EUROPEAN ECONOMY EUROPEAN COMMISSION DIRECTORATE-GENERAL FOR ECONOMIC AND FINANCIAL AFFAIRS

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1 EUROEAN ECONOMY EUROEAN COMMISSION DIRECORAE-GENERA FOR ECONOMIC AND FINANCIA AFFAIRS ECONOMIC AERS ISSN hp://europa.eu.n/comm/economy_fnance N January 5 An esmaed new keynesan dynamc sochasc general equlbrum model of he Euro area by Marco Rao**, Werner Röger*, Jan n Veld* and Rccardo Grard** *Drecorae-General for Economc and Fnancal Affars ** Jon Research Cenre

2 Economc apers are wren by he Saff of he Drecorae-General for Economc and Fnancal Affars, or by expers workng n assocaon wh hem. he "apers" are nended o ncrease awareness of he echncal work beng done by he saff and o seek commens and suggesons for furher analyses. Vews expressed represen exclusvely he posons of he auhor and do no necessarly correspond o hose of he European Commsson. Commens and enqures should be addressed o he: European Commsson Drecorae-General for Economc and Fnancal Affars ublcaons BU - -/8 B - 49 Brussels, Belgum ECFIN/7878/4-EN ISBN KC-AI-4--EN-C European Communes, 5

3 able of conens Inroducon... 3 he DSGE Model Esmaon Mehodology Solvng he model wh lnear approxmaons Maxmum lkelhood esmaon and nference Bayesan esmaon and nference Implemenaon: MCMC (Meropols-Hasngs Model comparson... 4 Esmaon ror dsrbuons arameer esmaes and shocks denfed VAR comparson Whch srucural shocks drve he euro economy?... Esmaed mpulse responses of srucural shocks Conclusons References... 4 Annex:... 4 A. Resuls from poseror maxmzaon... 4 A. oseror smulaon:... 4

4 Inroducon In recen years a new consensus has emerged n macroeconomcs n general and n model buldng n parcular, he so called New Keynesan aradgm (NKM. hs paradgm s well esablshed as can be seen from he promnen reamen n recen exbooks (see, for example Obsfeld/Rogoff and leraure surveys (se for example Clarda, Gal Gerler. In a sense he NKM paradgm combnes elemens from he RBC leraure wh more radonal Keynesan deas. radonal Keynesan models suffered from underdeveloped mcrofoundaons and a lack of long erm facors nfluencng he economy whch made hem subec o he ucas crque. I also dd no have a coheren heorecal explanaon for he sluggsh behavour of prces assumed. On he oher hand, RBC modellers bul her models up from he acons of opmsng economc agens whose choces are made whn specfed consrans. he New Classcal vew of RBC modellers saw busness cycles as largely he resul of shocks o producvy and preferences, and downurns as merely he opmal adusmen of he economy o such dsurbances. NKM models correc he RBC models by nroducng frcons n goods, labour and fnancal markes n order o provde a beer f wh acual daa, bu a he same me res o model he frcons explcly as consrans faced by households and frms. hs allows combnng opmal behavour wh rgdes n a way whch avods he ucas crque. he QUES model has been se up n he spr of a NKM model, wh a srong emphass on heorecal conssency of he behavoural equaons. However a he me when QUES II was nroduced he esmaon echnology for DSGE models was no suffcenly developed o allow for rgorous esmaon and esng of hese models. arge pars of hese models needed o be calbraed. Followng recen developmens n Bayesan esmaon echnques (see, e.g., Geweke 999 and Schorfhede, has become possble o esmae hese ype of models. Smes and Wouers (3 have been he frs o esmae such a model for he Euro area. hey followed Crsano, Echenbaum, and Evans ( and desgned a DSGE model for he Euro area feaurng prce and wage sckness, paral ndexaon of prces and salares, exernal capal formaon, varable capal ulsaon rae and sochasc shocks o each srucural equaon of he resulng model. Smes and Wouers (3 show ha he curren generaon of New-Keynesan DSGE models s suffcenly rch o capure he me-seres properes of he daa, as long as a suffcen number of srucural shocks s consdered. In parcular, s able o mach he degree of emprcal perssence found n he euro area daa for nflaon and wages que well. hs paper apples Bayesan esmaon echnques o a me seres daa se of he euro area and presens esmaes of a DSGE model. he purpose of hs paper s no o esmae he curren verson of he QUES model drecly wh hese mehods bu raher o esmae a prooype new generaon New-Keynesan DSGE model. hs model can hen serve as a benchmark for an esmaon of a QUES specfcaon. In fac n some dmensons he QUES model may need o be adused o come closer o a DSGE model. One of he common feaures beween he QUES II model and he esmaed New-Keynesan DSGE model presened n hs paper are ha boh, n he long run, closely resemble he sandard neoclasscal growh model. All behavoural relaons are derved from dynamc opmsaon problems of households and frms, wh opmsaon subec o echnologcal consrans, budge consrans and/or nsuonal consrans, ofen capured as adusmen - 3 -

5 coss. hs leads o a descrpon of economc behavour ha s a mxure of backward and forward lookng behavour. he man dfferences wh he QUES II model are n he specfcaon of consumpon. Whle consumpon n he QUES model s based on a permanen ncome model for fnely-lved households, as popularsed by Blanchard (984, n hs DSGE model n conras, consumpon s derved from neremporal opmsaon for nfnely lved households, lke n all oher curren DSGE models. However, consumpon s modelled more backward lookng by allowng for hab perssence (.e. consumpon decsons oday depend parally on he prevous paern of consumpon. On he oher hand, QUES allowed for lqudy consrans, a feaure sll mssng n he consumpon framework here. he dfferences n he nvesmen specfcaon are only of mnor mporance, wh a sronger emphass on adusmen coss here. he modellng of he labour marke s subsanally dfferen. Here, lke n oher DSGE models, hs s based on a neoclasscal labour supply wh monopoly power for workers. One of he dsngushng feaures of he QUES model s he labour marke specfcaon derved from a heorecal search model based on he work by ssardes (99. he esmaed model as presened here s sll ncomplee snce reas he Euro area as a closed economy. he closed economy seng was chosen because we frs waned o concenrae on he man aggregaes consumpon and nvesmen as well as on prces and wages and her neracons. However, addng a rade secor would be among our frs prores for furher exensons of hs model. he model wll hen nclude a more explc modellng of rade frcons whn he framework of convex adusmen coss, whch would dsngush from he QUES model, where rade s modelled hrough an ad-hoc specfcaon of adusmen lags n quanes and prces. An mporan reason for esmang a DSGE model was also o be able o compare esmaon resuls wh he exsng leraure and o make sure ha he esmaon yelds resuls whch are conssen wh he resuls obaned wh smlar specfcaons and smlar daases. he man goals of hs exercse are: Demonsrae ha models derved from economc heory can f Euro area daa, provded one allows for suffcen nsuonal resrcons. We compare he predcve performance of he esmaed DSGE model wh ha of a VAR model esmaed over he same euro area daa se. (We nend o conduc a smlar exercse for he US economy o see wheher nsuonal consrans play he same role here. Idenfy he man srucural shocks hng he Euro area economy n a heorecally conssen way. An advanage of an explc srucural model s he fac ha resduals can be gven a srucural nerpreaon,.e. we can denfy shocks whch orgnae from consumpon, echnology, labour supply, labour demand, nvesmen and fscal and moneary polcy. hs may be of added value n ryng o undersand he naure of he curren economc suaon. For example, he model denfes a declnng rend n governmen spendng, whch s reversed n recen years, a declne n prce mark-ups, reflecng ncreased compeve pressures, a rend ncrease n oal facor producvy n he 98s, followed by a declne n he lae 99s and a rend ncrease n labour supply, reflecng a declnng NAIRU. 3 rovde he ypcal response of he economy o he ndvdual shocks n he form of mpulse responses, lke n VAR sudes, wh he addonal benef ha confdence nervals can be provded o show he uncerany surroundng hese responses

