Direction des Études et Synthèses Économiques G 2016 / 05. MELEZE: A DSGE model for France within the Euro Area

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1 Drecon des Éudes e Synhèses Économques G 206 / 05 MELEZE: A DSGE model for France whn he Euro Area Benoî CAMPAGNE e Aurélen POISSONNIER Documen de raval Insu Naonal de la Sasque e des Éudes Économques

2 INSTITUT NATIONAL DE LA STATISTIQUE ET DES ÉTUDES ÉCONOMIQUES Sére des documens de raval de la Drecon des Éudes e Synhèses Économques G 206 / 05 MELEZE: A DSGE model for France whn he Euro Area Benoî CAMPAGNE* e Aurélen POISSONNIER** JUILLET 206 The auhors would lke o hank Jean-Gullaume SAHUC for hs fruful dscusson and advce on a frs verson of hs paper, as well as all parcpans o he D2E semnar a he Insee. Model codes are avalable upon reques. * Déparemen des Éudes Économques - Dvson «Éudes Macroéconomques» Tmbre G220-5, bd Gabrel Pér - BP MALAKOFF CEDEX Cres - LMA ** Commsson européenne. L aueur éa en pose à l Insee e afflé au Cres-LMA e École Polyechnque au momen de la rédacon de ce documen. Déparemen des Éudes Économques - Tmbre G20-5, bd Gabrel Pér - BP MALAKOFF CEDEX - France - Tél. : Fax : CEDEX - E-mal : d3e-dg@nsee.fr - Se Web Insee : hp:// Ces documens de raval ne reflèen pas la poson de l Insee e n'engagen que leurs aueurs. Workng papers do no reflec he poson of INSEE bu only her auhor's vews.

3 2 Mélèze : une modélsaon DSGE de la France au sen de la zone euro Résumé Mélèze Modèle économque lnéarsé d équlbre en zone euro es un modèle néo- Keynésen de ype DSGE avec les caracérsques suvanes : la France e le rese de la zone euro formen une unon monéare ; une fracon des ménages es non-rcardenne e consomme son revenu couran ; les enreprses son en concurrence monopolsque sur le marché des bens, e les ravalleurs le son sur le marché du raval ; les prx e salares son rgdes ; les bens de consommaon e d nvesssemen son exporés/mporés lbremen, ands que le raval e le capal son mmobles. Ce arcle déalle la résoluon e la calbraon du modèle ans que sa lnéarsaon. En parculer, nous défnssons l éa saonnare du modèle en nveau e nous explcons l ensemble des conranes de long-erme pesan sur la calbraon du modèle. Dans un deuxème emps, nous présenons le comporemen du modèle en réponse à dvers chocs ransores. Mos-clés : modèle DSGE, unon monéare Absrac MELEZE: A DSGE model for France whn he Euro Area MELEZE, sandng for Modèle économque lnéarsé d équlbre en zone euro lnearsed economc model of equlbrum n he euro area, s a new Keynesan DSGE model wh he followng characerscs: France and he res of he Euro area form a moneary unon; hey are populaed by nfnely lved households, of whch a consan fracon s non Rcardan, consumng all of her curren ncome; frms operae n monopolsc compeon on he goods marke, and so do workers on he labour marke ndsncly of her fnancal consrans; prces and wages are scky; consumpon and nvesmen goods can be freely expored/mpored, whereas workers and nsalled capal canno. The presen paper presens he resoluon and he calbraon of he model as well as s full lnearsaon. In parcular, we characerze he unque seady sae n levels for he real varables and explc he nduced consrans on he paramersaon. In a second par, we presen he behavour of our model wh respec o sandard ransory shocks. Keywords: DSGE model, moneary unon Classfcaon JEL : E0, F45

4 Conens Inroducon 4 2 Model 5 2. Goods and labour aggregaons Households Frms Fscal Auhores Fnancal Inermedaon Moneary Auhory, Prces and Inflaon Marke Clearng and relave prces Calbraon Classfcaon of parameers and resoluon of he seady sae Daa, calbraon and nverse nference Model dynamcs IRFs o sandard shocks Dscusson of he model specfcaon Non Rcardan households, Edgeworh complemenary/subsuably of prvae and publc spendng and her effec on consumpon Governmen spendng n he uly funcon compared o budge rules A Seady sae 52 B Lnearsaon 62 C Moneary polcy n a currency unon 72 D Frms and households dsperson 74 E Deermnaon of a unque and sable seady sae 76 F Oher IRFs 79 3

5 Inroducon Economc polcy analyss a he Insee s radonally focused on he use of large-scale macroeconomerc models namely Mésange Klen and Smon, 200. The Mésange model consruced on a hghly dealed macroeconomc accounng framework n lne wh Quarerly Naonal Accouns, feaures around 500 equaons, 0% beng behavoural economerc relaonshps. Is core long erm economc srucure s neo-classcal, whereas he model ncludes real and nomnal rgdes n he shor run. One man advanage of hs model s s ably o replcae pas observed daa and o gve precse and quanave nsghs for economc polcy evaluaons, manly focused on fscal evaluaons. However, Lucas crque Lucas, 976 saes ha he absence of a srong shor-run economc srucure and he absence of raonal expecaons mgh be weaknesses of such models. As such, economc modellng has focused on alernaves and developed a new modellng sream, namely he DSGE leraure. Conrary o macroeconomerc models, hese models focus less on gvng an exac descrpon of observed economc daa han on a srong heorecal and mcro-founded srucure answerng Lucas crque. As such, hey appear as an neresng parallel o macroeconomerc models, as evdenced by her large adopon oday whn he man naonal and nernaonal nsuons. Ths paper nroduces MELEZE, a fscal-polcy orened new-keynesan Dynamc Sochasc General Equlbrum DSGE model developed a he Insee. MELEZE s wo-counry moneary unon model amed a represenng he suaon of France whn he Euro area. Compared o he Mésange model, he presen model allows o focus more specfcally on quesons relaed o raonal expecaons and ancpaons of shocks, macroeconomc spllovers n a moneary unon, and endogenous behavours of he governmen. In parcular, MELEZE offers wo alernave choce of modellng for he governmen behavour. A frs opon s he mplemenaon of a radonal budge rules lnkng oday s publc consumpon o pas defcs as found n he nsuonal DSGE leraure. As an alernave, we also develop and propose a new approach, modellng he governmen as an opmzng agen maxmzng households welfare. Ths second modellng drecly relaes o he Ramsey polcy under bounded raonaly. More generally, MELEZE s srucure compares wh mos sandard ools developed n nernaonal nsuons and cenral banks, ye remans smple enough o be able o dsenangle mos economc reacons. Indeed, he consrucon of he model was conduced along hree objecves. Frs, needs o be refned enough o gve nsghful supplemenary polcy analyses usng a DSGE model raher han a macroeconomerc model, n parcular wh respec o fscal behavours. Second, should compare o Modèle Économque Lnéarsé d Équlbre en Zone Euro 4

6 sandard nsuonal models used a cenral banks and nernaonal organzaons and help o brdge he gap beween Mésange and such large-scale DSGE models. Las, should reman relavely small compared o large nsuonal DSGE models o boh allow for a beer undersandng of underlyng mechansms and for an easer ransmsson of he model nernally. Along hose lnes, MELEZE herefore ncludes all radonal ngredens found n he nsuonal DSGE lerraure, and s largely nspred by Smes and Wouers, 2002, 2003, 2005 or Chrsano, Echenbaum, and Evans, All n all, hese modellng choces allow o perform n MELEZE, all sandard macroeconomc polcy evaluaon exercses such as he sudy of permanen fscal reforms Campagne and Possonner, 206a, or he smulaon of labour and goods markes deregulaons Campagne and Possonner, 206b. Ths paper s organsed as follows. In Secon 2, we presen he model and derve he frs order condons for all economc agens. Secon 3 descrbes he mehodology and he daa used for he calbraon of MELEZE as a moneary unon model descrbng he suaon of France whn he Eurozone. Lasly, n order o gve a few nsghs on he behavour of our model, we presen he shor erm responses hrough he sudy of mpulse responses o a se of sandard polcy shocks Secon 4. The Appendx gves a full descrpon of he seady sae and lnearsed model, as well as addonal remarks on he desgn of moneary polcy n a currency unon, on he mpac of wage and prce dsperson n he model and on he unqueness and sably of he seady sae. 2 Model Non-echncal oulne In hs paper, we develop a DSGE model comparng wh sandard ools developed n nernaonal nsuons and cenral banks Chrsano e al., 2005; Smes and Wouers, The model consss of wo counres where connuums of frms and households nerac on he goods, labour and capal marke. Boh frms and households are consdered mmoble across counres. As advocaed by Mankw 2000, we dsngush beween wo ypes of households. A fracon of hese households s Rcardan, ha s no fnancally consraned. They hold fnancal asse or deb, own capal whch hey lend o frms n her counry once nsalled capal s assumed o become mmoble and also own fnancal nermedaon frms. Therefore, hey receve or pay neress and dvdends. These Rcardan households also choose her nvesmen each perod by arbrang beween capal and he rsk free asse. Non Rcardan households on he conrary are fnancally consraned and 5

