Liquidity and Exchange Rates: An Empirical Investigation

Transcription

1 Liquidiy and Exchange aes: An Empirical Invesigaion Charles Engel Seve Pak Yeung Wu Universiy of Wisconsin January 2, 209 (firs draf, November 208) Absrac We find srong empirical evidence ha economic fundamenals can well accoun for nominal exchange rae movemens. The imporan innovaion is ha we include he liquidiy yield on governmen bonds as an explanaory variable. We find impressive evidence ha changes in he liquidiy yield are significan in explaining exchange rae changes for all of he G0 counries. Moreover, afer conrolling for liquidiy yields, radiional deerminans of exchange raes adjusmen oward purchasing power pariy and moneary shocks are also found o be economically and saisically significan. We show how hese relaionships arise ou of a canonical wo-counry New Keynesian model wih liquidiy reurns. Addiionally, we find a role for sovereign defaul risk and currency swap marke fricions.

2 . Inroducion The economics lieraure on foreign exchange rae deerminaion has no had much success linking exchange-rae movemens o sandard macroeconomic variables. This problem has come o be known a he exchange-rae disconnec puzzle, as coined by Obsfeld and ogoff (2000).0F Our ack is o look for he role of he liquidiy reurn on governmen bonds in driving exchange raes. Engel (206) suggess ha his reurn he non-moneary reurn ha governmen shor-erm bonds provide because of heir safey, he ease wih which hey can be sold, and heir value as collaeral, which is someimes referred o as he convenience yield may be imporan in undersanding exchange rae puzzles.f2 Our sudy uses measures of he liquidiy yield on governmen bonds, as consruced by Du, e al. (208a). These measures ake he difference beween a riskless marke rae and he governmen bond rae o quanify he implici liquidiy yield on he governmen bond. Moreover, he Du, e al. measure correcs for fricions in foreign exchange forward markes and for sovereign defaul risk. The liquidiy yield can be associaed wih he deviaion from uncovered ineres pariy ha is now inroduced as a sandard feaure in open-economy New Keynesian models. I is usually included so ha he model can reproduce o some exen he observed volailiy of real exchange raes.2f3 Indeed, Iskhoki and Mukhin (207) show ha his deviaion is key o being able o accoun for he disconnec puzzle. These models ineviably rea he deviaion as an unobserved variable. One inerpreaion of our model and findings is ha he uncovered ineres pariy deviaion is indeed observable and can be well-measured by he relaive liquidiy yield on governmen bonds. The inuiion for why he governmen bond convenience yield influences he exchange rae is sraighforward. The liquidiy ha hese bonds provide is aracive o invesors, and influences heir invesmen decisions as if he bonds were paying an unobserved convenience dividend. The governmen bonds can pay a lower moneary reurn han oher bonds wih similar risk Engel (204) provides a recen survey. Iskhoki and Mukhin (207) is a recen aemp o build a model o accoun for he disconnec. One noable deerminan of nominal exchange rae movemens is he lagged real exchange rae, which arises from adjusmen o real exchange rae disequilibrium. This poin was made clearly by Mark (995), and has found srong recen suppor by Eichenbaum, e al. (208). 2 Krishnamurhy and Vissing-Jorgensen (202) and Nagel (206) sudy he convenience yield on U.S. Treasury asses. Valchev (207) also sudies a model in which he convenience yield plays a role in accouning for exchange-rae puzzles. del Negro e al. (208) find ha convenience yields accoun for he long-run drop in global real ineres raes. 3 See Kollmann (2002) for an early example. 2

3 characerisics, and sill be desirable. An increase in he liquidiy yield, as measured by he difference beween he privae bond reurn and governmen bond reurn, will ceeris paribus lead o a currency appreciaion much in he same way ha an increase in he ineres rae would affec he currency value. However, we noe ha in our equilibrium model, he liquidiy reurn and he ineres rae play somewha differen roles arising from he fac ha he moneary policy insrumen is he ineres rae ex-convenience yield. Thus, he ineres rae responds endogenously o inflaion in a way ha he convenience yield does no. We find for each of he so-called G0 currencies ha he relaive liquidiy yield (he home counry yield relaive o foreign counry yields) has significan explanaory power for exchange rae movemens.3f4 Moreover, using guidance from a sandard New Keynesian model bu augmened wih a role for liquidiy reurns on governmen bonds, we find ha he sandard deerminans of exchange rae movemens are saisically and quaniaively imporan afer conrolling for he liquidiy yields. In paricular, ineres rae differenials and a lagged adjusmen erm for he real exchange rae (as in Eichenbaum, e al. (208)) are also imporan deerminans of exchange rae movemens. We subjec our resuls o a large number of robusness ess, bu find he models perform consisenly well. Addiionally, we underake an insrumenal variables specificaion o conrol for possible endogeneiy of he relaive liquidiy yields, and again find consisenly srong suppor for he model. Our sudy is conemporaneous wih Jiang, e al. (208), bu wih he following differences: Our empirical specificaion is derived from a heoreical general equilibrium model.4f5 Our empirical work finds srong evidence for he role of governmen liquidiy yields, ineres raes and adjusmen oward purchasing power pariy for en differen currencies, while Jiang, e al. look only a he U.S. dollar. We do numerous robusness checks, and include an insrumenal variables specificaion. And, using he decomposiion of Du, e al. (208a), we find addiional explanaory power arising from defaul risk and forward marke fricions in a way ha is compaible wih our 4 Namely, Ausralia, Canada, Germany, Japan, New Zealand, Norway, Sweden, Swizerland, he Unied Kingdom and he Unied Saes. 5 Linnemann and Schaber (205) also posi a relaionship beween liquidiy reurns and exchange rae behavior. Their paper does no provide an empirical es of he relaionship beween he liquidiy reurn and exchange raes. Their model posulaes a negaive relaionship beween he liquidiy yield and ineres raes, conrary o he model of Nagel (206), Engel (206), and his paper, and conrary o he evidence in Nagel (206) and his paper. 3

