ARGEMmy: an intermediate DSGE model calibrated/estimated for Argentina: two policy rules are often better than one

Transcription

1 ARGEMmy: an inermediae DSGE model calibraed/esimaed for Argenina: wo policy rules are ofen beer han one Guillermo J. Escudé Cenral Bank of Argenina Paper presened o he conference on Quaniaive Approaches o Moneary Policy in Open Economies Federal Reserve Bank of Alana. May 5 6, 9

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3 COTETS ARGEMmy: an inermediae DSGE model calibraed/esimaed for Argenina: wo policy rules are ofen beer han one Inroducion The model Households Domesic goods rms Foreign rade rms Banks The public secor Marke clearing equaions, GDP, and he balance paymens Moneary Policy Permanen produciviy shocks Funcional forms for he auxiliary funcions The loglinear approximaion o ARGEMmy in marix form Baseline calibraion, and dogmaic priors Policy parameer sabiliy ranges Bayesian esimaion Opimal Moneary and Exchange rae Policy under Commimen The marix sysem for a linear quadraic opimal conrol framework Linear quadraic opimal conrol under full informaion and commimen umerical resuls on opimal policy rules and losses Conclusion Appendix. The non-linear sysem The main non-linear equaions in non-saionary forma The non-linear equaions in saionary forma Appendix : The recursive versions of he Phillips equaions Domesic in aion Wage in aion Impored goods in aion Appendix 3. The log-linear sysem of equaions Appendix 4. Model parameers and grea raios Appendix 5. Analysis of he seady sae and reference calibraion of he parameers The equaions wih all variables a heir seady sae levels Reference calibraion of parameers and grea raios Appendix Impulse Response Funcions Forecass of observable variables Mean forecass for observable variables Poin forecass for observable variables Observable variables The opinions expressed in his paper are he auhor s and do no necessarily re ec hose of he Cenral Bank of Argenina. 3

4 4 Smoohed shocks References

5 ARGEMmy: an inermediae DSGE model calibraed/esimaed for Argenina: wo policy rules are ofen beer han one. Inroducion The purpose of his paper is o advance in he consrucion and calibraion/esimaion of an inermediae DSGE model wih wo policy rules for Argenina and explore o wha exen wo policy rules can be beer han one. The BCRA s research deparmen currenly uses a very small and non-micro founded model wih wo policy rules which I designed a few years ago (MEP: Modelo Económico Pequeño (see Elosegui, Escudé, Garegnani and Soes Paladino 7)) as he backbone for a sysem of macro and moneary projecions. During 6-7 I consruced he much larger DSGE model ARGEM, mainly for research purposes. I seemed ha here was need for an inermediae sized DSGE model ha could be of help in bridging he gap beween he wo. ARGEMmy is he resul of his new e or. 3 Hopefully, i will help in bringing he DSGE modeling sraegy closer o he policy environmen. The new model has much of he fundamenal srucure of ARGEM: i includes banks as well as he abiliy o model a managed exchange rae regime by means of wo simulaneous policy rules (which may be feedback rules or no): he usual policy rule for achieving an operaional arge for he nominal ineres rae and an addiional policy rule ha re ecs he Cenral Bank s inervenion in he foreign exchange marke. I also has some feaures ha may be seen as an advance on ARGEM. In paricular, insead of a feedback rule on inernaional reserves, as in he curren version of ARGEM, I now use a feedback rule on he rae of nominal currency depreciaion ha includes a long run arge for inernaional reserves (as a raio o GDP). This seems closer o he way Cenral Banks ha sysemaically inervene in he foreign exchange marke acually inerpre heir inervenion, caring for he level of he exchange rae in he shor o medium run and he level of foreign exchange reserves in a longer run. Making speci c assumpions on moneary and exchange rae policy in Argenina is no easy. Afer wo hyperin aionary experiences Argenina xed is exchange rae o he U.S. dollar during he Converibiliy period (April 99-December ) wih he hope of puing and end o is long in aionary hisory. However, since he dollar oaed agains oher currencies (which represened 85% of Argenina s rade) The opinions expressed in his paper are he auhor s and do no necessarily re ec hose of he Cenral Bank of Argenina. 3 The feaures of ARGEM ha are suppressed in order o simplify he model are: ) invesmen, and hence he capial sock and is inensiy of uilizaion, implying ha wha is called consumpion in ARGEMmy should be inerpreed as absorpion (consumpion plus invesmen), ) he deposi rae, which is collapsed wih he Cenral Bank bond rae under he assumpion ha hey are perfec subsiues, 3) bank reserves in he Cenral Bank and Bank demand for foreign and domesic currency cash, 4) manufacured expors, which leaves only primary secor expors (commodiies). As a consequence of 4) in (his version of) ARGEMmy here is no Phillips equaions for manufacured expors. everheless, here is sill abundan nominal rigidiy in ARGEMmy since i includes hree Phillips equaions (wages, domesic goods, and impored goods), all wih Calvo syle sickiness plus full indexaion o he previous period s in aion for hose who do no opimize currenly. Also, impored goods prices are se in domesic (local) currency, generaing a slow pass-hrough of boh foreign prices and he exchange rae o domesic impor prices. 5

