A Theory of Capital Controls as Dynamic Terms-of-Trade Manipulation

Transcription

1 A Theory of Capial Conrols as Dynamic Terms-of-Trade Manipulaion Arnaud Cosino Massachuses Insiue of Technology, Cenre for Economic Policy Research, and Naional Bureau of Economic Research Guido Lorenzoni Norhwesern Universiy and Naional Bureau of Economic Research Iván Werning Massachuses Insiue of Technology and Naional Bureau of Economic Research We develop a heory of capial conrols as dynamic erms-of-rade manipulaion. We sudy an infinie-horizon endowmen economy wih wo counries. One counry chooses axes on inernaional capial flows in order o maximize he welfare of is represenaive agen, while he oher counry is passive. We show ha a counry growing faser han he res of he world has incenives o promoe domesic savings by axing capial inflows or subsidizing capial ouflows. Alhough our heory of capial conrols emphasizes ineres rae manipulaion, he paern of borrowing and lending, per se, is irrelevan. I. Inroducion Since he end of World War II, bilaeral and mulilaeral rade agreemens have led o dramaic ariff reducions around he world, conrib- We hank Jim Anderson, Pol Anràs, Oleg Iskhoki, Phil Reny, Bob Saiger, Jonahan Vogel, hree anonymous referees, and seminar paricipans a Columbia, Chicago Booh, he Cowles Foundaion conference, Yale, he Boson Fed, Harvard, he Inernaional Moneary Fund, and he Universiy of Wisconsin for very helpful commens. [ Journal of Poliical Economy, 2014, vol. 122, no. 1] 2014 by The Universiy of Chicago. All righs reserved /2014/ $

2 78 journal of poliical economy uing o a specacular increase in world rade ðsee Baier and Bergsrand 2007; Subramanian and Wei 2007Þ. Saring in he mid-1980s, he world has also experienced a dramaic increase in capial markes inegraion, wih increased cross-border flows boh across indusrial counries and beween indusrial and developing counries ðsee Kose e al. 2009Þ. In sum, he world has experienced a dramaic increase in inraemporal and ineremporal rade, as figure 1 illusraes. The mulilaeral insiuions ha promoe boh ypes of rade, however, have followed wo very differen approaches. The primary goal of he World Trade Organizaion ðwtoþ, and is predecessor he General Agreemens on Tariffs and Trade, has been o reduce relaive price disorions in inraemporal rade. The focus on relaive price disorions and heir associaed erms-of-rade implicaions in saic environmens has a long and disinguished hisory in he inernaional rade lieraure, going back o Mill ð1844þ and Torrens ð1844þ. This rich hisory is echoed by recen heoreical and empirical work emphasizing he role of erms-of-rade manipulaion in he analysis of opimal ariffs and is implicaions for he WTO ðsee Bagwell and Saiger 1999, 2011; Broda, Limao, and Weinsein 2008Þ. By conras, inernaional effors oward increased capial openness have emphasized he effecs of capial conrols on macroeconomic and financial sabiliy. Consequenly, he mulilaeral insiuions ha promoe capial marke inegraion, such as he Inernaional Moneary Fund ðimfþ, have aken a differen, more nuanced approach o ineremporal rade, as exemplified in he recen IMF recommendaions on he appropriae use of capial conrols ðsee Osry e al. 2010Þ. Alhough he ermsof-rade effecs emphasized in he inernaional rade lieraure have na- FIG. 1. Inernaional rade and financial inegraion. The dashed line wih he axis on he lef represens he sum of world expors and impors over world GDP ðsource: IMF World Economic OulookÞ. The solid line wih he axis on he righ represens he sum of world asses and world liabiliies over world GDP ðsource: updaed and exended version of daa se consruced by Lane and Milesi-Ferrei ½2007ŠÞ.

3 heory of capial conrols 79 ural implicaions for he analysis of opimal capial conrols, hese effecs play lile role in he exising inernaional macro lieraure. The objecive of his paper is o bridge he gap beween he rade approach o ariffs and he macroeconomic approach o capial conrols. We do so by developing a neoclassical benchmark model in which he only raionale for capial conrols is dynamic erms-of-rade manipulaion. Our objecive is no o argue ha he only moive for observed capial conrols is he disorion of relaive prices or ha he removal of such disorions should be he only goal of inernaional policy coordinaion. Raher, we wan o develop some basic ools o hink abou capial conrols as a form of ineremporal rade policy and explore he implicaions of his idea for how unilaerally opimal capial conrols should covary wih oher macroeconomic variables over ime. The saring poin of our paper is ha in an Arrow-Debreu economy here is no difference beween ineremporal rade and inraemporal rade. In such an environmen, one needs only o relabel goods by ime period, and he same approach used o sudy saic erms-of-rade manipulaion can be used o analyze dynamic erms-of-rade manipulaion. Our analysis builds on his simple observaion ogeher wih he imeseparable srucure of preferences ypically used in macro applicaions. One key insigh ha emerges from our analysis is ha for a counry rading ineremporally, unilaerally opimal capial conrols are no guided by he absolue desire o aler he ineremporal price of goods produced in a given period, bu raher by he relaive srengh of his desire beween wo consecuive periods. If a counry is a ne seller of goods daed and 1 1 in equal amouns and faces equal elasiciies in boh periods, here is no incenive for he counry o disor he saving decisions of is consumers a dae. I is he ime variaion in he incenive o disor ineremporal prices ha leads o nonzero capial conrols. This is a general principle ha, o our knowledge, is novel o boh he inernaional macro and inernaional rade lieraure. To illusrae his general principle in he simples possible way, we firs consider an infinie-horizon, wo-counry, one-good endowmen economy. In his model he only relaive prices are real ineres raes. We solve for he unilaerally opimal axes on inernaional capial flows in one counry, Home, under he assumpion ha he oher counry, Foreign, is passive. 1 In his environmen, he principle described above has sharp 1 Throughou our analysis, we assume ha he home governmen can freely commi a dae 0 o a sequence of axes. In he economic environmen considered in his paper, his is a fairly mild assumpion. As we formally esablish in Sec. III.D, if he home governmen can ener deb commimens a all mauriies, as in Lucas and Sokey ð1983þ, he opimal sequence of axes under commimen is ime consisen. To he exen ha bonds of differen mauriies are available in pracice and hey are we herefore view he model wih commimen as he mos naural benchmark for he quesion ha we are ineresed in.

