Capital Controls and Currency Wars

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1 Captal Controls and Currency Wars Anton Kornek Unversty of Maryland February 2013 Abstract Captal controls and other forms of captal account nterventon lead to nternatonal spllover effects that have recently rased concerns about global currency wars. Ths paper analyzes the welfare effects and the desrablty of global coordnaton of such polcy measures. We fnd that f controls are desgned to correct for domestc externaltes, the resultng equlbrum s nonetheless Pareto eff cent,.e. a global planner would mpose the same measures and there s no role for global coordnaton. We llustrate ths for a range of externaltes that have recently been nvoked as reasons for mposng captal controls: learnng externaltes, aggregate demand externaltes n a lqudty trap, and pecunary externaltes arsng from fnancal constrants. On the other hand, f controls are desgned to manpulate a country s terms-of-trade or f polcymakers face an mperfect set of nstruments, such as targetng problems or costly enforcement, then multlateral coordnaton s desrable n order to mtgate the neff cences arsng from such mperfectons. JEL Codes: Keywords: F34, F41, H23 captal flows, captal controls, currency wars, systemc rsk, global polcy coordnaton I would lke to thank Pol Antràs, Olver Blanchard, Ncolas Coeurdacer, Emmanuel Farh, Krstn Forbes, Rex Ghosh, Gta Gopnath, Nuno Lmao, Jonathan Ostry, Lus Servén, Joseph Stgltz, Roland Straub, Carlos Végh, Jaume Ventura, Jeromn Zettelmeyer and Jng Zhang as well as partcpants at semnars at the Bank of England, BC and CREI and at the 2013 ASSA Meetngs, the 2012 NBER Fall Meetngs and the ECB-BIS Conference on Global Lqudty for nsghtful dscussons and comments. I gratefully acknowledge fnancal support for ths research project from the IMF and from INET. I thank the IMF and Harvard for ther hosptalty durng part of ths project. Excellent research assstance by Jonathan Kreamer and Elf Ture s gratefully acknowledged. The vews expressed are those of the author and should not be attrbuted to the IMF. For contact nformaton see 1

2 1 Introducton Captal controls and other forms of captal account nterventon lead to nternatonal spllover effects that have led to consderable controversy n nternatonal polcy crcles n recent years (see e.g. Ostry et al, 2012) and have rased concerns about global currency wars. Ths paper determnes the welfare effects of such measures n a general equlbrum model of the world economy and analyzes under what condtons global coordnaton of captal account polces s desrable. We descrbe the spllover effects from captal account nterventon n an ntertemporal benchmark model of a global economy n whch ndvdual countres engage n borrowng and lendng. If one country mposes captal controls n the form of taxes on foregn borrowng, t reduces both borrowng and consumpton and pushes down the world nterest rate, leadng to greater nflows to other countres. In an augmented model, t also deprecates ts real exchange rate and apprecates the real exchange rate of other countres. Furthermore, we show an somorphsm between captal controls and reserve accumulaton: any level of captal controls can be replcated by a correspondng level of reserve accumulaton when the captal account s closed to prvate transactons. Next we study several types of externaltes that have recently been nvoked as reasons why ndvdual countres may want to mpose captal controls: learnng externaltes, aggregate demand externaltes n a lqudty trap, and pecunary externaltes arsng from external fnancal constrants. For each of these domestc dstortons, a natonal planner can mprove domestc welfare by mposng captal controls that offset the externalty, even though such controls create nternatonal spllover effects. The resultng global equlbrum s Pareto eff cent as long as natonal planners behave compettvely and mpose captal controls that offset domestc externaltes whle gnorng the general equlbrum effects of such controls. A global planner who nternalzes all nternatonal spllover effects cannot mprove on the descrbed allocaton. By contrast, f natonal planners refran from mposng captal controls to correct for domestc externaltes, global welfare s reduced. Conceptually, we can vew the natonal planners that nternalze domestc externaltes n dfferent countres but do not exert market power as compettve agents to whch the welfare theorems apply. Changes n the world nterest rate that stem from captal controls consttute pecunary externaltes that cancel out and do not mpede Pareto eff cency. We also fnd that a seemng arms race of escalatng captal controls does not necessarly ndcate neff cency but may be the tatonnement process through whch multple countres optmally adjust ther captal controls. On the other hand, captal controls to manpulate a country s ntertemporal termsof-trade consttute a beggar-thy-neghbor polcy and are Pareto neff cent. A natonal planner n a large country may face ncentves to exert market power over the country s ntertemporal terms of trade,.e. the world nterest rate. For example, f a lendng country restrcts ts lendng, t benefts from an ncrease n the world nterest rate. 2

3 Such monopolstc behavor reduces the global gans from ntertemporal trade and s Pareto-neff cent. If countres engage n such behavor, t s desrable to come to a global agreement that captal controls amed at manpulatng the world nterest rate wll not be used. The lesson for nternatonal polcy coordnaton s that t s mportant to dstngush between correctve captal controls that are mposed to offset domestc externaltes and dstortve captal controls that are desgned to manpulate a country s terms of trade. The former are generally desrable, whereas the latter are always undesrable. An addtonal motve for coordnatng captal controls arses when polcymakers face restrctons on the set of avalable polcy nstruments. For example, f captal controls not only correct dstorted ncentves to borrow/lend but also mpose an addtonal cost arsng from costly mplementaton or corrupton, then there s scope for global coordnaton of captal account polces: a global planner recognzes that adjustng all captal controls worldwde by the same factor may reduce the dstortons created by captal controls but would leave the margnal ncentves of all actors n the world economy unaffected. Lterature There s a growng recent lterature that fnds that captal controls may mprove welfare from the perspectve of a sngle country f they are desgned to correct domestc externaltes. An mportant example are prudental captal controls that reduce the rsk of fnancal crses, as analyzed n the small open economy lterature by Kornek (2007, 2010, 2011b), Ostry et al. (2010, 2011) and Banch (2011). Ths paper provdes a normatve analyss of the resultng general equlbrum effects and dscusses whether global coordnaton of such polces s desrable. 1 We fnd that n a benchmark case n whch natonal regulators can optmally control domestc externaltes, coordnaton s not ndcated. By contrast, Bengu (2011) studes the role for coordnaton between natonal regulators n a mult-country framework of bankng regulaton. He shows that lqudty n the global nterbank market s a global publc good. In the presence of such global externaltes, there exsts a case for global coordnaton of lqudty requrements. Earler work by MacDougall (1960), Kemp (1962), Hamada (1966), Jones (1967) and Obstfeld and Rogoff (1996) nvestgated how a natonal planner of a large country n the world economy may mpose captal controls to exert monopoly/monopsony power over ntertemporal prces. As n optmal tarff theory, such polces are beggarthy-neghbor,.e. they mprove natonal welfare at the expense of reducng overall global welfare. In a recent contrbuton to ths lterature, Costnot et al. (2011) analyze the optmal tme path of monopolstc captal controls under commtment and show how they can be used to dstort relatve prces n goods markets. Our paper contrasts the global welfare effects of dstortve (monopolstc) captal controls 1 Ostry et al. (2012) dscusses the multlateral aspects of polces to manage the captal account from a polcy perspectve. 3

