn. equiy is precisely such an asse. Domesic These basic mechanisms ha lead o home asse bias are fully operaive when we relax he simplifying assumpions of our baseline model. The only requiremens for home bias in nominal governmen deb are he presence of some deb revaluaion risk such as nominal risk ha can be hedged hrough nominal bonds and axes falling relaively more on he domesic agen. We view hese feaures as a realisic descripion of he behavior of he governmens of a leas he indusrialized counries. Similarly, he home equiy bias resul 4 We are following a long sanding radiion in inernaional macroeconomic models ha assumes ha governmen spending falls relaively more on domesic or non-raded goods. For a recen example, see Corsei and Peseni

4 is robus o some governmen spending on foreign goods as long as governmen spending shocks fall relaively more on domesic goods compared o foreign goods. A general resul of our paper is ha o generae equiy home bias, a suffi cien condiion is for he governmen s consumpion o be roughly more biased han he consumer s owards domesic goods. Moreover, while in our baseline model, we consider complee markes o derive analyical soluions and isolae he basic mechanisms a work, we relax his assumpion and show ha our resuls on home asse bias are sill valid under imperfec inernaional risk-sharing. To assess he empirical relevance of our paper in resolving he home asse bias puzzle, we underake wo exercises. Firs, we conduc a model based quaniaive evaluaion of our resuls. We presen a fully dynamic version of he wo counry model wih producion, numerically solve for porfolio choice under he realisic assumpion of incomplee markes and disorionary axes, and show ha a calibraed model is able o quaniaively mach he porfolio holdings observed in he daa. 5 Second, we discuss exising empirical evidence and conduc addiional empirical exercises ha validae he key mechanisms of our paper. We ackle quesions such as: does he daa provide suppor for a posiive correlaion beween realized real reurns on domesic bonds and axes? Is his correlaion driven by inflaion movemens? Is here evidence for a posiive correlaion beween domesic equiy reurns and governmen spending? Is governmen spending more biased owards domesic goods compared o privae consumpion? ome bias in nominal governmen deb has been negleced in he lieraure, while home bias in equiy has been exensively addressed. Since his lieraure is quie voluminous, here we discuss a se of approaches ha are direcly relevan for comparison wih our se-up. 6 One approach, exemplified in imporan papers by Kollmann 2006 and Obsfeld 2006, focuses on a preference bias of agens owards consuming domesic goods. This bias is moivaed by he empirical observaion ha he majoriy of privae consumpion falls on domesic goods. Then, wih only counry specific endowmen shocks, hese models generae domesic bias in equiy if he elasiciy of subsiuion beween domesic and foreign goods is less han one. The inuiion for his 5 Therefore, while our basic mechanism behind deb bias is reminiscen of he Ricardian equivalence resul in Barro 974, our resuls hold under a more general environmen. 6 For a recen survey of his lieraure, see Coeurdacier and Rey 20. 4

5 resul is he following. When a posiive endowmen shock his he domesic economy, he erms of rade deerioraes and he real exchange rae depreciaes. Since he domesic agen is biased owards consuming he domesic good and ha good has become cheaper, risk-sharing involves holding an asse whose reurns are relaively lower. Wih an elasiciy of subsiuion lower han one, he deerioraion in erms of rade is so srong ha he reurn on domesic equiy is in fac lower han ha on foreign equiy. Therefore, agens are biased owards holding domesic equiy. In hese models, equiy posiions are used o hedge agains real exchange rae risk and hey imply a high and posiive correlaion beween he real exchange rae and relaive equiy reurns. As van Wincoop and Warnock 2006 poin ou however, he empirical evidence for his mechanism appears o be no very srong since he daa shows a very low correlaion. Compared o his lieraure, our resuls hold even when we do no assume any preference bias in consumpion, ha is, when here is no real exchange rae movemen. This leads o a zero correlaion beween he real exchange rae and relaive equiy reurns. Therefore in our mechanism, equiy posiions are no used o hedge agains real exchange rae risk. Even for he empirically realisic case of consumpion home bias and hence real exchange rae movemen, since our incomplee markes model is driven by boh supply and governmen spending shocks, he correlaion beween he real exchange rae and equiy reurns is no pinned down o be high and posiive. Moreover, our resuls are robus o a wide range of values for he elasiciy of subsiuion beween domesic and foreign goods, including wheher i is greaer han or less han one. A second imporan approach, bes exemplified by eahcoe and Perri 2007, explains he observed equiy bias by a negaive correlaion beween relaive domesic equiy reurns and relaive non-diversifiable labor income. In heir business cycle model wih producion and invesmen, domesic equiy bias is an opimal way o risk share agains counry specific produciviy shocks. Given a posiive produciviy shock, labor income is higher and herefore agens will hold primarily domesic equiy if he reurn on i is lower han foreign equiy. In heir se-up, equiy is a claim o he capial sock and he relaive price of capial is equal o he relaive price of consumpion. A posiive produciviy shock depreciaes he real exchange rae and hereby, leads o a devaluaion of he domesic capial sock. Under a range of parameer values, his devaluaion is so srong ha he reurn on domesic equiy is lower 5

