Research Division Federal Reserve Bank of St. Louis Working Paper Series

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1 Research Division Federal Reserve Bank of S. Louis Working Paper Series Capial Conrols or Exchange Rae Policy? A Pecuniary Exernaliy Perspecive Gianluca Benigno Huigang Chen Chrisopher Orok Alessandro Rebucci And Eric R. Young Working Paper A hp://research.slouisfed.org/wp/202/ pdf July 202 FEDERAL RESERVE BAK OF S. LOUIS Research Division P.O. Box 442 S. Louis, MO 6366 he views expressed are hose of he individual auhors and do no necessarily reflec official posiions of he Federal Reserve Bank of S. Louis, he Federal Reserve Sysem, or he Board of Governors. Federal Reserve Bank of S. Louis Working Papers are preliminary maerials circulaed o simulae discussion and criical commen. References in publicaions o Federal Reserve Bank of S. Louis Working Papers (oher han an acknowledgmen ha he wrier has had access o unpublished maerial) should be cleared wih he auhor or auhors.

2 Capial Conrols or Exchange Rae Policy? A Pecuniary Exernaliy Perspecive Gianluca Benigno London School of Economics Chrisopher Orok Universiy of Missouri Federal Reserve Bank of S Louis Eric R. Young Universiy of Virginia Firs Draf: July 20 his Draf: July 28, 202 Huigang Chen MarkeShare Parners Alessandro Rebucci Iner-American Developmen Bank Absrac In he afermah of he global financial crisis, a new policy paradigm has emerged in which old-fashioned policies such as capial conrols and oher governmen disorions have become par of he sandard policy oolki (he so-called macro-prudenial policies). On he wave of his seemingly unanimous policy consensus, a new srand of heoreical lieraure conends ha capial conrols are welfare enhancing and can be jusified rigorously because of second-bes consideraions. Wihin he same heoreical framework adoped in his fas-growing lieraure, we show ha a credible commimen o suppor he exchange rae in crisis imes always welfare-dominaes prudenial capial conrols as i can achieve he firs bes unconsrained allocaion. In his benchmark economy, prudenial capial conrols are opimal only when he se of policy ools is resriced so ha hey are he only policy insrumen available. JEL Classificaion: E52, F37, F4 Keywords: Capial Conrols, Exchange Rae Policy, Financial Fricions, Financial Crises, Financial Sabiliy, Opimal axaion, Prudenial Policies, Planning Problem. he views expressed in his paper are exclusively hose of he auhors and no hose of he Iner- American Developmen Bank, he Federal Reserve Bank of S. Louis, he Federal Reserve Sysem, or MarkeShare Parners.

3 Inroducion In response o he economic wreckage brough abou by he recen global financial crisis, a new policy paradigm has quickly emerged in which old fashioned governmen disorions such as capial conrols or oher quaniaive resricions on credi flows are becoming par of he sandard policy oolki (he so called macro-prudenial policies). Faced wih srong capial inflows, appreciaing currencies, and progressively igher consrains on domesic moneary policy, many emerging counries have already adoped or ighened capial conrols (wih Brazil a well known case in poin). Echoing hese concerns wihin he emerging marke world, even he radiionally conservaive IMF changed is orhodox views on capial conrols and is now acively advocaing he use of such ools as par of he "macroprudenial" oolki. On he wave of his seemingly unanimous policy consensus, a new srand of heoreical lieraure has emerged conending ha such measures can be jusified on welfare grounds because of second-bes consideraions wih he ypical rigor of he DSGE mehodology (e.g., Bianchi and Mendoza, 200; Bianchi, 20; Jeanne and Korinek, 20a and 20b). 2 In his novel heoreical framework, he scope for policy inervenion arises because of a pecuniary exernaliy semming from he presence of a key relaive price in he collaeral consrain ha privae agens face. In his environmen, prudenial inervenions may be desirable because hey make agens inernalize he aggregae consequences of heir decisions, discourage financial excesses, and reduce he probabiliy of financial crises, possibly enhancing welfare. As Jeanne (202) pu i, his lieraure ransposes o inernaional capial flows he closed-economy analysis of he macroprudenial policies ha aim o curb he boom-bus cycle in credi and asse prices. Using he same heoreical framework of his new lieraure on pecuniary exernaliies, in his paper we show ha a credible commimen o a price suppor policy (in our case a promise o suppor he real exchange rae in crisis imes) always welfare-dominaes prudenial axes on deb (i.e. prudenial capial conrols), as hey can achieve he firs bes unconsrained allocaion. In paricular, he desirabiliy of capial conrols is confined o he case in which hey are he only policy ool available o he policymaker. he paper also conribues mehodologically o he lieraure on pecuniary exernaliies by showing ha Ramsey opimal policy should be he preferred approach o policy design raher han he social planner approach ypically used o sudy he normaive implicaions See also Lorenzoni (2008). See Benigno e al. (20, 202) for more deails on his new lieraure. 2 he radiional raionale for inroducing capial conrols ranged from reducing he volume of capial inflows o limi pressure on he exchange rae o allowing for a more independen moneary policy sance (Magud, Reinhar, and Rogoff 20).

