Foreign Exchange Reserves as a Tool for Capital Account Management

Transcription

1 Foreign Exchange Reserves as a Tool for Capial Accoun Managemen J. Sco Davis, Ippei Fujiwara, Kevin X.D. Huang and Jiao Wang Globalizaion Insiue Working Paper 352 Research Deparmen hps://doi.org/ /gwp352 Working papers from he Federal Reserve Bank of Dallas are preliminary drafs circulaed for professional commen. The views in his paper are hose of he auhors and do no necessarily reflec he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem. Any errors or omissions are he responsibiliy of he auhors.

2 Foreign Exchange Reserves as a Tool for Capial Accoun Managemen * J. Sco Davis, Ippei Fujiwara, Kevin X.D. Huang and Jiao Wang ± February 5, 2019 Absrac Many recen heoreical papers have argued ha counries can insulae hemselves from volaile world capial flows by using a variable ax on foreign capial as an insrumen of moneary policy. Bu a he same ime many empirical papers have argued ha only rarely do we observe hese cyclical capial axes used in pracice. In his paper we consruc a small open economy model where he cenral bank can engage in serilized foreign exchange inervenion. When privae agens can freely buy and sell foreign bonds, serilized foreign exchange inervenion has no effec. Bu we analyically prove ha when privae agens canno freely buy and sell foreign bonds, ha is, under acyclical capial conrols, opimal serilized foreign exchange inervenion is equivalen o an opimally chosen ax on foreign capial. Numerical simulaions of he model show ha a variable capial ax is a reasonable approximaion for serilized foreign exchange inervenion under he levels of capial conrols observed in many emerging markes. Keywords: Cenral bank, small open economy, foreign exchange reserves, capial conrols JEL Codes: E50; E30; F40 * We would like o hank Zheng Liu, Enrique Mendoza, Mark Spiegel, Marin Uribe, Yi Wen, Vivian Yue, and seminar paricipans a he Federal Reserve Banks of Dallas and Boson and Osaka Universiy, he China Meeing of he Economeric Sociey, and he Shanghai Macro Workshop for many helpful commens and suggesions. The views presened here are hose of he auhors and do no necessarily represen he views of he Federal Reserve Bank of Dallas or he Federal Reserve Sysem. Corresponding auhor: J. Sco Davis, Federal Reserve Bank of Dallas, 2200 N. Pearl Sree, Dallas, TX 75201, USA, sco.davis@dal.frb.org. Ippei Fujiwara, Keio Universiy and Ausralian Naional Universiy, ippei.fujiwara@keio.jp. Kevin X.D. Huang, Vanderbil Universiy, kevin.huang@vanderbil.edu. ± Jiao Wang, Universiy of Melbourne, jiao.wang@unimelb.edu.au. 1

3 1 Inroducion Repeaed cycles of capial flows ino and ou of emerging markes are a fixure of he financially inegraed global economy. Rey (2015) and Forbes and Warnock (2012) argue ha capial flows ino and ou of emerging markes are largely driven by global facors. Surges in capial inflows have led o alk of currency wars and he danger of overheaing in many emerging markes. Likewise, a sudden reversal of capial flows is ofen he reason behind financial and macroeconomic insabiliy in many emerging markes. Rey (2015) argues ha his cycle of capial inflows and ouflows means ha he rilemma of inernaional finance is acually more of a dilemma, and ha independen moneary policies are possible if and only if he capial accoun is managed. 1 In 2012 he IMF argued ha acive capial conrols migh be a useful policy insrumen o manage he macroeconomic and financial risks associaed wih large swings in capial inflows and ouflows (Inernaional Moneary Fund (2012)). This has led o a renewed ineres in capial conrols as a ool for acive capial accoun managemen. Jeanne e al. (2012) argue ha capial conrols properly designed... migh even be a regular insrumen of economic policy (p. 95). Farhi and Werning (2012) inroduce capial accoun managemen measures as a variable ax, τ, on he price of foreign bonds. 2 In his model, and ohers ha model capial conrols in a similar way, he variable ax affecs flucuaions in ne capial ouflows. This is a separae policy insrumen ha he policy maker can adjus in real ime o achieve some policy objecive like welfare maximizaion. Theory suggess ha hese variable capial conrols 1 The rilemma has been a feaure of he inernaional macroeconomics lieraure since Mundell (1963). The rilemma saes ha a counry canno simulaneously mainain a fixed exchange rae, an open capial accoun, and moneary policy auonomy. In echnical erms, he fac ha he combinaion of a fixed exchange rae and an open capial accoun lead o he loss of moneary policy auonomy is purely mechanical. When a cenral bank mainains a fixed exchange rae, he cenral bank s moneary policy akes he form of a rule saing ha he nominal exchange rae is held consan. So for insance, in response o a fall in ne capial inflows, he cenral bank is forced o raise he ineres rae o arac capial flows and preven depreciaion. 2 For oher examples of models wih his ype of variable capial conrol ax, see Schmi-Grohe and Uribe (2012b), Schmi-Grohe and Uribe (2012a), Cosino e al. (2014), De Paoli and Lipinska (2013), Korinek (2013), Farhi and Werning (2014), Benigno e al. (2016), Davis and Presno (2017), Aoki e al. (2016), Schmi-Grohe and Uribe (2016). 2