6 he oulne of he paper s as follows. Secon presens he model. In secon 3 dscusses he esmaon mehodology. Snce esmaon of hese models s non sandard a farly comprehensve explanaon wll be provded. Secon 4 presens he esmaon resuls. In order o provde a more nuve undersandng for he qualy of he f of hs model, a comparson wh a smple VAR model s gven. Secon 5 presens and nerpres he srucural shocks denfed by he model esmaes and secon descrbes he dynamc adusmen of he euro area economy o srucural shocks. he DSGE Model Households: he household secor decdes abou consumpon and asse accumulaon (ncludng fxed capal. Each household supples a specfc varey of labour n a monopolscally compeve fashon,.e. he household secor ses he wage gven he demand curve for labour. When makng decsons he household also faces adusmen coss for changng wages. hese adusmen coss are borne by he household (see budge consran. he household maxmses a uly funcon subec o a budge consran. he agrangan of hs maxmsaon problem s gven by ( Max U = = C λ β β C ( U ( C + V ( + Z( M / M + B + R V + R W γ w + w w M B V + AX he household maxmses a uly funcon over consumpon, lesure and real money balances. Followng he recen leraure we allow for hab perssence n consumpon. hs s an mporan modfcaon w. r.. he curren consumpon specfcaon n QUES whch was based enrely on a pure lfe cycle model. he curren verson allows for lagged adusmen of consumpon and we choose a logarhmc specfcaon C (a U C ε log( C habc ( = C where ε denoes a sochasc preference shock for consumpon n perod. hs specfcaon yelds he followng expresson for he margnal uly of consumpon (b C U C, = ε. ( C habc - 5 -

7 he consumpon ndex s self an aggregae over dfferen goods whch are mperfec subsues. he preferences of households are expressed by a CES uly funcon τ τ (c C C τ = d wh τ where τ measures he nverse of he me varyng elascy of demand of households for consumpon goods of ype. he erm τ s gven by (d τ = τ + τ ( Y Ypo + ε τ where τ ε s a auocorrelaed shock o he demand elascy. For labour supply we use a CES uly funcon (e where gven by ω κ s a possbly auocorrelaed labour supply shock. he margnal uly of lesure s κ V ( = ε ( wh κ >, ε κ (f V = ε ω(., he household decdes abou consumpon, asse accumulaon and he supply of labour (or more correcly abou wages and real money holdngs. he frs order condons of he household (FOCs wh respec o consumpon and fnancal wealh are gven by he followng equaons: U C (3a => U C, λ = C U (3b => λ + λ+ β = B R U M ζ (3c => Y R = M + he labour supply decson s slghly more complex, snce s assumed ha workers have a ceran marke power n he labour marke, because hey offer servces, whch are mperfec subsues o servces offered by oher workers. ha means aggregae labour demand of frms s a compose of labour suppled by ndvdual workers. oal employmen n producon s characersed by a CES funcon Wh an neres rae rule as specfed below, an opmaly condon for money would only deermne he desred money holdngs of he household secor whou any furher consequence for he res of he economy. For ha reason any furher dscusson on money demand s dropped here. - -

8 (4a θ θ θ θ d = wh θ > where he parameer θ deermnes he degree of subsuably beween labour suppled by ndvdual households. Correspondng o he CES aggregaor here exss a wage ndex (4b W θ θ = W hs echnology yelds a labour demand equaon as perceved by household (4c W = W θ In a monopolsc labour marke he elascy of subsuon beween dfferen ypes of labour s mporan for deermnng he mark-up of wages over he equlbrum wage. hs elascy s defned by (4d W W = θ W θ W = θ W. Now he wage seng rule can be derved akng dervaves of he agrangan w.r.. wages. Usng symmery: W = W and neglecng second order erms allows us o wre (5a U W W ( θ W W => V = λ γ wπ + λ+ βγ wπ +, θ where rule (5b W π s he growh rae of nomnal wages. hs can be reformulaed as a wage seng π w = C w W w ( mup + + γ w ω( R π wh κ w mup = θ where wage nflaon s deermned by he gap beween he reservaon wage and he real wage adused for a wage mark up. he forward lookng naure of wage seng s refleced by he forward wage nflaon erm. hs formulaon generalses he neoclasscal labour supply model along wo dmensons. Frs, by nroducng convex wage adusmen coss ( γ w >, workers wan o smooh wage adusmens, akng no accoun curren and fuure expeced labour marke condons. Second, because workers offer servces whch are mperfec subsues o servces offered by oher workers, hey can demand wages whch are above her reservaon wage. he reservaon wage s he margnal value of lesure, dvded by he Noce n he lmng case of perfec subsuably ( lm θ, he mark up approaches zero

