ARGEM: A Dynamic and Stochastic General Equilibrium Model for Argentina. Guillermo J. Escudé Banco Central de la República Argentina

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1 ARGEM A Dynamic and Sochasic General Equilibrium Model for Argenina Guillermo J. Escudé anco Cenral de la República Argenina This version, Ocober 5, 2006

2 2 ARGEM A Dynamic and Sochasic General Equilibrium Model for Argenina. Inroducion The las few years have seen an explosion of Dynamic and Sochasic General Equilibrium (DSGE) models buil for policy analysis and forecasing in indusrialized counries. The se of papers presened o he recen join U.S. Federal Reserve oard-european Cenral ank-imf conference "DSGE Modeling a Policymaking Insiuions Progress & Prospecs" is a signi can sample. The need for beer microfounded models ha can conribue o policy analysis is also experienced by developing counry Cenral anks, Argenina being no excepion. On op of he many di culies encounered in developed counries in building, calibraing and/or esimaing hese models, hose who seek o obain models ha can be relevan in he developing counry conex nd various addiional di culies. One of hese sems from he fac ha he models buil for indusrialized counries ypically assume a freely oaing exchange rae and hence can avoid modeling exchange rae policy. Mos developing counries do no have a pure exchange rae oa and heir Cenral anks regularly inervene in he foreign exchange marke wih varying degrees of inensiy and frequency. While he opposie "corner" of a pure ineres oa wih a moneary policy based on deermining a pah for he nominal exchange rae is no di cul o model, one of he challenges faced by developing counry modelers is o incorporae exchange rae inervenion as an addiional ool available for a Cenral ank ha also inervenes in he money marke (ypically by deermining a shor run ineres rae). This is one of he main objecives of his paper. The paper builds upon various recen developmens in moneary macroeconomic modeling, including Chrisiano, Eichenbaum and Evans (200) (CEE), Smes and Wouers (2003), Woodford (2003), and Adolfson, Laséen, Lindé and Villani (2005), o menion bu a few. The model is perhaps closes in srucure o Adolfson e al (2005), wih a number of signi can di erences ha include he following ) The Cenral ank can use alernaive moneary policies wihin he same overall framework, including a xed exchange rae policy, a crawling peg policy, in aion argeing wih a pure oa and in aion argeing wih a managed oa. In he laer case, he Cenral ank simulaneously inervenes in he foreign exchange and money markes wih wo parallel feedback policy rules. 2) Insead of posulaing an "asymmeric produciviy shock" we assume ha here is coinegraion beween he small domesic economy s (SDE) uni roo echnology shock and he large res of he world s (LRW). 3) The nancial closure of he SDE is di eren in ha households do no engage in exernal deb nor save in foreign asses. I is he governmen and banks ha rely on foreign funding, he cos of which is increasing in heir (derended) level of ne deb. A risk-adjused uncovered ineres pariy condiion naurally sems from anks pro maximizaion. 4) We have a full edged banking sysem. anks have a cos funcion ha is quadraic and dependen on heir loan and deposi socks, wih economies of scope beween lending and deposi aking aciviies. They have a echnical demand for cash, which is a (possibly so- The opinions expressed in his paper are he auhor s and do no necessarily re ec hose of he Cenral ank of Argenina. Mailing address gescude@bcra.gov.ar.

3 chasic and ime-varying) fracion of deposis and mus keep a regulaory fracion of heir deposis in non-ineres bearing reserves in he Cenral ank. Also, hey use he remaining fracion of heir deposis as well as foreign funds o nance rms demand for loans and he Governmen s exogenous demand for loans, o purchase Cenral ank bonds, and o lend (or borrow) in he inerbank marke. To add ineria in he "uncovered ineres pariy condiion" we assume ha a fracion of he banks, insead of forming expecaions raionally, have saic expecaions wih respec o nominal currency depreciaion. 5) The governmen ax srucure is minimal (jus lump sum axes), bu i can also nance is expendiures by issuing deb abroad, by obaining bank loans, and by using he Cenral ank s quasi- scal surplus. 6) The producion of inermediae domesic goods requires impored goods as inpus (in addiion o labor and physical capial services) and he rms ha engage in his producion obain bank loans o nance a sochasic fracion of he capial renal bill and he impored inpus bill (in addiion o a sochasic fracion of he wage bill). 7) Households use cash for consumpion and invesmen using a sylized ransacions echnology ha requires he use of domesic goods. Hence, cash is no in he uiliy funcion, and he resuling household demand for cash is dependen on privae absorpion (and he deposi ineres rae). 8) We assume consan (insead of sochasic and ime-varying) elasiciies of subsiuion. The res of his paper has he following srucure. Secion 2 presens he household opimizaion problem, which deermines heir consumpion and invesmen demands, he rae of uilizaion of physical capial, he dynamics of he sock of physical capial, heir cash and bank deposi demands, and heir nominal wage seing. Secion 3 presens he decisions of domesic goods producers, including heir demand for labor and physical capial services, heir demand for impored inpus and bank funding, heir supply of goods and heir nominal price seing. Secion 4 has he decisions of imporing and exporing rms, all of which have sicky local currency pricing. Secion 5 summarizes he main relaive prices in he paper and makes explici wha we mean by a Small Domesic Economy (SDE) in a Large Res of he World (LRW). Secion 6 models anks decision problem, which deermines heir demand for cash and required reserves, heir demand for foreign funds and for Cenral ank bonds, and heir supply of deposis and loans. Secion 7 inroduces he public secor, composed of he Governmen and he Cenral ank. The Cenral ank balance shee plays a signi can role in he modeling of he simulaneous inervenion in he money and foreign exchange markes. Secion 8 pus ogeher he marke clearing equaions, he balance of paymens equaion, and he relaion beween he domesic secor oupu and GDP. Secion 9 addresses a meaningful sample of he alernaive moneary policies ha may be accommodaed ino he overall srucure. Secion 0 liss he non-policy equaions of he non-linear sysem so far encounered. Secion ransforms his se of equaions so ha he variables are in saionary forma, and adds he alernaive ses of policy equaions. Secion 2 displays possible funcional forms for he various auxiliary funcions used, such as he invesmen adjusmen cos funcion, he funcion ha re ecs he coss due o non-normal inensiy of uilizaion of physical capial, he ransacions cos funcion, and banks risk premium funcion. Secion 3 saes our assumpions on he sochasic shocks ha impinge on he economy, wih emphasis on hose peraining o he inroducion of (exogenous) growh producing echno- 3