4 should be cyclical and should vary wih booms and buss in ne capial flows. Bu while hese variable capial axes are inuiive and easy o implemen in a model, he empirical evidence ha policy makers make use of hese variable capial conrols is lacking. Eichengreen and Rose (2014) and Fernnandez e al. (2015) find ha in pracice capial conrols are acyclical and do no respond o booms and buss in oupu, he curren accoun, or he real exchange rae. Klein (2012) and Forbes e al. (2015) argue ha emporary, episodic ype capial conrols, wha Klein refers o as capial conrol gaes, end o be ineffecive. 3 Moreover, Klein argues ha permanen capial conrols, wha he refers o as capial conrol walls, can be effecive a deflecing capial inflows (alhough hey may come a a high cos in erms of los growh, so while hey are effecive, wheher hey are beneficial is anoher sory). 4 We begin his paper wih wo simple empirical observaions. Firs, emerging markes mainain significan capial conrols, while he advanced economies have basically eliminaed capial conrols. These capial conrols are very persisen and unchanging, Klein s wallype capial conrols. Second, cenral bank foreign exchange inervenions are frequenly observed in emerging marke economies bu no in advanced economies. While cenral bank reserve accumulaion ends o be small and uncorrelaed wih oher ypes of capial flows in mos advanced economies, reserve accumulaion is a large and volaile componen of he balance of paymens in mos emerging markes, and i is highly correlaed wih capial inflows from abroad, indicaing ha many emerging marke cenral banks adjus heir sock of foreign exchange reserves in andem wih surges and sops in capial inflows in order o 3 Forbes e al. (2016) argue ha he episodic capial conrols ha Brazil pu in place during and afer he recen crisis did have he effec of deflecing capial flows away from Brazil and owards oher emerging markes, alhough hey argue ha he effec was more likely due o he signaling naure of imposing capial conrols and less due o he effec of he conrols hemselves. 4 Similarly, Ghosh e al. (2014) find ha capial conrols can be effecive a limiing he frequency and magniude of capial inflow surges. In line wih he heory of he rilemma, a number of papers show ha imposing capial accoun resricions leads o a significan increase in moneary policy auonomy, paricularly for counries wih a fixed exchange rae. See e.g. Shambaugh (2004), Obsfeld e al. (2005), Baba and Kokenyne (2011), Magud e al. (2011), and Klein and Shambaugh (2015). However in his paper we are enirely concerned wih counries wih a floaing currency and an independen moneary policy. 3

5 smooh flucuaions in he curren accoun. 5 In simple cross-counry regressions we show ha counries ha have greaer capial conrols end o be more acive in using foreign exchange inervenion. We hen consruc a small open economy dynamic sochasic general equilibrium (DSGE) model where he cenral bank can engage in serilized foreign exchange inervenion ha explain hese resuls. In he model we inroduce cash and a cenral bank balance shee ino a model of a small open economy. The cenral bank poenially has wo insrumens, he size of is balance shee and he composiion of is balance shee. Boh are se opimally o maximize household welfare. The firs insrumen deermines he money supply and hus he ineres rae, he second insrumen deermines he cenral bank s sock of foreign bonds, which can (poenially) be adjused o smooh flucuaions in ne capial flows. The effeciveness of serilized foreign exchange inervenion depends on fricions or adjusmen coss which deermine how easily privae agens can buy or sell foreign bonds, as in Gabaix and Maggiori (2015). We show ha when privae agens can freely buy and sell foreign bonds, serilized foreign exchange inervenion has no effec, and opimal policy wih wo insrumens, boh he size and composiion of is balance shee, is equivalen o opimal policy where he cenral bank only has one insrumen, he size of he balance shee. This finding of he ineffeciveness of serilized foreign exchange inervenion in a fricionless environmen echoes ha in Obsfeld (1981) and Backus and Kehoe (1989). In our conribuion we prove ha when privae agens canno freely buy and sell foreign bonds, opimal serilized foreign exchange inervenion is equivalen o he opimally chosen variable capial conrol ax from Farhi and Werning (2012). We provide analyical proofs of he wo ses of equivalence resuls. The model ha we use o prove hese equivalence resuls is very general, and we do no need o specify he funcional forms describing he behavior of privae agens. 5 In heir revised exchange rae classificaion sysem, Ilzezki e al. (2019), argue ha many counries fall ino he managed floa or managed peg caegory, and few counries ruly allow he exchange rae o floa. Similarly, Ghosh e al. (2016) find ha emerging marke cenral banks acively use serilized foreign exchange inervenion o smooh he booms and buss in ne capial inflows. Bussere e al. (2015) argue ha here is a complemenariy beween reserve accumulaion and capial conrols. 4

6 These equivalence resuls hold wihou recourse o firm side specificaions, and hold under any ype of fricions, or lack of fricions (nominal, financial, ec.) ha we see in oday s New Keynesian DSGE lieraure. We hen build a fully specified model for numerical simulaion of he equivalence resuls. The model is similar o he one in Chang e al. (2015). 6 We map he observed levels of capial conrols in he daa ino he adjusmen cos parameer in he model ha deermines how easily privae agens can buy or sell foreign bonds. As in Gabaix and Maggiori (2015), capial conrols increase he effeciveness of foreign exchange inervenion. We show ha under levels of capial conrols ha are observed in many emerging marke counries, serilized foreign exchange inervenion can be an effecive ool for capial accoun managemen. Under hese observed levels of capial conrols, a model wih an opimally chosen variable capial conrol ax is a reasonable approximaion o a more complex model wih a cenral bank balance shee and serilized foreign exchange inervenion. Thus in his paper we make a purely posiive conribuion. We show ha under he levels of acyclical "wall-ype" capial conrols ha are observed in many emerging markes, he cenral bank can use serilized foreign exchange inervenion o sabilize he curren accoun in he face of volaile capial inflows. Our equivalence resul provides a jusificaion for he use of a variable capial ax in a model as a capial accoun managemen measure even when hese variable capial axes are no observed in pracice. The remainder of his paper is organized as follows. In secion 2 we presen some simple descripive saisics describing capial conrols and cenral bank reserve accumulaion in boh advanced and emerging marke economies. The generalized small open economy model where he cenral bank can engage in serilized foreign exchange inervenion is presened in secion 3. The proof of he equivalence beween serilized foreign exchange inervenion 6 Liu and Spiegel (2015) also compare serilized foreign exchange inervenion wih variable capial conrols, bu in heir model, variable capial conrols apply only o capial inflows, no oal ne flows. Thus in heir version of variable capial conrols, he cenral bank does no have complee conrol over ne flows (i.e. he curren accoun) and hus hey find ha even when using variable capial conrols, here is room for welfare improvemen from serilized foreign exchange inervenion. 5