9 margnal uly of consumpon. ha means for a gven uly of lesure he reservaon wage ncreases wh a declne n he margnal uly of consumpon ha an addonal un of labour can buy. In esmang he wage rule wo furher generalsaons have been nroduced. Some search heorec generalsaons of he neoclasscal wage rule sugges rules where wages are ndexed o boh he reservaon wage and he margnal value produc of labour wh wegh bg reflecng he barganng srengh of workers (see, for example, Sh e al. (999. In order o allow for backward lookng behavour s assumed ha only a fracon sfw of workers form raonal expecaons of fuure wages, whle he remanng workers follow a smple rule of humb where expecaons are deermned by pas nflaon. hese wo modfcaons lead o he followng wage equaon (5c w π κ w w ( sfwπ + ( sfw C Y w W = ( bg + bgα η ( mup + + π γ w ω( R sfw Frms: here are N frms ndexed by. Because goods produced by ndvdual frms are mperfec subsues, frms are monopolscally compeve n he goods marke and face a demand funcon for goods gven by τ ( Y = s ( C + G + I Oupu s produced wh a Cobb Douglas producon funcon (7 Y = ( ucap K ( U α α wh capal and labour as npus. Frms can also decde abou he degree of capacy U ulsaon he level of echnology s subec o random echnology shocks ( ε and follows he auoregressve process U U U (8 log( U = ρ log( U + ( ρ log( U + ε. he obecve of he frm s o maxmse he presen dscouned value of s cash flows. Dynamc consderaons ener he problem of he frm because frm faces quadrac coss of changng capal, employmen and prces. Fnally frms mus also choose he opmal level of capacy ulsaon. (9-8 -

10 [ ] [ ] [ ] CA K K I K d q U K ucap Y d ucap ad ad I K ad adc I W Y d Max V ( ( ( ( (, ( ( (. = = δ η α α where = + + = l l l l rp r d s he dscoun facor, whch consss of he shor erm neres rae and a rsk premum (rp. he rsk premum can be subec o random shocks and generaed by he followng auoregressve process ( rp rp rp rp rp rp ε ρ ρ + + = ( For adusmen coss we choose he followng convex funconal forms ( (, ( /, ( ( I I K K W I K I I K ad wh ad W ad + + = = = + = γ ε γ π π γ γ ε * ( * ( ( ucap ucap a ucap ucap a ucap ad CA + = he frm deermnes labour npu, he capal sock, capacy ulsaon and prces opmally n each perod gven he echnologcal and admnsrave consrans as well as demand condons. he frs order condons are gven by: (a ( ( ( W W R Y V ε γ γ η α + = + => + (b ( ( = + + => + I I K q I R I K I I V γ ε γ (c ( ( (( ( + = + + => q rp r q ucap a ucap a a a a K Y K V δ η α (d ucap K Y ucap a a a ucap V η α ( ( (( = + => - 9 -

11 V τ (e => η = τ + τ Y Ypo + ε + γ [ βπ π ] ( ( Y Frms equae he margnal produc of labour, ne of adusmen coss, o wage coss. Wage coss nclude a sochasc wage cos shock. hs should be seen as shocks o admnsrave burdens relaed o curren employmen. As can be seen from he lef hand sde of equaon (a, he convex par of he adusmen cos funcon penalses n cos erms acceleraons and deceleraons of changes n employmen. Equaons (b-d only deermne he opmal capal sock and opmal capacy ulsaon. he frm equaes he margnal produc of capal o he renal prce of capal, adused for capal coss. he frm also equaes he margnal produc of capal servces (K*ucap o he margnal cos of capacy ulsaon. Equaon (e defnes he mark up facor as a funcon of he elascy of subsuon and changes n nflaon. We follow Smes and Wouers and allow for addonal backward lookng elemens by assumng ha a fracon (-sfp of frms keep prces fxed a he - level. hs leads o he followng specfcaon: τ (e η ( τ + τ ( Y Ypo + ε + γ [ β ( sfp * π + ( sfp π π ] = + + sfp Governmen secor: he governmen secor and fscal polcy s reaed n a raher rudmenary fashon. he share of governmen purchases (3a G / Y = gs + ε G flucuaes sysemacally wh he busness cycle accordng o he followng rule Y (3b gs = Y Ypo where Y g g ( measures he degree of auomac sablsaon of governmen expendure. Dscreonary fscal acon s characersed by he varable whch s allowed o be auocorrelaed process. Implcly s assumed ha governmen expendure s fnanced, by lump sum axes. G ε Cenral bank polcy rule (neres rae rule: Moneary polcy s modelled va he followng aylor rule, whch allows for some smoohness of he neres rae response o he nflaon and oupu gap (4a nom = lag * nom π M ( π π + ( lag * ( Ex. R + π + Y M ( Y Ypo ( Y + π M Ypo ( π π + + ε M Y M ( Y Ypo + - -

12 M he erm ε capures random dscreonary shocks o moneary polcy and π s a me varyng nflaon arge, specfed as follows π π π (4b π = ρ π + ( ρ π + ε. π ε s an..d. shock o he nflaon arge. I s assumed ha boh fscal and moneary auhores base her polces on a concep of poenal oupu whch s a smooh funcon of pas oupu (5 Ypo = ρ ypoypo + ( ρ ypo Y 3 Esmaon Mehodology We presen he frs aemp o apply a Bayesan esmaon approach o brng he model drecly o he daa. hs approach has been dscussed by many auhors n he leraure n he las few years (e.g. Schorfhede, ubk and Schorfhede, 3, Smes and Wouers, 3. Schemacally, he mehod consss of he followng seps: he non-lnear DSGE model s solved va a lnear approxmaon: a lnear raonal expecaon sysem s obaned ha mus be obanng a sandard lnear model n sae space form; he sae-space approxmaon of he orgnal non-lnear model allows he denfcaon of a lkelhood funcon (va e.g. Kalman recursons and a subsequen nference based on (maxmum lkelhood esmaon, ec.; usually heorecal model mply few, well defned shocks; unforunaely hs ofen mples sngulares n he deermnaon of he lkelhood (n he Kalman fler he number of shocks mus a leas be as large as he number of observables, mplyng he nroducon of addonal srucural shocks and/or measuremen errors; lkelhood-based nference presens a seres of ssues: specfcally he lack of denfcaon (global: mulple maxma; local: over-parameersaon,.e. he maxmum s gven by a complex muldmensonal combnaon/neracon srucure raher hen by a sngle pon n he parameer space; he Bayesan analyss s performed: pror dsrbuons for model parameers have o be defned, represenng he pror belefs of he analys on her plausble values, whch, n combnaon wh he lkelhood funcon, allows o oban he poseror dsrbuon; he Bayesan nference needs he use of sochasc smulaons, specfcally Markov Chan Mone Carlo (MCMC echnques, allowng o oban samples from he poseror on pdf of he model parameers and subsequenly o make an nference n whch he parameer uncerany and he shape of he lkelhood are aken no accoun; he model s fnally compared o an emprcal model; n he leraure hs s usually a VAR model. - -

