Development of MEGA-D: A DSGE Model for Policy Analysis

Transcription

1 Developmen of EGA-D: A DGE odel for Policy Analysis David Florian and Carlos onoro Banco Cenral de Reserva del Peru (BCRP) ay 2009 (preliminary) Absrac This paper summarizes he developmen of a DGE model for policy analysis a he Cenral Reserve Bank of Peru. The firs secions describe he imporance of he model, a small review of he projec and describe linear version of he model. The fourh and fifh secions describe some parameer-esimaion resuls and some policy exercises. The las secion describes he forecasing process and exercises wih he model. Keywords: DGE models, parial dollarizaion, Peru JEL Classificaion: F31; F32; F41; C11. The EGA-D projec has benefied from commens from paricipans a various seminars a he BCRP, Encuenro de Economisas 2006, 2007 and 2008, he Compuaional Economics eeing, onreal 2007, he LACEA conference in exico 2006, he Cenral Workshop Bank acroeconomic odeling organized by he Cenral Bank of Chile, he 2nd oneary Policy Research Workshop in Lain America and he Caribbean organized by he Cenral Reserve Bank of Peru and he CCB of he Bank of England and he Join Research eminar on odels of Equilibrium organized by he General CELA. We also hank Adrian Armas, Fabio Canova, Albero Humala, imon Poer, Gabriel Rodriguez, arco Vega, David Vavra for his suggesions and commens on drafs of he documen. In paricular, he auhors are indebed o Jean-arc Naal from he wiss Naional Bank for heir valuable suggesions and commens during his visi o he BCRP. Corresponding auhor: Carlos onoro, carlos.monoro@bcrp.gob.pe. The projec has benefied from he conribuion of Paul Casillo (BCRP) and Vicene Tuesa (currenly a he Deusche Bank), former members of he projec. This paper also summarizes some of he resuls from join work wih hose auhors and Carlos onoro. Also, arco Vega (BCRP) has largely conribued in he implemenaion of forecasing wih his model. 1

2 1. The EGA-D Projec 1.1 Why a general equilibrium model? In recen decades, academic research has emphasized he developmen of Dynamic ochasic General Equilibrium (DGE) models, whose key feaure is he use of microeconomic foundaions for modeling he behavior of he aggregae economy. This ype of models offers several advanages. Firs, microfundaions preven equaions arising from hese models o be subjec o he Lucas criique (1976). Also, his feaure allows o analyze he macroeconomic effecs of microeconomic phenomena, such as changes in he degree of compeiion beween firms, and analyze he effecs of economic policy measures from economic agens welfare poin of view. econd, he individual raionaliy behind he aggregae behavior is useful o analyze he impac of moneary policy on privae agens expecaions. oreover, raional expecaions differeniae effecs beween permanen and ransiory shocks and beween anicipaed and unanicipaed shocks. Third, he general equilibrium srucure mainain in he model he consisency beween flow and sock variables, such as invesmen wih respec o capial and he curren accoun balance wih respec o he ne foreign asses posiion. Las bu no leas, here is recen empirical evidence showing ha DGE models can have a beer forecasing performance han purely saisical models 1. The flexibiliy of hese models allows o solve a wide range of quesions relevan o he cenral bank, such as he role of financial fricions in he ransmission mechanisms (for example, wha are he effecs on he risk premium for increasing deb?, wha are he effecs of limiing he access o credi?), he role of fricions in he labor marke (for example, wha are he effecs of low of labor mobiliy?, wha are he effecs of he slow adjusmen in nominal wages?), effecs of changes in relaive prices (for example, wha happens when he erms of rade or he real exchange rae change?), implicaions of aggregae shocks o a specific secor (for example, wha are he differences beween an increase in produciviy in he radable secor respec o he non-radable secor?), among ohers. Addiionally, he larger srucure helps o disenangle he sources of macroeconomic flucuaions (eg, inflaion of recen years has been generaed by supply or demand shocks?). 1.2 Objeives The DGE model ha is being developed a he Cenral Reserve Bank of Peru (BCRP) has received he name of EGA-D, whose iniials in English mean Aggregae General Equilibrium odel wih dollarizaion. The EGA-D has been designed o include he main feaures of he Peruvian economy including parial dollarizaion-, in a mediumscale model ha can be easily exended o explain differen sylized facs or economic episodes. 1 ee Del Negro and ohers. 2

3 The main objecive of his model is o conduc policy analysis, namely forecas and simulaions condiional on he behavior of moneary (and / or fiscal) policy. Also, he model srucure can be used o decompose macroeconomic variables on he facors ha explain heir flucuaions (shocks), boh in hisory and forecas. Because of is design feaures, such as micro-foundaions, dynamics, uncerainy and raional expecaions, a poenial use of he model is he evaluaion of moneary policy measures using a welfare crierion. For example, we can assess he effecs of a lower reacion o he exchange rae or a sronger reacion o inflaion. Oher poenial uses of he model are he esimaion of non-observable variables such as he naural ineres rae 2, he poenial oupu, he real exchange rae equilibrium and he naural unemploymen rae for he Peruvian economy. The main advanage of he model in he esimaion of hese variables is he abiliy o esimae all of hem simulaneously. In his way, he forecas of he naural ineres rae in he model would be consisen wih he forecas of he poenial oupu and he real exchange rae equilibrium. Finally, he model can also be used o assess he impac of economic policy measures in he long erm using he seady sae equilibrium. Thus, from he seady sae of he model we can analyze he implicaions of policies such as ariff reducions, changes in ax levels, greaer financial marke developmen, increased compeiion in he goods markes, among ohers. 1.3 Brief review of he projec Because of he advanages previously menioned, DGE models are gradually being incorporaed as ools for policy analysis in cenral banks. Thus, mos of cenral banks ha operae under he EI are implemening such models in heir projecion sysems, for example, he Cenral Bank of weden - Riskbank (Ramses), Bank of Canada (TOTE), UA (IGA), Cenral Bank of Norway (TOTE), UK (BEQ), Chile (A), wizerland (DGE-CH) 3. Currenly, he BCRP is inegraing he EGA-D in is process of forecas and analysis of moneary policy. This projec began in 2006 a he Research Division of he Economic udies Deparmen. The firs phase of he projec was o wrie a documen ha recouns he main empirical regulariies of he Peruvian economy (Casillo, onoro and Tuesa 2007a). Also, a previous version of he model was esimaed wih Bayesian economerics (Casillo, onoro and Tuesa 2006a) and used o esimae nonobservable variables. Currenly he projec is implemening he forecas of macroeconomic variables using he laes version of he model (Casillo, onoro and Tuesa 2009). 2 Following Wicksell s definiion (1898), he naural ineres rae is he real ineres rae consisen wih price sabiliy. 3 ee Tovar (2007) for a review on he curren siuaion and challenges of hese models in he conduc of moneary policy. 3