6 han foreign equiy. This mechanism relies on a preference bias owards he domesic goods in consumpion and invesmen, which is no he case in our baseline model. Overall, our paper is independen from and complemenary o heirs, especially since we generae subsanial home bias in equiy holdings even in a model wihou invesmen. 7 In anoher ineresing approach, Coeurdacier e al 2007 generae home bias in equiies wihou requiring equiy posiions o hedge agains real exchange rae risk. In heir endowmen economy model, a new se of shocks, called redisribuive shocks, redisribue income randomly beween equiy and non-diversifiable income. These break he perfec correlaion beween he real exchange rae and relaive equiy reurns while creaing an incenive o hold domesic equiy. In he presence of such shocks, o hedge agains hem, agens wan o hold domesic equiy since in saes of he world where due o a posiive redisribuion shock, domesic equiy income is lower, non-diversifiable income will be higher. 8 In our paper, he shocks ha we use, governmen expendiure shocks, have already been exensively used in he lieraure, for example in Obsfeld 989 and Backus, Kehoe and Kydland Simple Model We sar wih a simple model for wo reasons. Firs, i enables us o derive exac analyical soluions ha provide inuiion for he mechanism behind our resuls. Second, i makes clear which assumpions are essenial o generae our resuls. 2. Baseline Seup We consider a wo-period = 0, wo symmeric counries home, foreign F model. The represenaive household in each counry sars wih iniial wealh and makes porfolio decisions in period 0 and consumes only in 7 Moreover, when preferences are no resriced o log uiliy, which is he baseline case of eahcoe and Perri 2007, heir model also predics a high and posiive correlaion beween he real exchange rae and relaive equiy reurns, which as we poined ou earlier, is low in he daa. 8 There is an empirical debae on he exisence and relevance of such a shock. See for example, Julliard In independen ongoing work, Coeurdacier and Gourinchas 2008 menion governmen spending shock as an alernaive o redisribive shock. In his paper, we explore he role of governmen spending horoughly. 6

7 period. Two goods, Y and Y F, are endowed o he respecive counries in period. Each counry has a governmen ha only axes he represenaive consumer in is counry, spends only on domesic goods, and is subjec o a budge consrain. The governmen issues nominal deb in period 0, spends in period, and axes and reires all deb in period. We allow for rade in governmen nominal bonds and claims on he realizaion of endowmens, which we inerpre as equiy rading. 2.. Consumers For simpliciy, in his secion, we resric he agen s preferences as given in assumpion below. Assumpion : The agens have log uiliy, no preference bias for domesic goods, and uni elasiciy of subsiuion beween domesic and foreign goods. The domesic represenaive agen hen maximizes he following expeced uiliy analogous for he foreign agen E 0 [ log C ] where C is he composie consumpion good and is subjec o he following budge consrains in period 0 and, respecively W 0 C + τ = R 0 B0 h P = B h 0 + B f 0 + q 0 E h 0 + q F 0 E f 0 and 2 + RF 0 B f 0 Q + Y P F E0 h P h P + Y F E f 0 Q P F f P F where E j 0 is he home agen s holding of claims o endowmen jɛ{h, f} in ime 0, B j 0 is he home agen s holding of nominal bonds in j currency, q j 0 is he price of a claim on endowmen j, and R j 0 is he nominal ineres rae on public deb of counry j. 0 Similarly, P j are he price indices for he respecive consumpion bundles, P ij is he price of good j in counry iɛ{h, f}, Q is he real exchange rae defined as Q = S P F, and τ P are axes. Since his is a woperiod model, a no-ponzi condiion implies ha he oal bond holdings of he consumer in period, B h +B f, should be greaer or equal o zero. In wriing eqn.3, we have already imposed he opimaliy condiion, B h + B f = 0. 0 Noe ha in eqn.2, we normalize he price level in boh counries and he nominal exchange rae o in period

8 As eqn.2 makes clear, here is no consumpion a = 0, bu a his dae, agens are allowed o rade asses. The home agen sars wih iniial wealh, W0, which is equal o his asse holdings in period 0. No consumpion or sorage echnology in period 0 implies ha he sum of he wealh of he wo agens should be equal o he sum of governmen debs and he value of he sock of equiy. We add an addiional resricion ha W0 = W0 F = W 0, where W 0 is a consan. In oher words, agens have a symmeric iniial endowmen of wealh. In period, afer he shocks are realized, households consume using heir resuling financial income less axes, as capured by eqn.3. The composie consumpion good is a Cobb-Douglas aggregae of domesic and foreign final goods C = C h C f 4 where C h and C f are home consumpion of he domesic and foreign goods. As is well known, expendiure minimizaion by he agen will imply he following uiliy-based aggregae price index a home P = 2 P h P f. The law of one price holds for he wo raded goods, implying P h = S P F h, P f = S P F f, and Q = S P F P expors o impors, facing he domesic economy is defined as P h P f The opimaliy condiions of he home consumer are =. The erms of rade, he raio of price of or as P F h P F f. E 0 [ R 0 C P ] = E 0 [ R F 0 C P F Q ] [ Y = E P h 0 q0 C P ] ] [Y F Q P F f = E 0 q0 F C P F 5 C h C f = P f P h. 6 The firs se of equaions show he sandard non-arbirage condiions for he four asses available while he second equaion governs he relaive demand of he home good wih respec o he foreign good. Noe he uniary elasiciy of subsiuion beween he wo goods and no preference bias in consumpion. 8

