The Possible Trinity: Optimal Interest Rate, Exchange Rate, and Taxes on Capital Flows in a DSGE Model for a Small Open Economy

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1 Vol. 8, June 25, 204 hp://dx.doi.org/0.508/economics-ejournal.ja The Possible Triniy: Opimal Ineres Rae, Exchange Rae, and Taxes on Capial Flows in a DSGE Model for a Small Open Economy Guillermo J. Escudé Absrac A radiional way of hinking abou he exchange rae (XR) regime and capial accoun openness has been framed in erms of he 'impossible riniy' or 'rilemma', in which policymakers can only have 2 of 3 possible oucomes: open capial markes, moneary independence and pegged XRs. This paper is an exension of Escude (A DSGE Model for a SOE wih Sysemaic Ineres and Foreign Exchange Policies in Which Policymakers Exploi he Risk Premium for Sabilizaion Purposes, 203), which focused on ineres rae and XR policies, since i inroduces he hird verex of he 'riniy' in he form of axes on privae foreign deb. These affec he risk-adjused uncovered ineres pariy equaion and hence influence he SOE's inernaional financial flows. A useful way o illusrae he range of policy alernaives is o associae hem wih he faces of a riangle. Each of 3 possible governmen inervenion policies aken individually (in he domesic currency bond marke, in he FX marke, and in he foreign currency bonds marke) corresponds o one of he verices of he riangle, each of he 3 possible pairs of inervenion policies corresponds o one of is 3 edges, and he 3 simulaneous inervenion policies aken joinly correspond o is inerior. This paper shows ha his inerior, or 'possible riniy' is quie generally no only possible bu opimal, since he CB obains a lower loss when i implemens a policy wih all hree inervenions. JEL E58 F38 O24 Keywords DSGE models; small open economy; moneary and exchange rae policy; capial conrols; opimal policy Auhors Guillermo J. Escudé, Cenral Bank of Argenina and Consejo Nacional de Invesigaciones Cieníficas y Técnicas, Buenos Aires, Argenina, gescude@bcra.gov.ar Ciaion Guillermo J. Escudé (204). The Possible Triniy: Opimal Ineres Rae, Exchange Rae, and Taxes on Capial Flows in a DSGE Model for a Small Open Economy. Economics: The Open-Access, Open-Assessmen E- Journal, Vol. 8, hp://dx.doi.org/0.508/economics-ejournal.ja Received January 27, 204 Published as Economics Discussion Paper March 28, 204 Acceped June 8, 204 Published June 25, 204 Auhor(s) 204. Licensed under he Creaive Commons License - Aribuion 3.0

2 Inroducion Foreign rade and capial ows consiue he wo fundamenal links beween he open economy and world markes. And boh are affeced by a hos of governmen policies, including ineres rae and exchange rae policies as well as differen possible inervenions in he free ow of nancial asses. A radiional way of hinking abou he exchange rae regime and capial accoun openness has been framed in erms of he `impossible riniy' or `rilemma'. According o his view, policymakers can only have wo of hree possible oucomes: open capial markes, moneary independence and pegged exchange raes (see Bordo 2003). Hisorically, during he gold sandard period here predominaed open capial markes and xed exchange raes bu moneary independence was lacking. Laer, during he Breon Woods period pegged exchange raes and moneary independence became possible since imporan capial conrols prevailed. During he pos-breon Woods period free capial mobiliy was again inroduced, leading counries o a difcul choice beween pegged exchange raes (wih he consequen loss of moneary independence) and oaing exchange raes (wih moneary independence). Emerging marke economies ha chose o have pegged exchange raes ended o have periodic deb, currency and banking crises. Hence, for some ime a `bipolar view' prevailed ha wih free inernaional capial markes mos counries had o choose beween very hard pegs and free oas. However, in many insances even very hard pegs, such as Argenina's Converibiliy (ha lased 0 years), led o severe riple crises. The nancial meldown has awakened new ineres in hese opics. There is a renewed ineres in acive FX reserves managemen and greaer concern for nancial sabiliy due o he grave macroeconomic risks ha nancial meldowns generae. Possibly because he main developed economies were hi hard by he crisis, here has ended o be a more recepive approach o opics ha were unil recenly frowned upon, including FX marke inervenion, sof capial conrols in normal imes and more invasive pracices during he managemen of crises. Even he IMF is ending o accep ha under some circumsances capial conrols may be useful and even necessary. Osry e al. (200), for example, poin ou ha capial conrols can help o address nancial sabiliy concerns, a leas when here are insufcien prudenial ools available. Obsfeld e al. (2008) 2

3 ry o explain why here has been such a dramaic rise in global inernaional reserve holdings (as a fracion of world GDP) during he pos-breon Woods era. They argue ha reserve accumulaion is an imporan ool for managing domesic nancial insabiliy as well as exchange raes in a world in which nancial globalizaion has ballooned and he domesic banking secor needs proecion agains differen possible sources of drains (ighs from currency or deposis) by means of he cenral bank's role as a lender of las resor. I is hese concerns, much more han he radiional rade-relaed needs ha led o such imporan accumulaions of inernaional reserves. Frazscher (202) invesigaes he moives for he use of capial conrols. He uses a broad se of macroeconomic and nancial variables for 79 counries during he period o assess which of four possible moives for he use of capial conrols are mos imporan (objecives relaed o FX policy, capial ow managemen, ensuring nancial sabiliy or general macroeconomic policy). He nds ha FX policy managemen has been a cenral moive for he use of capial conrols. In paricular, `counries wih a high level of capial conrols and counries acively raising exising conrols are hose ha end o have undervalued exchange raes and a high degree of exchange rae volailiy.' He also nds ha choices concerning capial ow resricions, especially over he pas decade, have been largely moivaed by concerns abou an overheaing of he domesic economy. Recen empirical research has found ha mos counries, insead of choosing wo of he hree policy opions of he `riniy', acually choose a middle ground where he hree opions are used wihou exremes. Aizenman e al. (200), for example, nd ha many counries choose o have a managed exchange rae wih limied nancial auonomy and conrolled nancial inegraion (see also Aizenman 202). A a heoreical level, Farhi and Werning (202) sudy capial conrol policy in a sandard open economy model wih xed exchange raes, building on Clarida e al. (2002) and Galí and Monacelli (2005, 2008). They use a non-moneary and non-sochasic model in which here is no endogenous risk premium o sudy he opimal use of capial conrols in response o differen shocks (produciviy, expor demand, erms of rade, foreign ineres raes and exogenous risk premia) under differen pricing assumpions (exible prices, rigid prices, one-period in advance price xing and Calvo price seing). They conclude ha capial conrols are more effecive he more closed is he economy, and ha hey are paricularly powerful 3