7 and a variable capial ax are presened in secion 4. The resuls from a numerical model are presened in secion 5. Finally secion 6 concludes. 2 Descripive Saisics on Reserve Accumulaion The index of capial accoun resricions from Chinn and Io (2006) is presened in Figure 1. This figure shows he simple average of he Chinn-Io index, KAOpen, updaed hrough 2015, for a sample of 23 advanced counries and a sample of 66 emerging marke and developing counries. We re-normalize he original Chinn-Io index o a 0-1 scale, where 0 represens no capial accoun resricions and 1 represens a closed capial accoun. The figure shows ha on average, advanced economies have fewer capial accoun resricions, and in 1970 he average value of he Chinn-Io index in he advanced economies was 0.50 and in emerging and developing economies i was around 0.7. The figure also shows ha over he pas 45 years, here has been a near monoonic decrease in he level of he Chinn-Io index of capial accoun resricions in he advanced economies, and now capial accoun resricions in he advanced economies are close o 0. Meanwhile capial accoun resricions in he emerging markes increased subsanially in he 1980s, before falling in he 1990s and 2000s. Ineresingly capial accoun resricions have acually increased slighly in he emerging markes since he crisis in The curren accoun (CA) is equal o savings minus invesmen, and is equal o a counry s ne savings. The capial and financial accoun (KA, for breviy, henceforh we refer o he capial and financial accoun by he colloquial erm capial accoun) is equal o capial ouflows minus capial inflows: he ne purchase of foreign asses by domesic residens (no he cenral bank) minus he ne purchase of domesic asses by foreign residens, and hus measures a counry s ne foreign asse purchases no including cenral bank foreign asse purchases. 7 Cenral bank ne purchases have a special line-iem in he balance of 7 Since he release of Balance of Paymens Manual 5 in 1993, he IMF and oher inernaional organizaions disinguish beween he capial accoun and he financial accoun when recording inernaional asse 6

8 paymens accouns, foreign exchange reserve accumulaion ( R). This leads o he fundamenal balance of paymens ideniy where a counry s ne savings should equal is ne purchases of foreign asses, boh by he cenral bank and he res of he economy, and hus CA = KA + R. 8 Some saisics describing he sandard deviaion of he curren accoun, capial accoun, reserve accumulaion and he componens of he capial accoun (Capial ouflows, OF, and Capial inflows, IF, as well as he subcomponens of ouflows and inflows, FDI flows, Porfolio flows, and Oher flows, where oher is mosly bank lending) are presened in Table 1. All capial flows are annual and all are normalized by GDP. The able presens he average sandard deviaion in he advanced and emerging marke economies over he period. To ensure ha any resuls are no driven solely by he 2008 crisis and subsequen recession, we also calculae he same saisics over he period. Reserve accumulaion is he leas volaile enry in he balance of paymens saisics in he advanced counries, where he sandard deviaion of reserve accumulaion is far smaller han he sandard deviaions of boh he curren accoun and he capial accoun, and also far smaller han any of he componens or subcomponens of he capial accoun. In conras reserve accumulaion is one of he mos volaile enries in he balance of paymens saisics in he emerging markes. The sandard deviaion of reserve accumulaion is nearly he same purchases. The capial accoun involves he ne purchase of all non-financial asses (e.g. land and naural resource righs, leases and licenses, markeing capial, brand names, and goodwill). The cross-border purchases of non-financial asses (he capial accoun) is generally very small relaive o cross-border purchases of financial asses (he financial accoun), and hus for breviy, we jus refer o all ne asse purchases as he capial accoun. 8 In his paper, we follow he simple asse/liabiliy approach from BPM6 accouning where a posiive ne purchase of foreign asses is recorded as posiive capial ouflows, as in Broner e al. (2013). Under his accouning sandard, posiive ne purchases of foreign asses would resul in a posiive capial and financial accoun. Some papers insead follow he direcion of flow principle from BPM5 accouning and consider ha posiive ne purchases of foreign asses by domesic residens is a cash ouflow from he domesic counry o be recorded wih a negaive sign, as in Forbes and Warnock (2012). Under his accouning sandard, a posiive ne purchase of foreign asses would be a cash ouflow and hus would resul in a negaive capial and financial accoun. Thus under BPM5 accouning, he balance of paymens ideniy is commonly wrien as he curren accoun plus he capial and financial accoun is equal o he ne change in reserves. 7

9 as he sandard deviaion of he curren accoun and he capial accoun, and i is greaer han he sandard deviaion of any of he subcomponens of he capial accoun. The correlaions beween reserve accumulaion and he componens of he capial accoun are repored in he op half of Table 2. The correlaion beween reserve accumulaion and any of he componens of capial ouflows is small in boh he advanced economies and he emerging markes. However, he able shows ha he correlaion beween reserve accumulaion and capial inflows is close o 0 in he advanced economies bu close o 0.5 in he emerging markes. The boom half of he able repors he correlaions beween he hree componens of he balance of paymens ideniy. We have already seen in Table 1 ha in he advanced economies, he sandard deviaion of he ne change in offi cial reserves is small. So no surprisingly, he correlaion beween he curren accoun and he capial accoun in he advanced economies is close o 1. The sandard deviaion of reserve accumulaion is high in he emerging markes, and reserve accumulaion is posiively correlaed wih capial inflows. As a resul, he correlaion beween reserve accumulaion and he capial accoun is close of 0.5 in he emerging markes. Tha negaive correlaion beween reserve accumulaion and he capial accoun, combined wih he fac ha reserve accumulaion is relaively volaile in he emerging markes, means ha he correlaion beween he curren accoun and he capial accoun is only around 0.5 in he emerging markes. Thus he level of capial conrols ends o be higher in emerging markes, and a he same ime reserve accumulaion is more volaile, and more highly correlaed wih capial inflows and oher iems in he balance of paymens in emerging markes. In Table 3 we regress he relaive sandard deviaion and correlaion of reserve accumulaion and oher iems in he balance of paymens on he naural log of he Chinn-Io capial accoun resricions index, KAOpen, across he 89 counries in he sample. The capial accoun resricions index is poenially endogenous, counries ha face very volaile exernal capial flows may impose 8

10 high capial accoun resricions, so in addiion o he OLS resuls, he able presens wo sage leas squares (TSLS) resuls where he Chinn-Io index is insrumened by a measure of domesic financial secor liberalizaion from Abiad e al. (2010). 9 The firs four lines of he able regress he relaive volailiy of reserve accumulaion on he measure of capial accoun resricions: firs he sandard deviaion of reserve accumulaion relaive o he sandard deviaion of he curren accoun, hen relaive o he sandard deviaion of he capial accoun, he sandard deviaion of capial inflows, and he sandard deviaion of capial ouflows. In nearly every case he coeffi cien of he capial accoun resricions index is posiive and significan, indicaing ha as capial accoun resricions increase, he volailiy of reserve accumulaion relaive o he oher iems in he balance of paymens increases. In he nex hree rows in he able, he dependen variable is a correlaion beween wo of he hree componens of he balance of paymens ideniy (CA = KA + R). As expeced, given he conras beween advanced and emerging markes in he earlier se of descripive saisics, he correlaion beween he curren accoun and he capial accoun falls as capial accoun resricions increase, and he correlaion beween reserve accumulaion and he curren accoun increases. Ineresingly here is no relaionship beween he capial accoun resricions and he correlaion beween reserve accumulaion and he capial accoun. Finally, in he remaining rows in he able, he dependen variable is he correlaion beween reserve accumulaion and one of he subcomponens of he capial accoun. As expeced, given he descripive saisics presened earlier, here is lile evidence ha capial accoun resricions affec he correlaion beween reserve accumulaion and capial ouflows, or any of he subcomponens of capial ouflows. Bu he coeffi ciens on he regressions involving he correlaion beween reserve accumulaion and capial inflows, or any of he subcomponens of capial inflows, are posiive and highly significan. 9 The Abiad e al. measure of financial liberalizaion conains boh a componen relaed o domesic financial liberalizaion and a componen relaed o inernaional financial liberalizaion (capial accoun openness). For an insrumen, we use he measure only relaed o domesic financial liberalizaion. 9