4 4 logical progress. Secion 4 presens he complee log-linearized sysem and pus i in a marix form suiable for numerical soluion. Finally, Secion 5 concludes. The paper has hree Appendixes. The rs conains a lenghy analysis of he sysems non-sochasic seady saes, which should be of help in he calibraion process. The second conains he deails of he more cumbersome log-linearizaions he Phillips equaions for domesic goods in aion and wage in aion. The hird liss he de niions of he compound parameers ha resul from he log-linearizaion of he model equaions. 2. Households In niely lived households are monopolisic compeiors in he supply of di ereniaed labor. There is a domesic marke for sae-coningen securiies ha are held by households, insuring hem agains pro and wage idiosyncraic risks (see Woodford (2003)). This makes households essenially he same in equilibrium, and allows us o mainain he represenaive household cion (i.e. dispense wih he complexiies ha sem from household heerogeneiy). Aside from hese sae-coningen securiies, hey hold nancial ne wealh in he form of domesic currency (M 0H ), and peso denominaed one period nominal deposis issued by domesic commercial banks (D ) ha pay a nominal ineres rae i D. We assume ha he Cenral ank fully and credibly insures deposiors, so he deposi rae is considered riskless. Households also inves a real amoun V o expand he sock of nal goods (capial goods) ha hey own and ren o rms, earning each period a real renal price i K. 2.. Physical capial, invesmen, and he rae of capial uilizaion The household decides a he rae of gross invesmen V (h), which conribues o he deerminaion of he quaniy of physical capial K + in period + hrough he following law of moion for he sock of physical capial K + (h) = K K (h) + z V V (h) V (h) V () V (h) where K is he (consan) rae of capial depreciaion, and z V is an economy wide saionary invesmen e ciency shock. As in Chrisiano, Eichenbaum and Evans (200), he second erm on he righ hand side is a represenaion of he echnology ha ransforms invesmen goods ino capial goods. These capial goods are rened by households o rms. We have no marke for capial goods in he model and hence no explici price for hese goods. As we see below, we do have a shadow price for insalled physical capial (as well as a renal rae). The funcion V () represens invesmen adjusmen coss, and is such ha in he seady sae rae of growh of V (which is z ), V ( z ) = 0 V ( z ) = 0 00 V ( z ) > 0 The household decision process includes esablishing he rae of capial uilizaion inensiy ha he rm will use (and pay for) in period for he sock of physical capial i rens. As Chrisiano e al (200) argue, allowing for elasic capial uilizaion has he bene cial properies of ) dampening movemens in marginal cos

5 by reducing ucuaions in he renal rae of physical capial and also 2) reducing he ucuaions in labor produciviy afer moneary policy shocks (see also Smes and Wouers (2002)). Le u represen he rae of capial uilizaion. Hence, he ow of physical capial services ha he rm uses as inpu is u K K F Using a rae of uilizaion of capial ha exceeds he normal (seady sae) level, however, is cosly (whereas a lower han normal uilizaion acually implies a savings in oal cos) and impinges in he ne reurn from rening. Le u (u ) be he amoun of real resources (domesic goods) used up (or saved) when he rae of uilizaion is u We assume ha his funcion is increasing and convex and we normalize unis so ha he seady sae rae of uilizaion is uniy, a which here are no coss (or savings) 0 u(u ) > 0 00 u(u ) > 0 and u () = 0 Hence, aking uilizaion adjusmen coss ino accoun, he ne reurn from rening K (h) unis of capial is i K u (h) u (u (h)) K (h) (2) Currency and ransacion coss The household holds currency M 0H because doing so i economizes on ransacion coss. We assume ha ransacions involve he use of real resources (domesic goods) and ha hese ransacion coss per uni of expendiure in consumpion and invesmen goods (privae absorpion) are a convex funcion M of he currency/absorpion raio $ (see Feensra (986)) $ M ($ ) 0 M < 0 00 M > 0 M 0H (h) P C C (h) + P V V (h) = 0H M (h)=p p C C (h) + p V V (h) where C is consumpion (of privae goods), P, P C and P V are he price indexes of domesic, consumpion, and invesmen goods, respecively. All price indexes are in moneary unis. The wo basic price indexes in he domesic economy are hose of domesically produced ( domesic ) goods, P, and impored goods P. The consumpion and invesmen price indexes are boh CES composies of hese basic price indexes, as we see below. For convenience, we de ne he relaive prices of consumpion and invesmen goods in erms of domesic goods p C P C p V P V P P When he currency/absorpion raio increases, ransacion coss per uni of absorpion decrease a a decreasing rae, re ecing a diminishing marginal produciviy of currency in reducing ransacion coss.

6 Sicky nominal wage seing We model nominal sickiness as in Calvo (983), adaped o discree ime (Roemberg (987)) and exended o (full) indexaion (Yun (996) and Chrisiano, Eichenbaum and Evans (200)). Household h 2 [0 ] supplies labor of ype h, and makes he wage seing decision aking he aggregae wage index and labor supply as parameric. Every period, each household has a probabiliy W of being able o se he opimum wage for is speci c labor ype. This probabiliy is independen of when i las se he opimal wage. When i can opimize, he household adjuss is wage rae by fully indexing o las period s overall rae of wage in aion. Hence, when i can se he opimal wage rae i mus ake ino accoun ha in any fuure period j here is a probabiliy j W ha is wage will be he one i ses oday plus full indexaion. Hence, he household faces a wage survival consrain, according o which he wage rae i ses a, W (h) has a probabiliy j W of surviving (indexed) unil period + j W +j (h) = W (h) W W W + W W +j W +j 2 (3) W (h) w w + w +j W (h) where we de ne he rae of wage in aion w W =W, and he cumulaive wage w w in aion beween + j 2 and j, wih 0 In deriving he rs order condiion for W (h) below we will use he following ideniy w j W +j (h) W +j w j = W (h) W w w + w +j w +j w +j w + = W (h) W w w +j (4) Anoher consrain he household faces is is labor demand funcion W (h) h (h) = h (5) W where W is he aggregae wage index, de ned as Z =( ) W = W (h) dh (6) 0 and where is he elasiciy of subsiuion beween di ereniaed labor services 2. When h ses he opimal wage, i mus ake ino accoun ha here is a probabiliy j W ha a ime + j is wage will be he W w (h) j, and ha hence he labor demand i faces is w W (h) j h +j (h) = h +j (7) W +j 2.4. The household opimizaion problem The household receives income from pro s, wage, ren, and ineres, and spends on consumpion, invesmen, axes, and ransacion coss. I s real budge consrain 2 We derive hese equaions from domesic inermediae rms cos minimizaion in secion 3.2 below.