6 6 and srongly appreciaed agains all currencies (from 995 o ), so did he peso, generaing loss of compeiiveness, high unemploymen and he expecaion of a regime shif. Afer he demise of Converibiliy and an inerim period of urbulence, he nominal exchange rae once again ended o be sable agains he dollar, albei a around 3 pesos per dollar (insead of, as during Converibiliy) unil recenly. There are now no insiuional resricions on changing he nominal exchange rae as here was during Converibiliy, nor on in uencing he domesic ineres rae hrough moneary policy. The Cenral Bank regularly inervenes boh in he money marke and in he foreign exchange marke, wih higher frequency in he second. 4 Due o he diversiy of exchange rae regimes Argenina has had in he las few decades (and he fac ha here is sill he possibiliy of fuure changes in he regime), I buil he model so ha i can handle di eren regimes. In paricular, here are wo policy rules (one for he ineres rae and anoher for he rae of nominal depreciaion), which may or may no be feedback rules. When hey are boh feedback rules, hey boh respond o deviaions of he year on year consumpion in aion rae from a arge (ha de nes he nonsochasic seady sae in aion) and deviaions of GDP and he rade balance raio (o GDP) from heir nonsochasic seady sae (SS) values. This re ecs a simulaneous concern for in aion, oupu, and curren accoun sabilizaion. In ARGEM I used he mulilaeral real exchange rae (MRER) insead of he rade balance raio. Bu hey are quie inerchangeable, since boh are direcly relaed o exernal balance objecives. I found i convenien here o use he rade balance raio because i was easier o express is seady sae value in erms of parameers ha may be esimaed insead of imposing a seady sae value ha would inroduce an unnecessary resricion in he esimaion process. Bu i may also be more naural o hink in erms of an equilibrium long run rade balance raio (ha re ecs he ne foreign deb servicing in he seady sae) in a policy rule or in a Cenral Bank loss funcion. everheless, he model can be formulaed using eiher variable, boh of which are endogenous in he SS. In his paper I summarize preliminary resuls on he Bayesian esimaion of a subse of he parameers in ARGEMmy using daa from he pos-converibiliy period. I found ha a model wih only a simple policy rule for he rae of nominal currency depreciaion yields a beer han one wih wo simple policy rules. Hence, I only repor resuls from he laer. I use he esimaed parameers o address he main objecive of his paper: o explore o wha exen a moneary and foreign exchange regime wih wo policy rules (i.e., a Managed Exchange Rae (MER) regime) may be superior o he usual alernaives: a Floaing Exchange Rae (FER) regime and a Pegged Exchange Rae (PER) regime. For his I place ARGEMmy wihin a linear-quadraic opimal conrol framework under commimen and perfec informaion, inroducing an ad-hoc quadraic Cenral Bank ineremporal loss funcion. I obain he opimal policy rules and minimum losses under di eren Cenral Bank preferences (or syles) and for he hree aler- 4 In an empirical paper, Garegnani and Escudé (4) sudy he role of he U.S. MRER as a fundamenal for Argenina s MRER. Escudé (8) sudies he simple nonlinear dynamics of he Argeninian economy during boh he Converibiliy and pos-converibiliy periods wihin a deerminisic model.

7 naive policy regimes. The preliminary resuls I show here indicae ha wo policy rules are usually beer han one. Indeed, in all he cases I acually compued, he MRER regime generaed a lower loss. Hence, having a model ha can re ec wo policy rules is no only of greaer generaliy han convenional models bu a leas for many Cenral Bank syles is he only way o represen a policy regime ha ges he Cenral Bank closer o is objecives. Alhough he model is consruced for a developing counry economy, I believe ha some of he cenral ideas are applicable o indusrialized counries, even counries like he U.S. which even hough i is he closes one can come o an example of a closed economy is neverheless open, making exchange rae developmens very imporan. In an empirical paper, S. Kim (3) esimaes a generalized srucural VAR o joinly analyze he e ecs of foreign exchange inervenion and ineres rae seing using daa for he U.S. for he pos Breon-Woods period. He correcly sresses he need for a uni ed empirical model for he analysis of wo policies ha obviously inerac. His resuls show ha here is pleny of such ineracion and he suggess he need o model foreign exchange policy explicily when addressing moneary policy and exchange rae developmens. The idea behind he use of wo policy rules in my modeling goes precisely in his direcion. If such a uni ed framework is needed for he U.S. economy, i is of course even more imporan in considering developing economies in which foreign exchange marke inervenion is rouinely praciced on a day o day basis. The res of he paper has he following srucure. Secion presens ARGEMmy in deail. Secion 3 arranges he log-linear approximaion o he model equaions for simple policy rules in a marix form suiable for model soluion. Secion 4 addresses he baseline calibraion. Secion 5 shows resuls from a search for he ranges in which he individual simple policy rule coe ciens mainain he saddlepah sabiliy of he model. Secion 6 conains preliminary Bayesian esimaion of a subse of he model parameers, including he persisence coe ciens and sandard errors of he exogenous shock processes. Secion 7 pus he se of non-policy log-linear equaions in a marix form suiable for opimal policy analysis, inroduces he Cenral Bank loss funcion used, summarizes he heory for opimal policy under commimen and full informaion, and shows numerical resuls for opimal policy rules and resuling losses for he hree policy regimes. Finally, secion 8 concludes. I relegae much of he maerial o Appendices, including he complee se of nonlinear and log-linear equaions, he derivaion of he recursive formulaion of he hree Phillips equaions, a deailed iniial calibraion of all he model parameers and resuling seady sae values of he endogenous variables, and a se of impulse responses for he simple policy rules model ha was esimaed.. The model.. 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 (3)). 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- 7

8 8 coningen securiies, hey hold nancial wealh in he form of domesic currency (M ) and peso denominaed one period nominal deposis issued by domesic commercial banks (D ) ha pay a nominal ineres rae i. They consume a bundle of domesic and impored goods and are unable o insure heir real incomes agains he e ec of domesic and foreign in aion and exchange rae developmens. I assume ha he Cenral Bank fully and credibly insures deposiors, so he deposi rae is considered riskless... The household opimizaion problem The household holds cash M because doing so i economizes on ransacions coss. I assume ha consumpion ransacions involve he use of real resources and ha hese ransacions coss per uni of expendiure are a decreasing and convex funcion M of he currency/consumpion raio $ : M ($ ) M < ; M > ; () $ M = M =P ; P C C p C C where C is a consumpion index, and P and P C are he price indexes of domesic goods and of he he consumpion bundle, respecively. For convenience, I have de ned he relaive price of consumpion goods in erms of domesic goods: p C P C : P All price indexes are in moneary unis. The wo basic price indexes in he SOE are hose of domesically produced ( domesic ) goods, P, and impored goods P. The consumpion price index is a CES composie of hese basic price indexes, as I deail below. The assumpion in () is ha when he currency/consumpion raio $ increases, ransacions coss per uni of consumpion decrease, bu a a decreasing rae ha re ecs a diminishing marginal produciviy of currency in he reducion of ransacions coss. I model nominal sickiness as in ARGEM (Escudé (7)). In paricular, households se wages under monopolisic compeiion wih sicky nominal wages. Household h [; ] is he sole supplier of 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 () W (h) W W +::: W +j W (h) w ;j;