4 in responding o ucuaions in he exogenous risk premium demanded by foreign invesors. A leas since he heyday of he Mundell-Fleming model, modeling he inermediae ground beween a rmly pegged (or xed) exchange rae and a freely oaing exchange rae has been waning. Unil very recenly he difculies involved in seing up a workable framework had no been surpassed, even wih such modern developmens in macroeconomic modeling such as he raional expecaions revoluion and DSGE modeling. In pracical research, however, he analysis of he middle ground policies have no faced subsanial difculies. For example, in IMF Aricle 4 repors on emerging marke economies, i has been radiional o sudy he developmens in he balance shees of he main insiuional secors (privae and public nancial insiuions, Cenral Bank (CB) and Treasury) in order o obain insigh ino acual exchange and ineres rae policies and heir consequences. In analyical macro modeling, however, here has been resisance o explicily modeling he nancial socks and ows of he main secors included in he model ha would make i possible o represen such policy middle ground as managed exchange raes. My research in he pas few years has been mainly focused in his direcion (Escudé 2006, 2007, 2009, 203) and has led o a workable framework in small open economy DSGE modeling where policymakers may use wo policy rules in order o deermine operaional arges for he nominal ineres rae as well as he rae of nominal currency depreciaion (or, alernaively, he CB inernaional reserves Escudé 2006). In Escudé (203) I show he funcioning of he framework in a relaively small DSGE model ha, excep for a few addiions, is a sandard moneary New Keynesian model. The addiions are basically ) an ad hoc risk premium funcion ha is posiively dependen on household foreign deb, 2) an ad hoc long-run arge for he CB inernaional reserves raio (o GDP), 3) CB issued domesic currency bonds ha are used for serilizaion, 4) a careful formulaion of he CB budge consrain along wih he assumpion ha here is an insiuional arrangemen whereby he CB ransfers (nances) any nancial quasi- scal surplus (deci) o (wih) he Treasury, hereby mainaining a consan ne In some of my previous papers i was banks ha obained funds abroad and hence faced hese risk premia. 4

5 worh and a balance shee srucure ha only changes during he ransiion, 5) a second policy rule where here is an operaional arge for he rae of nominal currency depreciaion ha may respond o he same variables (or gaps) as he policy rule for he nominal ineres rae and, addiionally, he gap beween he CB inernaional reserves raio and is long run arge, 6) he assignmen of explici insrumens for he inervenions in he domesic currency bond marke (sales or purchases o achieve he operaional arge for he nominal ineres rae) and he FX marke (sales and purchases of inernaional reserves o achieve he operaional arge for he rae of nominal currency depreciaion). In his framework, he CB always saises privae secor money demand and has a long run arge for he inaion rae (and hence for he rae of nominal depreciaion). The role of he CB balance shee equaion is simply o deermine he sock of domesic currency bonds ha he CB mus have in is liabiliies a he end of he quarer as a resul of is inervenions in boh markes. The concep of `serilized' FX marke inervenion is avoided because i implicily subordinaes exchange rae policies o ineres rae policies. In principle, boh policies are (equally) imporan and he serilizaion of any unwaned moneary effecs of he combined inervenions in he wo markes is reeced in he quarerly changes in he sock of CB bonds. The basic resul in Escudé (203) is ha, leaving aside implemenaion coss (which remain unmodeled), i is opimal for policymakers o use he wo policy rules, and consequenly wo operaional arges and insrumens. This is very inuiive since any one of he `corner' policies is obained by inroducing an addiional consrain: eiher absain from inervening in he FX marke, which implies keeping he CB reserves consan, or absain from inervening in he domesic currency bond marke, which implies keeping he CB domesic currency bonds ousanding consan. The presen paper is a naural exension of Escudé (203) since i inroduces he hird verex of he `riniy' in he form of axes on privae foreign deb. These affec he risk-adjused uncovered ineres pariy equaion and hence inuence he SOE's inernaional nancial ows. A useful way o illusrae he range of policy alernaives is o associae hem wih he faces of an isosceles riangle (as in Figure below). Each of hree possible governmen inervenion policies aken individually (in he domesic currency bond marke, in he foreign currency marke, and in he foreign currency bonds marke) corresponds o one of he verices of he 5

6 riangle, each of he hree possible pairs of inervenion policies correspond o one of he hree edges of he riangle, and he hree simulaneous inervenion policies aken joinly correspond o he riangle's inerior. This paper shows ha his inerior, or `possible riniy' is quie generally no only possible bu opimal, since he CB obains a lower loss when i implemens a policy wih hree inervenions. As in he paren paper, any of he boundary regimes are obained by inroducing addiional consrains o he policymakers' problem when a linear-quadraic opimal conrol framework is used. In he paren paper here were 2 corner policies and an inerior policy ha combined hem, and hey are represened by he base of he riangle in Figure. In he presen paper here are 6 border policies and an inerior policy ha combines he hree possible individual inervenions and hese policies are also represened in Figure. To implemen any of he 3 edge regimes, he insrumen ha corresponds o he opposie verex mus be kep consan. To implemen any of he 3 verex regimes, he insrumens ha correspond o opposie 2 verices mus be kep consan. The 3 insrumens are ) he sock of domesic currency bonds in he (liabiliy side of he) CB's balance shee, 2) he sock of FX reserves in he (asse side of he) CB's balance shee, and 3) he size of he ax or ax/subsidy scheme on household foreign currency liabiliies. In his paper here are wo alernaive implemenaions for he hird form of inervenion: eiher a ax on he sock of household foreign deb or a ax (subsidy) on he increase (reducion) of household foreign deb. Obviously, here is a cerain asymmery since he rs wo insrumens correspond o acual nancial insrumens ha have a marke in which he CB operaes in order o obain a desired operaional arge for he ineres rae or he rae of nominal depreciaion, whereas in he hird case he insrumen akes he form of a ax ha mus be colleced (or subsidy ha mus be besowed). Because mos of he model is exacly as in Escudé (203), only he exensions are deailed in he ex, leaving he exposiion of mos of he model as well as he full se of model equaions for he Appendix. 6

