Foreign Exchange Interventions, Capital Controls and Monetary Policy: The Case of China

Transcription

1 Foreign Exchange Inervenions, Capial Conrols and Moneary Policy: The Case of China Hao Jin November 17, 215 ABSTRACT China has mainained a closed capial accoun o he privae secor and channeled capial flows hrough he public secor by foreign exchange inervenions. This paper presens an open economy model ha incorporaes his capial accoun policy configuraion in order o sudy wheher foreign exchange inervenions can improve welfare in he presence of capial conrols, compared o an open capial accoun. Furhermore, I analyze how hese inervenions affec he conduc of moneary policy. I show ha opimal inervenions improve welfare by sraegically managing he erms of rade. In he presence of domesic nominal rigidiy, inervenions increase welfare even if moneary policy is se opimally. I find moneary policy effecively eliminaes domesic price disorions, while foreign exchange inervenions efficienly correc erms-of-rade exernaliies. Keywords: Foreign Exchange Inervenions; Capial Conrols; Moneary Policy; Chinese Economy; Welfare JEL Classificaion: D6; E52; F31; F38 I am deeply indebed o Eric Leeper and Juan Carlos Hachondo for heir advice and encouragemen. I am graeful o Amanda Michaud and Todd Walker for heir discussions and suppor. I hank Yoosoon Chang, Olivier Jeanne, Siming Liu, Guido Lorenzoni, Hewei Shen, Wenyi Shen, Fei Tan, Susan S.C. Yang and seminar paricipans a various places where I presened earlier drafs of his paper for helpful suggesions. All errors are my own. Deparmen of Economics, Indiana Universiy, Wylie Hall Rm 15, 1 Souh Woodlawn, Bloomingon, IN , USA. jinhao@indiana.edu

2 1 INTRODUCTION China s inegraion ino he global rade marke has been rapid and pronounced since he early 198s. Figure 1 shows ha he rade volume 1 accouns for no more han 15% of GDP when he inegraion sared; in less han hree decades i reaches over 6% of GDP. Despie he removal of rade barriers, capial accoun policy reform has shown lile progress. Figure 2 plos he Chinn and Io (26) capial accoun openness index for China agains he world average. No only is China s capial accoun openness far below he world average, i remains unchanged hroughou his period of rade inegraion. Should China move o a fully open capial accoun is he quesion of ineres in his paper. Having a good undersanding of China s curren capial accoun policy is crucial for any poenial policy reforms. In China, he sric regulaions on capial flows almos fall enirely on he privae secor and capial flows are channeled hrough he public secor. I label his policy combinaion a semi-open capial accoun regime. 2 The governmen in his capial accoun policy regime acs as a financial inermediary ha issues bonds o absorb domesic savings, and uses he proceeds o purchase foreign reserves, and vice versa. In pracice, his operaion is referred o as serilized foreign exchange inervenions. As a consequence, China s governmen has direc conrols over capial flows under he semi-open capial accoun policy regime. This paper sudies wheher a semi-open capial accoun can be welfare improving compared o a fully open capial accoun. The paper also examines he effecs of he semi-open capial accoun on he conduc of moneary policy. I address his quesion in a sandard open economy model wih counry-specific producs. The counry-specific goods assumpion can be inerpreed as a reduced-form way o capure China s comparaive advanage in producing labor-inensive goods. In his model, a erms-of-rade exernaliy arises naurally. When privae agens make producion decisions, hey do no consider he effec of heir acions on he relaive prices of he home oupu. For example, if a counry s produciviy improves, privae agens would borrow from abroad o inves and produce more. However, he increased supply of goods in he inernaional marke drives down heir relaive prices. This erms of rade deerioraion may be so large ha he oal income he counry receives from selling is producs in he inernaional marke is even lower han before produciviy improvemen. A benevolen governmen would inernalize his erms-of-rade exernaliy and produce less 1 The rade volume is measured as oal impors plus expors. 2 Bacchea, Benhima and Kalanzis (213) names his policy configuraion a semi-open economy. 2

3 4 35 Impors/GDP Expors/GDP Figure 1: China s Impors and Expors over GDP(%) Daa Source: China Naional Bureau of Saisics(NBS). The dash-do and dashed lines show China s impors and expors over GDP raio in percenage respecively. compared o he compeiive allocaions. One way for he governmen o manage he erms of rade is hrough he use of foreign exchange inervenions in he presence of capial conrols on privae capial flows, i.e. adoping a semi-open capial accoun policy regime. By shuing down privae access o he inernaional bond marke and allowing he public secor o accumulae inernaional bonds in he foreign exchange marke, he governmen is able o achieve a socially opimal level of capial flows. Alhough foreign exchange inervenions are cerainly no he only opions available o he governmen o influence capial flows, hey are valuable. Two main argumens characerize he benefis of incorporaing foreign exchange inervenions ino he policy maker s oolbox. Firs, alhough sae-coningen capial conrols have been suggesed o resric capial flows o achieve various goals, such as erms of rade manipulaion and macro-prudenial consideraions, 3 foreign exchange inervenions offer more flexibiliy. The work by Eichengreen and Rose (214) documens ha capial conrols rarely adjus wih shor-erm macroeconomic variables because of he negaive signal i may send ou o he marke, and he legislaion ime lag o insiue hem. This is consisen wih he evidence in figure 2 showing ha China has no reformed 3 See for example Farhi and Werning (214) for he use of capial conrols o manage erms of rade and Bianchi (211), Jeanne and Korinek (21) and Korinek (21) for he macro-prudenial objecive. 3