4 model.5f6 This laer is imporan because he premium on governmen bonds is influenced no only by he liquidiy yield, or convenience yield, of governmen bonds, bu also by defaul risk and fricions in forward markes for foreign exchange.6f7 We hink of he liquidiy reurn or convenience yield as arising from he usefulness of some governmen securiies eiher as collaeral for very shor-erm loans, or from he ease wih which hey can be sold for cash. Nickolas (208) defines liquid asses as: cash on hand or an asse ha can be readily convered o cash. An asse ha can readily be convered ino cash is similar o cash iself because he asse can be sold wih lile impac on is value. Bu here is only a fine disincion beween liquidiy so defined and safey as defined by Goron (207): A safe asse is an asse ha is (almos always) valued a face value wihou expensive and prolonged analysis. By design, here is no benefi o producing (privae) informaion abou is value, and his is common knowledge. From hese definiions, i is clear ha safe asses will be liquid, and liquid asses are safe. The role of safe asses in he global economy has been sudies exensively in recen lieraure. In Caballero e al. (2008), Mendoza e al. (2009), Gourinchas and ey (20), Maggiori (207), and Farhi and Maggiori (208), safe asses play a key role in accouning for global imbalances. Caballero e al. (205, 207) explore he role of a shorage of safe asses and heir role in he global financial crisis. Gourinchas and Jeanne (202) explore he consequences of a shorage of safe asses for he sabiliy of he global financial sysem. Liquidiy and is role in exchange-rae deerminaion has been explored from a variey of angles. The aforemenioned papers of Engel (206) and Valchev (207) offer models in which cerain asses have a convenience yield arising from heir liquidiy. Grilli and oubini (992) and Engel (992) are earlier, relaed works. Brunnermeier e al. (2009), Adrian e al. (2009) and Bruno and Shin (204) consider a liquidiy effec on exchange raes arising from banks balance shees. One can idenify he noions of liquidiy in hese sudies wih funding liquidiy, as defined in Brunnermeier and Peersen (2009), bu oher work has looked a he role of marke liquidiy. A prominen recen sudy is Gabaix and Maggiori (205) ha considers financial consrains ha preven full liquidiy o arbirage inernaional money markes. A relaed sudy is Pavlova and 6 A small bi of our preliminary findings were firs repored a a conference a he Bank for Inernaional Selemens on Inernaional macro, price deerminaion and policy cooperaion in Sepember, 207. The publicly available slides for ha lecure can be found a hps:// 7 In fac, Avdjiev, e al. (208) documen he role of deviaions from covered ineres pariy for he value of he U.S. dollar. 4

5 igobon (2008) which invesigaes he role of porfolio consrains. Melvin and Taylor (2009), Bani e al. (202), and Mancini e al. (203) empirically sudy of he role of liquidiy in foreign exchange markes. There is a long hisory of aribuing a role o he safe haven effec on currency values. ecenly, Faum and Yamamoo (206), which looks a his phenomenon during he global financial crisis, defines a safe currency as a currency ha increases is relaive value agains oher currencies as marke uncerainy increases. The idea of a safe haven effec is an old one see, for example, Dooley and Isard (985), Isard and Sekler (985) or Dornbusch (986). Here we could argue ha one channel for he safe haven effec is hrough he demand for safe asses. During imes of global uncerainy, cerain asses such as shor-erm governmen securiies become more valued for heir liquidiy. There cerainly can be oher channels hrough which he safe haven phenomenon works. Farhi and Gabaix (205) model safe haven currencies as ones ha appreciae during imes of global downurns, a concep ha has been esed empirically by analdo and Söderlind (200). Obsfeld and ogoff (2002) speak of risk more generally, which could encompass boh he liquidiy channel and he hedging channel. Secion 2, which guides our empirical work, presens an equilibrium New Keynesian model in which governmen bonds pay a liquidiy reurn. Secion 3 presens he resuls of our empirical invesigaion. Secion 4 concludes. 2. Liquidiy and Exchange aes Following Krishnamurhy and Vissing-Jorgensen (202), Engel (206), Nagel (206), and Jiang, e al. (208), we posi ha he ex ane excess reurn on shor-erm reasury bonds in one counry relaive o anoher is aribuable o an unobserved liquidiy payoff. In paricular, le i be he one-period ineres rae in he home counry governmen bonds (we presen he model in he conex of wo counries, home and foreign ). i m is he reurn on a shor-erm, one-period marke insrumen. The liquidiy premium represens he difference in m hese wo raes: γ = i i. For now, we assume ha here is no defaul risk on eiher insrumen. The empirical secion will adjus he reurns for defaul risk using credi defaul swap (CDS) daa. 5

6 Under his formulaion, we should observe γ > 0, as long as he reasury bond is more liquid. Invesors are willing o hold he governmen bond insead of he marke insrumen, because he reasury bond is more easily sold on markes, or is more readily acceped as collaeral. I may be he case ha some agens in he economy have no need for liquidiy, in which case heir holdings of he governmen bonds would be zero. In paricular, i migh be ha foreign agens hold no home governmen bonds because hey do no value he liquidiy of hose asses. Bu privae agens canno shor governmen bonds ha is, privae agens (in eiher economy) canno borrow a he rae i, because he asses hey issue do no have he same liquidiy as governmen bonds. m Analogously, in he foreign counry, here is a liquidiy yield given by γ = i i, where he variables wih he superscrip denoe he foreign-counry equivalens of he home-counry variables. We will assume ha, up o a consan foreign exchange risk premium (which we normalize o zero), uncovered ineres pariy holds for he marke insrumens: () i + Es s i =, m m + 0 where s is he log of he exchange rae (expressed as he home currency price of he foreign currency.) Le η be defined as he liquidiy reurn on home governmen bonds relaive o foreign governmen bonds: (2) η ( m ) ( m ) ( m m γ γ i i i i i i ) ( i i ) = = =. Then we can rewrie () as: (3) i + Es s i = η. + Tha is, he expeced excess reurn on foreign one-period governmen bonds (relaive o home bonds) is deermined by he liquidiy yield of home governmen bonds relaive o foreign bonds. 6