9 9 where he rae of wage in aion is de ned as W W =W, and he cumulaive w w wage in aion beween + j and is ;j, wih ; : In deriving he rs order condiion for W (h) below he following ideniy is used : W (h) W +j w ;j = W (h) W W +::: W +j W W +::: W +j W +j = W (h) W W W +j : (3) The household also faces he labor demand funcion for is paricular ype of labor as a consrain: W (h) h (h) = h ; (4) W where W is he aggregae wage index, de ned as: Z =( ) W = W (h) dh ; (5) and where is he elasiciy of subsiuion beween di ereniaed labor services 5. 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 : (6) W +j The household receives income from pro s, wage, and ineres, and spends on consumpion, axes, and ransacions coss. Is real budge consrain in period is: M (h) P + D (h) P = (h) P + M (h) P + ( + i ) D (h) P + W (h) h (h) P T (h) P + M M (h)=p p C C (h) + (h) (7) P p C C (h) where (h) is nominal pro s, h (h) is hours of work, 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 and leisure: E X j= j z C +j log [C +j (h) C +j (h)] + h z H +j h +j (h) + + ; (8) where is he ineremporal discoun facor, h is he maximum labor ime available (and hence he erm in square brackes is "leisure"), is a consan, is he inverse of he elasiciy of labor supply wih respec o he real wage, z C and z H are consumpion demand and labor supply shocks ha are common o all households. Consumpion ness habi formaion, where is a posiive parameer less han uniy. 5 I derive hese equaions from domesic inermediae rms cos minimizaion below.

10 The household s iner-emporal solvency is guaraneed by is inabiliy o incur in deb, which I assume does no bind in any nie ime: D +T ; 8T : (9) Household h chooses C +j (h); D +j (h); M ;H +j (h), (j=,,...) and W (h), by maximizing (8) subjec o is sequence of budge consrains (7), is combined labor demands and wage survival consrains (6), and is no deb consrains (9). Subsiuing for he labor demand consrains, he Lagrangian is hence: E X j= j fz C +j log [C +j (h) C +j (h)] + h () ( W ) j zh w +j + h W (h)! + ;j +j W +j ( +j (h) T +j (h) + +j (h) P +j P +j + M M +j (h)=p +j p C +j C +j(h) + ( + i +j ) D +j (h) P +j + ( W ) j W w (h) ;j h +j P +j p C +jc +j (h) + M +j M +j(h) P +j D +j (h) P +j P +j (h) + +j(h) P +j w W (h) ;j W +j : where j +j (h) are he Lagrange mulipliers, and can be inerpreed as he marginal uiliy of real income. Since (aside from heir labor ype) households only di er on wheher hey can choose he opimal wage, I eliminae he household index below, 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: D : C : z C z+ C E C C C + C + = ( + i ) E M : + M M =P p C C W : = E X 8 < : fw W W W +j! j= + = E + + = ' M M =P p C C ( W ) j +j h +j W +j P +j z H +j (h +j ) +j W +j =P +j p C () () (3) W +j (4) f W W W W +j! 9 = lim! D = : (5) ;

11 In () and (3) he domesic goods in aion rae + P + =P has been de ned, and in () he auxiliary funcion ' M gives he oal e ec on expendiure (i.e., including ransacions cos relaed expendiures) of a marginal increase in consumpion. I is de ned as: 6 which implies: ' M ($ ) + M ($ ) $ M ($ ) ; (6) ' M ($ ) = $ M ($ ) < : () shows ha in equilibrium he uiliy gain from a marginal increase in consumpion (lef side of he equaliy), equals he foregone marginal uiliy of real income i generaes, including ha which is relaed o ransacions coss (given by ' M (:)). () saes ha he loss in uiliy from marginally increasing he holding of deposis equals he expeced uiliy of he addiion o real ineres income i generaes nex period. And (3) saes ha he ne loss of uiliy from marginally increasing he holding of cash afer aking ino accoun he reducion in ransacions coss i generaes, is equal o he expeced marginal uiliy of having i available omorrow wih is purchasing power correced for in aion. Combining () and (3) yields: M =P M = ; (7) p C C + i which shows ha he opimum sock of currency as a fracion of expendiure in consumpion is such ha he reducion in ransacions coss generaed by a marginal increase in his raio equals he opporuniy cos of holding cash. Invering M gives he following demand funcion for cash as a vehicle for ransacions (someimes called liquidiy preference funcion): M =P = L ( + i ) p C C ; (8) where L (:) is de ned as: and is sricly decreasing, since: L ( + i ) ( M) + i ; L ( + i ) = M(:) ( + i ) < : From here on I replace he rs order condiion (3) by (8) and use (8) o eliminae he household currency o consumpion raio wherever i appears hrough he use of he following auxiliary funcions: e' M ( + i ) ' M (L ( + i )) ; e M ( + i ) M (L ( + i )) : (9) In paricular, () can be wrien as: z C E C C C + z C + = e' C M ( + i ) p C () 6 ' M (m=a) is he parial derivaive of [ + M (m=a)] a wih respec o a.