4 .6.5 World Average China Figure 2: Chinn-Io Capial Accoun Openness Index Daa Source: Chinn and Io (26). The dash-do and dashed lines show China and world average capial accoun openness index respecively. is capial accoun policy subsanially over he pas wo decades. Due o he exisence of poliical and pracical obsacles in implemening a sae-coningen capial conrol policy, he resuls in his paper sugges ha foreign exchange inervenions can be underaken o complemen a consan level of capial conrol and improve welfare. Second, foreign exchange inervenions in he presence of capial conrols can be welfare enhancing even if moneary policy chooses he ineres rae opimally. When nominal rigidiies are presen, in general i is no desirable for he moneary policy o anchor inflaion a zero for an open economy wih imperfecly subsiuable producs. 4 In his seing policy makers face wo arges, inflaion disorions and he erms-ofrade exernaliy, bu only one ool, he ineres rae. Policy mus balance he benefi of a favorable erms of rade wih he cos of greaer price disorions. This paper demonsraes ha including foreign exchange inervenions as addiional policy insrumens creaes a more efficien oucome by relaxing he policy consrains faced by policy makers, allowing hem o sraegically choose a pah of erms of rade wihou desabilizing he price level. More ineresingly, I find ha moneary policy is a more power ool o cope wih domesic price disorions, while foreign exchange inervenions arge 4 Corsei and Peseni (21), Benigno and Benigno (23) and De Paoli (29), among ohers, provide excellen heoreical invesigaions on his issue. 4

5 erms-of-rade exernaliies more effecively. This implies ha, alhough his no a case for resricing free capial movemens under fixed exchange rae arrangemen o reain independen moneary policy, as in Farhi and Werning (212) and Schmi-Grohé and Uribe (212), moneary policy should concenrae on domesic nominal fricions and leave he exernal adjusmens o open macroeconomic policy. The macroeconomic implicaions from he opimal conduc of inervenions in a semi-open capial accoun are he following: When domesic produciviy improves, privae agens wan o borrow from abroad o inves and produce, bu privae capial flows are resriced. The public secor acs as a financial inermediary ha borrows from he inernaional bond marke and lends o domesic agens in local currency bonds, bu a a smaller amoun han he privae secor s desired level. This sabilizes domesic oupu, inernaional goods rade, and relaive price movemens. In response o a rise of he foreign ineres rae, a benevolen governmen saves less or borrows more from overseas o comba he drop of aggregae demand for home producion. This miigaes he negaive impac of he exernal shock, and sabilizes he domesic economy. Noice ha he exchange rae regime is assumed o be flexible, however he opimal policy responses o shocks keeps real exchange rae relaively sable, hough no fixed, compared o he equilibrium in an open capial accoun policy regime. 2 LITERATURE REVIEW This paper is direcly linked o he normaive sudies of foreign exchange inervenions. Devereux and Yeman (214) examine he effec of including foreign exchange inervenion as an addiional policy ool on global welfare. Alhough hey reach he same conclusion ha i gives policy makers more freedom in maximizing welfare, hey focus on how he effeciveness of inervenions is affeced by exchange rae pass hrough, and inegraion of world goods and financial markes, I insead highligh how inervenions inerac wih capial conrols and moneary policy. This paper is closely relaed o Prasad (214) in which he auhor sudies opimal inervenions under capial conrols in a small open economy. We boh find ha inervenions can be welfare improving in his case because of he exisence of a erms-of-rade exernaliy. However, my model feaures endogenous capial accumulaion which is no only imporan o fi he model o Chinese daa, bu also influences he curren accoun movemens since invesmen goods flow across boarders as well as consumpion goods. In some cases, my model shows opposie curren accoun balance on impac in conras o he models wihou capial accumulaion. Chang, Liu and Spiegel (215) discuss opimal 5

6 moneary policy under China s unique exernal policy configuraion, capial conrols, exchange rae peg and serilized inervenions, as I do in his paper. However, in conras o heir approach o se up he inervenions o follow a simple response rule, I analyze he opimal inervenions and moneary policy joinly. Anoher more recen growing srand of lieraure sudies he opimal use of capial conrols o regulae capial flows for he purpose of erms of rade managemen. Some examples include De Paoli and Lipinska (213), Farhi and Werning (214) and Heahcoe and Perri (214). While his paper addresses he same source of inefficiency, I differ from hem by proposing he, more flexible, join use of a fixed level of capial conrols and sae-coningen inervenions o resric capial flows and improve welfare. Capial conrol has been also suggesed o be used o preven endogenous financial crisis as in Bianchi (211), Jeanne and Korinek (21) and Korinek (21). I absrac from he macro-prudenial consideraion of foreign exchange inervenions. Finally, a large number of papers have devoed heir aenion o he use of moneary policy o deal wih price disorions and erms-of-rade exernaliies. They find he domesic price level flucuaes as an opimal oucome because moneary policy has an incenive o deviae from flexible price equilibrium o obain a more favorable erms of rade. I demonsrae in his paper ha adding foreign exchange inervenions o he policy makers oolbox is beneficial, formally confirming he wo arges, wo insrumens resul in Chamon, Osry and Ghosh (212). I find moneary policy effecively eliminaes price disorions, while foreign exchange inervenions efficienly correc he erms-of-rade exernaliy. 3 MODEL In his secion I incorporae China s exernal policies ino an oherwise sandard open economy DSGE model. This open economy akes inernaional ineres rae as given, bu produces counry-specific inermediae goods ha are imperfec subsiues o foreign goods and are required in final oupu. The counry-specific goods assumpion can be inerpreed as a reduced-form way o capure China s comparaive advanage in producing labor-inensive goods. The asse marke is incomplee and only one-period risk-free bonds are raded. 3.1 HOUSEHOLDS This open economy is populaed by an infiniely lived represenaive household ha derives uiliy from consumpion, c, and disuiliy from hours worked, l. Specifically, he household chooses a sequence of consumpion, hours worked, capial invesmens and savings in domesic governmen bonds and iner- 6