4 2. Key Elemens and Assumpions of he odel 2.1 Overview The model has several feaures o replicae he main sylized facs of he Peruvian economy, which are linked o he srucure of he economy in quesion. For example, he model allows households and businesses o use wo currencies, he dollar and he ol, o conduc ransacions, pricing and issue deb. In his way, we are aking ino accoun he high degree of dollarizaion in he Peruvian economy. We also consider ha firms when borrowing pay a risk premium on op of he ineres rae se by he cenral bank, a ypical feaure of lile developed financial markes as in Peru. imilarly, we allow real wages o deviae from heir compeiive equilibrium, aking ino accoun he presence of unemploymen and he low response of real wages o flucuaions in aggregae demand, as observed in he Peruvian economy. Besides he feaures menioned above, he model allows for flows of goods, services and financial asses beween domesic and foreign agens, ypical of open economies. These flows explain he dynamics of balance of paymens and foreign deb in he model. I also assumes ha he inernal condiions of he Peruvian economy had no effec on he global economy, consisen wih he relaive size of he Peruvian economy o he res of he world. All hese characerisics wihin he model have implicaions for he design of moneary policy and is ransmission mechanism, which is summarized below. 2.2 The ransmission mechanism of moneary policy in he EGA-D Following he recen advances in he developmen of models for moneary policy analysis, he role for moneary policy in his model is based on: a) money b) monopolisic compeiion in he marke for final goods, and c) price sickyness. The presence of money in he model is crucial because i allows prices o be se in erms of moneary unis. However, unlike oher general equilibrium models, in his model here are wo forms of fia money: he ol and he dollar. In his way, we consider he fac ha in he Peruvian economy par of he pricing, rading and financial inermediaion is performed using U.. dollars. oreover, he monopolisic compeiion assumpion in he model allows firms o se prices. The opimal price of firms is proporional o heir marginal coss, which in urn depend on wages, produciviy, cos of capial, he erms of rade and he real ineres rae, among oher facors. The hird elemen, price rigidiies, imply ha firms canno change prices every period wihou incurring coss. Therefore, when seing prices hey mus consider no only he curren marginal coss bu also hose expeced for fuure periods. The combinaion of monopolisic compeiion and price rigidiies deermines in he model he aggregae supply curve (also called Phillips curve) o domesic prices, which relaes he dynamics of domesic inflaion o hree facors: a) expecaions inflaion, b) marginal coss and c) cos shocks no relaed o demand pressures (also known as cospush shocks). In he model, here are four main ransmission mechanisms of moneary policy o inflaion and economic aciviy: he ineres rae, expecaions, he financial acceleraor and he crowding ou in spending. 4

5 oneary policy in he model affecs direcly boh consumpion and invesmen by conrolling he rae of ineres, and conrol inflaion hrough hese effecs on aggregae demand. oneary policy is implemened via an ineres rae rule, which summarizes he preferences of he cenral bank o avoid he coss associaed wih inflaion and flucuaions in he economic aciviy and ineres raes. This rule evolves according o a) deviaions in inflaion expecaions respec o he inflaion arge, b) demand pressures, as measured by he level of economic aciviy and c) variaions in he exchange rae. I is also considered ha he ineres rae rule is highly persisen, consisen wih he behavior observed in mos cenral banks. Expecaions abou he fuure conduc of he moneary auhoriy and he macroeconomic variables are imporan in he ransmission mechanism of moneary policy. In he model, he ineres rae relevan o he decisions of consumpion and invesmen is he long-erm ineres rae, which is deermined by expeced increases in shor-erm ineres raes. o if i is expeced ha he increase in he shor-erm ineres rae is persisen, he impac on aggregae demand will be higher. imilarly, consumpion and invesmen depend on he level of expeced fuure aggregae demand and he fuure produciviy of capial, variables ha are also relaed o he fuure behavior of he cenral bank. This feaure of he model makes i a useful ool o analyze he macroeconomic implicaions of improvemens in cenral bank credibiliy. The predicabiliy of moneary policy in he model is crucial. If he cenral bank does no reac in a predicable way o he sae of he economy, i is possible o anchor inflaion expecaions o arge of he cenral bank. In addiion o ineres rae and he expecaions channels, he model consider oher ransmission channels of moneary policy, as he financial acceleraor. This block closely follows he work by Gerler, Naalucci and Gilchris (2007) and Deveraux, Lane and u (2006). In hese models, firms borrow in he financial sysem o finance invesmen by paying a risk premium ha depends on heir degree of leverage. Those who firms ha are highly leveraged mus pay a premium for higher risk han hose who are no. In his case, he impac of moneary policy is amplified because he cenral bank also affecs he risk premium. Thus, an increase in ineres raes reduces he value of corporae asses and is cash flow deerioraes, boh facors increase he risk premium amplifying and making more persisen he impac of moneary shocks in he economy. In he model, he financial acceleraor channel has an addiional feaure, financial dollarizaion. The model considers ha par of firms deb is denominaed in U.. dollars, herefore, his mechanism is riggered also by flucuaions in he exchange rae. In his case, an increase in he exchange rae increases he real value of company deb and consequenly heir risk levels. This leads banks o charge a premium for higher risk, increasing he cos of invesmen. In he model, he exisence of financial dollarizaion weakens he ransmission channel of ineres raes for moneary policy, bu amplifies he role of exernal shocks and he exchange rae. This resul is consisen wih he empirical evidence shows ha economies wih financial dollarizaion are more vulnerable o financial shocks 4. The oher channel of ransmission of moneary policy in he model is he crowding ou 4 For example, Levy Yeyai (2005) found ha depreciaions make a crisis more likely as he financial dollarizaion increases. oreover, Domac and arinez Peria (2004) show ha he liabiliy dollarizaion, he raio of foreign liabiliies wih respec o local asses, is posiively correlaed wih he probabiliy of a sysemic crisis. 5

6 in spending, hrough which he ineres rae affecs he real exchange rae. The real exchange rae, in urn, deermines he composiion of aggregae demand beween domesically produced goods and impored goods. When he real exchange rae lowers (consisen wih a conracionary moneary policy), domesic goods become more expensive and hus impors rise and expors are reduced. 3. The linear version of he odel In his secion we presen he log-linear version of he sysem of equaions of he model. Those ineresed in he non-linear version of he model can find useful reading Casillo, onoro and Tuesa (2009), however his paper is only available in a panish version. This sysem of equaions is obained by aking a firs order approximaion o he efficiency condiions of he consumer and firms problems around he seady sae. The resuling linear sysem is a se of sochasic difference equaions, whose soluion is a sysem of linear equaions linking he variables of he model wih endogenous sae variables. ae variables may be shocks such as produciviy or inernaional ineres raes, or lagged endogenous variables such as he level of capial from he previous period. There are several feaures of he model ha disinguish i sharply from he Keynesian models of he 70s. Firs, in he model all he parameers of he equaions are combinaions of srucural parameers relaed o preferences, echnology and he behavior of he cenral bank and governmen. In his sense, he model is no subjec o he Lucas criique. econd, expecaions in he model are raional and do no follow any ad hoc rule as in models from he previous generaion. Finally, he behavior of he cenral bank is defined by an ineres rae rule, as in mos cenral banks in he world, and no by a rule of he growh rae of he amoun of money as in he previous generaion of models. To make he presenaion of he model easier, he sysem of equaions ha describe he model have been grouped ino four blocks. The block of aggregae demand, including consumpion, invesmen, expors and impors. The aggregae supply block, which is deermined by he equaions for inflaion, he labor marke and he capial marke. The hird block, he exernal secor, summarizes he ineracion of his economy wih he res of he world. Finally, he fourh block is deermined by he policy rule of he cenral bank. The model has 50 principal equaions plus 8 auoregressive processes ha deermine he evoluion of exogenous shocks 5. Variables defined in lowercase correspond o he difference in neperian logarihms of he variable in levels wih respec o is seady sae. Tha is: x ln ln. 5 For he forecas exercises, we have used a version of he model ha also includes a commodiy secor and households facing borrowing consrains. Those characerisics where imporan o capure in dynamics of expors and consumpion in he forecasing exercises. Considering hese new mechanisms, he number of principal equaions becomes 78. 6