4 wth correctve captal controls that are desgned to offset domestc externaltes, as was nvoked by a rsng number of countres that have mposed such controls n recent years. Jeanne et al. (2012), Gallagher et al. (2012) and Ostry et al. (2012) dscuss the desrablty and the multlateral mplcatons of captal controls from a polcy perspectve. Persson and Tabelln (1995) show that coordnaton of natonal fscal and/or monetary polces s desrable f countres have ncentves to employ such polces to exert monopoly power over nternatonal prces. Kornek (2011a) analyzes the postve mplcatons of prudental captal controls n a mult-country settng. The lnk between reserve accumulaton and real exchange rate valuaton s also nvestgated n Rodrk (2008) and Kornek and Serven (2010). Ghosh and Km (2009) and Jeanne (2012) show how a combnaton of captal controls and tax measures can be used to undervalue a country s real exchange rate. These papers look at the exchange rate effects of varous captal account polces n a small open economy, whereas we focus explctly on global general equlbrum effects. Magud et al. (2011) provde a survey of the emprcal lterature on the effects of captal controls on the country mposng the controls. Forbes et al. (2011) and Lambert et al. (2011) nvestgate the spllover effects of captal controls emprcally. They fnd evdence that when Brazl mposed captal controls, there was dverson of captal flows to other countres that were expected to mantan free captal flows. 2 To the extent that the captal controls mposed by Brazl were mposed to correct a domestc dstorton, our analyss suggests that ths was a Pareto-eff cent equlbrum response and dd not ntroduce dstortons n the global allocaton of captal. 2 Benchmark Intertemporal Model We descrbe a world economy wth N 2 countres ndexed by = 1,...N and a sngle homogenous tradable consumpton good. Tme s ndexed by t = 0,... The mass of each country n the world economy s m [0, 1], where Σ N =1m = 1. (A country wth m = 0 corresponds to a small open economy.) 2.1 Country Setup Country s nhabted by a unt mass of dentcal consumers ndexed by z [0, 1] who value the consumpton c t of a tradable good accordng to the utlty functon U = t=0 β t u ( ) c t (1) 2 Forbes et al. (2011) also document negatve spllover effects on countres that were lkely to follow the example of Brazl to mpose controls. 4

5 where u ( ) s a standard neoclasscal perod utlty functon and β < 1 s a tme dscount factor, whch we assume constant across countres. 3 For smplcty we drop the ndex z of ndvdual consumers from our notaton. A representatve consumer n country starts perod t wth an endowment of yt of tradable goods and fnancal net worth b t, where the ntal fnancal assets b 0 n perod 0 are gven. He chooses how much to consume and how much to save by purchasng b t+1 zero coupon bonds at a prce 1/R t+1 that pay off one unt of tradable goods n perod t + 1, where R t+1 represents the gross world nterest rate between perods t and t + 1. Hs budget constrant n perod t s gven by c t + ( 1 τ t+1 ) b t+1 R t+1 = y t + b t + T t (2) τ t+1 > 0 τ t+1 < 0 b t+1 > 0 (saver) outflow subsdy outflow tax b t+1 < 0 (borrower) nflow tax nflow subsdy Table 1: Interpretaton of captal control τ t+1 The varable τ t+1 s a proportonal subsdy to bond purchases b t+1/r t+1. We assume that the requred revenue s rased as a lump-sum tax Tt = τ t+1b t+1/r t+1. Dependng on the sgns of b t+1 and τ t+1, we can nterpret the polcy measure τ t+1 n a number of dfferent ways, as captured by Table 1: If the country s a net saver, b t+1 > 0, then τ t+1 consttues a subsdy to savng,.e. a subsdy to captal outflows. Snce captal outflows go hand n hand wth postve net exports and snce there s a sngle homogenous good n our economy, we can also thnk of t as a subsdy to net exports. If the country s a net borrower, b t+1 < 0, then the varable τ t+1 can be nterpreted as a tax on foregn borrowng, or a tax on captal nflows. Snce captal nflows mply postve net mports, the tax can be thought of as an mport tarff. To ensure that bond demand s bounded, we mpose the assumpton that τ t+1 < 1, t. In the followng, we wll loosely refer to τ t+1 as the captal control mposed n perod t. Snce there s a sngle representatve consumer, hs borrowng/savng decsons map nto the current account statstcs of the economy. The term b t represents the gross return on savngs that the consumer receves at the begnnng of perod t. The fracton b t/r t captures how much the economy saved n perod t 1 n order to receve b t unts of goods n perod t. Therefore the nterest earnngs n perod t are b t (1 1/R t ). The trade balance tb t n perod t equals the dfference between new 3 In the followng analyss, we wll motvate nternatonal borrowng and savng by dfferences n endowments or output and ntertemporal consumpton smoothng consderatons. Temporary dfferences n dscount factors would offer an alternatve route. 5