13 From he compuaonal pon of vew, he lnear approxmaon and he soluon of he obaned RE can be done auomacally usng he DYNARE program (Jullard, 99, 3, whch apples he generalsed Schur decomposon soluon mehod (Klen,. DYNARE s a sofware for he smulaon of DSGE models, freely avalable and oally open source. resenly, an esmaon module s mplemened on DYNARE, o nclude he mos recen developmens n Bayesan esmaon macro-economc models n an exremely effcen and easy way. DYNARE s also exremely flexble, and allows o easly ncorporang problem specfc mehodologcal ssues or cusomsaons. 3. Solvng he model wh lnear approxmaons e a model be defned and frs order condons denfed. hs can be expressed as: E f y, y, y, ε ; θ = ( E E { ( + } { ε } = { ε ε '} = Σ where y s vecor of endogenous varables, ε s he vecor of exogenous sochasc shocks, θ s he vecor of parameers and E s he expecaon operaor. he non-lnear model s solved va a lnear approxmaon around he deermnsc seady sae y such ha f ( y, y, y,; θ =. A lnear raonal expecaon (RE sysem s obaned, wh forward lookng componens + (7 A E yˆ + + A yˆ + A yˆ + Bε =, where yˆ = y y he sysem s solved for he reduced form sae equaon n s predeermned varables (Blanchard and Kahn, 98; generalsed Schur form, Klen,. An observaon equaon s also added o lnk he observed varables (8 y yˆ = M ( y( θ + yˆ + η = G( θ yˆ E( η η ' = V ( θ E( ε ε ' = Q( θ + H ( θ ε y o he predeermned ones, obanng: where η s he measuremen error, f any. he sysem marces G, H, V and Q and he seady sae vecor y (θ are funcons of he vecor of srucural parameers θ of he orgnal model. Vecor θ ncludes he nose parameers Σ. he sae space represenaon (8 allows use of Kalman flerng for he compuaon of he log-lkelhood, and a subsequen nference based on (maxmum lkelhood esmaon, ec.. In he orgnal model specfcaon (, well-defned (and relavely few shocks are usually presen. If he number of shocks s smaller han he number of observed varables, sngulares n he Kalman fler wll be presen,.e. he probably dsrbuon of he observables p( Y θ (he lkelhood can be degenerae. hs mples he nroducon of addonal shocks unl he sysem becomes non-sngular, ncludng eher measuremen errors η (as e.g. n Ireland, 4, who also models he measuremen error as a VAR( process or addonal srucural shocks n he sae equaon (as e.g. n Smes and Wouers, 3. Rgorously, n such cases, as clearly saed by Schorfhede (, he evaluaon approach here appled wll lead o an assessmen of he modfed model raher han he orgnal one. In such cases, he parameer vecor θ wll be augmened for he addonal nose erms and, f any, also for he VAR coeffcens n he measuremen errors as n Ireland (4. In hs paper we follow he Smes and Wouers approach and nroduce a suffcen number of srucural shocks n he sae equaons. - -

14 3. Maxmum lkelhood esmaon and nference he sae space form of he lnear approxmaon obaned can be subec o a classcal lkelhood analyss. he sysem can be fed o a Kalman fler and he lkelhood funcon p( Y θ can be compued n a sandard way (Kalman, 9, Kalman and Bucy, 9 or, n he case of non-saonary models, wh exac nal Kalman flerng (Koopman, 997. hs allows performng maxmum lkelhood esmaon, usng a numercal opmsaon roune, obanng: ϑˆ = arg max p( Y θ M k ϑ R where Y s he nformaon se gven by a seres of observaons Y wh =,...,. Gven he parcular naure of he sae space model fed o he M opmsaon, n whch all marces of coeffcens are funcons of he srucural parameers θ : A = A(θ, B = B(θ, C = C(θ, D = D(θ, he algorhm for opmsaon also mples ha, for each parameer ral, he whole procedure prevously presened (log-lnearsaon, soluon of he RE model, mplemenaon of he Kalman fler and compuaon of he lkelhood value mus be repeaed. he lkelhood-based nference can presen furher problems, specfcally regardng he lack of denfcaon. global: he lkelhood funcon may have mulple maxma; local: he lkelhood funcon does no have a unque maxmum n he neghbourhoods of some θ *. o beer explan he laer case, n such suaons here exs many combnaons of model parameers ha provde he same lkelhood value,.e. he maxmum s no gven by a sngle pon n he parameer space, bu by a complex muldmensonal srucure. In some dscplnes hs s referred as over-parameersaon,.e. here are many parameer values or model specfcaons ha are compable wh he same emprcal evdence. hs also means ha he number of parameers o esmae s oo large. A rval remedy o can be o fx some parameers (n some cases mos of hem! and maxmse wh respec o he remanng ones, even f hs soluon can be regarded as arbrary. hs also mples ha he maxmsaon s compuaonally more dffcul han for sandard sae space models. Moreover, also he represenaon and summary of resuls s dffcul. For example, M nference s ofen accompaned by asympoc heory o provde confdence nervals, samplng dsrbuon of he M esmaes, ec. Bu wha f he maxmum s no unque? Moreover, he lack of denfcaon ofen leads o ll-condoned covarance marces (.e. he Hessan marx s ofen nearly sngular. akng no accoun parameer unceranes (or n oher words he shape of he lkelhood funcon can be herefore a very dffcul problem. All hese ssues call for a Bayesan approach, n whch pror nformaon s combned wh he lkelhood and whch s especally useful n problems wh many parameers and few observaons. he use of prors s very naural, snce economss have srong belefs abou plausble values of srucural parameers; parameers have a well-defned nerpreaon and have a bounded doman. From he compuaonal pon of vew, he use of a pror makes he opmsaon algorhm more sable, namely because curvaure s nroduced n he obecve funcon. Maxmsaon of he poseror s hence (relavely easer han he maxmsaon of he lkelhood. Moreover, parameer unceranes and he shape of he lkelhood (or beer of he poseror dsrbuon are reaed naurally by applyng sochasc smulaon approaches