7 When he home bonds are more liquid, he foreign bonds mus pay a higher expeced moneary reurn. Now, ierae equaion (3) forward, as in Campbell and Clarida (987) and ohers: (4) ( ) ( + + ) ( η + + η) lim + ( + ) k j j j k j= 0 j= 0 ( ). s = E i i i i E + Es k s s The uncondiional mean difference in he home and foreign ineres rae is denoed i i, and he ( ) mean of he relaive liquidiy reurn is η. Here, lim Es + k k( s+ s) k is he permanen componen of he nominal exchange rae in he sense ha Beveridge and Nelson (98) use ha erm in heir permanen-ransiory decomposiion. The erm s+ s represens he rend in he log of he nominal exchange rae. There is some consensus ha nominal exchange raes among high-income counries conain uni roos. For example, if moneary policy is se by a rule for money supplies, any permanen change in he money supply would lead o a permanen change in he nominal exchange rae. If moneary policy is se by an ineres-rae rule such as a Taylor, he exchange rae will conain a uni roo unless he ineres rae rule arges he nominal exchange rae.7f8 Equaion (4) already poins o he inuiion of our empirical specificaion. I says ha when he infinie sum of he expeced curren and fuure home ineres raes is rises relaive o he expeced infinie sum of expeced curren and fuure foreign ineres rae, he home currency appreciaes ( s falls). Tha is a well-known channel of influence, which is a work in, for example, he famous Dornbusch (976) model. However, his comparaive saics exercise is made holding he permanen componen of he exchange rae consan. All nominal ineres rae changes may no be he same. For example, in a radiional monearis model of exchange raes, a permanen one-ime increase in he moneary growh rae in he home counry would immediaely raise inflaion, and herefore raise he inflaion premium incorporaed in he nominal ineres rae. i i would increase for all ime periods, + j + j bu ha also ismplie an increase in he uncondiional mean of he relaive ineres raes, i i. In 8 See Benigno and Benigno (2008). 7

8 ha case, here would be no change in he firs erm on he righ hand side of equaion (4): ( ( )) + + E i i i i would be unaffeced. However, his change would lead o an increase in j j j= 0 he permanen componen of he exchange rae. The size of he increase is model-dependen, bu a classic resul is ha an increase in he growh rae of x percen leads o an immediae permanen depreciaion of greaer han x percen, which he lieraure referred o as he magnificaion effec.8f9 The conclusion is ha equaion (4) by iself, which represens he inernaional financial marke equilibrium condiion, is no sufficien o deermine he exchange rae. In order o deermine he exchange rae, we need a model of he deerminaion of ineres raes, and of he permanen componen of he nominal exchange rae.9f0 Before proceeding o close he model, we noe ha a higher relaive liquidiy reurn on home governmen bonds also leads o an appreciaion of he domesic currency. In his equaion, he liquidiy reurn and he ineres rae are jus wo componens of he reurn on governmen bonds, and so heir impac on he exchange rae is idenical. In he model ha we now presen, he ineres raes are he moneary policy insrumen, and are endogenously deermined. As a firs sep, we incorporae he model from Engel (206), based in urn on Nagel (206), in which he liquidiy reurn on he home bond is posiively relaed o he ineres rae: = i i + v, α > 0. (5) η α( ) Appendix A derives his equaion, exending he analysis of Engel (206). The posiive relaionship beween he relaive liquidiy reurn and he ineres differenial arises as in Nagel (206). Specifically, when he moneary auhoriy ighens moneary policy by reducing he supply of money and raising ineres raes, liquid asses ha can subsiue for money become more valued for heir liquidiy services and so pay a higher liquidiy reurn. The remainder of he model adops a New Keynesian framework. Firs, we assume ha nominal prices in each counry are sicky in nominal erms. In paricular, we posi ha here is 9 See, for example, Frenkel (976). 0 Here we differ from Jiang, e al. (208), who ake nominal ineres raes as exogenous and assume he nominal exchange rae is saionary. 8

9 local-currency pricing, so ha each firm, in boh counries, ses wo prices one in home currency for sale in he home counry, and one in foreign currency for sale in he foreign currency. We modify he sandard Calvo-pricing equaion in wo ways. Firs, we assume ha nominal prices mus be se one period in advance. We make his assumpion because, in pracice, he response of nominal prices o curren period shocks is so small relaive o he response of nominal exchange raes, ha a model wih predeermined prices beer represens realiy in an openeconomy framework. A fracion of firms, θ, are allowed o change heir prices opimally each period, bu he price hey se a ime is for he ime period. These firms se heir price according o p = E p, where rh, H p rh, is he price for firms ha rese heir prices (which is idenical for all such firms, because as in he sandard New Keynesian framework, hey face H idenical coss and demand funcions), and E p is he expeced opimal price for hese firms. The remaining firms do no change heir price opimally, bu we assume ha hese firms build in an auomaic price adjusmen based on he expecaion of he opimal inflaion. Their H H expeced inflaion is hen E p p. The expeced inflaion for firms ha adjus heir price is.0f H H given by E p p The firms ha adjus heir price opimally ake ino accoun any curren disequilibrium in prices in planning heir price increase, while he oher firms simply adjus a he equilibrium rae. We have: H H H H H H (6) p p = θ( E p p ) + ( θ)( E p p ).F2 The foreign currency price of home goods is se in a similar way: ( ) ( θ)( ) p p = θ E p p + E p p H H H H H H Since firms are seleced each period randomly o change heir price opimally, he price index a ime is he H same for hose ha change opimally and hose ha le heir price rise a he expeced equilibrium rae, p. 2 See Engel (208) for a sudy of he relaionship of he price seing behavior in his model compared o he more sandard Calvo pricing framework. 9

