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1 DANMARKS NATIONALBANK WORKING PAPERS 3 88 Jesper Pedersen and Søren Hove Ravn Danmarks Naionalbank Wha Drives he Business Cycle in a Small Open Economy? Evidence from an Esimaed DSGE Model of he Danish Economy December 3

2 The Working Papers of Danmarks Naionalbank describe research and developmen, ofen sill ongoing, as a conribuion o he professional debae. The viewpoins and conclusions saed are he responsibiliy of he individual conribuors, and do no necessarily reflec he views of Danmarks Naionalbank. As a general rule, Working Papers are no ranslaed, bu are available in he original language used by he conribuor. Danmarks Naionalbank's Working Papers are published in PDF forma a A free elecronic subscripion is also available a his Web sie. The subscriber receives an noificaion whenever a new Working Paper is published. Please direc any enquiries o Danmarks Naionalbank, Communicaion Desk, Havnegade 5, DK-93 Copenhagen K Denmark Tel.: (direc) or Fax : [email protected] Naionalbankens Working Papers beskriver forsknings- og udviklingsarbejde, ofe af foreløbig karaker, med henblik på a bidrage il en faglig deba. Synspunker og konklusioner sår for forfaernes regning og er derfor ikke nødvendigvis udryk for Naionalbankens holdninger. Working Papers vil som regel ikke blive oversa, men vil kun foreligge på de sprog, forfaerne har brug. Danmarks Naionalbanks Working Papers er ilgængelige på Inernee i pdf-forma. På websede er de mulig a opree e grais elekronisk abonnemen, der leverer en noifikaion ved enhver udgivelse af e Working Paper. Henvendelser kan rees il : Danmarks Naionalbank, Kommunikaion, Havnegade 5, 93 København K. Telefon: (direke) eller [email protected] De er illad a kopiere fra Naionalbankens Working Papers - såvel elekronisk som i papirform - forudsa, a Danmarks Naionalbank udrykkelig anføres som kilde. De er ikke illad a ændre eller forvanske indholde. ISSN (ryk/prin) 6-85 ISSN (online) 6-93

3 Resumé Esimerede DSGE-modeller er bleve e vigig redskab for empirisk fundere makroøkonomisk analyse gennem de senese år. I denne arikel præseneres en esimere DSGE-model for Danmark. Modellen er esimere ved hjælp af Bayesianske meoder basere på e daasæ besående af 3 makroøkonomiske variable. Modellen anvendes i ariklen il a idenificere de vigigse bidragsydere il konjunkurudsvingene i dansk økonomi. Resulaerne indikerer, a sød il udlande forklarer mere end 5 pc. af udsvingene i dansk BNP. Eksempelvis var de økonomiske ilbageslag, som rame Danmark i kølvande på den finansielle krise i 8, i høj grad dreve af udenlandske fakorer. Udviklingen i udlande spillede også en vigig rolle i årene op il krisen. Indenlandske fakorer bidrog dog også i sor omfang il de krafige økonomiske opsving i Danmark i disse år, mens finanspoliikken ikke var ilsrækkelig sram gennem opsvinge.

4 Wha Drives he Business Cycle in a Small Open Economy? Evidence from an esimaed DSGE Model of he Danish Economy Jesper Pedersen Danmarks Naionalbank and Universiy of Copenhagen Søren Hove Ravn Danmarks Naionalbank and Universiy of Copenhagen December 3 Absrac Esimaed DSGE models have become he sandard workhorse model for empirically based macroeconomic analysis in recen years. In his paper, we presen an esimaed DSGE model for Denmark. The model has been esimaed using Bayesian mehods and a daase consising of 3 macroeconomic variables. We use he model o idenify he mos imporan deerminans of business cycle flucuaions in Denmark. Our resuls indicae ha foreign shocks explain more han 5 pc. of he variaion in Danish real GDP. As an example, he recession ha hi Denmark in he wake of he recen financial crisis was o a large exen caused by foreign facors. Shocks originaing abroad also played an imporan role in he build-up o he crisis. However, domesic facors also conribued subsanially o he boom in Danish GDP in he years before he crisis, while fiscal policy was no suffi cienly conracionary during he boom. JEL classificaion: C, E7, E7, E3. Keywords: DSGE Models, Small Open Economies, Bayesian Esimaion. The auhors hank John Smid for many valuable commens and suggesions, and seminar paricipans a Danmarks Naionalbank, Sveriges Riksbank, and Norges Bank for useful discussions. The views expressed in his paper are hose of he auhors, and do no necessarily correspond o hose of Danmarks Naionalbank. Address: Danmarks Naionalbank, Havnegade 5, 93 Copenhagen, Denmark. [email protected]. Address: Danmarks Naionalbank, Havnegade 5, 93 Copenhagen, Denmark. [email protected].

5 Inroducion Over he las decade, a large number of policy insiuions have adoped a class of srucural models for forecasing and policy analysis. These so-called Dynamic, Sochasic General Equilibrium (DSGE) models mosly derive from he New-Keynesian radiion (see Woodford [3] or Galí [9] for exbook reamens), and are hus in accordance wih sae-of-he-ar academic research in macroeconomics; see e.g. Blanchard [9]. Following Smes and Wouers [3] and Smes and Wouers [7], he models are ypically esimaed wih Bayesian echniques. In recen years, he DSGE models of many insiuions have been improved hrough he addiion of a number of empirically relevan feaures, mos noably fricions in he labor marke (e.g., Galí e al. []) and in financial markes (e.g., Chrisiano e al. []). As a resul, a number of cenral banks now use esimaed DSGE models as heir primary ool for forecasing and policy analysis. In conras, in Denmark here is a longsanding radiion of using largescale macroeconomeric models for hese purposes. This includes he MONA model of Danmarks Naionalbank, he ADAM model developed by Saisics Denmark and used by he Minisry of Finance, and he SMEC model of he Danish Economic Councils. While he use of similar models in differen policy insiuions has a number of advanages in erms of ransparency, communicaion, and model developmen, radiional macroeconomeric models come wih a se of problems on heir own. One is he lack of forward-looking behaviour by privae agens, anoher is he exposure of hese models o he Lucas [976] criique. This criique is paricularly relevan when using he models for policy analysis, and less so when i comes o forecasing. In addiion, he vas majoriy of academic research in he field of moneary macroeconomics uses DSGE models as he heoreical workhorse, whereas macroeconomeric models have largely disappeared from he research agenda over he las couple of decades. In his paper, we presen an esimaed DSGE model of he Danish economy. The model builds on recen academic research as well as on models developed by oher cenral banks. We model Denmark as a small open economy as in Gali and Monacelli [5]. While he exchange rae is fixed owards he eurozone, reflecing Denmark s currency peg, we allow for flucuaions in he exchange rae owards he res of he world. Moreover, he model feaures a fairly deailed descripion of fiscal policy, which is he cenral sabilizaion ool in he Danish economy. Finally, we model labor marke fricions following Galí e al. [], inroducing a role for involunary unemploymen. The model is esimaed using Bayesian echniques. The esimaed parameer values are generally in line wih esimaes from similar sudies. To validae he model, we compare he esimaed impulse responses from he model o impulse responses esimaed from srucural VAR models of he Danish economy. We find ha he impulse responses from he DSGE model o shocks o domesic A non-exhausive lis includes he Riksbank, Norges Bank, and he Bank of England. One noable excepion is he DREAM model, which is, however, mainly a model for he long run.

6 governmen spending and o foreign oupu are roughly in line wih he VARbased evidence. For a shock o he policy rae of he European Cenral Bank, he DSGE model delivers a quaniaive impac on Danish oupu in line wih he daa, alhough he shape of he impulse responses are somewha differen. We use he esimaed model o shed ligh on he driving forces behind business cycle flucuaions in Denmark. The main finding of his analysis is ha foreign shocks are he mos imporan source of movemens in Danish GDP. Our variance decomposiion shows ha for he period 995- aken ogeher, foreign shocks accoun for around 5 percen of oupu flucuaions in Denmark a all frequencies. This resul is in conras o oher recen sudies of he effecs of foreign shocks in small open economies, e.g. Jusiniano and Preson [] and Adolfson e al. [7], who - somewha surprisingly - find ha foreign shocks explain less han 5 percen of oupu flucuaions in Canada and Sweden, respecively. I should be noed, however, ha he resuls of Jusiniano and Preson [] are a bi of a puzzle in he lieraure, where differen ways of resolving his issue have been proposed. Their resuls are also in conras o VAR-based evidence for he Canadian economy, see, e.g., Cushman and Zha [997]. The main reason for he sriking difference beween hese sudies and our resuls is Denmark s fixed exchange rae owards he euro, which opens up an imporan channel hrough which foreign shocks can be ransmied direcly o he Danish economy. For example, ineres rae decisions of he European Cenral Bank have a direc effec on consumpion and invesmen decisions of Danish households. Indeed, as discussed by Aasvei e al. [3], par of he explanaion for he surprisingly small resuls obained by Jusiniano and Preson [] is he lack of a direc effec of foreign shocks on domesic variables, and he lack of oher ransmission mechanisms han he inernaional rade channel. A fixed exchange rae resolves hese issues. 3 Furhermore, our finding of an imporan role for foreign shocks is in line wih empirical evidence based on VAR-sudies for Denmark (see Ravn and Spange [3]) as well as for oher small open economies (see, e.g., Cushman and Zha [997], or Aasvei e al. [3]). We also perform a hisorical decomposiion of deviaions in Danish oupu from is rend for he period 4-. This decomposiion confirms he imporance of foreign shocks. In paricular, he recen economic crisis in Denmark was o a large exen driven by shocks originaing abroad. Foreign shocks also conribued o he economic boom in Denmark in he years leading up o he crisis. However, domesic demand also increased subsanially in he years preceding he crisis. Finally, our analysis suggess ha shocks o he supply side may have played a more imporan role during he boom han previously hough, possibly due o an inflow of foreign workers, and in par because of he above-menioned use of macroeconomeric models which ypically ascribe lile imporance o he supply side. Due o Denmark s fixed exchange rae, i is mainly he job of fiscal policy- 3 I should be noed, however, ha while he choice of exchange rae regime is very imporan in his class of models, he empirical lieraure ends o find ha his choice is less criical for he driving facors behind business cycles. 3

7 makers o sabilize he domesic economy. In he years before he crisis, he high levels of domesic and foreign demand called for a igh fiscal policy. Our analysis shows, however, ha fiscal policy was no ighened suffi cienly during hese years so as o counerac he boom. Insead, fiscal policy shocks exered a neural or even simulaing effec on he Danish economy in hese years. The remainder of his paper is srucured as follows: In secion, we give a general inroducion o flucuaions in he Danish economy over he period we consider. We hen describe he model in secion 3, and he esimaion of he model in secion 4. In secion 5, we analyze some of he properies of he esimaed model, including is abiliy o mach impulse responses from VAR sudies. We hen perform a hisorical decomposiion of he quarer-oquarer movemens in he oupu gap in Denmark in secion 6. Finally, secion 7 concludes. In he appendix, we provide addiional deails on he model as well as a number of ables and graphical illusraions. Some sylized facs abou he Danish economy We sar wih a brief our of he developmen of he main Danish macroeconomic variables o se he sage for he modeling ask which lies ahead. The Danish economy experienced repeaed devaluaions of he krone during he 97 s and he beginning of he 98 s. This was he case unil 98 when a newly eleced governmen inroduced a currency peg vis-a-vis he German mark, which in 999 was changed o a peg agains he euro. The fixed exchange rae regime has succesfully been defended ever since. As can be seen in figure (), op-lef, in our daa sample here has only been a noeworhy posiive spread beween he Danish moneary policy rae and he equivalen in he eurozone on wo occasions: During he EMS crisis a he begining of he 99s and during he recen financial crisis. This confirms he high credibiliy of he Danish exchange rae regime. The op-righ graph in figure () shows wo among many challenges in esimaing a DSGE model for Denmark. Firsly, he quarerly growh rae of Danish real GDP is quie volaile relaive o as an example real GDP in he eurozone. This is no surprising: Denmark is a very small and very open economy. Secondly, we have included daa for he financial crisis bu i imposes anoher challenge when having a model wih posiive rend growh as i raises an end-poin problem. Tha is, he rend in he daa is heavily influenced by he financial crisis and we do no ye know wheher Danish GDP growh will reurn o he pre-crisis rend. We address his problem by including forecased daa, as explained in secion (4.). The boom-lef graph in figure () shows year-on-year inflaion raes. A necessary condiion for a successful fixed-exchange rae regime is ha he inflaion rae in pegging counry, Danmark, on average equals he inflaion rae in he, pegged counry, he eurozone. Alhough closely relaed, here is some evidence ha Danish prices have increased slighly more han prices in he eurozone in 4

8 our sample. Moreover, inflaion in Denmark is more volaile han inflaion in he eurozone. Turning o he componens on he naional accouns balance, privae consumpion has aken an increasing share of GDP in he Danish economy from he early s unil he oubreak of he financial crisis, afer which i plummes. Privae consumpion as a share of GDP has since no recovered o pre-crisis levels. Invesmen as a share of GDP dropped significanly during he brief inernaional recession in he lae 99 s/early s, bu recovered srongly unil he financial crisis, see figure (), boom-righ. Like mos oher counries, Denmark is affeced by globalisaion, which is refleced in increasing expor and impor shares, as showed in figure (), op-lef. The rend in expors and impors exceeds he rend in oupu. In he esimaion, his addiional growh is removed following, for example, Adolfson e al. [3].The collapse in world rade during financial crisis is also clear in Danish daa. I is noeworhy ha during he enire sample, Denmark has had posiive ne expors. Even hough he nominal Danish exchange rae is fixed owards he euro, ha does no imply ha he eff ecive, rade-weighed Danish exchange rae is consan, which can be seen in figure (), op-righ. These movemens clearly indicae ha a wo-counry seup for Denmark and he euro-area is no suffi - cien. As an example, he depreciaion of he effecive Danish krone from he onse of he financial crisis is likely o have helped Danish exporers survive he meldown of global rade. We include hese effecs in he model hrough a hree-counry seup: Denmark, he eurozone, and he res of he world. The res of he world consiss of he weighed sum of Denmark s rading parners excluding of course he rading parners which reside wihin he eurozone. The Danish labour marke has since he early 99 s experienced profound srucural reforms. This is refleced in a decrease in he naural rae of unemploymen and a corresponding decrease in acual unemploymen, as can be observed in figure (), boom-righ. In he same period he real wage has increased more or less wih oupu growh, while increased above rend during he boom before he financial crisis. We have no aemped o incorporae his downward rend in srucural unemploymen, which insead is lef for fuure research. Finally, urning o public deb and expendiures, Denmark s public finances displayed a fairly large primary surplus (relaive o GDP) during he years before he crisis. This urned ino a large defici afer he crisis, as seen in figure (), boom-lef. One reason behind he worsening of public finances is he expansionary fiscal policy conduced in order o miigae he effecs of he financial crisis. This can easily be seen from he large increase in he public consumpion o GDP raio saring from 9, alhough much of he increase in his raio is due o he drop in oupu. We will come back o he role of fiscal policy during he boom-bus cycle around he financial crisis. Firs we need o se up a model which can explain he movemens in Danish daa as presened in his secion. 5