6 savngs and the value of bond holdngs at the begnnng of the perod, tb t = y t c t = b t+1/r t+1 b t. The current account balance ca t s the sum of the trade balance and nterest earnngs, ca t = tb t + b t (1 1/R t ) = b t+1/r t+1 b t/r t, and corresponds to the change n the net asset poston of the country between the end of perods t 1 and t. 2.2 Strateges Representatve Consumer We wrte the utlty maxmzaton problem of a representatve consumer n recursve form as V ( bt) = max u ( ct) ( ) + βv b c t+1 (3) t,b t+1 The consumer takes Tt, R t+1 and τ t+1 as gven and maxmzes utlty subject to the budget constrant (2). Ths leads to the Euler equaton ( ) ( ) 1 τ t+1 u c t = βrt+1 u ( ct+1) (4) The Euler equaton mples a bond demand functon b t+1 ( Rt+1 ; τ t+1) that s strctly ncreasng n the captal control τ t+1. Strctly speakng, bond demand b t+1 s an equlbrum object that depends on the entre path of future nterest rates and captal controls, but t s useful to focus n partcular on ts dependence on ( R t+1, τ t+1). We mpose the followng assumpton: Assumpton 1 (Elastcty of Intertemporal Substtuton) The elastcty of ntertemporal substtuton s greater than the borrowng/consumpton rato of country, σ ( ) c b t > t+1/r t+1 c t ( Ths common assumpton guarantees that bond demand b t+1 Rt+1 ; τ t+1) s strctly ( ncreasng n R t+1 and can be nverted nto an ndrect bond demand functon Rt+1 b t+1 ; τ t+1). The assumpton s satsfed for all countres that are net savers and for net borrowers as long as ther borrowng s not too large n comparson to consumpton. See Appendx A.1 for a detaled dervaton. The mplcatons of ncreases n the world nterest rate on savng b t+1/r t+1 (as opposed to bond holdngs b t+1) depend on two effects: ( ) b t+1/r t+1 = b t+1/ R t+1 b t+1 R t+1 R t+1 (R t+1 ) 2 = b ( t+1 η (R t+1 ) 2 br 1 ) The frst term n the expresson n the mddle captures the substtuton effect a hgher nterest rate makes t more desrable to save, as we assumed. The second term 6

7 captures the ncome effect. For net borrowers, both terms are postve. For large savers, the ncome effect may offset the substtuton effect and may lead to smaller net savngs b t+1/r t+1 n response to an ncrease n the world nterest rate. For net borrowers and modest net savers, a rse n the world nterest rate s assocated wth a declne n consumpton, whch s necessary so net savngs can rse, c t/ R t+1 < 0. For large savers, the nequalty may be reversed. 2.3 Externaltes We wll ntroduce several types of externaltes nto our setup that have been dscussed as ratonales for mposng captal controls n the publc polcy debate, ncludng learnng externaltes, aggregate demand externaltes at the zero-lower-bound, and fnancal stablty externaltes. For now, we capture ther commonaltes n reduced form. We assume a natonal planner who recognzes that aggregate captal flows mpose an externalty that s captured by an extra utlty term n the socal welfare functon x t (tb t) that operates through the effects of captal flows on the trade balance tb t. We assume that x t ( ) s weakly convex but satsfes x t (tb t) < u (c t) for all allocatons that we consder. We use ths setup to derve a number of general results. In the ensung three sectons, we wll analyze the three cted examples of externaltes n more depth and show that our general results apply to each of these cases by mappng them nto ths reduced form framework. Natonal Planner The natonal planner pcks a seres of captal controls { } τ t+1 to t maxmze consumer welfare. She recognzes that welfare depends on the externaltes created by the trade balance, whch s an aggregate varable that each ndvdual consumer n country takes as gven. In a symmetrc equlbrum, the trade balance s tb t = b t+1/r t+1 b t and we denote the optmzaton problem of the planner as W ( b 0) = max {b t+1} t β [ t u ( ) ( )] yt + b t b t+1/r t+1 + x t b t+1 /R t+1 b t t=0 We assume that the planner acts compettvely and takes the path of world nterest rates as gven. One nterpretaton for ths s that country represents a small open economy wthn a regon of atomstc economes of total mass m, and therefore the natonal planner n each of the atomstc economes cannot affect the world nterest rate. We wll analyze the behavor of monopolstc natonal planners n large countres who nternalze ther market power over the world nterest rate n secton 7 on dstortve captal controls. The Euler equaton of a natonal planner who acts compettvely n world markets s u ( ) ( ) [ c ( ( )] t x t tb t = βrt+1 u ct+1) x t+1 tb t+1 (5) 7

8 Lemma 1 A natonal planner who acts compettvely corrects the domestc externaltes x t ( ) by mposng a captal control ( ) τ t+1 = x t (tb t) βr t+1 x t+1 tb t+1 (6) u (c t) Proof. By substtutng the descrbed captal control nto the Euler equaton of prvate agents (4), t can be seen that the control τ t+1 replcates the Euler equaton of the planner (5). The resultng allocaton therefore replcates the optmal allocaton chosen by the planner. 2.4 Equlbrum Defnton 1 (Compettve Equlbrum) For gven ntal bond holdngs {b 0} and captal controls { } τ t+1, a compettve equlbrum of the world economy s gven,t by consumpton allocatons {c t},t and bond holdngs { } b t+1 as well as nterest rates,t {R t+1 } t such that prvate consumers n each country solve ther optmzaton problem (3) subject to ther budget constrant (2) and the global bond market clears, B t+1 (R t+1 ; τ t+1 ) := N ( m b t+1 Rt+1 ; τ t+1) = 0 t (7) =1 In ths expresson, we defne τ t+1 = { } τ t+1 as the vector of captal controls across countres and B t+1 as the global excess demand for bonds n perod t, whch s by Assumpton 1 strctly ncreasng n R t+1. 4 For future use, we defne rest-of-the-world bond holdngs Bt+1 = j mj b j t+1 and we defne the upper-case varables C t and Y t as the weghted global sums of consumpton {c t} t and output {yt} t and smlarly for rest-of-the-world Ct and Yt. We defne the lassez fare equlbrum (LF) as the compettve equlbrum that prevals f all captal controls are set to zero τ t+1 = 0, t. Furthermore, we defne the Nash equlbrum among natonal planners (NP) as the compettve equlbrum that prevals f the natonal planner n each country mposes the captal control τ t+1, t gven by Lemma 1 to correct for domestc externaltes whle takng the captal controls of all other natonal planners and the world nterest rate as gven. Let us now focus on the effects of changes n captal controls on the equlbrum of the world economy. We perform a comparatve statc exercse n whch we assume that the natonal planner n country ncreases her captal control by dτ t+1 > 0. 4 Ths s our analogon of the Marshall-Lerner condton that an ncrease n the world nterest rate ncreases the global excess demand for bonds. 8