9 2..2 Governmen Each governmen sars in period 0 wih a sock of nominal deb home B 0, foreign B F 0 and collecs ax on is agen in period home τ, foreign τ F. In period, he home governmen analogous for he foreign governmen consumes only domesic goods and is subjec o he budge consrain B P = R 0 B 0 P τ + G h P h. 7 P By combining he ransversaliy condiions of he wo agens, B h +B f = 0 and B F f +B F h = 0, i follows ha B + BF P = 0, ha is, he oal deb of he P F wo governmens in period is equal o zero. ere, we add he assumpion ha each governmen pays any ousanding deb in period, ha is, B = BF P = 0. P F We hink ha his is a reasonable addiional resricion since oher possibiliies such as allowing B o be negaive and BF P P F counry would be subsidizing counry F o be posiive would imply ha governmen s consumpion. This resricion, along wih he opimaliy condiions of he agens, implies, B h = B f = B F h = B F f = 0. Moreover, we assume ha governmens sar wih he same amoun of deb, i.e., B0 = B0 F = B 0. From eqn.2, i follows hen ha W 0 > B Marke Clearing For goods, marke clearing condiions are C h + C F h + G h = Y C f + C F f + G F f = Y F. 8 In he marke for asses noice ha here is an ouside supply of claims on endowmens, which is normalized o, and of nominal bonds issued by he governmen. Marke-clearing condiions are hen 2..4 Uncerainy E h 0 + E F h 0 = E f 0 + E F f 0 = 9 B h 0 + B F h 0 = B 0 B f 0 + B F f 0 = B 0. 0 We allow for hree differen ypes of shocks. Firs, we assume ha a moneary auhoriy conrols he price level in period, which is a known value in period 9

10 0 plus an error in period. Tha is, P = P + ε and P F = P F + ε F. We moivae his shock as a policy-maker choosing he price level wih an error. In secion 3, hese policy shocks come from moneary policy hrough a Taylor-ype rule. Second, we allow for endowmen shocks Y = Ȳ + ε Y h, Y F = Ȳ f + ε Y f and hird, we ake governmen i s expendiure o be an exogenous process, G h = ε Gh and G F f = ε Gf. All ε j i are independen wih mean 0 and sandard deviaion σ j. We normalize he sandard deviaion of all he shocks o in he analyical secions of he paper and relax his simplificaion in secion Compeiive Equilibrium An equilibrium is a se of endogenous variables Φ N ha saisfies he consumer s maximizaion problem, governmen behavior, and marke-clearing condiions, given iniial condiions Φ I and exogenous processes Φ X. The endogenous variable se Φ N comprises of all consumpion allocaions, asse allocaions, prices, exchange raes, and axes of boh counries, ha is, Φ N = {C h, C f, C F f, C F f, E0 h, E f 0, B0 h, B f 0, E F f 0, E0 F h, B F f 0, B0 F h, P h, P f, P F f, P F f, Q, S, q 0, τ, τ F }. The iniial condiions se Φ I is given by he iniial amoun of governmen ousanding nominal bonds, pre-deermined ineress on hese bonds, and he iniial wealh of each agen, ha is, Φ I = {B 0, W 0, R 0, R F 0 }. The exogenous variable se Φ X encompasses he shocks in he economy, ha is, Φ X = {Y, Y F, G h, G F f, P, P F } Porfolio oldings In his simple se-up we derive opimal porfolio holdings using a guess-andverify mehod. In our economy, he allocaions from he social planner s problem and ha from rade of a complee se of sae coningen securiies coincide for some welfare weighs. As is well known, while considering equal welfare weighs for hese ex-ane idenical economies, he allocaions under complee markes are given by equaing he raio of marginal uiliies of he domesic and foreign agens o he relaive price of he domesic and foreign goods. 3 Tha is 2 When we allow governmen consumpion o fall on he foreign good in secion 2.3, he exogenous processes G f and G F h should be added o Φ X. 3 Noe ha we consider wo counries ha have he same level of iniial wealh. 0

11 C C F = Q = where he second equaliy holds because of no preference bias for domesic goods in consumpion. We guess ha in a compeiive equilibrium, our model wih rade in a limied number of asses, such as equiy and bonds, is able o replicae his complee marke allocaion ha would prevail wih a full se of sae coningen securiies. We hen back-ou equiy and bond holdings ha indeed suppor hese allocaions. Our main resul, given in Proposiion below, shows ha in his environmen, as an opimal oucome, here is complee home bias in nominal governmen bonds and equiy. These porfolio holdings are able o achieve perfec risk-sharing beween he counries. Proposiion. Given assumpion, i in he presence of nominal, endowmen, and governmen expendiure shocks, if ii he governmen axes only he domesic agen and iii all governmen expendiure falls on domesic goods, hen he agen holds a only he nominal bonds of her own governmen and b only domesic equiy. Proof. Using our marke compleeness conjecure leads o C C F = Q = 2 or C = C F. 3 Using eqns.6, 8, and 2 we ge C h = C F h = 2 Y G h ; C F f = C f = 2 Y F G F f. Plugging his back o eqn.4 yields C = 2 Y G h 2 Y F G F f 2 4