12 In (4), since all households ha can se heir opimal wage in make he same decision, he opimum wage rae is denoed W f. Hence, (5) and () imply he following law of moion for he aggregae wage rae (afer aking ino accoun ha in he Calvo seup, because opimizers are randomly chosen from he populaion, heir average wage rae in is equal o he average overall wage level (indexed by wage in aion) no maer when hey opimized for he las ime): W = W W W + ( W ) W f : () De ning he real wage in erms of domesic goods and he relaive wage beween he opimizers and he general level: w = W P ; he rs order condiion for W becomes: X = E ( W ) j +j h +j w +j j= ( ew W W +j ew = f W W ; W +j z+j H (h +j ) ew W +j w +j W +j ) : () And dividing hrough () by W and rearranging gives: ew W = W W W W! : (3) Hence, () becomes he non-linear Phillips equaion ha deermines he dynamics of wage in aion: 8 < : W X = E ( W ) j +j h +j w +j j= W W W! + W +j z H +j (h +j ) +j w +j W + +j 9 = ; : In Appendix I obain a recursive hree equaion version of his equaion which is acually used for simulaion and esimaion.... Domesic and impored consumpion So far I have ignored he open economy aribues of consumpion as well as produc di ereniaion. I now disinguish beween domesic and impored consumpion goods. The consumpion index used in he household opimizaion problem is acually a consan elasiciy of subsiuion (CES) aggregae consumpion index of domesic and impored goods: C = a D C C D C C + a C C C C (4) C C, ad + a = : (5)

13 C (> ) is he elasiciy of subsiuion beween domesic and impored consumpion goods. Also, C D and C are hemselves CES aggregaes of he domesic and impored (respecively) varieies of goods available: Z C D = Z C = 3 C D (i) di ; > (6) C (i) di ; > : (7) where and are he elasiciies of subsiuion beween varieies of domesic and impored goods in household expendiure, respecively. Toal consumpion expendiure is: P C C = P C D + P C : (8) Then minimizaion of (8) subjec o (5) for a given C, yields he following relaions: P = a C C D P C D P C = a P C C C C C (9) C : (3) Inroducing hese in (5) yields he consumpion price index: P C = a D (P ) C + a P C C : (3) Furhermore, i is readily seen ha a D and a in (5) are he shares of domesic and impored consumpion in oal consumpion expendiures: where a D = P C D = CD P C C ; a p C = a D = P C C P C C = p C p C C ; (3) p P P is he relaive domesic price of impors in erms of domesic goods, or inernal erms of rade (ITT). I calibrae a D below as o have home bias (a D > :5 > a ). Condiions (9), and (3) are necessary for he opimal allocaion of household expendiures across domesic and impored goods. Similarly, for he opimal allocaion across varieies of domesic and impored goods wihin hese classes, and using (6), (7), he following condiions hold: P (i) = P C D (i) P (i) = P C D C (i) C C C : Finally, dividing (3) hrough by P yields a relaion beween he relaive price of consumpion goods in erms of domesic goods and he ITT: h p C = a D + ( a D ) p Ci C :

14 4.. Domesic goods rms... 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 = Q (i) di ; > (33) 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. The nal domesic oupu represenaive rm solves he following problem each period: max Q (i) P Z Z Q (i) di P (i)q (i)di; (34) he soluion of which is he demand for each ype of domesic good as a fracion of aggregae domesic oupu ha is iself an inverse funcion of he good s price relaive o he aggregae domesic price index: P (i) Q (i) = Q : (35) P Inroducing (35) in (33) and simplifying, i is readily seen ha he domesic goods price index is: Z P = P (i) di : (36) Also, inroducing (35) ino he cos par of (34) yields: Z... Inermediae domesic goods P (i)q (i)di = P Q : A coninuum of monopolisically compeiive rms produce inermediae domesic goods using labor and impored inpus, wih no enry or exi. They face perfecly compeiive bundlers of impor goods and labor ypes. The producion funcion of rm i is: Q (i) = (z h (i)) bd D (i) bd (37) where and z are indusry-wide produciviy shocks (ransiory and permanen, respecively), D is he consumpion in producion of inermediae impored inpus, and h (i) is a CES index of all he labor ypes: Z h (i) = h (h; i) dh ; (38) where h (h; i) is he amoun of labor ype h used by he domesic rm i.

15 5..3. Marginal cos and inpu demands I assume ha a sochasic and possibly ime-varying fracion & of he cos bill is nanced by he domesic banking sysem. Le i L be he bank nominal loan rae. During period he rm formulaes is demand for bank loans aking ino accoun is expeced nancing needs in period +. Is oal variable cos in period is: + & i L W h (i) + P D (i) To maximize pro s, he rm mus minimize coss. I akes as given he wages W (h) se by he di eren households. Consider rs he minimizaion of oal labor cos: Z W (h)h (h; i)dh (39) subjec o a consan aggregae index of labor ypes (38). I 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: h (h; i) W (h) = W : (4) h (i) De ning he aggregae demand (over all rms) for labor of ype h: h (h) = Z h (h; i)di; and he aggregae demand (over all rms) for he labor bundle (over all households): h = Z h (h)dh; (4) implies he labor demand funcion (4) I used for he household problem. Furhermore, inroducing (4) in (38) yields: Z W = W (h) di ; con rming ha he Lagrange muliplier is indeed he aggregae wage index as he noaion implied. And inroducing (4) in (39) yields a more convenien expression for he wage bill of rm i: Z W (h)h (h; i)dh = W h (i): I now obain facor and bank loan demands by solving he following cos minimizaion problem: min f + & i L h (i); D(i) W h (i) + P D (i) g