9 Lemma 2 (Effects of Captal Controls) An ncrease n the captal control dτ t+1 > 0 n country 1. ncreases bond holdngs b t+1 and savng b t+1/r t+1 and reduces consumpton c t n country for a gven world nterest rate R t+1, 2. f m > 0, t also reduces the world nterest rate R t+1 and reduces bond holdngs Bt+1 and savng Bt+1/R t+1 whle ncreasng consumpton n the rest of the world. 3. The declne n the world nterest rate benefts all borrowng countres and hurts all savng countres. Proof. Pont 1 follows from mplctly dfferentatng the Euler equaton of the consumer to express b t+1/ τ t+1 > 0. We dvde by R t+1 and apply the perod t budget constrant to obtan the statements about savng and consumpton. For pont 2, we apply the mplct functon theorem to the global market clearng condton (7) to obtan dr t+1 dτ t+1 = m b τ B R < 0 (8) where the partal dervatves satsfy B R = m b R > 0 and B τ = m b τ > 0. The declne n rest-of-the world bond holdngs Bt+1 and savng Bt+1/R t+1 and the ncrease n rest-of-the-world consumpton Ct follow from market clearng. Pont 3 s obtaned by takng the dervatve of the welfare functon of ndvdual countres dw j = β [ t u ( ) c ( j t x j tb j b dr t)] j t+1 t+1 (R t+1 ) 2 0 dependng on bj t+1 0 Intutvely, captal controls ntroduce a wedge nto the Euler equaton of consumers that rases desred bond holdngs whle reducng consumpton today. Ths shfts the global excess demand for bonds B t+1 (R t+1 ; τ t+1 ) upwards. For the global bond market to clear, a declne n the world nterest rate s requred, whch makes the rest of the world supply fewer bonds (.e. save less) and consume more. The declne n the nterest rate benefts borrowers because they obtan credt at lower rates and hurts lenders because they earn less n nterest. Fgure 1 llustrates our fndngs graphcally for a world wth two countres, j of equal mass. R j (b j ) depcts the nverse bond supply of country j, R ( b ) represents the nverse bond demand n country n the absence of captal controls. The ntersecton of the two, marked by R LF and b LF, ndcates the lassez fare equlbrum of the economy. However, suppose that there s a negatve externalty assocated wth borrowng by country. Then a compettve natonal planner would demand less borrowng, as ndcated by R ( b ), and mpose a captal control τ on borrowng 9

10 R * R LF R NP R j (b j ) R ( b ) R * ( b ) b NP b LF b Fgure 1: Optmal captal control to nternalze domestc externaltes to make prvate agents nternalze the externalty. The resultng equlbrum exhbts less borrowng/lendng b NP and a lower world nterest rate R NP. Country j looses the surplus that s marked by the shaded area n the fgure. Numercal Illustraton To llustrate the effects of changes n captal controls numercally, we consder an economy of mass m > 0 wth CES utlty u (c) = c 1 1/σ / (1 1/σ). Assume a steady state wth βr = 1, b = 0, τ = 0 and c = y = C = Y constant. The two partal dervatves of the savng/output rato b /y wth respect to the captal control and the nterest rate are b /y τ = b τ/y = σ 1 + β b /y R = b R/y = βσ 1 + β An ncrease n the captal control or an ncrease n the world nterest rate both ncrease the net savngs of the country by approxmately half of the ntertemporal elastcty of substtuton. (The second expresson s pre-multpled by β because nterest s compounded n perod t + 1 whereas the captal control s mposed n perod t.) For the standard value of the elastcty of substtuton σ = 1/2, both an ncrease n the captal control or the nterest rate result n an ncrease n domestc savngs by approxmately a quarter percent of GDP. 5 5 We note that there s consderable dsagreement among economsts about the value of the ntertemporal elastcty of substtuton. See e.g. Bansal and Yaron (2004) for a dscusson. The 10

11 Country GDP $ b /R R/R World $69,899bn 1% Unted States $15,076bn $30.2bn 0.216% Chna $7,298bn $16.7bn 0.104% Japan $5,867bn $13.7bn 0.084% Brazl $2,493bn $6.1bn 0.036% Inda $1,827bn $4.5bn 0.026% South Korea $1,116bn $2.8bn 0.016% Table 2: Effects of 1% captal control on savng and the world nterest rate (Source: IMF 2011 IFS data and author s calculatons for σ = 1 2 ) Global bond demand as a fracton of world output B/Y satsfes B/Y R = B R/Y = βσ 1 + β We combne ths wth the expresson b τ/y = σ n equaton (8) to fnd that the 1+β effect of captal controls n country on the world nterest rate s dr t+1 /R dτ t+1 = b τ/r B R = m In short, f a country that has a relatve share m of world GDP mposes a 1% captal control, the world nterest rate wll declne by m %. Observe that ths expresson s ndependent of the ntertemporal elastcty of substtuton (as long as t s constant across countres). Accountng for the adjustment n the world nterest rate, the general equlbrum effect of a captal control n country s mtgated to a fracton (1 m ) of the partal equlbrum effect, db /y dτ = b τ/y + b R/y dr t+1 dτ t+1 = ( 1 m ) σ 1 + β. In Table 2, we llustrate the effects of captal controls on bond holdngs and the world nterest rate for a number of countres that were mportant players n global captal markets and/or currency wars n recent years. For example, Brazl represents 3.6% of the world economy. If the country ncreases a 1% captal control, t wll reduce captal nflows by $6.1bn, whch n turn lowers the world nterest rate by 0.036% accordng to our calbraton. formulas we derved delver transparent results for any value of the ntertemporal elastcty of substtuton preferred by the reader. 11