4 80 journal of poliical economy implicaions for he direcion of opimal capial flow axes. In paricular, i is opimal for Home o ax capial inflows ðor subsidize capial ouflowsþ in periods in which Home is growing faser han he res of he world and o ax capial ouflows ðor subsidize capial inflowsþ in periods in which i is growing more slowly. Accordingly, if relaive endowmens converge o a seady sae, hen axes on inernaional capial flows converge o zero. Alhough our heory of capial conrols emphasizes ineres rae manipulaion, he sign of axes on capial flows depends only on he growh rae of he economy relaive o he res of he world. Home may be a ne saver or a ne borrower; Home may have a posiive or a negaive ne financial posiion; if Home grows faser han he res of he world, i has incenives o promoe domesic savings by axing capial inflows or subsidizing capial ouflows. The inuiion for our resuls is as follows. Consider Home s incenives o disor domesic consumpion in each period. In periods of larger rade deficis, i has a sronger incenive, as a buyer, o disor prices downward by lowering domesic consumpion. Similarly, in periods of larger rade surpluses, i has a sronger incenive, as a seller, o disor prices upward by raising domesic consumpion. Since periods of faser growh a home end o be associaed wih eiher lower fuure rade deficis or larger fuure rade surpluses, Home always has an incenive o raise fuure consumpion relaive o curren consumpion in such periods. This is exacly wha axes on capial inflows or subsidies on capial ouflows accomplish hrough heir effecs on relaive disorions across periods. The second par of our paper explores furher he fronier beween inernaional macro and inernaional rade policy by inroducing muliple goods, hereby allowing for boh ineremporal and inraemporal rade. In order o mainain he focus of our analysis on capial conrols, we assume ha Home can sill choose is axes on capial flows unilaerally bu ha i is consrained by a free-rade agreemen ha prohibis good-specific axes/subsidies in all periods. In his environmen, we show ha he incenive o disor rade over ime does no depend only on he overall growh of he counry s oupu relaive o he world, bu also on is composiion. We illusrae he role of hese composiional effecs in wo ways. Firs, we esablish a general formula ha relaes ineremporal disorions o he covariance beween he price elasiciies of differen goods and he change in he value of home endowmens. Ceeris paribus, we show ha Home is more likely o raise aggregae consumpion if a change in he value of home endowmens is iled oward goods whose prices are more manipulable. In his richer environmen, even a counry ha is oo small o affec he world ineres rae may find i opimal o impose capial conrols for erms-of-rade consideraions as long as i is large enough o affec some inraemporal prices. Second, we illusrae hrough a simple

5 heory of capial conrols 81 analyical example how such composiional issues relae o cross-counry differences in demand. In a muligood world in which counries have differen preferences, a change in he ime profile of consumpion affecs no only he ineres rae bu also he relaive prices of consumpion goods in each given period. This is an effec familiar from he lieraure on he ransfer problem, which goes back o he debae beween Keynes ð1929þ and Ohlin ð1929þ. In our conex his means ha by disoring is consumers decision o allocae spending beween differen periods, a counry also affecs is saic erms of rade. Even if all saic rade disorions are banned by a free-rade agreemen, our analysis demonsraes ha, away from he seady sae, inraemporal prices may no be a heir undisored levels if capial conrols are allowed. We conclude by reurning o he issue of capial conrols and inernaional cooperaion, or lack hereof, alluded o a he beginning of our inroducion. We consider he case of capial conrol wars in which he wo counries simulaneously se axes on capial flows opimally a dae 0, aking as given he sequence of axes chosen by he oher counry. Using a simple quaniaive example, we show ha, far from canceling each oher ou, capial conrols imposed by boh counries aggravae he misallocaion of inernaional capial flows. Our paper aacks an inernaional macroeconomic quesion following a classical approach from he inernaional rade lieraure and using ools from he dynamic public finance lieraure. In inernaional macro, here is a growing heoreical lieraure demonsraing, among oher hings, how resricions on inernaional capial flows may be welfare enhancing in he presence of various credi marke imperfecions ðsee, e.g., Calvo and Mendoza 2000; Caballero and Lorenzoni 2007; Aoki, Benigno, and Kiyoaki 2010; Jeanne and Korinek 2010; Marin and Taddei 2010Þ. In addiion o hese second-bes argumens, here also exiss an older lieraure emphasizing he so-called rilemma : one canno have a fixed exchange rae, an independen moneary policy, and free capial mobiliy ðsee, e.g., McKinnon and Oaes ½1966Š or, more recenly, Obsfeld, Shambaugh, and Taylor ½2010ŠÞ. To he exen ha having fixed exchange and an independen moneary policy may be welfare enhancing, such papers offer a disinc raionale for capial conrols. In relaed work, Obsfeld and Rogoff ð1996þ apply opimal ariff argumens o sudy capial conrols in a wo-period, wo-counry, one-good endowmen economy model. In his environmen, he opimal ariff argumen in rade heory has obvious implicaions: if a counry borrows, i should ax capial inflows o decrease he world ineres rae; conversely, if i saves, i should ax ouflows o raise i. Our analysis highlighs ha his basic insigh is misleading: i is specific o he wo-period model and does no carry over o more general seings. As discussed earlier, i is no a counry s saus as a borrower or lender in erms of neiher