7 7 in period is M 0H (h) + D (h) P P = (h) P + i K u (h) u (u (h)) K (h) + M 0H (h) " M 0H (h)=p + M p C C (h) + p V V (h) + W (h) T (h) h (h) + (h) (8) P P P + + i D D (h) P P!# p C C (h) + p V V (h) where (h) is pre-ax nominal pro s, h (h) is hours of labor exerion, T (h) is lump sum axes ne of ransfers, and (h) is he income obained in from holding sae-coningen securiies. Household h maximizes an iner-emporal uiliy funcion which is addiively separable in he consumpion of privae goods C, public goods C G, and leisure E j fz C +j log [C +j (h) C +j (h)] + (9) + G log C G +j(h) G C G +j (h) + [h H z H +j + h +j(h) + ]g where is he ineremporal discoun facor, h is he maximum labor ime available (and hence he las erm in square brackes is "leisure"), and z C and z H are consumpion demand and labor supply shocks ha are common o all households. Consumpion ness habi formaion, where and G are less han uniy (see Fuhrer (2000) and Chrisiano, Eichenbaum and Evans (200)) ino a log uiliy funcion. Consumers hence care abou boh heir level of consumpion and heir rae of consumpion growh. Since he consumpion of public goods is no a decision variable for he household, he erm ha includes i is only relevan for he evaluaion of he welfare e ecs of alernaive scal policies. We drop i below for simpliciy. The household s iner-emporal solvency is guaraneed by is inabiliy o incur in deb, which we assume does no bind in any nie ime D +T 0 8T 0 (0) Household h chooses C +j (h) V +j (h) K ++j (h) u +j (h) D +j (h) M 0H +j (h), (j=,2,...) and W (h), o maximize (9) subjec o is sequence of budge consrains (8), physical capial accumulaion consrains (), is combined labor demands and wage survival consrains (7), and is no deb consrains (0). The Lagrangian

8 8 is hence E H z H +j + + W (h) w j " ( W ) j fz C +j log [C +j (h) C +j (h)] + h () P +j w W (h)! + j h +j h +j W +j w W (h) j W +j + M M 0H +j (h)=p +j p C +j C +j(h) + p V +j V +j(h) + +j (h)f +j(h) P +j + M 0H +j (h) + + i D D +j (h) M 0H +j P +j P +j + +j (h)f K K +j (h) + z+jv V +j (h) K ++j (h)gg T +j (h) P +j + i K +ju +j (h) u (u +j (h)) K +j (h)!# p C +jc +j (h) + p V +jv +j (h) +j (h) P +j D +j (h) P +j V+j (h) V V +j (h) + +j(h) g P +j where j +j (h) and j +j (h) are he Lagrange mulipliers (for he budge consrains and he capial accumulaion consrains), which can be inerpreed as he marginal uiliy of real income, and he shadow price of insalled physical capial, respecively. We will refer o and as he undiscouned Lagrange mulipliers Firs order condiions Since households only di er on wheher hey can choose he opimal wage, we eliminae he household index, and use W f o disinguish he newly opimal wage from he aggregae wage index W (which includes boh opimal and indexed wages). The rs order condiions for an opimum (including he ransversaliy condiion) are he following C z C C C E C + z C + C! M 0H =P = ' M p C C + p V V (2) V ( z V V ' V + E V + z+ V 0 V! M 0H =P = ' M p C C + p V V V+ V ) 2 V+ V (3) K + = E + K + + i K + u + u (u + ) (4) u K 0 u (u ) i K = 0 (5) D = + i D + E (6) +!# M 0H " + 0 M 0H =P + M = E p C C + p V (7) V +

9 9 W 0 = E 8 < fw w W w +j! ( W ) j +j h +j W +j P +j H z+jh H +j +j W +j =P +j w +j W f w W w +j! 9 = (8) lim! D = 0 (9) Several commens are in order on hese rs order condiions. Firs, we have used some auxiliary funcions o alleviae noaion. In (2) and (3) we have de ned he funcion ' M ha gives he oal e ec on expendiure (i.e., including ransacion cos relaed expendiures) of a marginal increase in absorpion 3 ' M ($ ) + M ($ ) $ 0 M ($ ) (20) ' 0 M ($ ) = $ 00 M ($ ) < 0 Observe ha ' M is decreasing in he money o absorpion raio $ and ha he e ec on expendiure generaed by a marginal increase in $ is given by he increase in expendiure wih he iniial money/absorpion raio, + M, plus he increase due o he reducion in he money/absorpion raio, $ ( 0 M ($ )). In analogous fashion, in (3) we have used he funcion ' V de ned as ' V V V V V 0 V (where V is he gross growh rae of V ) which gives he increase in gross invesmen ne of adjusmen coss (bu no of capial sock depreciaion) resuling from a marginal increase in he rae of gross invesmen growh. 4 (2) shows ha in equilibrium he uiliy gain from a marginal increase in consumpion, correced for he habi relaed reducion in uiliy i is expeced o generae nex period (lef side of he equaliy), equals he foregone marginal uiliy of real income i generaes, including ha which is relaed o ransacion coss (given by ' M ()). (3) shows ha he loss in uiliy from marginally increasing gross invesmen (measured hrough he undiscouned shadow price of insalled physical capial and including invesmen adjusmen coss) minus he discouned increase in uiliy i is expeced o generae nex period, equals he foregone marginal uiliy of real income i generaes (including ha which is relaed o ransacion coss). (4) saes ha he shadow value of a marginal addiion o insalled capial equals is discouned expeced shadow value nex period correced for capial depreciaion plus he discouned ne addiion o renal income i is expeced o generae. (5) saes ha whenever he marginal uiliy of real income and he sock of physical capial are di eren from zero (which we assume is he case for all ), he equilibrium rae of uilizaion of physical capial is such ha he marginal cos of having i di eren from he normal level equals is renal rae. Hence, his 3 ' M (m=a) is he parial derivaive of [ + M (m=a)] a wih respec o a. 4 ' V (V=V ) is he parial derivaive of [ V (V=V )] V wih respec o V. V

