What Drives the Business Cycle in a Small Open Economy? Evidence from an estimated DSGE Model of the Danish Economy

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1 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 November 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 variables spanning he sample period s quarer 995 o 4h quarer. We use he model o idenify he mos imporan deerminans of business cycle flucuaions in Denmark. Our resuls indicae ha shocks o foreign economies explain around 5 pc. of he variaion in Danish real GDP. The build up o he financial crisis and he bus was also driven by foriegn shocks as well as high domesic demand leading o price pressures, which fiscal policy did no comba suffi cienly. JEL classificaion: C, E7, E7, E3. Keywords: DSGE Models, Small Open Economies, Bayesian Esimaion. 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. jpe@naionalbanken.dk. Address: Danmarks Naionalbank, Havnegade 5, 93 Copenhagen, Denmark. shr@naionalbanken.dk.

2 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 of he Minisry of Finance and Saisics Denmark, 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 Jr [976] criique. In addiion, as already menioned, 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, implying ha many feaures of he model are quie sandard in he lieraure. Noably, we model Denmark as a small open economy as in Gali and Monacelli [5]. While he exchange rae is fixed owards he Euro area, 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. More ineresingly, 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.

3 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-, 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 [7], who - somewha surprisingly - find ha foreign shocks explain less han 5 percen of oupu flucuaions in Canada and Sweden, respecively. The main reason for his difference is Denmark s fixed exchange rae owards he euro, which opens up an imporan channel hrough which foreign shocks are ransmied direcly o he Danish economy. For example, he 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. 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 during he period This decomposiion confirms he imporance of foreign shocks. In paricular, he large boom in he Danish economy in he years leading up o he recen crisis, as well as he crisis iself, were o a large exen driven by shocks originaing abroad. However, domesic demand also increased rapidly in he years preceding he crisis, wih domesic consumpion and invesmen shocks conribuing significanly o he overheaing of he Danish economy by he ime he financial crisis hi. In urn, his is likely o have aggravaed he subsequen drop in economic aciviy. Due o Denmark s fixed exchange rae, i is he job of fiscal policymakers 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-o- 3

4 quarer 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 98s. This was he case unil 98 when a newly eleced governmen inroduced a currency peg vis-a-vis he German mark, and from 999, 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 euroarea 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 figure in figure () shows one of he challenges in esimaing a DSGE model for Denmark: The quarerly growh rae of Danish real GDP is quie volaile relaive o real GDP in he euro-zone as an example. This is no surprising: Denmark is a very small and very open economy. We have included daa for he financial crisis alhough i imposes anoher challenge when having a model wih posiive rend growh: This raises some end-poin problems, which we address by including forecased daa, as explained in secion (4.). The boom-lef figure in figure () shows year-on-year inflaion raes. A necessary condiion for he success of he fixed-exchange rae regime is ha he Danish inflaion rae on average equals he inflaion rae in he euro-zone. Alhough closely relaed, here is some evidence ha Danish prices have increased slighly more han prices in he euro-zone in our sample. Moreover, inflaion in Denmark is more volaile han inflaion in he euro-zone. Turning o he componens on he naional accouns balance, privae consumpion makes up an increasing share of GDP in he Danish economy saring from he early s unil he oubreak of he financial crisis, afer which i plummes and has since no recovered. Invesmen as a share of GDP drops 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 collapse in world rade during financial crisis is clear in Danish daa. I is noeworhy ha during he enire sample, Denmark has had posiive ne expors. 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]. Even hough he nominal Danish exchange rae is fixed owards he euro, 4

5 ha does no imply ha he effecive 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 kron 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 euroarea, 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 euroarea. The Danish labour marke has since he early 9 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. 3 The Model This secion ses up he model. The model is a modified version of a number of exising medium sized DSGE models like he Chrisoffel e al. [8], Adolfson [7], Burriel e al. []. The main building blocks of he previous menioned models are however modified o reflec key aspecs of he danish economy. 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 and given leaving room for assuming ha Denmark is a par of a currency union wih he euro-zone. However, ha does no imply ha exchange rae effecs have no played a role in he deerminaion of he Danish business-cycle, as an example he second and hird bigges rading parners are ouside he euro-zone being Sweden and he U.K. Consequenly, Denmark has seen some flucuaions in he effecive exchange rae and he model needs o reflec ha. 5