7 3.1 Aggregae demand The aggregae demand is deermined by he following equaion: y AB abs y y (1) where y represens he gross domesic produc (GDP), abs, he domesic demand or absorpion, y he expors and y he impors, respecively. oreover, AB, and correspond o he value in seady sae of he raios of absorpion, expors and def impors on GDP. Associaed o he GDP is he deflaor,, which is defined in relaive erms wih respec o he consumer price index (CPI): def rer (2) where is he index of expor prices relaive o he exernal CPI and is he impor price index relaive o he domesic CPI. rer is he real exchange rae defined as he value of he exernal CPI in erms of domesic currency in relaion wih he domesic CPI, which has he following dynamic: rer rer 1 s (3) where s is he percenage variaion of he nominal exchange rae, defined as he price of foreign currency in erms of domesic currency, is exernal inflaion y is inflaion of domesic CPI. All hese equaions of he EGA-D summarize he raional behavior of a ype of agen. For example, consumpion reflecs he decisions of household savings, he invesmen behavior of firms, and so on. The firs componen of aggregae demand, he domesic absorpion is deermined by he sum of consumpion, invesmen and governmen spending: AB abs c C INV inv g G (4) where C, INV and G are values in seady sae of he raio of consumpion, invesmen and public expendiure on he GDP. For simpliciy, his version of he model has assumed ha goods for consumpion, invesmen and public expendiure are idenical, consequenly have he same price index 6. 6 For his reason, equaion (4) doesn include relaive prices. 7

8 3.1.1 Consumpion Aggregae consumpion, c, is deermined by he sum of he consumpion decisions of all he agens in he economy: households, c fam fam c and enrepreneurs, c 1 fam where fam is he paricipaion in seady sae of household consumpion on oal consumpion. The fundamenal difference beween families and enrepreneurs is heir abiliy o access he financial marke. I is assumed ha families have access o an efficien credi marke, and consequenly do no face resricions o smooh heir consumpion, while employers have no access o his marke. To borrow, he laer agens have o offer guaranees. Those ha offer beer guaranees receive a lower ineres rae. This difference in he access o credi marke affecs he consumpion choices of each of hese agens. Household consumpion doesn depend on curren income, bu on permanen income and he real ineres rae. If he real ineres rae increases, families will choose o consume less in he curren period, and more in he fuure (saving). This raional behavior of households is refleced in he following Euler equaion: emp fam c emp c (5) u c i E E u 1 c1 (6) This equaion equals he reurn of savings o is cos. The cos of savings is deermined by he marginal uiliy, uc, ha households give away when posponing consumpion, while he profi or reurn on savings is deermined by he real ineres rae, i E 1, valued according o fuure marginal uiliy, E u c 1. Also, he marginal uiliy of consumpion is defined by: u c 1 1 c h fam 1 h h c fam 1 vm (7) where 0 h 1 is he degree of habis, vm is he effec of money on he marginal uiliy and is a preference shock. The marginal uiliy of consumpion in he model depends no only on he presen level of consumpion, as in radiional models, bu also on lagged consumpion and he nominal ineres raes in soles and dollars. The marginal value of consumpion depends on heir habis, which are a proporion of consumpion in he previous period. The exisence of habis is imporan because i generaes a dynamic response of aggregae consumpion o changes in real ineres rae more realisic from an empirical approach. When here are habis, consumpion does no reac insananeously o changes in he real ineres rae, bu he reacion is gradually reaching he maximum impac afer a few periods. Furhermore, he effec of money on he marginal uiliy has he following form: 1 1 b 1 where 1 1 b 1 b 1 DT DT vm 1 i (8) i, is he ineremporal discoun facor, is he 8

9 elasiciy of subsiuion beween consumpion and money and 0 b 1 deermines he DT relaive weigh of consumpion wih respec o money in he uiliy funcion. is he raio of ransacion dollarizaion, deermined by he relaive weigh of demand for money in dollars wih respec o he one in soles in he uiliy funcion. i and i are he nominal ineres raes in domesic and foreign currency, respecively. As shown in equaion (8), nominal ineres raes in domesic and foreign currency also affec household s consumpion hrough demand for money and he dollarizaion of ransacions. In he model, households need o mainain cash, wheher in soles or dollars, o consume. Households choose opimally he composiion of heir money balances in soles and dollars, by comparing he opporuniy cos in each currency wih he reducion in ransacion coss generaed by money holdings. The more money households keep, he more he ransacion coss associaed wih consumpion will be reduced. If nominal ineres raes are reduced, i is cheaper o mainain cash, and herefore he level of household consumpion increases because ransacions are cheaper 7. If households keep boh soles and dollars, hen also movemens in he foreign ineres rae will adversely affec household consumpion. On he oher hand, enrepreneurs consumpion have a differen dynamic. Enrepreneurs consume jus a fracion of heir wealh, which is deermined by he value of he ne worh of he enerprises hey own. Therefore, he consumpion of he enrepreneurs is proporional o changes in is ne worh, n : emp c n (9) The enrepreneurs ne worh is a key variable in he model because i affecs enrepreneurs consumpion and influences he dynamics of capial invesmen. When he ne worh of enrepreneurs is high (low), he risk premium paid by enerprises deb is lower (higher), and herefore i is opimal o inves more (less) Invesmen The oher componen of domesic absorpion is invesmen in physical capial. Invesmen is deermined from he firs order condiion of firms producing capial. Condiion known as "Tobin s Q," which in is log-linear form is given by he following equaion: where 1 / 1 q I inv inv E inv inv 1 1 I is he elasiciy of he adjusmen coss in seady sae. According o he above equaion, invesmen depends posiively on he price of capial, q, he expeced level of invesmen, E inv 1, and he pas level of invesmen, inv 1. This dynamic of invesmen reflecs he exisence of adjusmen coss, a facor ha induces firms o change more gradually invesmen. oreover, he more elasic are he adjusmen coss, invesmen adjuss more slowly o changes in he price of capial. (10) 7 This is rue under he assumpion ha money and consumpion are complemenary goods, which implies ha he rae of ineremporal subsiuion beween hese goods is less han one ( 1 ). 9