4 of his class of models. In fac we show ha he normaive implicaions of he social planner problem are in general sensiive o he specific definiion of effi ciency adoped, an issue ha does no arise in he conex of he Ramsey planner. As he vehicle o convey our message, we adop he same model economy as in he influenial aricle by Bianchi (20). 3 his is a wo-secor (radables and nonradables) small open, endowmen model economy wih an occasionally binding borrowing consrain. Borrowing is limied by he value of curren income generaed from boh he radable and nonradable secors. In his class of models, a financial crisis even (also labelled a Sudden Sop in capial or credi flows), only occurs when he consrain binds. In his framework, a capial conrol corresponds o a ax on inernaional borrowing, while an exchange rae inervenion is a policy aimed a conrolling he behavior of he relaive price of nonradables hrough a ax on eiher radable or nonradable consumpion. 4 More specifically in our framework here are hree possible disorionary policy ools (a ax on borrowing, a ax on nonradable consumpion and a ax on radable consumpion). We show ha he deb ax is welfare-dominaed by he oher wo ools: while wih he deb ax replicaes he consrained-effi cien allocaion, wih eiher one of he wo consumpion axes i is possible o achieve he unconsrained firs-bes allocaion. he opimaliy of prudenial capial conrols in his model environmen derives from a specific feaure of he planner problem in he conex of he endowmen economy. In he endowmen economy, here is no need o engage in any policy inervenion during crisis imes since he compeiive allocaion always coincides wih he consrained social planner s one in hose coningencies. he bes ha policy can do is hen o minimize he probabiliy ha a crisis occurs. As a resul, i becomes opimal o impose a ax on deb flows during ranquil imes. Bu his resul hinges criically on limiing he se of policy ools available o he policymaker. As we show in he paper, a properly-designed consumpion ax (on radable or nonradable consumpion) can achieve higher welfare by promising o manage he real exchange rae during crisis imes wih he aim of relaxing he borrowing consrain when i binds in bad imes. In fac, in he paper we find ha a commimen o a price suppor policy during crisis imes can undo he borrowing consrain compleely and, as a resul, i suppors an equilibrium in which agens behave as if hey were in he unconsrained firsbes allocaion during normal imes. he resul is ha crises cease o occur in equilibrium, 3 Bianchi (20) shows ha his model successfully reproduces he business cycle and he crisis dynamics properies of Argenine daa, and he uses i o quanify he opimal ax rae on foreign currency deb of one year mauriy. Mos of our resuls are analyical. 4 he inerpreaion of he real exchange rae as he relaive price of nonradables follows from Mendoza (2002), Caballero and Lorenzoni (2008) and Bianchi (20). 2

5 and he opimal policy reduces o a commimen o inervene along an off-equilibrium pah. Imporanly, as we shall see, he policy supporing such an equilibrium is ime-consisen. he promise o suppor he exchange rae, herefore, is a credible one. From a mehodological perspecive, he approach usually followed in he lieraure on pecuniary exernaliies is o compare he compeiive allocaion wih a social planner allocaion. In his comparison, he social planner is consrained by he same borrowing consrain ha privae agens face, bu inernalizes he general equilibrium effecs of her/his borrowing decisions on marke prices. One hen seeks a se of policy insrumens and corresponding rules which replicaes he social planner oucome in a decenralized equilibrium. An alernaive approach, along he Ramsey-radiion of he modern opimal axaion heory, endows he policymaker wih a se of insrumens and solves for he policy rules ha maximize welfare condiional on agens behaving as if hey were in he compeiive equilibrium allocaion. An imporan resul of his paper is ha, in his class of models wih endogenous borrowing consrains, he Ramsey opimal policy can achieve higher welfare han he consrained-social planner problem. his is because wih cerain policy ools he Ramsey planner can manipulae he relaive marke price ha eners he borrowing consrain so as o undo such consrain compleely. his resul poins o a fragiliy in he social planner approach which migh uninenionally limi he se of policy choices. In conras, a Ramsey approach condiional on a given se of insrumens naurally compares he relaive srengh of alernaive policy ools. Moreover he normaive implicaions of he social planner approach are sensiive o he definiions of effi ciency adoped. o define he planner problem in his class of models, one needs o specify how he relaive price ha ener he collaeral consrain is deermined in he social planner allocaion. he lieraure has followed eiher of wo alernaives proposed by Kehoe and Levine (993): one possibiliy (which hey refer o as he "general consrained-effi cien problem") is o impose as addiional consrain in he planner problem he compeiive equilibrium pricing rule. A second possibiliy, which hey refer o as he "condiionally-effi cien problem", is o deermine his relaive marke price by imposing as a consrain in he planner problem he compeiive equilibrium policy funcion for such price. In he paper, we compare he wo alernaive definiions of effi ciency commonly adoped in he lieraure and show how he normaive analysis of his class of models migh no be robus o such differences. For he specific case of he endowmen economy ha we examine here, hese wo alernaive definiions give exacly he same resuls. More generally, however, we show ha in he condiionally-effi cien problem he gap beween compeiive and 3

6 social planner allocaions will be much smaller han in he consrained-effi cien problem. his is because, in he former, he key marke price ha eners he collaeral consrain coincides in he wo allocaions for any given sae of he economy. From a policy perspecive, his implies ha he scope for policy inervenion (eiher when he consrain does no bind or when i does, labeled he ex ane or ex pos perspecives, respecively) will be reduced in he condiionally-effi cien problem relaive o he consrained-effi cien one. For insance, in he case of a producion version of our economy, we find ha changing he definiion of effi ciency changes compleely he resuls of he normaive analysis. Oher modeling approaches o capial conrols have been proposed in he lieraure. Cosino, Lorenzoni and Werning (202) in paricular sudy how capial conrols migh affec he iner-emporal erms of rade, while De Paoli and Lipinska (202) focuses on he inra-ermporal erms of rade. hese are complemenary sudies of he normaive properies of capial conrols. Our approach is based on he pecuniary exernaliy. he res of he paper is organized as follows. Secion 2 describes he model and is compeiive equilibrium. Secion 3 discusses he social planner allocaion under alernaive definiions of effi ciency. Secion 4 analyzes he implemenaion problem wih capial conrols. Secion 5 analyzes he implemenaion problem wih exchange rae policy. Secion 6 concludes. 2 he Model and Is Compeiive Equilibrium We consider a small open economy in which here is a coninuum of households j [0, ] ha maximize he uiliy funcion U j E 0 =0 { β u (C j ) }, () wih C j denoing he consumpion baske for an individual j and β he subjecive discoun facor. he period uiliy funcion is isoelasic: u (C j ) ρ (C j,) ρ. he consumpion baske, C, is a CES aggregae of radable and nonradable goods, where: 5 C [ ( ) ω κ κ C κ + ( ω) κ ( ) κ ] κ κ C κ. (2) 5 We omi he subscrip j o simplify noaion, bu i is undersood ha all choices are made a he individual level. 4