6 82 journal of poliical economy socks nor flows ha deermines he sign of he opimal capial ax. Insead, wha maers is he conemporaneous growh rae of a counry compared o ha of is rading parner. For insance, a counry in a seady sae may find iself being a debor or credior, from pas saving choices, ye he opimal capial ax a he seady sae is zero. Similarly, a counry expecing o cach up in he long run may run a curren-accoun defici oday ye subsidize capial inflows because i expecs poor growh in he shor run. On he inernaional rade side, he lieraure on opimal axes in open economies is large and varied. The common saring poin of mos rade policy papers, however, is ha inernaional rade is balanced. They herefore absrac from ineremporal consideraions. 2 While one could, in principle, go from inraemporal o ineremporal rade policy by relabeling goods in an absrac Arrow-Debreu economy, exising rade policy papers ypically focus on low-dimensional general equilibrium models, ha is, wih only wo goods. Jones ð1967þ uses opimal ariff argumens o sudy he axaion of capial movemens in a saic model wih wo ðfinalþ goods. In his model, inernaional capial flows correspond o impors and expors of physical capial, which can be hough of as a hird ðinermediaeþ good. Compared o he presen analysis, here is no ineremporal borrowing and lending. Oher excepions feauring more han wo goods offer only ðiþ parial equilibrium resuls under he assumpion of quasi-linear preferences, ðiiþ sufficien condiions under which seemingly paradoxical resuls may arise ðsee, e.g., Feensra 1986; Ioh and Kiyono 1987Þ, or ðiiiþ fairly weak resricion on he srucure of opimal rade policy ðsee, e.g., Dixi 1985; Bond 1990Þ. To summarize, here are no off-he-shelf resuls from he exising rade lieraure ha direcly apply o he dynamic environmen considered in our paper. In erms of mehodology, we follow he dynamic public finance lieraure and use he primal approach o characerize firs opimal wedges raher han explici policy insrumens ðsee, e.g., Lucas and Sokey 1983Þ. Since here are ypically many ways o implemen he opimal allocaion in an ineremporal conex, his approach will help us clarify he equivalence beween capial conrols and oher policy insrumens. Our focus on he opimal srucure of axes in an open economy is also relaed o Anderson ð1991þ and Anderson and Young ð1992þ. Compared o he presen paper, boh papers focus on he case of a small open economy in which he raionale for axes is he financing of an exogenous sream of governmen expendiures raher han he manipulaion of inerem- 2 A noable excepion is he paper by Bagwell and Saiger ð1990þ, hough heir focus is on self-enforcing rade agreemens. See Saiger ð1995þ for an overview of ha lieraure.

7 heory of capial conrols 83 poral and inraemporal erms of rade. Finally, since our heory of capial conrols models one of he wo governmens as a dynamic monopolis opimally choosing he paern of consumpion over ime, our analysis bears some resemblance o he problem of a dynamic monopolis opimally choosing he rae of exracion of some exhausible resources ðsee Sigliz 1976Þ. The res of our paper is organized as follows. Secion II describes a simple one-good economy. Secion III characerizes he srucure of opimal capial conrols in his environmen. Secion IV exends our resuls o he case of arbirarily many goods. Secion V considers he case of capial conrol wars. Secion VI offers some concluding remarks. II. Basic Environmen A. A Dynamic Endowmen Economy There are wo counries, Home and Foreign. Time is discree and infinie, 5 0, 1,..., and here is no uncerainy. The preferences of he represenaive consumer a home are represened by he addiively separable uiliy funcion ò b uðc Þ; 50 where c denoes consumpion; u is a wice coninuously differeniable, sricly increasing, and sricly concave funcion, wih lim c 0 u 0 ðcþ 5`; and b ð0; 1Þ is he discoun facor. The preferences of he represenaive consumer abroad have a similar form, wih aserisks denoing foreign variables. Boh domesic and foreign consumers receive an endowmen sequence denoed by fy g and fy * g, respecively. Endowmens are bounded away from zero in all periods in boh counries. We make wo simplifying assumpions: world endowmens are fixed across periods, y 1 y * 5 Y, and he home and foreign consumers have he same discoun facor, b 5 b *. Accordingly, in he absence of disorions, here should be perfec consumpion smoohing across ime in boh counries. 3 We assume ha boh counries begin wih zero asses a dae 0. 4 Le p be he price of a uni of consumpion in period on he world capial markes. In he absence of axes, he ineremporal budge consrain of he home consumer is 3 In Sec. III.C, we demonsrae ha our resuls generalize o an environmen wih aggregae flucuaions if consumers have consan relaive risk aversion ðcrraþ uiliy. 4 The assumpion of zero iniial asses is relaxed in Sec. III.D.

8 84 journal of poliical economy ò p ðc 2 y Þ 0: 50 The budge consrain of he foreign consumer is he same expression wih aserisks on c and y. B. A Dynamic Monopolis For mos of he paper, we will focus on he case in which he home governmen ses axes on capial flows in order o maximize domesic welfare, assuming ha he foreign governmen is passive: i does no have any ax policy in place and does no respond o variaions in he home policy. We will look a he case in which boh governmens se axes sraegically in Secion V. In order o characerize he opimal policy of he home governmen, we follow he dynamic public finance lieraure and use he primal approach. Tha is, we approach he opimal policy problem of he home governmen by sudying a planning problem in which equilibrium quaniies are chosen direcly and address implemenaion issues laer. Formally, we assume ha he objecive of he home governmen is o maximize he lifeime uiliy of he represenaive domesic consumer subjec o ðiþ uiliy maximizaion by he foreign consumer a ðundisoredþ world prices p and ðiiþ marke clearing in each period. The foreign consumer s firs-order condiions are given by b u *0 ðc * Þ 5 l* p ; ð1þ ò p ðc * 2 y * Þ 5 0; ð2þ 50 where l * is he Lagrange muliplier on he foreign consumer s budge consrain. Moreover, goods marke clearing requires c 1 c * 5 Y: ð3þ Combining equaions ð1þ ð3þ, we can express he planning problem of he home governmen as subjec o max fc g ò b uðc Þ 50 ò b u *0 ðy 2 c Þðc 2 y Þ 5 0: 50 ðpþ ð4þ