10 I is imporan o menion ha he inerpreaion of he "Tobin s Q" in his model wih imperfecions in he capial marke is differen from a model wih complee capial marke. When capial markes are complee, he price of capial reflecs he ne presen value of fuure marginal produciviy of capial. However, when markes are incomplee, he price of capial also capures he evoluion of he ne worh of enrepreneurs. In his case, when he ne worh of enerprises increases, hey will have greaer capaciy o borrow and herefore demand more capial, pushing up he price of capial. Deails of he capial marke, where q is deermined, are presened below in he secion Expors, Impors and Demand for Domesic Producs Inermediae goods producers expor par of is producion o he inernaional marke. As shown in he following equaion, wo variables deermine he level of expors: world demand y ) and he relaive price of expors o exernal CPI ( ) ( y F y (11) where F is he elasiciy subsiuion beween domesic and foreign goods. Thus, expors will increase when he world economy improves, or when hey become relaively cheaper. In urn, he relaive price of expors depends on expors price inflaion and exernal inflaion raes, as deailed in he following equaion: 1 (12) where is he inflaion of expor prices, which has he following dynamics: mc where 0 1 is he degree of indexaion of expor prices, 1 measures he sensiiviy of inflaion expors o marginal coss, which depends on he probabiliy ha an exporing firm does no change is price each period,. arginal coss of he expor secor are given by: E (13) mc mc rer (14) where mc are he marginal coss in erms of consumpion unis. Imporanly, in his model of expors price inflaion is no equivalen o he sum of price inflaion and changes in he exernal exchange rae. On he conrary, i is assumed ha changes in he above variables are passed on gradually o he price of expors. This assumpion, known in he lieraure as LCP (Local Currency Pricing), can beer explain he dynamics of expors o changes in he exchange rae. In paricular, i allows a more gradual and persisen adjusmen of hese variables o shocks in he economy. Also, he model assumes ha here is a degree of indexaion in he pricing of expors, addiional facor ha conribues o greaer persisence in he adjusmen of expor prices. 10

11 In he case of impors, as shown in he following equaion, is behavior depends on he level of domesic absorpion and is relaive price: y H abs (15) where H is he elasiciy of subsiuion beween impored goods and hose produced domesically. Thus, impors will grow when he level of domesic absorpion is higher or when heir relaive price is reduced. As in he case of expors, for impors is also considered ha he impor price is adjused gradually o changes in is deerminans. In paricular, i saisfies he following law of moion for impor prices, 1 (16) where is he inflaion of impored goods, which depends on heir levels of pas and expeced fuure, as well as on changes in marginal coss in his secor, mc : 1 mc 1 E mup (17) where 0 1is he degree of indexaion of impored prices and 1 K 1 measures he sensiiviy of impored inflaion wih respec o marginal coss. mup corresponds o cos-push shocks o he imporing secor. In his secor, real marginal coss are given by he cos of buying goods abroad relaive o he price of impors, which is equal o he rae of deviaions in he law of one price, mc he same ha has he following law of moion: lop (18) lop lop 1 s (19) I is imporan o noe ha he LCP scheme is quie flexible. Calibraing he parameers ha deermine and, can generae eiher a more or less persisen response of prices. Thus, for a calibraed low (high) price rigidiy, he expors and impors price inflaion also show a low (high) degree of persisence. imilar o he demand for impors, he demand for domesically produced goods, y, depends on domesic absorpion and is relaive price: H y H H H abs (20) where he relaive price of domesic prices on he CPI, H is inversely proporional o he relaive price of impors on CPI: H 1 Anoher aspec ha is imporan o highligh from he aggregae demand block, is he (21) 11

12 role ha fulfill he expecaions of he fuure sae of he economy. In he model, he equilibrium depends on expecaions formaion, and consequenly, on he way moneary policy is implemened Governmen expendiures For simpliciy, i is assumed ha governmen spending follows an exogenous auoregressive process of firs order: G g g (22) G Aggregae upply The second block of he model is he aggregae supply, which essenially deermines he evoluion of inflaion and marginal coss of firms. In an open economy, households consume locally produced and impored goods. Consequenly, inflaion is a weighed average of domesic inflaion and impored inflaion, as shown in he following equaion ( 1 ) H (23) In he model, he weigh of impored inflaion on overall inflaion coincides wih he degree of openness o he economy, ( 1 ). As menioned above, he dynamics of impored inflaion is deermined, among oher hings, by he exchange rae flucuaions and by pas and fuure levels of i. Therefore, he model implies ha he more open he economy is, he greaer he direc impac of changes in he exchange rae in overall inflaion hrough impored inflaion, ie he greaer he pass-hrough effec of he exchange rae. In urn, domesic inflaion is obained aggregaing he prices of final goods. Each of hese firms producing final goods have monopolisic power o se prices according o demand condiions. However, no all firms can do so because of price rigidiies. Following Calvo (1983), i is assumed ha in each period firms face a fixed probabiliy of changing prices. This probabiliy is independen of he misalignmen of he relaive price of he firm and he ime elapsed since he las ime he price change. This pricing mechanism implies ha only a fracion of hese price changes and ha he remaining firms keeps prices unchanged, and hus heir relaive prices are emporarily misaligned unil you have he opion of changing prices. Despie is unrealisic assumpions, he pricing mechanism o he Calvo has he advanage of faciliaing he aggregaion of he pricing decisions of firms and also be consisen wih he empirical evidence ha economies wih low inflaion, he frequency of price adjusmen is sable, as prediced by he model of Calvo 8. Addiionally, he model considers price dollarizaion (PD). The PD means ha a DP fracion of he final goods producing firms se heir prices in dollars. I is assumed ha prices in dollars are also rigid and follow he same Calvo s pricing mechanism. In 8 ee Nakamura and einsson (2007) and Alvarez (2007). 12

13 his way, he domesic inflaion appears o be a weighed average of inflaion in soles and inflaion in dollars plus he change in he exchange rae, as shown in he following equaion. The exisence of price dollarizaion implies ha a fracion of he prices of final goods are rigid in dollars, and herefore flucuaions in he exchange rae is immediaely ransferred o he domesic inflaion 9. However, his does no imply ha prices in dollars do no mee he domesic demand condiions. Unlike he prices of impored goods, whose prices are independen of he condiions of domesic demand, domesic prices in dollars will rise when aggregae demand acceleraes and will be reduced a he opposie. As menioned previously, one advanage of he Calvo pricing mechanism is ha i faciliaes he aggregaion of prices. Under his mechanism, he average price of domesic goods in he economy is simply a weighed average of he aggregae price of he previous period and seing he opimal price ha firms change prices. D where and represen he probabiliy of no changing prices in soles and. dollars o respecively, and p, o and p, he opimal prices se by he firms ha change prices in 1 p p D D H DP DP D s s p D p 1 D 1 soles and dollars, respecively. These firms choose he opimal relaive price considering ha wih some probabiliy he price hey se will no change in he fuure, and herefore, should reflec no only he curren cos and demand condiions bu also fuure. In his conex, wo variables deermine domesic inflaion: he real marginal coss of firms and expeced fuure inflaion. In he model, inflaion will be higher when firms expec higher fuure inflaion or higher real marginal coss. Higher fuure inflaion maers because i reflecs higher fuure marginal coss, and herefore implies he need for fuure increases in prices. Given he likelihood ha some firms may no adjus prices, if firms expec higher inflaion in he fuure i is bes o advance hose price increases oday. Addiionally, o improve he fi of he model o he daa, i was considered indexaion. This mechanism implies ha hose firms ha are no able o adjus prices benefi from an auomaic price adjusmen mechanism based on pas inflaion. Considering he aforemenioned ingrediens, he dynamics of domesic inflaion in soles and dollars is deermined by he following wo Phillips curves: D 1 D 1 mc D s, o 1 p D D, o 1 p mc D E 1 mup D D E 1 D mup (24) (25) (26) 9 ee onoro (2006) for evidence on he degree of price dollarizaion for Peru. 13