15 he prce o pay s ha Bayesan mehods are exremely compuaonally nensve. We descrbe he Bayesan roue n he nex secon. 3.3 Bayesan esmaon and nference Roughly speakng, Bayesan nference s based on pullng he maxmum lkelhood esmaes oward values hough as plausble a pror. From he Bayes heorem, he poseror dsrbuon s obaned as (9 p( θ Y ( ( = p Y θ p θ p( Y θ p( θ p( Y θ p( θ, ( θ Y p( θ summarsng all our nformaon (pror and lkelhood abou he parameer vecor θ. he lkelhood funcon s any funcon ( θ Y p( Y θ. Knowng he poseror dsrbuon, allows mplemenng he Bayesan nference. In general, he obecve of Bayesan nference can be expressed as E[ g( θ Y ] where g (θ s a funcon of neres (a forecas, he vecor of model parameers self, ec. and E[ g( θ Y g( θ p ( θ Y dθ ] = g( θ p( θ Y dθ = = * p ( θ Y dθ * * g( θ ( θ Y ( θ Y p( θ dθ p( θ dθ where p ( θ Y p( θ Y p( θ ( θ Y s any poseror densy kernel for θ. For example, for a quadrac loss funcon, he pon esmae of model parameers s gven by he poseror mean: ˆ θ = θp( θ Y dθ. he problem n Bayesan nference s ha he negrals nvolved have almos never an analycal soluon and need a numercal approach, specfcally hrough sochasc smulaon. he key sraegy s o generae draws of θ from he poseror dsrbuon dscussed n he nex secon Implemenaon: MCMC (Meropols-Hasngs p( θ Y. hs s he key concep of Mone Carlo smulaon s as follows. Assume a vecor of random varables θ wh a on pdf π (θ. If we can draw an..d. sample θ, θ,..., θ n from π (θ, we can approxmae he negrals by dscree sums: n ( g = / n g( θ E( g( θ = g( θ π ( θ dθ almos surely as n. = If he varance σ of g (θ s fne, hen ( n( g( θ E( g( θ ~ N(, σ provdes an esmaon error. he generc dsrbuon π (θ can be he poseror dsrbuon p( θ Y and hence Mone Carlo smulaon can be appled o solve he Bayesan nference problem. he Mone Carlo approxmaons can be hen used o compue predcons, mpulse response funcons, ec

16 he almos surely n equaon ( above means ha convergence s subec o some regulary condons of he funcon g (θ ; specfcally absolue convergence of he negral mus be sasfed, see Geweke (999. he requred sample from he poseror dsrbuon s a mulvarae sample. hs s no an easy problem and has been he subec of a huge amoun of leraure o fnd echnques for hs samplng problem: from accepance samplng, mporance samplng, o Markov Chan Mone Carlo approaches (Gbbs sampler and Meropols-Hasngs algorhm. he laer approach s probably he bes suable for he problem a hand and s he one whch s appled n all he recen leraure on Bayesan analyss of DSGE models. e us frs defne an m-saes Markov process x. We denoe he possble saes of x by S = { s,..., s m } and defne he ranson probables p pm = M O M pm pmm where s he probably of movng from sae o sae. e w( = [ w (,..., w ( ] an p m vecor of probables of x beng n sae n perod, hen he correspondng probables for perod + are w ( + = w( he Markov chan has an equlbrum dsrbuon f here exs a dsrbuon π such ha π = π ; A Markov chan s reversble f probably of s he same as : π p = π p. A chan ha s reversble has an equlbrum dsrbuon and o sample from he equlbrum dsrbuon one can sar he chan from any w( unl seles down o he equlbrum dsrbuon. A Markov chan s no d, snce he sample s serally correlaed. he dea of he Meropols algorhm s o consruc he ranson marx from an easy ranson marx Q (e.g. correspondng o a mulvarae normal dsrbuon, such ha has he desred equlbrum dsrbuon π (.e. he poseror dsrbuon. hs because we are no able o draw from he poseror dsrbuon (correspondng o π n our case, bu we are able o draw sample form a normal dsrbuon (correspondng o usng Q. Of course, only he Q ranson s no suffcen o assure convergence o π, so we have o add an addonal rule for he ranson o one sae o anoher. Suppose a eraon we are n sae and based on Q we draw a proposed sae acceped (or a probably. We defne a probably α ha he proposed sae s ha he new sae s reeced and we say n. o defne s α he probably α, we use he obecve dsrbuon π as follows: α = mn[, π / π ] and he resulng chan s reversble and has equlbrum dsrbuon π. In our specfc problem, he Meropols Hasngs algorhm s mplemened as follows: s s m - 5 -

17 Condonal on daa Y and a se of parameer values θ, he Kalman Fler s used o evaluae he log-poseror densy up o a consan: p( θ ( θ Y p( θ ; ~ Wh a numercal opmsaon roune he mode θ of he poseror densy can be esmaed, and he nverse Hessan Σ ~ a he mode compued; 3 Implemen he Random Walk Meropols Algorhm: a Draw a canddae parameer vecor ϑ from a umpng dsrbuon J s ( ϑ θ, wh ( s ~ J s ~ N( θ, c Σ [he Q ranson defned above ( s b he ump from θ s acceped ( θ = ϑ wh probably reeced ( θ ( s = θ ( s ( ϑ Y r = ( θ Y oherwse, wh p( ϑ ( s ( s (s p( θ (s Y ( s α s, s=mn(r, and he seres of draws { θ } s serally correlaed (no d bu, afer a burn n perod, converges o he desred poseror dsrbuon (e.g., draw, samples and reec he frs,. he speed of convergence s a crcal ssue of MCMC mehods. here no general rule of creron ha can assure ha he chan has converged. here are a number of nformal echnques o assess convergence, such as: n s plo / n s g( θ as a funcon of n s ; s= ( s sar he Markov-Chn a over-dspersed (.e. exreme values of θ and check wheher dfferen runs of he chan sele o he same dsrbuon; more general mehods, whch combne n a more rgorous way he wo above emprcal deas, such as he poenal scale reducon facor (SRF and s mulvarae exenson (Brooks and Gelman, 998; mplemened n DYNARE. Roughly speakng, hs es ams a verfyng ha he samples obaned wh a number of parallel chans are drawn from he same dsrbuon. When converged, he chan sasfes a weak low of large numbers,.e. he approxmaons ( and ( apply for he Markov chan, whch can hen be sued for he Bayesan nference. 3.4 Model comparson In he Bayesan framework, models are compared and ranked accordng o he negraed lkelhood (or margnal daa densy. Havng a se of models =,,M, he poseror wegh of he -h model s ( w ( Y = p ( Y θ p( θ dθ Θ and, f he models have equal pror probables, he poseror probably on model s w / w. As usual, he compuaon of hs negral s unfeasble analycally n mos cases, bu can be esmaed usng a sample from he poseror dsrbuon. Specfcally, he margnal daa densy of he DSGE model s here approxmaed wh Geweke's (999 modfed harmonc mean esmaor (mplemened n DYNARE. In he presen repor we make a prelmnary comparson wh a VAR( model, usng RMSE s. Recenly, Sms (3 provded a general dscusson abou pfalls of Bayesan model comparson mehods, hghlghng several ways hey end o msbehave. In hs vew, here s no pon n showng a prelmnary Bayesan comparson, comparng, e.g., he - -