9 heory of capial conrols 85 Equaion ð4þ is an implemenabiliy consrain, familiar from he opimal axaion lieraure. Given a sequence of domesic consumpion, condiion ð4þ is sufficien o ensure he exisence of a feasible, uiliy-maximizing consumpion sequence for Foreign. The argumen is consrucive: given fc g, he proposed sequence fc * g is obained from marke clearing ð3þ and he sequence of prices is compued from ð1þ, so ha ð2þ is implied by ð4þ, ensuring ha he foreign consumer s sufficien condiions for opimaliy are me. The Lagrangian associaed wih he previous planning problem is given by L 5 ò b uðc Þ 1 mò b u *0 ðy 2 c Þðy 2 c Þ: ð5þ In he nex secion we will solve ðpþ by looking for a consumpion sequence fc g ha maximizes L. Given he addiive separabiliy of preferences, his is equivalen o maximizing uðc Þ 1 mu *0 ðy 2 c Þðy 2 c Þ period by period. In online Appendix B, we show ha if ime is coninuous, hen any soluion of ðpþ mus be a maximand of L. This is sufficien o esablish ha our key resul, proposiion 1, holds under he assumpions of Secion II.A wihou furher qualificaion. In discree ime, a similar resul can be esablished if one allows he home governmen o choose loeries. In he absence of loeries, however, he se of maximands of L may no coincide wih he se of soluions of ðpþ. To avoid dealing wih eiher loeries or he echnicaliies associaed wih coninuous ime, we simply assume in he res of his paper ha u *0 ðy 2 c Þðc 2 y Þ is a sricly convex funcion of c for all y. This implies ha L is sricly concave and ha any soluion of ðpþ mus be a maximand of L. 5 III. Opimal Capial Conrols A. Opimal Allocaion We firs describe how home consumpion fc g flucuaes wih home endowmens fy g along he opimal pah. Nex we will show how he opimal allocaion can be implemened using axes on inernaional capial flows. Under he assumpions ha marginal uiliies are infinie a zero and ha foreign endowmens are bounded away from zero, opimal consumpion choices mus lie in ð0, Y Þ in all periods. Accordingly, we can 5 Since any soluion of ðpþ mus also be a soluion of he relaxed planning problem in which ð4þ holds as a weak inequaliy, he previous observaion derives from heorem 1 in Luenberger ð1969, 217Þ.

10 86 journal of poliical economy express he firs-order condiion associaed wih he maximizaion of L as u 0 ðc Þ 5 m½u *0 ðy 2 c Þ 2 u *00 ðy 2 c Þðc 2 y ÞŠ; ð6þ where m > 0 is he Lagrange muliplier on he implemenabiliy consrain. Since u is sricly concave, he lef-hand side is sricly decreasing in c ; and since u *0 ðy 2 c Þðc 2 y Þ is sricly convex, he righ-hand side is sricly increasing in c. Thus, condiional on m, here exiss a mos one value of c such ha equaion ð6þ is saisfied. Since he previous firsorder condiion mus be saisfied by any soluion of Home s planning problem, such a soluion mus be unique as well. 6 Equaion ð6þ leads o our firs observaion. Alhough he enire sequence fy g affecs he level of curren consumpion hrough heir effecs on he Lagrange muliplier m, we see ha changes in curren consumpion c along he opimal pah depend only on changes in he curren value of y. The nex proposiion furher shows ha here is a monoonic relaionship beween domesic consumpion and domesic endowmens along he opimal pah. Proposiion 1 ðprocyclical consumpionþ. For any wo periods and s, if he home endowmen is larger in s, y s > y, hen he home consumpion is also higher, c s > c. Figure 2 provides a graphical represenaion of he firs-order condiion associaed wih Home s planning problem. On he x-axis we have domesic consumpion c, which deermines foreign consumpion, Y 2 c, by marke clearing. The downward-sloping curve represens he marginal cos associaed wih reducing consumpion a home by one uni, he lef-hand side in equaion ð6þ. The solid upward-sloping curves represen he marginal benefi associaed wih reducing consumpion a home by one uni, he righ-hand side in equaion ð6þ. This capures boh he price of ha marginal uni, u *0 ðy 2 c Þ, and he change in he price of he inframarginal unis, u *00 ðy 2 c Þ. The opimal consumpion choices a daes and s correspond o he poin a which he marginal benefi of reducing domesic consumpion is equal o is marginal cos. For reference, we also plo mu *0 ðy 2 cþ represened by he doed upwardsloping curve. Is inersecion wih he downward-sloping curve represens an efficien level of consumpion. Is inersecion wih he solid upward-sloping curve occurs a he poin a which ne sales are zero: c 5 y. Figure 2 gives he inuiion for proposiion 1. As he endowmen increases from y o y s, he curve u 0 ðcþ does no move. A he same ime, he 6 Under he assumpion ha marginal uiliies are infinie a zero and ha foreign endowmens are bounded away from zero, one can also check ha such a soluion exiss. The formal argumen can be found in online App. B.

11 heory of capial conrols 87 FIG. 2. Consumpion is procyclical along he opimal pah marginal benefi curve shifs down, as he price decrease associaed wih a reducion in c applies o a larger amoun of inframarginal unis sold. This induces Home o consume more, explaining why consumpion is procyclical along he opimal pah. 7 As a preliminary sep in he analysis of opimal capial flow axes, we conclude his secion by describing how he wedge beween he marginal uiliy of domesic and foreign consumpion varies along he opimal pah. Formally, define ; u0 ðc Þ mu *0 ðc * Þ 2 1: ð7þ By marke clearing, we know ha c * 5 Y 2 c. Thus combining he definiion of wih he sric concaviy of u and u *, we obain he following corollary o proposiion 1. Corollary 1 ðcounercyclical wedgesþ. For any wo periods and s, if he home endowmen is larger in s, y s > y, hen he wedge is lower, s <. 7 To see why he sric convexiy of u *0 ðy 2 c Þðc 2 y Þ in c is no crucial for esablishing proposiion 1, noe ha any sequence fc g ha maximizes L mus be such ha c arg maxuðcþ 1 mu *0 ðy 2 cþðy 2 cþ period by period. Under he assumpion ha u * is sricly concave, uðcþ 1 mu *0 ðy 2 cþðy 2 cþ saisfies he single-crossing propery in ðc, y Þ. Thus he se of consumpion levels ha maximize L mus be increasing in y in he srong se order. To esablish ha consumpion is procyclical along he opimal pah, he only echnical quesion hen is wheher any soluion of ðpþ can be recovered as a maximand of L for some value of m. As we already discussed a he end of Sec. II.B, he answer in coninuous ime is always yes.