14 where 0 1 is he degree of indexaion and i i i 1 i i 1 sensiiviy of he inflaion rae respec o marginal coss, for i, D measures he D. mc and mc represen he marginal coss of firms wih domesic prices in soles and dollars, respecively, and mup relaes o cos-push shocks. arginal coss in erms of consumpion unis, mc, are defined by: mc H r 1 wp a (27) where 0 1 measures he share of capial in he producion funcion. The marginal coss depend on he price of he wo facors of producion: he real wages, wp, and he cos of rening capial, r H, prices ha are deermined in he labor and capial marke, respecively. Also, marginal coss depend on he oal produciviy of facors, a. Thus, marginal coss will be higher when oal facor produciviy is lower. When here is a drop in produciviy, producion facors need o be used more exensively o achieve he same level of producion. arginal coss of firms ha se heir prices in soles and dollars are respecively: mc mc D mc mc rpd (28) (29) As noed, he difference beween he marginal cos in unis of consumpion, mc, and D marginal coss mc and mc are he relaive price of goods priced in dollars on he CPI,, and he relaive price of goods priced in dollars compared o he goods wih prices in soles, rpd. These relaive prices have he following dynamics: 1 (30) rpd rpd 1 s D (31) Relaive prices affec real marginal coss of firms because hey are deflaed by he price index for each secor. For example, if he price of firms ha se prices in dollars D increases, is marginal cos mc is reduced wih respec o mc. This difference is refleced in he relaive price, rpd Labor arke The labor marke mees households who offer work and firms demanding i. To consider unemploymen in equilibrium, i is assumed ha here is a discrepancy beween he marginal rae of subsiuion beween consumpion and leisure, which deermines he labor supply and real wages. This discrepancy prevens households o work he number of hours hey wan and herefore here may be unemploymen in he 14

15 economy, depending on macroeconomic condiions. The following equaion shows he evoluion of real wages. As shown in equaion (32), he real wage adjuss gradually o changes in he marginal rae of subsiuion beween consumpion and leisure. wp wp 1 wp 1 wp mrs (32) where 0 wp 1 measures he degree of real rigidiy in he labor marke and wp is real wages. mrs is he marginal rae of subsiuion beween labor and consumpion and u is he marginal disuiliy of work, which are defined by: l mrs u l u l l u c (33) (34) which measures he inraemporal elasiciy of subsiuion beween consumpion and labor. The adjusmen will be more persisen when wp is larger. oreover, he marginal rae of subsiuion beween consumpion and leisure in urn is increasing in he level of consumpion. In his way, when he economy is expanding and consumpion is increasing, workers value leisure more and, consequenly, for he same level of real wages, labor supply is reduced. In urn, his lower labor supply pressure wages o rise, generaing an increase in marginal coss of firms. This relaionship beween he marginal uiliy of consumpion and labor supply is he channel hrough which he model generaes a posiive relaionship beween marginal coss and economic aciviy. Also, he demand for labor equals he real wage wih he sum of he marginal produciviy of labor and he real marginal coss: wp y l mc (35) This las equaion implies ha firms will demand more work when real wages are lower and aggregae demand is higher Capial arke The demand for capial condiion deermines ha he renal rae of capial services, equals he sum of marginal produciviy of capial and real marginal coss: H r, r H y u k 1 mc (36) where u represens he degree of uilizaion of capial. Also, he capial supply is deermined by invesmen in each period, inv, plus he accumulaion from prior periods ne of depreciaion: k inv 1 k 1 (37) where is he depreciaion rae. In his marke is deermined he price of capial and he cos of rening capial. The laer is par of he marginal coss of firms and herefore affecs he dynamics of inflaion. Enrepreneurs, who are he owners of capial lease a 15

16 fracion of his producion facor according o he following equaion: where u / u U E r rp DF DF i E i E s E K (38) is he inverse elasiciy of marginal cos of using capial. Thus, firms use more inensively capial when he renal rae is higher. As shown in equaion (38), he degree of capial uilizaion is deermined opimally o minimize he coss of depreciaion ha he higher use of capial generaes. Employers in urn inves in capial unil he poin where he expeced reurn on capial is equal o is cos, as shown in he following equaion: K where E r 1 is he expeced reurn on capial, rp is he risk premium paid by DF K employers and is he degree of financial dollarizaion. The reurn of capial, r, is deermined by he revenues generaed by he capial income,, plus capial gains ne of depreciaion, q q : 1 1 The cos of financing capial, however, depends on he financial condiions of enerprises via he risk premium, rp, ha firms pay o borrow money. This risk premium is higher when he leverage level is higher. The leverage level in urn will be higher when he deb level is higher or he ne worh of enrepreneurs is lower, as shown in he following equaion: rp n d (41) D / P D / P D / P where / K r u r H U H H R r 1 q q 1 is he elasiciy of risk premium and d N N N is corporae deb. The balance shee relae equiy and deb o he capial value of companies: H r (39) (40) n 1d q k KN KN (42) where KN is he raio of capial on ne worh in seady sae. The relaionship beween risk premium and he leverage degree of firms creaes an addiional ransmission channel for moneary policy shocks, known as he financial acceleraor. This channel amplifies and makes more persisen he effecs of moneary policy shocks, because i creaes a posiive correlaion beween risk premium and he ineres rae se by he cenral bank. This relaionship exiss because he value of capial, which are he asses of he enrepreneurs, depends negaively on he ineres rae. Thus, when he ineres rae increases, he price of capial decreases, and hus he value of he asses of enrepreneurs. This lower level of asses increases he leverage of enrepreneurs and generaes a greaer risk premium, which increases he impac of he moneary policy shock. The relaionship beween risk premium and he enrepreneurs leverage is no only saic bu raher dynamic. As shown in equaion (43), changes in he risk premium affecs ne worh in he fuure because i increases he liabiliies of he enrepreneurs. In his way, he ineres rae impacs risk premium for more han one period. 16