9 3 The Model This secion ses up he model. The model is closely relaed o a number of exising medium-sized DSGE models like he Chrisoffel e al. [8], Adolfson e al. [7], Burriel e al. []. The main building blocks of hese models are, however, modified o reflec key aspecs of he Danish economy as se ou in he previous secion. Denmark is a small open economy wih a fixed exchange rae agains he euro. In he model i is assumed ha his regime is percen credible. Effecively, his amouns o an assumpion ha Denmark is par of a currency union wih he eurozone. However, ha does no imply ha exchange rae effecs do no play a role in he deerminaion of he Danish business cycle. As an example, he second and hird mos imporan rading parners are ouside he eurozone (Sweden and U.K.). Consequenly, Denmark has seen some flucuaions in he effecive exchange rae and he model needs o reflec ha. The model herefore pus Denmark inside a currency union wih he eurozone bu also allows for rade wih wha will be denoed Res-of-he-World, RoW, which consiss of he Danish rading parners excluding counries wihin he eurozone. I is assumed ha he exchange rae vis-a-vis he RoW is floaing. The wo foreign counries, he eurozone and RoW, are assumed o be exogenously given and independen of each oher and especially of Denmark reflecing he small open economy assumpion. The problem of he household secor is seup in secion (3.), producion is presened in secion (3.3) and (3.4) while he consumers choice beween home produced goods and foreign produced goods is presened in secion (3.5). Fiscal and moneary policy are presened nex in secion (3.6), and he labour marke in secion (3.7). Finally, he foreign economies are described in secion (3.8), while secion (3.9) and (3.) presen he expors and impors secors. 3. Trends Fundamenally, here are wo ways of dealing wih he presence of non-saionary daa in an esimaed DSGE model. One is o wrie a saionary model, and derend all non-saionary variables before macching hem o heir model counerpars. The oher opion is o inroduce growh in he relevan variables in he model, so as o be able o esimae he model using he non-filered, nonsaionary daa series. In recen years, he laer approach has become bes pracice in he lieraure, no leas because he process of de-rending variables ha may have differen rend growh raes is complicaed and involves a loss of informaion. For his reason, we inroduce growh in our model. The firs sep is o idenify he relevan rends in he daa. Many recen sudies based on US daa include wo rends in he model; a oal facor produciviy (TFP) rend o accoun for he growh rae in oupu, and an invesmen-specific rend o accoun for he coninuous decline in he relaive price of invesmen goods, such as compuers, in erms of consumpions goods. 4 We follow his 4 See among ohers he sudies by Jusiniano e al. [], Chrisiano e al. [3] and Liu 6

10 pracice afer confirming ha he same wo rends are presen in Danish daa for our sample period. We can wrie he overall growh rae of he economy as: dγ = (da dz α ) α, () where da and dz denoe he growh rae of TFP and he (inverse) relaive price of invesmen, respecively. Finally, while he share of impors and expors o GDP has shown an upward rend over our sample period we have decided o derend hese variables, so ha he daa for impors and expors used in he esimaion follow he same rend as domesic GDP, see also secion (). This grealy simplifies he modeling ask as concerns he impor and expor secors. 3. Household Secor The problem of he represenaive household is o choose consumpion, C, holdings of domesic, B DK, and inernaional, B I, real bonds, capial, K, capial uilizaion, u, and he level of invesmen, I, so as o maximize is sream of discouned fuure uiliy, which is given by: ( ) E β N (i) +φ log (C hc ) η con N χ O + φ di, () = where < β < is he discoun facor, h > measures he degree of (exernal) habi formaion in privae consumpion. The second erm in he uiliy funcion denoes disuiliy of labor. We will define he variables and parameers associaed wih his in subsecion (3.7). Finally, con is a shock o he household s preference for consumpion oday versus omorrow, which is given by: con ( con = con ) ρcon exp ε con, (3) con where con >, < ρ con <, and where ε con is an i.i.d. sochasic process wih mean zero and variance σ con. Uiliy maximizaion is subjec o he following budge consrain: ( ) + τ V AT P C C + P I I + B DK + B I + T P P ( ( ) ) = Π + τ K r K u cap + τ K δ K z u (u cap ) K + R B DK + R ECB + exp( ψ d ( B I Y ) ( BI ) Y ) RP D B I RP D π DK π DK τ B B DK (R ) π DK + + ( τ n ) w N + κ U w U N, (4) where P is he overall price level o be defined below, T denoes real lump-sum axes, and Π is he profis obained from firms in he inermediae goods secor. e al. [3]. 7

11 Moreover, r K is he real renal rae on capial, and R and R ECB denoe he Danish and he foreign risk-free rae of ineres. Y is oupu, while N denoes hours worked, wih w represening he corresponding real wage rae, w W P. U N is he unemploymen rae, o be defined laer. We le τ V AT, τ K, τ B and τ n be he ax raes on consumpion (i.e., a VAT), capial, bond reurns and labor, while < κ U < is he compensaion rae in unemploymen benefis. δ K > is he capial depreciaion rae. We assume ha if he raio of foreign deb o GDP exceeds is seady sae level, Danish households will have o pay a risk premium on op of he ineres rae se by he ECB. This reflecs ha foreign invesors will be less willing o hold Danish deb. In urn, he higher ineres rae will make i less aracive for Danish households o borrow abroad, so ha evenually he deb-o-oupu raio will reurn o is seady sae level. In his respec, ψ d > measures he sensiiviy of he risk premium wih respec o he ne level of holdings of foreign bonds, or equivalenly, Denmark s ne foreign asse posiion. The assumpion of a risk premium on foreign bonds is only made o ensure a saionary model as in Schmi-Grohé and Uribe [3]. Wihou such an assumpion i would be possible for he consumers o borrow indefiniely in he inernaional bond marke and consume he proceeds. We assume ha each household does no inernalize he effecs on Denmark s ne foreign asse posiion, and hus on he risk premium, of changes in is individual inernaional borrowing or lending. We le RP D denoe a shock o he risk premium. This shock evolves as: ( RP D RP RP D = D RP D ) ρrp D exp ε RP D, (5) where RP D =, < ρ RP D <, and where ε RP D is an i.i.d. sochasic process wih mean zero and variance σ RP D. The degree of capial uilizaion is measured by he variable u, and is subjec o he capial uilizaion shock cap, i.e. an exogenous shock ha changes he degree of capial uilizaion. The funcion z u (u cap ) measures he cos of changing he degree of capial uilizaion, which we assume akes on he following funcional form: z u (u cap ) = c (u cap u) + c (u cap u), (6) where c, c > are parameers, and u is he seady sae level of capial uilizaion, which we se o. 5 The uilizaion shock cap evolves according o: ( ) ρcap cap cap = cap ε cap, cap where < ρ cap <, cap = is he seady sae value of he shock process, and is an i.i.d. normal shock. ε cap 5 When we solve he model, we hen need o scale he ax deducion from capial depreciaion and he uilizaion cos in he budge consrain wih he rend growh of invesmenspecific echnology so as o ensure ha hese are no eroded over ime. 8

12 The sock of capial evolves as follows: ( K = δ K) K + ( S ) Z T I, (7) ( I ) where S = κ I I γ I is he invesmen adjusmen cos funcion, wih he parameer κ I > measuring he cos of changing he invesmen level, and where γ I > denoes he seady sae growh rae of invesmen. Z T is a ransiory invesmen-specific echnology shock, which evolves according o: Z T ( Z T ) ρz Z T = Z T exp ε Z T, (8) wih Z T >, < ρ Z <, and where ε Z is an i.i.d. sochasic process wih mean zero and variance σ Z. Moreover, he model feaures a permanen invesmenspecific echnology shock Z P, so ha Z = Z T Z P. 6 The permanen componen follows he process: where, in urn, λ z λ z = Z P Z P ( λz λ z = λ z, (9) ) ρλz exp ε Z P. Thus, λ z denoes he ime growh rae of invesmen-specific echnology, while λ z > is he seady sae growh rae. ε λ Z is an i.i.d. sochasic process wih mean zero and variance σ λ Z, while < ρ λz <. The firs-order condiions relaed o he uiliy maximizaion problem of he household are as follows: P C P λ = β E λ + E π DK + λ con = (C hc ) ( + τ V AT ) ( R ECB B I exp( ψ d Y BI Y ), () ( RP D ) RP D ), () Q = βe [ λ + λ (r K +( τ K +)u + cap + + δ K τ K + z u (u + cap ) + ( δ K )Q + )], () ( ) τ K r K = z u (u cap ), (3) [ P I ( ) ] = Q Z T [ S S P I ] + βe Q + Z+ T λ + S I+ λ +I. (4) I 6 We poin ou for clariy ha he oal invesmen shock, Z, affecs he economy hrough equaion (7). We have however wrien he model in derended form and consequenly only he par of Z which is relaed o he ransiory par, Z T, shows up in (7). 9

13 Here, we le Q µ λ denoe he price of insalled capial, which differs from he price of new capial (i.e., he price of invesmen) due o he presence of invesmen adjusmen coss. λ and µ denoe he Lagrange mulipliers associaed wih he budge consrain and he law of moion for capial, respecively, in he opimizaion problem. Moreover, given he funcional form for z u (u cap ), i follows ha z u (u cap ) = c + c (u cap ), while for S, we obain ha S = κ I I ( I I γ I ). 3.3 Inermediae Goods Producers There is a coninuum (of uni lengh) of firms in he inermediae goods secor, each of which operaes under monopolisic compeiion. These firms are owned by he household. Each firm j uses privae and public capial as well as labor o produce a firm-specific oupu according o he following producion funcion: ( Y (j) D = A T K (j) η ( K ) G η ) α (N (j)) α, (5) where α, η > are parameers, K (j) = u cap K (j) is he effecive capial sock being uilised in a given period, D is a measure of price dispersion as described below, and A measures aggregae oal facor produciviy (TFP). I is assumed ha A consiss of wo erms; a ransiory componen A T, and a permanen componen A P, so ha A = A T A P. The ransiory componen evolves according o: A T A T = ( A T ) ρa A T exp ε A T, (6) wih A T >, < ρ A <, and where ε A T is an i.i.d. sochasic process wih mean zero and variance σ A. The permanen componen follows he process: A P A P = λ A, (7) where, in urn, ( ) ρλa λ A λa = exp ε A P, (8) λ A λ A wih λ A measuring he growh rae in aggregae echnology or TFP, while λ A is he seady sae growh rae, < ρ λa <, and where ε A P is an i.i.d. sochasic process wih mean zero and variance σ λ A. 7 The problem of each firm is o maximize is profis subjec o he producion funcion. This problem gives rise o he following firs-order condiions, where we have dropped he j s for simpliciy: r K = αy mc u cap K, (9) 7 As for permanen invesmen shock, Z, we poin ou for clariy ha he oal produciviy shock, A, affecs he economy hrough equaion (5). We have however wrien he model in derended form and consequenly only he par of A which is relaed o he ransiory par, A T, shows up in (5).

14 ( + τ n ) w = ( α) Y mc N, () where mc is he marginal cos of producion, which is idenical o he Lagrange muliplier associaed wih he producion funcion in he opimizaion problem. We inroduce sicky prices ino he model by assuming ha inermediae goods firms are subjec o saggered price seing. In paricular, following Calvo [983] each firm is only allowed o change is price in any given period wih probabiliy ( θ P ) <. Since all firms are idenical ex ane, his implies ha only a fracion ( θ P ) of firms will rese heir price each period. Of he remaining θ p firms, we allow a fracion Γ P o index heir price o he seady sae rae of inflaion, π, while he remaining fracion of firms keep heir price unchanged. When a given firm is allowed o re-opimize is price, i solves a dynamic opimizaion problem, aking ino accoun ha he price i ses is likely o prevail for θ p periods. We can wrie he resuling firs-order condiion as: P (j) = ɛ P ɛp E s= (βθ P ) s λ +s λ Y +s (j) mc +s P +k, () Y +s (j) where P (j) is he price se by inermediae firm j if i is allowed o change is price in period. As all firms are idenical, his price will be he same for all firms. Noe also ha we use he sochasic discoun facor of households, as hese are he owners of he firms. Finally, ɛ P is he elasiciy wih which final goods producers subsiue beween differen varieies of he inermediae good, and is given by: ( ) ɛ P ɛ P = ( ɛ P ) ρɛ P ɛ P exp ε ep, () where ε ep is an i.i.d. sochasic process wih mean zero and variance σ ɛp, and where < ρ ɛ P <. ɛ P > measures he seady sae elasiciy of subsiuion. We can hen wrie he evoluion of he aggregae price index as P = [ ( ) ɛ P ] θ P ( π Γ P P ) ɛp ɛ P + ( θ P ) P (3) highlighing ha he share ( θ P ) of prices are rese in each period. Finally, D measures he loss associaed wih price dispersion, and is given by ( ) ɛ P D = ( θ P ) P + θ P (π ) ɛp D. (4) and where π is he domesic inflaion rae of he Danish producer price index. 3.4 Final Goods Producers Firms in he final goods secor operae under perfec compeiion. They collec a variey of inermediae goods and repackage hese ino a final good o be used for

15 consumpion or invesmen. In doing so, hey solve a cos minimizaion problem by choosing inermediae inpu goods so as o produce he final oupu, Y, a he lowes possible price. Final goods producers aggregae inermediae goods according o: ( ) ɛp ɛ P ɛ P ɛ Y = Y (j) P dj. (5) We can wrie he price index of domesically produced final goods as: ( P = P (j) ɛp ) ɛ P dj where P (j) is he price se by inermediae goods firm j. 3.5 Final Consumpion and Invesmen Goods, (6) We assume ha households combine domesically, C DK, and foreign, C F, produced goods ino he final composie consumpion good, C, according o a consan elasiciy of subsiuion (CES) echnology: ( C = ϑ υc c ( ) C DK (( ) ) υc + ( ϑ c ) υc χ C C F υc ) υc, (7) where υ c > measures he elasiciy of subsiuion beween foreign and domesic goods, and ϑ c > measures he seady sae share of foreign and domesic goods in he consumpion baske, and hus also he degree of home bias in consumpion. Moreover, we follow Erceg e al. [] and Chrisoffel e al. [8] and assume ha here is a cos o adjusing he share of impored consumpion goods, represened by he funcion χ C, which is given by: χ C = χ C C F C ω I C F C, (8) wih χ C > measuring he adjusmen cos, and where ω I is an impor shock, which follows he process: ( ) ( ω I ω I ) ρim ω I = ω I exp ( ε Im ), (9) wih ω I >, < ρ Im <, and where ε Im is an i.i.d. sochasic process wih mean zero and variance σ Im. As in Erceg e al. [], he opimal composiion of final consumpion is found by choosing he values of C DK and C F ha solve a cos-minimizaion problem subjec o (7). The wo resuling firs-order condiions are: P DK P C = ( ϑc C DK ) ( υc ϑ υc c ) ( ) C DK (( ) ) υc + ( ϑ c ) υc χ C C F υc υc,

16 P F P C ( ϑ c ) = ( ( χ C )C F (ϑ νc c ) νc ( χ C (χ C ) C F ) (C DK ) νc + ( ϑ c ) νc (C F ( χ C )) νc ) νc, (3) which can be combined o yield: C DK C F = ϑ ( c P F ϑ c P DK ) υc ( ) [ χ C χ C ( χ C ) ] υc C F, (3) where P DK and P F denoe he price of domesic and foreign goods, respecively. Noe ha in he absence of adjusmen coss, he opimal composiion would depend only on he relaive price, he elasiciy of subsiuion and he seady sae consumpion shares. Likewise, firms combine foreign and domesic invesmen goods ino a final invesmen good using a similar CES echnology: ( I = ϑ υ I I ( ) I DK (( ) ) υ I + ( ϑi ) υ I χ I I F ) υ I υ I, (3) where he parameers are defined as above. The adjusmen cos funcion χ I is defined similarly o ha for consumpion goods, while he impor shock is he same. Cos minimizaion by firms herefore implies ha: I DK I F = ϑ ( ) I P F υi ( ) [ χ I ϑ I P DK χ I ( χ I ) ] υi I F. (33) Finally, we can wrie he relaive prices of consumpion and invesmen goods as follows: P C P = P F P DK ϑ c + ( ϑ c ) χ C ( ) χ C C F υ c υc, (34) P I P = P F P DK ϑ I + ( ϑ I ) χ I ( ) χ I I F υ I υ I, (35) while he relaed relaive inflaion raes are defined as: π C = P C P π P C, (36) P 3