10 0 condiion direcly deermines he opimal inensiy of uilizaion of physical capial as a funcion of he renal rae u = ( 0 u) i K (2) Insering his expression in (2) gives he following auxiliary funcion for he real reurn from rening one uni of capial afer aking uilizaion adjusmen coss ino accoun K i K ( 0 u) i K u ( 0 u) i K (22) i K (6) saes ha he loss in uiliy from marginally increasing he holding of deposis equals he discouned expeced uiliy of he addiion o real ineres income i generaes nex period. And (7) saes ha he ne loss of uiliy from marginally increasing he holding of currency afer aking ino accoun he reducion in ransacion coss i generaes, is equal o he discouned expeced marginal uiliy of having i available omorrow wih is purchasing power correced for in aion. Combining (6) and (7) yields! 0 M 0H =P M = (23) p C C + p V V + i D which shows ha he opimum sock of currency as a fracion of expendiure in consumpion and invesmen is such ha he reducion in ransacion coss generaed by a marginal increase in his raio equals he opporuniy cos of holding cash. Invering 0 M gives he following demand funcion for cash as a vehicle for ransacions (someimes called "liquidiy preference" funcion) M 0H P = L + i D p C C + p V V (24) where L 0 L + i D ( h + i D = 0 M ) 00 M() + i D + i D i 2 < 0 From here on we replace he rs order condiion (7) by (24) and also use i o eliminae he household currency o absorpion raio wherever i appears hrough he use of he following auxiliary funcions e' M () ' M (L ()) e M () M (L ()) (25) oe in (8) ha since all households ha can se heir opimal wage in make he same decision we have denoed he opimum wage rae f W. Hence, (6) and (3) imply he following law of moion for he aggregae wage rae (afer assuming ha he average wage rae of non-opimizers is he average overall wage level in indexed by wage in aion no maer when hey opimized for he las ime) W = W W w + ( W ) f W (26)

11 De ning he real wage in erms of domesic goods and he relaive wage beween he opimizers and he general level w = W P ew = f W W he rs order condiion for W becomes 0 = E ( W ) j +j h +j w +j ( ew w w +j And dividing hrough (26) by W we ge w +j H z+jh H +j ew w +j w +j w +j ) (27) ( w ) = W w + ( W ) ( ew w ) (28) which can be used o eliminae ew from (27), leaving a dynamic equaion in w. We will refrain from doing so in he non-linear model, mainaining wo dynamic equaions for each in aion rae (wage and domesic, impored and expored goods) for he sake of clariy in he analysis of he seady sae, bu we will eliminae his relaive wage (and he corresponding relaive prices for di eren ypes of goods) when we log-linearize he model Domesic and impored consumpion and invesmen goods So far we have ignored he open economy aribues of consumpion and invesmen, as well as he produc di ereniaion wihin hese classes. We now consider he household allocaion of consumpion and invesmen expendiures across hese produc classes and varieies. Firs we disinguish beween domesic and impored consumpion and invesmen goods. The consumpion index we used in he household opimizaion problem is acually a consan elasiciy of subsiuion (CES) aggregae consumpion index of domesic and impored consumpion goods C = a D C C D C C + a C C C C C C, ad + a = (29) C is he elasiciy of subsiuion beween domesic and impored consumpion goods. And C D and C are hemselves CES aggregaes of he domesic and impored varieies of goods available Z C D = 0 Z C = 0 C D (i) di > (30) C (i) di > (3) 5 The deailed log-linearizaion of (27) and (28) is in Appendix 2.

12 2 and are he elasiciies of subsiuion beween varieies of domesic and impored goods in household expendiure, respecively. We assume ha hese elasiciies hold for household expendiures in hese goods wheher hey are for consumpion or invesmen purposes. Toal consumpion expendiure is P C C = P C D + P C (32) Then minimizaion of (32) subjec o (29) for a given relaions C, yields he following P = a P = a C D P C C P C C D C C Inroducing hese in (29) yields he consumpion price index P C = C a D (P ) C + a P C (33) C (34) C C (35) Furhermore, i is readily seen ha a D and a in (29) are he shares of domesic and impored consumpion in oal consumpion expendiures a D = P C D P C C a = P C (36) P C C Wih invesmen demand we proceed in exacly he same way. V is a CES aggregae invesmen index of domesic and impored invesmen goods V = b D V V D V V + b V V V V V V, bd + b = (37) where V is he elasiciy of subsiuion beween domesic and impored invesmen goods, and V D and V are CES aggregaes of domesic and impored goods V D = V = Z 0 V (i) di > (38) V D (i) di > (39) Then i follows ha he invesmen price index is P V = and ha he following relaions hold b D (P ) V + b P P V V = P V D + P V V V (40)

13 3 P = b P = b V D P V V P V V D V V V V (4) V (42) b D = P V D P V V b = P (43) P V V Condiions (33), (34), (4), and (42) are necessary for he opimal allocaion of household expendiures across domesic and impored goods in consumpion and invesmen, respecively. Similarly, for he opimal allocaion across varieies of domesic and impored goods wihin hese classes, and using (30), (3), (38), and (39), he following condiions mus hold P (i) = P C D (i) P (i) = P C D C (i) C V D P (i) = P P (i) = P V V (i) V C (i) C V V 3. Domesic goods rms 3.. Final domesic goods There is perfec compeiion in he producion (or bundling) of nal domesic oupu Q, wih he oupu of inermediae rms as inpus. A represenaive nal domesic oupu rm uses he following CES echnology Z Q = 0 V Q (i) di > (44) where is he elasiciy of subsiuion beween any wo varieies of domesic goods and Q (i) is he oupu of he inermediae domesic good i. Then he nal domesic oupu represenaive rm solves he following problem each period Z max P Q (i) 0 he soluion of which is Z Q (i) di 0 P (i)q (i)di (45) P (i) Q (i) = Q (46) P Inroducing (46) in (44) and simplifying, i is readily seen ha he domesic goods price index is Z P = P (i) di (47) 0