17 In he model, he financial acceleraor has an addiional ingredien generaed by financial dollarizaion. The exisence of a fracion of corporae deb in dollars means ha he exchange rae also affecs he leverage degree and he risk premium, inducing a higher cos of financing for capial accumulaion. The negaive impac of a real depreciaion on ne worh will be higher when he degree of dollarizaion of deb is higher. The following equaion illusraes he combined effec of he wo facors menioned above: n K 1 v KN r q 1 k 1 KN 1rp 1 dp 1 FD FD 1 i i s 1 1 (43) The enrepreneurs ne worh evolves according o he reurn of heir asses, measured by he revenue generaed by he ren of capial plus valuaion gains and he cos generaed by is liabiliies. The laer is deermined by he real ineres raes in soles and dollars, and by variaions in he exchange rae, s. 3.3 Exernal ecor Two equaions summarize he ineracion of his economy wih he exernal secor, he balance of paymens equaion and he uncovered ineres rae pariy. The former resume he exchange of goods, services and capial beween residens and non-residen agens. In he model, his equaion is obained by aggregaing he budge consrains of households, firms and he governmen. The log-linear represenaion of he balance of paymens is he following equaion: b b b 1 1 def / b y i s bb resres 1 where b and res are he seady sae value of he raio of he ne foreign asses posiion and he remainder of he curren accoun over GDP, respecively. b is he ne foreign asses posiion in erms of consumpion unis, and b bb b is he elasiciy of he exernal risk premium. Three flows are imporan in his equaion, he flow of goods produced by foreign rade, which basically reflec he difference beween GDP and he level of domesic absorpion. The second is he capial flow, which is deermined by he change in he ne foreign asses posiion. Finally, he invesmen income flow includes he ineres paymens and valuaion effecs. Addiionally, he variable res considers he coss of monioring firms, he expendiure of using more inensively he capial, profis from imporers firms, he change in money holdings in dollars and he effec of deb denominaion due o financial dollarizaion: abs abs (44) 17

18 res res RP K KN 1 rp i dp k u u lop m s 1 1 RP Y KN 1 DF i s i Y (45) The oher equaion ha reflecs he behavior of he exernal secor is he uncovered ineres pariy condiion. This condiion is presened below, and deermines he evoluion of he nominal exchange rae, i i 1 pdi Es pdis pdi bb 1 (46) According o his equaion, he exchange rae appreciaes when he domesic ineres rae, i, increases, he ineres rae in foreign currency, i, is reduced or when he counry risk premium, which depends on he level of deb as percenage of GDP, bb, decreases. The parameer pdi measures he degree of smoohing of he exchange rae. If we solve s for in equaion (46) and ierae forward, we obain: s 1 1 s s 1 s j0 s j i j i j prem j where one can see ha if he parameer fixed exchange rae. On he oher hand, when he exchange rae is defined by pdi ends o 1, he model is quie close o a pdi ends o 0, like in he radiional case, s i j 0 j i j prem j and is equivalen o he sum of presen and fuures ineres rae differenials. In he laer case, he exchange rae responds well o he expecaions abou wha will happen in he fuure. The calibraion of a parameer pdi beween 0 and 1 smoohes flucuaions in he exchange rae and is consisen wih inervenion in he foreign exchange marke. Furhermore, i is assumed ha exernal variables such as oupu, he nominal ineres rae and inflaion ( y, i and, respecively) have he following auoregressive processes: y i 1 2 y y y 1 y y i i i 1 i i 2 1 (47) (48) (49) 18

19 3.4 The oneary Policy Rule The cenral bank implemens moneary policy conrolling he shor-erm ineres rae. To se his rae, he cenral bank injecs money ino he economy enough in such a way ha he equilibrium ineres rae is he rae se by he cenral bank. The moneary policy rule akes he following form: i i s y mon s y y 1 1 i i 1 (50) where, i >0, 1, s >0 y y >0. This rule conains several elemens ha are imporan o highligh. Firs, he cenral bank reacs increasing he ineres raes when inflaion exceeds he cenral bank's arge. econd, he increase in ineres raes compared o deviaions in inflaion is more han proporional o he increase in inflaion, as measured by he parameer 1, in his way ensures o generae increases in real ineres rae, and herefore induces a lower level of economic aciviy and lower inflaionary pressures. Third, movemens in ineres raes are persisen, which is measured by he parameer i > 0. Empirical evidence shows ha his is a feaure of moneary policy in many counries. There are several hypoheses o explain his behavior of he cenral bank, including one proposed by ichael Woodford, aribued his behavior of he Cenral Bank o is desire o affec expecaions of fuure inflaion. Oher hypoheses are based on he exisence of coss in he decision making process of he board of he cenral bank when here is heerogeneiy in preferences or informaion of members of he oneary Policy Commiee 10. An imporan aspec of he rule considered in he model is ha he cenral bank can reac sysemaically o changes in he exchange rae. This behavior of he cenral bank can be welfare improvemen in an open economy wih price dollarizaion 11. If firms se prices in dollars and hey have some rigidiy, flucuaions in exchange raes generaes changes in relaive prices ha are no efficien, and herefore, affec he allocaion of resources. In his case, he cenral bank can conribue o he welfare of sociey by reducing exchange rae volailiy. 10 onoro (2007), in a model wih oneary Policy Commiees, raionalizes he exisence of adjusmen coss in seing he moneary policy ineres rae. 11 ee for example Casillo (2007). 19

20 4. Esimaion In his secion, we presen he main resuls from he esimaion of he model. Casillo, onoro and Tuesa (2006b) presen a more deailed explanaion of he esimaion mehodology. 4.1 Daa problems The esimaion of he model using Peruvian daa has several problems. Firs, he adopion of he Inflaion Targe regime and change of he policy insrumen o he ineres rae in 2002 generaed a change in he behavior of nominal variables. For example, he shor-erm nominal ineres rae is much more volaile and has a higher mean in he period prior o he adopion of a Inflaion Targe regime (figure 1.A). Also, inflaion was reduced gradually from high levels of he early 1990s o reach levels of inflaion in developed counries in 2002 (Figure 1.B). These wo feaures indicae he presence of changes in he daa generaing process, in paricular he moneary policy rule and he price formaion (Phillips curve). econd, here is insabiliy in variables ha are considered as parameers by consrucion in he model, such as he degree of dollarizaion and rade openness (figures 1.C and 1.D). These variables are considered exogenous and consan in he model, bu he endogenizaion of hem would increase he complexiy of he model and could bring sabiliy problems o he equilibrium. Third, he non-saionary variables show he presence of more han one uni roo, for example, real oupu and erms of rade (figure E). This facor creaes a consisency problem beween he model and he daa, as DGE models canno work, a leas so far, wih more han one uni roo in endogenous variables. 4.2 Esimaion sraegy We use quarerly daa beween 1995 and 2007 of he main macroeconomic variables o esimae some parameers of he model shocks were considered: a permanen shock o he global echnology and 10 shocks ha follow an auoregressive process of order one 13. The uni roo in he model was given by a permanen shock on global echnology, which was used o conver non-saionary variables on saionary ones, and le consisency beween daa and he variables of he model. Regarding he rend in he nominal ineres rae and inflaion, he rend is removed by considering he midpoin of he announced annual inflaion arge in he period prior o formal adopion of he Inflaion Targe regime in Also, o conrol for changes in he moneary policy rule and he aggregae supply relaions, we esimae by sub-samples hose parameers associaed o hese equaions, aking as given all he oher parameers in heir enire sample esimaes. 12 The macroeconomic variables used were: produc, consumpion, invesmen, real exchange rae, nominal exchange rae, erms of rade, domesic ineres rae, inernaional ineres rae, inflaion and impored inflaion. 13 Among hese shocks are: echnology, domesic inflaion, mark-ups, mark-ups in he impor secor, moneary policy, consumer preferences, exernal moneary policy, invesmen, uncovered ineres rae pariy, he purchasing power pariy and exernal produciviy. 20