17 π I = P I P π Z P I P Z. (37) We poin ou ha PPP does no hold in his model due o he presence of home bias. Tha is, for equal cos of buying a baske consising of goods produced a home versus a baske consising of goods produced abroad, he Danish household would prefer he home baske. 3.6 Fiscal and moneary policy The role of he public secor in he model is o raise axes o be used for public consumpion, public invesmen, and ransfers. Public consumpion, C G, evolves according o: C G C G = ( C G C G ) ρg exp ( ε G ), (38) where ε G is an i.i.d. sochasic process wih mean zero and variance σ G, < ρ G <, and where C G is given by: C G = G Y Y (39) where Y denoes oal seady sae oupu, and G Y is he seady sae share of governmen spending of goods and services produced by he inermediae goods producers and public producion. As for governmen invesmens, we assume ha hese are implemened wih a lag. Specifically, we assume ha an invesmen ha is decided on in period can only be iniiaed in period + M and is finalized in period +N. In oher words, we allow for ime o build as well as ime o plan as in Leeper e al. []. To his end, we need o disinguish beween planned public invesmen denoed by I G,B and implemened public invesmen denoed by I G. Planned public invesmen evolves according o: ( ) I G,B I G,B ρig I G = I G exp ( ε IG ), (4) where ε IG is an i.i.d. sochasic process wih mean zero and variance σ IG, I G is he seady sae level of governmen invesmen, and < ρ IG <. Due o our assumpion of ime o build, implemened invesmen only adds o he sock of public capial wih a lag: K G = ( δ G) K G + I G,B N, (4) where δ G > is he depreciaion rae of public capial, and N is he number of periods i akes from an invesmen projec is decided upon and unil he invesmen is finalized. Noe ha invesmen-specific echnology shocks also affec he accumulaion of he public capial sock. This ensures a sable longrun relaionship beween he size of he public and he privae capial sock 4

18 along he balanced growh pah. 8 Moreover, o ake ino accoun ha planned invesmens affec he acual invesmen level (and hence, economic aciviy) wih a lag, we le acual public invesmen be given by: I G = N i=m φ I i I G,B i, (4) wih φ I i >, and where M is he number of periods ha pass from a projec is decided on unil i is iniiaed. I G is hus a measure of all ongoing governmen invesmen projecs a ime. On he revenue side, he governmen raises five differen ypes of axes: A labor income ax, τ N, a capial income ax, τ K, a value added ax, τ V AT, a ax on domesic bond reurns, τ B, and a lump-sum ax T. By adjusing he ax raes, he governmen ensures ha is ineremporal budge consrain, o be presened below, is always saisfied. This is done via he following ype of ax rule: ( ) ρx ( ) ( ρx )e X X = X ε X B /Y aux X ζ X X ω D, for X = { } τ N, τ K, τ V AT, τ B, T. Here, X is he seady sae value of X, while < ρ X <. ε X is a whie noise shock associaed wih shocks o each ax rae X. Moreover, ζ X > measures how srongly each fiscal insrumen reacs o deviaions of he deb-o-gdp raio from is long-run arge value, ω D, reflecing ha if he deb-o-gdp raio overshoos is long-run arge, one or more of he ax raes will evenually have o be raised. Finally, he dummy variable e aux X essenially swiches he adjusmen erm on or off. We can se his o zero in order o underake simulaion experimens in which he governmen only sars raising axes afer a cerain number of periods. We are now ready o presen he governmen s ineremporal budge consrain, which akes he following form: B DK + T R = R π DK B DK + G + w U N κ U, (43) where we have defined ax revenues T R and governmen expendiure G as: T R = T +τ V AT P C P C +τ K ( r K u cap δ K) K +τ N w N +τ B G = C G R π DK B DK, (44) + P I P I G. (45) Moreover, recall ha κ B denoes unemploymen benefis, while U is he unemploymen rae in he model, o which we reurn in he following subsecion. 8 As we shall see, he growh in invesmen-specific echnology is relaed o he negaive rend in he relaive price of invesmen goods such as high-ech producs, IT, sofware ec. Since many public invesmens also comprise such producs, i seems reasonable o assume ha public invesmens are also affeced by he negaive rend in he relaive price of hese. 5

19 Finally, we assume ha only percen of he public deb needs o be refinanced in each period, so ha changes in he ineres rae se by he ECB only has a percen impac on he ineres rae on public deb. Moreover, we assume ha he ineres rae a which he governmen borrows will increase if he raio of governmen deb o oupu exceeds is seady sae level. This reflecs ha he household secor, which buys he bonds issued by he Danish governmen, will demand a risk premium if hey are o hold he bonds. In echnical erms, his gives rise o he following condiion: R R = ( R R where ρ RDK =.8 and ψ G >. 3.7 The Labor Marke ) ρrdk [ ( ) ] R ECB ( ρrdk ) R exp(ψ B ECB G ω D ), (46) Y We model he labor marke following Galí e al. [] and we refer o ha paper for he deails. The model of Galí e al. [] may be seen as a somewha simpler alernaive o he well-known search-and-mach approach in he radiion of Diamond, Morensen and Pissarides. As discussed by Galí [], wha really maers (a leas quaniaively) for he dynamics of unemploymen flucuaions is nominal wage rigidiies and no search fricions. For our purposes, i herefore seems naural o sick o he formulaion of Galí e al. [], as i involves fewer equaions (as compared o he search-and-mach approach) in an already large model, and brings in fewer addiional parameers o be esimaed using Bayesian mehods. The main building block of our labour marke are wage-seing households and sicky wages. Jus as for he pricing behaviour of he firms in our model, sicky wages are achieved by assumpion using he heory of Calvo [983]. We assume he exisence of a represenaive household wih a coninuum of members indexed by (i, j) [, ] [, ] Here index i refers o differeniaed labour services. Hence, we assume he exisence of heerogeneous ypes of labour specialized in various fields. This implies ha each labour supplier has some marke power o se is wage. We assume he exisence of a coninuum of labour unions each represening he differen labour ypes. Index j refers o he household member s disuiliy from work. Hence, he household consiss of many labour ypes who each have a cerain degree of disuiliy from work. 9 We assume full consumpion risk sharing across he household and we give ha household a uiliy funcion. The full risk sharing implies ha we do no need o ake care of differen consumpion levels and hence marginal uiliies, and ha he individual members of he household have he household in 9 The parameer η N in he uiliy funcion will help us o deermine he seady-sae employmen, bu is lef ou in wha follows. 6

20 mind when maximizing uiliy. When hese members work, hey work full ime. Hence, labour supply movemens are iner-marginal and no inra-marginal. The assumpions abou households seing wages and working full ime implies ha he employmen level is deermined on he firm side - he household simply supplies he given number of workers a he going real wage. When he household chooses is labor supply i equalizes he marginal rae of subsiuion beween supplying more labour and consumpion o he real wage MRS χ O (N ) φ λ = w (47) where MRS U N, U C, is he household s marginal rae of subsiuion beween consumpion and leisure, and φ > is he inverse of he Frisch elasiciy. Tha is, φ measures by how much he households labor supply changes in percen when he real wage increases by one percen holding consumpion consan. Inuiively, a he opimum he disuiliy of working more mus be compensaed by wha he real wage can buy in uiliy erms. If no, he household would be able o reshuffl e beween consumpion and labour and achieve a higher uiliy. The variable O is defined as: O = wih z evolving according o: [ z = z ν z (C hc ) ( + τ V AT (C hc ) ( + τ V AT ) ( P C /P ) con = z λ, (48) ] ) ( ) ν P C /P, (49) con where ν [, ]. Following Galí e al. [], we may inerpre z as a smooh rend for (habi-adjused) aggregae consumpion. In oher words, O is smaller han one when consumpion grows faser han his smooh rend, and vice versa. As seen from (47), his implies a drop in he marginal disuiliy of labor, so ha each individual will be willing o work a a lower wage rae, ceeris paribus. The parameer ν deermines he srengh of he wealh effec on labor supply. Tha is, by how much labor supply is affeced by changes in wealh: If ν is close o, he wealh effec is quie srong, while he wealh effec disappears when ν ends o. Finally, in (47), he erm χ represens an exogenous shock o labor supply, which evolves according o: χ χ = ( χ χ ) ρχ exp (ε χ ), (5) where ε χ is an i.i.d. sochasic process wih mean zero and variance σ χ, while < ρ χ <. As discussed by Galí e al. [], a low value of ν is necessary o ensure ha no only employmen, bu also he labor force moves in a procyclical fashion in response o shocks originaing from he demand side. 7

21 In equilibrium, a given individual will paricipae in he labor marke if and only if he ne benefis from doing so exceed ha individual s oal disuiliy of labor. We can wrie his paricipaion condiion as: λ ( τ n ) w Υ (j), (5) where he lef-hand side measures he afer-ax real wage rae as measured in uiliy unis, and where Υ (j) χ O j φ represens oal disuiliy from working. Here i is imporan ha he individuals of each ype of labour i are ordered by heir disuiliy of labor and ha he condiion is relaed o he household s marginal disuiliy of work. Toal disuiliy from working hus consiss of he exogenous shock o labor supply χ, he endogenous process O as described above, and individual-specific labor disuiliy. This implies ha he labor force will consis of all individuals for which he above condiion is saisfied. We can wrie he labor force L in a symmeric equilibrium as: ( ) ( τ n φ L = ) w. (5) χ z Tha is, he labour force consiss of he j individuals for which condiion (5) is saified. The sum of hese paricipaion raes across labour ypes gives he model s aggregae labour force. Noice ha he labour force is ime-varying. I may increase, for example, due o labour supply shocks which decrease he marginal disuiliy of working. Nex we define our noion of unemploymen as U L N, i.e. he raio beween he labor force and oal employmen. Noice ha his definiion differs slighly from offi cial unemploymen measures, which are ypically given by L N L. However, around a log-linear approximaions, hese definiions of unemploymen are equal for small levels of unemploymen as is he case for Denmark. Define he (log) average wage markup in he economy as he difference beween he real wage and he marginal rae of subsiuion beween consumpion and work as µ w log(w ) φ (z + n + log (χ )). The wage markup varies as long as wages are no fully flexible, and i is non-zero as long as he labour marke is no fully compeiive. We can use his expression ogeher wih he paricipaion condiion, (5), o wrie µ w = φu, where u log (U ). Noice ha he naural rae of unemploymen is given by µ w = φu n. Hence, unemploymen in his model is due solely o a noncompeiive labour marke in which heerogenous ypes of labour can se a wage above he marke clearing wage, and unemploymen varies due o changes in he average wage markup in he economy. Tha is, due o wage rigidiies. The naural rae of unemploymen is higher he higher is he degree of monopolisic compeiion and he higher is he Frisch elasiciy of labour supply. When his 8

22 elasiciy is high, he members of he household are more willing o subsiue in and ou of employmen. Finally, we describe he wage formaion. Recall ha households supply differeniaed ypes of labor services, giving rise o monopolisic compeiion for labor. Furhermore, we assume ha households face Calvo-syle wage sickiness. The naure of he problem implies ha all households who can reopimize he wage rae in a given period choose he same wage w P according o he following firs-order condiion: w P (i) = ɛw ɛ W E (βθ W ) s λ +s N+s P (j) χ +s O +s λ N+s P, (53) (j) s= where < θ W < is he wage sickiness parameer, and ɛ W is he elasiciy of subsiuion beween labor ypes, which evolves according o: ( ) ɛ W ɛ W = ( ɛ W ) ρ ɛ W ɛ W exp ε ew, (54) where ε ɛw is an i.i.d. sochasic process wih mean zero and variance σ ɛw, and where < ρ ɛ W <. Of he remaining ypes of workers θ W, we allow a fracion Γ W o index heir wage o he seady sae rae of inflaion, while he remaining fracion keep heir wage unchanged. We can consequenly wrie he evoluion of he wage level in he privae secor as: w P = ( ) ɛ W [θ W π ΓW w P + ( θ W ) ( w P ] ) ɛ W ɛ W. (55) 3.8 Trade and he wo foreign economies As discussed in he inroducion and in secion (), Denmark s fixed exchange rae owards he euro implies ha we need o include wo foreign economies in he model: One (he eurozone, EA for shor) owards which Denmark has a fixed exchange rae, and one (he Res of he World; RoW for shor) owards which he exchange rae is fully flexible and exogenous for Denmark due o he small-economy assumpion and wih moneary policy given from he eurozone. The wo foreign economies are oherwise compleely idenical, and are aken as compleely exogenous, so ha movemens in he Danish economy does no affec he foreign economies. We also do no model rade or oher ineracions beween he eurozone and he res of he world. Each of foreign economies is described by a basic 3-equaion New Keynesian model, so ha for j = (EA, RoW ) we have: ( ) Y j Y j ρ j ( ) Y Y j = + Y j ρ j Y Y j Y j π j π j = ( ) π j ρ j + π j π ( π j π j ) ρ j 9 R j R j π j + π j π ( Y j Y j ) φ j φ j Y π ( ɛ j π, ( ) ɛ j Y, ɛ j, (56) Y ɛ j π ), (57)

23 R j R j = ( ) R j ρ j R R j ( π j π j ) Γ j π ( Y j Y j ) Γ j Y ρ j R ( ɛ j R, ɛ j R ). (58) Here, (56) is a hybrid dynamic IS-ype relaion ha links oupu o he real ineres rae, (57) is a version of a hybrid New Keynesian Phillips Curve linking he rae of inflaion o real aciviy, and (58) is a Taylor rule ha deermines moneary policy in each of he wo regions as a funcion of inflaion and economic aciviy. See Galí [9] for a deailed exposiion of he 3-equaion New Keynesian model. In urn, he shock processes in each of hese equaions are given as AR()-processes: ɛ j k, ɛ j k = ( ) ɛ j ρ j ɛ k k, ɛ j ε k,j, (59) k for j = (EA, RoW ) and k = (Y, π, R), and( where he ) ε k,j s are i.i.d. normal processes. The parameers in he IS curve ρ j Y, φj Y and he New Keynesian Phillips Curve ( ( ) ρ j π, φ j π), as well as he reacion parameers in he Taylor rule Γ j π, Γ j Y are chosen in line wih he lieraure, as described in he appendix. The six shocks are included in he esimaion o accoun for he conribuion o he Danish business cycle of foreign shocks. Finally, we can wrie world oupu and inflaion as: Y W Y W = π W π W = ( Y EA Y EA ( ) π EA ωx ( F X π EA F X ) ωx ( ) Y RoW ωx Y RoW, (6) π RoW ) ωx π RoW, (6) where he parameer ω X > measures he relaive size of he eurozone, and where FX denoes he change in he effecive exchange rae of he Danish krone. The effecive exchange rae is given by: F X F X = R ECB R ECB ε UIP R RoW, R RoW so ha he effecive exchange rae moves in response o ineres rae differenials beween he eurozone and he res of he world. ε UIP is an i.i.d. normal shock process. I may be diffi cul o disinguish ineres rae smoohing from persisence in he shocks hiing he ineres rae rule. We herefore decide o eliminae he laer by fixing he parameer ρ j ɛr = for j = (EA, RoW ).