7 do no hold any asse. Boh ypes of households also provde labour on monopolscally compeve marke. For hs reason, households are pad wh a mark-up over her margnal dsuly. Wage rgdes are added over he cycle, and each household can only rese s wage n adequaeness wh hs opmal consumponlesure arbrage wh an exogenous probably. In hs framework, here s no nvolunary unemploymen and labour adjuss only a he nensve margn hours worked. Households fnally consume boh domesc and mpored goods whch are paral subsues. For Rcardan households, beng non fnancally consraned allows hem o smooh her consumpon over me. Non Rcardan households on he conrary can no. Once her wage level s se, her labour supply s gven by frms demand, her ncome ensues whch hey consume enrely whn he same quarer. Frms produce parally subsuable goods from a sandard consan reurns o scale producon funcon. Producon facors are labour and capal. Toal facor producvy s exogenous and growng a he same pace across counres. A each perod frms opmze her relave demand n capal and labour o mnmze her producon cos, akng he aggregae wage and gross reurn on capal as gven. Paral subsuably allows frm o prce a mark-up over her margnal cos. Over he cycle, wh an exogenous probably each frm can rese s prce o maxmze s expeced dscouned profs, whle nernalsng s marke power. Those prce rgdes lead o a New Keynesan Phllps curve. The modellng of governmens behavour depars from he fscal and budge rules leraure used n quanave models o endogenze ax raes and publc spendng n order o ensure he governmen s budge consran. We consder here forward-lookng opmzng governmens. We nroduce unproducve publc consumpon as a proxy for acual publc spendngs, publc nvesmen, publc employmen and producon of publc servces alogeher. Ths consumpon eners households uly funcon ogeher wh prvae consumpon. Governmens maxmze he neremporal households uly under he publc budge consran whch s an approxmaon for he exac Ramsey problem. Alernavely, we also allow he governmen o behave accordng o a sandard budge rule lnkng publc consumpon wh pas defc and oupu gap. Furhermore, governmens collec axes on wages, capal ncome, dvdends, consumpon and nvesmen. They can dsrbue ransfers o boh ypes of households. They also hold deb boh a he seady sae and over he cycle. In addon o producon of real goods by he frms, a unon wde fnancal marke produces fnancal nermedaon servces boh for households and governmens. Fnancal nermedares capure on op of he neres rae se by he cenral banker a fee under he form of a deb elasc spread whch s akn o fsm. There are no rsk or agency ssues n our model so ha hs fee s no o be nerpreed as 6

8 a rsk premum of any knd. In pracce, hese fnancal nermedares ensure he closng of he model as exposed n Schm-Grohé and Urbe 2003 and have a very small producon compared o frms of he real secor. Noaons As much as possble, we keep sandard noaons hroughou hs paper C for consumpon, W for wage... A superscrp {, 2} wheher on an aggregae or on a parameer refers o he counry. Subscrps are used o specfy an operaon relaed o he varable e.g. hab on consumpon or labour, n parcular Cj refers o consumpon n counry of goods produced n counry j. Upper-case leers refer o aggregaes whle lower-case leers refer per GDP un aggregaes or somemes when we wan o emphasze ndvdual varables wage, labour and oupu per frm or capa. Throughou, τ s he ndex for a generc household and ε he ndex for a generc frm. R and NR superscrps relae o Rcardan and non Rcardan households respecvely. refers o me. A full dconary of varables and parameers s gven n Tables 3 and 4 n he Appendx. 2. Goods and labour aggregaons 2.. Aggregaon of producon whn counres We assume ha a connuum of goods of sze P s produced n he moneary unon. Goods n [ 0, pp ] are produced n counry, whle goods n ] pp, P ] are produced n counry 2. For formula generalzaon, we shall denoe p = p and p 2 = p. In each counry, domesc producon s aggregaed no a domesc good usng a Dx Sglz aggregaor Dx and Sglz, 977 wh an elascy of subsuon specfc o each counry. Ths modellng hypohess s nerpreable eher as he echnology of a perfecly compeve fnal good secor wh sole npus nermedae consumpon of he connuum of frms or as he relave preferences for each ype of goods of he fnal consumer. These hypoheses yeld he followng relaonshp beween he demand for goods produced by frm y ε, and he oal demand for producon of counry Y ={,2} : pp Y = Z pp 0 Y 2 = Z 2 pp θ y ε θ θ θ dε = pp P pp θ pp θ 2 y 2 ε θ2 θ 2 θ dε 2 P = pp θ 2 pp 0 θ y ε θ θ dε θ, 2. θ 2 y 2 ε θ2 θ 2 dε θ

9 where θ s he elascy of subsuon beween goods n counry and Z a consan of normalsaon. 2 Maxmsng consumpon under he budge consran or alernavely, mnmsng he prce for a bundle un yelds he correspondng producon prces: P = pp P Z pp θ ε θ dε 0 P 2 = P P Z 2 pp θ2 2 ε θ2 dε pp θ = pp θ pp θ 2 = pp 0 P ε θ dε θ, 2.3 θ 2 P The resulng relaonshps beween aggregaed and real prces and quanes read: y ε = Zθ P ε pp θ y 2 ε = P Z θ2 2 pp θ Labour aggregaon θ P 2 ε P 2 Y P = ε θ 2 P θ P Y 2 2 = ε P 2 pp P 2 ε θ2 dε θ Y pp, 2.5 θ 2 Y 2 pp. 2.6 The aggregaon of labour n boh counres s symmerc o ha of goods Dx Sglz. The populaon sze s se o N and a share n of households, ha s households n [0,nN], lve n counry. Households n [nn,n] lve n counry 2. For formula generalzaon, we shall denoe n = n and n 2 = n. Labour s hereafer assumed o be mmoble across counres. Household τ supples labour l τ, and demands he wage w τ, so ha he oal supply of labour and average wage n counry are L ={,2} and W ={,2}. L = nn θw L 2 = nn nn 0 θw 2 θ w θ lτ w θw dτ θw, 2.7 N θ2 w θ 2 lτ 2 w θw 2 dτ nn θw where θ w s he elascy of subsuon beween labour ypes n counry. 2 We ake Z = pp and Z 2 = pp o smplfy he algebra. Wh hs normalsaon, f prces P ε are all equal whn counry, hen he aggregae prce ndex s equal o he ndvdual prce P = P ε. In addon, each frm produces an equal share of oal oupu y ε = pp Y. 8

10 The correspondng wages are: W nn = nn θw W 2 N = θ nn w 2 0 w τ θ wdτ θ w, 2.9 nn w 2 τ θ2 wdτ θ 2w. 2.0 The resulng relaonshps beween aggregaed and ndvdual wage and labour supply read: lτ = nn l 2 τ = w τ W nn θ w L, 2. w 2 τ W 2 θ 2 w L Aggregaon of domesc and mpored prvae consumpon In boh counres, households have access o goods produced by each counry; domesc and foregn goods are paral subsues. We derve he case for consumpon, we assume ha nvesmen and consumpon goods are dencal so ha he same resuls apply o nvesmen as well. Aggregaon of mpored and domesc producon along wh he assocaed consumpon prce ndex are modelled as follows C = C α, Cj,α α α α α CPI = P α P j α 2.3, 2.4 where C s he prvae consumpon of counry and C j, s he prvae consumpon n counry of he aggregaed goods produced n counry j. α s he mpor share of counry and herefore a measure of rade openness. Noe ha we have he followng relaonshps: C, = C, + C2, 2.5 C = C, + C 2, bu CPI C = P C, + P2 C 2, 2.6 The aggregaon of domesc and mpored consumpon n boh counres yelds he followng relaonshps: C 2, = α P P 2 α C C, = α α P 2 P C 2.7, 2.8 9