7 Figure The 3 Inervenions OM: Open Marke operaions wih CB domesic currency bonds FX: Foreign exchange marke inervenion CC: (Capial Conrol) ax on household foreign currency bonds The res of he paper has he following srucure. Secion 2 conains he household decision problem and how i is affeced by he wo new forms of inervenion considered. Secion 3 shows he calibraions used for he model parameers and deails he calibraions ha are direcly relaed o he risk premium funcion ha foreign invesors are assumed o use o deermine he ineres rae hey demand. Secion 4 species he alernaive ineres rae, exchange rae, and capial conrol policies ha are available. Secion 5 shows how he model works and illusraes he effecs of he differen policy regimes on he variabiliy of he main arge variables in 3 alernaive frameworks available in Dynare for model soluion: a) 7

8 simple policy rules, b) opimal simple policy rules, and c) opimal policy under commimen and full informaion. Finally, Secion 6 has he conclusions, Appendix A shows he pars of he model which are lef ou in he main body of he paper, and Appendix B liss all he model equaions. Addiionally, wo Dynare model les are available, one for each of he wo possible implemenaions of he ax on foreign deb. 2 The model 2. Households An inniely lived represenaive household consumes a CES bundle of domesic and impored goods (C ) and holds nancial wealh in he form of cash (M ) and domesic currency denominaed one period nominal bonds issued by he CB (B ) ha pay a nominal ineres rae i and are considered riskless. The household also issues one period foreign currency bonds (D ) abroad ha pay a nominal foreign currency ineres rae i D. I is assumed ha foreign invesors are only willing o hold he SOE's foreign currency bonds if hey receive a risk premium τ D γ D ;γr over he inernaional riskless rae i which, as a funcion, is exogenously given (since he Res of he World -RW- is no modeled). This funcion varies direcly wih he SOE's aggregae foreign deb o GDP raio γ D and inversely wih he CB's inernaional reserves raio γ R (boh dened below). There is also an exogenous sochasic and ime-varying componen φ of he oal wedge ( + i D = + i ) beween he (foreign currency) gross ineres raes ha apply o he SOE and o he RW. φ can represen general liquidiy condiions in he inernaional capial marke and/or an exogenous componen of he risk-premium. The foreign currency gross ineres rae households face is hence: + i D = ( + i )φ τ D γ D ;γr ; () where τ D (:) is increasing and convex (τ D >, τ 0 D;γ D > 0 and τ 00 D;γ D > 0) in γ D, and decreasing (τ 0 D;γ < 0) in γ R R. The real exchange rae (RER), real foreign deb and inernaional CB reserves (in erms of foreign prices), and corresponding foreign 8

9 deb and CB reserves raios o GDP are: e S P ; d D P P ; r R P ; γ D = S D = e d ; γ R = S R = e r (2) P Y Y P Y Y where R is he CB inernaional reserves, S is he nominal exchange rae, P is he domesic goods price index, P is he price index of he goods he SOE impors, and Y is GDP. A second exogenous funcion τ M (:) represens gross ransacions coss, and inroduces he convenience of using cash. The household holds cash M o economize on ransacion coss because in order o purchase he consumpion bundle C i mus spend τ M (:)P C C where P C is he price index of he consumpion bundle. The funcion τ M γ M is assumed o be a decreasing and convex funcion (τ M > ; τ 0 M < 0; τ00 M > 0) of he cash/consumpion raio γm : γ M M P C C = m p C C ; (3) where p C is he relaive price of consumpion goods and m is real cash: p C PC ; P m M P : (4) The represenaive household maximizes an iner-emporal uiliy funcion which is addiively separable in (consan relaive risk aversion subuiliy funcions of) goods C and labor N : E β j σc j=0 σcc + j ξ + σ N N + j +σ N ; (5) where β is he ineremporal discoun facor, σ C, and σ N are he consan relaive risk aversion coefciens for goods and labor, respecively, and ξ is a parameer. The household budge consrain in period is: τ M γ M P C C + M + B S D = W N + Π Tax Tax DCol (6) +M + ( + i )B ( + i D )S D 9

10 where i is he nominal ineres rae ha CB bonds B pay each quarer, W is he nominal wage rae, Π is nominal pros, Tax is nominal lump sum axes ne of lump sum ransfers and Tax DCol is he governmen collecion from a ax (or subsidy) relaed o he household's foreign deb. The laer is he main innovaion in his paper wih respec o Escudé (203): here he governmen implemens eiher a ax or a ax/subsidy scheme o inuence capial ows from/o he RW. Le ax D be a ax rae relaed o household foreign deb (i.e., foreign currency liabiliies of domesic residens ha are asses of residens in he RW). Two differen foreign deb relaed conceps are considered: he rs is simply a ax on he level of household foreign deb (and in his case I use ax D for noaion); he second is more complicaed, since i is a ax on increases in he level of foreign deb and, symmerically, a subsidy on foreign deb cancellaions (and in his case I use he noaion axsub D o disinguish he fac ha in his case i is also a subsidy rae). In he erminology used below, increases (reducions) in he level of foreign deb are referred o as capial inows (ouows). This should pose no ambiguiy as, for simpliciy, households in his paper have no access o foreign asses. Consequenly, here are wo differen possible forms for Tax DCol in he household (nominal and real, respecively) budge consrain of period : Form (level): Tax DCol = ax D S D ; ax DCol = ax D e d : (7) Form 2 (change in level): Tax DCol = axsub D S (D D ); ax DCol = axsub D d e d π ; (8) where impored goods inaion π is dened as π P P : 0