7 he parameer κ is he elasiciy of inraemporal subsiuion beween consumpion of radable and nonradable goods, while ω is he relaive weigh of he wo goods in he uiliy funcion. We normalize he price of radable goods o and denoe he relaive price of he nonradable goods wih P. he aggregae price index is hen given by [ P = ω + ( ω) ( P ) κ ] κ. Here, we noe ha here is a one-o-one link beween he aggregae price index P and he relaive price P. Households maximize uiliy subjec o heir budge consrain, which is expressed in unis of radable consumpion, and a borrowing consrain. he asse menu includes only a one-period bond denominaed in unis of radable consumpion. Each household has wo sochasic endowmen sreams of radable and non-radable oupu, {Y } and {Y }. For simpliciy, we assume ha boh {Y } and {Y } are Markov processes wih finie, sricly posiive suppor. herefore he curren sae of he economy can be compleely characerized by he riple {B, Y, Y }. he budge consrain each household faces hus is C + P C + B + = Y + P Y + ( + r) B, (3) where B + denoes he bond holding a he end of period, and +r is a given world gross ineres rae wih β ( + r) <. Access o inernaional financial markes is no only incomplee bu also imperfec as we assume ha he amoun ha each individual can borrow inernaionally is limied by a muliple of his curren oal income: B + φ φ [ Y + P ] Y. (4) he key feaure of his inernaional borrowing consrain is ha i capures currency mismaches in he balance shee of our small open economy model (see Krugman 999 for a discussion). In fac borrowing in he model is denominaed in unis of radable consumpion, while boh he radable and he nonradable endowmen can be pledged as collaeral. Indeed, currency mismaches have been one of he main vulnerabiliy of emerging marke economies in he numerous financial crises in he 990s and he 2000s and in he ongoing European crisis. 5

8 While imposed in an ad hoc fashion, as in he relaed lieraure on pecuniary exernaliies and prudenial policies, his consrain can in principle be derived from explici microfoundaions. For insance, one way o jusify i is o refer o an environmen in which he borrower engages in fraud aciviies in he period in which he deb is conraced (see Bianchi 20 and Bianchi and Mendoza (200) for a discussion). We also assume ha in our economy here is a lower bound which is sricly greaer han he naural deb limi, B, such ha B B, for all. 6 his lower bound guaranees ha he compeiive equilibrium allocaion wihou governmen inervenion and he inernaional borrowing consrain (4) (i.e. he firs-bes unconsrained allocaion) is well defined. In paricular, i guaranees ha his equilibrium has an ergodic disribuion of deb wih finie suppor, and boh radable and nonradable consumpion have a sricly posiive lower bound, while he nonradable price also has finie suppor wih sricly posiive lower bound. Finally, in order o focus on non-rivial policies, we also assume ha, given Y and, when B = B, he compeiive equilibrium allocaion always violaes he borrowing Y consrain (4). 7 Households maximize () subjec o (3) and (4) by choosing C, C Lagrangian of his problem is L = E 0 =0 β [ µ ( Y ( [ ρ C ρ j, + λ B + + φ φ Y + P ] ) Y + + P Y B + + ( + r) B C P and B +. he wih λ and µ denoing he mulipliers on he borrowing consrain and he budge consrain, respecively. he firs order condiions of his problem are C : u (C )C C = µ, (5) C ) ] C : u (C )C C = µ P, (6) Combining (5) and (6) o obain B + : µ = λ + β ( + r) E [ µ+ ]. (7) ( ω) κ ( C ) κ ω κ (C ) κ = P, (8) 6 he naural deb limi is defined as he level of deb where radable consumpion C equals zero. In our model, his level equals (minus) he annuiy value of he lowes value of he radable endowmen. If C and C are srong subsiues, his consrain may bind; since he evidence is agains srong subsiuibiliy beween radable and non radable consumpion, we can ignore his possibiliy. 7 his resricion amouns o a lower bound on φ. 6

9 he compeiive equilibrium allocaion of he economy can be characerized by he firs order condiions (7) and (8) and he goods marke equilibrium condiions. he properies of he compeiive equilibrium of his economy are well known (see for insance Mendoza (2002) and Bianchi (20)). However, i is imporan o noe ha, while in his paper we shall focus on he normaive properies of his model, from a posiive perspecive, Bianchi (20) shows ha his very same model accouns reasonably well for observed business cycles (including he high volailiy of consumpion and he srong procyclicaliy of capial flows), as well as he incidence and severiy of financial crises, in Argenina. 3 Social Planner Equilibrium I is well known ha in our model environmen privae decisions fail o inernalize heir effec on he equilibrium relaive price ha eners he borrowing consrain, and such price in urn affecs he borrowing consrain, creaing ineffi cien amplificaion effecs. 8 In hese economies, herefore, here is scope for policy inervenion o improve upon he compeiive equilibrium allocaion. As in he relaed lieraure, in his paper, we focus on planning problems in which he planner faces he same credi consrain as he privae agens in he compeiive equilibrium. o define his planner s problem, one needs o specify how his relaive price is deermined in he social planner equilibrium. o do so, we follow Kehoe and Levine (993), who consider wo alernaives: 9 one possibiliy (which hey refer o as he "general consrainedeffi cien problem") is o deermine he relaive price by imposing as addiional consrain in he planner problem he compeiive equilibrium pricing rule (in our case equaion (8)). A second possibiliy, which hey refer o as he "condiionally-effi cien problem", is o deermine his relaive marke price by imposing as a consrain in he social planner problem he compeiive equilibrium policy funcion (in our case P = f CE (B, Y, Y )). 0 While in he specific case of our model here is no paricular reason o prefer one definiion o he oher, bu in general his choice is very imporan for he resuls of he normaive analysis of hese model environmens.in fac, for he specific case of he endow- 8 Such a mechanism operaes also if an asse price eners he collaeral consrain, such as he price of a fixed sock of land (e.g., Bianchi and Mendoza (200), Jeanne and Korinek (20a and 20b). Suiably modified, our analysis and resuls exend o hese alernaive environmens. 9 See also he discussion in Lorenzoni (2008). 0 his policy funcion is obained from he soluion of he non-linear sysem of equilibrium condiions ha define he compeiive equilibrium of he model. A policy funcion is he non-linear equilibrium relaion beween he endogenous variables of he model and is exogenous and endogenous sae variables (in our case, he riple { } B, Y, Y ). 7