12 88 journal of poliical economy A his poin, i is worh pausing o discuss how corollary 1 relaes o and differs from exising resuls in he rade policy lieraure. By equaions ð6þ and ð7þ, we have 52 u*00 ðy 2 c Þ u *0 ðy 2 c Þ ðc 2 y Þ: ð8þ Condiion ð8þ is closely relaed o he well-known opimal ariff formula involving he elasiciy of he foreign expor supply curve in saic rade models wih wo goods and/or quasi-linear preferences. This should no be oo surprising since measures he difference beween he marginal uiliy of domesic and foreign consumpion. According o equaion ð8þ, he wedge is posiive in periods of rade defici and negaive in periods of rade surplus. This capures he idea ha if ðime-varyingþ rade axes were available, Home would like o ax impors if c 2 y > 0 and ax expors if c 2 y < 0. Corollary 1, however, goes beyond his simple observaion by esablishing a monoonic relaionship beween and y. This novel insigh will play a key role in our analysis of opimal capial conrols. B. Opimal Taxes on Inernaional Capial Flows I is well known from he Ramsey axaion lieraure ha here are ypically many combinaions of axes ha can implemen he opimal allocaion ðsee, e.g., Chari and Kehoe 1999Þ. Here, we focus on he ax insrumen mos direcly relaed o world ineres rae manipulaion: axes on inernaional capial flows. 8 For exposiional purposes, we assume ha consumers can rade only one-period bonds on inernaional capial markes, wih he home governmen imposing a proporional ax v on he gross reurn on ne asse posiion in inernaional bond markes. Sandard argumens show ha any compeiive equilibrium suppored by ineremporal rading of consumpion claims a dae 0 can be suppored by rading of one-period bonds. As we discuss laer in Secion III.D, none of he resuls presened here depend on he assumpion ha one-period bonds are he only asses available. Wih only one-period bonds, he per-period budge consrain of he home consumer akes he form q a 11 1 c 5 y 1 ð1 2 v 21 Þa 2 l ; ð9þ 8 Oher ax insrumens ha could be used o implemen he opimal allocaion include ime-varying rade and consumpion axes ðpossibly accompanied by producion axes in more general environmensþ. See Jeanne ð2011þ for a deailed discussion of he equivalence beween capial conrols and rade axes.

13 heory of capial conrols 89 where a denoes he curren bond holdings, l is a lump-sum ax, and q ; p 11 =p is he price of one-period bonds a dae. In addiion, consumers are subjec o a sandard no-ponzi condiion, lim ` p a 0. In his environmen he home consumer s Euler equaion akes he form u 0 ðc Þ 5 bð1 2 v Þð1 1 r Þu 0 ðc 11 Þ; ð10þ where r ; 1=q 2 1 is he world ineres rae. Given a soluion fc g o Home s planning problem ðpþ, he world ineres rae is uniquely deermined as r 5 u*0 ðy 2 c Þ bu *0 ðy 2 c 11 Þ 2 1; ð11þ by equaions ð1þ and ð3þ. Thus, given fc g, we can use ð10þ o consruc a unique sequence of axes fv g. We can hen se he sequence of asse posiions and lump-sum ransfers a 5 ò ðp s =p Þðc s 2 y s Þ; s5 l 52v 21 a ; which ensures ha he per-period budge consrain ð9þ and he no- Ponzi condiion are saisfied. Since ð9þ, ð10þ, and he no-ponzi condiion are sufficien for opimaliy, i follows ha given prices and axes, fc g is opimal for he home consumer. This esablishes ha any soluion fc g of ðpþ can be decenralized as a compeiive equilibrium wih axes. A posiive v can be inerpreed as imposing simulaneously a ax v on capial ouflows and a subsidy v o capial inflows. Obviously, since here is a represenaive consumer, only one of he wo is acive in equilibrium: he ouflow ax if he counry is a ne lender, a 11 > 0, and he inflow subsidy if i is a ne borrower, a 11 < 0. Similarly, a negaive v can be inerpreed as a subsidy on capial ouflows plus a ax on capial inflows. The boom line is ha v > 0 discourages domesic savings while v < 0 encourages hem. Combining he definiion of he wedge ð7þ wih equaions ð10þ and ð11þ, we obain he following relaionship beween wedges and axes on capial flows: v : ð12þ The previous subsecion has already esablished ha variaions in domesic consumpion c along he opimal pah are only a funcion of he curren endowmen y. Since is only a funcion of c, equaion ð12þ implies ha variaions in v are only a funcion of y and y 11. Combining

14 90 journal of poliical economy equaion ð12þ wih corollary 1, we hen obain he following resul abou he srucure of opimal capial conrols. Proposiion 2 ðopimal capial flow axesþ. Suppose ha he opimal policy is implemened wih capial flows axes. Then i is opimal 1. o ax capial inflows/subsidize capial ouflows ðv < 0Þ if y 11 > y ; 2. o ax capial ouflows/subsidize capial inflows ðv > 0Þ if y 11 < y ; 3. no o disor capial flows ðv 5 0Þ if y 11 5 y. Proposiion 2 builds on he same logic as proposiion 1. Suppose, for insance, ha Home is running a rade defici in periods and 1 1. In his case, he home governmen wans o exercise is monopsony power by lowering domesic consumpion in boh periods. Bu if Home grows beween hese wo periods, y 11 > y, he number of unis impored from abroad is lower in period 1 1. Thus he home governmen has less incenive o lower consumpion in ha period. This explains why a ax on capial inflows is opimal in period : i reduces borrowing in period, hereby shifing consumpion from period o period 1 1. The oher resuls follow a similar logic. I is worh emphasizing ha, alhough he only moive for capial conrols in our model is ineres rae manipulaion, neiher he ne financial posiion of Home nor he change in ha posiion is he relevan variable o look a o sign he opimal direcion of he ax in any paricular period. The reason is ha he effec of a capial flow ax is o affec he relaive disorion in consumpion decisions beween wo consecuive periods. Therefore, wha maers is wheher he monopolisic/ monopsonisic incenives o resric domesic consumpion are sronger in period or 1 1. In our simple endowmen economy, hese incenives are purely capured by he growh rae of he endowmen, bu he same broad principle would exend o more general environmens. Proposiion 2 has a number of implicaions. Consider firs an economy ha is caching up wih he res of he world in he sense ha y 11 > y for all. According o our analysis, i is opimal for his counry o ax capial inflows and o subsidize capial ouflows. The basic inuiion is ha a growing counry will expor more omorrow han oday. Thus i has more incenive o increase expor prices in he fuure, which i can achieve by raising fuure consumpion hrough a subsidy on capial ouflows. For an economy caching up wih he res of he world, larger benefis from fuure erms-of-rade manipulaion are associaed wih axes and subsidies ha encourage domesic savings. Consider insead a counry ha a ime borrows from abroad in anicipaion of a emporary boom. In paricular, suppose ha y 11 > y and y s 5 y for all s > 1 1. In his siuaion, he logic of proposiion 2 implies ha, a ime, a he onse of he boom, i is opimal o impose