7 naional bonds o maximizes lifeime uiliy given by: E β = 1 c1 σ 1 σ 1 χ l1+η 1 + η, (3.1) where < β < 1 is he discoun facor, σ > is he household s risk aversion and η > is he inverse of he Frisch labor elasiciy. χ is an addiional parameer o ensure ha in deerminisic seady sae, labor hours consiue one hird of ime endowmen. The household receives ineres income from domesic and inernaional oneperiod risk-free nominal bonds, capial invesmen reurn, labor income and lump-sum ransfers from he governmen. The household consumes, invess in domesic capial marke and saves in domesic and inernaional bonds, B G and B F respecively. Trading in he domesic governmen bond marke involves no addiional cos, while adjusing posiions in he inernaional bond marke incurs a quadraic ransacion cos. The household s flow budge consrain is given by P c + P i + B G S B F + P Γ f ( S B F P ) =W l + R k 1 k 1 + R 1 B G 1 R 1 S B F 1 + P z, (3.2) where W is he nominal wage rae for labor inpu l and R k 1 is he nominal rae of reurn for capial supplied k 1. Capial sock accumulaion follows a linear law of moion, k = (1 δ)k 1 + i, (3.3) where δ is he capial depreciaion rae. Domesic governmen bonds pay gross nominal ineress R every period, whereas he foreign bonds pay R gross nominal ineress in foreign currency. S is he nominal exchange rae expressed as domesic currency in erms of dollars. B G > means households save in domesic marke, and B F overseas. > means households borrow from Adjusing inernaional asse posiions requires a quadraic porfolio adjusmen cos in erms of real domesic consumpion goods, Γ f ( S B F γ f 2 ( S B F P b F ) 2 and b F BF S P P ), where Γ f ( S B F P ) denoes he seady sae value of real foreign bond holdings S B F P. This follows Schmi-Grohé and Uribe (23) o ensure a saionary seady sae exiss in he model. I choose a very small γ f in he model calibraion o guaranee 7

8 saionariy. 5 Divide he household budge consrain by he home aggregae price level P and he opimal choices of domesic and inernaional bond holdings imply ha and λ = βr E λ +1 π +1, (3.4) λ e [1 γ f (b F e b F e)] = βr λ E +1 π+1 e +1, (3.5) where λ is he Lagrangian muliplier for he household s budge consrain and denoe he domesic and foreign inflaion raes by π +1 P +1 P and π+1 P +1 P respecively. P e S P is he real exchange rae, expressed as he amoun of home final goods per uni of foreign final goods. The firs opimaliy condiion (3.4) gives us he sandard consumpion Euler equaion, which saes ha he marginal rae of subsiuion beween oday and omorrow s consumpion mus equal o he discouned real reurn. The second firs order condiion (3.5) shows ha for domesic invesors o be willing o hold foreign asses, he ineremporal marginal rae of subsiuion mus equal o he foreign real reurn, ad- e jused for expeced changes of exchange rae E +1 e, ransacion coss, and discouning. 3.2 FIRMS FINAL GOODS FIRMS A represenaive final goods firm combines he domesically produced and impored inermediae goods o produce final non-radable goods ha are used for boh consumpion and invesmen. The final good is assumed o be produced by a CES aggregaion echnology, y = [(1 ν) 1 µ (y H ) µ 1 µ + ν 1 µ (y F ) µ 1 µ ] µ µ 1, (3.6) where µ > is he elasiciy of subsiuion beween home and foreign inermediae goods, and ν 1 deermines he share of local and impored goods in he composiion of domesic final goods. The final good producer chooses he following domesically produced and im- 5 I perform robusness checks o make sure he model dynamics is no driven by his assumpion. 8

9 pored inermediae good bundles o maximize profis, y H = (1 ν)(p H ) µ y, (3.7) y F = ν(p F ) µ y, (3.8) PH P where p H and p F PF P are he relaive prices of home and impored inermediae goods bundle o he final goods. The aggregae price index P of final goods is given by, P = [(1 ν)(p H ) 1 µ + ν(p F ) 1 µ ] 1 1 µ. (3.9) INTERMEDIATE GOODS FIRMS The home counry consiss of a coninuum of monopolisically compeiive firms producing a differeniaed inermediae good using labor and capial. Producion of good j is given by a Cobb-Douglas producion funcion, Q H (j) = exp(a )k α (j)l 1 α (j), (3.1) where a is a echnology shock ha follows an AR(1) process, a = φ a a 1 + ε a, (3.11) where ε a is an i.i.d disurbance wih sandard deviaion σ a. The markes for labor and capial are assumed o be perfecly compeiive such ha he capial-labor raio is given by, k = w α l r k 1 α. (3.12) Firms ha minimize producion coss have idenical marginal coss given by MC = (1 α) α 1 α α (R k )α W 1 α exp(a ) 1. The aggregaion echnology for inermediae goods bundles is given by, Q H = [ 1 ] 1+ɛ ( Q H (j) 1+ɛ 1 dj), (3.13) where ɛ deermines he elasiciy of subsiuion beween he differeniaed home inermediae goods. 9

10 Cos minimizaion by he final good producer implies he following individual home inermediae goods demand funcions, y H (j) = ( ) p H 1+ɛ ɛ (j) y H, (3.14) where p H PH (j) (j) denoes he relaive price of firm j s inermediae goods o home P H bundle of inermediae goods. P H (j) is he price charged by firm j in he domesic marke ( and P H is he home price index of inermediae goods bundle, where P H 1 ɛ. PH (j) 1 ɛ dj) The aggregae domesic demand is denoed by y H. The price seing is assumed o be sluggish following Calvo. Each period a fracion ω of firms canno adjus heir price. Firms ha are allowed o re-opimize heir price a ime maximize expeced discouned profis, E (βω) k λ +k [p H (j)y+k H λ (j) MC +ky+k H (j)], (3.15) k= subjec o individual firm s oupu demand (3.14). 3.3 FOREIGN ECONOMY I denoe all he foreign variables wih a superscrip aserisk. The foreign demand for home produced inermediae goods bundles is assumed o be, y H = ν (p H ) µ y, (3.16) where p H PH P foreign final goods. P H is he relaive price of home expored inermediae goods bundles o is he foreign currency price of domesic produced inermediae goods and P is he foreign price index. y H consiss he domesic expors o he foreign economy. This foreign demand curve is analogous o he home demand curve and can be derived from a symmeric foreign firm s problem. To keep he analysis simple and highligh he key mechanism, I do no model he foreign counry explicily. I assume he foreign oupu and price level o be consan, and foreign ineres raes are exogenous auoregressive process subjec o i.i.d. shocks. I assume a represenaive home expor firm ranspors domesic inermediae goods bundles o foreign counry, and prices he bundles compeiively in he foreign marke a all imes so ha P H S = P H. Similarly, home impors are compeiively priced as well. A foreign represenaive firm expors o home as long as he price is equal o he foreign price adjused for exchange rae. In oher words, we have P F = S P F, where 1

