R.E.M. 2.0 An estimated DSGE model for Romania

Transcription

1 R.E.M.. An esimaed DSGE model for Romania Mihai Copaciu Valeriu Nalban Crisian Bulee This draf: March 5 Absrac This paper describes he heoreical srucure and esimaion resuls for a DSGE model for he Romanian economy. Having as benchmark he model of Chrisiano e al. (), he addiional feaures we inroduce refer o parial euroizaion in he financial secor, oil as an inpu in producion process, dis-aggregaion of headline inflaion ino adminisered and core componens, Naional Accouns consisen measures for GDP volume and deflaor, and an exension of he foreign secor o a wo counry semi-srucural model. The model is esimaed using a relaively shor daase, subjec o poenial revisions and characerized by high uncerainy and volailiy. Is evaluaion is performed using a wide range of procedures, like impulse response funcions, measures of daa fi, variance and hisorical decomposiions, forecasing performance. The resuls highligh he significance of he added mechanisms in explaining he Romanian business cycle over he analyzed period, confirming also he overall abiliy of he model o supply heoreically and daa coheren policy analysis. Naional Bank of Romania. The views expressed in his paper are hose of he auhors and do no necessarily reflec he views of he Naional Bank of Romania. We hank Cezar Boţel and Crisian Popa for heir suppor. Valuable suggesions from Lawrence Chrisiano and Cosmin Iluţ are graefully acknowledged. Mihai Copaciu would like o exend his hanks o he Fulbrigh Commission for research suppor while being a visiing suden o he Deparmen of Economics, Norhwesern Universiy.

2 Conens Inroducion 4 The model 7. Srucure of he model - overview Producion secor Domesic producers Imporers Consumpion goods producers Invesmen goods producers Capial producers Exporers Banks Equilibrium in he financial secor Furher developmens in modeling he banking secor Enrepreneurs The individual enrepreneur Ne worh aggregaes Households The role of labor marke fricions Moneary and fiscal auhoriies Aggregae variables and (oher) marke clearing condiions Foreign secor The srucure of he foreign economies Aggregae exernal variables and (real e ecive) exchange raes Aggregae resource consrain, Naional Accouns consisen GDP and he GDP deflaor Aggregae resource consrain Naional Accouns consisen GDP The GDP deflaor Ne expors, curren accoun, ne foreign asses and he risk premium The risk premium Measuremen equaions and model-consisen filering Domesic variables Exernal variables Scaling and defining variables Esimaion Daa used in esimaion Calibraed parameers Core domesic model Excess growh raes parameers Prior disribuions

3 4.4 Shocks and measuremen errors Esimaion resuls Poserior parameer values Impulse response funcions Model momens and variance decomposiion Smoohed shock processes and hisorical decomposiion Relaive forecasing performance Moneary policy abroad: when ECB and FED move in opposie direcions Alernaive models Conclusions 6 6 Appendix 3 6. Esimaed exernal secor Esimaed parameers - excess rends Impulse response funcions

4 Inroducion In his paper we describe a DSGE model wih he heoreical srucure ailored and implemened for Romania (R.E.M.. - Romania s Economic Model). The model is buil on he usual new Keynesian small open economy framework, incorporaing sandard feaures used in his lieraure, such as monopolisic compeiion and price rigidiies, working capial channel, invesmen adjusmen coss, variable capial uilizaion and habi in consumpion. In he iniial sage, he model drew heavily upon he work of Chrisiano e al. (), which incorporae in he framework menioned before boh financial fricions in he form of a financial acceleraor along he lines of Bernanke e al. (999), and labor marke fricions in he spiri of he search and maching heory. As for he empirical par, we have as benchmark he work of Copaciu (), which esimaed he models in Chrisiano e al. () for Romania. Furhermore, he model was enriched along several dimensions, in order o accoun for he specific feaures of he Romanian economy, and a he same ime o saisfy he requiremens of regular forecasing exercises in he conex of he inflaion argeing regime in place. To accommodae he exisence of a significan share of foreign currency (EUR) denominaed loans in he local economy (approximaely 45% for new loans o non-financial corporaions), he financial secor of he model was adaped by inroducing wo ypes of enrepreneurs, according o he currency in which hey borrow. As he enrepreneurs are now exposed o exchange rae risk, his exension gives rise o balance shee e ecs in he model, such ha a depreciaion of he domesic currency has also a negaive influence on oupu, apar from a posiive impac hrough he ne expors channel. Alhough we inroduced wo ypes of banks o mach he demand of funds depending on he currency hey are denominaed, here is no currency mismach in heir balance shees, as he exchange rae risk is enirely ransferred o enrepreneurs, in line wih he empirical evidence for Romania. Las bu no leas, we calibrae he share of enrepreneurs borrowing in foreign currency (FC) relaive o hose borrowing funds denominaed in domesic currency (DC) by maching he empirical raio of foreign o domesic currency denominaed loans demanded by non-financial corporaions operaing in Romania over he analyzed period (5-4). The producion secor of he model was modified o include he use of (impored) oil as an inpu for inermediae goods. The movemens in global oil prices (se in US dollars) are refleced only parially in he price of oil in he domesic marke (incomplee pass-hrough), owing o he adopion of local currency pricing hypohesis, price rigidiy and monopolisic compeiion. The producion secor was furher adaped o accoun for he presence of a significan share of goods and services wih adminisered prices in he CPI baske (approximaely one fifh), following he approach of de Casro e al. (). Given ha he behavior of hese prices is relaed o he real marginal coss developmens o a lesser degree, here is a risk of obaining misleading resuls wihou modeling hese prices explicily, when esimaing he model or using i for analysis and forecass. Excluding he adminisered prices from he CPI baske is likely o o er a more relevan measure of he underlying inflaionary pressures, needed in he moneary policy decision process. Technically, he adminisered prices were inroduced in he model by assuming ha a fracion of he consumpion goods producers are no allowed o opimize heir prices, bu insead mus follow some exogenous indexaion 4