10 men economy ha we examine here, as we shall see below, hese wo alernaive definiions of effi ciency do no affec he resuls of he normaive analysis. In general, however, in he condiionally-effi cien problem he gap beween compeiive and social planner allocaions will be quaniaively smaller han in he consrained-effi cien problem. his is because, in he former, he relaive price ha eners he collaeral consrain (P in our case) coincides in he wo allocaions for any given sae of he economy. From a policy perspecive, his implies ha he scope for policy inervenion (eiher when he consrain does no bind or when i does, labeled he ex ane or ex pos perspecives, respecively) will be reduced in he condiionally-effi cien problem relaive o he consrained-effi cien one. his coincidence under condiional effi ciency is paricularly imporan when he borrowing consrain is binding (i.e., in crisis periods, according o he definiion of financial crisis adoped in he lieraure). In fac he coincidence implies ha he amplificaion mechanism induced by he consrain via is exernaliy on he relaive price in he compeiive equilibrium allocaion is "effi cien" in he sense defined above. Under condiional effi ciency, herefore, financial crises migh be "effi cien" evens ha disor he allocaion only ouside crisis saes. From a normaive perspecive, his implies ha he only scope for policy inervenion arises before enering a crisis sae, which biases he normaive resuls of he analysis. his issue is even more imporan for planning problems wih collaeral consrains ha depend on asse prices like in he case of Bianchi and Mendoza (200) and Jeanne and Korinek (20b). Asse prices are forward looking variables and, echnically, i is diffi cul or i migh be no feasible o compue he "consrained effi cien" planning problem because i becomes non-recursive in he naural se of sae variables. By using condiional effi ciency, he compuaional problem becomes racable a he cos of possibly biasing he normaive resuls. In relaed work, consisen wih sandard pracice in he opimal axaion lieraure, Benigno e al. (2009, 20, 202) and Lorenzoni (2008) use consrained-effi ciency. Bianchi and Mendoza (200) use condiional-effi ciency o sudy heir producion economy in which he collaeral consrain depend on an asse price. Ineresingly, however, Bianchi (20) uses consrained effi ciency o se up he planner problem for he endowmen version of his economy and condiional effi ciency in he planner problem of he producion version of his economy. Indeed, acual policy makers pursue boh crisis resoluion and crisis prevenion policies. In addiion, as Benigno e al (202) show, in an environmen in which he planner has scope for inervening boh in and ou of crisis saes, he economy s behavior in normal imes depends on is behavior in crisis imes. herefore, resricing he normaive analysis o environmens in which he crisis is "effi cien" is no only counerfacual bu may also bias he resuls in favour of ex ane policies. 8

11 As we noed already, in our simple model environmen, he specific definiion of effi ciency adoped does no affec he normaive analysis. oneheless, for illusraive purposes, and o help undersand he peculiar naure of he resuls in he relaed lieraure, in he res of his secion, we shall analyze he planner problem of our model under boh definiions of effi ciency. 3. he consrained-effi cien planning problem We firs sudy he consrained effi cien social planner problem. he planner maximizes () subjec o he resource consrains, he inernaional borrowing consrain from an aggregae perspecive and he compeiive pricing rule as in (8). By combining he household budge consrain wih he equilibrium condiion in he nonradables good marke, we obain he curren accoun equaion of our small open economy: C = Y B + + ( + r) B. (9) he nonradable goods marke equilibrium condiion implies ha C = Y. (0) From he perspecive of he planner, he inernaional borrowing consrain can be expressed as in (4), where he relaive price is deermined by he compeiive rule (8). he Lagrangian of he planner problem becomes L = E 0 β =0 +µ SP 2, (C ρ j,) ρ ( ) + µ SP, Y B + + ( + r) B C + ( [ ( ( ) Y C + λ SP B + + φ Y φ + ( ω)(c ) ωy ) κ Y ]), where µ SP,, µ SP 2, and λ SP denoe he corresponding Lagrangian mulipliers. he planner chooses he opimal pah for C, C and B +, and he firs order condiions for is problem are C : u (C )C C = µ SP, λ SP Σ SP, () C : u (C )C C = µ SP 2,, (2) where Σ SP φ P φ C Y [ B + : µ SP, = λ SP + β ( + r) E µ SP,+]. (3) ( ) = φ φ κ ( ω) ω ( ω)(c ) ω κ ( Y ) κ κ. 9

12 he key difference beween he planning allocaion and he compeiive equilibrium follows from examining equaions () and (5). From he planner perspecive, here is an addiional marginal benefi in consuming one more uni of radable consumpion, represened by he erm λ SP Σ, which capures he increase in he price of non-radable derived from he marginal increase of radable consumpion. his erms drives a gap beween he planner and he compeiive allocaion when he consrain does no bind bu is expeced o bind in he fuure wih posiive probabiliy. When he consrain binds for boh allocaions (i.e. in crisis saes), however, he compeiive equilibrium of he model is exacly he same as he social planner allocaion even under consrained effi ciency. his is because, in he special case of an endowmen economy, for any given sae in which he consrains binds in boh allocaions, consumpion of radables is he same across allocaions, driven by he consrain iself. In he special case of an endowmen economy, herefore, even under consrained effi ciency, financial crises are "effi cien" evens ha can disor only he allocaion ouside crisis saes. From a normaive perspecive, his implies ha he only scope for policy inervenion is before enering a crisis sae, which can bias he normaive conclusions of he analysis as we discussed above. 3.2 he condiionally-effi cien planning problem In he condiionally effi cien planner problem, he planner maximizes () subjec o he resource consrains, he inernaional borrowing consrain from an aggregae perspecive and he pricing funcion P borrowing consrain as B + φ φ = f CE (B, Y, Y ). So we can rewrie he inernaional [ Y + f CE (B, Y, Y )Y ]. he Lagrangian of he planner s problem becomes L = E 0 =0 β [ +µ SP 2, (C ρ j,) ρ + µ SP, ) ( C + λ SP ( Y ( Y he planner chooses he opimal pah for C, C for is problem are: C : u (C )C C B + + ( + r) B C [ Y + f CE (B, Y B + + φ φ ) +, Y ] ) )Y. and B +, and he firs order condiions = µ SP,, (4) ] C : u (C )C C = µ SP 2,, (5) 0