18 margnal daa densy obaned here wh he daa densy of a VAR( where he prors are defned wh a ranng se. As dscussed by Sms, such knd of comparson could be oally arbrary and meanngless. A full Bayesan comparson s beng mplemened, ryng o carefully address he ssues rased by Sms. 4 Esmaon 4. ror dsrbuons Srucural shocks. Afer n nally seng prors o nv-gamma, he radonal prors of sandard errors n Bayesan analyss, we preferred o se up fla prors n a relavely large nerval of values, reflecng more clearly our pror gnorance abou possble values of shocks. Above all n vew of a complee Bayesan comparson wh oher models (VARs, hs assumpon mgh be revsed by consderng, e.g., a ranng se. hs because oo large a pror range mgh unduly penalse he presen model, by gvng oo low wegh o he lkelhood (a oally unnformave pror n he range [-nf, nf] would gve a unformly zero wegh o any lkelhood value, mplyng he reecon of any model; see Sms, 3, for a full dscusson on hese maers. δ Concernng he shock o me-varyng δ (, we se a much smaller range, snce we do no ε wan δ o absorb whaever s mssed by he res of he model, bu we us allow he mnmum shock necessary o reconsruc he deprecaon pah. able.a rors srucural shocks Frms: F shock Deprecaon shock Dsrb. Mn Max U ε unform.e-. δ ε unform.e-. rp Rsk premum shock ε unform.e-. τ Mark-up shock ε unform.e-. W Wage cos shock ε unform.e-. Households: C Consumpon reference shock ε unform.e-. abour supply shock ε unform.e-. olcy: G Governmen expendure shock ε unform.e-. π Inflaon arge shock ε unform.e-. M Ineres rae shock ε unform.e

19 able.b rors shock perssence arameer Dsrbuon Mean S. dev. Suppor Frms: U F ρ bea.9.4 [ ] δ Deprecaon ρ bea.9.4 [ ] rp Rsk premum ρ bea.5. [ ] W Wage coss ρ bea.5. [ ] Households: abour supply olcy: Governmen expendure ρ bea.5. [ ] G ρ bea.9.4 [ ] π Inflaon arge ρ bea.5. [ ] Model parameers. he model parameers o be esmaed have a srucural economc nerpreaon and are herefore resrced o le n ceran nervals dcaed by economc heory or mpled by long run consrans. he followng ranges have been chosen for he ndvdual coeffcens: able rors model parameers arameer Dsrbuon Mean S. dev. Suppor Frms: Deprecaon rae δ bea.5.5 [.] Capacy ulsaon a bea.5.8 [.] Adusmen cos, capal γ K bea 5 5 [ 3] Adusmen cos, nv. γ I bea 3 [ ] Adusmen cos, labour γ bea 5 5 [ 3] Adusmen cos, prce γ bea 5 5 [ 3] Adusmen cos, wage γ bea 5 5 [ 3] W Mark-up, cyclcal τ bea -..3 [-. ] Share of fwd lookng prce seers sfp bea..5 [.5 ] Households: Hab perssence hab bea..5 [.9] abour supply elas. κ gamma.5.4 [ Inf] abour supply cons ω gamma..5 [ Inf] Barganng srengh bg bea [.75] Wage mark-up θ gamma.8 [ Inf] Share of fwd lookng wage seers sfw bea.8. [.5 ] - 8 -

20 olcy: Y Fscal response o ygap G bea.4 [- ] Ineres rae smoohng lag bea.8. [ ] π Ineres rae response, M bea..9 [.4] Y Ineres rae response, M bea..45 [.] π Ineres rae response, M bea.5.3 [.5 ] Y Ineres rae response, M bea.3. [.5] Smoohness, rend GD ρ YO bea.9.5 [.7 ] Noe: he followng parameers were fxed: oupu elascy of labour α =.594, dscoun facor β =.989, neres elascy money demand ζ = -.4, Mark-up level τ =.; he remanng parameers are deermned by seady sae consrans. a = ( r ss + r p + δ ( γ Iδ + s parameer of capacy ulsaon α α A = ss K ss echnology consan. r = ( τ ( α δ / I /( γ δ + δ r Rsk premum. ss I ss We denfed bea or gamma pror dsrbuons for model parameers 3. he pror Y specfcaon of sfp and M requred a parcular aenon, whereby we had o gve lower wegh o values ha were preferred by he lkelhood, bu ha mpled unreasonable dynamcal behavour n he mpulse responses. So, we se asymmerc dsrbuons ha Y prvleged he lower par of range for sfp and hgher par for M. hs mpled only a slghly worse f, bu a much beer model behavour n erms of heorecal consderaons. hs knd of approach s legmae n a Bayesan framework, and dsngushes from a plan consraned opmsaon, whch would be consdered much more arbrary. he fac ha we gve a smaller (bu non-zero! pror probably o some poron of he parameer ranges, always gves he possbly o he lkelhood o overrde hs assumpon, f he daa srongly suppors hypoheses abou such values ha were unlkely a pror. Moreover, hs approach does no rule ou possble msspecfcaon or he reecon of he presen model wh respec o compeng ones. In he laer case, he negraed lkelhood of he presen model would be penalsed wh respec o a compeng one ha provded more agreemen beween pror assumpons and lkelhood shape. he plos of he pror dsrbuons are gven below. he model was esmaed usng he followng egh seres as observaons: Y, I, C, K,, π, W, nom. 3 lease noe ha he suppor of bea dsrbuons mgh be larger han he ranges specfed n Secon, bu means and he sandard devaons are se n such a manner ha pror probably s larger han zero only n he accepable range

21 Fgure ror dsrbuons σ(ε C σ(ε δ σ(ε τ σ(ε G σ(ε π e σ(ε.e-5.e-5.e-5 σ(ε M.5..5 σ(ε U.5..5 σ(ε rp.5..5 σ(ε W a.5.5 barg 8 4 δ Y G..4. γ K

22 Fgure (con d ror dsrbuons. γ I γ γ γ W.5 hab lag ρ π κ ω ρ U ρ δ ρ G ρ ρ rp ρ W sfp 3 sfw 8 τ 3 π M 4 Y M θ π M Y M ρ YO arameer esmaes and shocks denfed he poseror esmaon followed he mehodology of Secon. Frs he mode of he poseror s esmaed usng a non-lnear opmsaon roune (values repored n he Annex. - -