5 rule. In addiion o oil as a new ype of impor, he exernal dimension of he model was modified by modeling he res of he foreign secor as a wo counry (Euro area and US/Res of he world) open economies new Keynesian semi-srucural model, maching he currency srucure of he Romanian foreign rade in goods and services. Given ha he foreign currency financial ransacions ake place only in EUR, exernal shocks have di eren e ecs on he domesic economy, according o he originaing counry. When aking he model o he daa, a number of issues were considered. Firs, o reconcile he specific growh raes of he observed variables wih he balanced growh pah of he model, we follow he approach of Argov e al. () for model consisen filering (secion 3). Second, we define he GDP volume and deflaor in a manner consisen wih he Naional Accouns measure (secion.9). Moreover, when esimaing he model, we use an endogenous prior approach as proposed by Chrisiano e al. (), bu we modify i in order o allow maching cerain momens only for a subse of variables. Las bu no leas, we esimae he exernal secor ouside he main model, using also an endogenous prior procedure and model consisen filering a la Argov e al. (). When esimaing he model we used a oal of 9 observed series covering 5Q3:4Q3 observaions. The limied sample is moivaed by some issues generally specific o emerging economies, like daa availabiliy, srucural breaks, or moneary policy regime changes. The block modeling he wo foreign economies was esimaed exogenously using 8 series and covering a longer sample. Par of he coe ciens were calibraed because of idenificaion issues or in order o mach cerain arges consisen wih he daa (like invesmen o oupu raio or he raio of foreign o domesic loans). The remaining parameers were esimaed in a Bayesian framework, augmened wih he endogenous priors procedure developed by Chrisiano e al. (). The model evaluaion oolki consiss of various sandard procedures ha were performed using poserior means of he esimaed parameers. Impulse response funcions revealed he imporance of he currency subsiuion, balance shee and wealh e ecs, capured when modeling wo disinc ypes of enrepreneurs (defined wih respec o he currency hey borrow in). Accordingly, he currency denominaion of foreign financial flows (EUR in our case) and he degree of euroizaion (he relaive shares of he wo ypes of enrepreneurs) maer for he reacion of secor specific and aggregae endogenous variables. The esimaed DSGE model was able o e cienly mach firs and second order momens as displayed by he daa. This oucome was favored by he echnical approaches implemened when esimaing he model: he excess rends as in Argov e al. () allowed o perfecly mach he means, while he endogenous priors as in Chrisiano e al. () improved he maching of sandard deviaions. Also, some unobserved variables rerieved by he Kalman smooher fi quie well he dynamics of heir daa counerpars, like bankrupcy raes, number of vacan jobs or he risk premium (as proxied by credi defaul swap or opion adjused spread). Variance decomposiion analysis a relevan moneary policy horizons (8 quarers) revealed he high conribuions of shocks originaing in he financial secor (risk premium and wo enrepreneurial ne worh innovaions) and imporers-exporers secor (markups a ecing exporers and impors for expors producers). These resuls highligh he imporance of boh financial fricions and open economy dimensions of he model. A he 5

6 same ime, he e ecs of labor marke fricions appeared o be of lile significance. The hisorical decomposiion of endogenous variables ino individual conribuions of srucural shocks during he analyzed period o ered relevan conclusions regarding he imporance of paricular innovaions during specific quarers. Demand side shocks appeared as imporan sources of oupu and privae consumpion dynamics, while financial secor (risk premium included) relaed shocks explain much of he flucuaions in invesmen, ineres rae spreads and exchange rae. Openness relaed variables (impors, expors, curren accoun) appeared o be driven by specific markup shocks, and also by innovaions in he risk premium. The in-sample (univariae and mulivariae) forecasing accuracy of he esimaed DSGE model compares well wih simple univariae mehods (like random walk and auo-regressions), bu is generally dominaed by he Bayesian VAR models predicions. We also made an aemp a simulaing a more complex scenario ha would mach he expeced near erm moneary policy developmens in Euro area and he US. Namely, we analyzed he reacion of endogenous variables o a simulaneous increase in he US and adecreaseinheeuroareaineresraes,fordi eren levels of euroizaion. As menioned before, changes in he exernal secor variables a ec he domesic economy hrough di eren channels. While a shock originaing in he US economy direcly influences domesic variables via he ne expors channel, a shock o he Euro area economy has an addiional direc impac hrough he balance shee channel, given EUR denominaion of foreign currency loans. Moreover, he imporance of he laer menioned mechanism depends posiively on he euroizaion degree of he domesic economy. Therefore, he increase in invesmen following he decrease in he EURIBOR ineres rae leads o a sronger increase in oupu when euroizaion is higher. If he foreign currency loans had been denominaed in USD, he increase in he US ineres rae would have led o a sronger decline in oupu in he more dollarized economy. 6

7 The model The heoreical model is an exension of Chrisiano e al. () allowing addiionally for: oil as an inpu in he producion of domesic goods, domesic and foreign currency borrowing in he case of enrepreneurs, he dis-aggregaion of consumer prices ino CORE and adminisered componens and an exended, wo regions, exernal secor. In presening he model in he following subsecions, when necessary, we will follow closely Chrisiano e al. ().. Srucure of he model - overview The srucure of he model is presened in figure. The producion secor consiss of inermediae goods producers, capial goods producers, imporers and final goods producers. Domesic inermediae goods reailer aggregaes he supply of such goods received from a coninuum of producers operaing in a monopolisic compeiion environmen. Any of he laer uses a producion funcion ha combines impored oil, capial services (provided by he enrepreneurs borrowing funds denominaed in domesic and foreign currency respecively) and labor, wih he combinaion of he las wo represening he value added (VA) in he economy. In he producion of inermediae goods, permanen and emporary echnology shocks a ec produciviy. The imporing secor comprises of four ypes of imporers ha buy a homogeneous good from foreign markes and di ereniae i ino consumpion, invesmen, expor goods and oil. For each of he above menioned caegories, inflaion evoluion is described by a new Keynesian Phillips curve, resuling from he assumpions of Dixi-Sigliz compeiive monopolisic framework and (local currency) nominal price sickiness, wih markup shocks a ecing marginal coss. Furhermore, for each caegory, excep oil imporers, a working capial channel is presen (i.e. firms finance in advance par of heir producion coss by inra-period loans). Thus, besides foreign inflaion and oil price shocks, here is also an impac of ineres raes on firms marginal cos. The domesic inermediae and he impored goods are used in he nex sage by he producers of final goods (using consan elasiciy of subsiuion producion funcions), resuling in final consumpion (CORE and adminisered prices goods), invesmen, expor and governmen goods. The only excepion is represened by oil goods, which, as menioned above, are being used in he producion of domesic inermediae goods only. The demand for final goods comes: from households for final consumpion goods, from he fiscal auhoriy for final governmen goods, from capial producers for invesmen goods, while expors are demanded from abroad. As opposed o foreign currency financial ransacions ha ake place only in EUR, exernal rade wih goods and services akes place boh in EUR and USD, as hey are he currencies used in he invoicing of more han 9% of inernaional rade ransacions having a Romanian eniy as counerpar. The exernal demand for domesic goods faced by exporers is also influenced by foreign demand shocks. Domesic ineres rae for he producers of domesic inermediae goods and foreign ineres rae for imporers. 7