13 B + : µ SP, = λ SP [ λ SP + φ φ βe +fb CE [ ] + β ( + r) E µ SP,+ (B +, Y +, Y +)Y +]. (6) he difference beween he consrained and he condiional effi cien problem emerges once we compare he firs order condiions of he wo problems. In he consrained effi cien problem he planner akes ino accoun he pecuniary exernaliy hrough his choice of radable consumpion (see ()); in he condiional effi cien problem he planner inernalizes he exernaliy via he choice of deb (see (6)). In fac we can rewrie he ineremporal condiion for B + as u (C )C C = λ SP + β ( + r) E [u (C + )C C ] + φ φ βe [ λ SP +fb CE (B +, Y+, Y+)Y+]. which is similar o he ineremporal condiion (3). Wih condiional effi ciency, in (6), when he consrain does no bind (i.e., when λ SP = 0 ), he marginal social benefi from reducing one uni of C depends on he covariance beween he fuure muliplier λ SP + and he sensiiviy of he price funcion o changes in deb, fb CE(B +, Y+, Y+). Inuiively, as we decrease B + (we reduce deb) we increase fuure consumpion of radables and hence he relaive price of non-radable, so ha fb CE(B +, Y+, Y+) < 0. A he same ime, he probabiliy of enering he consrained region omorrow increases wih B +, implying a posiive covariance beween λ SP + and fb CE(B +, Y+, Y+). Despie he formal differences, in he conex of our endowmen economy, he wo social planner allocaions deliver exacly he same allocaion in erms of radable consumpion and borrowing decisions, boh in ranquil and crisis imes. Bu his is generally no he case: for insance, for more general economies, such as he producion economy of Bianchi (20), Bianchi and Mendoza (20) or Benigno e al (202), he wo social planner allocaions would differ. o illusrae his poin, Figures and 2 show he policy funcions for deb, radable consumpion, and he relaive price of nonradables for he endowmen economy of Bianchi (20) as well as he producion economy sudied by Benigno e al (202). he picures plo he policy funcions of he compeiive and social planner equilibria under boh definiions of effi ciency, wih he wo economies calibraed as in Bianchi (20) and Benigno (202), respecively. In he endowmen case, he policy funcions of he social planner allocaion for radable consumpion and deb under alernaive definiions of effi ciency In he afermah of he

14 global financial crisis, a new policy paradigm has emerged in which old-fashioned policies such as capial conrols and oher governmen disorions have become par of he sandard policy oolki (he so-called macro-prudenial policies). On he wave of his seemingly unanimous policy consensus, a new srand of heoreical lieraure conends ha capial conrols are welfare enhancing and can be jusified rigorously because of second-bes consideraions. Wihin he same heoreical framework adoped in his fas-growing lieraure, we show ha a credible commimen o suppor he exchange rae in crisis imes always welfare-dominaes prudenial capial conrols as i can achieve he firs bes unconsrained allocaion. In his benchmark economy, prudenial capial conrols are opimal only when he se of policy ools is resriced so ha hey are he only policy insrumen available, boh in he consrained and unconsrained region (Figure ). he policy funcion of he relaive price of nonradables insead is differen under consrained effi ciency in he nonconsrained region. Such a difference in he policy funcion for P, however, is irrelevan in he endowmen economy since prices do no affec he real allocaion when he consrain is no binding. In he consrained region, in he endowmen economy, he price of nonradables falls dramaically boh in he compeiive equilibrium and in he social planner allocaion under boh definiions of effi ciency. his decline ses off he "Fisherian deflaion" mechanism emphasized in he pecuniary exernaliy lieraure a decline in P ha reduces he value of he nonradable endowmen, ighening he borrowing consrain and reducing he consumpion of radables, which in urn again reduces P, and so on. As Figure () shows, however, he collapse in P is "effi cien" in his model since he policy funcions in he compeiive and social planner allocaion coincide in crisis imes under boh definiions of effi ciency. In he more general case of a producion economy, he definiion of effi ciency maers. 2 As Figure 2 shows, he wo social planner allocaions differ significanly. In paricular, as we noed above, he gap beween he compeiive allocaion and he condiional effi cien planner problem is much smaller han he gap beween he consrained effi cien allocaion and he compeiive equilibrium. he implicaions of hese differences are summarized in Figure 3, which repors he ergodic disribuion of deb for hese hree allocaions. While he consrained effi cien allocaion has less deb han he compeiive allocaion (i.e., here is underborrowing), wih condiional effi ciency here is less borrowing han in he compeiive allocaion (i.e., here is overborrowing): changing definiion of effi ciency urns he resuls of he normaive analysis upside down. 2 In he producion economy of Benigno e al (202) he planner can manipulae no only he marginal rae of subsiuion beween radable and non radable goods, bu also heir marginal rae of ransformaion. 2