11 P F is he price of foreign goods in foreign marke. 3.4 TERMS OF TRADE AND REAL EXCHANGE RATE The erms of rade is defined as he expor prices over he impor prices, ToT ph. Rewrie he erms of rade as, p F ToT = S P P H and use he definiion of real exchange rae,, (3.17) e = S P P, (3.18) o obain a relaionship ha links he real exchange rae o erms of rade, e = [(1 ν)tot µ 1 + ν] 1 µ 1. (3.19) Since µ 1, (3.19) demonsraes ha he real exchange rae and erms of rade always move proporionally in opposie direcions. If he law of one price does no hold, for example because of he assumpion of Local Currency Pricing (LCP) 6, where each inermediae good s price is se independenly (and poenially sicky) in various markes, hen he igh connecion beween real exchange rae and erms of rade no longer holds. 3.5 GOVERNMENT BUDGET CONSTRAINT The governmen issues one period nominal bonds B G in he domesic marke o finance is ineres paymens, purchases of foreign reserves B FR, fixed expendiure G and lump-sum ransfers z o he households. The available policy insrumens crucially affec he conduc of opimal policy. I focus on he opimal use of foreign exchange inervenions and moneary policy in his paper, so I assume lump-sum ransfers passively adjus o balance he governmen s budges every period. Foreign exchange inervenions are assumed o be fully serilized such ha he governmen supplies more (less) domesic currency o offse foreign currency inflows (ouflows) associaed wih inernaional rade, and simulaneously sells (buys) domesic bonds o absorb he increased (decreased) money supply. As a consequence, he size of he governmen s balance shee is unchanged, only he composiion changes. 6 See Bes and Devereux (1996) for more deails abou he LCP assumpion. 11

12 The governmen s flow budge consrain is given by B G B FR S = R 1 B G R 1 BFR 1 S + P z + P G. (3.2) 3.6 BALANCE OF PAYMENT The balance of paymen of his open economy is wrien as, B F S B FR S = P H S Y H P F Y F R 1 S B 1 F R 1 S B 1 FR. (3.21) Impors and expors of goods are free of barriers. This represens he open rade policy China adops in he early 2s afer joining he WTO. The capial accoun on he oher hand is ighly regulaed. I define he capial accoun regimes below in secion MARKET CLEARING CONDITIONS The final goods and he inermediae goods markes clear, Y = C + I + G + Γ f ( S B F P ), (3.22) Q H = Y H + Y H. (3.23) In addiion, domesic and inernaional bond markes clear. 3.8 DEFINITION OF CAPITAL ACCOUNT REGIMES I classify capial accoun policy ino he following hree broad regimes, which depend on he policy insrumens available o he policy makers. Definiion 1. The capial accoun regimes are defined as: i) Open capial accoun (Open CA) regime, where b F R and b FR =,. ii) Semi-open capial accoun (Semi-open CA) regime, where b F = and b FR iii) Closed capial accoun (Closed CA) regime, where b F = and b FR =,. R,. In he open capial accoun regime, a counry s inernaional bond holding is deermined solely by he domesic privae agens wihou any inervenions. In conras, a counry s foreign bond posiion is compleely conrolled by he governmen in he semi-open capial accoun regime. In his case, he governmen acs as a financial inermediary beween he domesic privae secor and he inernaional bond marke, as suggesed by Song, Soresleen and Ziliboi (211). In he closed capial accoun 12

13 regime, since he counry is in financial auarky, neiher privae nor public secor has access o inernaional bond marke. 3.9 OPTIMAL POLICY IN OPEN AND SEMI-OPEN CAPITAL ACCOUNT REGIMES In an open capial accoun regime, policy makers se moneary policy ineres raes opimally. The benevolen governmen s problem consiss of maximizing (3.1) subjec o he sequence of counry level budge consrains (3.21) wih b FR = for all, he aggregae resource consrains (3.22), producion echnology (3.1), law of moion of capial (3.3), he balanced budge rule, and all he households and firms opimaliy condiions (A.1)-(A.15). 7 The full specificaion of he benevolen governmen s problem is in Appendix B. The benevolen governmen s problem in a semi-open capial accoun regime is analogous o he one in an open capial accoun regime. The key differences are: Firs, households lose access o he inernaional bond marke, which implies condiion (A.3) no longer holds. Second, he counry s budge consrains become p H e Y H p FYF R 1 bfr 1 e = b FR e. Lasly, policy makers have conrols over foreign exchange inervenions in addiion o moneary policy ineres raes. The seup of he governmen s problem is in Appendix C. 3.1 A COMPARISON BETWEEN OPEN AND SEMI-OPEN CAPITAL ACCOUNT REGIMES To highligh he key inefficiency in his model, I firs examine he flexible price equilibrium. The inermediae firms all se he same price when price sickiness is absen, so hey collapse o one represenaive firm. This firm chooses labor and capial in compeiive markes o maximize profis aking he relaive price of heir producions as given. I obain he following demand funcions of labor and capial, w = (1 α) ph QH l, (3.24) r k = α ph QH k, (3.25) The benevolen governmen knows ha he counry s supply of goods o he inernaional marke has an impac on he relaive prices of heir producs, and inernalizes his price effec when allocaing producion resources. More specifically, he benevolen governmen inernalizes he effec of producion on he relaive prices p H. The 7 See Appendix A for all he firs order condiions. 13