11 3 Model In he model here are wo counries, home and foreign. The home counry is of size n and he foreign counry is of size 1 n, and we consider he case of he small open economy where n 0. The home economy is populaed by a represenaive household and a coninuum of firms. There is a cenral bank which ses he domesic money supply, and under differen policy scenarios may se a ax rae on foreign borrowing/lending or may aler heir sock of foreign exchange reserves. In his secion, we will presen he analyical model in is general form wihou recourse o mos of he specific funcional forms of he model, o show ha our key analyical resuls hold broadly for a large class of models. In he nex secion, we will specify a se of funcional forms in a paricular model for numerical simulaions. 3.1 Households In he small open home economy, he represenaive household chooses consumpion, C, real money balances, M P, labor effor, H, and socks of domesic and foreign currency denominaed bonds, B and F, o maximize expeced lifeime uiliy given by: max E 0 =0 β U ( C, M ), H P (1) subjec o heir sequence of budge consrains: ( ) P C + M + B + (1 τ ) S F + P χω ˆF (2) = W H + M 1 + (1 + i 1 ) B 1 + ( 1 + Φ 1 i 1 ) S F 1 + Π + Π cb where U is an increasing, concave funcion, B is he household s sock of domesic currency denominaed bonds, F is heir sock of foreign currency denominaed bonds, S is he 10

12 nominal exchange rae (in unis of he home currency per unis of he foreign currency), P is he consumer price level, W is he nominal wage rae, i is he nominal ineres rae on home currency denominaed bonds, i is he nominal ineres rae on foreign currency denominaed bonds, Π represens he profis of domesic firms, τ is a ax on he purchase of foreign bonds, and Π cb represens he cenral bank profis. Boh firm and cenral bank profis ( ) are reurned lump sum o he household. β is he household s discoun facor. χω ˆF is an adjusmen cos and is a funcion of he household s holdings of foreign bonds, where ˆF = F F ss and F ss is he seady sae value of F. The funcion Ω ( ) is differeniable and sricly convex and saisfies Ω (0) = Ω (0) = 0, where Ω denoes he firs derivaive of Ω( ), as in Schmi-Grohe and Uribe (2003). Φ 1 is a risk premium shock ha affecs home counry borrowing in he foreign currency. Neumeyer and Perri (2005) show how imporan hese counry-specific risk premium shocks are for explaining business cycle flucuaions in an emerging marke economy. 10 Wih Λ denoed as he marginal uiliy of household consumpion in period, he firsorder condiions of he household s problem wih respec o B and F are: Λ P = β (1 + i ) E ( Λ+1 P +1 ) (3) ( ( )) ( ) (1 τ )S + P χω Λ ˆF = β (1 + Φ i Λ+1 ) E S +1 P P +1 (4) The variable τ is a policy variable. In one scenario we will give he cenral bank he abiliy o conrol his ax τ on he purchase of foreign currency denominaed bonds. In oher policy scenarios we will simply se τ = 0. The subsiuion of equaion (3) ino equaion 10 The ype of shock is no imporan for he analyical proofs of equivalence. We consider a shock o he world ineres rae, bu he same resuls would hold under oher ypes of shock common in he New Keynesian lieraure. 11

13 (4) gives: 1 + i 1 + Φ i = E ( Λ+1 P +1 S +1 ) E ( Λ+1 P +1 ) ( (1 τ ) S + P χω ( ˆF )) (5) In a linearized model we can ignore he covariance beween Λ +1 P +1 and S +1, and he ( ) E Λ+1 P +1 erms cancel ou of he numeraor and denominaor, leading o he familiar uncovered ineres pariy (UIP) condiion. We linearize he model laer in he numerical resuls secion, bu for now, we leave he UIP condiion in his more general form. Home households own home counry firms. For now we are agnosic abou he firm s producion funcion or any ype of fricions he firm faces. Those deails are no necessary for he analyical proofs of equivalence. We will fill in hose deails when discussing he funcional forms for he numerical simulaion model. 3.2 Moneary Policy The cenral bank solves a Ramsey problem o maximize household welfare in (1). We describe ha Ramsey problem and he planner s consrains laer in his secion. The cenral bank issues nominal money balances, M, and uses i o finance holdings of home currency and foreign currency denominaed bonds, B cb and F cb. I conducs moneary policy by adjusing he sock of money and is socks of home and foreign currency denominaed bonds subjec o is balance shee given by: M = B cb + S F cb (6) The cenral bank poenially has a few moneary policy insrumens. One moneary insrumen is he nominal money supply. Given he household s firs-order condiions wih respec o real money balances and domesic currency bond holdings, conrolling he nominal money supply is anamoun o conrolling he nominal ineres rae i The subsiuion of hese wo firs-order condiions yields he demand for real money balances as a funcion of he home nominal ineres rae. 12

