Reserve Accumulation, Growth and Financial Crises

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1 Reserve Accumulaion, Growh and Financial Crises Gianluca Benigno LSE and CEPR Luca Fornaro LSE December 212 Absrac We presen a model ha reproduces wo salien facs characerizing he inernaional moneary sysem: Fas growing emerging counries i) Run curren accoun surpluses, ii) Accumulae inernaional reserves and receive ne privae inflows. We sudy a wo-secor, radable and non-radable, small open economy. There is a growh exernaliy in he radable secor and agens have imperfec access o inernaional financial markes. By accumulaing foreign reserves, he governmen induces a real exchange rae depreciaion and a reallocaion of producion owards he radable secor ha booss growh. Financial fricions generae imperfec subsiuabiliy beween privae and public deb flows so ha privae agens do no perfecly offse he governmen policy. The possibiliy of using reserves o provide liquidiy during crises amplifies he posiive impac of reserve accumulaion on growh. The opimal reserve managemen enails a fas rae of reserve accumulaion, as well as higher growh and larger curren accoun surpluses compared o he economy wih no policy inervenion. The model is also consisen wih he negaive relaionship beween inflows of foreign aid and growh observed in low income counries. JEL Codes: F31, F32, F41, F43. Keywords: foreign reserve accumulaion, gross capial flows, growh, financial crises. We would like o hank Joshua Aizenman, Philippe Bacchea, Pierpaolo Benigno, Javier Bianchi, Edouard Challe, Gong Cheng, David Cook, Fabrizio Coricelli, José De Gregorio, Pierre Olivier Gourinchas, Jean Imbs and Alwyn Young for useful commens. We also hank seminar paricipans a he London School of Economics, Universià Bocconi, he Paris School of Economics, Universià Caolica del Sacro Cuore, he Herio-Wa Universiy, he Naional Bank of Serbia and he BIS and paricipans a he conference on Financial Sabiliy a he Hong Kong Universiy, he Aix-Marseille workshop on Open Macroeconomics, he conference on Exchange Raes and Exernal Adjusmen a he Swiss Naional Bank, he LBS conference on Developmens in Macroeconomics and Finance, he IGC workshop on Fiscal and Moneary Policy, he 212 Pacific Basin Research Conference a he FRBSF Cener and he conference on Inernaional Capial Flows and Spillovers in a Pos-Crisis World a he Bank of England. Financial suppor from he ESRC Gran on he Macroeconomics of Capial Accoun Liberalizaion is acknowledged. Luca Fornaro acknowledges financial suppor from he French Minisère de l Enseignemen Supérieur e de la Recherche, he ESRC, he Royal Economic Sociey and he Paul Woolley Cenre.

2 1 Inroducion One of he mos specacular recen rends in he inernaional moneary sysem is he considerable buil up of foreign exchange reserves by emerging counries, in paricular Eas Asian economies and China. 1 As shown by figure 1a, he average reserves-o-gdp raio in developing counries more han doubled beween 198 and 21, increasing from 9.5 o 23.3 percen. The increase has been paricularly marked in Eas Asia, where he average reserves-o-gdp raio passed from 15.5 percen in 198 o 55.3 percen in The large accumulaion of foreign reserves is no jus ineresing in iself, bu i also represens a key elemen for undersanding he direcion and allocaion of inernaional capial flows among developing economies. As noiced by Gourinchas and Jeanne (211), while he neoclassical growh model would sugges ha capial should be direced owards hose economies ha experience faser produciviy growh, in he daa we observe ha faser growing economies are associaed wih lower ne capial inflows (figure 1b). Moreover, Alfaro e al. (211) show ha he posiive correlaion beween curren accoun surpluses and growh is purely driven by public flows, while privae flows conform wih he predicions of he neoclassical growh model. In fac, hey find ha he curren accoun surpluses of fas growing economies are due o heir policy of fas accumulaion of inernaional reserves (figure 1c), while curren accoun deficis in counries ha experienced dismal growh performances are driven by inflows of foreign aid. Our main objecive in his paper is o provide a framework ha explains he join behavior of privae and public capial flows in fas growing emerging economies. sudy a wo-secor, radable and non-radable, small open economy. There are wo key elemens. Firs, firms in he radable secor absorb foreign knowledge by imporing inermediae inpus. This mechanism provides he source of growh in our economy, bu is benefis are no inernalized by individual firms since knowledge can be used freely by all he firms in he economy. Second, privae agens have limied access o inernaional financial markes and he economy is exposed o he risk of sudden sops in capial inflows. The combinaion of growh exernaliies and financial fricions provides a powerful incenive for he governmen o accumulae reserves. Firs, we show ha during ranquil imes he governmen can use reserve accumulaion o exploi he knowledge spillovers in he radable secor. In fac, an increase in foreign exchange reserves leads o a real currency depreciaion and o a reallocaion of producion oward he radable secor. This simulaes he use of impored inpus, he absorpion of foreign knowledge and produciviy growh. This mechanism is effecive as long as here is imperfec subsiuabiliy beween 1 See Ghosh e al. (212) for a discussion of he accumulaion of reserves by developing counries in he las hree decades. 2 Developing counries refer o a sample of 66 developing economies. Eas Asia refers o he unweighed average of China, Hong Kong, Indonesia, Souh Korea, Malaysia, Philippines, Singapore and Thailand. All he daa are from he World Bank Developmen Indicaors. We 1

3 Reserves (% of GDP) 6 5 Developing counries Eas Asia (a) Reserves in percen of GDP (b) Average per capia GDP growh and average curren accoun balances beween 198 and 21 (c) Average per capia GDP growh and average reserve accumulaion beween 198 and 21 Figure 1: Moivaing facs. Noes: he sample is composed of 66 developing counries. Eas Asia refers o he unweighed average of China, Hong Kong, Indonesia, Souh Korea, Malaysia, Philippines, Singapore and Thailand. Daa are from he World Bank Developmen Indicaors. 2