11 C 2, = α2 P 2 P α 2 C 2 C 2 2, = α2 α P 2 P 2 C 2 2.9, 2.20 The reparon of consumpons beween locally-produced goods and foregn ones depends on he degrees of openness conveyed by mpor shares α. Impored and domesc consumpon n counry respond o he erms of rade defned as T = P2, wh elasces α and α, respecvely: as P expeced, he dearer are mpor prces n relave erms, he more households consume domescallyproduced goods. 2.2 Households 2.2. Consumpon and nvesmen decson of Rcardan households In boh counres, we assume ha a fracon µ of households can parcpae o he fnancal markes. These households can borrow or lend money on an nernaonal marke see 2.5 and dong so have he possbly o smooh her consumpon across perods. Each household of hs ype τ maxmses her neremporal uly funcon subjec o her budge consran deermned by he recursve law of moon of prvae asses. Uly s smlar o Traband and Uhlg 20, ha s non separable, CES n consumpon wh exernal hab formaon n a mulplcave manner. 3 Dsuly of labour also allows for habs. 4 Ths funconal form s compable wh long erm growh Kng, Plosser, and Rebelo, 2002, as under hs form he dsuly of labour s concave for any value of he neremporal elascy of subsuon of consumpon, and also ensures a consan Frsch elascy. We also consder ha households derve uly from publc expendure and herefore redefne he consumpon bundle as a combnaon of prvae and publc expendures n a Cobb-Douglas fashon. Ths choce of specfcaon s a subcase of CES aggregaons as n McGraan, Rogerson, and Wrgh 997; Bouakez and Rebe 2007; Coenen, Mohr, and Sraub In all, a Rcardan household τ solves: C R, T max E τ,fa T τ,i T τ,k T τ T= β T UC R, T τ, C T VlR, T τ, L T WG T, G T As n Abel 990; Galí 994; Carroll, Overland, and Wel 2000; Fuhrer 2000, nroducng habs allows o accoun for he perssence of consumpon when esmang he model. I also allows for more realsc hump-shaped response funcons followng shocks. 4 Noe however, ha n he sandard calbraon of he model, hese habs on labour are mued. 0

12 subjec o he budge consran FA T FA T R τ = T ψ P T Ȳ Tr T CPI T +νc, T CR, T τ+ νd, T FA T τ+w T τlr, T τ D T τ+ νfd, T FD T τ + Φ T τ+ νk, T CPI T rk, T K T τ CPI T +νc, T I T τ 2.22 and he capal accumulaon equaon K T τ = δk T τ+ǫ,i T [ S I T τ I T τ Under he mos general form, we defne uly as: ] IT τ 2.23 UC R, τ, C VlR, τ, L WG, G = G h η g C R, τ C n N h c η G σ c σ c κ σc l R, τ L n N h l +σ l σc 2.24 E, β are respecvely he expecaon a me operaor and he dscoun facor; C R, τ s he consumpon of Rcardan agen τ n counry ; σc s he nverse neremporal elascy of subsuon. κ s he wegh assgned o labour n he uly funcon; σl s he nverse of he Frsch elascy. h c, h g, h l are he exernal hab formaon parameers on prvae and publc consumpons and labour. l R, τ s he labour supply of household τ and w τ s wage. FA τ s he household s τ asse holdngs a he end of perod whle FA s counry s aggregae level of prvae fnancal asses see he aomcy assumpon explaned n he followng paragraph on prvae asse dynamcs; R s he neres rae se by he moneary auhory n he unon; ψ s an neres premum on deb whose funcon s dealed subsequenly. ν c, s he ax rae on consumpon or value-added ax VAT hrough whch governmen expendure s parally fnanced. D s he dvdend pad by he frm o s owners axed a rae νd,, FD are equvalenly he dvdends pad by he fnancal secor axed a rae ν FD, and Φ τ a lump-sum ransfer from he governmen. Fnally, K τ s he capal sock of Rcardan households deprecang a rae δ and whch revenues are axed a rae ν K,.

13 Ȳ corresponds o he seady sae level of oupu, and Tr T = + g T corresponds o he deermnsc rend of our model, where g s he growh rae of TFP. In he capal accumulaon equaon, I τ s he nvesmen level wh an adjusmen cos5 S I T τ/i T τ dependng on prevous perod level of nvesmen. 6 As a resul, households pay for he full nvesmen allomen IT τ and a share S I T τ/i T τ s los n he nsallaon process. Ths adjusmen cos mgaes he flucuaons of capal sock and nvesmen n reacon o exogenous shocks. ǫ,i T represens an exogenous shock o hs cos somemes found crucal o replcae he busness cycle. The cosae varable for consran 2.23 s defned as q CPI +νc, mes he cosae varable of he budge consran 2.22 β λ, so ha q s he marke value of an addonal un of capal, ha s Tobn s margnal Q. The Euler equaon, he nvesmen decson and Tobn s Q for hs programme are dencal across households, and under he assumpon ha dfferences n labour and consumpon across Rcardan households are of second order, we aggregae hese frs order condons. 7 The Euler equaon descrbes he rade off beween consumpon and savngs on he fnancal marke: U β E U C R, + µ n N, C C R, µ n N, C V V L R, + µ n N, L L R, µ n N, L W G+, G W G, G R ψ where Π c, + s he nflaon of he consumpon prce ndex n counry. FA P Ȳ Tr Π c, +ν c, + + +ν c, = As n Smes and Wouers 2003 o Smes and Wouers 2007, hs cos s nroduce n order o smooh he reacon of nvesmen o shocks. Smlarly, we assume ha a seady sae S = 0, S = 0 and S > 0. 6 As n mos DSGE models, he nvesmen decson s conduced by households only. 7 The exen of hs approxmaon s explaned by Carroll 2000 n a more general conex. Whn a lnearsed model we gve a dealed analyss of dsrbuons n Appendx D. 2

14 Invesmen and he margnal value of capal are descrbed by he followng frs order condons: =q ǫ,i { S U + β E U U q =β E U S I I I I C R, + µ n N, C V C R, µ n N, C C R, + µ n N, C C R, µ n N, C V V V I I } L R, + µ n N, L L R, µ n N, L L R, + µ n N, L L R, µ n N, L W G+, G W G, q + ǫ,i + S G W G+, G W G, G q + I + I 2 + I I 2.26 νk, + δ+ rk, + +ν c, The laer, smlar o he Euler equaon on consumpon 2.25, descrbes he rade-off beween nvesmen n capal and consumpon Rcardan households asse dynamcs By assumpon, only unconsraned households can lend or borrow, her aggregae budge consran reads: FA = FA R ψ P Ȳ Tr CPI+ν c, C R, + Φ R, + ν K, + ν D, T CPI r K, FA + WR, L R, D T + νfd, FD K CPI +ν c, I 2.28 To make he cos of deb ncrease wh he level of ndebedness and also ensure he saonary of he model.e. rule ou un roos o ensure he convergence of fnancal asses afer shocks, see secon E, we nclude a premum on he neres rae ψ, whch s akn o a ransacon cos on holdng asses pad o an nernaonal fnancal nermedary and enforces a no-ponz scheme condon on he evoluon of asses see Secon 2.5. Ths premum depends posvely on f a = FA P Ȳ Tr, whch represens he level of ndebedness of prvae agens n counry n real erms, Ȳ beng he seady-sae value of oupu once derended n counry and Tr s deermnsc rend. The premum a household faces depends on he aggregae prvae asse holdngs of he counry or local fnancal condons, no on he household s prvae personal fnancal poson. Thus each household akes he premum as gven n s consumpon decson aomcy assumpon. As he model 3