14 opimaliy condiions wih respec o labor and capial become, w = (1 α) ph QH l + Q H p H, (3.26) l }{{ } price effec r k = α ph QH k + Q H p H, (3.27) k }{{ } price effec where p H = (3.7). [ ( )] 1 (1 ν) y µ according o he demand for home inermediae goods y H The righ hand sides of (3.24) and (3.26) represen he marginal produc of hiring an addiional labor hour and he lef hand sides are he real wage rae. When each individual firm makes is own producion decision, he firm akes he relaive prices of is oupu as given. However, he benevolen governmen knows ha when he counry s supply of goods increases, he relaive prices of is oupu are affeced. This price effec is capured in he las erm of equaion (3.26). If more producion suppress he relaive prices of domesic oupu, i.e. p H l <, his in urn lowers real wage rae. To mainain he level of labor income, households mus supply more labor, which reduces welfare. As a resul, i is opimal for he benevolen governmen o resric labor hiring, because privae agens do no inernalize he effec of heir acions on he aggregae prices and overesimae he marginal benefi of working. On he oher hand, if more labor hours increase he price of domesic oupu, i.e. ph l >, hen i is socially opimal o subsidize labor hiring. The exernaliy of individual producion decision on aggregae relaive prices is someimes referred as erms-of-rade exernaliy in he lieraure. In general, he direcion of price movemens o labor choice depends on he specificaions of uiliy, echnology and foreign demand funcions. The parameer values of impor and expor share and he elasiciy of subsiuion beween home and foreign goods also impac his relaionship. Analogous o labor choice, capial accumulaion is generally differen under he wo equilibria. The las erm in (3.27) reflecs he price effec ha privae agens do no ake ino accoun when making heir invesmen decisions. Therefore, a benevolen governmen discourages capial invesmen when addiional oupu deerioraes he purchasing power of home inermediae goods, and encourage invesmen oherwise. We have shown a erms-of-rade exernaliy exiss in his model and he decenral- 14

15 ized allocaions are generally subopimal. Now le us see how he adopion of a semiopen capial accoun regime can improve allocaion efficiency. The counry s aggregae resource consrain in a semi-open capial accoun regime is wrien as, C + I + G b FR e = Q H p H R 1 bfr 1 e. (3.28) By choosing he amoun of foreign reserves a counry accumulaes, he governmen is able o conrol he resources ha are available o he domesic households, hereby affecing heir consumpion, working and invesmen decisions. To see more clearly how a semi-open capial accoun regime affecs allocaions, I compare he firs order condiions wih respec o e from he governmen s problem in hese wo regimes. In an open capial accoun policy regime, he firs order condiion is wrien as, L = βc σ e e +1 R +1 e 2 π+1 θ 2, c σ 1 R 1 e 1 π θ 2, 1 }{{} consrains from rading inernaional bonds + θ 14, p H Y H + θ 14, (b F R 1 bf ) =, θ 18, + θ 17, p H (3.29) where he erms wih underbraces come from he he Euler equaion of inernaional bonds. The benevolen governmen has o ake ino consideraion households desire o align heir ineremporal consumpion allocaions o he world ineres raes when conduc opimal policy. On he oher hand, in a semi-open capial accoun regime where households canno rade inernaional bonds, θ 2, =. The firs order condiion wih respec o e becomes, L = θ 18, + θ 17, p H e + θ 14, p H Y H + θ 14, (b FR R 1 bfr ) =. (3.3) By no having he consrains of inernaional consumpion smoohing, he governmen has a sronger abiliy o influence he erms-of-rade compared o he decenralized allocaion. This improves welfare. Nex we invesigae he condiions under which a semi-open capial accoun canno improve welfare in his model compared o open capial accoun. The resuls are summarized in proposiion 1. Proposiion 1. A semi-open capial accoun regime canno improve welfare compared o open capial accoun regime if one of he following condiions is me: i). Home and foreign inermediae goods are perfec subsiues when produce final goods, i.e. 15

16 µ. ii). Demand for home expors are perfecly elasic, i.e. µ. iii). The producion of final goods does no use home inermediae goods, i.e. ν = 1 and ν =. Proof. See Appendix D Inuiively, he abiliy for a benevolen governmen o correc he erms-of-rade exernaliy in his model hinges on her influence on relaive prices of home oupu. This requires ha firs he home has some monopoly power over is oupu, and second, ha he benevolen governmen is able o change privae behavior. In he hree cases described in proposiion 1, he home loses is monopoly power over he goods i produces and relaive prices of home goods are fixed a heir seady sae level. Hence, a benevolen governmen canno improve upon compeiive equilibrium. Apar from hose hree condiions, in a semi-open capial accoun regime where foreign exchange inervenions can affec privae savings, a benevolen governmen generally improves welfare by choosing a differen allocaion compared o he compeiive one. 4 CALIBRATION The model is calibraed o a quarerly frequency. The saisics for he daa are compued from China daa for he period 2:Q1 o 213:Q4. The parameer values are summarized in able 1. The real ineres rae is se o 4 percen annually, which gives us a discoun facor β of.99. The risk aversion level σ is assumed o be 2. We se he inverse of he Frisch labor supply elasiciy η o be 2 as well. In China, he average impors and expors o GDP raios are approximaely 24% and 26% respecively, which implies he preference parameers for domesic goods in home and foreign counry are ν =.24 and ν =.26. The value for elasiciy of subsiuion beween home and foreign inermediae goods (µ) ypically ranges from 1 o 2 in he lieraure. We follow Chang, Liu and Spiegel (215) o choose µ = µ = 1.5, and hey lie wihin he range esimaed by Feensra e al. (214). We se he ransacion cos parameer γ f = 1e 5, o ensure ha he model dynamics is no affeced by his ransacion cos. For he inermediae goods firms, he producion share of capial is se o.6 and he depreciaion rae of capial is.5, which implies a 2% annual depreciaion rae. These numbers are higher han sandard values calibraed o he U.S. economy in he lieraure, however hey are necessary o replicae he high invesmen o GDP raio and capial invesmen reurns observed in China. I follow Gali and Monacelli (25) 16