23 hen, a sample from he poseror dsrbuon s obaned wh he Meropols algorhm usng he nverse Hessan a he poseror mode as he covarance marx of he umpng dsrbuon. he scale coeffcen was se o.5, allowng a good accepaon rae (5%. We ran 4 parallel Markov chans. Snce he refnemen of he convergence ess proceeded slowly by ncreasng he lengh of he chans, we decded o updae he covarance marx of he umpng dsrbuon accordng o he las poron (3% of he chans based on he nverse Hessan. hs allowed us o oban good convergence ess of 4 new chans (of 4, runs each based on he updaed covarance marx. Fgure Convergence es Meropols MCMC Mulvarae SRF de(σ x whn chan beween chan x 4 hs Fgure shows he convergence ess for Meropols MCMC. Upper panel shows he mulvarae poenal scale reducon facor, whch should be near o a convergence. ower panel shows he deermnan of he beween chans and whn chans covarance marces of he Mone Carlo sample. Afer dscardng he nal 7% of runs, we could proceed o he Bayesan nference. he followng fgures show he esmaed margnal poseror dsrbuons (black lnes, compared o prors (grey lnes and he pon esmae of he mulvarae mode (vercal dashed lnes. I s neresng o noe ha for some parameers he maxmum of he margnal dsrbuon s shfed wh respec o he mode of he mulvarae dsrbuon (n parcular γ K and γ I. hs mples ha such a local maxmum s n a very narrow regon wh almos zero mass, relaed o very specfc parameer combnaons. o gve an dea of hs, s neresng o - -

24 noe ha he log-poseror a he mode s abou 38, whle he Markov chans evolve n a range [37 379].e. almos log-pons lower wh respec o he mode. In spe of hs que hgh dfference n level, even mposng a sarng pon very near o he mode, he evoluon of he Markov chan evolved smlarly o he ones shown here, mplyng ha such a local opmum s locaed n a regon so small o mply an almos zero probably for a chan o fall here. In he Annex we also repor he values of he poseror mean wh confdence bands for he esmaed parameers. he logarhm of he margnal lkelhood for hs model s abou 33. Fnally, Fgure 4 shows he -perod ahead predcons of he model for he man model varables, ncludng he deprecaon rae δ and governmen expendure G. Dashed lnes are observaons; connuous lnes are model predcons. On he whole, he model fs he daa remarkably well. One pon ha s parcularly noeworhy s ha he model over-predcs M nom n he las years (coupled wh loose. ε Fgure 3 ror and poseror dsrbuons sandard errors srucural shocks and parameers σ(ε C σ(ε δ σ(ε τ σ(ε G σ(ε π e4.e4 5.e σ(ε e-5.e-5 9.e-5 σ(ε M σ(ε U.. σ(ε rp 4.. σ(ε W a 4 3 barg 3 δ 5 5 Y G γ K

25 Fgure 3 (con d ror and poseror dsrbuons sandard errors srucural shocks and parameers..5 γ I γ.5..5 γ γ W 8 4 hab lag 3 ρ π 3 κ 3 ω ρ U ρ δ.5 ρ G 3 ρ ρ rp.8.9 ρ W sfp sfw τ π M Y M θ π M Y M ρ YO

26 Fgure 4 -sep ahead predcon. C. δ. G.4 I nom 8 K..3 π W / Y VAR comparson If we compare he RMSE s of he DSGE model compued a he poseror mean, wh he RMSE s of a VAR( model wh he same 8 observed seres : Y, I, C, K,, π, W, nom. able 3 RMSE comparson wh VAR RMSE's VAR model (pos. mean C e- 8.58e- I 5.558e e- nom.4e-.8e- K e e e-7 π 4.573e- 9.93e- W/.994e e-5 Y.94e-5.547e-5 RMSE s of he DSGE are hgher bu of he same order of magnude han he VAR, excep for K, where he VAR performs much worse (RMSE s fory mes larger

27 5 Whch srucural shocks drve he euro economy? One of he maor advanages of he modellng approach used here s ha sysem esmaon of he model yelds, besdes he poseror dsrbuon of he model parameers, srucural shocks whch have an unambguous nerpreaon and whch can help us undersand he curren economc suaon. he srucural shocks denfed n he esmaon of hs model are shocks o households, frms, governmen and fscal polcy. Households are affeced by shocks o preferences for consumpon and labour supply. Frms are h by shocks o echnology, markups, adusmen coss for labour and capal and a rsk premum shock. Several aspecs of he esmaed shocks (fgure 5 and mpled unobserved varables (fgure are worh hghlghng. Demand Shocks he consumpon preference shock C ε appears slghly negave a he end of he esmaon sample. hs suggess lower preferences for consumers spendng and may be a reflecon of savngs uncerany concernng fuure pensons and ax lables. Noce, however, he sze of C he shock s no exraordnary large, gven he flucuaons of ε over he enre sample perod. Invesmen s h by wo auonomous shocks, a rsk premum shock and a shock o adusmen coss. he laer are unmporan and no furher consdered. he rsk premum rp shock ( ε does no show any parcular rend and appears o behave normally n recen years. hs suggess ha nvesmen flucuaons are explaned by fundamenals. he G smoohed auo-correlaed fscal polcy shock z( dsplays a urnaround n -. he fall n hs auo-correlaed shock shows clearly he fscal consoldaon perod sarng n he lae 98s, bu he declnng rend n governmen spendng s reversed n he early s. hs refues he vew ha fscal polcy has been overly resraned by he SG and been less counercyclcal over he las years. Supply shock Our Kalman fler esmaon allows o decompose observed oal facor producvy no a capacy ulsaon and a rue F componen (denoed as U. Accordng o hese esmaes U shows a rend ncrease n he second half of he 98s, a movemen along he rend n he 9s, bu a sharp declne n he lae 99s- early s. hus he fall n F n he recen pas s largely a srucural phenomenon and no he resul of a lack n demand, snce capacy ulsaon (UCA shows a normal cyclcal behavour n recen years. Noce, F s also one of he maor drvng forces of nvesmen and s herefore one of he fundamenal facors for he slowdown of nvesmen. rends and flucuaons n mark-ups are mporan measures for he supply poenal of he euro area economy. Accordng o hese esmaes he mark-up has declned on average snce he early 99s (η=-mark-up from around o 8%. hs could reflec ncreased compeve pressure due o goods marke reforms (nernal marke programme bu also ncreased pressure from global compeon. abour marke shocks W he model denfes a labour supply ( ε and a labour demand shock ( ε. he rend ncrease n labour supply (or n model erms a rend declne n he preference for lesure (Z( ε afer 995 s conssen wh he observaon of ncreased labour force parcpaon and a declnng NAIRU n he Euro area. Noce, however, he shock o labour supply has a pronounced cyclcal paern, whch suggess ha he smple wage rule used here does no ε - -