15 heory of capial conrols 91 resricions on shor-erm capial inflows, ha is, o ax bonds wih oneperiod mauriy and leave long-erm capial inflows unresriced. 9 This example provides a differen perspecive on why governmens may ry o aler he composiion of capial flows in favor of longer mauriy flows in pracice ðsee Magud, Reinhar, and Rogoff 2011Þ. In our model, incenives o aler he composiion of capial flows do no come from he fear of ho money bu from larger benefis of erms-of-rade manipulaion in he shor run. Finally, proposiion 2 has sharp implicaions for he srucure of opimal capial conrols in he long run. Corollary 2 ðno ax in a seady saeþ. In he long run, if endowmens converge o a seady sae, y y, hen axes on inernaional capial flows converge o zero, v 0. Corollary 2 is reminiscen of he Chamley-Judd resul ð Judd 1985; Chamley 1986Þ of zero capial income ax in he long run. Inuiively, he home governmen would like o use is monopoly power o influence ineremporal prices o favor he presen value of is income. However, a a seady sae all periods are symmeric, so i is no opimal o manipulae relaive prices. Noe ha a seady sae may be reached wih a posiive or negaive ne financial posiion. Which of hese cases applies depends on he enire sequence fy g. Our analysis demonsraes ha axes on inernaional capial flows are unaffeced by hese long-run relaive wealh dynamics. For insance, even if Home, say, becomes heavily indebed, i is no opimal o lower long-run ineres raes. In our model, even away from a seady sae, axes on inernaional capial flows are deermined by he endowmens a and 1 1 only. C. An Example wih CRRA Uiliy and Aggregae Flucuaions Up o now we have focused on he case of a fixed world endowmen. Thus we have looked a how opimal capial conrols respond o a reallocaion of resources beween counries, keeping he oal pie fixed. This provides a useful benchmark in which all flucuaions in consumpion reflec he incenives of he home governmen o manipulae he world ineres rae. Here we show ha if domesic and foreign consumers have idenical CRRA uiliy funcions, hen our resuls exend o economies wih aggregae flucuaions. We also ake advanage of his example for a simple exploraion of he magniudes involved wih opimal capial conrols in erms of quaniies and welfare. Our characerizaion of he opimal policy of he home governmen exends immediaely o he case of a ime-varying world endowmen: one 9 The ax on wo-period bonds is easily shown o be ð1 2 v Þð1 2 v 11 Þ 2 1, and proposiion 1 implies ha i is zero in our example.

16 92 journal of poliical economy jus needs o replace Y wih Y in equaion ð6þ. Under he assumpion of idenical CRRA uiliy funcions, uðcþ 5 u * ðcþ 5 c 12g =ð1 2 gþ wih g 0, his leads o a simple relaionship beween he home share of world endowmens, y =Y, and he home share of world consumpion, c =Y : c =Y 1 2 c =Y 2g 5 m 1 1 g c =Y 2 y =Y 1 2 c =Y : The lef-hand side is decreasing in c =Y, whereas he righ-hand side is increasing in c =Y and decreasing in y =Y. Thus he implici funcion heorem implies ha, along he opimal pah, he home share of world consumpion, c=y, is sricly increasing in he home share of world endowmens, y=y. Pu simply, if uiliy funcions are CRRA, proposiion 1 generalizes o environmens wih aggregae flucuaions. Now consider he wedge beween he marginal uiliy of domesic and foreign consumpion in period. Under he assumpion of CRRA uiliy funcions, we have 5 1 c =Y 2g 2 1: m 1 2 c =Y According o his expression, if c=y is sricly increasing in y=y along he opimal pah, hen is sricly decreasing. The same logic as in Secion III.B herefore implies ha opimal axes on capial flows mus be such ha v < 0 if and only if y 11 =Y 11 > y =Y. In oher words, if uiliy funcions are CRRA, proposiion 2 also generalizes o environmens wih aggregae flucuaions. As a quaniaive illusraion of our heory of capial conrols as dynamic erms-of-rade manipulaion, suppose ha foreign endowmens fy * g are growing a he consan rae g 5 3 percen per year and ha Home is caching up wih he res of he world. To be more specific, suppose ha he home endowmen is one-sixh of world endowmens a dae 0 and ha i is converging oward being one-hird in he long run, wih he raio y =y * converging o is long-run value a a consan speed h 5 0: Figure 3 shows he pah of he home share of world endowmens and consumpion, assuming a uni elasiciy of ineremporal subsiuion, g 5 1. For comparison, we also plo he pah for consumpion in he benchmark case wih no capial conrols. In his case, consisen wih 10 Tha is, we assume ha wih a 5 0:5 > y 0 =y * 0 5 0:2. y =y * 2 a 5 ðy 0 =y * 0 2 aþe 2h ;

17 heory of capial conrols 93 FIG. 3. Opimal allocaion and axes in a counry caching up. In he lef panel, he seeper solid line is he exogenous pah for he endowmen, he flaer dashed line is consumpion a he opimal policy of he home governmen, and he horizonal doed line is he efficien no-ax benchmark. In he righ panel, he upward-sloping solid line wih he axis on he lef is he capial flow ax and he downward-sloping dashed line wih he axis on he righ is he home-asses-o-world-gdp raio. consumpion smoohing, Home consumes a fixed fracion of he world endowmen in all periods. Alhough opimal capial conrols reduce consumpion smoohing, ineremporal rade flows are several imes larger han domesic oupu. The opimal ax on capial inflows is less han 1 percen a dae 0 and is vanishing in he long run, following he same logic as for corollary 2. We see ha he opimal ax on capial inflows decreases as he value of he home deb increases. Compared o he benchmark wih no capial conrols, opimal axes are associaed wih an increase in domesic consumpion of 0.12 percen and a decrease in foreign consumpion of 0.07 percen. Though he welfare impac of opimal capial conrols is admiedly no large in his paricular example, i is no much smaller han eiher he esimaed gains of inernaional rade or financial inegraion. 11 Figure 4 considers an alernaive endowmen pah in which Home falls behind in he shor run, before caching up in he long run. As in he previous example, Home is converging oward having one-hird of world endowmens, wih he raio y =y * converging o is long-run value a a consan speed h 5 0:05. Because of long-run consideraions, we see ha Home borrows in all periods. On he basis of he logic of a woperiod model, one migh herefore have expeced Home o have incenives o ax capial inflows in all periods o reduce domesic bor- 11 According o a fairly large class of rade models, he welfare gains from inernaional rade in he Unied Saes are beween 0.7 percen and 1.4 percen of real GDP ðsee Arkolakis, Cosino, and Rodriguez-Clare 2012Þ. Similarly, he welfare gains from swiching from financial auarky o perfec capial mobiliy are roughly equivalen o a 1 percen permanen increase in consumpion for he ypical non-oecd counry ðsee Gourinchas and Jeanne 2006Þ.