21 The esimaion of seleced parameers of he model was performed using Bayesian economerics. The algorihm used was he Random-Walk eropolis-hasings wih draws of he poserior disribuion, aking as a crierion of accepance raio beween 0.25 and We proceeded o esimae five models: a model wihou any form of dollarizaion, hree wih a ype of one dollar each and ha includes all hree ypes of dollarizaion a a ime. 4.3 Resuls Among he mos sriking resuls we have ha, according he Bayes facor, he model wih hree ypes of dollarizaion dominaes he oher models. I was observed ha he main ingredien ha helps o explain Peruvian daa is financial dollarizaion, because considering he Bayes facor, ransacion and price dollarizaion does no add much o he model relaive financial dollarizaion. Baseline odel Transacion Dollarizaion Price Dollarizaion Financial Dollarizaion Three ypes of dollarizaion Log-arginal Among he main resuls from he esimaion of he parameers, we obain ha: real fricions, such as rigidiies in he labor marke and adjusmen coss in invesmen, are imporan in all models. Also, prices are relaively more flexible han in developed economies, firms in Peru change prices on average once every 2 quarers. This is consisen wih he hisory of high inflaion in Peru. oreover, price indexaion is imporan in he esimaion of he Phillips curve. We also found ha he sandard deviaions of shocks are quie large relaive o hose esimaed for developed economies. Furhermore, he esimaion of he moneary policy rule shows ha he cenral bank has complied wih he Taylor principle and ha afer he adopion of he Inflaion Targe regime he response of he ineres rae o inflaion has increased, while he response o oupu and he exchange rae has been reduced. 5. Exercises: Analysis of he Transmission echanisms To show he main ransmission mechanisms behind he EGA-D, we presen hree simulaion exercises. These exercises are based on a paricular EGA-D version ha can be find in CT(2009). Figure 2, shows he impulse response funcions o a 1 percen conracionary and ransiory moneary policy shock for he main macroeconomic variables. This analysis is made aking ino accoun he effecs of dollarizaion and exchange rae inervenions on he moneary policy ransmission mechanism. Impulse response funcions sugges ha dollarizaion increases he exchange rae pass-rough o inflaion and reduces he impac of moneary policy on he oupu gap. Also, he exercise in figure 2 suggess ha exchange rae inervenion reduces he exchange rae volailiy and is effecs over inflaion. When dollarizaion is no presen, moneary policy is more effecive in affecing he oupu gap bu less effecive o affec inflaion, because dollarizaion reduces he power of he ineres rae channel bu makes sronger of he exchange rae channel. 21

22 In Figure 2, we display he impulse responses o an increase in he inernaional ineres rae. The resuls sugges ha for he case of high dollarizaion and no exchange rae inervenion, he oupu gap decreases significanly afer hree quarers. For he scenario wihou dollarizaion, he effec of an increase in he inernaional ineres rae is null afer hree quarers. Finally, figure 3 also plos he responses for he case of high dollarizaion and exchange rae inervenions. In his case, exchange rae inervenions compleely off se he conracionary effecs of an inernaional ineres rae increase, reducing vulnerabiliy of he domesic economy o exernal shocks. This difference is explained mainly by he balance shee effec or financial acceleraor mechanism in dollarized economies. The increase in he inernaional ineres rae generaes a nominal depreciaion of he domesic currency ha increases he real exchange rae. This increase in he real exchange rae generaes, when dollarizaion is high, a negaive balance shee effec ha reduces privae invesmen and more han offse he posiive effec of a nominal depreciaion on expors. Wihou dollarizaion, he negaive impac of he balance shee effec is no presen anymore; herefore, any increase on he real exchange rae generaes an increase on ne expors and hence greaer oupu gap. This mechanism makes moneary policy less effecive when sabilizing invesmen, and hrough his channel, he oupu gap. oreover, he financial acceleraor in a dollarized economy makes privae invesmen more sensiive o exernal shocks. In he absence of nominal fricions, moneary policy would have a minor role in sabilizing inflaion hrough aggregae demand. To analyze he role of nominal fricions, Figure 4 shows he responses o a moneary policy shock for boh cases: price rigidiies (in bold) and flexible prices. This figure suggess ha following an anicipaed moneary policy shock, oupu gap and inflaion decreases and nominal exchange rae appreciaes. This dynamic is qualiaively similar for boh cases. However, i is clear he imporance of nominal fricions o characerize he dynamics of he daa. In firs place, he model wih nominal fricions generaes a lower bu more persisen effec on inflaion. On impac, he fall in inflaion is no as srong as in he case wih flexible prices. This is because prices are adjused gradually. Consequenly, he conracion in he oupu gap is more pronounced and persisen. In general, nominal fricions add endogenous persisence o he dynamics of he model. Also, in he model wih flexible price he adjusmen occurs hrough prices and o a lesser exen hrough quaniies. In second place, he model wih nominal fricions helps o replicae he hump shaped response of inflaion and ou pu gap. This form is less eviden in he flexible prices case. Noe also ha in he flexible prices model he greaer impac on inflaion (in he curren period) is given by he exchange rae pass rough effec. 6. Forecasing Process ince mid-2008 he BCRP is implemening he use of EGA-D in forecasing. We have formed a eam comprised of members of he Research Division and he acroeconomic odeling Division. The forecasing process consiss of four main sages: he managemen of he daabase, he esimaion of he iniial poin, he forecasing process per se and he ransformaion of forecased variables in erms of naional accouns. 22

23 6.1 Daabase managemen On he daa managemen sage, we firs collec daa from various sources and make all he ransformaion needed o make daa consisen wih he model. We use differen daa ransformaions such as: expressing daa in logarihms, removing seasonaliy using Arima 12, making daa saionary by applying he Hodrick-Presco filer o all uni roo variables or by esimaing rends wihin a coinegraed long run sysem. Also, in order o avoid he end of sample problem of he HP filer, we exend he sample using ARA forecass of he variables, as explained below. The main advanage of using he HP filer o eliminae uni roos from non-saionary variables is ha i is easy o use. However, he use of his filer involves several problems. The firs problem is relaed o he inconsisency beween rends of he naional accouning ideniies. For example, if he following ideniy is rue for hree economic variables Y Z ; hen if each of he series is HP filered his ideniy will no necessarily be mainained in rends, so Y Z. oreover, he HP filer suffers from he problem of end-of-sample bias, because for he las observaions i brings closer he esimaed rend o he observed ime series. In pracice, we solve his problem exending he sample of he variables using an univariae ARA forecas of he hem. However, we are aware ha his mehodology also generaes a bias o he iniial forecas and makes difficul o idenify changes in rend. One las drawback when considering HP filer is ha, HP filering has no economic raionaliy so i makes difficul o communicae resuls. Alernaively o he use of filers, we can express he variables in firs differences. This mehodology is similar o he use of a linear rend for each series. Also, i has he advanage ha i is easier o explain and inerpre han he HP filer, because he discussion focuses on he growh raes of he variables, which are of common use in he discussion. However, he inconsisency problem of rends in ideniies sill remains as in he HP filer case. Currenly, we have designed a block independen of EGA-D for he esimaion of rends. This block consiss on a group of esimaed coinegraion regressions beween aggregae demand componens, such us consumpion and invesmen, and he poenial oupu. From hese regressions we consruc a gap for each componen of he aggregae demand. A similar mehodology is he one proposed by Cayenne, Gosselin and Kozicki (2008), which consiss on adding a separae sysem of equaions for rends on he DGE s linearized sysem. The advanage of his procedure is ha i is flexible enough o incorporae all he differen relaionships ha affec rends in order o capure he dynamics of he daa of a paricular economy. In addiion, he problem of inconsisency beween rends and macroeconomic ideniies is solved. 23