17 by seing ɛ = 6, yielding a seady sae mark-up of 1.2. The fracion of firms ha canno re-se heir prices is assumed o be.66, which implies ha, on average, he prices will be rese every hree quarers. Lasly, we specify he echnology shock persisence o be.9 wih sandard deviaion 1%. We also experimen wih 1 basis poins foreign ineres rae shocks wih a persisence of.9. Table 1: Parameers: Quarerly Saisic Parameer Value Households Discoun Facor β.99 Risk Aversion σ 2 Inverse of Frish Elasiciy η 2 Labor Hours χ 8.65 Preference for Foreign Goods ν.24 Preference for Domesic Goods ν.26 Elasiciy of Subs. beween Home and Foreign Goods µ 1.5 Elasiciy of Home Expors µ 1.5 Inernaional Capial Adj. Cos γ f 1e-5 Firms Capial Share α.6 Depreciaion Rae δ.5 Elasiciy of Subs. beween inermediae goods ɛ 6 Calvo Pricing ω.66 Shocks Tech. Shock Persisence ρ a.9 Tech. Shock Sd. Dev. σ a.1 Foreign Ineres Rae Shock Persisence ρ R.9 Foreign Ineres Rae Sd. Dev. σr.1 The daa and model implied seady sae values are repored in able 2. The invesmen o GDP is 43%, which is consisen wih he Chinese daa. The governmen expendiure o GDP raio is fixed a 14% based on he daa. The domesic and foreign goods preference parameers ν and ν are chosen o mach he seady sae values for expors and impors o GDP raio a 26% and 24% respecively. The consumpion o GDP raio is calculaed as 4% based on he parameer values assumed in able 1. Finally, alhough I do no arge he ne foreign asse posiion, he model implied seady sae ne foreign asses over GDP raio is quie close o he one observed from he daa a 49% and 42% respecively. Noe here he open and semi-open capial accoun policy regimes imply an idenical non-sochasic seady sae. 17

18 Table 2: Deerminisic Seady Saes Variable Daa Models Consumpion/GDP Invesmen/GDP Gov Spending/GDP Expors/GDP Impors/GDP Ne Foreign Asses/GDP Daa Source: China NBS, World Bank. The benevolen governmen s firs order condiions are compued using he algorihm developed by Levin e al. (26). The model is hen solved by second-order perurbaion mehods. 5 RESULTS: FLEXIBLE PRICES This secion analyzes he semi-open capial accoun regime under flexible prices. 8 Wihou nominal rigidiies, moneary policy does no affec he real allocaions of resources and welfare. In his case, policy makers essenially have only one insrumen, foreign exchange inervenions, in addiion o a closed capial accoun o he privae secor. This allows me o separae he welfare effec of foreign exchange inervenions from moneary policy. In secion 6, policy makers are given wo insrumens, moneary policy and foreign exchange inervenions, which allows us o examine policy ineracions. 5.1 WELFARE AND MACROECONOMIC VOLATILITY This main objecive of his paper is o invesigae he welfare differences beween an open capial accoun and a semi-open capial accoun. To evaluae welfare, I wrie household uiliy recursively as, Wel f = U(c, n ) + βe Wel f +1. (5.1) The welfare gain is measured as a percenage of consumpion ha a household is willing o give up in order o live in an alernaive economy raher han a benchmark 8 I se he Calvo parameer ω = 1e 6 o model flexible prices. 18

19 economy. Specifically, he welfare gain τ is defined as, E β u[(1 τ)c al, l al ] = E β u(c ben, l ben ). (5.2) = = Noice here we follow Schmi-Grohé and Uribe (26) o condiion he iniial sae being he deerminisic seady sae and hen compue he expeced welfare in differen policy regimes. Given ha he non-sochasic seady sae is he same across regimes in his model, his choice of iniial sae guaranees an idenical saring poin under all polices and akes ino consideraion he ransiion dynamics leading o he sochasic seady sae PRODUCTIVITY SHOCKS Table 3 presens he macroeconomic volailiy of seleced variables under alernaive policy regimes relaive o he benchmark, subjec o a one percen home TFP shock. Recall ha in he benchmark model, he home counry s bond posiions are deermined compeiively by he households wihou governmen inervenions and prices are flexible. The second column shows he sabiliy of he flexible price equilibrium in a semi-open capial accoun regime. In conras o he free flow equilibrium, mos of he macroeconomic variables exhibi less flucuaions excep aggregae inflaion and nominal exchange rae appreciaion rae. While he averages of consumpion and labor are almos idenical in hese wo regimes, he semi-open capial accoun regime sabilizes he economy and generaes a welfare gain of.6% consumpion equivalence relaive o he open capial accoun regime. In a semi-open capial accoun regime, he governmen is permied o accumulae foreign bonds hrough serilized inervenions, bu he privae secor loses access o he inernaional capial marke. This disors households ineremporal consumpion allocaions as hey are no able o equae heir marginal uiliy of consumpion wih world ineres raes. A he same ime, he governmen inernalizes he ermsof-rade exernaliy when choosing he bond posiion for he households. The benefi of a more favorable erms of rade dominaes he cos of ineremporal consumpion disorions, and lead o less volaile capial flows. This is consisen wih he finding of Farhi and Werning (214) in which he auhors sugges he use of leaning agains he wind capial conrols o smooh ou capial flows. Here, I show opimal inervenions in semi-open capial accoun regime sabilizes capial flows wihou he use of sae-dependen capial conrols. Figure 3 repors he impulse response funcions of seleced macroeconomic variables o a one-percen posiive domesic produciviy shock. I assume he economy 19