18 94 journal of poliical economy FIG. 4. Opimal allocaion and axes in a counry falling behind before caching up. In he lef panel, he seeper solid line is he exogenous pah for he endowmen, he flaer dashed line is consumpion a he opimal policy of he home governmen, and he horizonal doed line is he efficien no-ax benchmark. In he righ panel, he nonmonoonic solid line wih he axis on he lef is he capial flow ax and he downward-sloping dashed line wih he axis on he righ is he home-asses-o-world-gdp raio. rowing and, in urn, he world ineres rae. Ye we see ha when falling behind, he home governmen has incenives o subsidize raher han ax capial inflows. As discussed earlier, his occurs because capial conrols are guided by he relaive srengh of he desire o aler he ineremporal price of goods beween consecuive periods. In he shor run, he growh rae is negaive, hence he subsidy on capial inflows. The paern of borrowing and lending, per se, is irrelevan. 12 D. Iniial Asses, Deb Mauriy, and Time Consisency So far, we have focused on environmens in which ðiþ here are no iniial asses a dae 0 and ðiiþ one-period bonds are he only asses available. We now briefly discuss how relaxing boh assumpions affecs our resuls. We also show ha if more deb insrumens are available, he opimal allocaion is ime consisen: a fuure governmen free o choose fuure consumpion bu forced o fulfill previous deb obligaions would no wan o deviae from he consumpion pah chosen by is predecessors. 12 I should be clear ha he reason why a counry ha borrows may choose o subsidize raher han ax capial inflows is disinc from he reason why a counry may find subsidies raher han axes welfare enhancing in a saic model wih many goods ðsee, e.g., Feensra 1986; Ioh and Kiyono 1987; Bond 1990Þ. In he previous papers, he opimaliy of subsidies relies on complemenariies in demand across goods, which our model wih addiively separable preferences rules ou. Here, impored goods always face a posiive wedge, i.e., an impor ax, whereas expored goods always face a negaive wedge, i.e., an expor ax; see eq. ð8þ. The reason why a counry ha borrows may choose o subsidize capial inflows is ha axes on one-period bonds are relaed o, bu disinc from, saic rade axes; see eq. ð12þ. Specifically, for a counry ha borrows, a subsidy on one-period bonds, v > 0, is equivalen o a ime-varying impor ax, 11 > > 0; i does no require impor subsidies a any poin in ime.

19 heory of capial conrols 95 Le a,s represen holdings a ime of bonds mauring a ime s. Suppose ha he home consumer eners dae 0 wih iniial asse holdings fa 0; g` 50. The asse holdings now ener he ineremporal budge consrains of he home and foreign consumers. In paricular, he budge consrain of he foreign consumer generalizes o ò50 p ðc * 2 y * 2 a * 0; Þ 5 0; where a * 0; 52a 0; denoes iniial asse holdings abroad. The oher equilibrium condiions are unchanged, so Home s planning problem becomes max fc g b uðc Þ ò50 ðp 0 Þ subjec o ò b u * 0 ðy 2 c Þðc 2 y 1 a * Þ 5 0: 0; 50 ð13þ Compared o he case wihou iniial asses, he only difference is he new implemenabiliy consrain ð13þ ha depends on fy 2 a * 0;g raher han on fy g. Accordingly, proposiion 1 and corollary 1 simply generalize o environmens wih iniial asses fa * g` 0; 50 provided ha hey are resaed in erms of changes in y 2 a * 0; raher han changes in y. Throughou our analysis, we have assumed ha he home governmen can freely commi a dae 0 o a consumpion pah fc g. Now ha we have recognized he role of he iniial asse posiions, his assumpion may seem uncomforably resricive. Afer all, along he opimal pah, he deb obligaions fa * g` ;s s5 held a dae will ypically be differen from he obligaions fa * g` 0;s s5 held a dae 0. Accordingly, a governmen a laer daes may benefi from deviaing from he consumpion chosen a dae 0. We now demonsrae ha his is no he case if he governmen has access o bonds of arbirary mauriy. The basic idea builds on he original insigh of Lucas and Sokey ð1983þ. A any dae, he foreign consumer is indifferen beween many fuure asse holdings fa * g`. 11;s s511 Given a consumpion sequence fc * g ha maximizes her uiliy subjec o her budge consrain, she is indifferen beween any bond holdings saisfying ò p s ðc * s 2 y * s 2 a * 11;sÞ 5 0: ð14þ s511

20 96 journal of poliical economy As we show in Appendix A, his degree of freedom is sufficien o consruc sequences of deb obligaions fa * g` ;s s5 for all 1 such ha he soluion of subjec o max fc sg ò b s uðc s Þ s5 ò b s u * 0 ðy 2 c s Þðc s 2 y s 1 a * Þ 5 0 ;s s5 ð15þ coincides wih he soluion of ðp 0 Þ a all daes 0. In shor, if he home governmen can ener deb commimens a all mauriies, he opimal allocaion derived in Secion III.A is ime consisen. IV. Ineremporal and Inraemporal Trade How do he incenives o ax capial flows change in a world wih many goods? In a one-good economy, he only form of erms-of-rade manipulaion achieved by axing capial flows is o manipulae he world ineres rae. In a world wih many goods, disoring he borrowing and lending decisions of domesic consumers also affecs he relaive prices of he differen goods raded in each period. In his secion, we explore how hese new inraemporal consideraions change opimal capial flow disorions. In order o mainain he focus of our analysis on opimal capial conrols, we proceed under he assumpion ha Home is consrained by an inernaional free-rade agreemen ha prohibis good-specific axes/ subsidies in all periods. As in he previous secion, Home is sill allowed o impose axes on capial flows ha disor ineremporal decisions. This means ha while Home canno conrol he pah of consumpion of each specific good i, i can sill conrol he pah of aggregae consumpion. As we shall see, in general, he pah of aggregae consumpion can affec relaive prices a any poin in ime, hus creaing addiional room for erms-of-rade manipulaion, even for counries ha canno affec he world ineres rae. A. The Monopolis Problem Revisied The basic environmen is he same as in Secion II.A, excep ha here are n > 1 goods. Thus domesic consumpion and oupu, c and y, are now vecors in R n 1. We assume ha he domesic consumer has addiively separable preferences represened by