24 3.9 Expors The role of he expor secor is o buy final domesic goods, differeniae hem, se a price and sell hem o impor firms in he eurozone or he res of he world. The moivaion behind he inroducion of he impor and expor secors is o be able o model an imperfec pass-hrough from changes in prices and he exchange rae o he Danish economy hrough esimaion of he parameers in he expor- and impor relaions. Hence, we can le he daa deermine he degree of he pass-hrough. We can wrie he world demand for Danish expors, Ex, as: Ex = x Z Y W ( P X P x W ) ε W, (6) where he parameer ε W denoes he elasiciy wih which world consumers subsiue beween Danish and foreign goods. The demand for Danish expors is hus increasing in world oupu and decreasing in he raio beween he relaive price of Danish expors, P X, and he relaive world marke price, P x W. We define he laer as: P x W = P x W π W π DK, (63) where π W is he world inflaion rae, as described above. The relaive price of Danish expors, P X, is defined as: P X = P X π X π DK, (64) where π X is he inflaion rae in Danish expors price, as described below. Finally, he expor demand shock x Z evolves according o: x Z x Z = ( x Z ) ρex ( x Z exp ε XEx ), (65) where ε XEx is an i.i.d. sochasic process wih mean zero and variance σ εex, and where < ρ EX <. Firms in he expor secor are faced wih price rigidiies of he same form as in he domesic producion secor. We can herefore wrie he opimal expor price P X se by a given firm j in he expor secor ha is allowed o change is price in period as: P X (j) = ɛx ɛ X E s= (βθ X ) s λ +s λ Y W +s (j) mc X +sp X +k Y W +s (j), (66) where θ X is he Calvo sickiness parameer in he expor secor, and mc X is he marginal cos for he expor firms, which is simply given by he inverse of he expor price; mc X =. Finally, ɛ X P X is he elasiciy of subsiuion beween

25 he goods produced by each individual firm in he expor secor, which follows he process: ( ) ( ɛ X ɛ X ) ρɛ X ɛ X = ɛ X exp ε ex, (67) where ε ɛx is an i.i.d. sochasic process wih mean zero and variance σ ɛx, and where < ρ ɛ X <. Of he remaining θ X firms, we allow a fracion Γ X o index heir price o he seady sae rae of inflaion, while he remaining fracion of firms keep heir price unchanged. The inflaion rae in Danish expor prices will hen saisfy: = θ X ( π ΓX π X ) ɛ X + ( θ X ) ( P X P X ) ɛ X. (68) 3. Impors The srucure of he imporing secor can be described as follows: A coninuum of impor differeniaors impor a homogenous final good from foreign exporers, differeniae he good (say, by adding brand names), and sell he differeniaed producs o Danish households and firms, who, as described above, solve a cos minimizaion problem when hey choose beween impored and domesically produced goods. The world marke prize of impor goods, which in urn deermines he marginal cos of Danish impor differeniaors, is compued as a weighed average of prices in he eurozone and he res of he world. We can wrie he marginal cos for an impor differeniaor as: mc M = P xw P M, (69) where, as described in he previous subsecion, P x W is he relaive world marke price, and P M is he price of impored goods relaive o Danish goods; P M = P M π M π DK, (7) We define he inflaion rae of impor prices in Denmark, π M, below. Jus like domesic and exporing firms, he firms in he impor secor face sicky prices as in Calvo [983]. We can herefore wrie he opimal price P M chosen by a given impor differeniaor j ha is allowed o change is price in period as: P M (j) = ɛm ɛ M E s= (βθ M ) s λ +s λ Im +s (j) mc M +sp+k M, (7) Im +s (j) Our modeling of he impor secor involves one imporan drawback: Consider for example a siuaion where he US dollar appreciaes agains he Danish krone. In urn, his drives up he aggregae impor price faced by Danish households and firms, who in urn choose o buy fewer impored goods from he res of he world AND from he Euro area, even hough he exchange rae owards he Euro is unaffeced.

26 where θ M is he Calvo sickiness parameer in he impor secor. Im denoes Danish demand for impored goods, which consiss of wo erms: Impors used for consumpion by households, and impors used as invesmen goods by Danish firms. As shown in he appendix, we can wrie Danish impor demand as: Im = P C ( C C DK ) + P I ( I I DK P M ). (7) In he expression for he opimal price, ɛ M is he elasiciy of subsiuion beween he goods of each impor differeniaor, which follows he process: ( ) ( ɛ M ɛ M ) ρɛ M ɛ M = ɛ M exp ε em, (73) where ε ɛx is an i.i.d. sochasic process wih mean zero and variance σ ɛx, and where < ρ ɛ M <. Of he remaining θ M firms, we allow a fracion Γ M o index heir price o he seady sae rae of inflaion, while he remaining fracion of firms keep heir price unchanged.finally, analogous o he previous subsecion, he inflaion rae in Danish impor prices saisfies: = θ M ( π ΓM π M ) ɛ M + ( θ M ) ( P M P M ) ɛ M. (74) We finally poin ou ha he presence of saggered impor- and expor prices implies ha he model in he shor run allows for deviaion from he law of one price. Tha is, he same good can be sold a differen exchange-rae adjused prices in differen counries. 3. Marke Clearing We can wrie he aggregae resource consrain of he Danish economy as: Y = P C C DK + P I I DK + G + P I I G P P P Moreover, Denmark s ne foreign asse posiion is given by: ( R ECB B I ) B I exp( ψ d Y BI ) Y = π DK + z u (u ) K + P X P Ex. (75) B I + P X P Ex P M P Im, (76) so ha ne holdings of foreign asses increase if Danish expors exceed impors in a given period. 3. Saionary equilibrium and seady sae As already described, he model feaures wo deerminisic rends: growh in oal facor produciviy, A, and in invesmen-specific echnology, Z. This implies ha aggregae macroeconomic variables, such as oupu and consumpion, 3

27 flucuae around a balanced growh pah. In order o solve he model, we herefore need o rewrie he equaions in erms of derended saionary variables and find he seady sae of he saionary model. Observe ha we can wrie he compounded rend growh of hese wo variables as dγ (da dz α ) α, where we have aken ino accoun ha boh public and privae capial are affeced by invesmen-specific echnological progress. To obain a saionary equilibrium, we hen make he following ransformaions of he endogenous variables: We define Ỹ = Y Γ as he saionary counerpar of Y. Similarly, we define C = C Γ, G = G Γ, T = T Γ, BDK = BDK Γ, w = w Γ, and so forh, and we define K = K Z Γ, Ĩ = I Z Γ, and K G = KG Z Γ, where we have aken ino accoun ha capial and invesmen grow a a faser rae han oupu in he non-saionary model. We also define λ = λ Γ so as o ensure ha he shadow price of consumpion remains sable as he level of consumpion grows, and we le Q = Q Z, so ha he relaive price of invesmen goods changes over ime along wih invesmen-specific echnological progress. 3.. Seady sae We normalize GDP and he price level in all hree economies o in seady-sae. These normalisaions give us he res of he prices in he economy: Impor-, expor-, invesmen-, and consumer prices and heir relaive prices. We also assume ha he exchange rae is consan agains he euro and agains resof-world. Given he moneary policy regime in place in Denmark, he domesic nominal ineres rae is equal o he ECB nominal ineres rae. In seady sae risk premia for holding foreign bonds are zero. Moreover, all adjusmen coss are zero in seady sae, as all he variables o which hey apply grow a heir seady sae growh rae. Specifically, he cos of changing he impor conen of consumpion and invesmens, seady sae uilizaion coss, and invesmen coss are all zero in seady sae. Given seady sae expors and he CES funcions for privae consumpion and invesmen as well as seady sae invesmen, and imposing he law of one price and normalizing foreign oupu we can derive seady sae impors and he ne foreign asse posiion in he seady sae. Following Galí e al. [], we se he elasiciy of subsiuion among labour varieies, ε subw, such ha unemploymen in seady saes equals Naionalbanken s esimae of he naural rae of unemploymen of around 4 pc., see Andersen and Rasmussen []. The average quarerly growh rae of Danish real GDP in our sample is around.4 pc., while ha of he relaive invesmen price is -. pc. We use hese esimaes o deermine he seady saes of he wo processes which ogeher deermine he growh in he model, Λ A, Λ Z. Regarding he fiscal policy side of he model, we can observe he seady sae raios of public consumpion (public expendiures on goods and services as well as public employmen), public invesmen, all ax raes as well as he deb raio. Finally, seady sae lump-sum axes are deermined such ha public 4

28 deb obligaions can evenually be expeced o be honored. 4 Esimaing he model Our goal is o esimae all he srucural shocks in our model and a majoriy of he parameers. We ouline he economeric approach in secion 4., he daa and descripion of he shocks used in he esimaion in secion 4., he calibraed parameers in he model in secion 4.3, while our parameer esimaes and prior disribuions are discussed in secion Economeric mehodology We confron he model wih daa using Bayesian mehods. In his secion we only ouline he mehodology. For a more horough inroducion o Bayesian esimaion of DSGE-models, see among many Smes and Wouers [3], Smes and Wouers [7], An and Schorfheide [7], or a series of papers by Jesus Fernandez-Villaverde and coauhors; (Fernández-Villaverde [], Fernández- Villaverde e al. [] or Fernández-Villaverde and Rubio-Ramírez [7]). We follow he Bayesian approach for a number of reasons. Firsly, as is well-known he use of priors allows us o inroduce presample informaion and o reduce he dimensionaliy problem associaed wih he large parameers o daa raio. Secondly, Bayesian mehods have well-known and imporan compuaional advanages over maximum likelihood in larger DSGE models. Tha is, he use of simulaion provides us wih a much easier mehod o derive he marginal disribuion of he parameers in he model han he radiional frequenis maximum likelihood approach involving maximisaion. The use of priors gives curvaure o a highly dimensional likelihood-funcion, which is likely o be fla in many dimensions due o poorly idenified parameers. Even he mos sophisicaed algorihms have a hard ime finding he global maximum of such a funcion; i is much easier o simulae he poserior disribuion of he parameers han o maximize he likelihood funcion. Our goal is o repor feaures of he poserior disribuion. The Bayesian mehodology provides a mapping from he prior disribuion o he poserior hrough daa. Le Θ denoe all he parameers in he model we aim o esimae and le Y T denoe all he observed daa we will use in he esimaion. Le p (Θ) denoe he prior disribuion over hese parameers. The model implies a likelihood p ( Y T Θ ) and we hen have a poserior disribuion of Θ given by: p ( Θ Y T ) = p ( Y T Θ ) p (Θ) p (Y T ) (77) The poserior disribuion equals he prior disribuion imes he likelihood funcion divided by a scaling facor. I can perhaps be helpful o hink of Bayesian analysis as radiional maximum likelihood wih a penaly funcion in form of 5

29 he prior disribuion, p (Θ). Tha is, he prior disribuion assign low values o parameer values which he Bayesian economerician finds implausible. The poserior disribuion, p ( Θ Y ) T, summarizes he uncerainy regarding he parameer values. The poserior is diffi cul o characerize and we consequenly generae draws from i using a Meropolis-Hasings algorihm. The resuling empirical disribuion is used o obain poin esimaes, uncerainy bands ec. 4. Daa and shocks We esimae he model on daa running from 99 o 5. We use he firs 5 years as raining sample for he Bayesian esimaion which we aferwards discard in he analysis. This has he advanage ha iniial condiions in he hisorical shock decomposiion are likely o have vanished in he sample period, see also secion (6). We add he mos recen forecas produced by Naionalbanken for he 3-year period afer he sample o ge beer esimaes of he long erm rend in daa. The laer mus be seen as a consequence of he crisis period which migh bias he long-run growh rae downwards leaving a worse fi a he end of our sample. Sricly speaking we should allow for a srucural break bu we leave ha for fuure work. We use daa from 99 alhough he european currency union was no in place before 999. Hence, we weigh he coss of having less daa less han he coss of using daa from a group of counries wihin a currency union, which was no in place a ha poin in ime. We believe, however, ha he iniial eurozone counries o some exen shared business cycles already in 995, as also suggesed by Dam [8]. In esimaing he model, we use imes series for 3 macroeconomic variables. The following ime series for Danish variables are aken from Saisics Denmark and Naionalbanken: 3 Real GDP Privae consumpion Governmen consumpion including public producion Governmen invesmen Expors Impors Toal invesmen including invenories and consrucion Labour income ax Privae employmen Unemploymen (ne) Indusry nominal wages deflaed by CPI Invesmen deflaor PPI index Impor deflaor Expor deflaor Danish nominal ineres rae 3 See he appendix for a deailed descripion of he source for each daa series. 6

30 The Res of World -variables are defined as he weighed sum of GDP, inflaion or he policy rae of he Danish rading parners excluding rading parners wihin he eurozone. The eurozone and he Res of he World are approximaely of equal size. Daa is aken from he Ecowin daa base and OECD. For he foreign economies we use he following variables: Inflaion in he eurozone and in he res of he world Real GDP in he eurozone and in he res of he world ECB policy rae Implied res of he world policy rae Effecive exchange rae o esimaion, we ransform he ime series ino quarer-on-quarer growh raes, approximaed by he firs difference of heir logarihm. As explained above, in he model, we include a rend in produciviy and in he relaive price of invesmens goods. The variables in he model herefore have rends and consequenly, we do no demean daa. Also, a number of addiional ransformaions are made o ensure ha variable measuremen is consisen wih he properies of he model s growh pah. Firsly, we remove he sample growh rae differenials beween he expor and impor variables and Danish GDP, as hese variables in he sample have grown faser han GDP reflecing globalisaion, see figure () and he discussion in secion (). Secondly, for he effecive exchange rae we band-pass filer and demean he daa. Lasly, we HPfiler daa for he foreign economies as we do no model rends in he foreign economies. Daa for Denmark including he effecive exchange rae agains he res-ofworld is shown in figures (3), (4) and (5). The ime-series used in he esimaion for he foreign economies are shown in figure (6). 4.. Shocks The model includes all in all 7 srucural shocks bu we only use including he shocks from he exogenous AR-models for public consumpion, public invesmens and labour income ax in he esimaion of he model. Finally, we use he 6 shocks from he DSGE-model for he wo foreign economies: Public consumpion shock, ε G Perm. ech shock, ε A P Temp. ech shock, ε A T Temp. invesmen shock, ε Z T Cap. uilizaion shock, ε cap Consumpion shock, ε con Price markup shock, ε ep Wage markup shock, ε ew 7

31 Expor shock, ε XE x Impor shock, ε Im Impor price markup shock, ε em Expor price markup shock, ε ex Riskpremia shock, ε RP D Public invesmen shock, ε IG Tax on labour income shock, ε N EA price shock, ε pi,ea EA oupu shock, ε y,ea ECB ineres rae shock, ε r,ea RoW price shock, ε pi,rw RoW oupu shock, ε y,rw RoW ineres rae shock, ε r,rw UIP shock, ε UIP As already described, all shocks are assumed o feed ino firs-order auoregressive processes, excep for he shock o he ECB policy rae, he shock o he policy rae for he res of he world, and he UIP shock, which are all whie noise, and he shocks o public invesmen and he labour income ax, which follow higher-order auoregressive processes. The shocks which are no used in he esimaion are shocks o hree axes, capial income ax, ε K, VAT, ε V AT, and ax on bond income, ε B. These ax raes have been kep almos fixed hroughou he sample bu we keep he shocks in he model for policy experimens. We also do no include shocks o he rend in he relaive price of invesmen goods, ε Z P. Lasly, we do no use he labour supply shock, ε χ, as he model is no able o disinguish beween his shock and he wage markup shock in he esimaion. In he esimaion we assume ha all daa are measured wih measuremen error excep for he ECB policy rae Calibraion I is well known ha some parameers in DSGE-models are hard o idenify and we do no assume ha our model is any differen. Also, some parameers such as he depreciaion rae on privae capial, δ, are beer esimaed using micro daa. The parameers we have calibraed in he esimaion are shown in able (). Also, we do no esimae he sandard deviaions of non-esimaed shocks as described above, ε o, ε V AR, ε k and ε L, nor heir auoregressive parameers. These are only in use for policy analysis. 4.4 Parameer esimaes and Disribuions Tables (3), (4), and (5) show our assumpions regarding he priors and he resuls of he esimaion. Tha is, he poserior mode esimaes of he srucural parameers and he shocks in he model. 4 We do assume measuremen errors for he ineres rae in he res-of-world, as his variable is an arificial variable consruced mainly by aggregaing he moneary policy raes in Sweden, U.K. and he U.S. 8