15 wll be lnearsed, only he value of ψ and s frs dervave a he seady sae wll mpac he model dynamcs. We specfy ψ such ha ψ0 = 0 and ψx x > 0, so ha boh ndebedness and asse holdng ncur a cos pad o he nermedary, and he value of he premum ncreases wh deb. If a he aggregae level, households n counry are ne borrowers.e. FA 0, resden households have o pay an neres premum on her deb amounng o ψ f a. When he counry s ne lender, reurns are reduced by ψ f a capured by he nermedary. Ths mechansm s equvalen o fnancal nermedaon servces ndrecly measured FISIM, see secon Consumpon decson of non Rcardan households The remanng fracon µ of households does no have access o fnancal nermedaon and herefore, her consumpon canno be smoohed across perods. These non Rcardan households follow a rule-ofhumb: 0 = w τl τ+φ τ CPI +ν c, C τ 2.29 on aggregae 0 = W NR, L NR, + Φ NR, CPI+ν c, C NR, 2.30 As no asses are avalable o non Rcardan households, hey neher hold shares n domesc frms nor n he fnancal secor and hence do no receve dvdends. Moreover, n he absence of precauonary savngs of hese households n our model, non-rcardan households canno hold money as a paral subsue o bonds or capal and are unable o smooh her consumpon n me even parally. As a consequence, our model may overesmae her reacon o shocks Challe and Rago. For nsance followng a posve producvy shock, prces and wages beng scky, frms wll lower her labour demand. Whle Rcardan households can smooh her consumpon by sellng some asses, consumpon of he non Rcardan ones wll drop as a drec consequence of her decrease n payroll, hs lower demand wll n urn affec oupu negavely Labour supply decson and wage seng As we dd for consumpon goods, we model labour aggregaon wh a Dx Sglz funcon. Relaonshps beween labour and wages are herefore smlar o hose beween consumpon and prces see secon 2.. Unlke consumpon goods, labour s consdered mmoble and canno be mpored or expored. The relaonshp beween oal demand for labour and each household supply as a funcon of he demanded wage reads: lτ = n N w τ W θ w L 2.3 4

16 We assume wage sckness à la Calvo 983, wh parameer ξw denong he probably no o adjus wages a each perod. There s also paral ndexaon of wages on pas nflaon of consumpon prces accordng o parameer γw and ndexaon on argeed nflaon wh parameer γw. Wages are also ndexed on he deermnsc rend of TFP. 8 Households solve he followng program: max ξwβ w τ, l,tτe T UC T τ, C T V l,t τ, L T WGT, G T 2.32 T= subjec o he labour demand funcon: l,t τ = n N w,t τ W T θ w L T, 2.33 as well as her respecve budge consran, and he followng ndexaon rule: w T,T τ = w τ k= Π c, k γ w Π c, γ w Tr T Tr = w τγ T w,, 2.34 where w τ s he opmal wage se a me by household τ and w,t τ s s wage a me T when no rese beween me and T; l τ and l,t τ are he correspondng labour demands. ΓT w, denoes he ndexaon facor T k= Πc, k γ w Π c, γ w Tr T /Tr wh Π c, he seady sae nflaon of CPI. The frs order condon reads 0 =E ξwβ T l,t τ U CT τ, C T V l,t τ, LT WGT, G T T= U C τ, C V l τ, L T WG, G [ UC T τ, CT V l,t τ, L ] 2.35 T U CT τ, C T V + θ w w τγt w, l,t τ, L θw CPI T T +νc, T where one may recognze he sochasc dscoun facor beween me and T and beween brackes, he wedge beween he rao of he margnal uly of labour and consumpon and he real wage wh a erm n θ w represenng he marke power of households. Noe ha hs wage seng equaon s a he ndvdual level and herefore ha he assocaed uly funcon and wages depend on he ndvdual consumpon of household τ. However, as for he Euler and nvesmen equaons, we make he sandard assumpon ha ndvdual dsperson can be 8 These ndexaons are necessary o ensure ha he dsrbuon of wages does no dverge when here s non zero nflaon and exogenous growh a seady sae. 5

17 negleced see Appendx D. Alhough we can descrbe how wages and labour supply of reseers dffer from oher households, we can no do so for consumpon. Wh non separable uly, we are hus forced o assume ha non reseers and reseers have smlar consumpon whn each ype. 9 The res of he calculus seady sae and lnearsaon s dealed n he subsequen secons, bu because he consumpon of he Rcardan and non Rcardan household dffer, here wll be wo symmerc Phllps curves for wo dfferen wages Households ype aggregaon The nroducon of wo ypes of households resuls n addonal aggregaon rules for consumpon, labour and wages. As seen prevously, he exsence of wo dfferen Phllps curves for Rcardan and non Rcardan households mples ha her consumpon, labour and wage paerns dffer. In erms of consumpon, we now have for consumpon of good j n counry and oal consumpon: C j, = CNR, j, + C R, j, C = C NR, + C R, 2.36, 2.37 where C R, j, and C NR, j, respecvely denoe consumpon of Rcardan and non Rcardan households of good j n counry. Consumpon of he wo ypes of households s smply addve: boh ypes consume he same goods a he same prces wh he same mpored and domesc share. Labour and wages are no drecly addve, bu payroll s by consrucon. Smlarly o labour and wage n boh counres we defne aggregae labours and wages for boh ypes of households: L NR, = µ n N L R, θw = µ n N l τ NR, θw θ w θ w l τ R, dτ θ w θ w θ w θ w, 2.38 dτ θ w θ w Noe ha hese consumpons converge o he same seady sae and follow he same dynamc equaons respecvely he Rcardan Euler equaon for consumpon and he non Rcardan budge consran. 6

18 The correspondng wages are: W NR, = µ n N θw w τ θ wdτ NR, W R, = µ n N θw w τ θ wdτ R, θ w, 2.40 θ w. 2.4 Labour aggregaon read as follows: L = nn = L 2 = µ θ w µ θ 2 w θw nn 0 θ θ w w l τ θw θw dτ θ L NR, w θw + µ θ2 L NR,2 w θw 2 + µ θw θw 2 = nn L R, L R,2 θw θ θ w w θw θw l τ NR, θ w θ w θ θ w w dτ+ l τ θw θw dτ R, 2.42 θ2 θ2 w w θw 2 θw Wage aggregaon reads: W = µ W NR, θ w + µ W R, θ w θ w 2.44 In real erms, usng he varable used n he lnearsed model, hs also rewres: RW θ w = µ θ RW NR, w + µ RW R, θ w 2.45 wh RW he purchasng power of ne wages ha s deflaed by he counry s VAT ncluded CPI. 2.3 Frms We assume an exogenous and global echnologcal growh process n he form ζ = ǫζ, + g ζ, where g s he deermnsc growh rae of oal facor producvy, ζ he de-rended seady sae level of echnology, and ǫ ζ a possbly auocorrelaed sochasc producvy shock. In he res of he paper, we denoe Tr = + g he deermnsc rend of TFP. We assume ha echnology can be shared and ransferred whn he unon, so ha TFP growh s he same n boh counres. 0 0 However, he seady sae derended level of TFP, e. ζ, dffers across counres o ake no accoun he nal dfferences n wealh across counres. 7