20 sars from is seady sae. The figure plos percenage deviaions of each variable from is seady sae following he shock, over a 1-year period. The red dash-do lines show he model dynamics under open capial accoun regime and he blue solid lines represen he impulse responses under semi-open capial accoun regime. Firs, consider he compeiive equilibrium. When he counry becomes more producive, invesmen surges o ake advanage of higher reurns. Par of he increase in invesmen is funded by borrowing from he inernaional bond marke. The home wealh effec generaes a higher demand for foreign goods, moreover he demand for invesmen also increases home impors. A he same ime, he rise of domesic inermediae goods producion leads o an expendiure-swiching from foreign o domesic goods. The combined impac is he subsiuion effec dominaes a firs, causing ne expors o drop o defici. As he produciviy falls back, he wealh effec becomes dominan and ne expors swing back o surplus. The changes in erms of rade reflec his rade paern. Throughou he period, more domesic oupu ends o push down he erms of rade, while he higher demand for foreign goods a he beginning deerioraes he erms of rade furher. As a resul, he real exchange rae depreciaes. To beer undersand he welfare gains from inervenions, I proceed by adding capial conrols and foreign exchange inervenions in urn. In he closed capial accoun regime, consumpion rises sharply afer he produciviy advance, bu invesmen does no increase as much as free bond rade. On he one hand, inernaional bond rade permis capial o flow o he mos efficien use and improves producive efficiency. On he oher hand, i affecs he auomaic consumpion risk insurance provided by erms of rade, as sressed in Cole and Obsfeld (1991). As a consequence, he lifeime consumpion level is lower. Heahcoe and Perri (214) finds ha under cerain parameer values, he erms of rade insurance agains counry specific shocks dominaes, implying ha living in financial auarky is welfare improving. Alhough no repored, he baseline calibraion presened in his paper does no provide sufficien insurance for financial auarky alone o be welfare dominan. 9 Neverheless, when he governmen adops he semi-open capial accoun regime, welfare is higher han wih free bond rade. This is because he benevolen governmen is able o srike a balance beween producive efficiency and consumpion risk insurance wih inervenion as an addiional policy ool. As we can see from figure 3, he governmen holds a differen inernaional bond posiion on behalf of he counry in general compared o he one in open capial accoun regime. This is due o he fac ha 9 I confirm he findings by Heahcoe and Perri (214)(no repored). Financial auarky can be welfare improving when he elasiciy of subsiuion is low or when he impor share is high. 2

21 when an individual household makes his invesmen decision, he akes he prices of oupu sold in he inernaional marke as given. However, collecive individual producion decisions increase he oal supply of domesic goods in he marke and lower heir prices, i.e. deeriorae he erms of rade. On he oher hand, a consrained planner inernalizes he effec of more domesic supply on erms of rade. Deviaion from compeiive equilibrium is desirable if he benefi of a favorable erms of rade under lower domesic supply ouweighs he cos from losing some degree of ineremporal consumpion smoohing. Noice ha he direcion of capial flow may no even be he same in hese wo regimes. Also shown in figure 3, a benevolen governmen chooses o inves and work less, resuling in lower oupu and curren accoun deficis. Overall, he erms of rade is more favorable wih inervenions han wihou. I demonsrae his poin by calculaing he ne presen value of he difference in he erms of rade under he wo scenarios. This measure, given below, is posiive which means he overall erms of rade is more favorable wih inervenions. NPV(ToT) = (1 β) = β (ToT w/ ToT w/o ) > In pracice, his opimal policy can be implemened in he following way: Firs of all, he governmen does no allow capial flows hrough he privae secor. Iniially when he privae agens wan o borrow from abroad, he public secor acs as a financial inermediary ha borrows from he inernaional bond marke and lends o he domesic agens in local currency bonds, bu a a smaller amoun han he privae secor s desired level. Laer on, when he privae secor wans o save, he governmen issues domesic bonds o force privae secor o save a a higher rae han individual opimaliy and uses he proceeds o hold foreign bonds FOREIGN INTEREST RATE SHOCKS In his secion, I compare he welfare effecs of a foreign ineres rae hike across capial accoun policy regimes. This experimen can be hough of as when he Fed raises U.S. ineres raes, should China adop a semi-open capial accoun policy regime in response o such an exernal shock. The macroeconomic sabiliy looks similar when foreign ineres rae shocks hi he home economy. Table 4 displays he resuling volailiies. Almos all macroeconomic variables are more sable in a semi-open capial accoun regimes han in an open capial accoun regime. The consrained planner is able o choose he opimal pah of inernaional borrowing and saving o influence domesic producion so ha he purchasing 21

22 power of home producion is high when consumpion is low. This resuls a higher consumpion and lower work effor on average, and hey are less volaile. The welfare gain from adoping a semi-open capial accoun regime is sizable compared o he benchmark, abou.626% consumpion equivalence each period. I repor he impulse responses in figure 4. In open capial accoun regime, as illusraed by he dash-do lines, a higher foreign ineres rae induces home households o hold more foreign bonds. This drives down domesic invesmen and oupu. Home consumpion falls as well, bu labor hours rise. Home currency depreciaes in real value and he erms of rade worsen iniially. The domesic households swich o impor less foreign goods and expor more home goods because of he changes of erms of rade. How should he governmen inervene in he foreign exchange marke o cope wih his exernal shock in a semi-opimal capial accoun regime? The blue solid lines in figure 4 shows ha a benevolen governmen chooses o save less (or borrow more) in he inernaional bond marke compared o he free marke allocaion. This miigaes he fall of invesmen and oupu due o capial ouflows. The erms of rade and real exchange rae change less drasically, such ha he erms of rade is more favorable when he oupu is low and is less favorable oherwise. This manipulaion of relaive prices miigaes he fall of income due o lower oupu, sabilizes he economy, and improves welfare. To implemen he opimal policy responses in pracice, he Chinese governmen should borrow more han he privae secor s desire from overseas and channel hose exernal resources ino domesic economy by paying back ousanding governmen bonds. This offses some of he iniial capial fligh, and prevens RMB from sharp depreciaion. Overall, he real exchange rae exhibis less volailiy when foreign exchange inervenions are conduced opimally under capial conrols. This can be undersood as a correcion of he erms-of-rade exernaliy and provides a raionale for real exchange rae argeing. Neverheless, he nominal exchange rae appreciaion rae acually flucuaes more drasically when he economy is subjec o domesic produciviy shocks. This makes idenifying he source of disurbance a prioriy o policy makers if hey consider nominal exchange rae argeing. 6 RESULTS: STICKY PRICES The analysis so far has concenraed on he real side of he economy. When prices are flexible, moneary policy is neural and does no affec real allocaions, nor welfare. 22