32 4.4. s The prior disribuion for he esimaed parameers are shown in he lef column of he ables. Regarding he priors, we generally follow he lieraure and make broadly similar assumpions abou our priors, see Chrisoffel e al. [8], Adolfson e al. [3], Burriel e al. []. The prior disribuions for he parameers are chosen in conformiy wih he consrains on he parameer space implied by heory. For hose parameers ha are bounded beween and, we choose a sandardised bea disribuion. For parameers ha are bounded from below a zero, we have chosen eiher a gamma or an inverse gamma disribuion o model he prior disribuions. An easier way o evaluae he choices we have made regarding our priors is o plo hem. Firs, we discuss he poserior disribuions Poserior esimaes The righ hand side of ables (3), (4), and (5) show he poserior disribuion of he parameers for our preferred specificaion of he model. The enries in he poserior-mode column refer o he values of he esimaed parameers ha are obained by maximizing he model s poserior disribuion. The disribuions are compued based on a Markov chain wih 5. draws. We use Dynares build-in figures for convergence (no shown for breviy). We found ha he 5. draws was enough o obain convergence. We highligh he following in our esimaion resuls. On he labour marke, we find a elasiciy of labour supply of.9. The inverse of his parameer deermines he size of he elasiciy of employmen wih respec o he real wage holding consumpion consan. We noe ha he elasiciy is wih respec o employmen and no hours. Hence, he elasiciy deermines how many workers subsiue in and ou of employmen in response o changes in wages, and he parameer is no relaed o he hours worked by a paricular person. We find a value for υ above. This implies some degree of wealh effec on he labour supply. This has implicaions for, e.g., he size of he fiscal muliplier, see Monacelli and Peroi [8]. On he nominal side of he economy, we find some differences across secors of he economy. The esimae of he Calvo parameer is quie low for domesic goods, θ p, wih a value of around /. We obain a similar value for expor prices, bu a much higher value for impor prices. According o he model esimaes, wages are more sicky han prices. This migh reflec ha a large share of Danish wages are se according o -3 year wage agreemens. The relaive flexibiliy of expor prices migh reflec ha Danish exporers can no o a grea exen rely on he nominal exchange rae o adjus o changes in marke condiions. Also, he indexaion of expor prices is almos zero, while quie large for wages wih a value of around a half. Regarding he he shocks, we do no find ha some shocks dominae in he sense of having a very big sandard deviaion. Anoher way o check he qualiy of he esimaion is by comparing he 9

33 prior and poserior disribuions of each parameer. As discussed above, his is also a mehod o evaluae he choices we have made regarding he priors. This is done in figures (8) o (4). In general he figures show ha he daa is informaive abou he poserior disribuion. Tha is, he poserior disribuion is no equal o he prior. However, some parameers do seem o be defined by heir prior; as an example he capial uilizaion cos parameer. This may reflec ha our daa sample is no informaive abou hese parameers. Our parameer esimaes can from his perspecive be regarded as calibraed or can be viewed as being esimaed wih a high degree of ouside informaion. As revealed by he figures, some priors are se quie igh. Tha reflecs o a large degree a necessiy; wihou hese igh priors he model would no work well in some imporan dimensions like impulse response funcions. Finally, he poin esimaes for he auoregressive parameers of shock processes show ha some shocks are very persisen, especially hose relaed o emporary echonology shocks, consumpion shocks, and expor shocks. This may sugges ha he model has some diffi culies in generaing he level of endogenous persisence presen in he daa and herefore he model ops for hese exogenous shocks o be highly persisen. 5 Model properies Having looked a he prior-poserior plos, poin esimaes and smoohed shocks, we now move on o sudy he model s empirical properies. We do his by reporing he model s impulse-response funcions in secion (5.). Here for seleced we also compare impulse-response funcions wih he impulse-response funcions from a srucural VAR. We move on o sudy forecas-error-variance decomposiions for various horizons in secion (5.). We firs highligh some resuls from he model which may seem in conras o comparable resuls from oher medium-sized DSGE-models like he ones in Chrisoffel e al. [8], Adolfson e al. [3], or Burriel e al. []. The key o he differences is sraighforward: Denmark s fixed exchange rae regime. Firsly, he variance decomposiion shows ha foreign shocks are he mos imporan drivers of he Danish busines cycle. This sands in conras o exising resuls, see, e.g., Jusiniano and Preson []. The fixed exchange rae regime implies ha shocks originaing in he eurozone have a direc effec on he Danish economy. Hence, eurozone shocks are ransmied direcly o he Danish economy hrough he ineres rae, and herefore have a large impac on he Danish business cycle on op of he effecs via inernaional rade. 5 Secondly, all shocks which affec inflaion cause an over- or undershooing. This is because in he model all goods are radable and because he Danish economy 5 For example, while he effecs on he Danish economy of a rise in he ineres rae in each of he wo foreign regions are qualiaively very similar, he impac is roughly wice as big afer a rise in he euro-area ineres rae as compared o a rise in he ineres rae in he res of he world. 3

34 can effec neiher foreign prices nor exchange raes due o he fixed exchange rae regime and he small open economy assumpion. This implies ha he seady sae level of Denmark s erms of rade needs o be achieved evenually. This provides he economy wih a nominal anchor and ensures deerminacy of he model. The nominal anchor imposes a lo of resricions on he economy and give rise o differences beween he effec of shocks in he model in his paper and he previously menioned papers. 5. Impulse-response funcions We focus on a few of he mos imporan shocks in our analysis of he impulseresponse funcions, namely a ransiory echonology shock, a domesic price markup shock, a shock o foreign oupu, a shock o he ECB policy rae, and he mos imporan policy insrumen for Denmark, governmen spending. The ineres rae shock provides a view on he moneary policy ransmission mechanism from he ECB o he Danish economy, while he governmen spending shock boh provides a fiscal muliplier and an example of a demand shock. The firs hree shocks consiue examples of supply, cos-push, and foreign demand shocks respecively. We furher compare he moneary policy shock, he public consumpion shock and he foreign consumpion shock wih impulse-response funcions from a srucural VAR. We focus on he effecs on a subse of he endogenous variables in he model. 5.. Consequences of a emporary echonology shock The impulse-response o a posiive shock o he emporary echnology shock of size one sandard deviaion is shown in figure (9). A emporary echnology shock decreases real marginal coss and hence domesic prices iniially. However, he forward looking firms correcly anicipae higher supply and demand in he economy. As i urns ou, he higher demand effec in he esimaed economy rapidly miigaes he increase in inflaion. The increase in aggregae demand boh sems from he iniial lower prices bu also from wealh effecs on consumpion: The forward looking households realize ha hey have become more producive and hence richer wich induces hem o consume some of he wealh oday. This is amplified by a subsequen drop in he real ineres rae due o higher inflaion, which is no combaed hrough nominal ineres rae increases. The laer reflecs he fixed-exchange rae regime in Denmark. The more producive capial leads o an invesmen boom furher increasing demand. Expors fall due o he subsequen rise in inflaion. Togeher wih increasing impors, his couneracs he rise in domesic demand from invesmens and consumpion. Turning o he labour marke, higher produciviy increases supply of goods in he economy leading o an increase in he demand for labour. Tha is, he workers have become more producive which causes an ouward shif in he labour demand curve leading o higher real wage and employmen. This is he so-called classic effec, bu no he only effec. Workers have become more 3

35 producive and richer which makes hem decrease heir labour supply - a wealh effec on employmen. This pus a furher upward pressure on real wages bu downward pressure on employmen. If he model was model did no feaure any Keynesian effecs, employmen would fall in he absence of an increase in aggregae demand, as more goods can be produced wih fewer workers afer a echnology shock. However, as explained above, aggregae demand does rise and iniially pushes employmen up. 5.. Consequences of a domesic price markup shock The impulse-response o a one sandard deviaion posiive shock o he domesic price markup is shown in figure (). A posiive shock can be inerpreed as a siuaion in which domesic firms se a higher markup over marginal coss. Tha is, firms se a higher price, all else equal. This causes inflaion o rise, bu only in he firs few quarers, despie he fac ha he shock is quie persisen wih a half-life of around quarers. This is because he forward-looking firms anicipae ha he price increase leads o a decline in economic aciviy and hereby lower marginal coss. Ulimaely, firms seek o reesablish he opimal relaionship beween prices and marginal coss and herefore decrease heir prices over ime. The shock leads o lower oupu because households face higher prices. This effec is miigaed by lower real ineres raes, as he policy rae does no reac o he higher inflaion. Afer a few quarers, he decline in prices leads o an improvemen in compeiiveness and higher expors, which helps in driving oupu back owards he seady sae. The decline in aggregae demand causes employmen o fall and exers downward pressure on real wages Consequences of a shock o foreign demand While less obvious for he echnology and domesic markup shock, we have an observable variable for foreign demand, which in his case is measured by GDP in he res of he world. This series can be included ino a VAR and compared o he esimaed impulse-response funcions produced by he DSGE model. We do he same comparison for shocks o he ECB policy rae and governmen spending in he subsequen subsecions. We use he same daa as in he esimaion of he DSGE model. All series are in logs excep for inflaion, which is in levels. The VAR is idenified using a Choleski decomposiion. We order he shock variable, i.e. GDP in he res of he world, las in he VAR. This implies ha Danish variables in he VAR canno reac in he firs quarer o shocks o foreign GDP. By including he shock variable las in he causal srucure we ry o conrol for exogenous movemens in he oher variables in he VAR. This can be considered he mos cauious approach, as discussed by Abildgren []. The resuls for a shock o GDP in he res-of-world region are shown in figure (). Noice ha we do no provide SVAR resuls for all he endogenous variables in he figure. We look a a one percen increase in res-of-world oupu. 3

36 In he following quarers GDP in Denmark rises boh in he SVAR and in he DSGE-model hough he effec is much larger in he DSGE-model. Boh models predic a negaive response from around 4 quarers. The recession is, however, more severe in he DSGE-model han in he SVAR. The iniial larger response in he DSGE-model can be aribued primarily o he idenificaion sraegy in he SVAR. In he DSGE model expor booms. The boom pushes employmen and he real wage upwards wih higher marginal coss as a consequence, and hus higher inflaion. This higher inflaion is, as usual in our DSGE-model, followed by deflaion such ha he iniial loss of compeiiveness can be regained. The inflaionary iniial period implies a fall in he real rae of ineres, while he deflaion period implies an increase in he real rae of ineres, which explains he small response of consumpion. Finally, noice ha he uncerainy bands in he DSGE-model are much smaller han in he SVAR. This can be explained by he esimaion procedure in which he foreign block is esimaed seperaely of he Danish model. The uncerainy regarding parameer values in he foreign block, which obviously play a cenral role in his ype of shock, consequenly does no show up in he confidence bands Consequences of a shock o he ECB moneary policy rae Nex we consider he effecs of a shock o he ECB policy rae, which we include in levels in he VAR. This is he de faco moneary policy rae for he Danish economy in normal imes. In he VAR we order he ECB policy rae afer he real variables in he causual srucure, following Chrisiano e al. [999]. We normalize he shock so ha i is equivalen o a 5 basis poins increase in he ECB policy rae. The impulse responses from he VAR and he DSGE-model are picured in figure (). Noice ha again we do no provide SVAR resuls for all he endogenous variables in he figure. GDP in he VAR says unchanged in he firs quarer, which is due o he idenificaion of he VAR. GDP in he DSGE model falls around.5 percen on impac. The shock is less persisen in he DSGE-model han in he VAR-model and only saisically significan during he firs year or so. Noice ha in he DSGE-model a shock o he ineres rae in he eurozone does no imply ha he ineres rae is he only variable ha moves. The eurozone model is esimaed as a small scale DSGE-model along he line of Galí [9] and Woodford [3], see secion (3.8) and appendix (9). Hence, a posiive shock o he policy rae in he eurozone also causes a fall in GDP and inflaion in he eurozone. The fall in eurozone GDP pus downward pressure on Danish expors, all else equal. However, he fall in inflaion in he eurozone is smaller han he fall in Danish inflaion causing an improvemen in Danish compeiiveness. This depresses impors and simulaes expors and herefore GDP in Denmark. This explains he srong rebound of Danish GDP. We noice ha he iniial fall in GDP for Denmark as a consequence of conracionary moneary policy is of abou he same size as he esimaed effec in DSGE-models for he eurozone, see Chrisoffel e al. [8]. We also noice 33

37 ha he effecs of a moneary policy shock from he res-of-world economy are qualiaively similar, bu ha quaniaively speaking, he effecs are only lile more han half as big as he effec from he moneary policy shock from he eurozone. This is due o he fac ha he moneary policy rae eners direcly in he Danish economy, which parly explains why he foreign shocks conribue so much o he variaion in Danish GDP, as discussed in secion (5.) below Consequences of a governmen spending shock Ravn and Spange [3] perform a VAR-based analysis of he effecs of a emporary increase in public consumpion. We refer o ha paper for a deailed descripion of he VAR-model. Here we use and compare he resuls in ha paper wih he esimaed response o expansionay fiscal policy in he DSGE-model. Tha is, we compare he implied fiscal mulipliers. In figure (3) we compare he impulse response funcions from Ravn and Spange [3] o he impulse response funcions from he esimaed DSGE-model. For a deeper analysis of he effecs of fiscal shocks under fixed exchange raes in a DSGE-model we refer o Pedersen []. The following observaions from his analysis meri some commens. The fiscal muliplier in he DSGE-model resides wihin he confidence bands produced by he VAR-model alhough he mulipliers are somewha differen. As can be seen from he figure, he DSGE-model predics a fiscal muliplier of around.7, which is subsanially smaller han he fiscal muliplier prediced by he VAR of around.3. The resuls are comparable o he findings of Pedersen [], who discusses fiscal mulipliers in a DSGE-model calibraed o he Danish economy. Noe also ha once again, he confidence bands produced by he VAR are a lo wider han hose from he DSGE-model. The reason is ha he mos imporan parameer in deermining he impac of his shock; he persisence of he shock, has been calibraed so as o mach he esimaed persisence from Ravn and Spange [3]. This means ha here is no uncerainy surrounding his parameer, so ha he uncerainy surrounding he impac of he shock becomes small as well. The economic effecs driving he muliplier are quie sandard: Consumpion falls due o a wealh effec, impors increase, while expors decrease due o loss of compeiivenes as inflaion rises. The increase in inflaion is, however, shorlived: Danmark needs o regain compeiivenes and herefore he economy experiences deflaion. In he labour marke, he wealh effec gives rise o a righwards shif in he labour supply curve as he households feel poorer and hus work more. This pus downward pressure on wages and drives up employmen. A he same ime, however, he firms wish o mee he exra demand as heir prices are sicky and hey do so by hiring more labour, pushing real wages up. As seen from figure (3), real wages increase and herefore he demand effec on he labour marke wins. Tha is, he exisence of nominal rigidiies makes he wedges in he economy move counercyclically, driving up real wages. Afer some quarers real wages sar o fall. 34