8 Households buy he consumpion goods from final goods producers and supply labor services o he domesic inermediae goods producers. The saving process consiss of bank deposis in domesic and foreign currency. When maximizing heir uiliy, households face habi in consumpion, wih consumpion preference and labor disuiliy shocks influencing heir opimal decisions. In supplying labor services, households face employmen fricions wih is members alernaing beween being employed or no. Adding employmen fricions o he model is done in order o capure boh he exensive and he inensive margins of labor supply, as daa poins owards variaion in oal hours worked as coming from variaions in boh margins. As in Chrisiano e al. (), when employed, workers separae from heir employer eiher exogenously or endogenously (i.e. if heir individual produciviy is below a cerain, endogenously deermined, cuo ), while when unemployed hey do undireced search. Wages are renegociaed periodically hrough aomisic Nash bargaining. The decisions of agens in he presence of employmen fricions is also influenced by shocks o he bargaining power of workers, o he maching produciviy and o he dispersion of produciviy among workers. The invesmen goods producers mee he demand of capial goods producers, wih he relaive price of invesmen goods being influenced by an invesmen specific permanen echnology shock. Capial producers use invesmen goods o add o he previous sock of (undepreciaed) capial, before supplying he new capial owards enrepreneurs. When ransforming invesmen ino capial, hey face invesmen adjusmen coss, while heir opimal choice is influenced by marginal e ciency of invesmen shocks. The enrepreneurs buy capial from capial producers, se is uilizaion rae and ren capial services o inermediae goods producers. Enrepreneurs access loans o cover he par of he acquisiion cos of capial ha remains afer self-financing occurs. Financial fricions beween enrepreneurs and banks arise in he model given he presence of asymmeric informaion and cosly sae verificaion. There are wo ypes of enrepreneurs, financing hemselves by borrowing eiher in foreign currency (EUR in our case) or in domesic currency. The presence of foreign currency lending gives rise o balance shee e ecs. The opimal choice of enrepreneurs is also influenced by wo shocks specific o his secor: a shock o he ne worh of enrepreneurs and one ha impacs on heir idiosyncraic produciviy (i.e. risk shocks ). Lending o he enrepreneurs akes place hrough banks. There are wo ypes of banks: one ha deals wih enrepreneurs borrowing in domesic currency and one ha provides funds for hose borrowing in foreign currency. The sources of hese funds are represened by deposis, wih domesic currency deposis being provided by domesic households, while foreign currency funds come from boh domesic households and abroad. For he laer caegory of funds a premium, influenced also by exogenous shocks, is paid over he corresponding exernal ineres rae. The cenral bank ses he domesic moneary policy rae according o a Taylor rule. The fiscal auhoriy collecs axes, demands governmen goods from he corresponding producers and uses lump sum ransfers owards households o keep he budge balanced. We model he foreign secor as a wo counry (Euro area and US) open economies new Keynesian semi-srucural model, wih he price of oil in USD included, as an exogenous process. 8

9 Figure : Srucure of he model 9

10 . Producion secor Domesic inermediae goods, produced using capial services (provided by enrepreneurs borrowing in domesic and foreign currencies), labor supplied by households and impored oil, are combined wih di eren impored inpus, oher han oil, in order o produce (privae and governmen) consumpion, invesmen and expor goods demanded by households, governmen, capial producers and foreign expor reailers. A Dixi-Sigliz compeiive monopolisic framework is used in order o inroduce price sickiness for impored, inermediae domesic, consumpion and expored goods... Domesic producers A represenaive firm, operaing in a perfecly compeiive environmen, aking he price of oupu (P )andinpus(p i, ) as given, combine imperfecly subsiuable domesic goods ino a homogeneous good using he following consan elasiciy of subsiuion echnology: applez Y = Y i, d di d () where apple d < is he markup in he domesic goods marke. The profi maximizaion problem of he represenaive, domesic goods aggregaing (reailer) firm is: Z max Y = P Y P i, Y i, di () Y i, Solving he above problem resuls in he following demand schedule for any individual domesic inermediae good i: d P d Y i, = Y (3) P i, where Y is a shifer in he demand for Y i,. Given he demand equaion derived above and perfec compeiion in he final good marke, he resuling relaion beween he aggregae price index of he reailer and he prices of individual domesic goods is: applez P = P d i, di ( d) Each di ereniaed inermediae good is produced by monopolisic compeiive firms, indexed by i [, ], using he following echnology: Y i, = (! o ) o o o VA i, +! o o Oil m i, o o o o (4) z + (5) wih: VA i, = (z H i, ) (K i, ) (6) For simpliciy, we will coninue o refer o his ype of goods as domesic (inermediae) goods, alhough impored oil and par of he capial ha is financed by loans in foreign currency are used in is producion.