21 heory of capial conrols 97 ò b U ðc Þ; 50 where U is increasing and sricly concave, C ; gðc Þ is aggregae domesic consumpion a dae, and g is increasing, concave, and homogeneous of degree one. Analogous definiions apply o U * and C * ; g * ðc * Þ. In he absence of axes, he ineremporal budge consrain of he home consumer is now given by ò p ðc 2 y Þ 0; 50 where p R n 1 denoes he ineremporal price vecor for period goods and is he inner produc. A similar budge consrain applies in Foreign. As in Secion II.B, we use he primal approach o characerize he opimal policy of he home governmen. In his new environmen, he home governmen s objecive is o se consumpion fc g in order o maximize he lifeime uiliy of is represenaive consumer subjec o ðiþ uiliy maximizaion by he foreign represenaive consumer a ðundisoredþ world prices p, ðiiþ marke clearing in each period, and ðiiiþ a free-rade agreemen ha rules ou good-specific axes or subsidies. Consrain i can be deal wih as we did in he one-good case. In vecor noaion, he firs-order condiions associaed wih uiliy maximizaion by he foreign consumer generalize o b U * 0 ðc * Þrg * c ðc* Þ 5 l* p ; ð16þ ò p ðc * 2 y * Þ 5 0: ð17þ 50 Nex, noe ha if Home canno impose good-specific axes or subsidies, he relaive price of any wo goods i and j in period, p i =p j, mus be equal in he wo counries and equal o he marginal raes of subsiuion g i ðc Þ=g j ðc Þ and g * i ðc * Þ=g * j ðc* Þ. Accordingly, he consumpion allocaion ðc ; c * Þ in any period is Pareo efficien and solves C * ðc Þ 5 maxfg * ðc * Þ subjec o c 1 c * 5 Y and gðcþ C g c;c* ð18þ for some C. Therefore, consrains ii and iii can be capured by leing Home choose an aggregae consumpion level C, which idenifies a

22 98 journal of poliical economy poin on he saic Pareo fronier. The consumpion vecors a ime are hen given by he corresponding soluions o problem ð18þ, which we denoe by cðc Þ and c * ðc Þ. We can hen sae Home s planning problem in he case of many goods as max fc g ò b U ðc Þ 50 ðp 0 Þ subjec o ò b rðc Þ½cðC Þ 2 y Š 5 0; 50 ð19þ where rðc Þ ; U *0 ðc * ðc ÞÞrg * ðc * ðc ÞÞ: Equaion ð19þ is he counerpar of he implemenabiliy consrain in Secion II.B. In line wih our previous analysis, we assume ha rðc Þ ½cðC Þ 2 y Š is a sricly convex funcion of C. This implies he uniqueness of he soluion o ðp 0 Þ. B. Opimal Allocaion Wih many goods, he firs-order condiion associaed wih Home s planning problem generalizes o U 0 ðc Þ 5 m rðc Þ ycðc Þ yc 1 yrðc Þ ½cðC Þ 2 y Š yc ; ð20þ where m sill denoes he Lagrange muliplier on he implemenabiliy consrain. Armed wih condiion ð20þ, we can now follow he same sraegy as in he one-good case. Firs, we will characerize how fc g covaries wih fy g along he opimal pah. Second, we will derive he associaed implicaions for he srucure of opimal capial conrols. The nex proposiion describes he relaionship beween domesic consumpion and domesic endowmens along he opimal pah. Proposiion 3 ðprocyclical aggregae consumpionþ. Suppose ha beween periods and 1 1 here is a small change in he home endowmen dy 11 5 y 11 2 y. Then he home consumpion is higher in period 1 1, C 11 > C, if and only if yrðc Þ=yC dy 11 > 0. In he one good case, yrðc Þ=yC simplifies o 2u *00 ðy 2 c Þ, which is posiive by he concaviy of u *. Therefore, wheher domesic consumpion grows or no depends only on wheher he level of domesic en-

23 heory of capial conrols 99 dowmens is increasing or decreasing. In he muligood case, by conras, his also depends on he composiion of domesic endowmens and on how relaive prices respond o changes in C. In order o highligh he imporance of hese composiional effecs, in an economy wih many goods, consider he effec of a small change in domesic endowmen ha leaves is marke value unchanged a period prices. Tha is, suppose rðc Þdy In he one-good case, his can happen only if he endowmen level does no change, hereby leading o a zero capial flow ax. In he muligood case, his is no longer rue. According o proposiion 3, consumpion would grow if and only if r 0 i ðc Þ Cov r i ðc Þ ; r iðc Þdy i11 > 0: Here, wha maers is wheher he composiion of endowmens ils oward goods ha are more or less price sensiive o changes in C. We will come back o he role of his composiional effec in more deail in Secion IV.D. C. Opimal Taxes on Inernaional Capial Flows In line wih Secion III.B, le us again assume ha consumers can rade only one-period bonds on inernaional capial markes. Bu compared o Secion III.B, suppose now ha here is one bond for each good. Since he home governmen canno impose good-specific axes/subsidies, i mus impose he same proporional ax v on he gross reurn on ne lending in all bond markes. So he per-period budge consrain of he domesic consumer akes he form p 11 a 11 1 p c 5 p y 1 ð1 2 v 21 Þðp a Þ 2 l ; where a R n 1 now denoes he vecor of curren asse posiions and l is a lump-sum ax. As before, he domesic consumer is subjec o he no- Ponzi condiion, lim ` p a 0. The firs-order condiions associaed wih uiliy maximizaion a home are given by U 0 ðc Þg i ðc Þ 5 bð1 2 v Þð1 1 r i ÞU 0 ðc 11 Þg i ðc 11 Þ for all i 5 1; :::;n; ð21þ where r i ; p i =p i is a good-specific ineres rae. Le P ; min c fp c : gðcþ 1g denoe he home consumer price index a dae. Wih his noaion, he previous condiions can be rearranged in a more compac form as