6 The model herefore pus Denmark inside a currency union wih he eurozone bu also rades 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 euro-zone 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 foriegn produced goods is presened in secion (3.5). Fiscal and moneary policy are presened nex in secion (3.6), he labour marke in secion (3.7), and lasly secion (3.9) presens he marke for expors, and secion (3.) impors. 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. 3 We follow his pracice afer confirming ha he same wo rends are presen in Danish daa for our sample period, i.e 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 See among ohers he sudies by Jusiniano e al. [], Chrisiano e al. [3] and Liu e al. [3]. 6

7 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 con log (C hc ), () where < β < is he discoun facor, h > measures he degree of (exernal) habi formaion in privae consumpion, and 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 + τ K δ K z u (u ) 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 B 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. 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 B < is he compensaion rae in unemploymen benefis. δ K > is he capial depreciaion rae. Finally, 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 7

8 made o ensure a saionary model as in. 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 D RP 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 funcion z u (u ) measures he cos of changing he degree of capial uilizaion, which we assume akes on he following funcional form: z u (u ) = c (u u) + c (u u), (6) where c, c > are parameers, and u is he seady sae level of capial uilizaion, which we se o. 4 Finally, he household also akes he law of moion for capial ino accoun: ( 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, (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. 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 λ Z. 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 <. 4 In he budge consrain, we hen need o scale he ax deducion from capial depreciaion and he uilizaion cos wih he rend growh of invesmen-specific echnology so as o ensure ha hese are no eroded over ime. 8

9 The firs-order condiions relaed o he uiliy maximizaion problem of he household are as follows: P C λ = P con (C hc ) ( ), + τ V AT () ( ) λ = β E λ + E π DK R ECB B I ( ) exp( ψ d BI RP D ), () + Y Y RP D [ λ+ ( Q = βe r K ( ) ( + τ K λ + u+ + δ K τ K + z u (u + ) + δ K) ) ] Q +, ( ) () τ K r K = z u (u ), (3) P I P = Q Z T [ S S I ] + βe [ Q + Z T + λ + S λ +I ( I+ I ) ]. (4) 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 ), i follows ha z u (u ) = c + c (u ), 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 (K (j) η ( K G ) η ) α (N (j)) α, (5) where α, η > are parameers, K (j) = u 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 ) ρa A T = A T exp ε A, (6) wih A T >, < ρ A <, and where ε A 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) 9

10 where, in urn, λ A λ A = ( λa λ A ) ρλa exp ε λ A, (8) 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 λ A is an i.i.d. sochasic process wih mean zero and variance σ λ A. 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 K, (9) ( + 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 I o index heir price o he seady sae rae of inflaion, 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 A (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 ) ρ ɛ P ɛ P = ɛ P exp ε ɛp, () where ε ɛp is an i.i.d. sochasic process wih mean zero and variance σ ɛp, and where < ρ ɛ P <. We can hen wrie he evoluion of he aggregae price index as (jek dee udryk) P = [ ( ) ɛ P ] θ p P ɛp ɛ P + ( θ p ) P, (3)

11 highlighing ha he share ( θ p ) of prices are rese in each period, and where π is he domesic inflaion rae of he Danish producer price index. Finally, D measures he loss associaed wih price dispersion, and is given by 3.4 Final Goods Producers ( ) ɛ P D = ( θ p ) P + θ p (π ) ɛp D. (4) 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 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, (6) where, P (j), is he price se by inermediae goods firm j. 3.5 Final Consumpion and Invesmen Goods 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)

12 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, 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 υc ( ) [ χ C ϑ c P DK 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 ϑ I ( P F P DK ) υi ( χ I ) [ χ I ( χ I ) I B ] υi. (33) Finally, we can wrie he relaive prices of consumpion and invesmen goods as follows: P C P F υ c υc P = ϑ c + ( ϑ c ) DK P χ C ( ) χ C, (34) C B

13 P I P = P F P DK ϑ I + ( ϑ I ) χ I ( ) χ I I B υ I υ I, (35) while he relaed relaive inflaion raes are defined as: π C = P C P π P C, (36) P π I = P I P π Z 3.6 Fiscal and moneary policy P I P Z. (37) 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 = ( I G,B I G ) ρig 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) 3