11 Inroducing () in (6) and dividing by P, he real budge consrain is: τ M γ M p C C + m + b e d = w N + Π ax ax DCol (9) P + m + ( + i ) b ( + i π π )φ τ D γ D d ;γr e ; where ax DCol can adop one of he wo possible forms ((7) or (8)), and real CB bonds, he real wage, real lump sum axes, and domesic inaion, are dened as: π b B P ; w W P ; ax Tax P ; π P P : The ax DCol erm in (9) is he only change in he household real budge consrain wih respec o he paren model in Escudé (203). To simplify, i is assumed ha here is no impored goods inaion in he non-sochasic seady sae (NSS) (π = ). In he case of axsub D, if a shock makes he household foreign deb d emporarily increase and a some poin i begins o decrease (unil i again reaches is long run or non-sochasic seady sae (NSS) value), he governmen rs collecs he (disorionary) ax during some ime and a some poin begins o reurn i as a subsidy. This makes he deci closing lump-sum ax decline during he iniial phase, and increase during he second phase o compensae for he subsidy. I is assumed in his paper ha in he NSS ax D or axsub D are posiive and less han uniy. 2 The household chooses he sequence C + j ;m + j ;b + j ;d + j ;N + j j=0;:::; ha maximizes (5) subjec o is sequence of budge consrains (9) (and iniial values 2 The special case ax D = 0 or axsub D = 0 is he model in Escudé (203).

12 for he predeermined variables). In he axsub D case, he Lagrangian is hence: ( C E β j + j σc j=0 σ C ξ N +σ N + j + σ N + λ + j w + j N + j + Π + j + m P + j! +( + i + j ) b + j m + j τ M π + j p C + j C + j ( + i + j)φ + j τ D e + j d + j π + j p C + jc + j m + j b + j e + j d + j ; e + jr + j Y + j Y + j )) + axsub+ D j e+ j d + j ax + j ; + j π + j axsub D + j where (9) has been rearranged by gahering he erms in d and d, respecively (afer insering (8)). β j λ + j are he Lagrange mulipliers, and can be inerpreed as he marginal uiliy of real income. 3 In he simple ax D case he only change is ha (apar from subsiuing ax D for axsub D ) he ax erm wihin he square bracke disappears. For boh forms of ax on foreign deb, he rs order condiions for an opimum for variables C, m, b, and N, are exacly he same as in he paren paper: C : C σc = λ p C ϕ M m =p C C (0) m : λ + τ 0 M m =p C C = βe (λ + =π + ) () b : λ = β ( + i )E (λ + =π + ) (2) N : ξ N σ N = λ w (3) Only he rs order condiion for d is affeced by he inroducion of he conrol on capial ows and i differs for he wo cases: Form (level): λ ax D e = β( + i )φ E λ + e + π + e d ϕ D ; e r Y Y (4) 3 A no-ponzi game condiion is implici and yields he ransversaliy condiion lim! β d = 0 ha prevens households from incurring in Ponzi games. 2

13 Form 2 (change in level): λ axsub D e (5) λ = β( + i )φ E + e + e d ϕ D ; e r axsub+ D Y Y π + In (0) and he las wo expressions, he auxiliary funcions ϕ M and ϕ D ha have been inroduced for convenience are dened as: ϕ D γ D ;γr τd γ D ;γr + γ D τ 0 D;γ γ D D ;γr ; (6) ϕ M γ M τm γ M γ M τ 0 M γ M ; where τ 0 D;γ γ D D ;γr represens he parial derivaive of τd wih respec o γ D. As in Escudé (203), combining () and (2) gives he demand funcion for cash: m = L ( + i ) p C C ; (7) where L (:) is dened as: L ( + i ) ( τ 0 M) + i ; (8) h and is sricly decreasing, since L 0 ( + i ) = τ 00 M (L ( + i ))( + i ) 2i < 0. Under he assumpion ha he CB always saises cash demand, (7) is henceforh he `cash marke clearing condiion'. Using (0) o eliminae λ from (2) and (3) yields he Euler equaion and he household's labor supply, respecively:! C σc C+ σc ϕ M m =p C = β ( + i )E C ϕ M m + =p C + C ; (9) + π C + N =! w ξ p C C σc ϕ M m =p C C σ N ; (20) 3

14 where in he rs of hese π C P C =P C is he gross rae of inaion of he baske of consumpion goods and he ideniy p C =p C = πc =π is used. Finally, he deniion of he RER in (2) gives he ideniy e =e = δ π =π, where δ S =S is he rae of nominal depreciaion of he domesic currency. Hence, (5) may be wrien as: ( λ+ = β( +i )φ E ϕ D γ D ;γr axsub+ D λ π + axsub D δ +!): (2) Eliminaing β using (2) yields: λ + ( + i )E λ π + λ = ( + i )φ E + ϕd (e d =Y ;e r =Y ) axsub+ D λ π + axsub D δ + : Using he fac ha he expeced value of he produc of wo random variables is he produc of he expeced values plus he covariance of he wo variables, gives λ + ( + i )E λ π < E λ + ϕd (e = ( + i )φ λ π + E d =Y ;e r =Y ) axsub+ D δ axsub D + = : +Cov λ + λ π + ; ϕ D (e d =Y ;e r =Y ) axsub+ D δ + ; : axsub D Therefore, o a rs order approximaion he covariance erm can be ignored and he risk-adjused UIP equaion is simply: + i = ( + i )φ E ϕd (e d =Y ;e r =Y ) axsub D + axsub D δ + (22) = ( + i )φ E + ϕ D (e d =Y ;e r =Y ) axsub+ D δ axsub D + where in he second equaliy ϕ D (:) + ϕ D (:) is used. Noice ha an increase in axsub D has he effec of increasing he domesic ineres rae (ceeris paribus), while an expeced increase in he nex period has he opposie effec. Hence, 4