16 6 subjec o (37), where Q (i) is given. The problem is he same for all rms, so I eliminae he rm index. The rs order condiions are: + & i L W h = b D MC Q (4) + & i L P D = ( b D )MC Q ; (4) where MC is he Lagrange muliplier (and has he obvious inerpreaion of marginal cos). Adding hese equaions erm by erm and dividing by P gives: + & i L w h + p D = mc Q ; (43) where I de ned he real wage w and real marginal cos mc : w W P ; mc MC P : Furhermore, inroducing he rs order condiions (4)-(4) in he producion funcion (37) yields he following expression for he real marginal cos: mc = + & i L (w ) bd p b D ; (44) where is he e ciency wage and w W z P w z b D b D b D b D : Aggregae demand funcions for h and D are obained direcly from (4)-(4) and (44): h = p b D w D = ( b D ) b D b D w Also, dividing (4) by (4) erm by erm gives he relaion: w h = p Q =z (45) Q : (46) bd b D p D : (47) Finally, he aggregae real demand for bank loans by rms in period is: L P = & E w + h + + p + D + = & b D E (w + h + ) : (48)

17 7..4. Sicky nominal price seing Firms make pricing decisions aking he aggregae price and quaniy indexes as parameric. Every period, each rm has a probabiliy D 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 D 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 D of surviving (indexed) unil period + j: where P +j (i) = P (i) + ::: +j P (i) p ; : Below I make use of he following ideniy: P (i) P +j p ;j : (49) p ;j = P (i) : (5) +j P Hence, I can express he rm s pricing problem as: X p max E j P (i) D P D ;j ;+j mc +j (i) Q +j (i) (i) subjec o j= P +j Q +j (i) = Q +j P (i) P +j p ;j : D ;+j is he pricing kernel used by domesic rms for discouning, which is equal o households ineremporal marginal rae of subsiuion in he consumpion of domesic goods beween periods + j and : D ;+j j U C D ;+j : U C D ; oe ha he marginal uiliy of consuming domesic goods may be obained from he marginal uiliy of consuming he aggregae bundle of (domesic and impored) goods. Speci cally: U C D ; = U C; dc dc D = U C; a C D C D C C = U C; P P C = U C; p C where he second equaliy if obained by di ereniaing (5) wih respec o C D, and he hird comes from (9). Hence, using (), he pricing kernel of domesic rms is: D ;+j j U C D ;+j U C D ; = j +j e' M ( + i +j ) e' M ( + i ) Hence, he rm s rs order condiion is he following: ( X = E () j D ep +jq +j ( +j ) j= P +j j D +j : (5) D mc +j ) ; : (5)

18 8 Since all opimizing rms make he same decision I call he opimum price P e and drop he rm index. In he (modi ed) Calvo seup, because opimizers are randomly chosen from he populaion heir average price in is equal o ha period s overall price index (indexed by he previous period s in aion) no maer when hey opimized for he las ime. Hence, (36) implies he following law of moion for he aggregae domesic goods price index: P = D (P ) + ( D ) P e Dividing hrough by P and rearranging yields: : (53)! ep = ( ) D ( ) : (54) D where I de ne he opimal o average domesic relaive price: ep = e P P : Hence, using (54) I can express (5) as he (non-linear) Phillips equaion ha deermines he dynamics of domesic in aion: 8! 9 X < = E () j D +jq +j ( +j ) ( ) D ( ) = : D mc +j +j ; : j=.3. Foreign rade rms There are wo ypes of foreign rade rms: compeiive primary goods producing rms ha expor all heir oupu, and monopolisically compeiive imporers wih sicky local currency pricing..3. Primary expors producing rms Firms in he expor secor use domesic goods and "land" (represening naural resources) o produce an expor commodiy. Land is assumed o be xed in quaniy, hence generaing diminishing reurns. I assume ha he expor good is a single homogenous primary good (a commodiy). Firms in his secor sell heir oupu in he inernaional marke a he foreign currency price P X. They are price akers in facor and produc markes. The price of primary goods in erms of he domesic currency is merely he exogenous inernaional price muliplied by he nominal exchange rae (vis a vis a rade-weighed baske of currencies): S P X : I also assume ha here is a mean one i.i.d. "climae" shock z A ha can make he harves greaer or smaller han expeced. In order o obain a lagged response in a simple way I assume ha in period expor rms sign conracs by which hey commi o delivering heir (as ye unknown due o he "climae" shock) ( + 4)-period harves (i.e., nex year, same quarer) a known -period uni prices and exchange raes. Hence, hough in heir expor revenues have predeermined prices and exchange rae hey earn more or less han hey expeced according o he realizaion of he "climae" shock.

19 Le he producion funcion employed by rms in he expor secor be he following: X = (z 4 ) ba Q DX 4 b A z A ; b A < ; (55) where Q DX is he amoun of domesic goods used as inpu in he expor secor, and z is he same permanen produciviy shock we used for domesic secor rms. These rms maximize expeced pro E X +4 = S P X E X +4 P Q DX subjec o (55). The rs order condiion yields he expor secor s (facor) demand for domesic goods: Q DX = z b A e p b A (56) or equivalenly: Q DX 9 = b A e p E X +4 ; (57) where I de ned he SOE s mulilaeral real exchange rae (MRER) and exernal erms of rade (XTT): e S P ; p P P X ; P where P is he price index of he foreign currency price of he SOE s impors. The XTT is exogenous as i is compleely deermined in he Res of he World (RW). Also, insering he facor demand funcion in he producion funcion shows ha opimal expors vary direcly wih he lagged produc of he MRER and he XTT: X = z 4 b A e 4 p b A b 4 A z A : (58) According o my assumpions, he real value of expors in erms of domesic goods is: S 4 P X 4 X = e 4p 4X b A e 4 p b 4 A = z 4 z A P e e b A ; (59) where I de ned he year on year domesic in aion a as: e = 3 : Henceforh, a ilde over an in aion or growh rae variable will have he same year on year meaning. (oe ha he ilde in he auxiliary funcions e' M (:) and e M (:) has an enirely di eren meaning.).3.. Impored goods rms Final impored goods Perfecly compeiive imporing 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 = (i) di ; > ;