38 There is one common heme from he analysis of he impulse response funcions in his secion: Increasing prices, due o eiher cos-push, produciviy shocks or demand shocks, leads o a subsequen deflaionary period as he erms of rade need o rever o he iniial value. If no, Denmark would be loosing compeiveness indefiniely, and hence a share of world rade. This is because Denmark is a small open economy which canno influence he macroeconomic sae of is rading parners and due o he fixed echange rae: Deflaion is he only means o regain he iniial erms of rade. 5. Forecas-error-variance decomposiions In ables (6), (7), and (8) we show he conribuion of he srucural shocks in he model o he forecas error variances of a seleced se of observed variables. This exercise ries o provide a quaniaive insigh as o which srucural shocks on average in he esimaed model during he sample period give rise o variabiliy in he endogenous variables in he model. For simpliciy we only look a he variance decomposiion for he s, 4 h, and 4 h quarer, and in wha follows we concenrae on he variance decomposiion for real GDP. The ables illusrae ha foreign shocks are very imporan drivers of he Danish business cycle. The group of srucural shocks originaing in he wo foreign economies (inflaion, oupu, ineres raes, and he effecive exchange rae) accoun for beween 6 percen of he variaions in real GDP a he very shor erm, quarer, and 7 percen a longer horizons, 4 quarers. In paricular, he shock o oupu in he euro-area is by far he larges conribuor o movemens in Danish GDP a all horizons. This should no be surprising, as Denmark is a very small and open economy wih a fixed exchange rae owards he Euro. Anoher imporan source of GDP variaions is he emporary echnology shock, which accoun for -5 percen of he variaions in real GDP a all horizons. Domesic price markup shocks accoun for around 5 percen a all horizons. While our finding ha variaions in Danish GDP are o a large exen driven by shocks from abroad may no seem very surprising, i does sand in conras - and remarkably so - o he resuls of Jusiniano and Preson []. Afer esimaing a small open economy model in he radiion of Gali and Monacelli [5] for Canada, hey sudy he conribuion of shocks o he US economy for fluacuaions in Canadian GDP. They find ha US shocks accoun for less han 3 percen of he movemens in a number of Canadian macroeconomic variables, including GDP, a all horizons. In line wih his resul, he esimaed DSGE model of he Swedish Riksbank, see Adolfson e al. [7] also ascribes less han percen of GDP flucuaions in Sweden o foreign shocks. Obviously, he main difference beween Denmark and hese oher small open economies is ha Denmark has pegged is currency o he Euro, whereas Canada and Sweden boh have a flexible exchange rae. Aasvei e al. [3] sugges wo main reasons for he small explanaory power ypically assigned o foreign shocks in esimaed small open economy models: The absence of oher cross-counry 35

39 linkages han he rade channel (for example via financial markes or consumer and invesor senimens), and he lack of direc effecs of foreign-economy shocks on domesic variables (for example hrough common shocks). A fixed exchange rae fills boh of hese gaps, as i makes way for anoher channel, he ineres rae channel, hrough which shocks originaing in he eurozone have a direc effec on he Danish economy. As he variance decomposiion shows, he conribuion of shocks in he eurozone is much larger han ha of shocks in he res of he world for oupu flucuaions a medium and long horizons, as well as for movemens in inflaion and privae consumpion a all horizons. This confirms ha eurozone shocks are ransmied direcly o he Danish economy hrough he ineres rae, and herefore have a large impac on he Danish business cycle on op of he effecs via inernaional rade. Finally, even hough he ransmission of shocks works hrough he ineres rae, he variance decomposiion shows ha ineres rae shocks in he eurozone are much less imporan han oupu shocks. The explanaion is ha movemens in he eurozone ineres rae, which is se according o a Taylor rule, are primarily driven by shocks o eurozone oupu and inflaion, whereas moneary policy shocks are less imporan. These insighs, which are confirmed by he variance decomposiion of he eurozone ineres rae, merely sugges ha he rule-based componen of moneary policy is much more imporan han moneary policy shocks, in line wih a number of empirical sudies, see e.g. Chrisiano e al. [999]. 6 Applicaion - Hisorical Shock Decomposiion In his paper we focus on a hisorical shock decomposiion of Danish real GDP for he period 4 o he presen and leave forecasing exercises and counerfacual analysis o fuure work. We focus on his period as i compromise he build up o he financial crisis, Lehman s collaps and he subsequen period. We decompose real GDP ino he conribuions of he model s srucural shocks. To faciliae he presenaion, we group he srucural shocks ino five caegories: markup, demand, produciviy and capaciy shocks, he foreign economies and fiscal policy. Markups: Domesic, expor and impor price markup and wage markup shocks Demand: Consumpion, invesmen, impor, expor shocks Produciviy and capaciy: Temporary and permanen echonology shocks, uilizaion shock Foreign shocks: All shocks o producion, inflaion, ineres raes and uip-shocks from euroarea and res-of-world Fiscal policy: All shocks o axes and public consumpion and invesmen 36

40 We show in figur (4) he combinaion of srucural shocks which according o he model have given rise o he hisorical developmen in real GDP for Denmark in period 4-. The hick line in figur (4) shows he acual developmen in GDP around an esimaed growh rae and we will in wha follows denoe i as he oupu gap. 6 The sum of all he srucural shocks add up o he quarer-o-quarer growh rae for GDP. A group of variables aken ogeher has conribued posiively o growh in GDP in a given quarer if heir sum is posiive. In he beginning of our sample GDP is below rend bu on a upward pah afer he low-growh period during he beginning of he 9 s. This cycle ends a he beginning of he s. Around his period, he Danish economy experienced a shorlived and mild economic downurn. This downurn was succeeded by a large upurn culminaing a he oubreak of he financial crisis. Denmark was, as many developed economies, hi hard by he financial crisis causing a large oupu gap, which says negaive for he remainder of he sample. The nex subsecions dig deeper ino he effecs of hese 5 subgroups of srucural shocks on he hisorical developmen of real GDP in Denmark. We will look a he full sample bu emphasize he build up o he financial crisis and he following downurn. 6. Foreign shocks The firs observaion we make is ha by comparing he 5 subgroups he group of foreign shocks provides he greaes impac on he hisorical developmen of Danish real GDP. This confirms he resuls in he variance decomposiion in secion (5.). In figure (5) we have decomposed he sum of he foreign shocks in he respecive shocks wihin he group: Producion, inflaion, ineres raes in he wo economies as well as shocks o he exchange rae. The Danish economy booms along wih he global economy from 5 unil he oubreak of he financial crisis. From 8, foreign shocks exer a srong negaive impac on he producion gap in Denmark. As can be seen from figure (5), a he onse of he financial crisis he conracion in oupu is couneraced by low ineres raes in boh he eurozone and res-of-world. Laer on, he zero lower bound sars o bind and herefore he ineres raes conribue negaively o GDP growh; he economic siuaion would prescribe even lower ineres raes bu cenral banks are resriced by he zero lower bound. A he end of our sample, he conribuion of he foreign secors is roughly zero. This is he resul of wo offseing effecs: While he res-of-world block exers a posiive effec, likely reflecing he economic recovery and mainained expansionary moneary policy in he US, he euro-crisis sill conribues negaively o he growh in Danish GDP. 6 This is no equivalen o he oupu gap in DSGE erminology. We leave he DSGE oupu gap - he difference beween acual oupu and he level of producion which would have prevailed in he absence of any nominal rigidiies - o fuure work. 37

41 6. Demand shocks Shocks o domesic demand conribued o he srong growh in Danish GDP before he oubreak of he financial crisis, as seen from figure (4). We show in figure (6) he conribuion of each shock in his group o movemens in he oupu gap. The subgroup consiss, as an example, of invesmen shocks. A posiive shock o invesmens means ha a given invesmen in capial in he curren period leads o a bigger increase in he sock of insalled capial in he nex period han wha would normally be he case. In he model a shock o invesmen also consiss of residenial invesmens as we do no have a separae residenial secor in he model, and because he observed daa series for invesmens consiss of all invesmens as we wish o cover he enire naional accoun. We herefore assign an imporan par of he posiive invesmen shocks during he period 5-8 o higher residenial invesmens. From figure (6) we also observe ha shocks o Danish households preferences for impored goods conribued posiively o he oupu gap during he period 5-8. This may reflec ha Danish households were more eager o buy Danish goods and services han usually. A possible explanaion o his may be ha Danish households consumed a lo of residenial goods and services. 6.3 Markup shocks We now urn o he group which consiss of shocks o he economy s markup shocks. This subgroup consiss of shocks o wage and price markups (domesic prices, impor prices and expor prices). We decompose he conribuion of he markup shocks o he growh rae in real GDP in figure (7). In he build-up o he financial crisis, he markup shocks aken ogeher affeced he oupu gap negaively. This is primarily due o he domesic price markup shock which was relaively high before he crisis. The economic inuiion behind his observaion is ha domesic producers in hose years uilized he exraordinary high domesic and foreign demand o increase heir margins more han usually. Tha is a sign of an overheaed economy. A bi more surprising is ha figure (7) shows ha he wage markup shock affeced GDP posiively during he build up o he financial crisis, 5-8. This implies ha he wage markup was relaively low in hese years. Looking back a figure () in secion (), a relaively smooh increase can be observed in he indusrial wage deflaed by he consumer price index, along wih a fall in unemploymen and a srong increase in employmen (no shown). Only in he laer phase of he build-up o he financial crisis an equally srong increase in real wages can be observed. The limied wage increases may be aribued o inflows of foreign labour and increases in he labour force. To explain hese movemens he model idenifies a decrease in he wage markup, which conribues posiively o GDP growh. The subsequen bus leads o a downward pressure on prices due o a drop in demand. As hey anicipae falling domesic and foreign demand, domesic producers lower heir margins, which affecs GDP posiively. On he conrary, 38

42 he wage markup conribues negaively o he growh rae in GDP. This can be explained by a rapid increase in unemploymen, while wages did no fall accordingly, see also figure (). 6.4 Produciviy and capaciy shocks The decomposiion in figure (4) poins o produciviy and capaciy (or supply) shocks as an imporan driver of he boom during he years 5-7 and, o a smaller exen, he subsequen bus. This may seem somewha surprising a a firs glance. In his subsecion, we argue ha his finding is in line wih he daa as well as wih economic heory. Firsly, he daa for derended hourly produciviy shows a similar paern over he relevan period. Secondly, during his period, oupu was booming while inflaion remained fairly low and sable, suggesing ha shocks originaing on he supply side played an imporan role for business cycle flucuaions. We emphasize ha produciviy and capaciy shocks should no be inerpreed as a facor behind he overheaing of he Danish economy and he associaed loss of compeiiveness agains Denmark s rading parners. From a DSGE perspecive he economy s response o produciviy shocks is effi cien and hence does no call for economic sabilizaion policy. Raher, our findings sugges ha he acual overheaing of he Danish economy during hese years may have been smaller han previously hough as he economy seems o have been able o expand poenial producion. This poins o he imporance of idenifying he fundamenal drivers of he business cycle especielly if policy makers wish o reac o oupu gaps. Figure (7) shows he movemens in measured hourly produciviy in he Danish non-farm secor. The figure illusraes ha from around 3 and unil he end of 6, produciviy growh was in fac above he esimaed rend for our sample period. From lae 6, measured produciviy hen dropped massively, reaching is rough in he fourh quarer of 8 a he peak of he financial crisis. This developmen fis fairly well wih he produciviy shocks observed by our esimaed model during he same years. In paricular, he large posiive produciviy shocks in 5-6 and he subsequen reversal coincides closely wih he daa, alhough he model-implied reversal seems o lag he daa by a few quarers. In addiion, we suspec ha oher relaed facors may have conribued o he model-implied produciviy shocks during he boom. This includes inflow of foreign workers, which probably played a role in keeping marginal coss down during hese years as well he role of China in keeping impored inflaion on a relaively low level. Overall, figure (7) illusraes ha supply-side facors are likely o have played an imporan role in he Danish boom-bus cycle during he mid- s. In general, he years leading up o he recen crisis were characerized by a boom in oupu wihou an associaed rise in inflaion, as evidenced, for insance, by he quarerly growh raes in Danish producer prices displayed in figure (5). Danish inflaion ook off only during he final par of he boom, i.e. from he second half of 7 onwards. Even hen, par of he increase in inflaion was 39

43 driven by a global rise in food and energy prices. This sounds almos like a exbook descripion of he effecs of a supply shock; enabling firms o increase producion a an unchanged level of marginal coss. In ligh of his, i is no surprising ha our model ascribes a leas par of he boom in oupu o facors originaing on he supply side. 6.5 Fiscal policy In a fixed exchange rae regime such as Denmark s, moneary policy can no be used o dampen domesic demand and price pressures. This implies ha fiscal policy plays he role as he main sabilizaion insrumen in he Danish economy. Our analysis so far has indicaed ha he large posiive oupu gap in Denmark before he financial crisis can be aribued o a combinaion of supply side facors and a srong growh in domesic as well as foreign demand. From a sabilizaion perspecive, such a siuaion would call for a conracionary fiscal policy so as o dampen he growh in aggregae demand. However, figure (4) shows ha during he boom years, discreionary fiscal policy, which in our seup is defined as he conribuion from he group of fiscal policy shocks o he oupu gap, exered a small bu mosly posiive effec on oupu. In oher words, fiscal policy appears o have been oo expansionary, or a he very leas no suffi cienly conracionary, during he boom years. In 9, Denmark adoped an expansionary fiscal policy in response o he financial crisis. From figure (4) his is refleced in posiive conribuions from discreionary fiscal policy. Due o he large auomaic fiscal sabilizers in he Danish economy, Denmark s public finances suffered, and from, he fiscal simulus was wihdrawn and replaced by fiscal auseriy. By consrucion, he effecs of auomaic fiscal sabilizers do no show up in figure (4), as hese are no associaed wih heir own se of srucural shocks o he economy, bu insead work by aenuaing oher shocks. As a robusness check we compare he conribuion of discreionary fiscal policy shocks in he esimaed model o oher available measures of he effecs of fiscal policy. In Denmark, he effec on GDP from discreionary fiscal policy are radiionally measured by he so-called (one-year) fiscal effecs. Fiscal effecs measure he conribuion from discreionary fiscal policy on he growh rae of GDP relaive o a siuaion in which fiscal policy is neural. As an example, a neural sance of governmen spending may be hough of as a siuaion in which he growh rae of public spending follows he seady-sae growh rae of GDP. A posiive fiscal effec hus implies ha he discreionary par of fiscal policy in a given year conribues posiively o he growh in real GDP. The fiscal effecs are calculaed by he Minisry of Finance and he Economic Council, and are based on he change in expendiure/revenues for a given iem on he primary governmen balance and he associaed muliplier for ha iem in he radiional macroeconomeric models used by hese insiuions. Differences in he fiscal effecs repored by he wo insiuions may herefore arise due o differences in he models used and due o differen assumpions as regards a neural fiscal policy. 4