15 if axsub D increases iniially and is subsequenly expeced o fall, boh have he effec of increasing he domesic ineres rae (ceeris paribus). In he case of he simple ax on he level of deb, o a rs order approximaion he UIP equaion is: + i = ( + i )φ ϕd (e d =Y ;e r =Y ) ax D E δ + (23) = ( + i )φ + ϕ D (e d =Y ;e r =Y ) +ax D ax D E δ + : 2.2 The public secor The public secor includes he Governmen and he CB. The CB issues currency (M ) and domesic currency bonds (B ), and holds inernaional reserves (R ) in he form of foreign currency denominaed riskless bonds issued by he RW. The CB supplies whaever amoun of cash is demanded by households, and can inuence hese supplies by changing R or B, i.e. inervening in he foreign exchange marke or in he domesic currency bond marke. I is assumed ha CB bonds are only held by domesic residens and ha he CB ransfers is quasi-scal surplus o (or has is quasi-scal deci nanced by) he Governmen each period, mainaining is ne worh a zero each period. 4 Hence, he CB balance, for all, is: m + b = e r : (24) The Governmen spends on goods, receives he quasi-scal surplus (or nances he quasi-scal deci) of he CB, and collecs axes. I is assumed ha scal policy consiss of an exogenous auoregressive pah for real governmen expendiures as a (gross) fracion (G ) of privae consumpion τ M (:) p C C, collecing he ax on privae capial ows, and collecing whaever lump-sum axes are needed o balance he budge each period. The Public Secor real ow budge consrain is hence: ax = (G )τ M m =p C C p C C q f ax DCol ; (25) 4 See Escudé (203) for more deails. 5

16 where he real quasi-scal surplus includes ineress on CB asses and capial gains or losses on CB inernaional reserves: q f = + i r =δ e π [( + i ) ] b ; (26) π and he real domesic currency value of he ax collecion relaed o capial ows is eiher (7) or (8). Since he descripion of he res of he model is exacly he same as in Escudé (203) i is relegaed o Appendix A. 2.3 Funcional forms for auxiliary funcions The funcional forms used for he endogenous risk premium and ransacion coss funcions are he same as in Escudé (203): τ D γ D ;γr τ D α = + α 2 γ D + α 3 γ R ; α ;α 2 ;α 3 > 0; (27) τ M γ M τ M β = + + β 2 γ M β ; β 3 ;β 2 ;β 3 > 0; (28) which, according o deniions (6), imply: ϕ D γ D ;γr ϕ D = + τ D α 2 γ D + α 2 γ D + α 3 γ R γ M ϕ M = + τ M β + β 2 γ M 3 + β 2 γ M : ϕ M For convenience, dene he respecive ne funcions as: ; (29) τ D (:) = τ D (:) ; ϕ D (:) = ϕ D (:) (30) τ M (:) = τ M (:) ; ϕ M (:) = ϕ M (:) : The parial elasiciies of τ D and τ M (used below in calibraions) are, respecively: ε τd;; = α 2 γ D α 2 γ D + α 3 γ R α 3 γ R ; ε τd;2; = α 2 γ D + α 3 γ R (3) ε τm; = β 3 β 2 γ M + β 2 γ M : (32) 6

17 Finally, he liquidiy preference funcion (8) ha resuls from (28) is: 2! 3 m p C γ M = L ( + i ) 4 β β 2 β β : C β 2 +i 3 Calibraion of parameers and he non-sochasic seady sae In his secion he calibraed parameers ha are used in he exercises below are shown and he calibraion procedure used is only deailed inasmuch as i differs from ha of he paren paper. Since he only expansion in his paper is ha here is eiher a ax or a ax/subsidy scheme relaed o foreign deb (even in he NSS), he res of he calibraions are he same as in Escudé (203), which he ineresed reader can consul. I is convenien o sress ha, alhough Argenine daa has been used for some of he calibraions, he main objecive has been o have a calibraed SOE economy similar in many respecs o some of hose mos cied in he lieraure (e.g., Galí and Monacelli 2005 and De Paoli 2006) bu endowed wih he innovaions ha allow for he sysemaic and simulaneous use of ineres and nominal depreciaion policy rules. The following are immediaely obained from he NSS versions of various equaions: 5 er=y = γ R ; π = π C = π T ; δ = π T =π ; π = π X = p = ; +i = π T =β: (33) Table summarizes he calibraed values of he main model parameers, along wih some comparisons wih parameer values used in oher SOE models, and he calibraed NSS values of some of he endogenous variables (or raios of endogenous variables). 6 5 See he complee se of equaions in Appendix B. 6`E.S.' denoes `elasiciy of subsiuion', G_M sands for Galí and Monacelli (2005), and De P for De Paoli (2006). 7

18 Table Parameers This paper G-M De P β Ineremporal discoun facor σ C Relaive risk aversion for goods.5 σ N Relaive risk aversion for labor α Probabiliy of no adjusing price θ E.S. beween domesic goods θ C E.S. domesic vs. impored goods.5 3 a D Coef. for share of domesic goods b A Coef. in prod. funcion for commodiies 0.5 ε τd; Elasiciy of risk funcion τ D (ed=y;er=y ) 0 ε τd;2 Elasiciy of risk funcion τ D (ed=y;er=y ) 0 ε L Elasiciy of L ( + i).02 NSS values of endogenous variables or raios Y GDP.443 G Gov. Expend. o privae consumpion.9 π T Inaion arge.05 γ D Household foreign deb o GDP 0.5 γ R CB foreign reserves o GDP 0.3 m=y Household cash o GDP 0.08 π RW expor goods inaion + i RW ineres rae :03 0:25 φ RW exogenous liquidiy/risk premium :005 0:25 The sandard errors and persisence parameers used for he six shock variables are given in Table 2. They were calibraed aking ino accoun he available ime series for Argenina and he RW during he period : public consumpion o GDP in he case of σ G, impored and expored goods inaion as hey conform Argenina's XTT, in he cases of σ π and σ π, Libor 3 monhs in he case of σ i, and balance of paymens informaion on privae secor foreign debs and ineres paymens as well as he auhor's calculaion of he spread over Libor 3 monhs, in he case of σ φ. The only cases in which he sandard deviaions were aken exacly according o he daa are he cases of σ i ; σ π, and σ π. 8