14 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 along he balanced growh pah. 5 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, as given by he projecs ha were iniiaed a leas M periods ago and have no ye been finished. On he revenue side, he governmen raises six 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. 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 B, (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 δ K) K +τ N w N +τ B R π DK B DK, (44) 5 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. 4

15 G = C G + 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. 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 >. ) ρrdk [ ( ) ] R ECB ( ρrdk ) R exp(ψ B ECB G ω D ), (46) Y 3.7 The Labor Marke 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 adding fewer equaions (as compared o he search-and-mach approach) o 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 household and sicky wages. As for he pricing behaviour on behalf of he firms in our model, sicky wages are acheived 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 heerogenous ypes of labour specialized in various fields. This implies ha each labour 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 members disuiliy from work. Hence, he household consiss of many labour ypes who each have a cerain degree of disuiliy from work. 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 5

16 need o ake care of various consumpion levels and hence marginal uiliies and ha he individual members of he household have he household in mind when maximizing uiliy. When hese members work, hey work a full day. Hence, movemens on he labour markes are movemens on he inra-margin and no on he iner-margin. The assumpion abou household seing wages and working a full day implies ha he employmen level is deermined on he firm side - he household simply supply 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 realwage increases by one percen holding consumpion consan. Inuiively, in opimum he disuiliy of working more mus be compensaed by wha he realwage can buy in uiliy erms. If no, hen he household would be able o reshuffl e beween consumpion and labour inpus and achieve a higher uiliy. The variable O is defined as: O = wih z evolving according o: [ z = z υ z (C hc ) ( + τ V AT (C hc ) ( + τ V AT ) ( P C /P ) con = z λ, (48) ] ) ( ) υ 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. 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. 6 Finally, in (47), he erm χ represens an exogenous shock o labor supply, which evolves according o: ( ) ρχ χ χ = χ exp (ε χ ), (5) χ 6 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. 6

17 where ε χ is an i.i.d. sochasic process wih mean zero and variance σ χ, while < ρ χ <. 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 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 for each ype of labour i are ordered by heir disuiliy of labor and ha he condiion is relaed o he marginal disuiliy of work o he household. 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 is he j for which condiion (5) is saified wih equaliy. Summing over hese paricipaion raes across labour ypes gives he model aggregae labour force. Noice ha he labour paricipaion is ime varying. I can as example increase due o labour supply shocks which decreases he marginal disuiliy of work. 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 rae which is given by L N L. However, around a log-linear approximaions, hese definiions of unemploymen are equal for small levels of unemploymen. 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 flexble and 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 rae is given by µ w = φu n. Hence, unemploymen in his model is solely due 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 7

18 naural rae of unemploymen is higher he higher is he degree of monopolisic compeiion and he higher is he of frisch labour elasiciy; ha is by how much does he household increase heir labour supply when he realwage increases by pc.: The higher is his elasiciy he more willing are he members of he household o subsiue in and ou of employmen. Finally, we describe he wage formaion. Observe 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 P (j) = ɛ P ɛp E s= s= (βθ W ) s λ +s λ (βθ p ) s λ +s λ N+s P (j) χ +s O +s N+s P, (53) (j) Y +s (j) mc +s P +k, (54) Y +s (j) 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 ɛw, (55) where ε ɛw is an i.i.d. sochasic process wih mean zero and variance σ ɛw, and where < ρ ɛ W <. Finally, we can wrie he evoluion of he wage level in he privae secor as: w P = [ ( ) θ w w P ɛ W + ( θ w ) ( w P ] ) ɛ W ɛ W. (56) 3.8 Trade and he wo foreign economies As discussed in he inroducion, Denmark s fixed exchange rae owards he euro implies ha we need o include wo foreign economies in he model: One (he euro area, EA for shor) owards which Denmark has a fixed exchange rae, and one (which we label he Res of he World; RoW for shor) owards which he exchange rae is fully flexible. 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. Each of hem 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 8 R j R π j + π φ j Y ( ) ɛ j Y, ɛ j, (57) Y