14 The second insrumen has o do wih he cenral bank s abiliy o conrol he capial accoun. Here we consider wo scenarios. In boh scenarios he second insrumen is deermined by he soluion o a Ramsey problem o maximize household welfare in (1). In he firs, he cenral bank s sock of foreign currency bonds is held fixed a is seady sae value, F cb = F cb ss, bu he cenral bank can adjus he variable ax τ on he purchase of foreign currency denominaed bonds by privae agens. In he second scenario, his variable ax τ = 0, bu he cenral bank can adjus he sock of foreign currency bonds on heir balance shee, F cb. The cenral bank earns a posiive ineres rae on is asses bu pays no ineres on is liabiliies, so is seigniorage revenue is given by: (M M 1 ) ( B cb ) ( (1 + i 1 ) B 1 cb S F cb ( ) ) 1 + Φ 1 i 1 S F 1 cb (7) = i 1 B cb 1 + (S S 1 ) F cb 1 + Φ 1 i 1S F cb 1 In addiion if he cenral bank can charge a variable ax τ on purchases of foreign bonds hen he revenue from his ax is τ S F. The cenral bank also faces an adjusmen cos, denoed by χ cb Ω( ˆF cb = F cb F cb ss. saisfies Ω (0) = Ω (0) = 0. cb ˆF ), o adjusing is sock of foreign currency denominaed bonds, where Recall ha he funcion Ω( ) is differeniable and sricly convex and Thus he cenral bank profis are given by seigniorage revenue ne of any ax revenue and bond adjusmen cos: Π cb = i 1 B 1 cb + (S S 1 ) F 1 cb + Φ 1 i 1S F 1 cb τ S F P χ cb cb Ω( ˆF ) (8) 13

15 3.2.1 Bond Marke Clearing Condiions Home currency denominaed bonds are held exclusively by home counry households and he home counry cenral bank. Thus he marke clearing condiion for home currency denominaed bonds is: B + B cb = 0 (9) Foreign counry bonds are held by home households, he home counry cenral bank, foreign households, and he foreign counry cenral bank: nf + nf cb + (1 n) F + (1 n) F cb = 0 (10) Noe ha in he limi where n 0, his consrain does no link home counry household and cenral bank holdings of foreign currency denominaed bonds, F and F cb, and is no a consrain from he perspecive of he home counry. 3.3 The balance of paymens ideniy Cenral bank profis in equaion (8), he cenral bank s balance shee in equaion (6), and he home currency bond marke clearing condiion in equaion (9) can be subsiued ino he household s budge consrain in equaion (2) o yield he budge consrain for he small open economy: ( ) ( ( ) P C W H Π + S F + F cb 1 + Φ 1 i 1) S F 1 + F 1 cb (11) = P χω( ˆF ) P χ cb Ω( ˆF cb ) The firs erm in his economy-wide budge consrain, P C W H Π represens ne impors of he home counry, or he negaive of he rade balance and hus his economywide budge consrain can be rewrien as he fundamenal balance of paymens ideniy, 14

16 where he curren accouns equal o he capial accoun plus he ne change in cenral bank foreign exchange reserves, CA = KA + R. Specifically, he curren accoun is equal o ne expors plus ne primary ineres income (ne ineres income on foreign currency denominaed bonds): CA = W H + Π P C + Φ 1 i 1S F 1 + Φ 1 i 1S F 1 cb P χω( ˆF ) P χ cb cb Ω( ˆF ) The capial accoun is equal o he negaive change in he household s sock of foreign currency denominaed bonds: KA = S F S F 1 (12) And finally he change in he cenral bank s sock of foreign currency denominaed bonds is given by: R = S F cb S F cb 1 (13) 4 Proofs of wo equivalence resuls The Ramsey policymaker ses policy o maximize household welfare (1) subjec o srucural consrains ha include he economy-wide budge consrain (11), he UIP condiion (5), a se of firs order condiions from households uiliy maximizaion, a se of firs order condiions from firms profi-maximizaion and cos-minimizaion problems, and marke clearing condiions. We presen here analyical proofs of our wo equivalence resuls. Firs we show ha, when households can freely buy and sell foreign currency denominaed bonds, Ramsey opimal policy when he cenral bank adjuss is sock of foreign bonds is equivalen o he oucome 15

17 under Ramsey opimal policy when he cenral bank does no use foreign exchange reserves as an addiional policy insrumen. In oher words, wih an open capial accoun his addiional policy insrumen is redundan. Second, we prove ha Ramsey opimal policy when he cenral bank uses a variable ax rae on privae holdings of foreign currency denominaed bonds as an addiional policy insrumen is equivalen o he oucome under Ramsey opimal policy when he cenral bank insead uses foreign exchange reserves as an addiional policy insrumen bu households canno buy or sell foreign bonds. Specifically we consider Ramsey opimal policy under four policy scenarios: 1. In he firs, he cenral bank s only insrumen is he money supply. The cenral bank has no separae insrumen for capial accoun managemen (i.e., τ = 0 and ˆF cb = 0). Households can buy and sell foreign bonds freely (i.e., he capial accoun is open). 2. In he second, he cenral bank has wo insrumens, he money supply and he variable ax rae τ on households holdings of foreign currency denominaed bonds. 3. In he hird, he cenral bank has wo insrumens, he money supply and is sock of foreign currency denominaed bonds F cb. Households canno buy or sell foreign bonds (i.e., he capial accoun is closed so ˆF = 0). 4. In he fourh, he cenral bank has wo insrumens, he money supply and is sock of foreign currency denominaed bonds F cb. Households can buy and sell foreign bonds freely (i.e., he capial accoun is open). A crucial firs sep in our analyical proofs is o noe ha among he consrains faced by he Ramsey policymaker, he policy insrumens τ and F cb appear in only wo condiions, he economy wide budge consrain (11) and he UIP condiion (5). Thus hese are he only wo condiions ha may differ across he four policy scenarios. All oher condiions in he planner s consrain se are idenical across he four scenarios. 16

18 4.1 Proof of equivalence beween Scenarios 1 and 4 In boh Scenario 1 and Scenario 4 he UIP condiion (5) akes he following form since in boh scenarios τ = 0: 1 + i 1 + Φ i = E ( Λ+1 P +1 S +1 ) E ( Λ+1 P +1 ) (S + P χω ( ˆF ) ). (14) ( ) As discussed before, in a linearized model he E Λ+1 P +1 erms will cancel ou of he numeraor and denominaor of he righ hand side of his expression, leading o he familiar UIP condiion. We will do his laer in a numerical model, bu for now, we leave he UIP condiion in he more general form, as our equivalence proofs do no rely on being able o ( ) ( ) say E Λ+1 P +1 S +1 = E Λ+1 P +1 E (S +1 ). Scenario 1 In his scenario he cenral bank does no use foreign exchange reserves as an addiional policy insrumen, so F cb = F cb ss and ˆF cb = 0. Togeher wih he propery Ω (0) = 0, his implies ha he economy-wide budge consrain (11) simplifies o: ( ) ( ) ( ) P C W H Π + S F + Fss cb 1 + Φ 1 i 1 S F 1 + Fss cb (15) = P χω( ˆF ). Scenario 4 In his scenario he cenral bank uses foreign exchange reserves F cb addiional policy insrumen, so he economy-wide budge consrain (11) remains as: as an ( ) ( ( ) P C W H Π + S F + F cb 1 + Φ 1 i 1) S F 1 + F 1 cb = P χω( ˆF ) P χ cb Ω( ˆF cb ). (16) For his proof, he presence of χ (for boh Scenarios 1 and 4) and χ cb (for Scenario 4) is a sandard device for closing he small open economy model. To serve his echnical purpose 17