19 Table 2 Calibraion of shock variables Sandard deviaions Persisence parameers σ ε 0:0 ρ ε 0:8 σ G 0:03 ρ G 0:85 σ i 0:0046 ρ i 0:7 σ φ 0:05 ρ φ 0:3 σ π 0:0295 ρ π 0:2 σ π 0:0424 ρ π 0:4 ρ πxn 0:8 The res of he sandard deviaions were calibraed aking boh he daa (excep for σ ε ) and he resuling heoreical sandard deviaion and variance decomposiion for GDP wih a baseline calibraion of (38) and (39): h = 0:8, h 2 = 0:8, k 4 = 0:8, and he res of he coefciens equal o zero. This implied diminishing he observed sandard deviaion of G (from in a simple AR() esimaion from which he value for he persisence parameer ρ G was aken), which seemed o weigh oo heavily in he volailiy of Y, and increasing he sandard deviaion of φ (from ), which seemed no o weigh enough. Aside from he inroducion of he new simple policy rule ((40) below) and he ax equaion (eiher (7) or (8)), he only equaion ha changes wih respec o he previous paper is he Risk-adjused UIP ((22) or (23)) which, using (29) and (33) and manipulaing, gives a he NSS: Tax on level of deb: ϕ D = ax D β( + i )(φ =π ) (34) Tax on change of deb: ϕ D = axsub D β( + i )(φ =π ) : (35) 9

20 The risk funcion parameers α, α 2 and α 3 in (27) need o be calibraed. Firs, noe ha (3) gives direcly ε τd; = α 2 γ D + ε τd; + ε τd;2 (36) ε τd;2 = α 3 γ R + ε τd; + ε τd;2 (37) which, given calibraed values for he elasiciies and he grea raios, yield: ε τd; α 2 = γ D + ε τd; + ε τd;2 α 3 = ε τd;2 γ R : + ε τd; + ε τd;2 Equaions (36) and (37) also imply + ε τd; + ε τd;2 = + ε τd; = α 2 γ D + α 3 γ R ; + α 3 γ R α 2 γ D + α 3 γ R ; from which ϕ D = α + α 3 γ R α 2 γ D + α 3 γ R 2 = α + ε τd; + ε τd;2 + ετd; : Therefore, using eiher (34) or (35) he value of α akes wo differen forms, according o he assumpion on he capial conrol ax: Tax on level of deb: α = ax D β(+i )(φ =π ) + ε τd; + ετd; + ε τd;2 Tax on change of deb: axsub D β(+i α = )(φ =π ) : + ε τd; + ετd; + ε τd;2 20

21 In order o be able o reasonably compare he wo alernaive forms of capial conrols, heir NSS values can be calibraed so ha he non-ax variables have he same NSS values. In paricular, his requires ha he risk premium have he same value in he NSS. Looking a (34) and (35), a lile algebra shows ha for his o be he case he following relaion beween ax D and axsub D mus hold: ax D = axsub D [ β( + i )(φ =π )]: 4 Ineres rae, exchange rae, and capial conrol policies As in Escudé (203), in his paper he CB uses o sabilize he SOE's macroeconomy eiher I) simple policy rules or II) opimal conrol under commimen and full informaion. The simple rules may be Ia) simple and wih exogenous coefciens, or Ib) simple and wih opimal coefciens. In case Ia), he simple ineres rae rule is a feedback rule, and he simple rules for nominal depreciaion and he ax/subsidy on capial ows may or may no involve feedback. In case Ib), he CB is assumed o obain he values of he coefciens in he policy rules by minimizing a weighed average of he squared deviaions of cerain arge (endogenous) variables from heir NSS values. When he CB uses II) (i.e., opimal policies under commimen and full informaion), he simple policy rules disappear and he CB obains he rajecories for he inermediae arges (nominal ineres rae, nominal rae of depreciaion) and he ax rae (or ax/subsidy rae) by minimizing an expeced discouned ineremporal quadraic loss funcion of he arge variables. In Escudé (203) i was shown ha when he arge variables are he inaion rae, GDP, and he RER, i is `always' beer o use wo policy rules insead of one of he wo `corner' regimes of Floaing Exchange Rae -FER- or Pegged Exchange Rae -PER- (which can equivalenly be called Floaing Ineres Rae -FIRregime). In he FER regime he CB absains from inervening in he FX marke and has an inermediae arge for he nominal ineres rae, while in he PER regime he CB absains from inervening in he domesic currency bond marke and has an inermediae arge for he rae of nominal depreciaion. In he Managed Exchange Rae -MER- regime, on he oher hand, here are wo simple rules: one for he nominal rae of ineres and an anoher for he rae of nominal currency 2

22 depreciaion. I urned ou ha i was `always' beer wo use he MER regime, in he sense ha he CB obains lower losses under his regime for any se of CB preferences for inaion, GDP, or RER sabilizaion. The reason for his gain in using wo rules is ha he CB can hus beer exploi privae capial ows for is sabilizaion purposes, given he fac ha hese ows are (mainly) joinly deermined by he risk-adjused Uncovered Ineres Pariy condiion (UIP) and is policy rules. Deermining boh ends of he UIP equaion by means of he operaional arges in he wo policy rules has a crucial effec on he foreign-deb o GDP raio, which is assumed o deermine he risk assessmen of foreign invesors and hence he wedge beween he domesic ineres rae and he expeced rae of depreciaion of he currency. This paper sars from ha poin and explores he effecs of adding an addiional policy rule: one ha involves he paricular form of `capial conrol' device (ax D or axsub D ) inroduced in he previous secions. As shown above, a ax on foreign deb or a ax/subsidy scheme on privae capial ows becomes an inegral par of he risk-adjused UIP equaion. Hence, if he CB has a policy rule for deermining he level of hese axes or axes/subsidies, i has an addiional insrumen ha can affec privae capial ows. Wih he same mehods used in he previous paper, his paper shows ha i is generally opimal o use 3 policy rules insead of eiher 2 or, and for he same reasons. Hence, he Triniy of ineres rae, exchange rae, and capial conrol policies in he SOE is no only Possible, bu is also Opimal. 7 In he MER regime, he CB, hrough is regular and sysemaic inervenions in he domesic currency bond (or `money') and foreign exchange markes, aims for he achievemen of wo operaional arges: one for he inerbank ineres rae i ; and anoher for he rae of nominal depreciaion δ. When here are simple policy rules, he CB can uses operaional arges for i and δ ha respond o deviaions of he consumpion inaion rae (π C ), GDP (Y ) and/or he RER (e ) from heir respecive NSS levels. The rae of nominal depreciaion can addiionally respond o deviaions of he CB's inernaional reserves (IRs) o GDP raio from a long run arge (γ R ). In his paper, here is an addiional policy rule ha deermines he ax 7 However, i is shown below ha in he Ramsey case i is only marginally beer o use he 3 conrol variables insead of only he ineres rae and ax/subsidy rae. 22