11 and K i, = apple (! k ) / k K DC i, k k +(! k ) / k K FC i, k k k k (7) where: VA i, is value added in he economy having a (! o )shareingrossoupuy i, ; Oil m i, is impored oil enering he producion of domesic inermediae good wih share! o ; o is he elasiciy of subsiuion beween impored oil and value added; H i, represen homogeneous labor services used by firm i, wih share ( ) (, ) in oal value added; K i, are aggregae capial services rened from enrepreneurs having a share (, ) in value added; Ki, DC are capial services rened from enrepreneurs borrowing in domesic currency (DC), wih! k (, ) represening heir mass in he producion of aggregae capial services; Ki, FC are capial services rened from enrepreneurs borrowing in foreign currency (FC), wih! k (, ) represening heir mass in he producion of aggregae capial services; k represens he elasiciy of subsiuion beween capial services caegories 3 ; is a saionary produciviy shock; z + is he aggregae echnology shock, represening a combinaion of invesmen ( ) and neural uni-roo (z )echnologyshocks z + = z ( ) ; is a fixed cos ha grows wih he aggregae echnology rae and makes possible o impose zero profis in seady sae, hence being consisen wih he no enry or exi assumpions. Any individual inermediae goods producer acs compeiively on facor markes, solving he following cos minimizaion problem: K DC i,,kfc i, min,h i,,oil m i, W R f H i, + subjec o (5), (6) and (7), where: 3 Since all enrepreneurs are idenical K DC i, r DC,k P i, Ki, DC + =! k K DC,enrep. i, r FC,k P i, Ki, FC + P m,oil Oili, m (8) and K FC i, =(! k )K F C,enrep. i,.

12 W R f H i, represen he labor coss of he firm adjused in his case by R f ha reflecs he presence of a working capial channel, in which firms finance in advance par of heir wage bill by loans, wih R f = f R + f where R is he gross nominal ineres rae and f is he proporion of he wage bill ha is financed in advance 4 ; R j,k K j i, are he coss wih he rened capial services, wih rj,k gross nominal renal rae scaled by P i,, where j {DC, FC}; being he associaed P m,oil Oili, m is he cos wih oil inpu. The firs order condiions associaed wih he above opimizaion problem are: H i, : W R f =( )mc P i, VA i, H i, 6 4 (! o ) (! o ) o o o VA i, +! o o VA i, Oil m i, o o o o o K DC i, : r DC,k = mc VA i, K i,!k K i, Ki, DC 6 k 6 4 (! o ) (! o ) o o o VA i, +! o o VA i, Oil m i, o o (9) o o o K FC i, : r FC,k = mc VA i, K i, (!k ) K i, Ki, FC 6 k 6 4 (! o ) (! o ) o o o VA i, +! o o VA i, Oil m i, () o o o o o Oili, m : P m,oil P i, = mc 6 4! o (! o ) o o o VA i, +! o o Oil m i, Oil m i, o o o o o () () plus he producion funcion (5) associaed wih he FOC wih respec o he Lagrange muliplier. In he above expressions, mc represens he real marginal cos (whereas mc P i, is he nominal marginal cos and also he associaed Lagrange muliplier). Solving he above equaions for mc yields: mc = apple d (! o ) Pi, VA P i, o +(!o ) P m,oil i, o o 4 Similar wih Chrisiano e al. (5), he presence of he working capial channel is necessary o accommodae he empirical evidence according o which prices may rise afer a hike in he moneary policy rae given ha firms finance par of heir variable inpus by shor erm loans. (3)

13 where Pi, VA is defined as: P VA i, P i,! W R f apple! k B ( ) P i, r DC,k k +(!k ) r FC,k k k C A (4) where, as Chrisiano e al. () poin ou, d acs like a ax shock (markup shock in he linearized version of he model) ha is no presen in he producion funcion. Each firm exercises monopolisic power over is produc, given he demand coming from he aggregaing firm. Price seing a firm level is modeled in a ime dependen fashion à la Calvo. Therefore, wih probabiliy d, each firm can reopimize is price, wih he implied duraion of price quoaion being d. Wih complemenary probabiliy d firms canno reopimize and index heir price o a combinaion of las period inflaion and curren cenral bank s inflaion arge given by: P i, ( ) apple d ( c ) apple d P i, (5) where apple d measures he degree of indexaion o las period inflaion ( ), wih he complemenary probabiliy reflecing he indexaion o he curren inflaion arge ( c ). Firms ha reopimize heir prices choose he new price o maximize he presen discouned value of profis, ha is: E X j= j +j[p i,+j Y i,+j mc +j P +j Y i,+j ] (6) subjec o he demand given by (3), where +j is he Lagrange muliplier from household s opimizaion problem, reflecing heir ownership of firms 5. Domesic homogeneous goods are used in he producion of governmen, consumpion, invesmen and expor goods. An imporan noe should be made here: in a model wihou oil enering he producion of domesic inermediae goods, Y is usually considered as a proxy for he gross domesic produc. In our case, VA represens he gross value added, while a naional accouns consisen definiion of GDP is presened in secion Imporers Imporing secor comprises of four ypes of firms ha buy a homogeneous good from foreign markes and di ereniae i ino consumpion goods, C m i,, invesmen goods o be finally used by capial producers, I m i,, and expor goods, X m i,, before monopolisically supplying hem o he corresponding reailers, wih he laer operaing in a perfecly compeiive environmen. As for impored oil goods, Oil m i,, used in he final sage by he inermediae domesic goods producers, he price of he homogenous good is se in USD. We describe he problem generically for a firm belonging o caegory, where {C, I, X, Oil}. 5 The deailed derivaion of he price seing problem and he associaed firs order condiions are presened in he Appendix of Chrisiano e al. (). 3