20 where is he elasiciy of subsiuion beween varieies of impored goods in consumpion. Maximizing pro s (as in (34) for nal domesic oupu rms) gives he demand funcion ha he inermediae imporer of good i faces: P (i) = P (i) : (6) The resuling (domesic currency) price index for impored goods is: and he impor cos bill is: Z P = P (i) di ; (6) Z P (i) (i)di = P : Inermediae impored goods 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. They purchase he bundled nal good a he price S P, where P is he foreign currency price index of he impored bundle and S is he nominal exchange rae (pesos per uni of foreign currency). oice ha S P is hus he marginal cos for hese rms. Their pricing (in he domesic currency) follows 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: P+j(i) = P (i) +::: +j P (i) ;j; ; : (6) 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! : (63) Hence, hey solve: max E P (i) ( X P j (i) ;j ;+j +j (i) P+j j= S +j P +j P +j ) subjec o (63). ;+j is he pricing kernel used by imporing rms for discouning. I is equal o households ineremporal marginal rae of subsiuion in he consumpion of impored goods beween periods + j and : ;+j j U C ;+j : U C ;

21 The marginal uiliy of consuming impored goods may be obained from he marginal uiliy of consuming he aggregae bundle of (domesic and impored) goods. Speci cally: U C ; = U C; dc dc = U C; a C C C C P = U C; P C = U C; p p C where he second equaliy if obained by di ereniaing (5) wih respec o C, and he hird uses (3). Hence, using () he pricing kernel of impor secor rms is: j +j : (64) Hence, afer eliminaing he rm index, he rs order condiion for inermediae imporing rms is: = E X ;+j j U C ;+j U C ; j= = j +je' M ( + i +j ) p +j e' M ( + i ) p ( ep ( ) j +j +j ( +j) P +j ; S +j P +j P +j Since all opimizing rms make he same decision, I call he opimal impor price ep. Hence (6) and (6) imply he following law of moion for he aggregae domesic currency impor price index: ) : P = P + ( ) ep : (65) where Using he de niions of e and p, I can express he preceding equaions as: X = E ( ) j ep +j +j ( +j) e +j +j p +j j= = + ( ) ep ; ep P e P is he relaive price beween opimized and overall impored goods. Eliminaing ep, yields he Phillips equaion for impored goods in aion: X = E ( ) j +j +j ( +j) j= 8 >< A +je +j p +j 9 >= >; : oice ha e = S P p P re ecs he deviaion (whenever i di ers from ) from he Law of one Price for impored goods.

22 .4. Banks I assume ha here is a compeiive banking indusry, wih no enry, exi, or mergers. Banks are owned by households, and are price akers in nancial markes. They obain funds in he inernaional marke B B, supply one period deposi faciliies o households D, and use he proceeds o supply one period loans o rms L, lend (or borrow) in he inerbank marke, and purchase (or sell) Cenral Bank bonds B CB. Any inerbank loans cancel ou and pro s ha arise from period - operaions are disribued o owners in period, so he balance shee consrain for he represenaive bank is: L + B CB = D + S B B : (66) I assume ha deposis are perfec subsiues for Cenral Bank bonds (so hey earn he same ineres rae i ) bu households may no inves direcly in hese bonds (possibly because here is a minimum amoun allowed for such invesmens which only he banks can achieve). I assume ha ineres on banks foreign deb is paid ou in he following period, jus before pro s are disribued o owners. Since banks business is assumed o be in domesic currency, hey face (uninsurable) exchange rae uncerainy. For every uni of foreign currency hey repay hey mus expec o have pesos in he amoun of E + ( + i B ); where i B is he nominal ineres rae hey are charged abroad and + is he nominal rae of currency depreciaion: + = S + S : I assume ha banks mus pay a (risk and/or liquidiy) premium over he inernaional riskless rae i for he funds hey obain abroad. Since I do no model he res of he world, he premium (funcion) is exogenously given. I has an exogenous sochasic and ime-varying componen B (ha can represen general liquidiy condiions in he inernaional marke) as well as an endogenous (more risk-relaed) componen p B (:) ha is an increasing convex funcion of he GDP adjused (individual) bank foreign deb. Individual banks hus fully inernalize he fac ha heir individual foreign deb decision deermines he foreign currency ineres rae hey face, which is: + i B = ( + i ) B S B B + p B ; (67) P Y where I assume p B > and p B >. Banks have a real cos funcion ha depends on he (previous period s) real loan creaing aciviies of he bank. I assume his cos funcion is quadraic. Speci cally, I assume he following real cos funcion: C+ B = L bb z P b B >

23 The represenaive bank maximizes expeced pro each period: E B + = i L L + i B CB D E + i B S B B P bb L subjec o is balance shee consrain (66), and is supply of foreign funds consrain (67). The soluion o his problem gives he supply of loans as a simple linear funcion of he loan margin i L i (68) and he opimal amoun of foreign funding in he form of a "risk-adjused uncovered ineres pariy" relaion (69): L S = z P b B il i i = E + ( + i ) B S B B + ' B P Y where he following auxiliary funcion has been de ned: z P 3 (68) ; (69) ' B (a) p B (a) + ap B (a) = p B (a) [ + " B (a)] ; (7) where " B (a) a p B (a) p B (a) is he elasiciy of he endogenous risk premium funcion. Given L S, D S, and B B, he aggregae bank demand for Cenral Bank bonds is given by he aggregae bank balance shee consrain: B CB;D = D S + S B B L S : (7).5. The public secor The public secor is made up of he Governmen and he Cenral Bank..5.. The Governmen The Governmen issues foreign currency denominaed bonds in he inernaional markes and pays ineres on hese bonds, spends on goods, and collecs axes. I assume ha scal policy consiss of exogenous pahs for nominal lump-sum ax collecion (T ) and real expendiures (G ). The Governmen nances any resuling de ci by issuing foreign currency denominaed bonds (B G ). I assume ha an inegral componen of scal policy is he (credible) commimen o achieve a long run arge for he foreign deb o GDP raio ( GT ). To hold foreign currency denominaed governmen bonds, foreign invesors charge a risk premium over he risk-free foreign ineres rae. 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. I assume ha he laer is an increasing funcion of he public secor ne foreign liabiliy o GDP raio. Hence he gross ineres rae on he governmen s foreign deb is: + i G = ( + i ) G " S B G + p G P Y R CB!# where p G >, and RCB is he Cenral Bank s inernaional reserves. The Governmen ow budge consrain is: : (7) S B G = P G T + ( + i G )S B G : (73)