4 privae and public flows. Indeed, in he neoclassical growh model he accumulaion of inernaional reserves would be offse by privae capial inflows. Insead, in our framework he offseing effec is no complee because he risk of a sudden sop limis he willingness of privae agens o accumulae deb in response o an increase in he sock of reserves by he governmen. Hence, while he economy as a whole runs a curren accoun surplus and gahers foreign reserves, he privae secor accumulaes foreign liabiliies, consisen wih he empirical findings of Alfaro e al. (211). Second, we show ha he presence of knowledge exernaliies provides an incenive for he governmen o use reserves during financial crises, in order o counerac he loss of access o privae credi by firms in he radable secor. Indeed, our framework reproduces he paern of gross capial flows observed by Broner e al. (211) in emerging markes. During financial crises boh gross inflows, in he form of privae credi, and gross ouflows, in he form of reserve accumulaion, decrease, since he governmen uses is sock of reserves o provide loans o firms ha have los access o foreign financing. Through his channel, reserve managemen posiively affecs growh by cushioning he impac of financial crises on oupu and produciviy growh. We hen examine he normaive implicaions of reserve accumulaion. We firs show ha a social planner ha is unconsrained in erms of policy ools would choose no o accumulae reserves bu o rely on secoral subsidies. We argue, similarly o wha Korinek and Servén (21) sugges, ha in pracice secoral subsidies may conflic wih WTO rules or oher rade agreemens. In his case, a policy of reserve accumulaion can be used o circumven hese resricions. We compue wihin a class of simple rules he opimal reserve policy and we find ha, despie being a second-bes policy ool, he welfare gains from opimal reserve managemen can be significan. As an example, we find ha he gains from public inervenion in capial flows for a counry ha is opening iself o inernaional capial markes are in he order of a 1 percen permanen increase in consumpion. Moreover, we find ha he bulk of hese welfare gains come from he use of reserves during financial crises. Finally, we show ha our model also raionalizes he negaive relaionship beween inflows of foreign aid and growh observed in low income counries. We model foreign aid as public loans provided o he governmen by foreign insiuions. We show ha inflows of foreign aid lead o an appreciaed real exchange rae, less producive resources in he radable secor and slower accumulaion of knowledge and growh, in he spiri of he resource curse lieraure. 3 The res of he paper is srucured as follows. We sar by discussing our key assumpions and he relaed lieraure. Then, in secion 2 we inroduce he framework. Secion 3 presens he social planning allocaion and discusses he poliical barriers ha 3 The daa can also be explained by he fac ha donors may wan o allocae more aid o he counries wih lower growh. However, he empirical evidence provided by Rajan and Subramanian (211) is consisen wih he mechanism described by our model. 3

5 may preven a governmen from implemening he firs bes hrough secoral subsidies. Secion 4 provides inuiion abou he effec of reserve managemen. Secion 5 presens he resuls of our policy experimen on financial liberalizaion and provides esimaes of he welfare gains from implemening he opimal reserve policy. Secion 7 considers he impac of inflows of foreign aid. Secion 7 concludes. Discussion of key elemens. Our heory ress on wo key elemens: he exisence of knowledge spillovers in he radable secor and he limied and inermien access o inernaional credi markes. Here we discuss he empirical evidence ha underpins hese assumpions. We sudy an economy ha grows by absorbing foreign knowledge. The exisence of inernaional knowledge spillovers is well esablished in he lieraure on global growh. The foundaions for he heoreical sudy of cross-counry knowledge flows were laid down by Grossman and Helpman (1991), while Klenow and Rodriguez-Clare (25) sress how a model of he world economy has o feaure inernaional knowledge spillovers in order o be consisen wih he growh paerns observed in he daa. There is also a sizable lieraure emphasizing he role of rade in faciliaing he ransmission of knowledge across borders. The idea is ha in order o have access o he inernaional pool of knowledge a counry has o impor foreign producs or expor o foreign markes. We choose o focus on he ransmission of knowledge hrough he impors of inermediae inpus because we feel ha his is he channel for which more empirical evidence is available. Our saring poin is he empirical analysis of Coe e al. (1997). They find ha impors of capial goods and maerials represen a key channel hrough which discoveries made in developed counries spill over o developing economies. Subsequen research, surveyed by Keller (24), has confirmed he significan role of impors in he process of inernaional knowledge diffusion. More recenly, plan-level evidence on he posiive impac of impors of inermediae goods on produciviy has emerged. For insance, Amii and Konings (27) using Indonesian plan-level daa find a posiive effec on produciviy from a decrease in ariffs on inermediae inpus. Anoher line of research has ried o idenify a posiive effec on produciviy from exporing. This may happen, for example, if exporing allows firms o become familiar wih foreign echnologies ha increase heir produciviy, he so called learning-by-exporing effec. Isolaing his effec is hard, because he mos producive firms end o self-selec hemselves ino he expor secor. Despie his difficuly, some firm-level evidence in suppor of learning-by-exporing effecs has been find by Blalock and Gerler (24), using Indonesian daa, and by Park e al. (21), who use daa from Chinese firms. Imporanly, our qualiaive resuls would carry hrough in a model in which firms absorb foreign echnology by exporing, raher han by imporing inermediae inpus. 4 4 There is a long-sanding radiion in he growh lieraure ha emphasizes he role of learning-bydoing effecs. This lieraure, ha daes back o Arrow (1962), sees he accumulaion of knowledge 4