14 Again, he producion funcion of he domesic reailer of impored goods ha operaes in a perfecly compeiive environmen is shown in (7), wih he demand schedule for any individual impored good i resuling from he profi maximizaion problem being given by (8). applez m = m i, m, di m, (7) m i, = m! P m, m, m, (8) P m, i, The associaed marginal cos for he individual firm imporing quaniy m i, is: NMC m, = m, S ef P R, (9) where m, behaves again like a markup shock ha does no appear in he producion funcion; S ef is he e ecive 6 nominal exchange rae; P is he e ecive foreign price level and R, represens he e ecive nominal ineres rae paid by firms given he presence of a working capial channel. The expression for R, is given by: R, = R + () where R is he e ecive foreign nominal ineres rae and is he proporion of inpus ha is financed in advance by loans aken in foreign currency. For oil impored producs, is assumed o be zero, while he exernal price is se in US dollars. Thus, he associaed individual marginal cos is given by: NMC m,oil = m,oil Toal value of impors for firms belonging o caegory is: wih he similar quaniy for oil being defined as: S RON/USD P oil,usd () S ef P R, m () S RON/USD P oil,usd Oil m (3) The price seing problems of he imporing firms are similar wih ha of he inermediae goods producers. Consequenly, each firm producing good m i, exercise monopolisic power over is produc, given he demand coming from he domesic reailer of impored goods. Firms ha canno reopimize heir price, index i o a combinaion of las period inflaion and curren cenral bank s inflaion arge given by: P m, i, m, applem, ( c ) apple m, P m, i, (4) 6 E ecive variables are a combinaion of EUR and USD relaed variables, as defined in secion.8. 4

15 where apple m, measures he degree of indexaion o las period inflaion m,, wih he complemenary probabiliy reflecing he indexaion o he inflaion arge ( c ). Wih probabiliy m,, each firm can reopimize is price in order o maximize he presen discouned value of profis, ha is: E X j= j +j[p m, i,+j m i,+j m, +j Sef +j P +jr, +j m i,+j] (5) subjec o he demand given by (8), where +j is he Lagrange muliplier from household s opimizaion problem, reflecing heir ownership of firms. The firs order condiions associaed wih he price seing problem are presened in he Appendix of Chrisiano e al. (). Again, whenever he case, for oil he problem should ake ino accoun ha he foreign currency price is in US dollars and no working capial channel is assumed. A noe should be made regarding he currency in which impor or expor prices are se. The approach presened here assumes, boh for expors and impors, local currency pricing (i.e. prices are se in he currency of he counry where goods are consumed) insead of producer currency pricing (i.e. prices are se in he currency of he producer). This approach, ogeher wih price rigidiy in a monopolisic environmen, generaes an imperfec pass-hrough of (presen and expeced) exchange rae changes in expor and impor prices, wih more rigid prices resuling in a lower pass-hrough of exchange rae variaions, hrough he impac on marginal cos, on impor and expor prices inflaion 7. Excep he oil impored producs ha are used as inpus in he producion of domesic inermediae goods as described in secion.., he nex sage of he producion process implies assembling domesic homogeneous and impored goods from reailers ino final goods. This is done by perfecly compeiive firms operaing in he invesmen secor. The supply of final goods mees he demand coming from capial goods producers. As for he consumpion and expor impored goods, hese are supplied by reailers o a coninuum of final goods producers, as described in he following secions...3 Consumpion goods producers In consrucing he consumpion goods secor, we depar from Chrisiano e al. () by inroducing wo sages of producion, whereas in heir seup he final consumpion was produced by a represenaive compeiive firm ha combined homogenous domesic inermediae goods and homogenous impored consumpion goods using CES echnology 8. We adaped he framework, following closely de Casro e al. (), in order o accoun for a feaure of he Romanian economy, namely he exisence of a relaively high share of goods and services wih adminisered prices in he CPI baske. These include elecriciy, naural gas, heaing, some pharmaceuical producs and accoun for approximaely a fifh of he CPI baske. Romania agreed wih he European Commission o gradually deregulae prices 7 Alhough empirically prices are more rigid in developed economies compared wih emerging ones, Zorzi e al. (7) do no find significan di erences regarding exchange rae pass-hrough on impor and consumer prices beween hese groups of counries. 8 The wo sages of producion are presen also in Chrisiano e al. () for he expor secor, as explained in secion..6. 5

16 for elecriciy and naural gas in he coming years. Therefore, he calendars for deregulaion provide valuable informaion wih respec o he fuure evoluion of adminisered prices. The inroducion of he adminisered prices provides also a echnical advanage when using he model for forecasing, by allowing he forecas o be condiioned on he informaion from he deregulaion calendars. In he firs sage of producion, a coninuum of producers indexed by i [, ] combine homogenous domesic inermediae goods and homogenous impored consumpion goods using CES echnology, resuling in a range of di ereniaed consumpion goods C i, : C i, = n (! c ) / c C d i, c c +(! c ) / c C m i, o c c c c (6) where! c is he share of impored consumpion goods (Ci,), m and c is he elasiciy of subsiuion beween inpu goods. The cos minimizaion problem gives he demands for inpus as follows: NMC Ci, d c c =(! c ) C i, (7) NMC Ci, m c c =(! c ) P m,c C i, (8) Again, NMC c is he nominal marginal cos, wih he real one being given by: mc c = NMCc P c = P n o (! c ) P c +(! c )(P m,c ) c c In he second sage, he final consumpion goods C are produced by a represenaive, compeiive reailer using he di ereniaed consumpion goods C i, : P c applez C = (C i, ) c c di The opimizaion problem of he reailer yields he demand funcion for individual consumpion goods and he consumpion price: P c C i, = i, P c (9) (3) c c C (3) applez P c = P c i, ( c) c di (3) Wih he aim of aking ino accoun he exisence of adminisered prices, we follow de Casro e al. () and consider wo ypes of individual consumpion goods producers, wih fracions! adm and (! adm ), di ering only wih respec o heir price seing behavior. Following he NBR erminology, we refer o he non-adminisered prices as CORE prices, 6