10 We do no (need o) specify here he soluion for he opimal equilibrium price, bu nex we use he fac ha here is no pricing o marke in he equilibrium price in he LCP model deviaions from he law of one price only occur because of misalignmens ha arise as he exchange rae changes bu prices only slowly adjus. We have: H H H H H H (7) p p = θ( E p E s p ) + ( θ) ( E p p ( E s s ) ). Subracing (7) from (6), we find: H H H H H H (8) E s s p p ( p p ) θ ( p s p ) + =. The expeced change in he pricing o marke arises from he adjusmens of he fracion θ of firms ha se heir prices equal o he expeced equilibrium price. An analogous equaion can be derived for he prices se by he foreign firm: F p in foreign currency for sale in he foreign counry, and F p in home currency for sale in he home counry: F F F F F F (9) E s s p p ( p p ) θ ( p s p ) + =. We assume ha consumpion preferences over he wo goods are idenical so ha he real exchange rae is driven enirely by he deviaions from he law of one price ha arise from pricing o marke. The log of he consumer price baske in each counry is a weighed average of he logs of he prices of foreign-produced and home-produced goods. Taking he weighed average of equaions (8) and (9), we arrive a: (0) π π = θq + E s s. In his equaion, q is he log of he real exchange rae (he price of he consumer baske in he foreign counry relaive o he home counry), π is home consumer price inflaion beween 0

11 and, and π is foreign consumer price inflaion. Noe ha because prices are se one period in advance, he inflaion raes, π and π, are observable a ime. Under his specificaion of price adjusmen, he real exchange rae is a saionary random variable and long-run purchasing power pariy holds. The pricing o marke disequilibria are expeced o dissipae over ime. The final componen of he model is he characerizaion of moneary policy behavior. We model his as a very simple Taylor rule. In he home counry: () i = σπ + u. We impose he so-called Taylor condiion, σ >, which is a sabiliy condiion in our model. u is a deviaion from he moneary policy rule. There is an analogous equaion in he foreign counry, which arges consumer price inflaion in ha counry. Subracing he foreign Taylor rule from he home Taylor rule gives us: (2) σ ( π π ) i i = + u u. We assume ha he relaive error erms in he moneary rules follow a firs-order auoregressive process: (3) u u δ ( u u ) = + ξ, where ε is a mean-zero, i.i.d. random variable. Equaions (3), (5), (0) and (2) he inernaional financial marke equilibrium condiion, he model of he liquidiy premium, he (relaive home o foreign) open economy Phillips curve, and he (home relaive o foreign) moneary policy rule give us a complee dynamic sysem for he real exchange rae, inflaion and ineres raes. The model incorporaes slow adjusmen of he real exchange rae because of nominal price sickiness, governed by he parameer θ, he fracion of he firms ha rese heir price opimally each period. As Eichenbaum, e al. (208) have recenly emphasized, empirically almos all of he adjusmen of real exchange rae comes hrough adjusmen by he nominal exchange rae. Tha is, inflaion raes in each currency play lile role

12 in he expeced convergence of he real exchange rae o is uncondiional mean (which is normalized o zero, meaning he deviaions from he law of one price are expeced o disappear in he long run.) Eichenbaum, e al. demonsrae ha his empirical regulariy can be capured in a New Keynesian model wih srong inflaion argeing (large value of σ.) When inflaion argeing is srong, inflaion has a low variance even if he variance of he real exchange rae is large. If inflaion does no move enough o achieve real exchange rae adjusmen, ha role is lef o he nominal exchange rae. The sources of shocks in his simplified model are moneary shocks (in equaion (2)) and liquidiy shocks in equaion (5). We have already noed ha moneary shocks are assumed o be follow an A() process. We assume ha here is persisence in liquidiy, and ha v also follows a firs-order auoregressive process: (4) v = ρv + ε, where ε is mean-zero, i.i.d., and 0 ρ <. The model can be solved by hand. For he real exchange rae, we find: (5) ( ) ( + α) ( σ ( + α) + θ ) ( ( ) ) ( ) ( ( ) ) σ + α + θ σ + α + θ q = ( π π ) ( u u ) v. θ θ σ + α δ θ σ + α ρ The inflaion variables a ime are predeermined, so (5) expresses he real exchange rae in erms of predeermined and exogenous variables. A relaive moneary ighening in he home counry (an increase in u u ) causes a real appreciaion of he home currency. Similarly, an increase in he liquidiy yield on home governmen bonds leads o a real appreciaion. Noe ha as inflaion argeing becomes more sringen, so σ is larger, he real exchange rae reacs more o moneary policy shocks if δ < θ. If ρ < θ, a larger σ increases he response of he real exchange rae o changes in he relaive liquidiy reurn. We assume in all following discussion ha boh of he preceding inequaliies are saisfied. Also, he greaer price sickiness (smaller θ ), 2

13 he larger he response of he real exchange rae o moneary policy shocks and he relaive liquidiy reurns. We noe ha he nominal ineres differenial is simply a linear combinaion of he predeermined relaive inflaion raes and he exogenous errors in he moneary policy rules, as given by equaion (2). I is inuiive o replace he moneary errors, using (2), wih ( ) u u = i i σ π π. Then wih some rearranging, we can wrie he soluion for he real exchange rae in erms of relaive inflaion, he nominal ineres rae differenial, and he liquidiy shock: (6) ( ( ) ) ( ( ) ) ( )( ( ) ) ( ( ) ) ( ) ( ( ) ) q δ σ + α + θ + ( ) α σ + α + θ π π ( i i ) σ + α + θ = v. θ σ + α δ θ σ + α δ θ σ + α ρ In his equaion, igher moneary policy is represened by higher nominal ineres raes, which imply a currency appreciaion. For our empirical analysis, we will derive an expression for s s. Noe ha (7) s s = q q + π π. The price adjusmen equaion (0) gives us: (8) π π θ θ η θ ( α)( ) = q + E s s = q + i i + = q + + i i + v. The second equaliy comes from he financial marke equilibrium condiion, (3), and he hird equaliy is derived from he specificaion for liquidiy reurns, (5). Subsiuing (6) and (8) ino (7) and rearranging, we find: 3