6 In our model produciviy growh hrough he absorpion of foreign knowledge is presen only in he radable secor. We make his sark assumpion o simplify he exposiion, bu our qualiaive resuls would remain in a seing in which knowledge spillovers are sronger in he radable secors compared o he non-radable ones. Rodrik (28) provides some indirec evidence consisen wih his assumpion. He finds ha real exchange rae depreciaions simulae growh in developing counries and ha his effec is increasing in he size of he radable secor. In addiion, Rodrik (212) considers crosscounry convergence in produciviy a he indusry level and finds ha his is resriced o he manufacuring secors. This finding is consisen wih he idea ha inernaional knowledge spillovers are confined o, or a leas more inense in, he manufacuring secors. Since manufacuring represens he bulk of he secors producing radable goods, Rodrik s finding lends suppor o our assumpion ha knowledge spillovers are more imporan in he radable secors. Finally, in our model knowledge is a non-excludable good, and hence i can be used freely by any firm in he economy. We sill lack a good empirical undersanding of he exen o which knowledge can be appropriaed by individual firms. However, i seems reasonable o assume ha, a leas parly, he knowledge accumulaed inside a firm can spill over o oher firms. For example, his may happen rough imiaion or hrough he hiring of workers ha embody he echnical knowledge developed in a rival firm. Indeed, he assumpion ha knowledge is only parially excludable is a feaure of he mos influenial endogenous growh frameworks, such as he models developed by Romer (1986), Romer (199), Grossman and Helpman (1991) and Aghion and Howi (1992). I is imporan o sress ha, while we assume ha knowledge is a compleely non-excludable good, he mechanism ha we describe would sill hold in a framework in which knowledge is parially excludable. We now urn o our assumpions abou financial markes. We consider an economy ha periodically sees is access o inernaional credi markes curailed. This assumpion is mean o capure he sudden sop episodes, ha is periods in which capial inflows are severely reduced, experienced by many emerging counries. These episodes are ofen associaed wih banking crises and deep recessions. In our model, sudden sops have a negaive impac on producion because hey inerfere wih firms abiliy o secure rade credi and hence o saisfy heir demand for impored inpus. Mendoza (21) shows ha a model wih his feaure is able o capure he behavior of measured TFP around sudden sop episodes. Moreover, Mendoza and Yue (211) provide empirical evidence on he fall in he use of impored inpus around crisis episodes culminaing in a sovereign defaul. Our specificaion of financial fricions also allows us o capure he negaive long run impac of crises on growh highlighed by he empirical analysis of Cerra and Saxena as a by produc of he producion process. Krugman (1987) and Young (1991) are early sudies of learning-by-doing effecs in open economy models. Our qualiaive resuls would hold in a model in which learning-by-doing is he engine of growh, as long as learning-by-doing effecs are sronger in he radable secor and no fully inernalized by firms. 5

7 (28). During financial crises he governmen can use is sock of foreign exchange reserves o provide rade credi o firms, so as o help firms o overcome he loss of access o foreign financing. Cenral banks in emerging counries ofen use reserves o provide dollar loans o banks o avoid disrupions in rade credi during sudden sops. For insance, his was he case in Korea and Indonesia during he 1997 Asian Crisis and in Brazil in More recenly, several emerging counries used reserves o conain disrupions in rade credi following he 28 financial crisis. 6 More broadly, our model capures he posiive impac of acive reserve managemen on oupu during financial crises. Dominguez e al. (212) show how emerging counries used heir sock of reserves o miigae he fall in oupu in he afermah of he 28 financial crisis. Relaed lieraure. This paper is relaed o several srands of he lieraure. Our framework provides a plausible explanaion for he negaive correlaion beween produciviy growh and capial inflows in developing counries observed by Prasad e al. (27), Gourinchas and Jeanne (211) and Alfaro e al. (211). Gourinchas and Jeanne (211) and Alfaro e al. (211) find ha he curren accoun surpluses observed in fas growing developing economies is driven by heir policy of reserve accumulaion and his moivaes our focus on foreign exchange reserves. The cenral role of governmen inervenion in shaping capial flows o developing counries relaes our paper o he so-called Breon Woods 2 perspecive on he inernaional moneary sysem of Dooley e al. (23), according o which he large accumulaion of inernaional reserves by he public secor in emerging economies is par of an expor-led growh sraegy. Our paper is also relaed o Rodrik (28), who provides empirical evidence in favor of a causal link from real exchange rae undervaluaion o growh. From a heoreical perspecive, our paper is conneced o he growing lieraure providing formal models ha reproduce he negaive correlaion beween growh and capial inflows characerizing developing counries. Examples include Aghion e al. (26), Angeleos and Panousi (211), Broner and Venura (21) and Sandri (21). These papers all focus on privae capial flows, while in our model he negaive correlaion beween growh and capial inflows is driven by reserve accumulaion by he public secor. Aguiar and Amador (211) provide a model in which public flows may generae a negaive correlaion beween growh and capial inflows, bu he mechanism ha hey emphasize is differen from ours. In fac, in heir model he governmen decreases is sock of foreign 5 Ronci and Wang (26) describe cenral banks inervenions o finance rade credi during hese episodes. In 1997, he Bank of Korea used 2.3 billion dollars from is sock of reserves o provide loans o banks o finance impors of raw maerials and purchase expor bills of exchange from exporers. In Indonesia he cenral bank deposied 1 billion dollars of is inernaional reserves in 12 foreign banks as a guaranee o leers of credi issued by Indonesian banks for he financing of impors by expor-oriened firms. Finally, in Brazil he cenral bank provided 1.8 billion dollars beween Augus 22 and early 23 o banks o mee demand for expor finance. 6 See Chauffour and Farole (29). 6

8 deb in order o credibly resrain from expropriaing he reurn from privae invesmen, hus simulaing invesmen and growh. In conras, in our framework reserve accumulaion by he public secor shifs producive resources oward he radable secor in order o exploi he knowledge spillovers coming from he impors of foreign capial goods. Our paper is also relaed o he lieraure examining he deerminans of reserve accumulaion in emerging markes. Aizenman and Lee (27) and Korinek and Servén (21) emphasize he link beween reserve accumulaion and growh exernaliies, while Durdu e al. (29) and Jeanne and Rancière (211) focus on he precauionary moive of holding inernaional reserves. In Bianchi e al. (212) reserves are used as a buffer agains rollover risk. Bacchea e al. (211) sugges ha he accumulaion of foreign reserves can be used o supply saving insrumens o domesic agens when domesic financial markes are imperfec and privae agens have limied access o foreign credi. Our framework encompasses he firs wo approaches and differs criically from he exising lieraure in he modeling of public versus privae capial flows. 2 Model We consider an infinie-horizon small open economy. Time is discree and indexed by. The economy is populaed by a coninuum of mass 1 of households and by a large number of firms. Firms are owned by he households and produce radable and nonradable consumpion goods. Moreover, firms producing he radable good engage in financial ransacions wih foreign invesors. There is also a governmen ha manages foreign exchange reserves. 2.1 Households The represenaive household derives uiliy from consumpion and supplies inelasically one uni of labor each period. The household s lifeime expeced uiliy is given by E [ = ] β C1 γ. (1) 1 γ In his expression, E [ ] is he expecaion operaor condiional on informaion available a ime, β < 1 is he subjecive discoun facor, γ > is he coefficien of relaive risk aversion and C denoes a consumpion composie good. C is defined as a Cobb-Douglas aggregaor of radable C T and non-radable C N consumpion goods 7 C = ( C T ) ω ( C N ) 1 ω, (2) pah. 7 A Cobb-Douglas consumpion aggregaor is needed o ensure he exisence of a balanced growh 7