17 having a (! adm )weighinhecpibaske,andoheirproducersascoreproducers, indexed by i [! adm, ]. They exercise monopolisic power over heir produc, given he demand coming from he reailer. We model heir price seing process à la Calvo, wih c represening he probabiliy ha firms canno reopimize heir prices. In his laer case, each producer i [! adm, ] indexes is las period price (Pi, core ) by a weighed average of las period inflaion ( c ) andcurren cenral bank s inflaion arge given by: P core i, c apple c ( c ) applec P core i, (33) Each firm ha has he possibiliy o rese heir price chose i so as o maximize he presen discouned value of is profis, given by: E X j= j +j[p core i,+j NMC c +j]c i,+j (34) subjec o he demand given by (3), where +j is he Lagrange muliplier from household s opimizaion problem, reflecing heir ownership of firms. The firs order condiions associaed wih he price seing problem are analogous o he ones for domesic inermediae and impored goods price seing problems. Similar o he seup in de Casro e al. (), he! adm fracion of consumpion good producers, indexed by i [,! adm ], are unable o chose heir prices opimally, bu follow an exogenous pricing policy. In each period, wih probabiliy adm, firms wih adminisered prices index heir price wih he curren cenral bank inflaion arge: P adm i, whereas wih complemenary probabiliy wih he following indexaion facor: c P adm i, (35) adm hey are allowed o index heir prices adm ( c ) 4 adm " 4 q q 5 v adm mc c mc c 5 # v adm adm p core p c adm Z adm adm (36) where 4 = Q 4 j= c j is he annual inflaion rae, q /q 5 is he annual change in real e ecive exchange rae, mc c /mc c 5 is he annual change in he real marginal cos of consumpion goods producers, p core /p c is he relaive price of CORE goods o consumpion goods price. Z adm is an AR() process, accouning for unexpeced shifs in adminisered prices, while adm,vadm,v adm are parameers governing he indexaion rule. The specificaion of he rule is inended o capure he backward-looking naure of he adminisered price dynamics, while a he same ime allowing for influence from he real exchange rae and he real marginal cos. The adminisered price index is defined as: P adm! adm Z!adm P c i, c c di (37) 7

18 The expression yields furher he equaion for adminisered price inflaion: apple adm = ( adm ) adm c + adm ( c ) c c (38) Given (3), we express overall CPI index as a weighed average of CORE index and adminisered price index: apple P c =! adm P adm c +(! adm ) P core wih he corresponding inflaion rae being defined as: c = P c, where P P c core aggregae CORE price index...4 Invesmen goods producers c c (39) is he The producion funcion of invesmen goods used by a represenaive compeiive firm is given by: I + INV + a DC (u DC )! KDC k + a FC (u FC )(! k ) = n(! i ) / i I d i o i i +(! i ) / i (I m ) i i wih facor demands given by: K FC i (4) I d =(! i ) P i i I + P INV + a DC (u DC )! KDC k + a FC (u FC )(! k ) FC K (4) I m =! i P i i P m,i I + INV + a DC (u DC )! KDC k + a FC (u FC )(! k ) FC K where:! i is he share of impored invesmen goods; i is he elasiciy of subsiuion beween inpu goods. Toal invesmen, ha is, I + INV + a DC (u DC )! KDC k + a FC (u FC FC )(! k ) K, is made of: I -invesmengoodspurchasedoincreasehesockofphysicalcapial; INV -changeininvenories; - an invesmen specific permanen echnology shock; (4) a DC (u DC capial ( )! KDC k DC K + a FC (u FC )(! k ) and )mainenance. K FC FC K, represening he goods used for physical 8

19 The inroducion of INV is moivaed by he need o reconcile he model consrains wih he naional accouns GDP daa. I is exogenously deermined, by assuming ha he share of invenories in I,hais inv = INV I, follows an AR() process. inv = inv inv + inv inv + " inv, (43) Chrisiano e al. () inroduce an uni roo (wih drif) shock,, ha capures he decline in he relaive price of invesmen goods. In order o have a balanced growh pah (in nominal erms), he decline in he relaive price of invesmen needs o have a counerpar given by he assumpion ha he growh rae of invesmen in real erms is higher han ha of he oher (demand defined) GDP componens (i.e. µ z +,) byexaclyhegrowh rae of, ha is: µ,. Also, capial uilizaion rae, uj, is defined as u j = Kj, whereas K j a j (u j )represenshecorrespondinguilizaioncosfuncion,asdefinedinsecion.4,wih j {DC, FC}. Replacing he above facor demands in he producion funcion resuls in he following relaion beween prices: P i = n (! i ) P i +(! i ) P m,i wih he corresponding inflaion rae being defined as: i = P i. P i..5 Capial producers i o i (44) There is a large, fixed number, of idenical and compeiive capial goods producers. They combine invesmen goods and old capial in order o produce new insalled capial, using he following echnology: x I = x + F (I,I, )=x + S I (45) where is a marginal e ciency of invesmen (MEI) shock as in Jusiniano e al. () and S is an invesmen adjusmen coss funcion as in Chrisiano e al. (5). Taking ino accoun ha he price of old and new capial is he same given he uni value of he marginal rae of ransformaion, he ime profis for hese producers are: k = P P k, applex + S I I I Each capial producer solves he following maximizaion problem: ( ) X n max E +n k +n I +n,x +n n= I P P k, x P i I (46) where E is he ime condiional expecaion, is he muliplier in household s budge consrain. Seing x +n =( ) K +n in he above maximizaion problem is consisen wih profi maximizaion (in fac any value of x is profi maximizing) and marke clearing, (47) 9

20 resuls in he following opimaliy condiion linking he price of insalled capial and he price of invesmen goods: I : apple P i + P P k, S I I + I S I I (48) E + P + P k,+ + S I+ I I I = wih he aggregae sock of physical capial evolving according o he following accumulaion equaion: K + =! k KDC + +(! k ) K FC + =( )! k KDC +(! k ) FC I K + S I I (49) where! KDC k + is aggregae physical capial demanded by enrepreneurs borrowing in FC domesic currency, while (! k ) K + is he similar measure for hose enrepreneurs ha borrow in foreign currency...6 Exporers Similar o consumpion producers, here are wo sages in he producion of expors. Firs, monopolisic expor producers develop a range of di ereniaed goods using as inpus domesic goods and impors used in he producion of expors. While acing compeiively on facor markes, each firm exercise monopolisic power over is produc, given he demand coming from he expor reailer. Second, he reailer assembles individual expor goods (X i, )inoahomogeneousexporgood(x ), meeing he demand of foreigners. The laer variable is defined as: where: P foreign GDP; P x X = P x f Y P (5) is he e ecive foreign price index for homogeneous goods; Y is e ecive is he e ecive price index (in foreign currency) of expors and f represens he elasiciy of foreign demand for domesic expors. The reailer operaes in a perfecly compeiive seup, using a Dixi-Sigliz aggregaor given by: applez X = (X i, ) x x di wih he resuling demand for individual expor goods and he expor price index being: P x X i, = i, P x (5) x x X (5)