15 hese differences are refleced also in he probabiliy of a crisis and he welfare ranking beween allocaions, which are compleely reversed by changing he effi ciency definiion. Wih condiional effi ciency we have a higher probabiliy of crisis han in he compeiive equilibrium, while wih consrained effi ciency he probabiliy is lower. By he same oken, wih condiional effi ciency, he welfare gains of moving from he compeiive equilibrium o he social planner allocaion are more han /00 of hose wih consrained effi ciency (swiching from 0.8 percen of permanen consumpion o percen). 3 4 Capial Conrols We now sudy he implemenaion of he social planner allocaions hrough a ax on newlyissued deb. In wha follows we will refer o i as a capial conrol consisen wih he res of he lieraure. In he compeiive equilibrium, he household s budge consrain becomes C + P C = Y + P Y + B + ( + τ B ) + ( + r) B, (7) where τ B > (<)0 is a subsidy (or a ax) on deb issued a ime, and is a lump sum ransfer or ax. In he compeiive equilibrium he governmen budge consrain mus also hold: = τ B B +. (8) All oher assumpions are he same as above. In paricular, inernaional financial marke access is consrained by (4) as before. As in he case wihou governmen inervenion, we make he same assumpion on he lower limi of deb B B for all. he compeiive equilibrium allocaion is hen characerized by u (C )C C ( + τ B ) = λ + β ( + r) E [u (C + )C C ] (9) wih [ λ B + + φ [ Y + P Y ]] = 0 φ ( ω) κ ( C ) κ ω κ (C ) κ = P along wih he goods marke equilibrium condiion. We now analyze he exen o which i is possible o use ( ) + τ B o decenralize he social planner equilibrium under he wo alernaive definiions of effi ciency discussed above. 3 Welfare gains are generally small in he lieraure because financial crises are rare evens. 3

16 4. Consrained-effi ciency Under consrained-effi ciency, we can rewrie he Euler equaion for he planner problem as u (C SP )C SP C + λ SP Σ SP = λ SP + β( + r)e [u (C+)C SP SP C + λ SP +Σ SP +]. (20) + Recall ha he Euler equaion for he compeiive equilibrium (9) is ( + τ B )u (C )C C = λ + β( + r)e [u (C + )C C + ]. (2) he following proposiion hen holds: Proposiion. In an economy defined by (), (3), and (4), wih a ax on deb τ B as he governmen policy insrumen, here exiss policy for τ B under which compeiive equilibrium allocaion implemens he social planner one Bianchi (20). Proof. Since he resource consrains and he credi consrains are idenical in he compeiive equilibrium and he social planner problem, we are only concerned wih he ineremporal Euler equaions (20) and (2). In order for he compeiive equilibrium allocaion o coincide wih he social planner one, he governmen mus se ( τ B = u (C SP )C SP C ) ( λ SP Σ SP β( + r)e [λ SP +Σ SP +] ) (22) where he superscrip SP denoes he values from he social planner problem. Wih his sae-coningen policy rule, he Euler equaions are idenical and hence he wo allocaion coincide. As Bianchi (20) noes, when λ = 0 and E [ λ SP +Σ SP +] > 0, so ha he credi consrain is no currenly binding bu in he nex period i will bind wih posiive probabiliy, τ B is negaive (i.e., is a ax). On he oher hand, when he consrain binds, seing τ B = 0 implemens he consrained effi cien allocaion since he borrowing of he planner and he privae agens coincide. Q.E.D. So he ax on deb (or capial conrol) is precauionary in he sense ha by axing deb oday he planner can lower he probabiliy of a crisis omorrow. he ax is zero for levels of deb a which he consrain binds in he curren period. I is only when he consrain does no bind oday bu will bind omorrow wih a posiive probabiliy ha he ax does ake negaive values. he sae coningen ax policy rule ha implemens he consrained effi cien allocaion also has oher properies summarized by he following proposiion: 4

17 Proposiion 2. he ax policy above is boh Ramsey opimal and ime-consisen. However i does no achieve he firs bes unconsrained allocaion. Proof. he ax policy above, ogeher wih he household firs order condiions,replicaes he soluion of he social planner problem wih consrained-effi ciency, which is idenical o a Ramsey problem for his economy. he Ramsey planner maximizes () subjec o (0), (4), (7), (9), (8) and (8). he ax policy (22) along wih he household firs order condiions saisfy he Ramsey consrains and replicae he social planner equilibrium so ha he ax policy is Ramsey opimal. In addiion, since he ax policy decenralizes he social planner problem, which is a recursive problem ha can be represened by value ieraion and only depends on he curren sae {B, Y, Y }, he equilibrium would be subgame perfec and ime-consisen. o see ha he social planner problem does no achieve he firs-bes unconsrained allocaion, noice ha, if he firs-bes unconsrained allocaion were achieved (λ 0 for all ), he FOCs of he social planner problem (4), (5), and (6) would be idenical o he FOCs of compeiive equilibrium wihou he inernaional borrowing consrain (4). herefore since β( + r) <, B would evenually converge o he lower limi B where he credi consrain (4) would be violaed by assumpion. Q.E.D. 4.2 Consrained-effi ciency Since he social planner problem under condiional effi ciency delivers he same allocaion as under consrained effi ciency, i is immediae o show ha under he former definiion of effi ciency he same policy funcion for τ B as in (22) would implemen he social planner equilibrium wih he same properies. 5 Exchange Rae Policy We now consider alernaive policy insrumens. In he conex of our endowmen economy here are wo alernaive opions: axing radable or nonradable consumpion. As we shall see, hese policy ools have a direc inerpreaion in erms of exchange rae policy. Indeed, hey direcly conrol he relaive price of nonradable goods, which in he conex of his economy is a measure of he real exchange rae. 5

18 5. ax on nonradables consumpion Le s sar by examining he nonradable consumpion ax. When we inroduce a ax on nonradable consumpion, ( + τ ), he consrain ha each household faces becomes C + P ( + τ )C = Y + P Y + B + + ( + r) B, (23) where τ > (<) 0 is a ax (or a subsidy) on nonradable consumpion and > (<) 0 is a governmen lump-sum ransfer (or ax). As in he case of capial conrols, we assume ha he governmen runs a balanced budge: = τ P C. (24) hus, he compeiive equilibrium is now characerized by he following condiions: u (C )C C = λ + β ( + r) E [u (C + )C C ] (25) wih ( ω) κ ( C ) κ ω κ (C ) κ [ λ B + + φ [ Y φ = P + P ( + τ ). (26) ] ] Y = 0. (27) oe here ha (26) direcly links he relaive price of nonradables o he ax on nonradables. I is also eviden ha in an economy in which he borrowing consrain does no bind, his policy ool is neural in he sense ha i will no affec he consumpion allocaion bu only he real exchange rae. In fac, he Euler equaion and he goods marke equilibrium condiions are all ha is needed o deermine consumpion of nonradables and radables. In our endowmen economy, however, his ax is no longer neural when he consrain binds and can be used o affec he collaeral value, and hence also he allocaion of radable consumpion. he following proposiion esablishes how he use of such a ax can assure ha he consrain is never binding in equilibrium in our economy (λ 0 for all ) via is impac on he relaive price on non radable. Proposiion 3. In an economy defined by (), (4), (23) and (24)in which a ax on nonradable consumpion τ is he governmen policy insrumen, here exiss a policy for τ ha decenralizes he firs-bes unconsrained allocaion and i is ime-consisen. Proof. For a given sochasic process of { } Y, Y and a given sae B, le B+ uncon be he 6