12 2.5 Welfare Analyss Let us now analyze the global eff cency of captal controls that are mposed to correct domestc externaltes. Even though the prevous subsecton llustrated that captal controls may lead to sgnfcant spllover effects, we show here that unlaterally mposed optmal controls nonetheless lead to a Pareto eff cent global outcome. Then we proceed to nvestgatng the scope for Pareto-mprovng captal controls that make all countres better off, ether by provdng compensatory transfers or by regulatng flows n both nflow and outflow countres. We start our welfare analyss wth the followng result: Proposton 1 (Eff cency of Unlaterally Correctng Externaltes) The Nash equlbrum among natonal planners (NP) n whch each natonal planner mposes the captal control τ t+1, t gven by lemma 1 to correct for domestc externaltes s Pareto eff cent. Proof. An allocaton s Pareto eff cent f t maxmzes the weghted sum of welfare of all countres for some vector of welfare weghts { φ > 0 } N subject to the global resource constrant m (yt c t) = m tb t = 0 t, to whch we assgn the Lagrange =1 multpler β t ν t, { max β t φ m [ u ( yt tbt) ( } )] + x tb t + νt m tb t {tb t},t t The optmalty condton to ths problem s φ [ u ( c t) x ( tb t)] = νt (9) The Nash equlbrum among natonal planners satsfes ths optmalty condton for all, t f we normalze ν 0 to an arbtrary postve value and set φ = ν 0 / [u (c 0) x (tb 0)] and ν t+1 = ν t / (βr t+1 ) t > 0. The proposton s a verson of the frst welfare theorem. If each natonal planner determnes her country s optmal bond demand and acts compettvely, the general condtons of the frst welfare theorem apply and the resultng compettve equlbrum s Pareto eff cent. After each natonal planner has nternalzed her domestc externaltes, her bond demand correctly reflects the country s socal margnal rate of substtuton between consumpton today and tomorrow. In the global market for bonds, the margnal rates of substtuton are all equated to the world nterest rate and the resultng equlbrum s Pareto eff cent. The spllover effects on the world nterest rate from mposng captal controls therefore consttute eff cent pecunary externaltes. They reflect the response of the market to the balance of demand and supply for bonds. As we emphaszed n Lemma 2, such pecunary externaltes ental redstrbutons between borrowers and lenders, but Proposton 1 shows that they do not lead to Pareto neff cences Pareto optmalty s ndependent of redstrbutve concerns. 12

13 Eff cency of Lassez-Fare Equlbrum A straghtforward corollary to Proposton 1 s that the lassez fare equlbrum s generally not Pareto eff cent f some countres are subject to externaltes from nternatonal captal flows. Arms Race of Captal Controls Optmally mposed captal controls may lead to dynamcs that look lke an arms race, but ths does not necessarly ndcate neff - cency. Suppose that there s one lendng country l as well as two borrowng countres and j that ( each ) have captal controls n place n order to correct a domestc externalty x t b t+1, whch s ncreasng and convex n b t+1 and smlarly ( ) for country j. Assume that country experences an exogenous ncrease n x t b t+1 that rases the optmal captal control τ t+1. As a result, the supply of captal to country j ncreases,.e. b j t+1 rses, and t s optmal for country j to rase ts captal control as well. However, based on the response of country j, country may fnd t optmal to ncrease ts captal control τ t+1 yet further. The resultng dynamcs may gve the appearance of an arms race but are nonetheless eff cent. As long as the condtons of Proposton 1 are satsfed, ths arms race s the mechansm of tatonnement through whch the eff cent equlbrum s restored. In the descrbed example, each successve round of ncreases n captal controls wll be smaller and the captal controls n the two countres τ t+1 and τ j t+1 wll converge towards the eff cent levels, whch nvolves hgher captal controls n both borrowng countres and reduced lendng by country l Implementaton Proposton 2 (Indetermnacy n Implementaton) Consder a compettve equlbrum allocaton wth ntal bond holdngs {b 0 } and captal controls { } τ t+1 that,t mplement an allocaton of consumpton {c t},t and bond holdngs { } b t+1. A global,t planner can mplement the descrbed consumpton allocaton va a contnuum of alternatve compettve equlbra, n whch nterest rates, captal controls and bond holdngs dffer. Proof. There s a one-to-one mappng between a gven allocaton of consumpton {c t},t and of trade balances {tb t},t because tb t = y t c t, t. An compettve equlbrum mplements a gven allocaton of trade balances f and only f tb t = b t+1 R t+1 b t, t (10) In the followng, we wll demonstrate that a global planner can pck alternatve combnatons of bond holdngs and nterest rates to mplement the same allocaton of trade balances. We lmt our attenton to pckng bond holdngs and nterest rates and refer to equaton (4) for the mpled level of captal controls. 13

14 We start from a gven compettve equlbrum allocaton n a world economy wth N countres. Consder a global planner who perturbs bond holdngs { bt+1} for T perods (for b t+1 ndexed from t + 1 to t + T ) and perturbs nterest rates {R t+1 } for T + 1 perods (from t + 1 to t + T + 1). Ths provdes the planner wth (N 1) T degrees of freedom to determne bond holdngs, snce he needs to observe market clearng every perod, and T + 1 degrees of freedom to set nterest rates for T + 1 perods, for a total of NT + 1 degrees of freedom. (The planner can always adjust captal controls n each country so as to make the chosen level of bond holdngs optmal for consumers n each country, gven the chosen nterest rate.) If the planner wants to make these perturbatons whle keepng consumpton {c t},t fxed at all tmes, he has to keep the trade balance gven by equaton (10) unchanged for all {1,...N} and, n partcular, for the T + 1 perods from t to t + T n whch the perturbed varables enter the expresson for the trade balance. Market clearng m b t+1 = 0 mples that f equaton (10) s satsfed for N 1 countres n a gven perod, t automatcally holds for country N. Therefore the requrement to keep consumpton fxed mposes (N 1) (T + 1) constrants on the planner. If the planner perturbs bond holdngs and nterest rates for suff cently many perods T N 2, then he has more degrees of freedom than constrants and there s a contnuum of bond holdngs and nterest rates that mplement the descrbed consumpton allocaton. The proposton reflects that there s an ndetermnacy n mplementaton because the global planner has NT + 1 ndependent nstruments ((N 1) T captal controls plus T + 1 world nterest rates) at hs dsposal to satsfy (N 1) (T + 1) ndependent equlbrum condtons. As we wll see later, ths ndetermnacy hands the planner a powerful mechansm to crcumvent bndng fnancal constrants. To provde further ntuton we consder the smplest possble example n whch the planner perturbs bond holdngs for T = 1 perod n a world economy wth two countres N = 2, satsfyng the condton for ndetermnacy, T > N 2: Example 1 (Two Countres) Assume a world economy wth two countres, j of equal mass and focus on the Nash equlbrum among natonal planners (NP). By market clearng, observe that b j t+1 = b t+1 t. W.l.o.g. assume that country s a lender b s+1, b s+2 > 0 n perods s and s + 1. A global planner can set b s+1 to an arbtrary level b s+1 > max { tb s+1, 0 } whle leavng all consumpton allocatons { c t, ct} j as well as { } b t t+1 unchanged. t s Proof. For all consumpton allocatons to reman unchanged, the global planner has to observe two constrants tb s = b s+1 R s+1 b s and tb s+1 = b s+2 R s+2 b s+1 By market clearng the analogous condtons for country j are lnearly dependent, reflectng that the planner s subject to (N 1) (T + 1) = 2 constrants. The planner 14