23 or ax/subsidy relaed o foreign deb, which in principle can respond o he same hree basic arge variables as he preceding rules. Bu i has been deemed preferable o be a lile more specic by making i also respond o he deviaions in he exogenous risk/liquidiy shock φ, given ha his shock variable direcly affecs he UIP equaion and ha such shocks are empirically imporan for emerging marke economies. There may also be hisory dependence (or ineria) in any of he feedback rules hrough he presence of he lagged operaional arge variable. Hence, he simple rules in he case of ax D are he following: 8 + i + i = + h0 i π C + i π T h h2 Y e h3 (38) Y e δ δ = δ k0 π C δ π T k k2 Y e k3 γ R k4 Y e γ R (39) ax D ax D = ax D ax D j0 π C π T j Y Y j2 e e j3 φ φ j4 : (40) Any one (or any wo) of hese simple rules can be replaced by a corresponding equaion ha simply mainains a corresponding endogenous variable a is NSS value. As in Escudé (203), in he case of he rs wo of hese policy rules he insrumen (b and r ) ha he CB uses (a high frequency) o achieve he respecive operaional arge (for i or δ ) are endogenous variables. Hence, when he CB absains from inervening in he bond or FX marke i keeps he corresponding insrumen consan. Specically, when here is a FER regime, he second of he above simple rules mus be replaced by an equaion ha keeps he sock of CB foreign currency reserves consan a he NSS level (r = r). And when here is a PER regime, he rs of he above simple rules is replaced by an equaion ha keeps he sock of CB domesic currency bonds consan a he NSS level (b = b). In he presen paper, here is he addiional possibiliy ha he governmen (assumed o generally coordinae wih he CB) absain from acively using capial conrols. In ha case, he hird simple policy rule above is replaced by he equaion 8 Variables wihou a ime subscrip denoe NSS values. In he ax/subsidy case simply replace ax D wih axsub D. 23

24 ha keeps ax D (or, axsub D, which for succincness is no repeaed below) a is NSS level. Hence, he hree possible subsiuing equaions are, respecively: b = b; r = r; ax D = ax D : (4) As Figure 2 illusraes, here are seven possible `policy regimes', corresponding o he seven `faces' of he riangle (or 2-simplex). The hree verices (0-faces) of he riangle represen he `pure' policies in which here is only one rule, and hence he oher wo are replaced by heir subsiues. The hree edges (-faces) of he riangle represen he hree policy regimes in which wo of he rules operae and he hird is replaced by is subsiue. And he inerior (2-face) of he riangle represens he case in which all hree rules are used (he Possible Triniy). This laer policy regime is denominaed Managed Exchange Rae wih Capial Conrol (MER+CC). The boom edge of he riangle (including is wo verices) represens he hree policy regimes sudied in Escudé (203) (in which here were no capial conrols). These hree regimes keep ax D consan a is NSS level (which in he paren paper was no dened bu in his paper may be zero or posiive). The MER regime uses he rs wo of he above simple policy rules and replaces he hird policy rule by ax D = ax D. Paring from he MER regime, he Floaing Exchange Rae regime (FER) addiionally replaces he second policy rule by r = r, and he Pegged Exchange Rae regime (PER) insead addiionally replaces he rs policy rule by b = b. The upper lef edge of he riangle (FER+CC regime) adds he capial conrol rule o he ineres rae rule, and he upper righ edge of he riangle (PER+CC regime) adds he capial conrol rule o he nominal rae of depreciaion rule. 24

25 Figure 2 The 7 ineres rae, depreciaion rae, and capial conrol regimes verices: rule and insrumen edges: 2 rules and insrumens inerior: 3 rules and insrumens The op verex of he riangle is he policy which only uses he capial conrol rule and keeps he wo usual insrumens consan a heir NSS levels. I may come as a surprise o many ha such a policy rule easily makes he model saisfy he Blanchard-Kahn condiions for sabiliy and deerminacy. In fac, using he calibraions deailed in Escudé (203) and secion 3 above, and saring from he baseline simple policy rule dened in he second column of Table 3, each coefwww.economics-ejournal.org 25

26 cien can vary individually wihin he (very wide) inervals given by he hird column wihou impairing he Blanchard-Kahn condiions: 9 So far, simple policy rules have been considered, wheher heir coefciens are exogenously given or opimal in he sense ha hey represen he minimum of an ad-hoc CB loss funcion. The laer case is handled by means of he `osr' (opimal simple rule) Dynare command. In he case of opimal policy under commimen here are no simple policy rules, he corresponding equaions disappear, and hence here are more endogenous variables han sysem equaions. The pahs for he endogenous variables ha lack an equaion (he se or a non-empy subse of he hree inermediae arges) are obained as soluions o he opimal conrol problem in which he CB minimizes he expeced discouned sum of all (presen and) fuure losses. This case is handled by means of he `ramsey' Dynare command. The appropriae combinaion of `insrumens' (i.e., he conrol variables whose pahs are obained as opimum for he opimal conrol problem) mus be chosen, and he corresponding subsiue equaion(s) mus be inroduced for hose of he hree possible `insrumens' variables ha are no used as such. For example, for solving he model for he MER+CC regime under `ramsey' using Dynare, he opion `insrumens=(ii,dela,axsubd)' for he `ramsey' command mus be used and he hree simple rules are simply eliminaed (wih no subsiue equaion). Bu for he remaining 6 policy regimes a leas one of hese insrumens is no used. In paricular, for he FER+CC regime he opion o use is `insrumens=(ii,axsubd)', he rs and hird simple rules mus be eliminaed (wih no subsiue equaion) and he second policy rule mus be replaced by r = r. Analogously, for he PER+CC regime, he opion o use is `insrumens=(dela,axsubd)', he second and hird simple rules mus be eliminaed (wih no subsiue equaion) and he rs policy rule mus be replaced by b = b. As an example of he hree policy regimes in which only one insrumen is used le us ake he case of he CC regime. In his case, he opion o use is `insrumens=(axsubd)', he hird simple rule is eliminaed (wih no subsiue equaion) and he rs wo policy rules are subsiued by b = b and r = r. 9 Only values of he j k up o 00 in absolue value are repored, bu he negaive values can be much higher in aboslue value. 26