14 4 Also, inroducing (46) ino he cos par of (45) yields Z 0 P (i)q (i)di = P Q 3.2. Inermediae domesic goods A coninuum of monopolisically compeiive rms produce inermediae domesic goods using labor, capial, and impored inpus, wih no enry or exi. They face a perfecly compeiive physical capial renal marke and perfecly compeiive bundlers of impor goods and labor ypes. The producion funcion of rm i is Q (i) = ( K F (i) a (z h (i)) a b F (i) b z F D if his is posiive 0 oherwise. and z are indusry-wide produciviy shocks. K F is he ow of services rendered by he (hired) sock of capial when used a he inensiy deermined by he households ha own hem, F is he use of impored inpus. z F D is a xed cos ha grows along wih he economy and can be used o calibrae pro s in he seady sae 6. h (i) is a CES index of all he labor ypes (48) Z h (i) = h (h i) 0 dh (49) where h (h i) is he amoun of labor ype h used by he domesic rm i. The producion decision of i is subjec o he demand funcion of nal goods producers (46) and he price survival consrain, whereby he price i ses a, P (i) has a probabiliy of surviving (indexed) unil period + j Marginal cos and inpu demands Exending he assumpions in Chrisiano, Eichenbaum and Evans (200) and in Adolfson e al (2005) o he use of physical capial and impored goods, and allowing for randomness in he fracions of he di eren inpu coss ha are bank nanced, we assume ha sochasic fracions W of he labor bill, K of he capial renal bill, and of he impored inpu bill are nanced by he domesic banking sysem. Le i L be he nominal bank loan rae. Then we may wrie oal variable cos as where 7 K P i K K F (i) + W W h (i) + P F (i) q = + q i L = q + q + i L q = K W (50) To maximize pro s, he rm mus minimize coss. Consider rs he minimizaion of oal labor cos Z 0 W (h)h (h i)dh (5) 6 Chrisiano, Eichenbaum and Evans (200), for example, calibrae pro s o zero. 7 The las expression is convenien for log-linearizing.

15 subjec o a consan aggregae index or labor ypes (49). We call he Lagrange muliplier W. I does no depend on i since he problem is he same for all rms. Then he minimizaion resuls in i s inverse demand funcion for labor ype h W (h) = W h (h i) h (i) De ning he aggregae demand for labor of ype h h (h) = Z 0 h (h i)di and he aggregae demand for he labor bundle h = Z 0 h (i)di 5 (52) (52) implies he household labor demand (5) we used for he household problem. Furhermore, inroducing (52) in (49) yields Z W = W (h) di 0 con rming ha he Lagrange muliplier is indeed he wage index. And inroducing (52) in (5) yields a more convenien expression for he wage bill of rm i Z 0 W (h)h (h i)dh = W h (i) We now obain facor and bank loan demands by solving he following cos minimizaion problem min K F (i)h(i) F (i) f K P i K K F (i) + W W h (i) + P F (i)g subjec o (48), where Q (i) is given. The problem is he same for all rms, so we eliminae he rm index. The rs order condiions are K P i K K F = abmc Q + z F D (53) W W h = ( a)bmc Q + z F D (54) P F = ( b)mc Q + z F D (55) where MC is he Lagrange muliplier. Adding hese equaions erm by erm shows ha oal variable cos is K P i K K F + W W h + P F = MC Q + z F D and ha MC is indeed he nominal marginal cos. Furhermore, inroducing he rs order condiions and (50) in he producion funcion (48) yields he following expressions for he nominal marginal cos MC = = z ( z ( a)b h f a)b MC K P i K a i W a b W P b (56) + i L P i K ab ( W a)b P b

16 6 where we de ned a a ( a) a b b b ( b) b and he auxiliary funcion f MC + i L K + K + i L ab W + W + i L ( a)b + + i L b f 0 MC + i L > 0 Hence, he (own) real marginal cos is mc MC P = f MC ( a)b + i L i K ab w p b (57) z where p P P is he relaive (domesic currency) price beween impored and domesic goods. We refer o his relaive price as he inernal erms of rade. Aggregae demand funcions for h, K F, and F are obained direcly from (53)-(55) and (56). oe ha hey all depend on he loan rae, hrough he q (q = W K ). Also, he resuling aggregae nominal demand for bank loans by rms is L F = f L + i L MC Q + z F D (58) where we de ned he auxiliary funcion f L + i L ab K + ( a)bw + ( b) + K i L + W i L + i L ab = (= K ) + ( + i L ) + ( a)b (= W ) + ( + i L ) b + (= ) + ( + i L ) f L 0 + i L < Sicky nominal price seing As in he case of households, rms make pricing decisions aking he aggregae price and quaniy indexes as parameric. Every period, each rm has a probabiliy of being able o se he opimum price for is speci c ype of good and whenever i can opimize i adjuss is price by fully indexing o las period s overall rae of domesic in aion. Hence, when i can se is opimal price i mus ake ino accoun ha in any fuure period j here is a probabiliy j ha is price will be he one i ses oday plus full indexaion. Hence, he rm s price survival consrain saes ha he price i ses a, P (i) has a probabiliy j of surviving (indexed) unil period + j where ideniy P +j (i) = P (i) + +j P (i) (59) q j (60) q 0 As in he case of wages (see (4)), we make use of he following P +j (i) P +j q j = P (i) (6) +j P

17 7 Hence, we can express he rm s pricing problem as max E P (i) subjec o q P (i) j j +j Q +j (i) mc +j (i) Q +j (i) + z +j F D P +j Q +j (i) = Q +j P (i) P +j q j +j is he pricing kernel used by rms for discouning, which is equal o households ineremporal marginal rae of subsiuion in consumpion beween periods + j and +j = j U C+j = +je' j M + i D +j U C e' M ( + i D ) j +j where U C is he household s marginal uiliy of consumpion in correced for habi, and he second equaliy derives from (2) and (25). The rs order condiion is he following (afer dropping he rm index) ( ) ep 0 = E () j +j Q +j +j mc +j (62) P +j Since all opimizing rms make he same decision we call he opimum price e P. Hence, (47) and (60) imply he following law of moion for he aggregae domesic goods price index P = (P ) + ( ) P e (63) Proceeding as we did wih he wage in aion Phillips equaion, we de ne he relaive opimal o average domesic price ep = e P P and express he preceding equaions as 0 = E () j +j Q +j ( +j ) ep +j mc +j = + ( ) (ep ) 4. Foreign rade rms We follow Adolfson e al (2005) in allowing for an imperfec pass-hrough of exchange rae ucuaions by recurring o monopolisically compeiive impor and expor rms ha se prices wih sickiness and local currency pricing. ecause he "small open economy" concep is no always used wih he same meaning, we refer o he domesic economy as a "small domesic economy" (SDE) and explain wha we mean by his below. An aserix as a superscrip ha is no followed by