15 can therefore pck the three varables { b s+1, R s+1, R s+2 } subject to only two constrants. If the planner pcks bond holdngs b s+1 b s+1, then he has to rescale R s+1 by the same factor as bond holdngs so that the fracton b s+1/ R s+1 = b s+1/r s+1 remans constant and the trade balance n perod s s unchanged. Snce the gross nterest rate R s+1 s restrcted to be postve, ths s only possble for b s+1 that s of the same sgn as b s+1. 6 Furthermore, the planner has to change R s+2 n the opposte drecton so that the trade balance n perod s + 1 s unaffected, R s+2 = b s+2 tb s+1 + b s+1 where the terms b s+2 and tb s+1 + b s+1 need to be of equal sgn for the gross nterest rate to be postve. The captal controls requred to mplement these bond postons need to be scaled n proporton to the world nterest rate to guarantee that the Euler equatons of consumers hold n perod s, and smlarly n perod s τ s+1 R s+1 = 1 τ s+1 R s+1 In the two country example, the global planner has 3 nstruments { b s+1, R s+1, R } s+2 to meet 2 ndependent equlbrum condtons. In a gven perod s, a parallel ncrease n all captal controls τ s+1 and τ j s+1 (.e. a subsdy to outflows n country and a tax on nflows n country j) reduces global demand for bonds and lowers the world nterest rate proportonately to the change n captal controls. Ths redstrbutes from the savng country to the borrowng country. In the followng perod, captal controls τ s+2 and τ j s+2 are reduced (.e. a tax on outflows n country and a subsdy to nflows n country j) to rase the world nterest rate and redstrbute from borrowers back to lenders. We wll show below that ths mechansm provdes a global planner wth a powerful tool to relax temporarly bndng fnancal constrants n the world economy. The example also hghlghts why the global planner generally needs to perform ths perturbaton over multple perods f the number of countres s greater than two (except n knfe-edge cases). If N = 3 but T = 1, we would allow the planner to choose bond holdngs { } b t+1 for only one perod and nterest rates {R t+1, R t+2 } for two perods. If the planner wants to perturb these varables wthout affectng consumpton allocatons n the economy, he has N T + 1 = 4 ndependent choce varbles but needs to satsfy the constrant (10) for perods t and t + 1, mplyng 6 If we mpose the restrcton that the gross nterest rate s bounded above some postve value, for example because of the zero-lower-bound on the nomnal nterest rate, then the set of permssble perturbatons s further reduced. Further mplcatons of the zero-lower-bound on nomnal nterest rates are dscussed n secton 5. 15

16 (N 1) (T + 1) = 4 constrants. It s mpossble for the planner to devate from the orgnal allocaton whle satsfyng all four constrants, except n knfe-edge cases when these constrants are lnearly dependent. 7 One such knfe-edge case s f we focus on a steady state equlbrum n whch the bond postons of countres are unchanged over three consecutve tme perods so that the constrants (10) for perods t and t+1 are lnearly dependent. Another mportant example of such a knfe edge case s the followng: Example 2 (Identcal Countres) Assume a world economy wth N dentcal countres wth zero bond holdngs that experence domestc externaltes and mpose domestcally optmal captal controls τ t+1 > 0 n a gven tme perod t. The consumpton allocatons of the Nash equlbrum among natonal planners (NP) can be replcated by settng the captal controls n all countres to zero, τ t+1 = 0. The ntuton s that captal controls have no wealth effects from changes n the nterest rate f bond postons { } b t+1 are zero, as s the case for dentcal symmetrc countres. Techncally, the term b t+1/r t+1 n constrant (10) s unaffected by a change n R t+1. Lowerng captal controls across all countres just mples a hgher world nterest rate, all consumpton allocatons are unchanged. We wll take advantage of ths result n secton 8 to show how coordnaton between countres can be used to reduce mplementaton costs when captal controls are costly to mpose Pareto-Improvng Captal Controls If the objectve of a global planner s not to acheve Pareto eff cency but the more strngent standard of achevng a Pareto mprovement, then captal controls generally need to be accompaned by transfers. Even f captal controls are Pareto eff cent, they stll lead to changes n the world nterest rate (.e. pecunary externaltes) that redstrbute between borrowng and lendng countres. In the followng proposton, we show that access to lump-sum transfers enables a global planner to always mplement a Pareto mprovement when correctng for the domestc externaltes n any number of economes. Proposton 3 (Pareto-Improvng Captal Controls, Wth Transfers) Startng from the lassez fare equlbrum, a global planner who dentfes domestc externaltes { ( )} x t b N t+1 /R t+1 wth at least one x =1 t ( ) 0 can acheve a Pareto mprovement by settng captal controls n all countres such that τ t+1 = τ t+1 and engagng n compensatory nternatonal transfers ˆT t 0 that satsfy ˆT t = 0. 7 Ths s always the case n a steady state equlbrum n whch the bond postons of all countres are unchanged over two consecutve perods. 16

17 Proof. Denote the savng/consumpton { allocatons} and the assocated world nterest rate n the lassez fare equlbrum by c,lf t, b,lf t+1 and { } Rt+1 LF and n the global planner s equlbrum { that } results from mposng optmal captal controls τ t+1 and transfers by c,gp t, b,gp t+1 and { } Rt+1 GP. Assumng the planner provdes transfers ˆT t = c LF, t c GP, t,t + blf, t+1 bgp, t+1 Rt+1 GP t,t, then ˆT t = 0 snce both sets of allocatons (LF and GP ) satsfy market clearng. Furthermore, gven these transfers, consumers n each country can stll afford the allocaton that prevaled n the lassez fare equlbrum. For non-zero captal controls, the allocaton dffers from the lassez fare equlbrum snce the Euler equatons (4) and (5) dffer. Gven that the old allocaton s stll feasble, revealed preference mples that every country s better off under the new allocaton. In an nternatonal context, compensatory transfers may be dff cult to mplement. As an alternatve, we show that a planner who can coordnate the captal control polces of both nflow and outflow countres can correct the domestc externaltes of ndvdual economes whle holdng the world nterest rate constant so that no wealth effects arse. As a result, the global planner s captal control polces consttutes a global Pareto mprovement at a frst-order approxmaton. The followng lemma demonstrates how a global planner can manpulate the world nterest rate by smultaneously adjustng the captal controls n all countres worldwde; then we show how ths mechansm can be used to undo changes n the world nterest rate and the assocated wealth effects f ndvdual countres unlaterally mpose captal controls. Lemma { } 3 Consder a compettve equlbrum wth an allocaton of bond holdngs b j t+1 and a seres of captal controls { } τ j j,t t+1 and world nterest rates {R j,t t+1} t. A global planner can ncrease the world nterest rate n a gven perod by dr t+1 whle keepng the bond allocatons for all countres constant by movng the captal control n each country j = 1...N by dτ j t+1 = bj R dr t+1 b j (11) τ Proof. We set the total dfferental of the bond demand functon of a gven country j to zero, db j t+1 = b j R dr t+1 + b j τdτ j t+1 = 0 and rearrange to obtan equaton (11). Snce db j t+1 = 0, all future allocatons are unaffected by the descrbed perturbaton. Corollary 1 (Pareto-Improvng Captal Controls, No Transfers) Assume an exogenous margnal ncrease n the domestc externalty n country that rases the t 17