14 (9) ( ) ( ) ( + α) ( σ ( + α) + θ ) ( ) ( ) ( ( ) ) ( + )(( + ) ( + ) ) ( + ) ( + ) ( ) θ( σ ( + α) δ) θ( σ ( + α) δ) ( ) ( ( ) ) θ + δ σ + α σ + α + θ s s = q i i v σ α δ θ σ α δ θ σ α ρ α θ δ σ α δ θ δ σ α δ + i i + v Our daa direcly measures he liquidiy reurn, η, raher han he innovaion, v, so we use equaion (5) o replace v = η α i i. Also, because he ineres rae differenial and he liquidiy reurn are srongly serially correlaed, we find i informaive o specify he i i i i and i i, and η η and η, raher v wih ( ) empirical relaionship in erms of ( ) han in erms of i i, i i, η and η. The soluion is much cleaner and easier o inspec if we assume a his poin ha he serial correlaion of he wo error erms are equal, so δ = ρ. Making hese subsiuions, we find: (20) ( ) ( ) ( ) ( θ + ρ ) ( σ ( + α) + θ ) θ( σ ( + α) ρ) ( ) ( ( ) ) θ + ρ σ + α σ + α + θ s s = q i i i i + σ + α ρ θ σ + α ρ ( i i η ) ( ( ) η η ) + + Our empirical specificaion for he depreciaion of he exchange rae includes, firs, an error correcion erm as he nominal exchange rae adjuss o disequilibrium in he real exchange rae. Second, he change in he ineres differenial affecs he exchange rae as in sandard New Keynesian models. Third, he change in he relaive liquidiy reurn on governmen bonds plays a role in influencing he exchange rae. Lagged levels of he relaive ineres differenials and liquidiy reurns capure he dynamic adjusmen. Under he parameer resricions of he model specifically, σ >, α > 0, 0 θ <, 0 ρ <, and ρ < θ ceeris paribus, an increase in q, and increase in i i ( i i ), and an increase in η η all lead o a decline in s. Tha is, he home currency appreciaes o correc for a real undervaluaion, and i appreciaes in response o a relaive increase in eiher he home ineres rae or he home liquidiy reurn. Before urning o he daa, we noe a few feaures of our empirical specificaion based on (20). As in our model, we follow convenion and rea nominal exchange raes as non-saionary s 4

15 random variables. In ligh of much evidence, from Mark (995) o more recen empirical evidence in Engel (206) and Eichenbaum, e al. (208), he real exchange rae is saionary and he nominal exchange rae adjuss in he direcion of resoring purchasing power pariy. elaive ineres raes and relaive liquidiy reurns are saionary. We allow dynamics by including conemporaneous and lagged values of hese variables. Because hese variables are serially correlaed, we ener hem in he specificaion as in (20) wih he firs difference in he reurns and he lagged level of he reurns. This reduces he mulicollineariy ha would be presen if hese variables were included in conemporaneous and lagged levels, and gives us he naural inerpreaion ha changes in relaive ineres raes and changes in relaive liquidiy yields influence changes in he log of he nominal exchange rae. Finally, we noe ha (20) was derived under he simplifying assumpion ha moneary policy shocks and liquidiy shocks are equally serially correlaed, δ = ρ. Equaion (20) implies ha he coefficiens on he change in he relaive ineres raes and he change in he relaive liquidiy yields are he same, bu ha would no hold in general if δ ρ, so our empirical specificaion does no consrain hose coefficiens o be equal. 3. Empirical Invesigaion of Treasury Liquidiy and Exchange aes In his secion, we presen our empirical resuls. We firs describe how we consruc he measure of reasury liquidiy in 3.. Subsecion 3.2 presens our baseline resul ha he change in he relaive reasury liquidiy reurns is srongly correlaed wih exchange rae movemens. We show our resuls are robus o conrolling for cerain marke fricions in subsecion 3.3. Finally, in subsecion 3.4, we furher confirm ha counry-specific reasury liquidiy maers. Throughou he secion, we denoe he foreign variable as X if he conex is no counry j specific. For example, we use i for he foreign ineres rae on a reasury bond. Whenever needed, we denoe he variables of a foreign counry j as X j,, for example, i j, for he ineres rae of a reasury bond for he foreign counry j. 5

16 3.. Consrucion of Liquidiy Measure The word liquidiy appears in differen economic conexs wih differen meanings. Here, i refers o a non-observable non-pecuniary reurn ha invesors enjoy when holding he asse. We measure he erm i i in equaion () by using he foreign exchange forward minus spo rae m m spread, f, + s : m m (2) ( ) ( ) = + η i i i i f, + s i i where f is he log of forward rae and, + s is he log of he spo exchange rae, boh expressed in home currency price of a foreign currency. There are wo ways o inerpre η. Firs, as he erm m m ( i i ) ( i i ) suggess, i is a relaive measure of difference beween markeable securiies and reasury bond yield in he home and foreign counry. This inerpreaion comes direcly from he model. Second, as described by f s + i i, he firs hree erms can be undersood as he payoff of a synheic home reasury, + bond ha is consruced by buying he foreign reasury bond, eliminaing exchange rae risks by enering a forward conrac. Since he home reasury bond and he synheic home reasury bond pay equivalen pecuniary reurns, he difference beween he wo gives a measure of he relaive difference in liquidiy services he home and foreign reasury bonds provide. In he case where he U.S. is assumed o be he home counry, Du, e al. (208a) denoes he η erm here as he U.S. Treasury Premium, Φ jn,,, which is he n-year deviaion from covered ineres pariy beween governmen bond yields in he Unied Saes and counry j. Jiang, e al. (208) ake he U.S. as he home counry, and define η as a cross-counry average over en large markes relaive o he dollar. We employ he procedure developed by Du, e al. (208a) o obain η for any pair of home currency i and foreign currency j (00 pairs in oal) for he G-0 currencies. To give a sense of how his liquidiy measure behaves, we plo he liquidiy measure agains he nominal exchange rae of each home currency i and foreign currency j in Figure. For each ime period, we ake a simple average across foreign currency j o improve visual represenaion. I is ineresing o see 6