21 applez P x = P x x i, di ( x) The producion funcion of he i h specialized exporer is given by: X i, = n (! x ) / x X d i, x x +(! x ) / x X m i, o x x x x (53) (54) wih he following demands for inpus resuling from he cos minimizaion problem: NMC Xi, d x x =(! x ) X x R x i, (55) P NMC X m,x x x i, =(! x ) x R x P m,x X i, (56) where x behaves again like a markup shock ha does no appear in he producion funcion;! x is he share of impored goods used in he producion of expors (X i, ); R x represens he gross nominal ineres rae paid by exporing firms given he presence of a working capial channel. The expression for R x is given by: R x = x R + x (57) where R is he domesic nominal ineres rae and x is he proporion of inpus ha is financed in advance by loans aken in domesic currency. NMC x is he nominal marginal cos in he cos minimizaion problem, wih he real marginal cos being defined as mc x = NMCx S P and having he following represenaion: x mc x = x R x n o (! S P x x ) P x +(! x )(P m,x ) x x (58) Inegraing (55) and (56) over he (,) coninuum of specialized exporers resuls in he aggregae demand of he exporing secor for domesic inermediae and impors used in he producion of expors goods. Each exporer exercise monopolisic power over is produc, given he demand coming from he aggregaing firm. Again, (local currency) price seing a firm level is modeled in a ime dependen fashion à la Calvo, wih x represening he probabiliy ha firms canno reopimize heir prices. In his laer case, hey index heir las period price (Pi, x ) bya weighed average of las period inflaion ( x ) andseadysaeinflaionofexpors( x, assumed equal wih he seady sae value of foreign inflaion, given ha prices are se in foreign currency) given by: P x i, x apple x ( x ) applex P x i, (59) Wih probabiliy x exporers reopimize heir prices and choose he new price o maximize he presen discouned value of profis, ha is:

22 E X j= subjec o he demand given by (5). j +j[p x i,+jx i,+j mc x +jp x +jx i,+j ] (6).3 Banks Banks are imporan in he model, as hey represen he inermediary hrough which financial ransacions beween agens ake place. In modeling he financial secor we depar from Chrisiano e al. () in he following wo dimensions: firs, we assume here are wo ypes of enrepreneurs according o he currency denominaion of he loan hey ake from he banks: hose ha borrow in domesic currency (DC) represening a fracion! k of he oal populaion of enrepreneurs and hose borrowing in foreign currency (FC) represening he remaining fracion,! k. All he foreign currency ransacions ha go hrough he financial secor are assumed o be in euros. I is also assumed ha each ype of enrepreneurs deals wih a specific bank an here is no ransiion from one ype o he oher for boh enrepreneurs and banks. second, here are wo ypes of (consolidaed) banks: one ype operaes enirely using domesic currency, while he oher one uses only foreign currency producs. The laer (! k )unismakeriskyloansoenrepreneursborrowinginforeigncurrency,while he remaining! k deal wih enrepreneurs borrowing in domesic currency, each ype using a financial conrac as described in secion.4. Banks operaing wih domesic currency raise deposis from domesic households and channel he funds owards he corresponding enrepreneurs. On he oher hand, banks dealing wih foreign currency funds raise deposis in foreign currency from domesic households and from abroad 9 and channel hem owards he enrepreneurs borrowing in foreign currency. Households savings in domesic currency are remuneraed a he deposi rae (assumed here, given he absence of oher fricions, equal wih inerbank ineres rae. As for foreign currency funds, hey are remuneraed wih a foreign ineres rae, indexed wih a risk premium. A perfecly compeiive environmen is assumed for banks. A ime, bank i operaing wih domesic currency funds collecs deposis, D+(i), DC from domesic households a cos R and channels hem owards he corresponding enrepreneurs in form of a loan L DC +(i). As for each bank i operaing wih foreign currency denominaed funds, i collecs deposis D+(i) FC from abroad and domesic households, a cos R EUR, lending he funds L FC +(i) owards he corresponding enrepreneurs. Boh when aracing and lending foreign currency denominaed funds, banks pay/receive an ineres rae ha is adjused wih a risk premium. In his simple seup financing in foreign currency from abroad or from domesic households 9 Foreign borrowing can be hough here in erms of ne foreign liabiliies. In he absence of oher fricions, i is assumed here ha he moneary auhoriy manages he liquidiy on he inerbank marke such ha he inerbank ineres rae is equal wih he moneary policy ineres rae.

23 are assumed o be perfec subsiues D FC,hh + (i)+fb + (i). However, his does no necessarily mean ha he wo componens are no idenifiable. Toal deposis in foreign currency resul from he corresponding enrepreneurs problem, while exernal financing (FB + )represensheexernalliabiliiesofhedomesiceconomy,havingalawofmoion derived from he balance of paymens ideniy. The foreign currency deposis of he households are rerieved as residual. The Bernanke e al. (999) ype of financial conracs beween banks and enrepreneurs for boh domesic and foreign currency denominaed loans are described in deail in secion Equilibrium in he financial secor Marke clearing condiions for deposis: Z D DC +(j)dj =DeposisupplyinDC (6) =DeposidemandinDC= Z!k D DC +(i)di =! k D DC + (6) Z D FC,hh + (j)dj + Z FB + (j)dj = Deposi supply in FC (63) Z =DeposidemandinFC= D+(i)di FC =(! k Marke clearing condiions for loans beween banks and enrepreneurs:! k )D FC + (64)! k D DC + =SupplyofDCloans =DemandofDCloans= Z!k L DC +(i)di =! k L DC + (! k )D FC + =SupplyofFCloans =DemandofFCloans= Z L FC +(i)di =(! k! k )L FC +.3. Furher developmens in modeling he banking secor There are a number of simplifying assumpions made ha can be relaxed/modified in order o furher develop he banking side of he model. For example, perfec compeiion was assumed for banks. One can insead proceed along he ways presened in Gerali e al. (), separae each (consolidaed) bank in deposi and lending unis and assume ha deposi unis 3