18 optmal unlateral captal control by dτ t+1 > 0 n perod t. A global planner can correct for ths whle keepng the world nterest rate constant dr t+1 = 0 to avod ncome and wealth effects by adjustng dτ j t+1 dτ t+1 = m b τ B R bj R b j τ and dτ t+1 dτ t+1 = 1 m b R B R In the resultng equlbrum, bond holdngs { } b j t+1 are altered but, by the envelope j theorem, welfare s unchanged at a frst-order approxmaton. Proof. If the planner mplemented the unlaterally optmal ncrease dτ t+1 > 0 n the captal control of country, then the world nterest rate would move by dr t+1 /dτ t+1 = m b τ/b R. Accordng to Lemma 3, the move n the nterest rate can be undone f the captal controls of all countres j = 1...N are smultaneously adjusted by dτ j t+1/dr t+1 dr t+1 /dτ t+1, whch delvers the frst equaton of the proposton. The second equaton s obtaned by addng the ntal unlateral response of the captal control plus the adjustment gven n the frst equaton wth j =. In the resultng equlbrum, the ncrease n the externalty dτ t+1 s corrected but the world nterest rate s unchanged. Furthermore, for a constant world nterest rate, the change n welfare that results from a margnal change n bond holdngs s dw j ( ) = βt 1 τ ( j t+1 u ct) j + β t+1 u ( ) c j t+1 = 0 R t+1 db j t+1 drt+1 =0 For non-nfntesmal changes n captal controls, changes n bond holdngs b j t+1 have second-order effects on welfare (.e. effects that are neglgble for nfntesmal changes but growng n the square of the devaton) even f the world nterest rate s held constant. Under certan condtons, e.g. f there are only two types of countres n the world economy, a global planner can undo these second-order effects va further adjustments n the world nterest rate R t+1. In Fgure 1 on page 10, a natonal planner corrects for a negatve externalty to borrowng τ n country. A global planner could acheve a Pareto mprovement by splttng the burden of regulatng captal flows between the two countres. He would tax outflows n country j such that 1 τ j = R NP /R LF and tax nflows for the remanng part of the externalty such that 1 τ 1 τ = n country. As a 1 τ j result, the nterest rate would be unchanged at R LF and the welfare loss by country, ndcated by the shaded area n the fgure, would be lmted to the Harberger trangle between b NP, b LF and R LF. 8 8 Snce there are only two countres n ths example, country could be compensated for ths second order loss by rasng the nterest rate on the remander of ts bond holdngs, as descrbed n Lemma 3, achevng an unambguous Pareto mprovement. 18

19 Such a polcy response shares certan characterstcs wth voluntary export restrants (VERs) n trade polcy: If a borrowng country mposes controls on captal nflows, the world nterest rate wll declne and all lendng countres experence negatve wealth effects. However, f lenders restrct outflows by mposng controls of ther own, they can keep the surplus. A global planner would share the burden of adjustment between borrower and lender n proporton to ther elastctes of demand and supply so as to keep the world nterest rate constant. Numercal Illustraton Assumng the economy starts n a steady state (as descrbed n the llustraton n secton 2.4), an ncrease n the externalty n country that would call for an optmal unlateral response dτ t+1 n the country s level of captal controls can also be corrected by settng dτ t+1 dτ t+1 dτ j t+1 dτ t+1 = 1 m = m In short, the country that experences the externalty corrects only a fracton (1 m ) of t and the rest of the world mposes a captal control to correct the remanng fracton m correspondng to the country s weght n the world economy. For example, small open economes would meet the burden of adjustment by themselves snce m = 0 and they do not affect the world nterest rate. For large economes, we refer to the country weghts mpled by Table 2 on page 11. For example, f Chna experenced a postve externalty from current account surpluses that calls for a 1% unlateral subsdy to captal outflows, then a global planner who follows the descrbed scheme would mpose a 0.90% subsdy on outflows n Chna and a 0.10% subsdy to nflows n the rest of the world to keep the world nterest rate unchanged. Smlarly, f Brazl experenced a 1% externalty from captal nflows, the global planner would mpose a 0.97% tax on nflows to Brazl and a 0.03% tax on outflows n the rest of the world n order to keep the world nterest rate stable. 3 Generalzatons Ths secton generalzes our benchmark setup from the prevous secton along three dmensons. Frst, we extend the model to nclude a real exchange rate and delneate condtons under whch there s an somorphsm between captal controls and real exchange rate nterventon. Second, we show that our results are robust to ntroducng uncertanty ether f there s only a sngle real bond traded n global captal markets or f there s a complete market and polcymakers have a complete set of nstruments. Thrd, we ntroduce nvestment and captal nto our model to show that the equ- 19