24 6.2 Esimaion of he iniial poin A fairly imporan ask when doing forecasing wih a DGE model is he esimaion of he iniial poin. The iniial poin of he forecas is he value of all he model variables in he previous period o he forecasing exercise. The main problem in esimaing he iniial poin is ha no all he variables of he model are observable. For example, for he Peruvian economy here is no informaion on he Tobin s Q, he marginal coss, he ne asse value of he enrepreneurs and so on. We have applied wo differen mehodologies when esimaing he iniial poin of he forecasing horizon. The firs mehodology is he esimaion of all he non observable variables by implemening he smoohing Kalman filer o he EGA-D. The main advanage of his mehod is ha here is consisency beween he model, daa and he esimaion of nonobservable variables. However, is use has shown ha he esimaion of non-observable variables is quie sensiive o he informaion se. The iniial poin esimaion can vary significanly when inroducing new informaion. Also, he esimaion of some variables can be very poor. For example, when we compare he acual variables wih is Kalman filer esimaes, we see ha boh can differ significanly. For example, Figure 5 shows ha he differences beween he acual and he esimaed value of some variables, such as nominal depreciaion, governmen spending, foreign oupu and he real exchange rae can be quie considerable. The second mehod consiss o complee only he se of sae variables wih he bes informaion se available. EGAD-D has 40 sae variables, of which of hem 17 are observable. For he remaining 23 sae variables we have found proxies for 9 of hem. For he sae variables wih no informaion a all we have assumed ha hose variables are in he seady sae a he iniial poin. 6.3 The forecasing process The forecasing sage is quie similar o he forecasing process used in ohers models a he BCRP, such as he Quarerly Projecion odel (PT) 14. To make a forecasing exercise wih EGA-D all he exogenous variables mus be projeced using informaion from specialiss or saellie models. Then, we use he raional expecaion soluion of he model in order o forecas he endogenous variables 16 quarers ahead. The forecasing plaform is developed using he IRI oolbox for alab. I consiss mainly on dividing he forecasing horizon in wo pars. The firs one is he medium erm forecas horizon, which incorporaes specialiss projecions of he exogenous variables unil a medium erm forecas horizon of 8 o 12 quarers. The second par is he long erm forecas horizon, which complees he projecions of he exogenous variables up o 16 quarers from auoregressive processes ha define hose exogenous variables. The projecion of all he endogenous variables is obained by inroducing all 14 For more deails, see he paper: "odelo de Proyección Trimesral", Documeno de Trabajo N , Banco Cenral de Reserva del Perú. 24

25 he rajecories of he exogenous variables ino he model soluion. 6.4 Re-ransforming he forecased variables In he las sage, we re-ransform he forecased variables in erms of naional accouns variables. In oher words, we recover he iniial ransformaions ha made in he daa managemen sage, adding he esimaed rends and seasonaliy and expressing all he variables in levels. I is imporan o menion ha we have added some addiional variables o he model in order o make i compaible wih he daa. For example, in he version of he model ha is used for forecasing we include a wo differen definiions of he exchange rae: bilaeral and mulilaeral. The former is he one wih respec o he U.. dollar and he laer respec o a baske of currencies. We use in he model he bilaeral exchange rae in he equaions relaed o dollarizaion, since his is he exchange rae ha is relevan for hose relaionships. On he oher hand, we use he mulilaeral exchange rae in hose equaions relaed o inernaional rade. In he original version of he model here isn an explici disincion beween hese wo variables, because he res of he world is no modeled a block of counries bu as a unique large economy. We have made oher adjusmens o he model, such as a difference of impored inflaion ha affecs he CPI and he one ha affecs he GDP deflaor. Also, we include oher imporan mechanisms no included in he model CT (2009). These mechanisms are relaed o he conclusion of Non Ricardian agens, which helps o capure he effecs of fiscal policy, and inclusion of a commodiies exporing secor. In Figure 6 we presen a forecasing exercise for core inflaion using informaion a he end of each quarer of 2007 using boh models: EGA-D and PT. The main observaion is ha in all cases he EGA-D projeced an increase in inflaion in he following periods slighly higher han he one projeced by he PT. This would be explained because in he EGA-D inflaion and he oupu gap depend more on fuure expecaions of hese variables. 25

26 7. Conclusions This paper summarizes he developmen of EGA-D, a DGE model for policy analysis, a he Cenral Reserve Bank of Peru. Among he main findings is ha dollarizaion reduces he power of moneary policy o affec oupu and increases he vulnerabiliy of he economy o shocks from he exernal ineres rae. Also, he esimaion of model parameers by Bayesian economerics show ha financial dollarizaion is imporan o explain he Peruvian daa. Furhermore, i is found ha compared wih developed economies, prices are more flexible and he volailiy of shocks is greaer. I also shows he firs resuls of he implemenaion of he model in he projecion of macroeconomic variables, including inflaion. We also describe he forecasing process wih he EGA-D currenly in developmen a he BCRP. This research is par of a projec developed by he Research Division of he Economic udies Deparmen a he Cenral Reserve Bank of Peru, which aims o improve he projecion of inflaion of BCRP. The srucure of he model presened is quie flexible and herefore can be expanded o incorporae oher ingrediens ha are considered imporan o explain he ransmission mechanism of moneary policy and o make policy analysis for Peru. 26

27 Figures I n erba n k I n e r e s R a e Inflaion Rae e a n = D = 5. 3 e a n = D = ean = 6.3.D = 3.5 ean = 2.1.D = Figure 1.A Figure 1.B Financial Dollarizaion Inernaional Trade Openness % Credi in Dollars % 3 in Dollars Figure 1.C Figure 1.D Real GDP and Terms of Trade (1994 = 100) Real GDP Index Terms of Trade Figure 1.E 27

28 Figure 2: Dolarizaion Conrafacual; IRFs o a Domesic Ineres Rae hock 28

29 Figure 3: Dolarizaion Conrafacual; IRFs o a Foreign Ineres Rae hock 29

30 Figure 4: Effecs of Nominal Rigidiies; IRFs o a Domesic Ineres Rae hock 30

31 Figure 5: Esimaion of he iniial poin wih he Kalman Filer; example of observable variables. 31