12 and o eqn.6 yields P h P f = Y F G F f Y G h ; P h P = 2 Y F G F f Y G h Combining eqns.3 and 7 leads us o 2 and P F f P F = Y G h 2. 2 Y F G F f 5 C + R 0 B 0 P + G h P h P = + R 0 B0 h P + RF 0 B f 0 P F + E h 0 Y P h + E f P 0 Y F P F f P F 6. Using eqns.4 and 5 in 6 we ge 2 Y G h 2 Y F G F f 2 + R 0 B 0 + R 0 B0 h P + RF 0 B f 0 P F + E h 0 Y 2 P + G h 2 Y F G F f Y G h Y F G F f Y G h E f 0 Y F 2 = Y G h Y F G F f The marke compleeness condiion is hen saisfied only if we can find E0 h, E f 0, B0 h, and B f 0 ha saisfy he above equaion for all realizaions of shocks and are no coningen on hem. The unique asse allocaion ha fulfills his requiremen is B0 h = B0, B f 0 = 0, E0 h = and E f 0 = 0. Compeiive equilibrium prices ha suppor hese consumpion and asse allocaions are hose ha saisfy q 0 = q F 0 = W 0 B 0 and R 0 = R F 0 and eqn. 5. Complee home bond bias is an opimal oucome because i provides insurance agains nominal shocks and he resuling movemen in axes. To see his, ignoring governmen spending shocks for now, noice from eqn.7 and B = 0 P ha here is a clear negaive relaionship beween he price level and he axes a home in period. This implies a posiive correlaion beween reurns on domesic bonds and domesic axaion. Then from eqn.3 and ignoring equiy posiions for now, i is clear ha by holding primarily domesic governmen bonds, he agen will be able o hedge agains he movemen in axaion ha resuls from a shock o he domesic price level. In paricular, holding foreign nominal bonds will lead o exposure o foreign price shocks wihou being compensaed by he resuling ax movemen. We wan o emphasize ha he only requiremens for our resul are some uncerainy wih respec o he price level, as well as he fac ha he governmen axes only her ciizen 2 2.

13 Complee home equiy bias is an opimal oucome because i provides insurance agains governmen spending shocks and he resuling movemen in axes. When a domesic governmen spending shock his, domesic axes have o increase o fulfill he budge consrain. Given his increase in axes, he agens would like o hold more of an asse ha has a higher rae of reurn. When governmen spending falls only on he domesic good, i increases he relaive price of he domesic good compared o he foreign good. This can be seen clearly from he expression P h = Y P f F GF f. This implies ha he relaive Y Gh raes of reurn on domesic equiy are higher, since he difference in reurns beween domesic and foreign equiy is given by Y P h Y F P f. ence, opimal equiy porfolios are biased domesically. Noe ha as shown in Cole and Obsfeld 99, wih assumpion, equiy allocaion wih only endowmens shocks is indeerminae, as all possible combinaions of equiy allocaions achieve perfec risk sharing. This is because he erms of rade movemen perfecly pools all risk arising from endowmen shocks, regardless of equiy holdings. 4 P ere, we inroduce governmen expendiure shocks in addiion o endowmen shocks, and have shown ha his resul can be overurned, and ha here is a specific allocaion for equiy which achieves he complee marke allocaion. In fac when governmen spending falls only on domesic goods, i leads o a complee home bias in equiy holdings. Finally, we wan o emphasize ha our proof makes clear ha equiy and bond porfolio decisions are separable as posiions on hese asses are aken o insure agains differen shocks. Thus, if we had a se-up where here is rade only in bonds and only nominal shocks, opimal bond posiions would imply complee home bias as in proposiion. Similarly, if we had a se-up where here is rade only in equiy wih governmen spending and endowmen shocks, opimal equiy posiions would imply complee home bias as in proposiion. 2.3 Model Exensions To assess he robusness of our resuls, we now allow for general preferences and relax he simplifying assumpion on governmen spending we made above. The 4 To see he Cole and Obsfeld 99 indeerminacy resul wih only endowmen shocks, noe ha in ha case, he condiion o be saisfied reduces o: + E0 h Y E f 0 Y F 2 R 0 Bh 0 P + RF 0 Bf 0 P F Y F Y for: B0 h = B0, B f 0 = 0, and any value of E0 h. Y Y F 2 Y 2 Y F 2 + R 0 B 0 P 2. This condiion can be saisfied = 3

14 represenaive consumer maximizes [ C σ ] E 0 σ σ > 0 where C is now defined as C = [ a η η C h η + a η C f η ] η η η η > 0 7 where η is he elasiciy of subsiuion beween home and foreign goods and a denoes he relaive preference of domesic over foreign goods, wih a > 0.5 implying home consumpion bias in preferences. Expendiure minimizaion by he agen will imply he following uiliy-based aggregae price [ index a home P = a ] P h η η + a P f η. Moreover, as a generalizaion, we specify ha he governmen spends a consan fracion of is oal consumpion on domesic goods as given by G h = xg f and G F f = xg F h where x > 0. This means ha if x >, governmen consumpion is biased owards he domesic good Complee Markes We firs consider a se-up wih only governmen spending and nominal shocks, which implies complee markes upo a firs-order approximaion. As shown exensively in he lieraure saring wih Lucas 982, in an environmen wih idiosyncraic shocks o endowmen and no consumpion bias in preferences, he agen s opimal allocaion for claims on he realizaion of hese endowmens would seek complee diversificaion of his counry-specific risk. ere we show ha his resul can be overurned, and subsanial home equiy bias can be generaed as an opimal porfolio decision, when sochasic governmen expendiure is biased owards domesic goods. In he appendix in proposiion 2 we show ha domesic holdings of home equiy, denoed here for simpliciy by θ, are given by θ = 2 + [ + x 2a 2 2a x σ 4ηaa + ] 2a σ 8 G f 5 The exogenous processes for governmen expendiures are hen G = G h P f P = ε Gh and G F = G F h P F h P F + G F f P F f P F = ε Gf. P h P + 4