20 lbrum n a world economy n whch each natonal planner unlaterally mposes her optmal captal control s stll Pareto eff cent. 3.1 Real Exchange Rates and Reserve Accumulaton Polcymakers are often concerned about the effects of captal flows on the real exchange rate. To capture such effects, we extend our benchmark model to nclude a non-traded good n each country, whch allows us to ntroduce a real exchange rate. We dstngush varables that refer to traded versus non-traded goods by the subndces T and N. We mantan our assumpton that there s a sngle homogenous traded good whch s the numerare good, and we denote the relatve prce of non-traded goods n country by p N, whch consttutes a measure of the real exchange rate. 9 Observe that we ndex p N by country snce the prces of non-traded goods n dfferent countres are dfferent. A representatve consumer n country values tradable and non-tradable consumpton accordng to the functon V ( bt) = β t u ( ) c T,t, c N,t We denote the partal dervatves of the utlty functon as u T = u/ c T,t and smlar for u N, u NT etc. We mpose the assumptons u T > 0 > u T T, u N > 0 > u NN and u NT u T u N u T T > 0,.e. the two goods are complements or at most mld substtutes n the utlty functon of domestc agents. 10 The perod 0 consumer budget constrant augmented by non-traded goods s c T,t + p N,tc N,t + ( ) 1 τ t+1 b t+1 /R t+1 = yt,t + p N,tyN,t + b t + Tt (12) The consumer s optmalty condtons are ( ) ( ) ( 1 τ t+1 ut c T,t, c N,t = βrt+1 u T c T,t+1, cn,t+1) (13) p N,t = u ( N c T,t, cn,t) ( ) (14) u T c T,t, c N,t The frst optmalty condton s analogous to the Euler equaton (4) and defnes bond demand b t+1 as an ncreasng functon of the world nterest rate R t+1 under Assumpton 1. The second optmalty condton states that the real exchange rate 9 The off cal defnton of the real exchange rate s the prce of a consumpton basket of domestc goods expressed n terms of a consumpton basked of foregn goods. Ceters parbus, a rse n the relatve prce of non-tradables ncreases the prce of a consumpton basket of domestc goods, mplyng a strctly monotonc relatonshp between the off cal real exchange rate and our measure p N. 10 Emprcally, Mendoza (1995) and Stockman and Tesar (1995) fnd that traded and non-traded goods are clear complements. 20

21 s the margnal rate of substtuton between traded and non-traded goods. Market clearng for non-traded goods requres that c N,t = y N,t. The structure of the real exchange rate model s such that the results from our benchmark model carry over. To put t formally: { Corollary } 2 (Real Exchange Rate Model) For gven levels of non-traded output y N,t, the real exchange rate model s somorphc to our benchmark model, wth,t the real exchange rate beng a strctly ncreasng functon of tradable consumpton p N,t = p N (c T,t ). Proof. To show the somorphsm, we defne the utlty functon u ( ( ct,t) = u c T,t, yn,t for each country by substtutng the market-clearng condton for non-traded goods c N,t = y N,t. Ths utlty functon satsfes the restrctons requred by the benchmark model. Non-traded consumpton and endowment cancel from the budget constrant (12). The remanng problem s dentcal to our benchmark setup and leads to dentcal optmalty condtons. After substtutng the market-clearng condton n (14), we observe that tradable consumpton s the only endogenous varable drvng the real exchange rate. The dervatve p N,t c T,t = u NT u T u N u T T (u T ) 2 > 0 s postve by our earler assumptons on the utlty functon. The ntuton s that hgher avalablty of traded goods mples that non-traded goods, whch are n fxed supply n the economy, become relatvely more valuable. Captal controls shft tradable consumpton from one country to another, and the real exchange rate moves n lne wth tradable consumpton. For example, an ncrease n the captal control n country deprecates the exchange rate p N,t / τ t+1 < 0 there and tends to apprecate the real exchange rate n the rest of the world. Remark Introducng an addtonal tax nstrument τ N,t+1 on non-tradable consumpton that s rebated lump-sum does not affect real allocatons. Such a tax scales down the real exchange rate p N,t by a factor 1+τ N,t+1, but market clearng mples that nontradable consumpton s unchanged. Therefore the tax does not affect the margnal utlty of tradable consumpton and the ntertemporal Euler equaton of consumers Ths observaton would change f we endogenze the supply of non-tradable goods: a tax on non-tradable goods reduces ther relatve supply, whch decreases the margnal utlty of tradable goods u T and nduces consumers to save more n nternatonal captal markets. ) 21

22 3.1.1 Reserve Accumulaton We extend our framework to study reserve accumulaton. 12 Assume a planner n country accumulates bond holdngs a t on behalf of domestc consumers, where any accumulaton/decumulaton a t+1 /R t+1 a t s fnanced/rebated va lump-sum transfers. We may thnk of these bond holdngs as reserves. Ths changes the perod t budget constrant of consumers to c T,t + p N,tc N,t + a t+1 + ( ) 1 τ t+1 b t+1 R t+1 = y T,t + p N,ty N,t + a t + b t + T t (15) In the followng, we dstngush two dametrcally opposed cases. We descrbe the captal account n an economy as open when domestc consumers can trade nternatonal bonds b t+1, as we have assumed so far. By contrast, we call the captal account closed when domestc consumers are forbdden from borrowng or savng abroad. Ths mposes the constrant b t+1 = 0 t. Proposton 4 (Reserve Accumulaton) () Under open captal accounts, domestc consumers undo any reserve holdngs a t+1 by adjustng ther prvate bond holdngs such that b t+1 = b t+1 a t+1, where b t+1 corresponds to the optmal choce of consumers n the absence of reserves. () Under closed captal accounts, reserve accumulaton cannot be undone. It reduces domestc consumpton c T,t / a t+1 < 0 and deprecates the real exchange rate p N,t / a t+1 < 0 of country. If the mass of the country s postve, t also reduces the world nterest rate R t+1 / a t+1 < 0. () There s a one-to-one correspondence between a gven level of captal controls τ t+1 under open captal accounts and a gven amount of reserve accumulaton a t+1 under closed captal accounts. Proof. For part (), assume an equlbrum wth zero reserves a t+1 = 0 t and denote the assocated level of prvate bond holdngs by b t+1. If a planner accumulates a nonzero level of reserves a t+1 0 n some perods, then an allocaton n whch prvate bond holdngs satsfy b t+1 = b t+1 a t+1 wll leave all other varables unchanged and wll therefore satsfy the optmalty condtons of the consumer. If consumers have unconstraned access to captal markets, then reserve accumulaton s neffectve, even f the planner has mposed prce controls τ t+1 on nternatonal captal flows. What matters for the real allocatons of the consumer s solely the level of captal controls τ t+1, not the level of reserves a t+1. Ths s a form of Rcardan 12 Ths extenson can be ntroduced ether n our benchmark model or n the model wth a real exchange rate. We opt for the latter snce ths naturally allows us to dscuss the mplcatons of reserve accumulaton for the real exchange rate. 22