24 4.5.. The Cenral Bank The Cenral Bank issues currency (M ) and domesic currency bonds B CB, and holds inernaional reserves R CB in he form of foreign currency denominaed riskless bonds issued by he RW. I assume ha Cenral Bank bonds are only held by domesic banks. The ( ow) budge consrain of he Cenral Bank is: M + B CB = M + B CB S R CB S R CB = M + ( + i )B CB ( + i )S R CB (74) i S R CB + (S S ) R CB i B CB : The second erm in square brackes afer he las equaliy is he Cenral Bank s quasi- scal surplus (QF ). I includes ineres earned and capial gains on inernaional reserves minus he ineres paid on is bonds. I assume ha he Cenral Bank ransfers is quasi- scal surplus (or de ci) o he Governmen every period. Hence, is ne wealh is consan. Furhermore, assuming is ne worh is zero, he Cenral Bank s balance shee "consrain" is always preserved: M + B CB S R CB = M + B CB S R CB = : (75) The Cenral Bank supplies whaever amoun of cash is demanded by households, and can in uence hese supplies by changing R CB or B CB, i.e. inervene in he foreign exchange marke or in he inerbank cum Cenral Bank bond marke The consolidaed public secor Adding (73) and (74) erm by erm and using (75) gives he consolidaed public secor budge consrain: S B G = ( + i G )S B G (T P G ) QF ; (76) where QF is he Cenral Bank s quasi-surplus: QF i + ( S =S ) S R CB i B CB (77) The Governmen sells foreign currency bonds in inernaional capial markes o he exen ha he sum of is capial repaymens and ineres paymens on hese bonds exceeds he sum of he domesic currency value of he Cenral Bank s quasisurplus and he Governmen s primary surplus (T P G )..6. Marke clearing equaions, GDP, and he balance paymens In he labor marke, he household supply of labor h equals domesic rms demand (45): h = bd p w b D Q z : (78) In he loan marke, bank loan supply (68) equals loan demand by rms (48), yielding he following expression for he loan rae: i L = i + bb & E b D (w + h + ) = i + bb & z b E z+ D w + h + : (79) z

25 In he domesic goods marke, he oupu of domesic rms Q mus saisfy nal demand from households (including ransacions cos relaed consumpion of oupu) and he Governmen, as well as inermediae demand from he expor and banking secors: Q = [a D + e M ( + i )] p C C + G + z b A e p b A + z b B il i : (8) Expendiure in oal impors p, is he sum of household and rm demand: where he second equaliy uses (47). GDP in erms of domesic goods is: p = ( a D ) p C C + p D (8) = ( a D ) p C C + bd b D w h ; Y = p C C + G + e 5 4p 4 e X p ; (8) where expors and impors are given by (59) and (8), respecively. The balance of paymens and rade balance equaions are: B G +B B R CB = (+i G )B G + + i B B B + i T B = P X 4 X P = P where I use he year on year impor in aion a : e = p 4 X e 3 : R CB T B ; (83).7. Moneary Policy The model allows for di eren moneary and exchange rae policy regimes. My baseline is wha I call a Managed Exchange Rae (MER) regime. In his regime, he Cenral Bank, hrough is regular inervenions in he 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 agains a rade-weighed baske of currencies. Using fairly general feedback rules, he Cenral Bank responds o deviaions of he consumpion year on year in aion rae (e C ) from a arge (e T ), and o deviaions of derended GDP and he rade balance o GDP raio (and possibly is lagged value) from he SS levels of he respecive variables 7. Variables wihou a ime subscrip denoe non-sochasic seady sae 7 Wih more microfoundaion, insead of he deviaions from he nonsochasic seady sae levels one would like o use deviaions from naural levels ha are based on privae welfare. In a closed economy seing, Roemberg and Woodford (999) and Woodford (3) show ha he levels ha correspond o a reference economy wih no nominal rigidiies (bu subjec o he same shocks as he model economy) have a solid microeconomic jusi caion based on household welfare. However, De Paoli (6) shows ha in an open economy seing he same kind of calculaions lead o more complex arge levels where merely assuming no nominal rigidiy is no enough. In his paper I use an ad-hoc loss funcion for he Cenral Bank insead of a microfounded one and compleely sidesep he issue by assuming ha boh he simple policy rules and he Cenral Bank loss funcion (ha leads o he opimal policy rules) respond o he deviaions from he nonsochasic seady sae. (84)