19 2.3. Producon facors opmsaon Frms hre domesc labour a he cos W +νw,, where ν w, s he payroll ax rae leved by he governmen on frms. Frms also ren capal from households a rae r k,. In real erm he renal cos of demanded capal K d, ε s hen r k, K d, ε pad a me. In nomnal erms, hs cos equals r k, K d, εcpi : he value of he rened capal n currenes equal o he real capal sock mes s marke prce CPI.2 Noe ha capal from prevous perod s used for producon a me assumng nsallaon delays. Therefore a marke equlbrum, we have on aggregae K d, = K. In each counry, frm ε produces he dfferenaed good y ε wh he followng echnology: y ε, = α ζl ε K d, α ε a cos W+ν w, L ε+r k, CPIK d, ε, 2.46 where α s he share of capal coss n value added. For sake of smplcy, alhough may prove emprcally relevan Challe and Rago, we do no assume ha Rcardan and non Rcardan households correspond o dfferen ypes of workers. Frms hre boh ypes of households ndsncly. Every perod, frms can rese he quany of each producon facor hey use akng wage, axes and renal cos as exogenous. The arbrage condon beween labour and capal demand yelds: α α = W +νw, L ε r k, K d, εcpi on aggregae α α = W +νw, L r k, K CPI 2.47 The margnal cos of producon s dencal across frms and does no depend on s sze: MC ε = MC = RMC = MC P Prce seng = α α α α α α α α W ζ RW ζ +ν w, α +ν c, +ν w, r k, CPI α 2.48 α r k, α CPI P 2.49 The prce seng follows Calvo process n each counry. Frm ε can rese s prce wh exogenous probably ξ. Producers know he relaonshp beween her prce and he demand for her produc No axes on labour ncome socal conrbuon, ncome ax are pad by households here. The seady sae s no affeced by hs assumpon bu he reacon of wages o hs ax s affeced n he shor-erm. 2 The prce of capal s by convenon he same as he prce of nvesmen, whch s dencal o he prce of consumpon as we assume ha boh goods are dencal. 8

20 and choose her prce P ε so as o maxmse her expeced prof under ha consran: max E P ε T= β ξ T λ T subjec o ỹ,t ε = p P P εỹ,t ε W T +νw, T L,T ε rk, T CPI T Kd,,T ε, 2.50 P,T ε P T θ Y T, 2.5 y,t ε = ζ L,T ε α K d,,t ε α, 2.52 α α = W +νw, r k, K d, P,T ε = P ε T k= L ε, 2.53 εcpi Π k γ p Π γ p = P εγ T, 2.54 where he Lagrange mulpler λ T s he margnal uly of a represenave Rcardan households n counry. 3 ỹ,t ε s he demand for goods produced by frm ε of counry a me T when s prce was las rese a me. γ p s he parameer of prce ndexaon on pas nflaon and Γ T denoes T k= Π γ p k Π γ p. So P,T ε = P εγt s he prce of good ε of counry a me T when s prce was las rese a me. Noe ha Π s he nflaon of goods produced n counry and dffers from nflaon of he consumpon prce ndex CPI, whch ncludes nflaon from mpored goods as well. Π s he seady sae value of Π. The frs order condon reads: 0 = T= β ξ T λ T Y T p P Dvdends dsrbuon θ P εγt PT P εγ T θ θ MC T 2.55 Frms canno save or nves, so hey redsrbue her profs o households. Ths dsrbuon can be hough of as dvdends o frms owners, f negave s smlar o a recapalsaon of he frm. Therefore, we assume ha only unconsraned households, who have access o fnancal and nvesmen markes, are pad such dvdends D. D = PY W+ν w, L r k, K CPI 2.56 D = P Y RMC These households own he frms, so logcally her uly eners he prce-seng program. Ths s however neural on he lnearsed Phllps curve apar from a redefnon of β when here s long erm growh, a redefnon whch does no depend on households ype. 9

21 2.3.4 Aggregae producon funcon We assume ha he producon funcon s dencal across frms. We can compue he aggregaed producon funcon based on he defnon of Y as a funcon of y ε: Y = p P p P θ = α ζl 0 K d, θ y ε θ θ θ dε αp P θ p P 0 L ε α L K d, α ε K d, θ θ dε θ θ 2.58 whch smplfes because of equaon 2.47 = α ζl K d, αp P θ p P 0 L ε L θ θ dε θ θ = α ζl K d, α 2.59 I follows ha he producon funcon on aggregae ncludes a measure of frm sze dsperson. The producvy shock could be assumed o encompass boh aspecs: ndvdual producvy and sze dsperson; however he pure producvy shock appears on s own n he Phllps curve on prces hrough he margnal cos of producon. Hence, followng he common mplc assumpon n hs leraure, we assume ha dsperson s sable enough for o be aken as consan, assumpon verfed a frs order see Appendx D. Moreover a he seady-sae, frms are all dencal, ha s of same sze p P. I follows ha he seady sae value of he dsperson ndex s =. 2.4 Fscal Auhores By and large, he purpose of governmens s o smulae domesc producon, labour and ndvdual consumpon, as well as o provde wh publc and collecve goods and servces. In he real world, fscal polcy s mplemened hrough a large number of nsrumens such as publc expendures, nvesmen, or employmen, as well as hrough he axaon and socal conrbuon sysem. However, hs large number of nsrumens canno be modelled n deals and one need o resor o smplfcaons. Tax sysem Frs, n MELEZE, we assume ha ax raes over consumpon, labour and capal ncomes are exogenous and are dscreely chosen by governmens. Ths choce s conssen wh a low varably of apparen ax raes n he daa over he calbraon perod. 20

22 Transfers Second, n he presen model, governmens can rase lump-sum axes or comm o lumpsum ransfers o households. In he baselne behavour of MELEZE, hese ransfers are held consan. However, we allow for poenal exogenous ransfers shocks, argeed on Rcardan or/and non Rcardan households. Here, nomnal lump-sum ransfers from he governmen are addve Φ = ΦNR, + Φ R,, and we chose he mos smple way o dsrbue ransfers defaul seng, ha s n proporon o her populaon share: Φ NR, = µ Φ and ΦR, = µ Φ. These ransfers can easly be endogensed o reflec he redsrbuve polcy of he welfare sae whn he cycle. A seady sae, any redsrbuon weghs can be raonalzed by he relave weghs assgned by he governmen o boh ypes of households. Publc expendures In he absence of publc producon or employmen n he presen model, we capure and encompass all remanng dmensons of publc nervenon hrough publc expendures. In order o model fscal polcy, hese expendures are decomposed beween an endogenous componen answerng o economc developmens and an exogenous and dscreonary componen. In sandard DSGE models, he endogenous behavour s eher modelled as he soluon o a Ramsey opmaly problem or hrough budge rules esmaed ex ane. In he followng secons, we ake a closer look a dfferen budge rules and presen an alernave o he Ramsey approach o model publc expendures. Moreover, and o model he perssence of governmen expendures he welfare sae canno be dramacally reshaped overngh, we nroduce habs on publc consumpon n he households uly funcon Budge and fscal rules Budge rules can be mplemened n dfferen ways all relyng on he ad hoc descrpon of governmens spendngs as a funcon of observable endogenous varables.. Exogenous publc spendng In closed economy when fscal polcy s no he purpose of he model, he governmen behavour can be grealy smplfed: one can assume he absence of axes, exogenous publc expendure, and publc deb as a mere counerpar of prvae asses. In hs specfc case, lump-sum ransfers are assumed o balance he governmen budge consran. For nsance, Negro, Schorfhede, Smes, and Wouers 2007 or Jusnano and Prmcer

23 consder a budge rule of he followng form: G = g Y 2.60 where g s an exogenous dsurbance followng he process: log g = ρ g log ḡ + ρ g log g + σ g,ε g, 2.6 However, such a rule can no be ncorporaed n our open economy model. As here s explc publc deb, here mus be some mechansm ensurng he exsence of a seady sae for publc expendure and deb alogeher n boh counres. 2. Endogenous spendng whou dsorve axes Corse, Meer, and Müller 200, n a moneary unon model, consder hree fscal nsrumens, namely spendng, ransfers and deb modelled as follows: G = Ψ gg Ḡ + Ψ gg G + Ψ gyy Y, f +Ψ PA gd Φ P = Ḡ P G CPI Ḡ Ψg + Ψ d PA CPI P + ε g, where Y, f denoes he level of oupu ha would preval under flexble prces and wages. A seady sae wh hese specfcaons, here s no publc deb. Publc spendng may be made exogenous Ψ gy = Ψ gd = 0, n whch case ransfers adjus auomacally o ensure he convergence of publc deb o s seady sae. Corse e al. 200 compare he prevous case o a suaon where publc spendng s adjused endogenously o conrbue o he convergence of publc deb and may n addon be pro or conra cyclcal dependng on he value of Ψ gy. 3. Endogenous spendng wh dsorve axes In models where fscal polcy s more dealed, adjusmen can be made hrough ax raes. For nsance, Caron and Guyon 202 consder ha he VAT rae follows a fscal rule whch enables her moneary unon model o reach a seady sae: 4 ν c, ] ν c, = ρ G ν c, ν c, + ρ G [β BG pa pa + β DG pa pa 2.64 Under hs form, he VAT rae wll gradually adjus o equalze he publc deb o s argeed level. 4 Oher nsrumens avalable are socal conrbuons, ransfers or publc expendures. 22