19 wihou creaing any maerial fricions or disorions oherwise, i suffi ces o se χ and χ cb o being infiniesimally small. In fac in he curren conex an infiniesimally small χ also serves a dual purpose for making he capial accoun effecively open, which is a condiion assumed in boh Scenarios 1 and 4. Hence we presen wihou loss of generaliy our proof of equivalence beween Scenarios 1 and 4 for he case where χ and χ cb go o zero. I hen follows ha he righ hand sides of boh (15) and (16) go o zero, and so does he las erm in he denominaor on he righ hand side of (14). As a resul, he cenral bank s and households holdings of foreign currency denominaed bonds become perfec subsiues, and hus he cenral bank s use of foreign exchange reserves as an addiional policy insrumen in Scenario 4 does no maerially relax (of course neiher does i ighen) he consrain faced by he Ramsey policymaker beyond ha in Scenario 1. As such, he Ramsey soluion would give rise o idenical curren accoun and oher welfare-relevan macroeconomic variables across Scenarios 1 and 4, and i is only a maer how he (idenical) oal amoun of foreign currency denominaed bonds held a home would be disribued beween households and he cenral bank across he wo scenarios. 4.2 Proof of equivalence beween Scenarios 2 and 3 Scenario 2 In his scenario he cenral bank uses a capial conrol gae τ as an addiional policy insrumen, bu i does no use foreign exchange reserves as a ool for capial accoun managemen so F cb = F cb ss and budge consrain (11) reduces o: ˆF cb = 0. Given he propery Ω (0) = 0, he economy-wide P C W H Π + S ( F (2) = P χω ) + Fss cb ( ) ) 1 + Φ 1 i 1 S (F (2) 1 + Fss cb ( ) (2) ˆF, (17) 18

20 while he UIP condiion (5) akes he general form: 1 + i 1 + Φ i = ( ) E Λ+1 P +1 S +1 ( ) ( ( )). (18) E Λ+1 P +1 (1 τ ) S + P χω (2) ˆF Scenario 3 In his scenario he cenral bank uses foreign exchange reserves F cb as an addiional policy insrumen, bu households canno buy or sell foreign currency denominaed bonds, ˆF = 0. Togeher wih he propery Ω (0) = 0, his implies ha he economy-wide budge consrain (11) reduces o: ( ) P C W H Π + S F ss + F cb(3) ( ) ) 1 + Φ 1 i 1 S (F ss + F cb(3) 1 = ( ) P χ cb cb(3) Ω ˆF. (19) Since wih a closed capial accoun households canno opimally choose heir holdings of foreign currency denominaed bonds, he Ramsey policymaker does no face as a consrain he UIP condiion (5), which is derived by combining he households firs order condiions for heir opimal choices of home and foreign bonds. Therefore, proving he equivalence beween Scenarios 2 and 3 is o prove ha (17)-(18) in Scenario 2 and (19) in Scenario 3 yield idenical consrain ses for he Ramsey policymaker. Noe ha we have used he superscrip (2) in equaions (17)-(18) and he superscrip (3) in equaion (19) o make a disincion beween Scenario 2 and Scenario 3 for he households and cenral bank s holdings of foreign currency denominaed bonds, bu no for oher variables. This is he only disincion ha needs o be made across hese wo alernaive scenarios given ha he wo policy regimes are equivalen in erms of generaing feasible choices of variables ha are relevan for households welfare. We can se he households adjusmen cos parameer χ in Scenario 2 and he cenral bank s adjusmen cos parameer χ cb in Scenario 3 equal, say, o some posiive number χ ha can be made arbirarily small and inerpre his presence for he echnical purpose of 19

21 closing he small open economy model. The equivalence beween Scenarios 2 and 3 cerainly holds under his inerpreaion. Bu he equivalence beween he wo scenarios acually holds more generally. In fac i holds even when χ akes on any posiive value. This generaliy can be imporan since χ may also be used o proxy foreign exchange marke imperfecions faced by he home counry, in addiion o echnically close he small open economy model. Thus our proof of he equivalence beween Scenarios 2 and 3 below does no resric o he case ha χ is an infiniesimally small number. We ake wo seps o prove ha (17)-(18) in Scenario 2 and (19) in Scenario 3 generae idenical consrain ses for he Ramsey policymaker. Firs, for any F (2) and oher variables ha saisfy (17)-(18) and oher privae secor opimaliy condiions under a variable capial ax rae τ in Scenario 2, here exiss a corresponding choice of foreign exchange reserves in Scenario 3 given by: ˆF cb(3) = ˆF (2), (20) which yields idenical home oal holding of foreign currency denominaed bonds and oher variables ha saisfy (19) and oher privae secor opimaliy condiions. Second, for any variables ha saisfy (19) and oher privae secor opimaliy condiions under a foreign exchange inervenion F cb(3) of variable capial ax rae τ in Scenario 2 given by: in Scenario 3, here exiss a corresponding choice ( ) τ = 1 + P ( ) (1 + Φ i χω cb(3) ) E Λ+1 P +1 S +1 ˆF ( ), (21) S (1 + i ) S E Λ+1 P +1 ha via influencing he price of foreign currency denominaed bonds would induce households o choose heir holding of he foreign bonds equal o: ˆF (2) = ˆF cb(3), (22) 20