15 and ha he agen holds only domesic nominal bonds. 6 a = 0.5, eqn.8 reduces o θ = 2 Noice ha for η + x x +. 9 In his case, we also show in proposiion 2 ha eqn.9 implies home equiy bias whenever x >. For a general value of a using eqn.8, we find numerically ha once we assume σ > 0.2, 7 x > is sill a suffi cien condiion for home bias in equiy, regardless of he value of η. Wha is he inuiion for his resul? As before, when a posiive domesic governmen spending shock his, domesic axes have o increase o fulfill he budge consrain. Given his increase in axes, he agens would like o hold more of an asse ha has a higher rae of reurn. When governmen spending falls relaively more on he domesic good, since i is effecively a posiive demand shock, i increases he relaive price of he domesic good compared h f ˆP ˆP + o he foreign good,. Since he relaive rae of reurn on domesic h equiy is given by Ŷ ˆP ˆP Ŷ F f + ˆP ˆP h f = ˆP ˆP, i is now higher han before. ence, opimal porfolios are biased domesically as i provides a hedge agains axaion resuling from governmen expendiure shocks. Noice ha θ is a decreasing funcion of x, if x >. The inuiion is clear: in response o a governmen expendiure shock, x slighly above would make he relaive reurns on domesic equiy only slighly higher and so a huge asse posiion is needed o hedge agains he axaion movemen, which is invarian o he composiion of governmen expendiure. Finally, by comparing eqn.9 wih eqn.8, we see ha here is greaer home bias in equiy holdings when a > 0.5 compared o a = 0.5, whenever η is lower han. The inuiion for his resul is he following. Wih a > 0.5, here is an addiional channel for governmen spending o affec equiy holdings since given a governmen spending shock, he real exchange rae appreciaes leading o a higher price for he domesic good. Now because he domesic agen is more biased owards he domesic good, which has become more expensive relaive o he foreign good, and she has relaively inelasic demand as η <, she needs o hold more 6 Noe ha we are considering governmen spending and nominal shocks while excluding endowmen shocks. 7 The lieraure, for example, Coeurdacier e al 2007, usually assumes eiher log-uiliy or σ >. 5

16 of he asse wih higher reurns. Wih governmen spending falling relaively more on domesic good, for he same reasons described before, domesic equiy is precisely such an asse Incomplee Markes We have used marke compleeness so far o help us show our mechanisms clearly. A necessary robusness check of our resuls however, is marke incompleeness since empirical evidence suggess ha here is imperfec risk sharing in inernaional financial markes. 8 We ake up his ask by allowing for nominal, governmen spending, and endowmen shocks wih rade in nominal bonds and equiies. This will imply ha markes are incomplee, even up o a firs order approximaion. Moreover, here is a clear rade-off in he problem of equiy allocaion: while endowmen shocks call for full diversificaion, he home-biased governmen expendiure shock leads o home bias in equiy. In he appendix, we show using recenly developed echniques, ha for a = 0.5, he home equiy allocaion, θ, is given by θ = 2 + η x 2 2 η 2 + x x The opimal nominal bonds allocaion is B0 h = B0, ha is, full home bias once again. 9 The firs erm in eqn.20, which leads o θ =, reflecs he 2 hedging moive agains idiosyncraic endowmen shocks. The second erm reflecs hedging agains governmen spending shocks. When x =, governmen spending shock does no affec he erms of rade, and hence his erm is zero and opimal equiy holdings are fully diversified. In his siuaion, we have a generalized version of he Lucas 982 model wih governmen shocks. When x > however, he second erm is posiive, leading o a home bias in equiy holdings. The expression makes i clear ha his resul does no 8 See for example, Corsei e al Complee marke models predic perfec comovemen beween he real exchange rae and relaive marginal uiliies beween counries. In he absence of preferenc shocks, his implies a perfec comovemen beween he real exchange rae and relaive consumpion bewween he counries. This implicaion is srongly rejeced empirically. This is also known as he Backus-Smih puzzle in he lieraure. 9 Noe ha even here we are normalizing he variance of all he shocks o uniy. Of course, wih incomplee markes, he relaive variances of he shocks plays a role in porfolio holdings. Bu, we have absraced from his issue here o keep he presenaion cleaner and focused and o allow a direc comparison wih he complee markes case analyzed earlier. In he quaniaive exercise in secion 3, he variances of he differen shocks will be calibraed from daa. 6

17 depend on he value of η. In fig., we plo he value of θ for differen values of η. Noice ha as x increases above, here is a rade off beween he shocks: while governmen expendiures shocks push he allocaions o sar high and o decrease monoonically, endowmen shocks push for diversificaion. The sum of hese effecs leads o an iniial increase and subsequen decrease of home bias in equiy allocaion, as x increases. In he case of incomplee markes and any value for σ and a > 0.5, we show he sysem of equaions o be solved in he appendix. The final analyical soluion for porfolio holdings urns ou o be cumbersome and we resor o numerical soluions o find he condiion for home bias in equiy. We are paricularly ineresed on how hese allocaions depend on x, he fracion of governmen consumpion on domesic goods and he degree of consumers home bias, greaer han a a a a. A robus resul is ha for reasonable values of σ, x roughly again generaes home equiy bias, regardless of he value of η. In he appendix, we plo he resuls for for σ =.5 and for differen values of a and η. I is clear ha for all x > This approximae bound x > a a as shown in proposiion 3 in he appendix. a, he home bias on equiy is high. a can be made exac in he case of log-uiliy, We see ha here he change from he case wih complee markes, or incomplee markes bu wih a = 0.5, is ha he necessary and suffi cien condiion o generae home bias in equiy is now x > a a as opposed o x >. In oher words, now we need he governmen o be more biased han he consumer in order o generae home bias in equiy, bu he resul is sill independen of he value of η. Why does he case wih incomplee markes and a > 0.5 require more bias in governmen spending compared o he cases we have analyzed before? The fundamenal reason is ha wih incomplee markes and a > 0.5, he real exchange rae moves in response o he shocks, and hence here arises a hedging moive agains his real exchange rae movemen. In essence, since a a deermines he exen of agen s bias in consumpion and he resuling role for real exchange rae hedging, x > a a is needed o ensure ha he erms of rade movemen due o governmen shocks couneracs he real exchange rae movemen. Anoher imporan resul in his case is ha due o marke incompleeness, moneary policy affecs he erms of rade and has real effecs even wih log uiliy. As a resul, we show in he appendix ha while here is sill subsanial home bias in bonds, he agen does no hold only domesic bonds as i can improve insurance by holding some foreign 7