28 properly accoun for he dynamc adusmen of wages over he busness cycle. On he oher W hand, he upward rend of Z( ε reflecs he ncrease n non-wage labour coss over he sample. Ineresngly hs rend has sopped n he lae 99s, possbly reflecng a success of varous labour marke reform measures nended o reduce regulaory burdens for frms relaed o employmen. Moneary polcy shocks M he moneary polcy shock ε s negave for he years afer. hs would sugges a looser moneary sance han suggesed by he esmaed aylor rule. hs could be lnked o an underesmaon of he declne n he nflaon obecve π, whch shows a clear rend declne, bu may neverheless underesmae he acual declne n he moneary polcy s nflaon obecve. hs s one aspec ha may need furher aenon n fuure exensons of hs model. Fgure 5 Esmaed smoohed shocks a he poseror mean.5 ε C -4 x ε δ. ε τ x -3 z(ε G x -3 ε π z(ε x ε M ε U z(ε rp z(ε W Noe: f shocks are auo-correlaed, he auo-correlaed funcon s ploed (z(ε - 7 -

29 Fgure Unobserved varables.94 η.3 q. r U π ucap Ypo

30 Esmaed mpulse responses of srucural shocks In hs secon, we presen he esmaed mpulse responses of he nne srucural shocks n our model. he mpulse response are generaed on he bass of he reduced form represenaon of he model (polcy and reacon funcons - see annex. hs s parcularly smple, snce he reduced form s a lnear model (formally equvalen o a mulvarae ARMA. hey depc he responses for he endogenous varable followng a one-perod shock o each of he srucural shocks (whch are n mos cases auo-correlaed, each for a 5 year ( perods horzon. A full Bayesan IRF analyss s here presened, pckng, samples ou of he full Mone Carlo sample and compung IRF s for each of hem. Fnally, he mean pah (sold lnes and he confdence band (dashed lnes can be obaned, as shown n he Fgures. Fgure 7 Consumpon preference shock C ε. Y(% vs ε C I(% vs ε C.8 C(% vs ε C x -3 K(% vs ε C x -3 (% vs ε C M/(% vs ε C -. 8 x -5 π vs ε C -4 5 x -3 W/(% vs ε C nom(% vs ε C C Fgure 7 presens he esmaed effec of a consumpon preference shock (. hs shock s a combned shock affecng consumpon and lesure choce and has a drec mpac on consumpon and labour supply (hrough λ. he effec of hs preference shock s o rase consumpon by. percen, and employmen by.7 per cen (n he second perod afer he shock. he boos o demand rases nflaon and nomnal neres raes rse, bu he presence of adusmen coss lms he exen of he prce rse. he shock leads o crowdng ou of nvesmen and a decumulaon of capal. ε - 9 -

31 δ Fgure 8 Shock o deprecaon rae ( ε. Y(% vs ε δ I(% vs ε δ. C(% vs ε δ K(% vs ε δ (% vs ε δ -.5. M/(% vs ε δ x -4 π vs ε δ -.. W/(% vs ε δ nom(% vs ε δ δ(% vs ε δ Fgure 8 depcs a shock o he deprecaon rae of.5 per cen on mpac. hs mples an ncrease n he cos of capal of. percenage pons. hs shock s hghly perssen, n fac s has no dsappeared afer perods, due o he large esmaed auocorrelaon erm n he deprecaon rae. he ncrease n he cos of capal leads o a declne n nvesmen and he capal sock, lower real raes, hgher consumpon, hgher real wages and lower employmen. Noe however, he large confdence bands, whch sugges a large margn of uncerany surroundng hs ype of shock

32 τ Fgure 9 Shock o prce mark-up ( ε 5 x -3 Y(% vs ε τ. I(% vs ε τ 5 x -3 C(% vs ε τ x -3 K(% vs ε τ x -3 (% vs ε τ x -3 M/(% vs ε τ -5 3 x -4 π vs ε τ -.5. W/(% vs ε τ nom(% vs ε τ Fgure 9 shows ha, followng a posve prce mark-up shock, here s a ump ncrease n nflaon and nvesmen, oupu and consumpon declne. As oupu and nvesmen fall, labour demand s also lower and employmen falls. As he shock s ransory, he effecs fade away and have dsappeared afer 3 years

33 Fgure Shock o governmen spendng ( ε G.3 Y(% vs ε G I(% vs ε G C(% vs ε G K(% vs ε G (% vs ε G.3 M/(% vs ε G 8 x -4 π vs ε G. W/(% vs ε G nom(% vs ε G 4 3 Fgure shows he mpulse response o a governmen spendng shock. hs shock s a perssen shock wh an auocorrelaon of.98, bu he overall effec on GD s shor-lved. he mpac mulpler s small, no larger han., and he ncrease n spendng leads o crowdng-ou of consumpon, and n parcular of nvesmen, whch falls by.4 per cen a s peak. hs crowdng-ou of nvesmen leads o a reducon n he capal sock. he effec on oupu s emporary and over a longer horzon, oupu becomes negave. he small mulpler for a perssen fscal spendng shock s n lne wh resuls of he QUES model, n whch permanen fscal expansons have much smaller oupu effecs han ransory shocks. he ump n nflaon s surprsng and seems a odds wh emprcal regulares. I appears ha he peak nflaon response s already reached n he second quarer. hs hgh responsveness of nflaon s parly due o he hgh esmae of he forward nflaon erm sfp. Emprcal sudes employng VARs show generally posve oupu effecs of an ncrease n governmen spendng, bu ofen hese esmaes are surrounded by large confdence nervals. ero ( fnds for mos counres posve oupu effecs afer an ncrease n spendng, bu n he pos 98 sample, hese posve effecs are small and shor-lved. he effec on nvesmen s n accordance wh many emprcal sudes whch fnd he sronges crowdngou of spendng shocks for nvesmen (Alessna e al.,

34 Fgure Negave shock o employmen ε. Y(% vs ε. I(% vs ε. C(% vs ε. K(% vs ε (% vs ε -. M/(% ε x -4 π vs ε W/(% vs ε nom(% vs ε -.5. x -3 Z(ε vsε Fgure shows he mpulse response of a posve shock o lesure (a negave employmen shock. hs s a hghly auo-correlaed shock wh a hgh perssence of.99, as s clear from Z( ε. Employmen falls, and he reducon n labour supply has a negave mpac on nvesmen and oupu. As consumers ancpae lower ncomes, consumpon also falls

35 Fgure roducvy shock U ε.3 Y(% vs ε U.8 I(% vs ε U.3 C(% vs ε U.5 K(% ε U (% vs ε U. -. M/(% vs ε U x -4 π vs ε U W/(% vs ε U nom(% vs ε U -.. x -3 U vs ε U Fgure plos he esmaed effec of a producvy shock n he model. Oupu, nvesmen and consumpon rse, whle prces fall. However, he fall n nflaon s moderaed by he presence of prce adusmen coss. Employmen falls on mpac, bu over me labour supply ncreases as real wages are hgher. Moneary polcy reacs by lowerng nomnal neres raes, bu moneary polcy s no accommodang enough o preven prces fallng. I s mporan o noe ha hs producvy shock s no a permanen supply shock, bu fades away gradually