24 operae, when dealing wih reail cliens, in a monopolisic compeiion environmen. In his way, one can sudy how he ineres rae pass-hrough a ecs he ransmission of moneary policy shocks in he economy. Anoher assumpion regards he lack of an explici role for bank capial in he model. Again, he model can be adaped along he lines of Gerali e al. () in order o have a role for bank equiy in a ecing loan supply condiions. Furhermore, he ineracion of banks in he inerbank markes can be exended o allow, for example, for deparures of he inerbank ineres raes from he policy rae given he liquidiy managemen policy of he cenral bank. Las bu no leas, minimum reserve requiremens, boh for domesic and foreign currency deposis, can be inroduced in he model, as addiional policy ools. One can proceed in a simple way and assume ha reserves kep a he cenral bank are remuneraed wih a zero ineres rae and ha commercial banks keep no excess reserves wih he moneary auhoriy. Boh hese assumpions, wih he firs one being, a leas for emerging economies, sronger han he second one, can be relaxed, for example, along he lines presened by Glocker and Towbin ()..4 Enrepreneurs Chrisiano e al. () inroduce financial fricions in he model using he purely asymmeric informaion and cosly sae verificaion model of Bernanke e al. (999), as implemened by Chrisiano e al. (3). Considering he exisence of asymmeric informaion (i.e. he individual enrepreneur observes he individual projec reurn afer operaing he projec, while he bank does no observe i), a classic equilibrium concep canno be used given ha he demand for loans would be infinie for any ineres rae. Therefore, one needs o rely on an equilibrium concep based on a sandard nominal deb conrac beween banks and enrepreneurs ha specifies boh an ineres rae and a loan amoun. The main di erence compared wih he approach presened by Chrisiano e al. () is ha we assume here are wo ypes of enrepreneurs according o he currency denominaion of he loan hey ake from banks: hose ha borrow in domesic currency (DC) represening a fracion! k of he oal populaion of enrepreneurs and hose borrowing in foreign currency (FC, euros in our case) represening he remaining fracion,! k. Unsal (3) evaluaes he impac of macroprudenial policies in a calibraed wo counry model in which enrepreneurs from he smaller economy borrow in domesic or foreign currency. However, relaive o our approach, he raio of enrepreneurs borrowing in domesic relaive o hose borrowing in foreign currency is undeermined in his model, while in our model is calibraed o mach he empirical observed domesic o foreign currency raio of new loans o nonfinancial insiuions. Moreover, he does no ake ino accoun he imperfec subsiuion beween capial (services) provided by enrepreneurs o he inermediae domesic goods However, in a Bernanke e al. (999) conex, as he one presened here, some of he enrepreneurs can be viewed as financial firms. Dib (a) and Dib (b) allow for an explici role for (cosly o raise) bank capial ha is subjec o regulaory requiremens. They inroduce in he spreads he enrepreneurs face a componen reflecing he impac of (macroprudenial) regulaion. Furhermore, he model is evaluaed wih di eren Taylor rules, some of hem incorporaing financial variables (e.g. he deviaion of credi from is seady sae value). 4

25 producers. Regarding he laer aspec, our approach is similar wih ha of Verona e al. (), which exends he model of Chrisiano e al. () wih a shadow banking sysem. As menioned before, i is also assumed ha each ype of enrepreneurs deals wih specific banks an here is no ransiion from one ype o he oher for boh enrepreneurs and banks. Inside each ype (DC or FC), a any poin in ime, here are enrepreneurs wih all di eren levels of ne worh and for every level of ne worh here is a su cienly large mass of enrepreneurs ha experience a cerain produciviy shock and deal wih a specific bank. As menioned before, banks are perfecly compeiive and borrow he funds from households (domesic for deposi unis dealing wih enrepreneurs borrowing in domesic currency and domesic and foreign 3 for hose borrowing in foreign currency) a nominally non coningen ineres raes. There is free enry and no risk for each ype of banks, so here is no problem in being able o pay R /R EUR back, since i is assumed ha banks of each ype, alhough hey do no know which enrepreneurs are going o pay back heir loans and which no, are dealing wih a su cienly large number of enrepreneurs. Now, alhough each bank observes he average reurn across enrepreneurs, in order o observe he individual ex pos reurn i has o pay a monioring cos ha is proporional o he asses he bankrup enrepreneur has afer he idiosyncraic shock was realized 4. The cosly sae verificaion echnology also implies ha enrepreneurs ha canno pay back heir loans ruly reveal 5 heir sae o he banks and urn over all heir resources..4. The individual enrepreneur Figure, adaped from Chrisiano e al. (), presens he iming of evens inside a ime period ( +)foranenrepreneurbelongingoaclasswihacerainlevelofneworhn belonging o any of he wo ypes assumed, j {DC, FC}. For each ype of enrepreneurs, a he end of period, he enrepreneurs from a class wih a cerain level of ne worh, ha is N DC or N FC, buy new physical insalled capial from capial producers in a compeiive marke a price P P k,. Enrepreneurs access loans o cover he par of acquisiion cos of capial ha remains afer self-financing occurs, wih he amoun of demanded loans being given by: L DC,NDC + = P P k DC,NDC, K + N DC,NDC + S RON/EUR L FC,NFC + = P P k FC,NFC, K + N FC,NFC + (65) where: L DC,NDC + are domesic currency loans; S RON/EUR L FC,NFC + are foreign currency loans, expressed in domesic currency. As i can be observed from he las equaion, 3 The source of foreign borrowing is no specifically modeled. I is assumed here ha he ulimae source of hese funds are foreign households. I can as well be foreign banks, muual funds, ec. wihou any di eren impac on he behavior of he model. 4 Anoher way o deal wih monioring coss, which in he discussed framework can be hough of reflecing he liquidaing coss of he bankrup enrepreneur, is o assume ha hey are proporional o he asses of he enrepreneur before he idiosyncraic shock is realized. 5 There is no incenive for enrepreneurs no o repor he rue realizaion of he idiosyncraic produciviy shock since he repor is irrelevan when he realizaion is above he cuo produciviy level, while he resources urned when he produciviy is below cuo are lower in value han he ineres paymens one would make by reporing an above cuo level of realized individual produciviy. 5