44 In he DSGE model he effec on GDP of discreionary fiscal policy is measured by he size of he green columns in figure (4). I may be useful o hink of hese columns as impulse responses where he size of he shock is compued in he esimaion of he model. The baseline for he impulse responses is he model s seady sae in which discreionary fiscal policy is neural. Hence, here is a fairly close connecion beween he effecs of fiscal policy in he DSGE model and he fiscal effecs. In figure (8) we compare he fiscal effecs compued by he Minisry of Finance and he Economic Council wih he fiscal policy shocks from he DSGEmodel, i.e. he green columns in figure (4) ransformed o an annual basis. The main impression is ha he differen ways of measuring fiscal policy yield roughly he same resuls. In mos years, here is a fairly close link beween he hree measures. There are some differences beween he fiscal effecs and he effecs from he DSGE-model; especially in 999- and in 5. However, here are also noable differences beween he fiscal effecs as compued by he Minisry of Finance and he Economic Council. This suggess ha while he exac conribuion of fiscal policy in a given year may be hard o measure, he hree differen approaches give rise o similar conclusions for he sample period aken ogeher. 7 Conclusion In his paper, we have se up a newly developed DSGE-model for he Danish economy, and shown and explained how o esimae i using Bayesian echniques. We have presened esimaion resuls and examined he empirical properies hrough impulse-response funcions and variance decomposiions. Our resuls indicae ha he model has economically plausible properies. Finally, we have used he model o compue a hisorical shock decomposiion of Danish real GDP growh. The model is, however, no finished and we expec a coninuing developmen in ligh of economic and academic developmens. We can easily poin o some improvemens: We have no provided a DSGE-based oupu gap, he model does no have inpus of impored goods in he producion funcion, and finally, and perhaps mos imporanly, he model does no feaure house prices, financial fricions or banking. In he fuure, we plan o incorporae hese elemens in he model. Also, we hink ha he se of possible applicaions of his model is fairly large. As an example, we have no alked abou forecasing or counerfacual analysis in his paper. 4

45 8 Appendix A: The Daa As described in he main ex, we use imes series for 3 macroeconomic variables. These include 6 Danish series, 6 foreign series, and he effecive Danish exchange rae. The Res of World -variables are defined as he weighed sum of GDP, inflaion or he policy rae of Denmark s rading parners excluding he rading parners wihin he eurozone. We ransform he ime series ino quarer-on-quarer growh raes, approximaed by he firs difference of heir logarihm. In he following, we describe he source of each of he variables used in he esimaion. Real GDP: Danmarks Naionalbank, MONA (variable name: fy). Privae consumpion: Danmarks Naionalbank, MONA (fcp). Governmen spending: Danmarks Naionalbank, MONA (fco). Governmen invesmen: Danmarks Naionalbank, MONA (fio). Expors: Danmarks Naionalbank, MONA (fe). Impors: Danmarks Naionalbank, MONA (fm). Toal privae invesmen: Danmarks Naionalbank, MONA (fip; chained sum of all ypes of privae invesmen, including invenories and consrucion). Labor income ax: Danmarks Naionalbank, MONA (bsda). Privae Employmen: Danmarks Naionalbank, MONA (qp+qs). Unemploymen: Danmarks Naionalbank, MONA (ul / (qp+qo+qs) ). Indusry nominal wages deflaed by CPI: Danmarks Naionalbank, MONA (lna / pcp). Invesmen deflaor: Danmarks Naionalbank, MONA (pip; relaive price of oal privae invesmen). Producer price index: Danmarks Naionalbank, MONA (pyfbx). Impor price deflaor: Danmarks Naionalbank, MONA (pm). Expor price deflaor: Danmarks Naionalbank, MONA (pe). Danish nominal ineres rae: Danmarks Naionalbank, MONA (idi, quarerly rae). Effecive Danish exchange rae: Danmarks Naionalbank, MONA (efkrks). eurozone inflaion: OECD (obained from Ecowin). 4

46 Res of World inflaion: OECD (Ecowin). eurozone real GDP: OECD (Ecowin). Res of World real GDP: OECD (Ecowin). ECB policy (nominal) ineres rae: OECD (Ecowin). Res of World implied nominal ineres rae: OECD (Ecowin). 9 Appendix B: The eurozone and res of world models The main impacs of he foreign counries on he Danish economy work hrough rade and ineres raes. We consequenly aim for he mos flexible model for hese wo economies and downplay he microfoundaions Furher, we do no aim o esimae a common rend for all he hree economies as he daa poins o differen seady sae growh raes in oupu. Denmark s role as a small open economy implies ha we can model he foreign economies as being exogenous o he Danish economy. Also, we do no aim o model he inerrelaions beween he eurozone and res of he world, and we consequenly do no model rade beween hese wo economies. We do, however, include a UIP-relaion beween he policy rae in he wo counries so ha we can pin down he effecive exchange rae beween Denmark and res of world. The model equaions are shown in secion (3.8) while he parameer esimaes are shown in able (). We use he same sample as for he Danish economy. Daa are HP-filered and shown in figure (6). We esimae he inernaional linkages using a wo-sep procedure: In he firs sep, we esimae he wo separae small-scale DSGE models of each of he foreign blocks. In he second sep, where we esimae he main model for Denmark, we include hese esimaed relaions, and hen esimae he shocks in he foreign models by including again he daa for he foreign economies. 43

47 Appendix C: Marke Clearing In his appendix, we demonsrae ha all markes clear in he model. Sar from he budge consrain of he household, which reads: ( ) + τ V AT P C C + P I I + B DK + B I + T P P ( ( ) ) = Π + τ K r K u + τ K δ K z u (u ) K + R B DK + + R ECB exp( ψ d ( B I Y π DK + ( τ n ) w N + κ B w U N. ) BI )B I Y π DK τ B B DK (R ) π DK + Now use he governmen s budge consrain o inser for B DK side, and rewrie o obain: ( ) + τ V AT P C C + P I ( R I + P P π DK on he lef-hand B DK + G + w U N κ B T R ) + B I + T ( ( ) ) = Π + τ K r K u + τ K δ K z u (u ) K + R B DK + R ECB + exp( ψ d ( B I Y π DK + ( τ n ) w N + κ B w U N. ) BI )B I Y π DK τ B B DK (R ) π DK + Nex, inser he expressions for T R and G presened in he main ex, as well as for profis, which we can wrie as Π = Y w N r K u K : ( ) + τ V AT P C P C + P I P I + B I + T ( Y w N r K u K ) ( ( τ K ) r K u + τ K δ K z u (u )) K R B DK R ECB exp( ψ d ( B I Y P C π DK = T + τ V AT C + τ K P +τ B R π DK B DK R π DK ) BI )B I Y π DK ( τ n ) w N κ B w U N ( r K u δ K) K + τ N w N B DK C G P I P I G w U N κ B. + τ B B DK (R ) π DK 44

48 We can now begin o cancel ou erms: P C C + P I R I + B I Y + z u ECB (u ) K P P = C G P I P I G, which we can rewrie as: Y = P C C + P I I +C G + P I I G +z u (u ) K + B I P P P exp( ψ d ( B I Y R ECB Now apply he resource consrain as defined in he main ex: P C C DK + P I I DK + C G + P I I G P P P = P C P C + P I P I + C G π DK + z u (u ) K + P X Ex P + P I I G + z u (u ) K + B I P exp( ψ d ( B I Y R ECB π DK ) BI )B I Y ) BI Y exp( ψ d ( B I Y π DK P X Ex P C ( C C DK ) P I ( I I DK P P P π DK The final sep is o apply he equaion deermining Denmark s ne foreign asse posiion, which reads as: B I = B I R ECB R ECB Inser his o obain: P X Ex P C P P which we can rewrie as: P C P exp( ψ d ( B I Y π DK exp( ψ d ( B I Y π DK ( C C DK ( C C DK Im = P C ) BI Y ) ) BI Y ) R ECB = B I ) B I + P X P Ex P M P exp( ψ d ( B I Y Im B I = P X P Ex P M P Im. ) P I ( I I DK ) P = X Ex P M Im, P P P ) P I ( C C DK ( I I DK P ) = P M P ) + P I ( I I DK which is he expression for impors used in he main ex. P M ) Im ) BI Y, (78) ) ) B I ) BI Y B I.. ) B I Tables and figures 45

49 disribuion Poserior disribuion Type Source Mean s.d. Mean Mode s.d. Median 5 pc. 95 pc. Parameers for euroarea model Weigh on expeced oupu ρ EA Y Normal Weigh on real rae of ineres φ EA Y Normal Weigh on expeced inflaion ρ EA π Normal Weigh on oupu φ EA π Normal Policy ineres rae smoohing parameer ρ EA R Normal Persisence of shock o oupu ρ EA ɛ Y Bea Persisence of shock o inflaion ρ EA ɛ π Bea Shock o oupu ɛ EA Y Inv. gamma Shock o inflaion ɛ EA π Inv. gamma Moneary policy shock ɛ EA R Inv. gamma Policy ineres rae, reacion o inflaion Γ EA π Calibraed.5 Policy ineres rae, reacion o inflaion Γ EA Y Calibraed.5 Parameers for res of world model Weigh on expeced oupu ρ RoW Y Normal Weigh on real rae of ineres φ RoW Y Normal Weigh on expeced inflaion ρ RoW π Normal Weigh on oupu φ RoW π Normal Policy ineres rae smoohing parameer ρ RoW R Bea Persisence of shock o oupu ρ RoW ɛ Y Bea Persisence of shock o inflaion ρ RoW ɛ π Bea Shock o oupu ɛ RoW Y Inv. gamma Shock o inflaion ɛ RoW π Inv. gamma Moneary policy shock ɛ RoW R Inv. gamma Policy ineres rae, reacion o inflaion Γ RoW π Calibraed.5 Policy ineres rae, reacion o inflaion Γ RoW Y Calibraed.5 Table : Esimaed and calibraed parameers for he foreign counries: This able repors he prior disribuion and he poserior mode esimaes of he srucural parameers for he model. 46

50 Value Parameer explanaion Explanaion β.99 Discoun facor To mach annualized SS real rae δ K.5 Privae capial depreciaion Sandard value ɛ P 6 Sub. beween good Markup of %, sandard α.3 Capial share SS labour share in producion ψ d. Risk premia for inv. in foreign bonds Small bu keep model saionary ɛ W 3 Sub. beween laboures Naural rae of unemploymen of 4% ψ G. Ela. of Danish ineres rae risk premia wr. deb Corsei e al. ωx.5 Relaive size of foreign counries Average hrough period η.5 Public capial influence in producion Microdaa, Kamps 4 δ G.5 Depreciering of public capial Sandard ɛ X 6 Sub. beween expor goods Markup of %, sandard ɛ M 6 Sub. beween impor goods Markup of %, sandard φ I Immediae implemenaion of pub. inv. Time-o-build, Leeper e al. [] φ I i i=,,3 3 s-3rd q. implemenaion of pub. inv. Time-o-build, Leeper e al. [] ζ T.5 Ela. of lump-sum axes wr. public deb S. model is saionary κu.5 Unemploymen compensaion LR average for he sample ū SS capial uilizaion cos Simplificaion c.349 Se s. ū= Simplificaion ϑc.6 Degree of home-bias in con. Impor conen in oal privae consumpion ϑi.5 Degree of home-bias in inv. Impor conen in invesmens. Table : Calibraed parameers: This able shows ha parameers which are calibraed in he esimaion. 47

51 disribuion Poserior disribuion Type Source Mean s.d. Mean Mode s.d. Median 5 pc. 95 pc. Preferences and producion Habi formaion h Bea SW Wage indexaion ΓW Bea Medea Price indexaion ΓP Bea Medea Impor price indexaion ΓM Bea Medea Expor price indexaion ΓX Bea Medea Calvo, wages θw Bea SW Calvo, impor price θm Bea SW Cavlo, expor price θx Bea SW Calvo, price θp Normal SW Elasiciy ɛ W Normal ADLS Frisch labour supply φ Normal Gali Pref. for degree of wealh-effec ν Bea Gali Invesmen adj. cos κi Normal SW Uilizaion adj. cos C Normal Cos of adj impor in C. χc Normal Medea.. Cos of adj impor in I. χi Normal Medea.. CES ela. C. υc Gamma SW CES ela. I. υi Gamma SW Table 3: Esimaed parameers: This able repors he prior disribuion and he poserior mode esimaes of he srucural parameers for he model. ADLS7 refers o Adolfson (7), SW3 refers o Smes and Wouers (3), Medea refers o Fernández-Villaverde e al. (9) and Gali refers o Galí e al. () 48

52 disribuion Poserior disribuion Type Source Mean s.d. Mean Mode s.d. Median 5 pc. 95 pc. Persisence of shocks Persisence of perm. ech. shock ρ AP Bea SW Persisence of emp. ech. shock AT Bea SW Persisence of C. shock ρ con Bea SW of price markup shock ρ ɛp Bea SW Persisence Persisence of inv. shock ρ ZT Bea SW Persisence of expor shock ρ X Ex Bea SW Persisence of impor shock ρ Im Bea SW Persisence of expor price markup shock ρ e X Bea SW Persisence of impor price markup shock ρ e M Bea SW Persisence of riskpremia shock ρ RP D Bea SW Persisence of wage markup shock ρ ɛw Bea SW Persisence of labour income ax shock ρ n Bea SW Persisence of capaciy uilizaion shock ρ cap Bea SW Sd. of shocks Perm ech shock ε A P Inv. gamma e Wage markup shock ε ew Inv. gamma Temp. ech shock ε A T Inv. gamma Consumpion shock ε con Inv. gamma Price markup shock ε ep Inv. gamma Invesmen shock ε Z T Inv. gamma Inv. gamma Expor shock ε xe x Impor shock ε Im Inv. gamma Impor price markup shock ε em Inv. gamma Expor price markup shock ε ex Inv. gamma Riskpremia shock ε RP D Inv. gamma Public consumpion shock ε G Inv. gamma Public invesmen shock ε IG Inv. gamma Tax on labour income shock ε n Inv. gamma EA price shock ε Π,EA Inv. gamma EA oupu shock ε y,ea Inv. gamma ECB policy rae shock ε r,ea Inv. gamma RoW oupu shock ε y,rw Inv. gamma RoW price shock ε Π,RW Inv. gamma RoW ineres rae shock ε r,rw Inv. gamma UIP shock ε UIP Inv. gamma Uilizaion shock ε cap Inv. gamma Table 4: Esimaed parameers: This able repors he prior disribuion and he poserior mode esimaes of he srucural parameers for he model. ADLS7 refers o Adolfson (7), SW3 refers o Smes and Wouers (3), Medea refers o Fernández-Villaverde e al. (9) and Gali refers o Galí e al. () 49

53 disribuion Poserior disribuion Type Source Mean s.d. Mean Mode s.d. Median 5 pc. 95 pc. Sd. of measuremen errors Inflaion, RoW pierow Inv. gamma Oupu, RoW Y RoW Inv. gamma Ineres rae, RoW RRoW Inv. gamma Inflaion, EA pieea Inv. gamma Oupu, EA Y EA Inv. gamma Ineres rae, EA RECB Inv. gamma Unemploymen U Inv. gamma Employmen Np Inv. gamma Wages W p Inv. gamma Oupu Y BNP Inv. gamma Consumpion C Inv. gamma Invesmens I Inv. gamma Inflaion piedk Inv. gamma Impor M Inv. gamma Expor X Inv. gamma Impor prices pm Inv. gamma Expor prices pe Inv. gamma Exchange rae fx Inv. gamma Invesmen deflaor pi Inv. gamma Table 5: Esimaed parameers: This able repors he prior disribuion and he poserior mode esimaes of he srucural parameers for he model. 5

54 Forecas horizon: quarer Real GDP Consumpion Invesmen Expor Impor Inflaion Real wages Employmen Unemploymen Public consumpion shock Perm ech shock Wage markup shock Temp. ech shock Consumpion shock Price markup shock Invesmen shock Expor shock Impor shock Impor price markup shock Expor price markup shock Riskpremia shock Public invesmen shock Tax on labour income shock EA price shock EA oupu shock ECB policy rae shock RoW oupu shock RoW price shock RoW ineres rae shock UIP shock Capial uilizaion shock Table 6: Variance decomposiions: This able repors poserior mean esimaes for he forecas-error-variance decomposiion of seleced variables a he quarer horizon. The decomposiion is conduced only for he srucural shocks par of he forecas errors, while he shares of he forecas errors due o measuremen errors and unobserved sae variables are skipped. 5