19 policy funcion of nex period deb and P,uncon be he relaive price in he curren period in he economy defined by () and (3) bu wihou credi consrain (4). Define ˆP o be he minimum price such ha he credi consrain would be me if i exised, ˆP = max { + + φ Y φ 0, Buncon In he economy wih credi consrain, he Ramsey planner maximizes () subjec o (0), (4), (26), (23), (24) and (25) and can se τ such ha ˆP ( + τ ) P,uncon so ha he credi consrain does no bind. In oher words, le ˆτ = P,uncon / ˆP. hen any τ (, ˆτ ] is he ax rae which eliminaes he credi consrain. Under his ax policy, λ = 0 for all and he compeiive equilibrium coincides wih he firs bes unconsrained allocaion. Moreover, his policy saisfies he firs order condiions of he compeiive equilibrium allocaion. φ φ Y }. Since he Ramsey planner can achieve a bes he unconsrained allocaion, his ax policy is he opimal soluion o he Ramsey problem in which he governmen chooses opimally he non-radables consumpion ax. Such policy is compleely deermined by he curren sae {B, Y, Y } and herefore i is ime-consisen. Q.E.D. he proposiion esablishes a ax policy ha is able o replicae he unconsrained firs bes allocaion: his policy promises o relaxes he borrowing consrain by supporing he relaive price of non radeable whenever he consrain binds in such a way ha he consrain never binds in equilibrium. Under his policy, during ranquil imes, privae agens behaves as if he consrain does no exis. In doing so heir consumpion of radables goods will be higher han in he compeiive allocaion and in he consrained social planner allocaion. For a given endowmen of nonradable goods, his equilibrium enails a higher relaive price of nonradables during ranquil imes, which in urn increases he borrowing capaciy of privae agens, and makes he borrowing consrain never binding ex pos. hree remarks are in order here. Firs, he proposiion above shows ha exchange rae policy dominaes he precauionary capial conrol policy discussed in Secion 4 in welfare erms. In fac, under opimal policy wih τ he probabiliy of a financial crisis is zero and he economy replicaes he unconsrained firs-bes allocaion. In conras, capial conrols can achieve only a second bes allocaion. Second, he policy funcion for τ is a promise o inervene off he equilibrium pah (i.e. when he consrain bind, which never happens in equilibrium) and eliminaes compleely he effecs of he pecuniary exernaliy. More broadly, his ype of policy can be inerpreed as a price suppor inervenion ha avoids he collapse of he relaive prices (including asse 7

20 prices) when a crisis does occur. Bu since he crisis sae never occurs, he policy acually is never enaced in equilibrium. Imporanly, his policy commimen is a ime consisen equilibrium. hird, he Ramsey allocaion achieves higher welfare han he social planner allocaion defined in Secion 3. his couner-inuiive resul is due o he fac ha he social planner problem is consrained by he pricing rule as defined in (8). In conras, he Ramsey problem in which he policy ools is he ax on nonradables consumpion is consrained by (26). he Ramsey planner herefore can manipulae he relaive price of non radables direcly so as o undo he consrain compleely wihou creaing furher disorions. From his resul i follows ha he normaive prescripions obained by comparing he social planner allocaion wih he compeiive equilibrium are sensiive o he way in which alernaive policy ools affec he specificaion of he pricing equaion. In his sense, i becomes eviden ha he normaive analysis of his class of models suggess ha a beer way o conduc he normaive analysis is by he compuaion of he opimal Ramsey problem condiional on he se of available insrumens raher han he social planner problem as usually done in he relaed lieraure. In fac in he Ramsey problem he pricing equaion is par of he se of relaions describing he privae secor s behavior. 5.2 ax on radables consumpion We now consider a ax on radable consumpion as he governmen s policy ool. Each household now faces he following budge consrain: ( + τ )C + P C = Y + P Y + B + + ( + r)b. (28) As before, he governmen budge consrain coninues o be balanced: = τ C. (29) hus, he compeiive equilibrium is now characerized by he following condiions: u (C )C C + τ = λ + β ( + r) E [ u (C + )C C + + τ + ]. (30) wih ( ω) κ ( C ) κ ω κ (C ) κ = P + τ. (3) 8

21 [ λ B + + φ [ Y + P Y ]] = 0. (32) φ We noe here ha he ax on radable consumpion now affecs no only he inraemporal relaive price (see (3)), bu also he ineremporal allocaion of resources (see (30)). Despie his ineracion, he nex proposiion shows ha i is possible o find a sae coningen ax policy ha replicaes he oucome of he opimal nonradable ax policy. Proposiion 4. In an economy defined by (), (3), (28) and (29) wih a ax on radable consumpion τ as he governmen insrumen, here exiss a policy for τ ha decenralizes he firs-bes unconsrained allocaion and i is ime-consisen. Proof. Le he opimal non-radable consumpion ax be τ. I is easy o see ha in he Ramsey problem, if we se = +τ +τ, we achieve he firs bes unconsrained allocaion and λ 0. Since he ax on radable consumpion affecs also he ineremporal allocaion of resources (30) we need o show ha he ax policy ha replicaes he unconsrained firs bes equilibrium is consan so ha he ineremporal margin is no affeced. As in he previous proposiion, such policy is naurally ime-consisen. By comparing Euler equaions in boh social planner problem and compeiive equilibrium, and using λ 0, i is suffi cien o find τ so ha + τ = [ ] u (C+ SP )CSP C + E +τ + E [u (C+)C SP SP ], (33) C+ and he inernaional borrowing consrain (4) is saisfied, in order for he compeiive equilibrium o achieve he unconsrained firs bes allocaion. Firs we noe ha a consan ax policy will saisfy (33). Secondly, by inspecion of he firs-bes unconsrained allocaion, non-radable price has a sricly posiive lower limi. herefore here exiss τ such ha he borrowing consrain (4) is always saisfied for any τ τ ). hus, any consan ax policy of he form τ τ τ ) is an opimal policy such ha he compeiive equilibrium replicaes he firs bes unconsrained allocaion. Q.E.D. 6 Conclusions In response o he recen global financial crisis, a new policy paradigm has quickly emerged. In his new paradigm, macro-prudenial policies i.e., old fashioned governmen disorions 9