18 bonds. In conclusion, herefore, we have shown ha in a variey of seings, complee or incomplee markes, log uiliy or general CRRA uiliy, home consumpion bias or no, a suffi cien condiion for home bias in equiy is ha he governmen spending is more biased owards domesic goods as compared o he consumer. We have also shown ha he resul of home bias in bonds is valid when we allow for he aforemenioned exensions. Mos imporanly, we generae home equiy bias wihou depending on he value of η, he elasiciy of subsiuion beween domesic and foreign goods Lieraure We now briefly discuss relaed lieraure ha uses a similar model environmen as he one we considered above. We are no aware of any oher papers ha has shown equilibrium governmen deb porfolios o be predominanly domesic. Devereux and Suherland 2006 have an endowmen economy model wih nominal bonds, bu he bonds are inside asses in ne zero supply. 2 heir model, where nominal demand is exogenous, a posiive domesic endowmen shock has a negaive effec only on he domesic price level. Therefore, domesic bond reurns are high precisely when oupu is high. In order o hedge agains he endowmen shock, agens herefore, ake a shor posiion in domesic nominal bonds. In our model, in conras, a domesic endowmen shock affecs boh he domesic and foreign price levels by he same amoun. Thus, governmen deb posiions canno be used o hedge agains oupu risk. In fac, wih only endowmen shocks, domesic and foreign governmen bonds are perfec subsiues. Nominal bonds are herefore used o hedge agains idiosyncraic counry specific price level shocks, which as we have explained before, creae a posiive correlaion beween axes and reurns on domesic bonds. For home equiy bias, he lieraure using an endowmen economy model is fairly large. Firs, as explained in deail in Obsfeld 2006 and Coeurdacier 20 We have also checked ha all our resuls are robus o oher model exensions such as allowing for inflaion indexed bonds and for a par of governmen spending o be endogenous. The resuls are available on reques from he auhors. 2 Engel and Masumoo 2009 presen a model where here is rade in forward conracs on nominal foreign exchange. This is essenially he same as allowing for rades in inside nominal bonds denominaed in differen currencies. Again, hey do no consider governmen ouside nominal bonds and he associaed opimal porfolio holdings, which is he focus of our paper. In 8

19 e al 2007, he previous lieraure can generae home bias in equiy only by saring wih he assumpion ha a > 0.5. In his paper, we generae equiy home bias even when a = 0.5. Second, even afer assuming a > 0.5, for reasonable degree of risk aversion, he mechanism requires ha η, he elasiciy of subsiuion beween domesic and foreign goods, be approximaely less han. 22 There is a grea deal of uncerainy in he empirical lieraure regarding he value of η, and mos esimaes pu i above. 23 Given his, we view he fac ha our resul is independen of he value of η o be a significan srengh of our proposed mechanism. To drive home he difference from he previous lieraure, able 2 compares resuls for equiy holdings only wih endowmen shocks, wih hose in our model wih governmen spending shocks and endowmen shocks and a > 0.5, ha is, secion The resuls are for σ =.5. The able makes clear ha he inroducion of a governmen spending shock ha is biased owards domesic good leads o home bias in equiy, even when η >. The previous lieraure, on he oher hand, relies on η <, which is ouside he range of mos empirical esimaes. Moreover, he previous lieraure s mechanism which generaes home equiy bias in response o endowmen shocks by relying on a > 0.5 and η <, implies a srong posiive correlaion beween he real exchange raes and equiy reurns. This is because equiy posiions are used o hedge agains real exchange rae risk. As van Wincoop and Warnock 2006 find however, his correlaion is close o 0 in he daa. In our se up, when a = 0.5, he real exchange rae upo firs order is zero, and here is no correlaion beween he real exchange rae and relaive equiy reurns. We view his as anoher srengh of our mechanism since i clearly shows ha equiy bias is no a resul of hedging agains real exchange rae risk. Even when here is home consumpion bias in preferences, and hence real exchange rae movemen, since we have boh governmen spending shocks and endowmen shocks, he correlaion beween real exchange raes and equiy reurns is no pinned down o be high and posiive. For example, when we compue Cov 0 relaive equiy reurns, ˆQ /V ar 0 relaive equiy reurns in he model of secion 2.3.2, for η =.2 and x = 4, i is and for η =.5 and x = 4, i is In our se-up wih nominal and endowmen shocks, [ bond holdings will be compleely domesic, while equiy holdings will be given by 2 + ] 2a ρ ρ+4ηρ a+2a. Noice ha 2 equiy holdings are fully diversified if a = 0.5 or ρ =. 23 See Coeurdacier e al 2007 and ciaions herein. 24 Benigno and Nisico 202 argue ha focusing on his saic correlaion beween real 9