9 where < ω < 1 denoes he share of expendiure in consumpion ha he household allocaes o he radable good. Each period he household faces he following flow budge consrain C T + P N C N = W + Π T + Π N. (3) The budge consrain is expressed in unis of he radable good. The lef-hand side represens he household s expendiure. We define P N as he relaive price of he non-radable good in erms of he radable good, so C T + P N C N is he household s consumpion expendiure expressed in unis of he radable good. The righ-hand side represens he income of he household. W denoes he household s labor income. Π T and Π N are he dividends ha he household receives from firms operaing respecively in he radable and in he non-radable secor. For simpliciy, we have assumed ha domesic households do no rade direcly wih foreign invesors. As we will see below, households can access inernaional financial markes indirecly hrough heir ownership of firms. Each period he represenaive household chooses C T and C N o maximize expeced uiliy (1) subjec o he budge consrain (3). The firs order condiions are ωc 1 γ C T = λ (4) (1 ω)c 1 γ C N = λ P N, (5) where λ denoes he Lagrange muliplier on he budge consrain, or he household s marginal uiliy of wealh. By combining (4) and (5), we obain he sandard inraemporal equilibrium condiion ha links he relaive price of non-radable goods o he marginal rae of subsiuion beween radable and non-radable goods P N = 1 ω ω C T C N. (6) According o his expression, P N is increasing in C T and decreasing in C N. In wha follows we will use P N as a proxy for he real exchange rae. 2.2 Firms in he radable secor The radable secor is mean o capure a modern secor characerized by dynamic produciviy gains and open o financial ransacions wih foreign invesors. Firms in he radable secor produce using labor L T, an impored inermediae inpu M and he sock of accumulaed knowledge X, according o he producion funcion Y T = ( X L T ) αt M 1 α T, (7) 8

10 where Y T is he amoun of radable goods produced in period and < α T < 1 is he labor share in gross oupu in he radable secor. Knowledge is non-rival and can be freely used by firms producing radable goods. Firms in he radable secor have access o inernaional credi markes. Firs, hey can rade in a non-coningen one period bond denominaed in unis of radable goods ha pays a fixed gross ineres rae R. A he end of he period he represenaive firm disribues o he households he dividends Π T = Y T W L T P M M B +1 + RB T. (8) In his expression B denoes he firm s holding of foreign bonds a he sar of period. When B < he firm is a borrower. W is he wage paid o workers in he radable secor, P M governmen. 8 is he price of he impored inpu and T are lump-sum axes paid o he Second, firms in he radable secor are subjec o a working capial consrain. A fracion φ of he inermediae inpus has o be paid a he beginning of he period and requires working capial financing. To finance heir working capial, firms have access o inraperiod loan conracs. Under hese conracs, he funds borrowed by firms a he sar of he period have o be repaid a he end of he same period. We assume ha he ineres rae charged on inraperiod loans is equal o zero. The domesic governmen provides an amoun D of working capial loans. The remaining par φp M M D has o be covered using inraperiod loans from foreign invesors. In addiion, we inroduce financial fricions by assuming ha a he end of he period each firm can choose o defaul on is debs oward inernaional invesors. In case of defaul inernaional invesors are able o collec an amoun of radable goods equal o κ X. 9 borrowing consrain To preven defauls, inernaional invesors impose on domesic firms he φp M M D RB κ X, (9) where κ measures he ighness of he borrowing consrain. On he lef-hand side, we have he ne liabiliies of he firm a he beginning of period. Noice ha boh he ineremporal loans and he loans used o finance he working capial expenses ener he consrain. We inroduce credi shocks in he model by assuming ha he parameer κ is sochasic. In wha follows we refer o a financial crisis as a period in which he borrowing consrain (9) holds wih equaliy. Each period he represenaive firm chooses L T, M and B +1 o maximize is expeced 8 The assumpion ha axes are paid by firms in he radable secor, raher han by households, is made o simplify he exposiion and i does no affec our resuls. 9 The presence of he erm X in he borrowing consrain ensures he exisence of a balanced growh pah. Alernaively, we could assume ha invesors can recover a fracion of he oupu produced by he firm. However, his alernaive formulaion would complicae he derivaion of a numerical soluion, wihou adding significan insighs o our analysis. 9