22 which yields idenical home oal holding of foreign currency denominaed bonds and oher variables ha saisfy (17)-(18) and oher privae secor opimaliy condiions. The above wo seps ogeher esablish ha Scenarios 2 and 3 are isomorphic in erms of generaing idenical feasible choices of welfare-relevan variables for he Ramsey policymaker. This is o say ha a se of welfare-relevan variables is feasible for he Ramsey policymaker in Scenario 2 if and only if i is feasible for he Ramsey policymaker in Scenario 3. This esablishes he equivalence of he wo scenarios. In paricular, he Ramsey soluion produces idenical home oal holding of foreign currency denominaed bonds (hus idenical curren accoun as well as oher welfare-relevan macroeconomic variables) across he wo scenarios, alhough he disribuion of he oal holding beween households and he cenral bank differs across he wo regimes. I is imporan o emphasize ha he only condiions in he Ramsey policymaker s consrain se ha maer for our proof of he equivalence resuls are he economy-wide budge consrain and he UIP condiion, where all oher opimaliy condiions relevan o privae secors are idenical across he four policy scenarios. I is irrelevan o he equivalence resuls how exacly he funcional forms describing he behavior of he privae agens are specified, because such specificaions will be idenical across he four scenarios. I should also be sressed ha he equivalence resuls hold wihou recourse o firm side specificaions, and hey hold under any ypes of fricions (nominal, financial, ec.) ha we see in oday s New Keynesian DSGE lieraure incorporaed ino he firm side. This means ha our equivalence resuls apply o a wide range of macroeconomic models ha are ofen used in New Keynesian DSGE lieraure. The equivalence resuls hold quie generally. 5 Numerical Resuls When presening numerical resuls, we firs define some specific funcional forms o replace he generalized forms in he model presened in he las secion and we define he deails of 21

23 he firm side. We hen discuss calibraion of his numerical model and a mapping beween observed levels of capial conrols and he adjusmen cos parameer χ. We hen presen impulse responses o a risk premium shock for some key variables in he model. Finally we presen he momens of some key variables in he model and show how hese change under differen policy scenarios and parameer values. 5.1 Funcional forms for numerical model Funcional forms for he household In he numerical resuls he specific funcional form for he household s uiliy funcion is given by: U ( C, M ), H = ln (C ) + φ P m ln ( M P ) ψ H1+η 1 + η (23) The aggregae consumpion good is simply he aggregaion of domesic and impored goods from individual firms aggregaed in he CES funcion: C = v 1 θ + (1 v) 1 θ [ (( 1 ) 1 σ n n 0 CH (i) σ 1 σ [ (( 1 ) 1 σ 1 1 n n CF ) σ ] θ 1 θ σ 1 di (j) σ 1 σ ) σ ] θ 1 θ σ 1 dj θ θ 1 (24) where θ is he elasiciy of subsiuion beween home and foreign goods, and σ is he elasiciy of subsiuion beween goods from differen firms wihin he same counry. From he aggregaor funcion in equaion (24), he demand for eiher he home consumpion good from firm i or he foreign consumpion good from firm j are given by: ( P C H H (i) = v P H C F (j) = (1 v) (i) ( P F ) σ ( P H P F 22 (j) P ) θ C (25) ) σ ( S P F P ) θ C

24 and he corresponding demand funcions in he foreign economy are given by: ( P (j) = v F (j) C F P F C H (i) = (1 v ) ( P H ) σ ( P F P H (i) P ) θ C (26) ) θ C ) σ ( P H S P where P H (i) is he price se by he home counry firm i (in home currency), and P F (j) is he price se by foreign firm j (in he foreign currency). The share of impored goods in he home consumpion baske is given by 1 v and he share of impored goods in he foreign consumpion baske is given by 1 v. Thus he various price indices are given by: ( 1 P H = n ( 1 P F = n 0 1 n [ P = v ( P H [ P = v ( P F P H 1 n ) 1 (i) 1 σ 1 σ di P F ) 1 (j) 1 σ 1 σ dj ) 1 θ ( ) ] 1 + (1 v) P F 1 θ 1 θ S ( ) ) 1 θ P + (1 v H 1 θ ] 1 1 θ ) S (27) (28) where 1 v = (1 n) λ, 1 ν = nλ, and in he limi as n 0, v = 1 λ, 1 n n (1 v ) = λ, where λ is he seady-sae impor share Funcional forms for he firm Firm i [0, n] produces Y (i) of oupu for he domesic and expor markes. The firm s oal oupu is produced by hiring h (i) of homogenous labor service from domesic households a nominal wage W. Marke clearing in he labor marke requires ha he oal demand for labor by firms is equal o he supply of labor from households: 1 n h n 0 (i) di = H. Aggregae 23

25 firm profis, which are reurned lump-sum o households, are given by: Π = 1 n The firm s oupu is simply a linear funcion of is labor inpu: n 0 Π (i) di. Y (i) = h (i) (29) Thus he firm s marginal cos is simply equal o he wage rae and firm profis are given by Π (i) = ( P H ) ( (i) W C H +τ (i) + 1 n n CH +τ (i) ). In period, he firm will be able o change is price wih probabiliy 1 ξ p. If allowed o change heir price in period, he firm will se prices o maximize: P H (i) = arg max E P H(i) β ( ) τ τ ξ p Λ+τ Π +τ (i) (30) τ=0 The firm ha can change prices will se is price o: P H (i) = σe β ( ) τ τ ξ p Λ+τ W +τ (i) ( C+τ H (i) + 1 n n CH +τ (i) ) τ=0 (σ 1) E β ( ) τ τ ( ξ p Λ+τ C H +τ (i) + 1 n n CH +τ (i) ) (31) τ=0 Firms ha can rese prices in period will all rese o he same level, so P H (i) = P H. We subsiue his opimal price ino he price index P H = ( 1 n P H n 0 (i) 1 σ di ) 1 1 σ. Since a firm has a probabiliy of 1 ξ p of being able o change heir price, hen by he law of large numbers in any period 1 ξ p percen of firms will reopimize prices. Thus he price index can be wrien as: ( ( ) P H = ξ p P H 1 σ ( ) ( ) ) ξp P H 1 σ 1 σ (32) Thus he aggregae resource consrain for he home economy is given by: H = 1 n n 0 [ ( ) P H θ ( ) Y (i) di = (1 λ) P H θ ] C + λ C P S P H (33) 24