22 such as capial conrols or oher quaniaive resricions on credi flows have become par of he sandard policy oolki arguably because hey can preven or miigae financial crises. On he wave of his seemingly unanimous policy consensus, a new srand of heoreical lieraure is conending ha such measures can be rigorously jusified on welfare grounds (e.g. Bianchi, 20; Bianchi and Mendoza 200; Jeanne and Korinek 20b). his lieraure reaches his conclusion by comparing compeiive equilibrium allocaions wih ha of a social planner. In our work we compare he compeiive equilibrium and social planner allocaions sudied in he lieraure wih hose characerized by he soluion of a Ramsey opimal policy problem. Our main resul is ha exchange rae policy always dominaes capial conrols in welfare erms. his policy is ime-consisen and delivers he firs bes unconsrained allocaion. In conras, prudenial capial conrols can a bes achieve a second-bes allocaion of resources in which he collaeral consrain coninues o limi borrowing and gives rise o he occasional crisis. he reason for his resul, which is in sharp conras o he exising lieraure, is ha a Ramsey planner can deliver an allocaion wih higher welfare han he consrained social planner in his class of models. his resul follows from he fac ha he Ramsey planner in his environmen can choose policies o direcly manipulae he key relaive price ha eners he borrowing consrain and, condiional on he available policy ools, can relax he consrain by supporing his key marke price. We sugges here ha fuure work on macroprudenial policies should follow he modern opimal axaion approach as in he Ramsey radiion. While a social planner problem can lead one o idenify he need for policy inervenion, i is no informaive on he relaive meri of alernaive policy ools o do so. In conras, working direcly wih he Ramsey problem requires one o specify he se of policy insrumens before he analysis, which naurally induces one o consider policy insrumens ha lead o he bes oucomes. Moreover, we have shown ha he specificaion of he consrained social planner problem migh be very sensiive o he definiion of effi ciency adoped, possibly biasing he normaive analysis significanly. For insance, in he case of a producion economy, we show ha changing he definiion of effi ciency changes compleely he resuls of he normaive analysis. I follows ha he normaive analysis of his class of models should eiher jusify carefully he definiion of effi ciency adoped, show robusness o he alernaive, or more simply, adop he Ramsey approach which is fully ransparen in erms of he consrains imposed on he normaive analysis. 20

23 References [] Benigno, G., H. Chen, C. Orok, A. Rebucci, and E.R. Young (2009), Opimal Policy for Financial Sabiliy, unpublished manuscrip, available a: hp:// [2] Benigno, G., H. Chen, C. Orok, A. Rebucci, and E. R. Young (20), Revisiing Overborrowing and Is Policy Implicaions, in L. Céspedes, R. Chang and D. Saravia (Eds.), Moneary Policy under Financial urbulence, Cenral Bank of Chile. [3] Benigno, G., H. Chen, C. Orok, A. Rebucci, and E.R. Young (202), Financial Crises and Macro-Prudenial Policies, Journal of Inernaional Economics, forhcoming. [4] Bianchi, J. (20), Overborrowing and Sysemic Exernaliies in he Business Cycle, American Economic Review 0(7), pp [5] Bianchi, J. and E.G. Mendoza (200), Overborrowing, Financial Crises and Macro- Prudenial axes, BER Working Paper o. 609, aional Bureau of Economic Research. [6] Caballero R. and G. Lorenzoni (2009), "Persisen Appreciaions and Overshooing: A ormaive Analysis", unpublished manuscrip. [7] Caballero, R.J. (200), Sudden Financial Arres, IMF Economic Review 58(), pp [8] Cosino. A., G. Lorenzoni and I. Werning (202), A heory of Capial Conrols as Dynamic erms-of-rade Manipulaion, mimeo, MI. [9] De Paoli, B. and A. Lipinska (202), Capial Conrols: a normaive analysis, mimeo, Federal Reserve Bank of ew York. [0] Jeanne, O. (202) Capial Flow Managemen, forhcoming in he AER papers and Proceedings [] Jeanne, O. and A. Korinek (20a), Excessive Volailiy in Capial Flows: A Pigouvian axaion Approach. American Economic Review Papers and Proceedings 00(2) pp [2] Jeanne, O. and A. Korinek (20b), Managing Credi Booms and Buss: A Pigouvian axaion Approach, unpublished manuscrip. 2

24 [3] Kehoe,.J. and D. Levine (993), Deb-Consrained Asse Markes, Review of Economic Sudies 60(4), pp [4] Krugman, P. (999), Balance Shees, he ransfer Problem, and Financial Crises, Inernaional ax and Public Finance 6(4), pp [5] Lorenzoni, G. (2008), Ineffi cien Credi Booms, Review of Economic Sudies 75(3), pp [6] Magud,.E., C.M. Reinhar, and K.S. Rogoff (20), Capial Conrols: Myh and Realiy A Porfolio Balance Approach, BER Working Paper 6085, aional Bureau of Economic Research. [7] Mendoza, E.G. (2002), Credi, Prices, and Crashes: Business Cycles wih a Sudden Sop, in Edwards, S. and J.A. Frankel (eds.), Prevening Currency Crises in Emerging Markes, Universiy of Chicago Press and aional Bureau of Economic Research. [8] Mendoza, E.G. (200), Sudden Sops, Financial Crises and Leverage: A Fisherian Deflaion of obin s Q, American Economic Review 00(5), pp