17 ha here is already a negaive relaionship beween he mean exchange rae and mean liquidiy measure, meaning a higher reasury liquidiy relaive o he res of he G0 currency counry is associaed wih a srong currency conemporaneously. In Table, we repor he correlaion coefficien beween he liquidiy measure and ineres rae differenial for each home currency i and foreign currency j. The correlaion coefficiens are posiive for each currency i. This verifies he posiive relaionship beween he relaive liquidiy reurn and he ineres differenial in (5), and is consisen wih he empirical findings of Nagel (206) for he U.S. Unless oherwise specified, our sudy uses end-of-monh monhly daa from January 999 o December F3 We use exchange raes and forward raes from Thomson euers Daasream. The consumer price indexes and unemploymen raes are from he IMF IFS. The governmen yield daa is obained from Bloomberg, Daasream and cenral banks. The LIBO swap raes are from Bloomberg. The Credi Defaul Swap daa is from he IHS Marki. The gold price and VIX index are from FED and he governmen deb o GDP daa is from he BIS credi o he non-financial secor daase (nominal value). We provide he daa source deails in Appendix A2 and summary saisics for he variables we used in Appendix A3. Supplemenary Appendix A4 repors a large number of robusness checks. We employ panel fixed effec regression in all he repored esimaes o make use of cross-counry ime series informaion bu a he same ime allow for ime-invarian heerogeneiy. 3.2 Baseline esuls To invesigae he empirical relaionship beween reasury liquidiy and exchange raes for he G0 counries, we esimae he following panel monhly fixed effec regression from equaion (20): s = α + β q + β ( η ) + β ( i ) + β ( η ) + β ( i ) + u, (22) j, j j, 2 j, 3 j, 4 j, 4 j, j, where i = i i, X = X X for any variable X. 3 Whenever needed, we linearly inerpolae he quarerly variable o monhly variable. For example, we inerpolae he Ausralia and New Zealand CPI o obain monhly real exchange raes. 7

18 Table 2A repors he regression coefficien esimaes of (22). 3F4 Each row of he able represens he esimaion resuls ha ake he counry of he currency in he firs column as he home counry and res of he nine counries as he foreign counries. When consrucing he variables, we use one-year forward raes and one-year governmen yields.4 F5 The real exchange raes are consruced using consumer price levels. Firs, consisen wih our heoreical predicion and he empirical resuls of Eichenbaum, e al (208), he coefficien esimaes for q j, are all negaively significan, implying ha real exchange raes adjus hrough nominal exchange raes. The average coefficien esimae is approximaely , implying a 2.3% adjusmen of he nominal exchange rae in he direcion of he long-run real exchange rae, per monh. I is ineresing o noe ha he esimaed adjusmen of he dollar exchange rae is around half he size of he average (across currencies) adjusmen coefficien, suggesing a more persisen real exchange rae. Second, we find ha a posiive change in he relaive ineres rae (home minus foreign) drives a conemporaneous home currency appreciaion, which maches he radiional ineres rae and exchange rae relaionship. While almos all moneary, sicky-price models of exchange raes predic such a relaionship, empirical suppor for even a conemporaneous relaionship beween ineres raes and exchange raes has no been universally srong in previous sudies.5f6 I may be ha he imporance of he ineres rae channel requires conrolling for he error-correcion erm and liquidiy yields, as in our specificaion. We find he ineres rae effec is srongly saisically significan for all en currencies. The average coefficiens, across he currencies, is -4.77, which means ha a 00 basis poin increase in he annualized ineres rae in he home currency relaive o he foreign counry leads on average o a 4.77 percen appreciaion from he previous monh. Our main novel resuls concern he effecs of he liquidiy yield on exchange raes. The coefficien esimaes for η j, + are all negaive and saisically significan a he % level, wih a range from o This indicaes a 2.46% o 6.64% home currency appreciaion in a monh when here is a posiive change of 00 basis poins (annualized rae) in relaive liquidiy. The saisical significance and economic significance of hese coefficien esimaes are sriking 4 To keep he able visibly clear, we only repor he main coefficien esimaes of ineres and refer readers o he supplemenary appendix for he full regression ables. 5 See he discussion and robusness below for he choice of one-year enor. 6 See Engel (204) for a recen survey. 8

19 given he well-known exchange rae disconnec puzzle. We find ha he relaive reasury liquidiy exhibis a very srong relaionship wih exchange rae movemens for all he G-0 counries. Omiing he liquidiy reurn For comparison, we also conduc he regression (22) bu excluding he liquidiy yield variables. Tha is: s = α + β q + β ( i ) + β ( i ) + u, (23) j, j j, 2 j, 3 j, j, The regression esimaes are repored in Table 2B. The coefficien esimaes on lagged real exchange raes and change in ineres rae differenial remain negaively significan for all counry pairs. However, he wihin -squared for his specificaion are universally much lower compared o Table 2A. This indicaes including relaive reasury liquidiy reurns brings srong explanaory power o exchange rae deerminaion, in addiion o and independen of he radiional facors. Esimaion on sub-samples Nex, we invesigae wheher he relaionship beween reasury liquidiy and exchange raes are driven by he Global Financial Crisis or he pos-crisis period. In Table 2C, we re-esimae (22) bu spli he sample period ino wo periods, pre-2008 and pos (and including) We see ha he conemporaneous relaionship beween he change of he liquidiy measure and he change of exchange raes holds in boh ime periods. As in he full sample, all of he esimaed coefficiens on he impac of he esimaed governmen liquidiy reurn are negaive. They are all individually saisically significan a he one percen level in he pos-crisis period. In he pre-crisis daa, he p-values for hese coefficiens are all less han 0.0 excep for Japan (where i is sill below 0.0) and Swizerland (which is marginally insignifican.) The coefficien esimaes in all cases have larger values in absolue erm afer 2008, ranging from -3. o In addiion o he significan and larger coefficiens, he pos are markedly improved, wih a maximum of 33%, reflecing he imporance of he relaionship beween he reasury liquidiy and exchange rae deerminaion.6f7 7 In an unrepored counry by counry esimaion of (22), he maximum 2 is 5%, which is he AUD JPY pair. 9