23 In his secion, I exend he model o include sicky prices. This no only generaes anoher source of inefficiency, i also gives policy makers an addiional effecive policy ool, he moneary policy ineres rae. I examine how he moneary policy and foreign exchange inervenions inerac o deal wih he inefficiencies presened in he exended model. The resuls show ha hese wo policy insrumens have separae arges. While moneary policy effecively reduces domesic price disorions, foreign exchange inervenions under capial conrols are paricularly useful o correc he erms-of-rade exernaliy. In fac, he opimal moneary policy reurns he economy o nearly flexible price allocaions, while he inervenions help o capure all he welfare gains from inernalizing he erms-of-rade exernaliy. This can be seen from comparing he lef and righ panel of ables 3 and 4. The lef and righ panels are almos idenical, which indicaes he macroeconomic sabiliies and welfare are very close wih or wihou price disorions and moneary policy subjec o eiher domesic TFP shocks or foreign ineres rae shocks. To make sense of his resul, le us break down he able by comparing column by column. Firs, he firs and hird column are equilibria in an open capial accoun regime. These wo columns indicae ha opimal moneary policy nearly undoes all he price disorions and resores he flexible price equilibrium, even if an incenive o deviae from i in a beneficial way o influence erms of rade, as noed by Corsei and Peseni (21) among ohers, exiss. The second and las columns show equilibria in semi-open capial accoun regime under flexible prices and sicky prices respecively. While no exac, hey look very similar o each oher. 1 I conclude ha in his model wih baseline calibraion, policy makers should use moneary policy o arge domesic price fricions, while adoping a semi-open capial accoun regime o arge-erms ofrade exernaliies. Since he general shapes of impulse response funcions look very similar o hose under flexible prices, I focus on he explanaions of nominal variables. Afer a posiive produciviy shock, higher aggregae supply drives down he domesic price level, bu also depreciaes home currency, making foreign goods more expensive. Higher impor prices pull up home aggregae inflaion and he nominal exchange rae depreciaes. The opimal moneary policy ineres rae rises in response o sabilize he economy. Noice ha he changes of domesic inflaion are quaniaively very small, indicaing he flexible price equilibrium is replicaed. If a foreign ineres rae increase occurs, aggregae demand falls and domesic inflaion drops. However, he exchange rae 1 Mos of hem differ by a magniude of 1e-4. 23

24 sill depreciaes due o he capial flighs, and as a resul, aggregae inflaion rises. Moneary policy lowering he ineres rae o comba he negaive spill-over effecs of foreign ineres rae hike. 7 SENSITIVITY ANALYSIS In his secion, I perform sensiiviy analysis o check he impac of parameer values on my resuls. I alered four key parameers, he elasiciy of subsiuion beween home and foreign goods in producing final goods, he elasiciy of foreign demand for home expors, and home expor and impor shares. Table 5 and 6 presen he welfare gains under differen parameer values across policy regimes. The firs wo variaions of parameer values make home goods less subsiuable, and he las variaion indicaes greaer rade inegraion. Overall, he resuls confirm he findings of proposiion 1. By comparing welfare gains across differen parameerizaions, I find when he consrained planner s abiliy o manipulae relaive prices of home produced goods increases, i amplifies he welfare gains from foreign exchange inervenions. Also noice ha real exchange rae becomes less volaile in he semiopen capial accoun regime across differen parameerizaions. The las wo columns show he welfare gains when he price adjusmens are sluggish and moneary policy is conduced opimally. Alhough quaniaively small, he opimal moneary policy under sicky prices in an open capial accoun regime achieves a welfare gain compared o flexible prices allocaions. This is no surprising, as he planner s greaer abiliy o manage relaive prices gives moneary policy a sronger incenive o deviae from he flexible price equilibrium, and resuls a beer oucome. The las column is almos idenical o he firs column, indicaing he join use of moneary policy and foreign exchange inervenions is sufficien o bring he equilibrium back o he allocaions under flexible price wih semi-open capial accoun. Those resuls hold under boh TFP and foreign ineres rae shocks. Overall, he main resul ha moneary policy alone resores he economy back o flexible price equilibrium and inervenions correc mos of he erms-of-rade exernaliy sill holds. 8 CONCLUSION This paper sudies opimal foreign exchange inervenions in a semi-open capial accoun policy regime in which he public secor has access o he inernaional bond marke bu he privae secor does no. This policy regime corresponds o he Chinese economy. I find ha opimal inervenions under capial conrols can improve welfare 24

25 over a fully open capial accoun by sraegically manipulaing he erms of rade. In paricular, when an economy receives posiive produciviy shocks, he consrained planner accumulaes foreign reserves and forces he privae secor o save more han heir desired level. When he foreign counry raises world ineres rae, i is opimal for he home economy o resric privae capial fligh. In hese wo cases, he home economy resiss real exchange rae movemens. In he presence of domesic nominal rigidiy, inervenions can lead o a welfare gain even if moneary policy is se opimally. I find separae roles for hese wo policy insrumens. While moneary policy more effecively eliminaes domesic price disorions, foreign exchange inervenions more efficienly correc erms-of-rade exernaliies. Noice ha he model assumes perfec pass-hrough of exchange rae which is no suppored by empirical evidence. An incomplee pass-hrough ha brings anoher price disorion may break down he dichoomy of moneary policy and inervenions. I leave his for fuure research. 25