26 where he price dispersion wedge H ξ p ( 1 + π H ) σ H 1. = 1 n n 0 ( P H (i) P H ) σ di = ( 1 ξp ) [ 1 ξ p (1+π H ) σ 1 1 ξ p ] σ σ 1 + For he simulaions he model is driven by a shock o Φ, he risk premium on borrowing in he foreign currency. This shock follows an exogenous AR(1) process and is he only source of sochasic flucuaions in he model Funcional form of he bond adjusmen coss The funcional form of he foreign currency denominaed bond adjusmen cos funcions for he household and cenral bank are given by: ( S ) 2 (x x ss) 2, (34) Ω (ˆx ) = 1 2 P for x = F or F cb Calibraion of he numerical model The full lis of model parameers are presened in Table 4. The firs five parameers, he Calvo price sickiness parameer, he discoun facor, he labor supply elasiciy, he elasiciy of subsiuion across goods from firms in he same counry, and he elasiciy of subsiuion beween home and foreign goods, are all se o values commonly found in he lieraure. The seady-sae impor share λ = The coeffi cien on labor in he household s uiliy funcion, ψ, is se such ha in he seady sae, household consumpion and labor effor are boh equal o one. The coeffi cien on real money balances in he household s uiliy funcion, φ m, is se such ha he seady sae velociy of money is equal o one. The only exogenous shock in he model, Φ follows an AR(1) process wih persisence The sandard deviaion of he shock is normalized o one. We mus assume a seady sae composiion of he cenral bank s balance shee. Assume ha 90% of he cenral bank s asses are home currency denominaed bonds and 10% are 25

27 foreign currency denominaed bonds. In he analyical proofs in he previous secion we simply se he bond adjusmen coss, χ and χ cb, o a small and posiive number o close he model. In hese numerical simulaions we can use he household s bond adjusmen cos o calibrae he openness of he capial accoun. We assume ha he cenral bank can freely buy and sell foreign bonds, and we se χ cb = If households can buy and sell foreign bonds jus as freely, χ χ cb = 0. As capial accoun resricions increase, χ χ cb increases. I is possible o creae a mapping from an observed measure of capial accoun resricions, like he Chinn-Io index used in Secion 2, o he model parameer χ. Begin by considering he empirical relaionship beween he log of he Chinn-Io index and he sandard deviaion of reserve accumulaion relaive o he sandard deviaion of he curren accoun, SD ( R) /SD (CA), or he empirical relaionship beween he log of he Chinn-Io index and he correlaion beween he curren accoun and he capial accoun in Table 3. The wo-sage-leas-squares regression of SD ( R) /SD (CA) on he log of KAOpen yields a consan erm of 1.08 and a coeffi cien of 0.10 and he wo-sage-leas-squares regression of Corr (CA, KA) on he log of KAOpen yields a consan erm of 0.44 and a coeffi cien of 0.07; he fied values of SD ( R) /SD (CA) daa or Corr (CA, KA) daa as a funcion of KAOpen from hese esimaed parameers are ploed in he op panel of Figure 2. The nex sep is o calculae SD ( R) /SD (CA) model and Corr (CA, KA) model as a funcion of he household s bond adjusmen cos parameer χ. This is ploed in he second panel in Figure 2. In he op panel, each value of KAOpen leads o fied values of SD ( R) /SD (CA) daa and Corr (CA, KA) daa. In he middle panel each value of χ leads o values of SD ( R) /SD (CA) model and Corr (CA, KA) model in model simulaions. For each value of KAOpen, we choose he value of χ ha minimizes he sum of squared deviaions beween he values of SD ( R) /SD (CA) or Corr (CA, KA) in he model and he daa: 26

28 χ (KAOpen) = arg min (SD ( R) /SD (CA) model SD ( R) /SD (CA) daa )2 + (Corr (CA, KA) model Corr (CA, KA) daa ) 2 The mapping beween KAOpen in he daa and he parameer χ in he model is shown in he hird panel of Figure 2. When KAOpen is close o zero, indicaing an open capial accoun, he corresponding value of χ is close o zero. When KAOpen is close o 1, indicaing a closed capial accoun, he corresponding value of χ is around 0.10, which, under his parameerizaion is he value of he household bond adjusmen cos ha would effecively close he capial accoun. 5.2 Numerical resuls when capial accoun is perfecly open or closed Firs we will consider resuls from numerical simulaions of he model under he exreme cases of a perfecly open capial accoun or a perfecly closed capial accoun. This is akin o he four scenarios presened earlier in he analyical proofs in Secion 4. Recall ha scenarios 1 and 2 are he wo scenarios where he cenral bank does no engage in serilized foreign exchange inervenion. In scenario 1 he cenral bank s only insrumen is he money supply (and hus he nominal ineres rae). In scenario 2 he cenral bank has wo insrumens, he money supply and he variable ax τ on he purchases of foreign bonds. In hese wo scenarios, assume ha privae agens face he same bond adjusmen coss as he cenral bank, χ = χ cb. In scenarios 3 and 4 he cenral bank can engage in serilized foreign exchange inervenion. In scenario 3 he capial accoun is closed, which in his numerical model is achieved in he limi as χ. In scenario 4 he capial accoun is open, which in his numerical model is achieved in he limi as χ 0. 27

29 The impulse responses are presened in Figures 3 and 4. These plo he responses o a one sandard deviaion shock o he risk premium on foreign borrowing (a 100 basis poin shock). In he impulse responses, scenario 1 is represened by he RED impulse response, scenario 2 is represened by he BLUE impulse response, scenario 3 is represened by he GREEN impulse response, and scenario 4 is represened by he BLACK impulse response. The responses of he home counry curren accoun, capial accoun, change in cenral bank foreign exchange reserves, and he variable ax rae τ are presened in Figure 3. The responses for he curren accoun, capial accoun, and change in reserves measure he deviaion from he seady sae, in percen of GDP. And hus a 100 basis poin increase in he risk premium leads o an increase in he curren accoun of abou 5-7% of GDP. Turning o he firs policy scenario, where he cenral bank has no separae insrumen for capial accoun managemen (he Red impulse response). The increase in he risk premium on foreign borrowing leads o a fall in ne capial inflows (an increase in he capial accoun), and when he cenral bank canno adjus he sock of foreign exchange reserves, he capial accoun is simply equal o he curren accoun. In he second policy scenario, he cenral bank can adjus he variable ax τ on foreign borrowing (he Blue impulse response). The increase in he curren accoun (he increase in ne savings) in scenario 1 is greaer han opimal, so if given a separae insrumen o manage he capial accoun, he cenral bank will cu τ. As seen in he household budge consrain in equaion (2), his will raise he price of foreign currency denominaed bonds, encouraging households o sell foreign bonds (borrow more from abroad, even a he higher ineres rae since he fall in τ will raise he price of foreign bonds, and hus lower heir reurn, parially offseing he exogenous increase in he ineres rae of foreign currency denominaed bonds). Given his policy inervenion he increase in he capial accoun (and increase in he curren accoun) is no as severe as i would have been when he cenral bank has no capial accoun managemen insrumen. In he hird policy scenario, he variable ax rae τ = 0, bu he cenral bank can 28