27 Table 3 CC simple policy rule Individual coefcien BK sabiliy ranges Coefcien Baseline value Sabiliy range j o -.85 [.00 o 00 j o 33 j o 7 j o 2 j o 00 I should be clear ha in he case of he Ramsey problem, he opimal policy under any one of he six `boundary' regimes canno dominae he opimal rule under he MER+CC regime due o he fac ha in any of he laer he governmen imposes a leas one addiional resricion on iself (`ies is hands'), hence relinquishing is use of one or more of is poenial `conrol' variables and using insead one or more of he possible subsiue equaions. For he same reason, he opimal loss for a `verex' policy (one of he verices of he riangle) canno be greaer han he opimal loss for an `edge' policy (one of he sides of he riangle) ha has ha verex as one of is exremes. Hence, here is a clear hierarchy here: he opimal loss for he MER+CC regime is less han or equal o he opimal loss of he MER, FER+CC, or PER+CC regimes (is edges), he opimal loss of he MER regime is less han or equal o he opimal loss of he FER or PER regimes (is verices), he opimal loss of he FER+CC regime is less han or equal o he opimal loss of he FER or CC regimes (is verices), and he opimal loss of he PER+CC regime is less han or equal o he opimal loss of he PER or CC regimes (is verices). Wha is of ineres is he exen o which an addiional insrumen reduces he loss, he ranking of he losses wihin he hree edges and wihin he hree verices, and how he relaive losses vary wih differen CB preferences (or `syles'). 27

28 Table 4 MER regime wih simple policy rules Simple policy rules Resuls Coefcien values Variable Mean Sd. Dev. h 0.3 k pic h 2. k -0.4 Y h k 2 0. e h k ii k 4-0. dela d gammad varphid axsubd The role of a ax/subsidy in capial inows/ouows in sabilizaion 5. Preliminary illusraion of he effecs of inroducing capial conrols hrough simple policy rules Firs, le us illusrae how he inroducion of a variable ax/subsidy scheme on capial ows can achieve sabilizaion objecives, by which is mean a reducion in he sandard deviaion (s.d.) of cerain arge variables. Le us assume ha iniially here is a MER regime wih he simple policy rules dened in he rs four columns of Table 4. Running he model gives he s.d. shown in he las column for some of he ypical arge variables (π C ; Y ; e ), inermediae arge variables (i ; δ ), and hree variables relaed o household foreign deb ( d, γ D, ϕ D ). Since axsubd is no used as an insrumen in he MER regime is s.d. is zero. The model was hen run using a MER+CC regime which has he same wo policy rules as in he MER regime and an addiional simple policy rule for he ax/subsidy scheme shown in columns 5 and 6 of Table 5. his able shows ha he s.d. for consumpion inaion has been reduced by 37.4%, whereas he s.d. for GDP and he RER have boh increased by 5.2%. 28

29 Table 5 MER+CC regime wih simple policy rules Simple policy rules Resuls % Ch. Coefcien values Variable Mean Sd. Dev. vs. MER h 0.3 k j pic % h 2. k -0.4 j -0.2 Y % h k 2 0. j e % h k j ii % k 4-0. j dela % d % gammad % varphid % axsubd % The s.d. for he wo operaional arges in he MER regime (he nominal ineres rae and he rae of nominal depreciaion) have been reduced by 22.9% and 26.%, respecively. Of course, his has been achieved by increasing he s.d. for axsubd inniely (since i was null under he MER regime and now i is posiive), and he s.d. for d, γ D and ϕ D by 42.5%, 58.6% and 58.3%, respecively. Figures 3 and 4 show he Impulse Response Funcions (IRFs) corresponding o a surprise reducion in he exogenous risk/liquidiy premium φ. Under he MER regime, he liquidiy shock induces households o ake advanage of he cheaper funds and hereby increase heir foreign deb on impac and increase heir consumpion. However, he shock also generaes real appreciaion, making expors fall. This negaive effec predominaes over he increase in consumpion, so GDP falls. Figure 4 shows he IRFs afer he ax/subsidy scheme has been inroduced (and hence here is a MER+CC regime). The behavior of households is seen o be quie differen in he iniial quarers. Insead of iniially increasing heir foreign deb hey reduce i (hereby obaining a subsidy) and insead of increasing heir consumpion, hey reduce i. Insead of a real appreciaion, here is now an iniial real depreciaion, increasing expors. The laer effec neuralizes he fall in consumpion, so here is no iniial effec on GDP bu subsequenly i rises for a few quarers, since consumpion recovers faser han expors sar o fall. 29

30 Figure 3 Negaive shock o φ MER regime 0.0 pic 0.02 Y 0.05 e ii dela d x 0 3 varphid C X In essence, he inroducion of he ax/subsidy scheme generaes during he iniial quarers a subsiuion of expensive foreign funds for cheap governmen funds (ha pay no ineres). I can be concluded ha governmens ha use a MER regime wih he coefciens shown above in a SOE prone o signican RW liquidiy shocks and have a sronger preference for sabilizing consumpion inaion han GDP or he RER have somehing o gain by inroducing a ax/subsidy scheme on capial ows. 30

31 Figure 4 Negaive shock o φ MER+CC regime 5 x 0 3 pic 0.02 Y 0.05 e ii dela d x 0 3 varphid C X This exercise is only an illusraion of how he ax/subsidy scheme can change he dynamic pahs of variables ha ypically ineres policymakers mos. One should bear in mind ha he IRFs illusrae he effec of he inroducion of he ax/subsidy scheme on he (deerminisic) dynamics of he model when here is a shock o he exogenous risk/liquidiy premium, whereas he sandard deviaions of he endogenous variables shown in Tables 4 and 5 above illusrae he sochasic properies of he whole se of shock variables. Table 6 below show he variance decomposiions of he variables corresponding o he wo exercises. They show ha he four really signican shocks in he model are hose ha hi public expendiures (G), he exogenous risk/liquidiy premium (φ -phisar), and he inaion raes for impors (π -pisar) and expors (π -pisarx), whereas he shocks on produciviy (ε-epsilon) and he world ineres rae (i -isar) individually accoun for a mos 5.7% of he variances of he arge variables. 3