11 sream of dividends discouned by he households marginal uiliy of wealh [ ] E β λ Π T, (1) subjec o he borrowing consrain (9). The opimaliy condiions are given by = α T Y T = W L T (11) (1 α T )Y T = P M M ( 1 + φ µ λ ) (12) λ = βre [λ +1 + µ +1 ] (13) µ ( φp M M D RB κ X ) =, µ, (14) where µ denoes he muliplier on he borrowing consrain. Equaion (11) represens he opimal demand for labor, which implies equaliy beween he marginal produc of labor and he wage. The opimal demand for impored inpus is given by equaion (12). When he borrowing consrain is no binding (µ = ), he marginal produc of he impored inpu is equaed o is price. When he borrowing consrain is binding (µ > ), firms are unable o purchase he desired amoun of impored inpus. This shows up in he equaion as an increase in he marginal cos of purchasing one uni of he impored inpu. Equaion (13) is he modified Euler equaion for he case in which inernaional borrowing migh be consrained. The expecaion of a fuure binding borrowing consrain has an effec similar o an increase in he cos of ineremporal deb ha induces agens o decrease heir borrowing. Finally, equaion (14) is he complemenary slackness condiion for he borrowing consrain. 2.3 Knowledge accumulaion The sock of knowledge available o firms in he radable secor evolves according o X +1 = ψx + M ξ X 1 ξ, (15) where ψ and ξ 1. This formulaion capures he idea ha impors of foreign capial goods represen an imporan ransmission channel hrough which discoveries made in developed economies spill over o developing counries. As menioned above, we assume ha knowledge is a non-rival and non-excludable good. This, combined wih he assumpion of a large number of firms in he radable secor, implies ha firms do no inernalize he impac of heir acions on he evoluion of he economy s sock of knowledge. 1

12 2.4 Firms in he non-radable secor The non-radable secor represens a radiional secor wih sagnan produciviy, closed o financial ransacions wih foreign invesors. The non-radable good is produced using labor, according o he producion funcion Y N = ( ) L N αn. Y N is he oupu of he non-radable good, L N is he amoun of labor employed and < α N < 1 is he labor share in gross oupu in he non-radable secor. 1 The dividends disribued by firms in he non-radable secor can be wrien as Π N = P N Y N W L N. (16) In his expression we have used he fac ha in equilibrium firms in boh secors produce and ha his requires equalizaion beween he wages offered in he wo secors. Profi maximizaion implies α N P N L N α N 1 = W. (17) This equaion represens he opimal demand for labor from firms in he non-radable secor. Similar o firms in he radable secor, firms in he non-radable secor equae he marginal produc of labor o he wage rae. 2.5 Credi shocks The only source of uncerainy in he model concerns κ, he parameer ha governs he sum ha foreign lenders can recover in case of defaul. Our aim is o model an economy in which ranquil imes alernae wih crises. The simples way o capure his is o assume ha κ can ake wo values, κ H and κ L wih κ H > κ L. We will choose values for κ H such ha when κ = κ H he borrowing consrain (9) does no bind, while he value for κ L will be such ha when κ = κ L he borrowing consrain may bind, depending on B and on he acions of he governmen. As menioned above, we refer o a period in which he borrowing consrain binds as a financial crisis. Moreover, denoing by ρ i for i = H, L he probabiliy ha κ = κ i knowing ha κ 1 = κ i, we will se ρ H >.5 so ha crises are rare evens and ρ L > 1 ρ H so ha crisis evens have some persisence. 2.6 Governmen The governmen collecs axes from firms in he radable secor T, provides working capial loans D o firms and rades in foreign exchange reserves F X. 11 In he spiri of 1 To ensure consan reurns o scale in he producion of non-radable goods, we can assume ha producion is carried ou using labor and land according o a consan-reurns-o-scale Cobb-Douglas aggregaor. The producion funcion in he main ex obains if he supply of land is fixed and normalized o one. 11 In our framework he accumulaion of reserves is financed hrough lump-sum axes. In pracice, cenral banks finance he accumulaion of foreign reserves by issuing domesic currency, i.e. hrough seignorage. We leave for fuure research a sudy of he disorions induced by he financing of reserve 11

13 Gerler and Karadi (211), we assume ha lending from he governmen enails some efficiency losses. Specifically, we assume ha in order o lend o firms a sum equal o D, he governmen has o employ an amoun of radable goods equal o D /(1 θ), wih θ 1. Of his amoun, D is repaid by firms o he governmen a he end of he period, while D θ/(1 θ) is los during he inervenion. Hence, he higher θ is, he less efficien is he governmen in providing liquidiy o firms. We can hen wrie he governmen budge consrain expressed in unis of radable goods as F X +1 = R F X θ F X + T D 1 θ, (18) where R F X is he gross ineres rae paid on reserves. To capure some defining feaures of foreign exchange reserves, we assume ha he ineres rae paid on reserves is no greaer han he ineres rae charged on privae loans (R F X canno hold negaive amouns of foreign reserves R) and ha he governmen F X. (19) Moreover, he resources employed o provide working capial loans o firms a he sar of he period canno exceed he sar of period holdings of foreign reserves D 1 θ RF X F X. (2) To simplify he analysis, we resric our aenion o simple forms of inervenion. In paricular, we assume ha o finance reserve accumulaion he governmen levies a ax equal o a fracion χ of he oupu of radable goods during ranquil imes, while following a bad credi shock he governmen ses he ax o zero, ha is T = { χy T if κ = κ H (21) if κ = κ L where χ 1. In addiion, we assume ha during crises he governmen provides loans o firms unil heir borrowing consrain sops binding or unil he size of he inervenion exceeds a fracion χ W K of he sar-of-period sock of reserves. Formally, we assume ha D = Min ( φp M M unc RB κ X, χ W K (1 θ)r F X F X ), (22) where χ W K 1 and M unc is he amoun of inermediae inpus ha firms would choose in absence of financial fricions, ha is if φ =. hrough seignorage. 12