24 In he European Commsson model QUEST III, Rao, Roeger, and n Veld 2009 consder a much rcher fscal polcy. I s assumed ha he governmen reacs o s own measure of he oupu gap, whch dffers from he wedge beween oupu under saggered and flexble prces usually consdered for moneary polcy analyss. Ths varable nfluences governmen spendng, publc nvesmen and he ncome ax rae. Pensons and unemploymen benef reac o he populaon srucure and aggregae wages. A lump-sum ax ensures he convergence of publc deb o a argeed level a seady sae by reacng o boh deb and defc. Modellng governmens behavour hrough fscal rules s a flexble approach, however s subjec o wo ssues. Frs, budge rules posulae a behavour raher han an objecve for he governmen and are herefore subjec o he Lucas crque as hey do no denfy srucural parameers for he governmen s behavour. Second, when desgnng a budge rule, one should be parcularly cauous as rules may no be compable wh he exsence and unqueness of he model s soluon f long-erm solvency of he governmen s no properly ensured Opmzng governmen: a smplfed approach o he Ramsey problem Raonale The nroducon of raonaly n DSGE models hsorcally and naurally lead o he defnon of an opmal governmen behavour as a normave benchmark, namely he Ramsey polcy. Indeed, n a nernally conssen DSGE approach, governmens seek o maxmze he welfare of her domesc households, and s herefore naural o defne he objecve of fscal auhores as he maxmzaon of he neremporal uly of households. In he presence of raonaly, hs maxmsaon s ndeed subjec o he publc budge consran bu also o he full se of model consrans. In parcular, when choosng he opmal level of publc expendures G, he governmen nernalzes s ndrec mpac on households consumpon and labour supply, and herefore households uly. One srengh of hs sandard Ramsey approach s s robusness o he Lucas crque as defnes a srucural behavour conssen wh he hypoheses of he model. In addon, as we nroduce governmen spendng n he uly funcon n MELEZE, hs Ramsey approach appears o be even more srongly jusfed. However, solvng a Ramsey problem s boh analycally and numercally complex when no nfeasble n large models, especally whn he busness cycle, as well as unrealsc as does no embody polcal choces observed n he real world ha may depar from opmaly. Ths reason underles he classcal choce of ad hoc budge rules n DSGE models. As an alernave o hese rules, we propose a new approach based on a smplfed verson of he Ramsey problem where he governmen sll maxmzes households uly subjec o s ransfers/ax 23

25 revenues budge consran, however no akng no accoun all oher consrans. Concreely, he governmen solves he Ramsey problem akng endogenous varables oher han publc expendures as gven such as CT τ and L T τ here5. As a resul, such a governmen focuses only on he uly derved by households hrough he drec acon of he governmen raher han hrough second urn effecs on consumpon and labour. As for budge rules, hs remans nconssen wh he DSGE approach of a full knowledge of economc mechansms by agens. However, hs may also be nerpreed as a dffculy for fscal auhores o exacly assess he mpac of s polces on he economy. Closer o he full Ramsey problem, we beleve hs approach o be more robus o he Lucas crque han radonal budge rules as parally mcro-founds he behavour of he governmen. However, boh approaches suffer from he same paradoxes when embedded n a general equlbrum model solved under raonal expecaons. Frs, n order o solve for such a model, expecaons of all agens are assumed formed hrough he enre model. I s hen paradoxcal o assume ha eher he governmen maxmzes s objecve under a subse of consrans or maxmzes an mplc objecve hrough a rule defned ousde he model. Second, boh modellng are only smple descrpons of fscal auhores and do no encompass real-world phenomena such as he wll of auhores o ge reeleced ha may nduce sub-opmal behavours. 6 Program and objecve of he governmen As he governmen now seeks o maxmse he neremporal flow of uly across all households τ, defnng weghs for each households e. he cumulave s gven by he aggregaon of hese nerem- dsrbuon funcon F, he governmen s objecve O G poral flows: 7 O G = τ { } E β T g UC T τ, CT VL T τ, L T WG T, G T dfτ T= } = E β T g WG T, GT {UC T τ, C T VL T τ, L T dfτ T= τ }{{} = E T= β gt WG T, G T Ω T 2.65 Under he reasonable assumpon ha he governmen canno dsngush households whn he same sub-group 8, denong ωg R, he wegh on Rcardan agens, and neglecng he nra-group dsperson n 5 Ths choce of modellng s equvalen o consder ha he governmen behaves under bounded raonaly. 6 See for nsance, he publc choce heory leraure. 7 Wh separable uly, he governmen can resrc o maxmze he neremporal flow of uly W sep GT, G T alone. UCT τ, C T and VL T τ, L T erms dsappear. 8 Tha s for nsance, he governmen canno dsngush and wegh dfferenly wo Rcardan households. However, can pu a dfferen wegh on Rcardan and non Rcardan agens. 24

26 labour and consumpon, he weghng facor Ω rewres: Ω T = n Nωg R, U + ωg R, n NU C R, T µ n N, C T V C NR, T µ n N, C T V L R, T µ n N, L T 2.66 L NR, T µ n N, L T All n all, n he mos general case, he governmen s program s as follows: max G β T TE T g WG T, GT Ω TC R,,PA T= wh WGT, G T G = s.. PA = T, CNR, T h G η σ c g PA R ψ g P Ȳ Tr + ν c, CPI C + I +ν D, PA + νw,, C T, LR, T, LNR, T, L T 2.67 W L + ν k, D + ν FD, FD P G Φ r k, CPIK where PA denoes he nomnal publc asses of counry a he end of perod, and Φ ransfers o households. are nomnal Noe ha he real neres rae for governmens dffers from ha of households because her consumpons are prced dfferenly, governmens buyng exclusvely domesc producon. Also he aomcy hypohess made for households relave o he asse marke does no hold for governmens and her deb prema dffer ψ versus ψ g. Besdes, he dscoun facor of he governmen needs no be equal o ha of households. On he one hand, he governmen, as an nsuon, s longer lved han s czens and for hs reason could pu a hgher wegh on fuure uly han households do. On he oher hand, as polcal enes amed a sasfyng voers and wnng elecons, governmens may also pu a hgher wegh on he near fuure. Solvng for he prevous program yelds he followng Euler equaon for governmen consumpon ha defnes he defaul behavour of fscal auhores n MELEZE: E β W G+, G Ω ++β ge + W 2 G+2, G + Ω R ψ g +2 g W G, G Ω + β ge W 2 G+, G Ω + PA PA P Ȳ Tr Π + P Ȳ Tr ψ g PA P Ȳ Tr =