18 8 a leer (hough i may be preceded by one) means ha he variable is exogenous in he model and refers o he "large res of he world" (LRW). Hence, P and Q are he LRW s "domesic" price and quaniy indexes and P is is impor price index. And an aserisk in a superscrip ha is followed by a leer in a price index means ha i refers o prices in foreign currency and may or may no be an exogenous variable in he model. For example, he SDE s expor rms se expor prices P in he foreign currency (local currency pricing) which are endogenous variables, while P refers o he SDE s impor price index in foreign currency and is exogenous. 4.. Impored goods rms Final impored goods Perfecly compeiive (rade) rms produce (or bundle) nal impored goods using he oupu of monopolisically compeiive inermediae impored goods producers. The represenaive rm in his secor uses he following CES echnology Z = 0 (i) di > where is he elasiciy of subsiuion beween varieies of impored goods in consumpion and invesmen as well as in heir use as inpus for domesic goods rms. Maximizing pro s (as in (45) for nal domesic oupu rms) gives he demand funcion ha he inermediae imporer of good i faces P (i) = P (i) where boh price indexes are in he domesic currency. The resuling (domesic currency) price index for impored goods is and he impor cos bill is Z P = P (i) di (64) 0 Z Inermediae impored goods 0 P (i) (i)di = P A coninuum of monopolisically compeiive rms generae inermediae impored goods. They buy a bundled nal good abroad a he foreign price and urn i ino di ereniaed goods o be sold in he domesic marke in domesic currency (see Adolfson e al (2005)). They purchase he bundled nal good a he price S P, where P is he foreign currency price index of he impored bundle (which we assume di ers from he LRW s "domesic" price index P ) and S is he nominal exchange rae (pesos per uni of foreign currency). oe ha S P is hus he marginal cos for hese rms. Their pricing (in he domesic currency) follows

19 he same seup we used for rms producing domesic inermediae goods, wih a probabiliy of opimal price seing and full indexaion when hey can opimize price. According o he price survival consrain, he price P (i) he rm ses a has a probabiliy j of surviving (indexed) unil + j 9 P+j(i) = P (i) + +j P (i) j 0 (65) Due o his, when he rm opimizes i akes ino accoun ha here is a probabiliy j ha he demand for is good in + j will be +j (i) = +j P (i) j P +j! (66) Hence, hey solve max E P (i) ( P j (i) j +j +j (i) P+j ) S +j P+j P+j subjec o (66). Afer eliminaing he rm index, he resuling rs order condiion is ( ) ep 0 = E ( ) j +j +j ( +j) S +j P+j (67) P +j P+j Since all opimizing rms make he same decision, we call he opimal impor price ep. Hence (64) and (65) imply he following law of moion for he aggregae domesic currency impor price index P = P + ( ) ep (68) We now de ne he real exchange rae and he relaive price beween opimized and overall impored goods e S P ep P e P Hence, using our de niion of he inernal erms of rade p, we can express he preceding equaions as 0 = E ( ) j +j +j ( +j) ep +j P e +j p +j = + ( ) ep 4.2. Expored goods rms Each of a coninuum of inermediae exporing rms purchases he nal domesic good a is price P (which is hence is marginal cos) and di ereniaes i o sell in di eren foreign markes wih local currency pricing.

20 20 Final expored goods The goods are purchased by a represenaive perfecly compeiive nal expor rm ha has a CES echnology Z = 0 (i) di > where is he elasiciy of subsiuion in he res of he world for he impored goods ha originae in he SDE. Maximizing pro, as in he previous cases, gives he demand funcion each inermediae exporing rm faces from he nal exporers P (i) = P (i) (69) oe ha he price P (i) is in foreign currency. The resuling foreign currency price index for expored goods is Z P = P (i) di (70) 0 and he foreign currency cos bill for he represenaive nal exporing (bundling) rm is Z P (i) (i)di = P 0 oe ha in he demand funcion for expors (69), is he res of he world s impors from he SDE (which we can alernaively wrie as ) and P is he res of he world s aggregae impor price from he SDE (no o be confused wih he SDE s aggregae impor price from he LRW P ). Hence, we can alernaively wrie (69) as P (i) = (i) We furher assume ha he res of he world s aggregae impors from he SDE is relaed o is oupu (Q ) and is oupu price index (P ) by = x Q P P P where x is an expor demand shock. oe ha he relaive price in he las expression can be wrien as where we de ned P P = P P P P p P p P = p p P P as he SDE s exernal erms of rade and he LRW s inernal erms of rade. The rs of hese relaive prices is endogenous in our model due o exporers price

21 seing, as we furher elaborae below. The second is clearly exogenous in our model. oe ha we do no assume ha he law of one price prevails in he long run (non-sochasic seady sae). In he conex of monopolisic compeiion, any good produced by a rm in he domesic economy is no produced by any oher rm in he world. Hence, he law of one price only means ha any domesic good i mus be sold in he res of he world a he same price i sells domesically afer expressing i in foreign currency P (i) = P (i)=s, and ha any good i produced in he LRW mus be sold domesically a he price P (i) = S P (i). We see no reason o assume such lack of marke segmenaion, even in he model s long run. Inermediae expored goods Inermediae expor rms se prices in foreign currency aking he foreign price and quaniy indexes P,, as parameers. The local (foreign) currency pricing of inermediae exporing rms follows he same seup we used previously, wih a probabiliy of opimal price seing and full indexaion when hey can change price. Hence, according o heir price survival consrain hey face a probabiliy j of having he price hey se a survive (indexed) unil + j P +j(i) = P (i) + +j P (i) 2 j (7) Hence, when aking (69) as a consrain, hey mus consider ha here is a probabiliy j ha heir demand in + j will be +j (i) = +j P (i) j P +j! (72) When hey can se heir opimal price hey solve max P E (i) j +j +j (i) subjec o (72). The rs order condiion is ( P (i) j P+j ( ep 0 = E ( ) j +j +j ( +j) P +j P +j S +j P +j ) P +j S +j P +j ) Since all opimizing rms make he same decision we call he opimal foreign currency expor price P e, and (70) and (7) imply he following law of moion for he aggregae price level of expors P = P + ( ) ep (73) To simplify hese expressions as we did previously, noe rs ha he own marginal cos of inermediae expor rms is he inverse of he produc of he SDE s RER and is exernal erms of rade P S P = e p