26 6 values. I assume ha he long run in aion arge (which is also he seady sae level of in aion) is posiive: e T >. (In pracice, I also assume i is consan). I inroduce hisory dependence in he wo feedback rules hrough he presence of he lagged operaional arge variable, as well as a long run arge for inernaional reserves in he case of foreign exchange marke inervenion. The simple feedback rules are he following: where + i = T R ( + i ) h e C e T! h Y =z (Y =z ) T h h3 S T B =P Y ; (85) T BT and T R z h ; h ; h ; h ; h h 6= : (86) = F XI ( ) k e C e T S R CB! k k k3 Y =z S T B =P Y (87) (Y =z ) T T BT k5 exp(" ) = (P Y ) CBT where F XI k ; k5 6= : (88) " is an i.i.d. nominal depreciaion rae policy shock (wihou persisence). The muliplicaive erms ( T R ) and ( F XI ) in he feedback rules are designed so as o obain a non-sochasic seady sae where he in aion arge is achieved and he nominal rae of depreciaion is consisen wih i. 8 During he ransiion, he coe ciens in hese feedback rules indicae he direcion and magniude of Cenral Bank responses o deviaions of each of hese variables from heir arges. They ranslae he Cenral Bank high frequency acions (hourly, daily or weekly) o he model s quarerly frequency. CBT is a long run arge for he Cenral Bank reserves o GDP raio, and T BT is a long run arge for he rade balance o GDP raio. The laer should be consisen wih he counry s long run foreign deb service (and, hence, wih he scal assumpions which are explici in he model). 9 In order o be able o accommodae non-feedback policies, eiher one of he feedback rules (or boh) can be replaced by a simple auorregresive rule: he ineres rae feedback rule by an AR() on Cenral Bank bonds or, if here is a feedback rule for he rae of nominal depreciaion, on Cenral Bank inernaional reserves, and he nominal depreciaion rae feedback rule by an AR rule on he same variable or on Cenral Bank inernaional reserves. Such non-feedback rules imply policies more akin o an auomaic pilo ype of moneary and/or exchange rae policy. For opimal policies, in secion 7 I explicily model wo exreme policy regimes ha resul in models ha are nesed wih respec o he general model. In a 8 oice ha I could jus as well say ha "he nominal rae of depreciaion arge is achieved and he in aion rae is consisen wih i". 9 I deal wih he nonsochasic seady sae a lengh in Appendix 5.

27 Floaing Exchange Rae (FER) regime he Cenral Bank absains from inervening in he foreign exchange marke. Hence, he policy rule for he rae of nominal depreciaion is eliminaed and so is he Cenral Bank foreign exchange reserves variable (in real erms and made saionary) r CB = R CB = z P, by replacing i wih is SS value r CB as a parameer. In a Pegged Exchange Rae (PER) regime, he Cenral Bank absains from inervening in he money marke. Hence, he policy rule for he ineres rae is eliminaed and so is he Cenral Bank domesic currency bonds variable (in real erms and made saionary) b CB = B CB = (z P ), by replacing i wih is SS value b CB as a parameer. Alhough he paper speci cally addresses he case of wo CB policy rules, noe ha he model could be modi ed o re ec an insiuional arrangemen in which he CB is in charge of moneary policy while he Governmen (Treasury) is in charge of he foreign exchange policy. This would require a few changes in he model (since he CB balance shee would no be enough o re ec he resricion ha involves shor run deb, FX reserves, and CB cash liabiliies) and he assumpion of full coordinaion beween he wo agencies so ha he loss funcion would correspond o he consolidaed governmen (and no exclusively he CB)..8. Permanen produciviy shocks Growh is inroduced in he model hrough he SOE s permanen produciviy shock z and is relaion wih is equivalen in he RW: z. I assume ha he RW s permanen produciviy growh z z =z is governed by an exogenous process: z = z z ( z ) z exp " z ; (89) where " z is an i.i.d. echnology shock. On he oher hand, he SOE s permanen produciviy growh z z =z is assumed o be governed by he following sochasic process: z = z z z z z z exp " z 7 ; (9) where " z is an i.i.d. echnology shock and z z =z is he raio beween he permanen produciviy levels in he SOE and he RW. During he ransiion, he growh rae of he RW in uences he growh rae of he SOE hrough he coe cien z, while he growh rae of he SOE has no in uence on he rae of growh of he RW. Also, he persisence coe ciens may be di eren, and he disurbance erms may be correlaed. oice ha he following ideniy holds: z z = z =z z =z = z z : (9) I assume ha in he non-sochasic SS he produciviy levels and growh raes in he RW and he SOE are equal: z = and z = z. (89)-(9) are addiional model equaions. I am hence assuming ha here is a coinegraing relaion beween he (logs of he) permanen echnology shocks in he LRW and he SOE which includes a direc lagged in uence of he LRW s rae of echnological growh on ha of he SOE bu no reciprocal in uence. This appears consisen wih he inuiive noion of a SOE ha is also less developed and hence is echnological innovaions have an insigni can in uence on he LRW s innovaions bu absorbs a signi can fracion of he LRW s innovaions.

28 8.9. Funcional forms for he auxiliary funcions The speci c funcional form I use for he ransacions cos funcion is he following: M ($ ) a M $ + $ b M + c M ; a M ; b M > : (9) There is a saiaion level of he cash/consumpion raio afer which he funcion becomes increasing in is argumen. Obviously, only he decreasing porion of he funcion is relevan. There are hree parameers for calibraion: a M, b M, c M. According o (8), he resuling liquidiy preference funcion is: $ = m p C c = L ( + i ) " b M a M + +i # +b M : (93) Hence, he money marke clearing equaion and he ransacions cos equaion (wo of he model equaions), are: e M = a M " m = b M " a M + +i b M a M + +i # " +b M + # +b M p C c (94) b M a M + +i # b M +b M + c M : (95) Also, he resuling auxiliary funcion for he oal e ec on expendiure of a marginal increase in consumpion (6) is: giving anoher of he model equaions: ' M ($ ) = + c M + ( + b M ) $ b M ; e' M = + c M + ( + b M ) " b M a M + +i # b M +b M : (96) oe ha (95) and (96) are used as model equaions merely o make oher equaions simpler. From (94) I derive he elasiciy of cash demand (as a fracion of consumpion) wih respec o he gross ineres rae ha is useful for calibraion: " m = $ +b M ( + b M ) b M ( + i ) : (97) For he bank risk premium I use he following funcional form: p B e b B =y B B e b B =y ; B > ; B > : (98) Hence, in he risk-adjused uncovered ineres pariy equaion (7) ' B (:) is: ' B e b B =y = B ( B e b B =y ) ; (99)