19 π j π j = R j R j = ( ) π j ρ j + π j ( ) R j ρ j R R j π ( π j π j ( π j π j ) Γ j ) ρ j π ( Y j Y j π ( Y j Y j ) Γ j Y ) φ j π ( ɛ j π, ɛ j π ρ j R ( ɛ j ) R, ɛ j R, (58) ). (59) Here, (57) is a hybrid dynamic IS curve ha links oupu o he real ineres rae, (58) is a version of a hybrid New Keynesian Phillips Curve linking he rae of inflaion o real aciviy, and (59) 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 e j k,, (6) k for j = (EA, RoW ) and k = (Y, π, R). 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. 7 The six exogenous shocks (he e j k, s) 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 = ( Y EA Y EA ) Ω ( Y RoW Y RoW ) Ω, (6) π W ( ) π EA Ω ( π W = F X π RoW ) Ω π EA F X π RoW, (6) where he parameer Ω measures he relaive size of he euro area, and where FX denoes he change in he effecive exchange rae of he Danish krone. 3.9 Expors The role of he expor secor is o buy final domesic goods, differeniae hem, and sell hem o impor firms in he euro area or he res of he world. We can wrie he world demand for Danish expors as: Ex = x Z Y W ( P X P x W ) ε W, (63) 7 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 ). 9

20 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, (64) 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, (65) where π X is he inflaion rae in Danish expors price, as described below. Finally, he expor demand shock x Z evolves according o: where ε xz x Z x Z = ( x Z ) ρx Z x Z exp ) (ε xz, (66) Z is an i.i.d. sochasic process wih mean zero and variance σ εx, and where < ρ ε X Z <. Firms in he expor secor are faced wih price rigidiies of he same form as in he domesic 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), (67) 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 he goods produced by each individual firm in he expor secor, which follows he process: ( ) ( ɛ X ɛ X ) ρ ɛ X ɛ X = ɛ X exp ε ɛx, (68) where ε ɛx is an i.i.d. sochasic process wih mean zero and variance σ ɛx, and where < ρ ɛ X <. Finally, he inflaion rae in Danish expor prices will hen saisfy: = θ X ( π X ) ɛ X + ( θ X ) ( P X P X ) ɛ X. (69)

21 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 euro area and he res of he world. 8 We can wrie he marginal cos for an impor differeniaor as: mc M = P xw P M, (7) 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) 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 ). (73) 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 = ( ɛ M ) ρ ɛ M ɛ M exp ε ɛm, (74) 8 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.

22 where ε ɛx is an i.i.d. sochasic process wih mean zero and variance σ ɛx, and where < ρ ɛ X <. Finally, analogous o he previous subsecion, he inflaion rae in Danish impor prices saisfies: = θ M ( π M ) ɛ M + ( θ M ) ( P M P M ) ɛ M. (75) 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 + z u (u ) K + P X P Ex. (76) Moreover, Denmark s ne foreign asse posiion is given by: B I = R ECB exp( ψ d ( B I Y π DK ) BI Y ) B I + P X P Ex P M P Im, (77) 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, 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 Γ (A Z 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.

23 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. We furher impose a ha adjusmen coss are zero in seady sae: cos for 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 imposing he law of one price and normalizaions of foriegn oupu, he CES-funcions for privae consumpion and invesmens, and seady sae invesmens, 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 he Naionalbanken 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. The average change of he relaive invesmen price is -.. We use hese esimaes o deermine he seady saes of he wo processes which ogeher deermines he growh in he model, Λ A, Λ Z. Finally, regarding he fiscal policy side of he model, we can from daa observe seady sae raio of public consumpion (public expendiures on goods and services as well as public employmen), public invesmens, all ax raes as well as he deb raio. A he very end of he model, seady sae lump sum axes are deermined such ha public debs evenually can 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 3

24 Fernandez-Villaverde and coauhors; (Fernández-Villaverde [], Fernández- Villaverde e al. [9] 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 find i hard o find 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: p ( Θ Y T ) = p ( Y T Θ ) p (Θ) p (Y T ) (78) The poserior disribuion equals he prior disribuion imes he likelihood funcion divided by a scaling facor. I can perhaps be helpful o hink of Baysian analysis as radiional maximum likelihood wih a penaly funcion in form of he prior disribuions, 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, which is our main reason behind using he Bayesian approach. The resuling empirical disribuion is used o obain poin esimaes, impulse response funcions ec. which we will discuss in secion (5). 4. Daa and shocks 4.. Daa 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 provided by Naionalbanken for he 3 year period afer he sample o ge beer esimaes of he long 4