55 Forecas horizon: 4 quarer Real GDP Consumpion Invesmen Expor Impor Inflaion Real wages Employmen Unemploymen Public consumpion shock Perm ech shock Wage markup shock Temp. ech shock Consumpion shock Price markup shock Invesmen shock Expor shock Impor shock Impor price markup shock Expor price markup shock Riskpremia shock Public invesmen shock Tax on labour income shock EA price shock EA oupu shock ECB policy rae shock RoW oupu shock RoW price shock RoW ineres rae shock UIP shock Capial uilizaion shock Table 7: Variance decomposiions: This able repors poserior mean esimaes for he forecas-error-variance decomposiion of seleced variables a he quarer horizon. The decomposiion is conduced only for he srucural shocks par of he forecas errors, while he shares of he forecas errors due o measuremen errors and unobserved sae variables are skipped. 5

56 Forecas horizon: 4 quarer Real GDP Consumpion Invesmen Expor Impor Inflaion Real wages Employmen Unemploymen Public consumpion shock Perm ech shock Wage markup shock Temp. ech shock Consumpion shock Price markup shock Invesmen shock Expor shock Impor shock Impor price markup shock Expor price markup shock Riskpremia shock Public invesmen shock Tax on labour income shock EA price shock EA oupu shock ECB policy rae shock RoW oupu shock RoW price shock RoW ineres rae shock UIP shock Capial uilizaion shock Table 8: Variance decomposiions: This able repors poserior mean esimaes for he forecas-error-variance decomposiion of seleced variables a he quarer horizon. The decomposiion is conduced only for he srucural shocks par of he forecas errors, while he shares of he forecas errors due o measuremen errors and unobserved sae variables are skipped. 53

57 6 5 Nominal ineres raes Denmark Euroarea 3 GDP in Denmark and euroarea Denmark Euroarea Q o Q growh raes Q997Q3QQ35Q7Q3QQ Q997Q3QQ35Q7Q3QQ3 Quarers Inflaion in Denmark and euroarea Con./GDP (lef) and Inv./GDP (righ).5.5 Q o Q growh raes Annual percenages Quarers Denmark Euroarea 5 Consumpion (lef axis) Invesmen (righ axis) 995Q997Q3QQ35Q7Q3QQ3 Quarers 995Q997Q3QQ35Q7Q3QQ3 Quarers Figure : Sylized facs abou he Danish economy. 54

58 55 5 Expor Impor Trade/GDP share Effecive exchange rae Index Q997Q3QQ35Q7Q3QQ3 Quarers 995Q997Q3QQ35Q7Q3QQ3 Quarers Public con./gdp and public defici/gdp Defici/GDP (righ axis) G/GDP (lef axis) Q997Q3QQ35Q7Q3QQ3 Quarers Percenage of GDP Percenage of GDP 4 Percenage of labour force Index Unemploymen and real wage Real wage (righ axis) Unemploymen (lef axis) Q997Q3QQ35Q7Q3QQ3 Quarers Figure : Sylized facs abou he Danish econom 55

59 Q Q growh in real GDP 3 Q Q growh in real privae consumpion 3 Percenages Percenages 3 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q growh in real privae invesmens Q Q growh in expors Percenages Percenages 4 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q growh in impors 5 Percenages 5 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Figure 3: Transformed observed ime series This figure shows he ime series of he observed variables used in he esimaion of he model. 56

60 Q Q growh in real wages Q Q growh unemploymen.5.5 Percenages Percenages 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q growh in privae employmen Q Q growh in public consumpion Percenages Percenages 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q growh in public invesmens Q Q growh in implied ax on labour income Percenages Percenages 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Figure 4: Transformed observed ime series This figure shows he ime series of he observed variables used in he esimaion of he model. 57

61 Demean Danish policy rae Effecive nominal exchange rae vis a vis Res of World Percenages, quarerly Bandpass filered, Index 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q PPI inflaion for Denmark Q Q inflaion in impor deflaor Percenages Percenages 6 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Q Q growh inflaion in invesmen deflaor Q Q growh in expor deflaor Percenages Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 4 Percenages Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Figure 5: Transformed observed ime series This figure shows he ime series of he observed variables used in he esimaion of he model. 58

62 HP filered inflaion in euroarea HP filered oupu in he euroarea Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 3 Demean ECB policy rae x HP filered inflaion in Res of World Percenages, quarerly 8 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 4 HP filered Res of World oupu Demean policy rae in Res of World.... Percenages, quarerly 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Quarers Figure 6: Transformed observed ime series This figure shows he ime series of he observed variables used in he esimaion of he model. 59

63 Produciviy per hour (derended) Q 997Q 999Q Q 3Q 5Q 7Q 9Q Q Figure 7: Derended Measured Hourly Produciviy This figure shows he ime series of measured hourly produciviy in he non-farm secor. 6

64 Parameer: h Parameer: Γ W Poserior Poserior Parameer: Γ P Parameer: Γ M Poserior Poserior Parameer: Γ X Parameer: θ W 8 6 Poserior 8 6 Poserior Parameer: θ M Parameer: θ P Poserior 5 Poserior Figure 8: and poserior and poserior disribuions of he esimaed parameers. 6

65 Parameer: ε W Parameer: φ Poserior 3.5 Poserior Parameer: ν Parameer: κ I.5 Poserior 8 Poserior Parameer: c Parameer: χ C Poserior Poserior Parameer: χ I. Parameer: υ C Poserior.8.6 Poserior Figure 9: and poserior and poserior disribuions of he esimaed parameers. 6

66 Parameer: θ X Parameer: υ I 8 Poserior Poserior Parameer: ρ A P Parameer: ρ A T 4 Poserior 5 4 Poserior Parameer: ρ con Parameer: ρ εp 5 4 Poserior 7 6 Poserior Parameer: ρ ZT Parameer: ρ X Ex 5 Poserior 5 4 Poserior Figure : and poserior and poserior disribuions of he esimaed parameers. 63

67 Parameer: ρ Im Parameer: ρ e X 5 4 Poserior 7 6 Poserior Parameer: ρ e M Parameer: ρ RPD 5 Poserior 5 Poserior Parameer: ρ εw Parameer: ρ N 8 Poserior Poserior Poserior Parameer: ρ CAP 6 4 Parameer: ε CAP Poserior x 3 Figure : and poserior and poserior disribuions of he esimaed parameers. 64

68 Parameer: ε A T Parameer: ε A P Poserior 3 5 Poserior x 3 5 Parameer: ε con Parameer: ε e W Poserior 5 Poserior Parameer: ε e P 5 Parameer: ε Z T 5 Poserior 5 Poserior Parameer: ε E x Parameer: ε e M Poserior Poserior Figure : and poserior and poserior disribuions of he esimaed parameers. 65

69 Parameer: ε Im Parameer: ε G Poserior 6 5 Poserior Parameer: ε RPD Parameer: ε IG Poserior 6 Poserior Parameer: ε π,ea 5 Parameer: ε N Poserior 3 Poserior Parameer: ε r,ea 5 Parameer: ε π,rw Poserior Poserior Figure 3: and poserior and poserior disribuions of he esimaed parameers. 66

70 Parameer: ε UIP Parameer: ε r,rw Poserior 5 Poserior Parameer: ε y,rw 7 Parameer: ε e X Poserior 4 Poserior Parameer: ε y,ea Poserior Figure 4: and poserior and poserior disribuions of he esimaed parameers 67

71 Shock: ε y,ea Shock: ε r,ea Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 x 3 Shock: ε r,rw 3 Shock: επ,rw x 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Figure 5: Smoohed shocks This figure shows he smoohed esimaes of he models srucural shocks used in he esimaion based on he poserior mode esimaes of he model s srucural parameers. 5 x 3 Shock: ε π,ea 5 x 3 Shock: ε y,rw 68

72 995Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 x 3 Shock: εe W 5 x 3 Shock: ε e X Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Figure 6: Smoohed shocks This figure shows he smoohed esimaes of he models srucural shocks used in he esimaion based on he poserior mode esimaes of he model s srucural parameers. 5 x 3 Shock: ε UIP 5 x 3 Shock: ε e M 5 x 3 Shock: ε e P 69

73 Shock: ε con 5 x 3 Shock: ε RPD Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Shock: ε Z T Shock: ε Im Q 997Q3 Q Q3 5Q 7Q3 Q Q3 995Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Figure 7: Smoohed shocks This figure shows he smoohed esimaes of he models srucural shocks used in he esimaion based on he poserior mode esimaes of he model s srucural parameers. 5 x 3 Shock: ε E x 7

74 Shock: ε A P Shock: ε G Q 997Q3 Q Q3 5Q 7Q3 Q Q3 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3. Shock: ε IG Shock: ε N Q 997Q3 Q Q3 5Q 7Q3 Q Q3. 995Q 997Q3 Q Q3 5Q 7Q3 Q Q Q 997Q3 Q Q3 5Q 7Q3 Q Q3 995Q 997Q3 Q Q3 5Q 7Q3 Q Q3 Figure 8: Smoohed shocks This figure shows he smoohed esimaes of he models srucural shocks used in he esimaion based on he poserior mode esimaes of he model s srucural parameers. 5 x 6 Shock: ε CAP x 3 Shock: ε A T 7

75 8 x GDP Privae consumpion x Dev. from seady sae 3 Privae invesmen 3 Expor x x Dev. from seady sae 3 Impor 3 Inflaion (PPI) x x Dev. from seady sae 4 3 Real wage x 5 5 Quarers 4 Employmen x 5 5 Quarers Dev. from seady sae Figure 9: Effecs of a Temporary Technology shock This figure shows he mean (solid lines) and he 7 and 9 percen equal-ail uncerainy bands (doed lines) of he impulse responses of seleced variables o a emporary echonology shock equal o one sandard deviaion. The responses are repored as percenage deviaions from seady sae. 7

76 x GDP x Privae consumpion Dev. from seady sae x Privae invesmen Expor x Dev. from seady sae 4 Impor 4 Inflaion (PPI) x x Dev. from seady sae x 3 Real wage Quarers Employmen x 5 5 Quarers Dev. from seady sae Figure : Effecs of a Domesic price markup shock This figure shows he mean (solid lines) and he 7 and 9 percen equal-ail uncerainy bands (doed lines) of he impulse responses of seleced variables o a domesic price markup shock equal o one sandard deviaion. The responses are repored as percenage deviaions from seady sae. 73

77 GDP GDP, res of world 5 5 Dev. from seady sae Privae consumpion Inflaion (PPI) 5 5 Dev. from seady sae Expor Impor Dev. from seady sae.. Real wage 5 5 Quarers.3.. Employmen 5 5 Quarers Dev. from seady sae Figure : Effecs of a shock o GDP in res-of-world This figure shows he mean (solid lines) and he 7 and 9 percen equal-ail uncerainy bands (doed lines) of he impulse responses of seleced variables o a emporary echonology shock equal o one sandard deviaion. The responses are repored as percenage deviaions from seady sae. The red and blue lines are from he DSGE-model. The cyan and hick doed black lines are from a SVAR. 74

78 GDP ECB policy rae Dev. from seady sae Privae consumpion Inflaion (PPI) Dev. from seady sae 3 Expor Impor x Dev. from seady sae Real wage Dev. from seady sae 5 5 Quarers Employmen 5 5 Quarers Figure : Effecs of a shock o he ECB policy rae This figure shows he mean (solid lines) and he 7 and 9 percen equal-ail uncerainy bands (doed lines) of he impulse responses of seleced variables o a emporary shock o he ECB policy rae equal o.5 basis poin increase in he policy rae. The red and blue lines are from he DSGE-model. The cyan and hick doed black lines are from a SVAR. 75

79 GDP 5 5 Effec on public consumpion Dev. from seady sae Privae consumpion Inflaion (PPI) Dev. from seady sae Expor Impor Dev. from seady sae.. Real wage 5 5 Quarers.3.. Employmen 5 5 Quarers Dev. from seady sae Figure 3: Effecs of a fiscal policy shock This figure shows he mean (solid lines) and he 7 and 9 percen equal-ail uncerainy bands (doed lines) of he impulse responses of seleced variables o a emporary fiscal policy shock equal o one percen of GDP. The responses can herefore be inerpreed as mulipliers. The red and blue lines are from he DSGE-model. The cyan and hick doed black lines are from a SVAR. 76

80 4 Shock Decomposiion of Danish real GDP Markup shocks Demand Produciviy/capaciy Foreign shocks Percenage deviaion from rend growh rae Fiscal policy 5 4Q 5Q 6Q3 7Q4 9Q Q Q3 Q4 Quarers Figure 4: Hisorical Shock Decomposiion for real GDP This figure shows he hisorical quarer o quarer growh raes in Danish real GDP (solid lines) decomposed ino he srucural shocks in he model. The shocks are grouped ino 5 caegories as explained in he ex. Real GDP growh is repored in deviaion of he seady-sae mean growh rae of approximaely.4 percen per quarer. Residual conribuions, which capure he influence of he iniial sae of he economy and measuremen errors, are no shown. The decomposiion have been compued using he poserior mode esimaes of he model s srucural parameers. 77

81 3 Decomposiion of foreign shocks 3 4 UIP shock Ineres rae, RoW Ineres rae, ECB Inflaion, RoW Inflaion, EA Oupu, EA Percenage deviaion from rend growh rae 5 4Q5Q6Q37Q49QQQ3Q4 Quarers Oupu, RoW Figure 5: Hisorical Shock Decomposiion, shocks from foreign economies This figure shows he combined conribuion of he caegory named foreign secor (solid lines), as explained in he ex. The shocks in his caegory are shocks o GDP, inflaion, ineres raes and he uip shocks. Residual conribuions, which capure he influence of he iniial sae of he economy and measuremen errors, are no shown. The decomposiion have been compued using he poserior mode esimaes of he model s srucural parameers. 78

82 .5 Decomposiion of demand shocks.5.5 Expor Impor Invesmen Percenage deviaion from rend growh rae Consumpion.5 4Q5Q6Q37Q49QQQ3Q4 Quarers Figure 6: Hisorical Shock Decomposiion, demand shocks This figure shows he combined conribuion of he caegory named demand (solid lines), as explained in he ex. The shocks in his caegory are preference shocks affecing consumpion, invesmen shocks, impor and expor shocks. Residual conribuions, which capure he influence of he iniial sae of he economy and measuremen errors, are no shown. The decomposiion have been compued using he poserior mode esimaes of he model s srucural parameers. 79

83 .8 Decomposiion of markup shocks Expor price markup Wage markup Domesic price markup Percenage deviaion from rend growh rae Imporprice markup.6 4Q5Q6Q37Q49QQQ3Q4 Quarers Figure 7: Hisorical Shock Decomposiion, markup shocks This figure shows he combined conribuion of he caegory named markup shocks (solid lines), as explained in he ex. The shocks in his caegory are markup shocks o domesic-, impor-, and expor prices as well as he wage markup shock. Residual conribuions, which capure he influence of he iniial sae of he economy and measuremen errors, are no shown. The decomposiion have been compued using he poserior mode esimaes of he model s srucural parameers. 8

84 Effec on GDP from discreionary fiscal policy. DSGE Model MF EC procen Figure 8: Effecs of fiscal policy in he DSGE model and fiscal effecs The DSGE effecs consis of he conribuions o he oupu gap from shocks o governmen spending, governmen invesmen and he implied labor income ax. Tha is, he green columns in figure 4. The fiscal effecs are obained from various publicaions of he Minisry of Finance (MF) and he Economic Council (EC). 8

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