22 22 ex, we de ne he relaive price beween opimizing and overall expor prices ep P e P and express he dynamic equaions for expor prices as ep 0 = E ( ) j +j +j ( +j) = +j + ( ) ep 5. A review of some imporan relaive prices e +j p +j Char I highlighs he inernaional pricing of he model. The SDE s and he LRW s main moneary price indexes P, P, and P, P, P, respecively, are shown in he wo cenral columns. For each here is a domesic price index and an impored price index, each in erms of is own currency. The wo ouer columns show he main relaive prices. In each economy, he relaive price beween impored and domesic price indexes de nes he domesic erms of rade (DTT) p and p, respecively. In he LRW, however, we also disinguish an expor price index P, di eren from is domesic price index P. Hence, here is an addiional relaive price p beween is impor and expor goods, boh in is "domesic" currency (i.e. foreign currency), which is he SDE s exernal erms of rade. Also, in each economy a cerain price index is convered ino he corresponding expor price index hrough local currency pricing (i.e. pricing in he parner s currency) and his is he rade parner s impor price index. However, in he case of he SDE we do no disinguish beween is domesic and expor goods, so i is he domesic goods ha are expored o he LRW. The solid arrows indicae he local currency pricing of exporers. Also, for each economy, he domesic price index is convered ino he parner s currency hrough he exchange rae P =S and S P, respecively. Finally, in each economy he he RER is de ned as he relaive price beween he parner s expor bundle, convered o he domesic (or "domesic") currency hrough he nominal exchange rae, and he domesic bundle. The SDE s real exchange rae (RER) is he relaive price beween impored goods as hey are purchased in he LRW by imporers and domesic goods, boh expressed in a common currency e S P (74) P Here, P is he res of he world s expor price index and, hence, is an exogenous variable in our model. Wih he same de niion, he LRW s RER urns ou o be is expor o domesic relaive price divided by he SDE s RER e P =S P = P S P P P = p e

23 23 Relaive Prices SDE Char I Domesic Currency Moneary Prices SP * Moneary Prices P/S Relaive Prices RERs e=sp * /P e * = P/ SP * = p * / e P P * Inernal TT p = P /P p * = P * / P * = p * p * P P * SDE s Exernal TT p * = P * / P * P * LRW Foreign Currency The numeraor is obviously exogenous in our model, bu he denominaor is clearly endogenous. Since he SDE is insigni can in size in relaion o he LRW, is acions have no in uence in he LRW s allocaion of resources. The SDE s inernal erms of rade (ITT) is he relaive price beween impored and domesic goods as faced by households and domesic rms p P (75) P I is a raio beween wo domesic currency prices. Wih he same de niion, he LRW s ITT is a raio beween is impored and "domesic" goods prices (boh in foreign currency) p P P = P P P P = p p (76) and i is equal o he produc of he SDE s TT and he LRW s expor o domesic relaive price index. 6. anks We assume ha here is a perfecly compeiive banking indusry. anks, like rms, are owned by households, and are price akers in nancial markes. They obain funds in he inernaional marke, supply one period deposi faciliies o households D, and use he proceeds o supply one period loans o rms and he governmen L = L F + L G, lend (or borrow) in he inerbank marke, purchase (or sell) Cenral ank bonds C, and hold vaul cash M 0 as well as regulaory reserves R in he Cenral ank. Any inerbank loans cancel ou and pro s are disribued o owners period by period, so he aggregae balance shee consrain for he represenaive bank is L + C + M 0 + R = D + S (77) We assume ha vaul cash is a (echnical) fracion of deposis, and ha inerbank deposis are perfec subsiues for Cenral ank bonds (so hey earn he same ineres rae i ). Since we also assume ha he Cenral ank does no pay

24 24 ineres on regulaory reserves, banks keep hese a he minimum, which is assumed o be a proporion R of deposis. Hence, (77) is equivalen o L + C = ( R )D + S (78) We assume ha he ineres rae on banks foreign deb is paid ou in he following period. Since banks business is (assumed o be) in domesic currency, hey face exchange rae uncerainy. For every uni of foreign currency hey repay hey mus expec o have pesos in he amoun of where E e +( + i ) = and e, are he rae and he expeced rae of nominal peso depreciaion. To add some addiional ineria, we assume ha a fracion of banks has raional expecaions and ha he remaining fracion has simple saic expecaions by which S S e + = Excep for his heerogeneiy in expecaions, all banks are he same. Hence, on average he expeced rae of nominal depreciaion is e + = E + + We also assume ha mus pay a premium on he inernaional riskless rae i. Since we do no model he res of he world, he risk premium (funcion) is exogenously given. I has an exogenous componen. (a risk premium shock) as well as an endogenous componen p () ha is an increasing funcion of he rend adjused (individual) bank foreign deb (see Turnovsky (2000) and Schmi- Grohé and Uribe (2003)). Individual banks hus fully inernalize he fac ha heir individual foreign deb decision deermines he foreign currency ineres rae hey face, which is + i = ( + i ) + S + p (79) P z where z is he sochasic rend in produciviy, and we assume p 0 > 0 and p 00 > 0. anks have a real cos funcion ha depends on he real deposi and loan creaing aciviies of he bank. We assume his cos funcion is quadraic and implies ha here are economies of scope beween lending and deposi aking aciviies (see Freixas and Roche (997), chaper 3). Speci cally, we assume he following real cos funcion C = C (L D z P ) = (80) " = 2 2 # a L L + a D D 2a L D 0 2 z P z P z P z P = a L L 2 + a D D 2 2a 0 L D 2 (z P ) 2 a L > a 0 > 0 a D > a 0

25 25 We make he assumpion ha a a L a D a 2 0 > 0 The represenaive bank maximizes pro each period D = + i L L + ( + i ) C + i D + i S C (L D z P )z P e + subjec o is balance shee consrain (78) and is supply of foreign funds consrain (79). The soluion o his program gives he supply of loans and deposis in erms of he loan margin i L i and he deposi margin ( R ) ( + i ) + i D, and he opimal amoun of foreign funding in he form of a "risk-adjused uncovered ineres pariy" relaion L S = z P a fa D + i L ( + i ) + (8) +a 0 ( R ) ( + i ) + i D g D S = z P a fa L ( R ) ( + i ) + i D + (82) +a 0 + i L ( + i ) g + i = E + + ( + i S ) ' (83) P z where we de ned following auxiliary funcion for he muliplicaive gross risk adjusmen o he uncovered ineres pariy S ' + P z + p S + P z S p 0 P z S (84) P z Given our assumpions on p () he condiion a > 0 is necessary and su cien o ensure ha he rs order condiions yield maximum pro s. The resuling opimal bank cos and (pre-ax) pro are C = 2a fa D i L 2 i + a L ( R ) ( + i ) + i D 2 +2a 0 i L i ( R ) ( + i ) + i D g z P = C + S 2 p 0 P z S P z Given L S, D S, and, he aggregae bank demand for Cenral ank bonds is given by he aggregae bank balance shee consrain CD = ( R )D S + S L S (85) 7. The public secor The public secor is made up of he Governmen and he Cenral ank.