20 3 Dynamic Model wih Producion 3. Seup In his secion we presen a fully dynamic infinie-horizon model wih producion so ha we can underake a realisic quaniaive exercise. We consider wo symmeric producion economies, each populaed by a represenaive agen. Each counry specializes in he producion of one radable final good. Wihin each counry, he agen consumes a domesically produced good and an impored good. Boh of he radable goods are produced in differeniaed brands by a coninuum of monopolisically compeiive firms of measure. A brand of a given good is an imperfec subsiue for all oher brands of ha good. Firms use only labor, ha is supplied compeiively and is immobile beween counries, in heir producion process. For simpliciy, here are no inermediae and non-radable goods in he model. Furhermore, prices are fully flexible. In each counry, here is also a governmen ha supplies one period non sae-coningen nominal bonds and axes he labor income of he represenaive agen and profis of he firm. The governmen conducs moneary policy using a ineres rae rule and fiscal policy using a rule for axes. Agens in each counry can rade claims o aggregae profis of he firms and hold domesic and foreign bonds wih reurns denominaed in he respecive currencies. Since here are hree sources of aggregae uncerainy in he model: produciviy shocks, moneary shocks, and governmen spending shocks, and asse rade is limied o only equiies and nominal bonds, markes are incomplee and herefore, risk-sharing of he counry-specific shocks is imperfec. 3.. Consumer A represenaive agen a home maximizes he expeced presen discouned value of uiliy E =0 [ C σ β L +ν σ λ + ν ] 0 < β <, σ > 0, ν > 0, λ > 0 2 where C is he composie domesic consumpion good and L is domesic labor supply. The agen is subjec o he period budge consrain exchange raes and equiy reurns could be misleading in a dynamic conex. 20

21 C + Bh P + Bf P F Q + q E h + q F E f Q = τ L w L 22 + R B h P + RF B f P F Q + q + Π E h + q F + Π F Q E f where B h, B f, E h, and E f are holdings of domesic nominal bonds, foreign nominal bonds, claims o aggregae afer-ax profis of domesic firms, and claims o aggregae afer-ax profis of foreign firms purchased in period o be brough ino period. 25 Moreover, P is he aggregae domesic price level, P F is he aggregae foreign price level, Q is he real exchange rae, q is he real price of one uni of claim o domesic profis, q F is he real price of one uni of claim o foreign endowmen, Π is afer-ax aggregae real profis of domesic firms, Π F is afer-ax aggregae real profis of foreign firms, R is he nominal ineres rae on domesic bonds accruing o bond holdings in period bu known in period, R F is he nominal ineres rae on foreign bonds accruing o bond holdings in period bu known in period, τ L is he rae of labor income ax, and w is he real wage a home. For fuure purposes, define real wealh of he home agen W as W = Bh P + Bf P F Q + q E h + q F E f Q. The composie consumpion good C is a CES aggregae of domesic C h and foreign C f final goods as defined in secion 2.3. The home consumpion good C h is produced in differeniaed brands c h by a coninuum of monopolisically compeiive home firms indexed j and of measure, and is defined as [ C h = 0 c h j θ θ dj ] θ θ θ > 23 where he elasiciy of subsiuion among he brands is given by θ. Similarly, he foreign consumpion good C f is produced in differeniaed brands c f 25 We follow Devereux and Suherland 2006, Engel and Masumoo 2009, and Benigno and Nisico 202, among ohers, in modelling equiies his way: as claims on profis of monopolisically compeiive firms. 2

22 by a coninuum of monopolisically compeiive foreign firms indexed f and of measure, and is defined as [ C f = 0 c f ] θ f θ θ θ df where he elasiciy of subsiuion among he brands is given by θ. 24 As is well known, expendiure minimizaion by he agen will imply a uiliy-based aggregae price index a home, P, exacly as in secion 2.3. Expendiure minimizaion will also imply he following domesic price level of [ ] θ he home consumpion good P h = 0 ph j θ dj, where p h j is he domesic price level of brand j of he domesic good, and he following domesic price level of he foreign consumpion good P f = [ 0 pf f θ df ] θ, where p f f is he domesic price level of brand f of he foreign good. Similarly, given he definiion of he consumpion goods and he price levels, manipulaion of he demand curves a he brand level gives c h j C h = p h j P h θ c f j C f = p f P f θ j. 25 The law of one price holds among he radable brands and hence we have p h j = S p F h j p f f = S p F f f 26 where p F h j and p F f f are he foreign price level of price of he brand j of he domesic good and brand f of he foreign good. Given he definiion of he consumpion indices and he price indices resuling from expendiure minimizaion, he opimizaion problem of he consumer, ha is maximizing eqn.2 wih respec o C, B h, B f, E h, E f, and L, subjec o eqn.22, resuls in [ C σ = E C σ = E β P R C σ + P + [ ] β q + + Π+ C σ + q ] [ ] βp F R F Q + = E C σ, 27 + P F + Q [ ] β q F = E + + Π F + Q+ C σ 28 + q F Q λ L ν = C σ τ L w