14 2.7 Marke clearing and compeiive equilibrium Marke clearing for he non-radable good requires ha he amoun consumed is equal o he amoun produced C N = ( ) L N αn. (23) Combining (23), wih he households budge consrain (3), he definiions of firms profis in he radable and non-radable secors (8) and (16), and he governmen budge consrain (18), we obain he marke clearing condiion for he radable good C T = Y T P M M B +1 + RB F X +1 + R F X F X θ 1 θ D. (24) Finally, equaing he demand and supply of labor gives L T + L N = 1. (25) We are now ready o define a raional expecaion equilibrium as a se of sochasic processes {C, C T, C N, P N, λ, Y T, L T, L N, M, B +1, µ, W, X +1, F X +1, T, D } = saisfying (2), (4)-(7), (11)-(14), (17)-(18) and (21)-(25), given he exogenous process {κ } =, he governmen policy { χ, χ W K} and iniial condiions B, F X and X. The model has a balanced growh pah in which C T, Y T, M, P N, B +1 and W all grow a he same rae as X. The real exchange rae grows a a posiive rae in he balanced growh pah because produciviy in he radable secor exhibis posiive rend growh, while produciviy in he non-radable secor is fixed. This is he classic Balassa- Samuelson effec. Since also GDP = Y T P M M + P N Y N grows a he same rae as X, we will refer o he growh rae of he sock of knowledge as he growh rae of he economy. 2.8 Discussion: public and privae capial flows A novel feaure of our framework is he disincion beween public capial flows in he form of foreign reserves F X and privae capial flows B. Before we move forward in he analysis, we wan o emphasize he roos of he imperfec subsiuabiliy beween he inernaionally raded privae bond and foreign reserves. The firs difference is relaed o he fac ha in our framework domesic agens have an imperfec access o inernaional privae capial markes. In fac, domesic agens are subjec o an occasionally binding borrowing consrain ha limis heir access o foreign credi. Crucially, he possibiliy of he consrain being binding in he fuure affecs agens behavior also when hey are no consrained. In paricular, a posiive probabiliy of hiing he consrain in he fuure limis he accumulaion of privae deb during periods in which access o foreign credi is pleniful. We also assume ha foreign reserves provide a lower reurn compared o privae bonds (R F X R). Moreover, similarly o 13

15 wha is also assumed in a firs-generaion currency crises model, reserves are subjec o a lower bound (F X ) so ha hey can only be accumulaed. These feaures make he wo asses imperfec subsiues. We noe here ha imperfec subsiuabiliy beween B and F X would hold even if R F X = R as long as here is a possibiliy ha he borrowing consrain ha privae agens face migh be binding. This feaure of he model creaes he key difference wih respec o he neoclassical growh model in which he accumulaion of foreign reserves would be exacly offse one-for-one by privae capial inflows. I also differs from he radiion in inernaional finance as in Kouri (1981) and Branson and Henderson (1985) in which imperfec subsiuabiliy is exogenously assumed raher han arising endogenously. From our reading of he lieraure he disincion beween he privae and public naure of capial flows is novel and differs from exising conribuions ha idenify he inernaional reserves accumulaed by he governmen wih he economy s sock of ne foreign asses. Reassuringly, our model is consisen wih he cyclical paern of gross capial flows characerizing developing counries as described by Broner e al. (211). In our framework ranquil imes are periods of posiive capial inflows, in he form of increases in privae deb, as well as posiive capial ouflows, in he form of accumulaion of official reserves. Conversely, during crises here is a rerenchmen in gross capial flows. Capial inflows diminish as firms cu heir sock of foreign deb, while capial ouflows fall because he governmen employs is sock of reserves o miigae he impac of he crisis. Because of hese effecs, in our model gross capial flows are procyclical, consisen wih he findings of Broner e al. (211) Social planner Before considering he foreign reserve policy, we firs characerize he social planner allocaion. This is useful o build inuiion abou he source of inefficiency in he compeiive equilibrium ha creaes scope for policy inervenion. The planner maximizes domesic households uiliy (1), subjec o he economywide resource consrains (23), (24) and (25), he borrowing consrain (9) and he wo consrains on reserve managemen (19) and (2). Imporanly, he social planner akes ino accoun he effec ha impored inpus have on he accumulaion of knowledge, and so also he equaion describing he evoluion of he sock of knowledge (15) eners as a consrain in he planner s problem. Appendix A provides a formal characerizaion of he social planning allocaion. Here we noice ha, as long as R F X < R, he social planner chooses no o hold reserves, ha is she ses F X +1 = for every. 13 Inuiively, he social planner chooses no o hold 12 Moreover, Broner e al. (211) find ha developing counries reduce heir sock of official reserves during crises. 13 If R F X = R he planner may hold foreign reserves, bu imposing F X +1 = for every on her allocaion does no preven he planner from reaching he firs bes. See he appendix for he deails. 14

16 reserves because hey represen an inefficien saving vehicle compared o foreign bonds, as hey pay a lower ineres rae. This happens nowihsanding he fac ha reserves can be used o provide liquidiy during crises. To undersand his resul, noice ha he working capial consrain is affeced by he privae ne foreign asse posiion a he beginning of period. Due o he lower ineres rae paid on reserves compared o privae bonds, he mos efficien way from he social planner perspecive o relax he consrain in period is by reducing he ne deb posiion in period 1 (i.e. increasing B ), raher han accumulaing reserves and using hem in he even of a crisis. As showed in appendix A, he social planner allocaion is characerized by he same equaions as he compeiive equilibrium in which F X +1 = D = is imposed in every period. 14 The only difference is given by equaion (12), he opimaliy condiion ha deermines he choice of impored inpus. In fac, in he social planner allocaion equaion (12) is replaced by ( ) P M 1 + φ µsp λ SP = (1 α T ) Y ( ) T 1 ξ ( )) X λ SP +1 Y+1 + βξ E (α T µ SP +1 M M λ SP T + κ +1, X +1 λ SP +1 }{{} growh exernaliy where µ SP is he Lagrange muliplier on he borrowing consrain (9) and λ SP is he Lagrange muliplier on he resource consrain for radable goods (24). The lef-hand side of his expression represens he marginal cos of increasing he use of impored inpus, aking ino accoun he impac of he borrowing consrain, capured by he erm µ SP. The firs erm on he righ-hand side is he benefi from he increase in he oupu of radable goods generaed by an increase in he use of impored inpus. These wo erms are equivalen o he ones ha would arise in he compeiive equilibrium allocaion (12). The second erm on he righ-hand side is specific o he social planner problem and capures he benefis derived from he increase in he sock of knowledge implied by an increase in he use of impored inpus. Increasing he sock of knowledge is beneficial for wo reasons. Firs, he social planner inernalizes he fac ha a higher usage of impored inpus oday leads o higher knowledge and higher produciviy omorrow and hus o a higher amoun of radable goods produced in he fuure. Second, he social planner inernalizes he fac ha an increase in produciviy omorrow relaxes he borrowing consrain by increasing he sum ha foreign invesors can recover in case of defaul. These wo effecs imply ha in every period he amoun of impored inpus used is higher in he social planner allocaion han in he compeiive equilibrium wihou policy inervenion. Because of his, he economy grows a a faser rae under he social planner allocaion compared o he compeiive equilibrium wih no policy inervenion. 14 To be precise, if he economy sars wih a posiive amoun of reserves (F X > ) and i is hi by a bad credi shock during he firs period (κ = κ L ) he planner may use he iniial sock of reserves o finance working capial and D may be posiive. Even in his case, F X +1 = for any and so D = for any >. 15