26 The Governmen The Governmen issues foreign currency denominaed bonds in he inernaional markes, obains loans from banks and pays ineres on hese loans, spends on goods, and collecs axes. We assume ha scal policy consiss of exogenous pahs for nominal lump-sum ax collecion (T ), nominal bank loans (L G ), and real expendiures (G ). I nances any resuling de ci by issuing foreign currency denominaed bonds ( G ). The exogenous pahs are assumed o be compaible wih a nie non-sochasic seady sae for governmen deb. To hold foreign currency denominaed governmen bonds, foreign invesors charge a risk premium over he risk-free foreign ineres rae (i ). As in he case of banks, he risk premium (funcion) is exogenously given and is assumed o have an exogenous sochasic componen (an exernal nancing shock) and an endogenous componen which is an increasing funcion of he rend adjused public secor ne foreign liabiliy. Hence he gross ineres rae on he governmen s foreign deb is "!# + i G = ( + i ) + G S G + p R C G (86) P z where p 0 G > 0, and RC is he Cenral ank s inernaional reserves. The Governmen ow budge consrain is S G = P G + i L L G T + ( + i G )S G (87) To simplify, we assume he ineres on bank loans is paid by he governmen wihin he period The Cenral ank The Cenral ank issues currency (M 0 ), domesic currency bonds C, and deb ceri caes o banks for non-remuneraed reserves R, and holds inernaional reserves R C in he form of foreign currency denominaed riskless bonds issued abroad. We assume ha Cenral ank bonds are only held by domesic banks. The ( ow) budge consrain of he Cenral ank is M 0 + C + R S R C = M 0 + ( + i ) C R ( + i )S R C = (88) M 0 + C + R S R C + i C i S R C (S S ) R C We assume ha he Cenral ank ransfers is real quasi- scal surplus or de ci o he Governmen every period. This includes all he facors ha would oherwise change he ne worh of he Cenral ank ineres earned and capial gains on is inernaional reserves ne of ineres paid on is bonds, i.e. he second erm in square brackes in (88). Hence, he Cenral ank s balance shee consrain is always preserved M 0 + R = S R C C (89) In our model, his equaion implicily de nes he Cenral ank s backing of is moneary base (M 0 + R ) wih is inernaional reserves ne of is bond liabiliies. The Cenral ank supplies whaever moneary base is demanded by households

27 and banks, and can in uence hese supplies by changing R C in he foreign exchange or inerbank markes). or C 27 (inervene Adding (87) and (88) gives he consolidaed public secor budge consrain M 0 + C + R + S G = P G T + i L L G + M 0 + (90) R C +( + i ) C + R + ( + i G )S G ( + i )S R C 8. Marke clearing equaions, he balance paymens and GDP 8.. Marke clearing In he physical capial renal marke, marke clearing implies ha he household supply a he opimal inensiy level equals domesic rms demand ( 0 u) i K mc K = ab ( + W i L ) i K Q + z F D (9) In he labor marke, he household supply h mus equal domesic rms demand h = ( mc a)b Q + z ( + W i L F D (92) ) w In he loan marke we have L S = L, where he laer is loan demand by rms and he governmen. Hence, from (58) we obain L P = f L + i L mc Q + z F D + LG P (93) oe ha in he las hree equaions mc is given by (57). In he deposi marke we have D S = D, where he laer is deposi demand by households. Hence, combining his wih (82) yields D a L ( = z R ) ( + i ) + i D + a 0 + i L P a L a D (a 0 ) 2 ( + i ) (94) In he inerbank cum Cenral ank bond marke, inerbank loans cancel ou and Cenral ank supply C mus equal aggregae bank demand CD as given by (85) C = ( R )D + S L (95) where Cenral ank supply is derived from is balance shee consrain (89). In he currency marke, he supply of currency mus equal household and bank demand M 0 = L + i D P C C + P V V + D (96) where he Cenral ank supply is again derived from (89). In he domesic goods marke, he oupu of domesic rms Q mus saisfy nal demand from households, he governmen, and he LRW, as well as inermediae demand for abnormal capial uilizaion coss, ransacion coss, and bank coss Q = a D p C C + b D p V V + G + + u (( 0 u) +e M + i D p C C + p V V + z C i K )K (97) where C are he real resources used up by he banking secor, as given by (80).

28 The balance of paymens Toal impors, is he sum of household and rm demand P = ( a D ) P C C + ( b D ) P V V + P F (98) The nominal aggregae household budge consrain (where he cancel ou) can be wrien as M 0H M 0H + (D D ) = + W h + I K u u (u ) P K (99) +i D D + e M + i D P C C + P V V T Here is he sum of pro s from all hree ypes of rms (domesic, expor, and impor) as well as banks = D = P Q W h P i K u K P F i L L F (00) + P ( ad ) p C C + ( b D ) p V V + F S P + S P P + f i L i L + ( R ) ( + i ) + i D D ( + i )S P C g Consolidaing (90), (99) and (00), aking ino accoun (97) and he consolidaed balance shee consrain of banks and rms yields he balance of paymens consrain R C R C G G +i R C i G G i = P P (0) 8.3. GDP Using (36), (43), and (98), we can express domesic oupu (97) as Q = p C C + p V V + + G p C + V Q + Q D + p Q = p C C + p V V + + G p + Q D + p Q = Y + Q D + p Q where we de ned inermediae oupu of domesic and impored origin and real GDP in erms of domesic goods as Q D = u (( 0 u) i K Q = F )K + e M + i D p C C + p V V + z C Y = p C C + p V V + + G p (02) 9. Moneary Policy We have endeavored o include banks and he cenral bank wih some deail in order o be able o consider alernaive moneary (including exchange rae) policies wihin a uni ed framework. In he model, he Cenral ank, hrough is regular inervenions in he inerbank and foreign exchange markes, is able o aim for