20 This se of resuls provides evidence ha reasury liquidiy a he individual counry level plays an imporan role in exchange rae deerminaion. This conrass he belief ha here is a special role of he USD or he U.S. Treasury bond. We find ha individual counry reasury liquidiy oher han he U.S. is also imporan in undersanding exchange rae flucuaions. One-monh forward raes As we have noed, in our baseline regressions we use one-year forward raes and one-year governmen yields as regressors, while he regressions are conduced in monhly frequency. The choice of one-year enor is a radeoff beween model consisency and daa availabiliy. Ideally, for model consisency, we would use one-monh forward raes and governmen yield o consruc he variables. However, he daa availabiliy of one-monh governmen yield is raher limied for some of he sample counries. In addiion, in secion 3.4, we use credi defaul swap (CDS) daa o make an adjusmen for he probabiliy of non-repaymen of governmen deb. The CDS daa is more exensively available only for enor of one year or above. Therefore, we use one-year forward raes and one-year governmen yields o consruc he variables in our analysis. To be fully consisen wih he model, invesors would need o have no uncerainy abou he one-monh own-currency reurn on one-year bonds, bu he variaion in ha reurn (annualized) relaive o he one-year ineres rae is very small relaive o changes in exchange rae. The monhly correlaion of oneyear and one-monh ineres raes is over 0.90 in our sample for all counries. Neverheless, o make sure our resul is robus o he choice of enor, we repor in Table 2D he regression coefficien esimaes of equaion (22), using one-monh forward raes and onemonh governmen yield daa.7 F8 The empirical relaionship beween he change of nominal exchange rae and he independen variables are largely consisen wih he resul we discussed in Table 2A, which use one-year forward raes and one-year governmen yields daa. In ligh of his, o make our empirical resuls comparable across differen specificaions, we use one-year forward raes and one-year governmen yields hroughou he analysis. 8 Norway is excluded in his exercise as a home counry and foreign counry due o lack of Norway one-monh governmen yield daa. 20

21 Insrumenal variable regressions This empirical analysis shows a srong relaion beween he relaive reasury liquidiy and he exchange rae. In his subsecion, we insrumen for he liquidiy reurns, which allows us o give a causal inerpreaion ha a change in he relaive reasury liquidiy leads o a change in he bilaeral exchange raes. As we have already discussed in he inroducion, reasury bonds are more valuable han similar markeable securiies because of heir safey and liquidiy. Our firs se of insrumens are measures of changes in global uncerainy. In he face of his uncerainy, here may be a safehaven demand of reasury bonds which is refleced in he relaive liquidiy reurn. We use several differen measures of global uncerainy: he log of VIX, log of he gold price, G0 cross-counry average square inflaion raes, G0 cross-counry average unemploymen raes, G0 cross-counry average square of change in bilaeral exchange raes and cross-g0 counry average absolue change of bilaeral exchange raes. The VIX and oil price are well-known measures for global uncerainy. The oher four variables are mean o capure he fac ha when global uncerainy is high, inflaion, unemploymen and exchange rae volailiy end o be high as well. We posi ha hese cross-counry insrumens are exogenous o bilaeral exchange rae movemens because of heir global naure. Tha is, we hypohesize ha he channel hrough which global uncerainy affecs he value of one currency relaive o anoher is he relaive reasury premium. Our second se of insrumen gauges he scarciy of liquid asses available in an economy. We adop general governmen deb o GDP for each counry as an insrumen. The smaller general governmen deb, he more valued a he margin hose insrumens are for heir liquidiy services, hence hey pay a higher liquidiy yield. Our underlying assumpion is ha he general governmen deb o GDP raio influences exchange rae movemens only hrough heir liquidiy effec. The sample of counries we considered are developed economies wih independen fiscal policy and moneary policy, so i is no he case ha here is fiscal dominance ha deermines inflaion and currency values. Specifically, we conduced he same panel fixed-effec regressions as (22) bu we insrumen he variables η j, + and η j, by he level and he change of he insrumens discussed above.8 F9 In Table 3, we repor he regression coefficiens of he insrumenal variable regressions. 9 Whenever needed, we linear inerpolae he insrumens in he firs sage regressions. 2

22 The insrumened change of reasury liquidiy has a negaive coefficien in 9 ou of 0 regressions and significanly negaive in 8 of hem. The coefficien he change of reasury liquidiy of CHF is posiive bu he sandard error is large, indicaing hey are no significanly differen from zero. Overall, we find ha he insrumen variable regressions are consisen wih wha we find in he baseline resul and offer empirical suppor of he causal relaionship ha a change in relaive reasury liquidiy causes exchange rae movemens. 3.3 Decomposing he Liquidiy Measure have Up o his poin, we have mainained he assumpion ha markes are fricionless, so we η f, + s i i = + o serve as a measure of relaive reasury liquidiy. In his subsecion, we discuss some fricions ha could possibly drive he movemen of η oher han he liquidiy of governmen bonds. As we have noed, η can be inerpreed as he difference of a synheic home Treasury bond f, s + + i and a home reasury bond i. There are wo possible fricions o consider sovereign defaul risk and a currency derivaive marke fricion. These fricions are imporan in he recen lieraure in inernaional finance, and here are readily available prices ha can be used o quanify hese fricions.9 F20 Firs, invesors migh no be able o consruc he synheic home reasury bond as we have posied because of some disorions in currency derivaive markes. If covered ineres pariy held for marke reurns, we should find f, s + IS = + IS, where IS ( IS ) refers o he home (foreign) reurn on LIBO swaps. For example, Du, e al. (208b) argue ha in recen years, for some currencies (paricularly, when he U.S. dollar is he home currency), hey find IS < f + s + IS, bu financial insiuions do no underake he arbirage ha would resul, in riskless profis. In order o earn hose profis, banks would need o go shor in dollars, and purchase he foreign currency on he spo marke and go long in foreign currency (which hey sell forward.) Such an arbirage invesmen, while risk free, expands he size of he financial insiuions balance shees, and may cause hem o run afoul of regulaory consrains. Financial 20 See Della Core, e al. (208) for he effecs of sovereign defaul on exchange raes. Du, e al. (208b) invesigae deviaions from covered ineres pariy and Ajdiev, e al. (208) consider he relaionship beween he currency swap fricion and he exchange rae. 22