17 I is possible o decenralize he social planner allocaion in he compeiive equilibrium by subsidizing he purchase of impored inpus a rae τ = βξ P M ( X M ) 1 ξ ( λ SP +1 Y+1 E (α T µ SP λ SP T + κ +1 X +1 λ SP )), while financing he subsidy using lump-sum axes. This subsidy scheme is able o resore he firs bes, bu in pracice his form of inervenion migh be poliically hard o implemen. For insance, a governmen migh no be able o openly subsidize firms in he expor secor due o he exisence of rade agreemens such as he WTO rules. In he nex secion we show how an appropriae managemen of foreign exchange reserves can serve as a second bes policy o inernalize he growh exernaliies in he radable secor, wihou breaking he rules dicaed by free rade agreemens. 4 Reserve policy and growh In his secion we discuss he mechanisms hrough which a policy of reserve accumulaion during ranquil imes and liquidiy provision during crisis imes works. In paricular we are ineresed in providing inuiion on how foreign reserves can be used as a second bes policy ool aimed a inernalizing he growh exernaliies in he radable secor. We sar by examining he impac of foreign reserve accumulaion in saes in which he borrowing consrain is no binding. Combining equaions (11), (12) and (17) and using he fac ha when he borrowing consrain does no bind µ =, we obain he demand for impored inpus, M, as a funcion of he real exchange rae, P N ( 1 αt M = P M ) 1 α T X 1 α N P N α T X ( P M 1 α T ) 1 α T α T 1 1 α N. When he real exchange rae appreciaes (P N rises) he demand for impored inpus decreases. Inuiively, an increase in P N, he relaive price of non-radable goods, increases he marginal produc of labor in he non-radable secor. This causes a shif of labor ou of he radable secor ha decreases he produciviy of he impored inermediae inpus and induces firms o reduce M. This suggess ha in order o increase he use of impored inpus and he growh rae of he economy above heir compeiive equilibrium values, he governmen can implemen policies ha reduce P N, ha is o engineer a real exchange rae undervaluaion. 15 To undersand he link beween reserve accumulaion and real exchange rae deerminaion in ranquil imes, we combine equaions (6), (18) and (24) and use he fac ha 15 We refer o a policy-induced real exchange rae undervaluaion when he real exchange rae, ne of he Balassa-Samuelson effec, is undervalued in he compeiive equilibrium allocaion wih policy inervenion compared o is value in he laissez-faire equilibrium. 16

18 during ranquil imes D = o obain P N = 1 ω ω Y T P M M B +1 + RB F X +1 + R F X F X. C N Holding everyhing else consan, his equaion implies a negaive relaionship beween P N and F X +1. The inuiion is simple: In order o accumulae foreign reserves he governmen needs o wihdraw resources from he privae secor. Since only radable goods can be sold o foreigners in exchange for reserves, he governmen mus appropriae radable goods from he privae secor. 16 Privae agens are hen forced o reduce heir consumpion of radable goods. This leads o a real exchange rae depreciaion which in urns simulaes producion in he radable secor and impors of he inermediae good. Through his channel, a policy of accumulaing reserves during ranquil imes has he poenial o increase he growh rae of he economy and o inernalize, a leas parly, he growh exernaliies presen in he radable secor. Clearly, in general equilibrium a change in F X +1 affecs all he oher endogenous variables. In paricular privae agens end o offse he impac of he increase in foreign reserves on consumpion by borrowing from abroad. Indeed, in a model in which privae borrowing and reserves are perfec subsiues, he accumulaion of F X +1 would be counerbalanced by a corresponding decline in B +1. In our framework he imperfec subsiuabiliy beween he wo asses prevens privae agens from compleely offseing he acions of he governmen. We now illusrae he general equilibrium implicaions of a policy of reserve accumulaion during ranquil imes by examining how he sochasic seady sae of our economy varies when we change he value of χ, our proxy for he resources employed o accumulae reserves during ranquil imes. 17 The six panels of figure 2 show he long-run mean values of he following variables: he growh rae of GDP, he percenage deviaions of he real exchange rae from is value in he equilibrium wih no policy inervenion, he rade balance-o-gdp raio, he privae ne foreign asses-o-gdp raio, consumpion of radable goods and aggregae consumpion as a funcion of χ, he fracion of radable oupu devoed o reserve accumulaion during ranquil imes. The real exchange rae is normalized by he sock of knowledge o conrol for he Balassa-Samuelson effec. The same normalizaion is applied o consumpion of radable goods and o aggregae consumpion. As suggesed by he parial equilibrium analysis, he growh rae of he economy is increasing in he amoun of resources devoed o reserves accumulaion during ranquil imes. Sronger accumulaion of foreign exchange reserves also produces a depreciaion 16 In our model, we can hink of radable goods as a proxy for he inernaional currency. 17 More precisely, for each value of χ we solved he model numerically. Then we drew a 1 periodslong simulaion, discarded he firs 1 periods, and compued he long run average values of he variables of ineres. In all he simulaions we se χ W K =, deails on he value of he oher parameers are provided in secion