23 Eqns are he familiar euler equaions wih respec o he four asses ha are available while eqn.29 deermines labor supply decisions of he agen by equaing he marginal rae of subsiuion beween leisure and consumpion wih afer ax real wage. The budge consrain and he opimizaion problem of he foreign represenaive agen is enirely analogous and is no presened here o conserve space Firms Each brand j of he domesic good is produced by a single home firm j using he following linear producion funcion y j = A l j 30 where y j is he domesic oupu of brand j, A is he counry-specific produciviy shock ha follows an exogenous process, and l j is he labor demand by firm j. Firms hire labor in a compeiive marke aking he wage as given and he labor used is homogenous across all firms j. The firms are idenical excep for he fac ha hey produce differeniaed brands for he same good. The process for produciviy is given by log A = ρ A log A +ɛ a,. Firm j maximizes real profis, ha is revenue less labor coss, given by p h j y j w P l j 3 subjec o eqn.30 and eqn.25, leading o he familiar pricing equaion p h j = θ w θ P A 32 where monopolisically compeiive firms charge a price ha is a mark-up imes he nominal marginal cos. The aggregae afer ax real profis of he firms in he domesic economy can be wrien as Π = τ π P h w A P Y P and he opimizaion decision of he individual domesic firms gives 33 P h P = θ θ w A

24 The opimizaion problem of he foreign firms is enirely analogous and is no presened here o conserve space Governmen The home governmen faces he following period budge consrain B P = R B P τ L w L τ π P h w A P Y P + G h P h P + G f P f P 35 where B is oal nominal deb issued by he home governmen in period and G h and G f respecively are he home governmen s spending on domesic and foreign good. 26 The raio of labor ax revenue vs. profi ax revenue is for simpliciy, consan τ L w L where y is a parameer of our model. [ = y τ π P h w A P Y ] P 36 We assume here ha governmen spending over he differeniaed brands of he domesic and foreign goods is defined in he same way as for he consumer wih he same elasiciy of subsiuion over he brands. Tha is, [ G h = 0 g h j θ θ dj ] θ θ [ G f = 0 g f ] θ f θ θ θ df. 37 The raio of governmen spending over domesic vs. foreign good is for simpliciy, consan G h = xg f 38 where x is a parameer of our model. Governmen spending follows an exogenous process G P = G F h F h + G F f P F f P F Q P F = ρ G G h + ɛ g, Noice we have no lump-sum axes and allow he governmen o ax boh he labor income of he home agen and he profis of home firms so ha he model can be aken o he daa realisically. 24

25 In his paper, we do no consider explici opimal governmen policy and use simple rules as descripions of governmen policy. The governmen conducs moneary policy using a ineres rae rule given by R = γ 0 P /P γ expɛ r, 40 where he ineres rae shock follows he exogenous process log ɛ r, = ρ R log ɛ r, + e r, and fiscal policy using a rule for oal ax revenue responding o real value of deb τ L w L + τ π P h w A P Y P B φ = φ 0. 4 P Again, he foreign governmen s descripion is compleely analogous and symmeric Marke Clearing Marke clearing for goods implies c h c F f j + c F h f + c f j + g h j + g F h j = A l j 42 f + g f f + g F f f = A F l F j. Similarly, marke clearing for asses implies E h B h + E F h = E f + E F f = 43 + B F h = B B f + B F f = B F and oal labor demand by firms equaling labor supply implies 0 l jdj = L ere we assume ha axes reac o curren levels of real deb. This is jus for exposiional convenience and does no affec our resuls. We also experimened wih alernae ax rules where curren axes depend on differen weighed sums of lagged levels of governmen deb, hereby keeping he governmen solven wihou fiscal policy deermining he price level. Quaniaive resuls were very similar. In addiion, in he special case where all axes are lump-sum, a numerical exercise showed ha all ha maers for porfolio allocaion is how he presen value of life-ime axes adjuss o innovaions in he real value of deb. 25

26 3..5 Compeiive Equilibrium An equilibrium is a se of quaniies, c h j, c f j, c F h j, c F f j, l j, l F j, E h, E f, B h, B f, B, E F f, E F h, B F f, B F h, B F, τ L, τ π prices, p h j, p f j, p F f j, p F f j, Q, S, q, q F, w, w F, R, R F, and exogenous processes A j, A F j, G, G F, ɛ r,, ɛ r, for all 0, ha saisfy eqns Quaniaive Analysis ere we conduc a quaniaive analysis of our producion model o invesigae wheher he asse holdings ha our model predics mach he ones observed in he daa. We solve he model using approximaion mehods around a nonsochasic symmeric seady sae. The approximaed equaions are provided in he appendix. Since markes are incomplee, we compue seady sae asse holdings using he same mehodology deailed in he appendix for secion Calibraion Nex, we describe in deail how we calibrae he various parameers in our model. Preference parameers: We se β, he discoun rae, as 0.99, so ha he quarerly real ineres rae is 4%, and using he esimaed value of σ, he risk aversion parameer, in Smes and Wouers 2008, se i o.5. We choose υ, he inverse of he Frisch elasiciy of labor supply, o be 4. In accordance wih many papers in inernaional macroeconomics, such as Chari e al 2002, we pick a, he parameer governing home bias in consumpion, as There is no empirical consensus in he lieraure on he value of η, he elasiciy of subsiuion beween domesic and foreign goods, so we consider a range of values from This range encompasses values used in he lieraure such as Coeurdacier e al 2007 and Chari e al We se θ as, which implies a before-ax profi share in he economy of 9%. This value is in he ballpark of he lieraure. 28 Policy parameers: For he parameers governing moneary and ax policy rules, γ and φ, respecively, o ensure he exisence and uniqueness of he price level, a suffi cien condiion is γ, φ > in which case moneary policy 28 Roemberg and Woodford 997 esimae profi share o be 5% while Giannoni and Woodford 2003 esimae i o be 4%. 26