27 2.5 Fnancal Inermedaon The saonary of an open economy model s no sraghforward. As explaned by Schm-Grohé and Urbe 2003, n a small open economy model, can be ensured by some modellng elemens, whch are usually no mcrofounded. The leraure on moneary unon model usually borrows he same soluons. In our model, we mcrofound one of Schm-Grohé and Urbe s proposals deb elasc spreads and nroduce a smplfed nernaonal fnancal marke. We assume ha here exss an nernaonal fnancal marke for asses prvae or publc. On he fnancal marke, nermedares can borrow money from he cenral bank of he moneary unon o fnance publc or prvae cred, and conversely borrow money from agens o depos a he cenral bank. Through fnancal nermedares, prvae resp. publc agens can borrow or lend money by payng a deb prema ψ resp. ψ g. The neres rae for he exchange beween he cenral bank and he fnancal nermedary s he neres rae se by he cenral bank. We assume ha fnancal nermedares work n perfecly compeve marke. They operae a war on prces spreads, up o a pon where hey make no prof. To ensure he orhogonaly of fnancal nermedares wh respec o he res of he moneary unon, we assume ha her unque cos s he refnancng cos vs-à-vs he cenral bank. Assumng so generaes no wage paymen or capal and nermedae consumpon purchases n hs branch of acvy hence no ransfer beween he real economy whn he moneary unon and fnancal operaors locaed ousde hs unon. Therefore developmens on he fnancal marke do no affec he res of he sysem. The opmsaon program of fnancal nermedares s no needed o close our model. One could for nsance assume ha fnancal acves are based srcly ou of he moneary unon, for nsance n England or n Swzerland. As a resul, f households or he governmen n counry are ne borrowers.e. FA 0 or PA 0, hs agen has o pay an neres premum on hs deb amounng o ψ f a, ψg pa. When he agen s ne lender, reurns are reduced by hs same spread capured by he nermedary. Ths mechansm s equvalen o fnancal nermedaon servces FISIM, see Fgure. In our model, here s no explc rsk or asymmery of nformaon so ha he fnancal nermedaon comes down o he spread beween he refnancng rae offered by he Cenral Bank and he marke rae se by he commercal bank whou rsk, erm or oher premum. Concreely, he aggregae cash needs fnancal nermedares borrow from he cenral bank are he oppose of all agens asse holdngs: CN = FA + FA 2 + PA + PA

28 Ineres rae Fnancal nermedary ψ g R - ψ Cenral banker PA 0 FA Asse Fgure : Deb elasc spreads are smlar o FISIM The producon of fnancal nermedaon servces assocaed s gven by he amoun of spread pad oday by agens on her sock of fnancal asses avalable a he end of prevous perod: FA FY = ψ PA =,2 P Ȳ FA Tr + ψ g =,2 P Ȳ PA 2.72 Tr As for good producng frms, we assume ha fnancal nermedares are owned by Rcardan households. However, ownershp s ransnaonal. We do no nroduce n he model any labour or capal for he fnancal nermedaon ndusry and smply assume ha all benefs are pad lump-sum o Rcardan households FD,2. Moreover, hese benefs are pad n proporon θ f a c.f. secon A.9. FD = θ f a +θ f a FY 2.73 FD 2 = +θ f a FY 2.74 FA FD + FD 2 = ψ PA =,2 P Ȳ FA Tr + ψ g =,2 P Ȳ PA 2.75 Tr In real erms, hs rewres: FA k PA k FY P Ȳ = ψ Tr k=,2 P Ȳk k FAk Tr P Ȳ + ψ g Tr k=,2 P Ȳk k PAk Tr P Ȳ 2.76 Tr 27

29 Denong f d FD P Ȳ Tr, we have: f d = θ f a +θ f a FY P Ȳ Tr = θ f a +θ f a ψ f a f a + ψg pa pa f d 2 = +θ f a FY P 2 Ȳ2 Tr + T θ [ ] ψ f a 2 f a2 + ψg pa 2 Tr pa2 Π Tr = +θ f a ψ f a 2 f a2 + ψg pa 2 pa2 + θ [ ] ψ f a T f a + ψg pa Tr pa Π 2 Tr Also, o mmc he nerbank overngh markes where banks clear her daly poson owards he cenral bank by lendng or borrowng accordng o he refnancng rae, we assume ha a each perod, he fnancal nermedares clear her poson owards he cenral bank: CN = FA + FA 2 + PA + PA 2 = Ths zero cash needs condon can also be read as publc deb beng held enrely by households whn he unon. In secon E we show ha assumng no aggregae deb n he moneary unon a seady sae mples hs zero cash needs consran a all daes. Ths consran ensures ha he model sasfes he Walras law,.e. ha once all markes are cleared, hree ou of four laws of moon of asses publc and prvae n boh counres mply he fourh one. The economc propery of beng Walrassan mples ha he seady sae s sable and he soluon o he lnearsed model s unque. 2.6 Moneary Auhory, Prces and Inflaon The cenral bank ses he nomnal neres rae R common o boh counres hrough a Taylor rule Taylor, 993, where reacs o boh curren nflaon of he consumpon prce ndex and o he oupu gap. R = R ρ R Π unon,vat Π rπ Ỹ r y ρ 2.80 where Π unon,vat and Ỹ are respecvely he VAT-ncluded average nflaon of consumpon n he moneary unon, and he oal oupu gap of he moneary unon see Appendx C.. R s he neres-rae 28

30 arge of he cenral bank and Π s exogenous nflaon arge. r π and r y are he Taylor rule weghs assgned o nflaon and he oupu gap, ρ s he neres-smoohng parameer. As here s no unon-wde maxmzng households embedded n he model, unon aggregae prce ndex and aggregae oupu gap canno be drecly nferred. A way o bypass hs ssues can be o assume ha for nsance, he aggregae prce ndex s consumpon weghed geomerc average of he naonal prce ndexes as n Eggersson, Ferrero, and Raffo 204. In our model, we choose o derve approxmaon of he naonal-accounng exac defnons of boh he aggregae prce ndex and he aggregae oupu gap for he moneary unon. The dervaons are presened n Appendx C. and allow o defne: Π unon,vat = Π + + νc,2 CPI 2 C 2 + ν C, CPI C c,,vat + Π + + νc, CPI C + ν C,2 CPI 2 C 2 c,2,vat 2.8 Ỹ unon = Y + T Ȳ + Y 2 θ + θ T Ȳ where Π unon,vat refers o he VAT-ncluded CPI nflaon. 2.7 Marke Clearng and relave prces Every perod, markes clear n quanes n boh counres: Y = C, + Cj, + I, + Ij, + G In values, hs becomes: PY = PC, + I, +Pj C j, + I j, +P G + PC j, + Ij, Pj C j, + I j,, 2.84 whch can also be wren under he well-known form: P Y = CPI C + I +P G + P X P j M, 2.85 where X s he expors sold o counry j a he prce of he domesc good. Lkewse, he mpors M are bough from counry j a prce P j. Because demand for foregn goods s addressed by households for consumpon and nvesmen, we have M = C j, + I j, = Xj. Moreover, he relave prces of consumpon RPC = CPI P are equal o: wh respec o producon ne of axes 29

31 RPC = We denoe he erms of rade α P 2 P RPC 2 = α P 2 P , 2.87 T = P2 P Calbraon The model beng derved, Appendx A deals he seady saes relaonshps beween varables. Takng no accoun all hese relaonshps mposes crucal resrcons on srucural parameers, endogenous raos o GDP, as well as on endogenous varables n level. We calbrae our quarerly model as o mach he suaon of France whn he Eurozone 9 over he perod , and as o say coheren wh he radonal DSGE leraure for srucural parameers. 3. Classfcaon of parameers and resoluon of he seady sae We dsngush hree ypes of parameers: srucural parameers, polcy parameers and endogenous parameers. Indeed, due o he large numbers of seady sae resrcons o accoun for, some parameers canno be calbraed freely and are acually endogenously deermned by he seady sae equaons. Srucural parameers are parameers echnology, preferences, ec. deemed purely exogenous, accounng for mechansms ousde of he model and no suscepble o change across smulaons. Polcy parameers corresponds o dscreely chosen parameers by fscal and moneary auhores such as he nflaon arge and he ax raes. Lasly, endogenous parameers are consraned by he full seady sae model and need o be solved for. In all, parameers are sored as follows: Srucural: n, N, µ, σc, σl, η, h c, h l, h g, α, ζ, g, ξ, θ, γ p, ξw, θw, γw, δ, β, β g, κ, α, ψ, ψ g Polcy: ν c,, ν w,, ν k,, ν d,, ν f d,, Φ, Π, r y, r Π Endogenous: R, pa, f a, gy, cy, y, T, θ, and oher endogenous seady sae values of endogenous varables. The number of frms p, P are mue hroughou he model, he scale of producon beng defned by he sze of populaons n, N and producves ζ. Followng hs choce, we explc a sequenal mehod for he resoluon of he seady sae ha mnmzes he number of smulaneous equaons sysems o solve. Ths resoluon s mplemened under R and he man gudng lnes are as follows: 9 counres: Belgum, Germany, Ireland, Greece, Span, Ialy, Luxembourg, Neherlands, Ausra, Porugal and Fnland. 30