23 insiuions ha held home asses could sell hose and acquire synheic home asses, bu hey migh be unwilling o do so if hey value he home asses for non-pecuniary reasons. Hence, when home asses are especially valued, hen τ f, + s+ IS IS will be high, and he home currency will be srong. The same relaionship could arise if here were defaul risk on LIBO raes, as migh have been he case in 2008 during he global financial crisis. When foreign LIBO is considered risky, τ is high, and he home currency is srong. Furhermore, even if he currency derivaive markes are fricionless, he reasury bond yields migh include expeced defaul risk. If he home reasury bond is regarded as defaul-free (say, he U.S. Treasury bond), bu he foreign reasury bond is expeced o defaul wih some probabiliy (say, he Japanese Governmen Bond, due o is high deb o GDP raio), hen he difference beween he synheic home reasury bond and home reasury bond could be differen no jus because of he difference in reasury liquidiy bu also he difference in defaul premium. We define l j, as he home minus foreign counry j expeced defaul loss on reasury bonds, so ha he expeced relaive reurn on home governmen bonds is i i l. To measure he erm l j,, j, j, we make use of he informaion from he credi defaul swap (CDS) marke. A CDS conrac insures he buyer from credi even. In he case of sovereign defaul, he CDS sellers make paymens o he buyers o compensae for he loss in he credi even. Buyers of CDS pay premium o CDS sellers for geing he insurance. Therefore, he CDS premium quoe is an appropriae insrumen o reflec he marke implied expeced defaul loss. We ake he home minus foreign difference of CDS premium quoes as he measure for he expeced defaul loss erm, i.e. l = CDS CDS. j, j, componens: To adjus for hese fricions, as in Du, e al. (208a), we can wrie η j, as a sum of hree (24) ηj, = τ j, l j, + λj,, 23

24 where λ is a residual erm. In he fricionless scenario above, we will have τ =, = so j, j, l j 0 η = λ. Tha is, j, j, λ can be undersood as he relaive reasury liquidiy, afer adjusing for he j, currency derivaive marke fricion and credi defaul risk. We below summarize he componens of η j, inroduced in his subsecion: 20F2 (25) τ = f s + IS IS, l = CDS CDS, λ = η τ + l j,, + j, j, j, j, j, j, j, In all cases, we use IS and CDS daa wih one-year enor as he CDS daa is exensively available only for enors of one-year or above. Wih hese decomposed componens on hand, we modify he baseline regression by puing each of he componens ino he equaion. Specifically, (26) s = α + β q + β λ + β τ + β l + β i j, j j, 2 j, 3 j, 4 j, 5 j, + βλ + βτ + βl + βi + u 6 j, 7 j, 8 j, 9 j, j, As discussed above, we expec o find a negaive esimae of β 3, because a larger τ j, indicaes an unwillingness o sell home asses o buy he foreign currency, which appreciaes he home currency. The esimaed β 4 should be posiive, since a larger l j, means here is a greaer defaul risk for home governmen bonds. λ j, is he residual measure of he change in he home relaive o foreign liquidiy yields, and for ha we posi a negaive value of β 2. As in our model, we should also find negaive values for he esimaes of β and β 5. We esimae he regression in wo ways. Firs, since CDS daa for many of he sample counries are only available afer 2008, we sar he sample from 2008M and esimae (26). Second, o make use of he full sample informaion and es wheher he adjused liquidiy measure is imporan in explaining he change of exchange raes hroughou he sample, we esimae he regression from 999M, bu excluding he variables involving CDS daa ( l j, + and l j, ). 2 Deails of he full derivaion of hese expressions are available a Du, e al. (208a). 24

25 In Table 4A, he coefficien esimaes on λ i, +, which represens he effec of change of he reasury liquidiy afer adjusing for credi risk and derivaive marke fricion, are sill significanly negaive in all cases. The range of coefficien is from o -7.08, indicaing a monhly 3.22% o 7.08% immediae home currency appreciaion when here is a monhly posiive change of 00 basis poins (annualized rae) in relaive liquidiy. These coefficiens are also larger han he coefficiens of η i, + esimaed in Table 2A or Table 2C. These resuls reaffirm our baseline resul ha here is a srong linkage beween reasury liquidiy and exchange rae. In many cases, we also see ha credi risk variaion and derivaive marke fricion are imporan variables in explaining he change of exchange raes.2 F22 The posiive coefficien on l j, + indicaes ha an increase in home defaul risk relaive o foreign defaul risk is associaed wih an immediae home currency depreciaion. Holding he nominal reasury ineres rae fixed, an increase in defaul risk implies he defaul risk adjused nominal ineres rae goes down, resuling in a home currency depreciaion. There are wo ways we could inerpre he negaive coefficien on τ j,. Firs, he channel could go hrough he change in IS IS. If here is defaul risk in he IS conrac an increase j, in he home IS rae drives a home currency depreciaion. Second, he channel could go hrough he change in f, + s. In he case in which τ j, is posiive, marke condiions are now more favorable o borrow in home currency and consruc a synheic home marke bond han before. As explained by Du, e al. (208b), his could be he case ha when here is excess inernaional demand for boh he home asses and forward conrac o hedge exchange rae risk in invesing in home asses, herefore he financial inermediaries have o mark up he forward rae f, as, + issuing a forward conrac is cosly for hem. This mark-up of he forward rae hen goes hand in hand wih a srong home currency ha is driven by excess inernaional demand. To confirm our resuls are robus o differen specificaions, we conduc he esimaion in (26) by including one or wo sub-componens a a ime. The resuls are repored a Table 4B. Once again, we find he regression coefficiens for λ j, + are significanly negaive in all cases. 22 See Della Core, e al. (208) who find similar findings of he relaionship beween exchange rae and sovereign risk. 25