19 GDP growh χ χ Real exchange rae χ Privae ne foreign asses/gdp Consumpion of radables χ Trade balance/gdp χ Aggregae consumpion χ Figure 2: Impac of reserve accumulaion. Noes: χ is he fracion of radable oupu devoed o reserve accumulaion during ranquil imes. The real exchange rae, ne of he Balassa-Samuelson effec, refers o he percenage change of P N /X wih respec o is value in absence of governmen inervenion (χ = ). The rade balance is defined as Y T P M M C T. The privae ne foreign asses-o-gdp raio is defined as B +1 /GDP. Consumpion is normalized by he sock of knowledge. In all he simulaions we se χ W K =, deails on he value of he oher parameers are provided in secion 5.1. of he real exchange rae and an increase in he rade balance-o-gdp raio. Boh of hese effecs are driven by he fall in he consumpion of radable goods caused by he wihdrawal of resources from privae agens. The increase in he producion of radable goods implied by he real exchange rae depreciaion also conribues o he improvemen in he rade balance-o-gdp raio. Figure 2 shows ha as he governmen increases he pace a which i accumulaes foreign exchange reserves he privae foreign deb-o-gdp raio rises. As we menioned above, his occurs as privae agens parially offse he increase in public savings implied by faser reserve accumulaion by decreasing privae savings and hence by accumulaing more foreign deb. 18 De-rended consumpion of radable goods and aggregae consumpion are boh decreasing in he rae of reserve accumulaion. This highlighs a key rade-off ha deermines he impac on welfare of governmen inervenion. On he one hand, faser reserve accumulaion induces higher growh and his has a posiive effec on welfare. On he oher hand, in order o accumulae foreign exchange reserves he governmen has o subrac resources ha would oherwise be consumed, and his affecs welfare negaively. 18 For very high raes of reserve accumulaion he privae foreign deb-o-gdp raio decreases wih he growh rae of he sock of reserves. This happens because he posiive impac of reserve accumulaion on producion and hence on GDP ouweighs he growh in he sock of privae deb. However, he sock of foreign deb increases monoonically wih he resources devoed o reserve accumulaion. 18

20 Credi shock GDP Impored inpus Time Time Time Real exchange rae Privae foreign deb Foreign exchange reserves Time Time wih inervenion w/o inervenion Time Figure 3: Inervenion during crises. Noes: All he variables are normalized by heir firs-period value. Privae ne foreign deb is defined as B +1. Foreign exchange reserves refer o F X +1. In all he simulaions we se χ =.9. In he model wih inervenion χ W K is se equal o 1, while in he model wihou inervenion χ W K is se equal o. Deails on he value of he oher parameers are provided in secion 5.1. The balance beween hese wo effecs deermines wheher reserve accumulaion during ranquil imes has a posiive or negaive impac on welfare, as we will documen laer. We now urn o he impac of crisis-imes inervenions. During crisis imes, he borrowing consrain binds and he amoun of impored inpus used in producion is given by M = X κ L + RB + D φp M. This equaion makes clear ha in order o increase he amoun of impored inpus used by firms above is value in he equilibrium wihou inervenion, he governmen has o provide working capial loans during crisis evens (i.e. se D > ). Hence, in he model he exisence of growh exernaliies in he radable secor, coupled wih financial fricions, provides a jusificaion for he use of reserves during crises. Figure 3 compares he response o a negaive credi shock for wo differen economies To consruc his figure, we simulaed he economy wih χ =.9 and χ W K = 1 for 1 periods, discarded he firs 1 periods and hen colleced all he periods wih a negaive credi shock (κ = κ L ). We hen consruced windows around each period wih a bad credi shock going from 2 years before he shock o + 12 years afer. We hen colleced he median pah for κ and he median iniial values for he sae variables B 2 and F X 2 across all he windows. Finally, we fed his pah for he credi shock and hese iniial condiions o he model wihou inervenion during crises (χ W K = ) and o he 19

21 The solid lines refer o an economy in which he governmen does no inervene during he crisis (χ W K = ). When he bad credi shock his he economy in period 3, firms become borrowing consrained, hey are forced o cu heir impors of inermediae inpus and his negaively affecs producion of radable goods and GDP. The real exchange rae depreciaes because households have o cu heir consumpion of radable goods and because labor flows oward he non-radable secor, hus increasing he supply of nonradable goods. Moreover, since credi shocks are persisen, households decrease heir sock of iner-emporal foreign deb in order o self-insure agains he increased risk of a fuure bad credi shock. The dashed lines refer o he case in which he governmen uses is sock of reserves o provide working capial loans o firms in he radable secor (χ W K > ). When he bad credi shock his he economy, he governmen sars drawing down is sock of reserves o finance he purchase of impored inpus. This mues he impac of he credi shock on GDP and on he real exchange rae. In addiion, he bad credi shock generaes a milder decrease in foreign deb compared o he case wih no inervenion, because households anicipae ha he governmen will inervene in case of a fuure bad credi shock. Noice ha he crisis enails a permanen difference in he level of GDP beween he wo economies. This sems from he fac ha in our model an economy hi by a crisis never fully recovers o is pre-crisis growh pah. 2 Because of his reason, inervening during crises has a posiive impac on he average growh rae of he economy. One ineresing feaure of he model is ha he relaionship beween growh and he real exchange rae depends on wheher he economy is borrowing consrained or no. In fac he binding borrowing consrain reverses he negaive relaionship beween growh and real exchange rae observed during ranquil imes. This happens because o simulae growh during crises he governmen has o provide loans o firms in he radable secor. This shifs producive resources oward he radable secor, allowing households o consume more radable goods. A he same ime, he producion of nonradable goods decreases and so he real exchange rae appreciaes, creaing a posiive relaionship beween real exchange rae, use of impored inpus and growh. 5 Financial liberalizaion and opimal managemen of foreign exchange reserves In his secion we use our framework o describe he impac of inernaional reserve managemen on he ransiion from financial auarky o a regime in which foreign borrowing is allowed, bu limied by he borrowing consrain (9). This experimen demonsraes he model s abiliy o reproduce he paern of growh, capial flows and reserve accumumodel wih inervenion (χ W K = 1). 2 Cerra and Saxena (28) provide empirical evidence showing ha counries ha are hi by a crisis hardly ge back o heir pre-crisis growh pah. 2