32 . Frs, gven he exogeney of β, β g and Π, he Euler equaons of boh he households and he governmens Equaons STEADY. and STEADY.6 defne he deb o oupu raos pa and f a as funcons of he nomnal neres rae R. As such, he zero cash need condon Equaon STEADY.7 can be nerpreed as a marke clearng condon defnng he prce of bonds R dependng on he supply publc deb and demand prvae savngs for fnancal asses. 2. Second, we solae a frs sysem of equaons composed of naonal marke clearngs Equaon STEADY.9, he defnons of he rade balance hrough boh fnancal flows Equaon STEADY.4 and rade flows Equaon STEADY.3, he zero cash need condon Equaon STEADY.7 and he governmens budge consrans Equaon STEADY.2. Ths sysem allows o compue he nomnal neres rae R, he rade balance o producon rao b, governmen spendngs gy, consumpon and nvesmen o producon raos cy + y RPC, as well as he relave sze of nomnal value added across counres θ = θ/ T = Ȳ / TȲ A second sysem of smulaneous equaons corresponds o he deermnaon of he share of non Rcardan agens n consumpon s c and payroll s wl gven exogenous fracons of non Rcardan agens µ. Ths sysem consss of boh he non Rcardan households budge consrans Equaon STEADY.3 and he consumpon-lesure arbrages Equaon STEADY A hs pon, Equaon STEADY.6 allows o compue he level of labour supply n boh economes. The resoluon s closed by compung he level of producon n boh counres wh use of Equaon STEADY.7 and he erms of rade T = Ȳ /Ȳ 2 /θ. 5. Ohers endogenous raos are hen merely compued usng sraghforward combnaons of prevous varables. 3.2 Daa, calbraon and nverse nference Values for srucural parameers, when possble, are chosen from he sandard leraure on DSGE models, hese parameers beng esmaed eher by Bayesan mehods on macro daa or drecly on mcro daa. Based on a large leraure revew, 20 Table 2 presens he calbraon of srucural parameers as well as her sources. 20 Traband and Uhlg 20, Roeger, Varga, and n Veld 2008, Marn and Phlppon 204, Smes and Wouers 2002, Annccharco, D Do, and Felc 203, Vogel 202, Coenen e al. 202, Eggersson e al. 204, Rao e al. 2009, Everaer and Schule 2008, Bayoum, Laxon, and Pesen 2004, Hø j, Jmenez, Maher, Ncole, and Wse 2007, Kaplan, Volane, and Wedner 204, Bussere, Callegar, and Ghron 20, European Commsson s Ques III R&D model for France 3

33 DATA MELEZE EA 2 excl. FR FR EA 2 excl. FR FR Oupu n 2000 GDP Oupu n 2000 VA excl Fnancal Oupu per capa average growh rae, %,5 %,2 %,2 % Workng age populaon n ,3 25,7 0,3 25,7 Hours worked per week snce ,5 34,3 34,6 34,3 Gross Op. Surplus o VA 48 % 40 % 46 % 46 % Gross wages o VA 52 % 57 % 54 % 54 % Nomnal 3 monh Eurbor 3,8 % - 4,0 % 4,0 % Inflaon CPI 2,0 %,6 % 2,0 % 2,0 % Prvae consumpon o GDP rao 57 % 55 % 58 % 58 % Publc consumpon o GDP rao 9 % 23 % 22 % 23 % Invesmen o GDP rao 22 % 2 % 20 % 9 % GFCF o Capal rao - 7 % 9 % 9 % Trade balance 2 % % 0 % 0 % Impors from Euro area parner 3 % 2 % 3 % 2 % PPP GDP, snce 2002,00,07,00,07 PPP CPI, snce 2003,00,06,00,06 Publc deb -5 % -37 % -5 % -38 % Prvae asses ncludng frms S excl. S3 34 % 4 % 50 % 4 % Ne fnancal poson S2 7 % -3 % % -3 % Tax revenue n GDP 40 % 44 % 37 % 40 % Implc ax rae on consumpon 20 % 20 % 20 % 20 % Consumpon ax ncome n GDP % % 3 % 3 % Implc ax rae on labour 38 % 39 % 38 % 39 % Labour ax ncome n GDP 2 % 22 % 8 % 8 % Capal ax ncome n GDP 8 % 0 % 7 % 8 % Transfers n GDP 6 % 7 % 7 % 9 % Sources: Eurosa Naonal accouns, nflaons, Eurbor, Purchasng Power Pary PPP, Gross Fxed Capal Formaon GFCF, populaon, Labour Force Survey -ncl. Secondary job, Insee Capal Sock Accouns Daa are averaged from 995 o 2007 o exclude he crss. Dependng on avalably, samples may sar afer 995. EA 2 excl. FR sands for a 2-members Euro area excludng France and FR for France. n bllonen curren prces annualsed aged from 5 o 64 n mllons share of mpors from EU parners n prvae consumpon Table : Acual daa for France and he Euro Area and he correspondng endogenous values a seady sae wh our calbraon 32

34 Unon-wde Srucural parameers France Eurozone Technology parameer α Consensus, ANA Deprecaon rae δ Consensus Capal rgdy S Smes and Wouers 2005 Populaon sze N ANA TFP growh rae g ANA,Coenen e al. 202 Moneary polcy Inflaon Π Consensus, ECB Smoohng parameer ρ Barhélemy, Marx, and Possonner 2009 Wegh on nflaon r π -.6 Barhélemy e al Wegh on oupu gap r y Barhélemy e al Naonal specfc Populaon share n ANA Trade openess α ANA Subsuably beween goods θ 6 6 Ques III Subsuably beween workers θw 4 4 Smes and Wouers 2005, GEM, QuesIII TFP scale facor ζ ANA, GDP arge Wegh on labour dsuly κ ANA, Hours worked arge Households dscoun facor β ANA, Deb o GDP arge Governmen dscoun facor β g Own calbraon see Secon 3.2 Inverse rsk averson σc.3.3 Smes and Wouers 2005 Inverse Frsch elascy σl 2 2 Smes and Wouers 2005 Wegh on publc consumpon uly η see nfra. Consumpon habs h c Smes and Wouers 2005, NAWM Labour habs h l 0 0 Smes and Wouers 2005 Publc consumpon habs h g Smes and Wouers 2005 Share of non-rcardan agens µ QuesIII, Marn and Phlppon 204 Prce rgdy ξ Barhélemy e al Wage rgdy ξw Smes and Wouers 2005 Prce ndexaon γ p Smes and Wouers 2005 Wage ndexaon γw Smes and Wouers 2005 Households fnancal premum ψ slope Auhors Governmen fnancal premum ψ g slope Auhors Fscal polcy Consumpon ax rae ν c, 20.3% 9.5% Eurosa Labour ax rae ν w, 39.% 37.7% Eurosa Capal ax rae ν k, 2.0% 7.0% Eurosa Transfers o GDP rao Φ 9.4% 7.4% Eurosa ANA sands for Annual Naonal Accounng daa. For France, daa are from he Insee, whereas nernaonal comparson whn he Eurozone s conduced based on Eurosa daa. Consensus ndcaes a value close o a large number of sandard DSGE models. Table 2: Srucural parameers 33

35 In parcular, he specfcaon of households uly s a crucal deermnan of he behavour of he model. As hghlghed n Everaer and Schule 2006, he esmaon and denfcaon of hese wo parameers, and n parcular he Frsch elascy of labour supply, s very sensve o he mehodology mcro or macro and he sample consdered. Traband and Uhlg 20 calbrae her model o an nverse Frsch elascy of σ l = for France or he EU, n lne wh Kmball and Shapro 2008 for he US. They also consder an alernave based on Cooley and Presco 995 wh σ l = 0.33 for he US. These values are n lne wh he busness cycle leraure and close o values esmaed by Bayesan mehods, as for nsance n he dfferen versons of Smes and Wouers model wh σ l = 2.4 Smes and Wouers, 2003, σ l = 2.0 Smes and Wouers, 2005 boh for he EU and σ l =.9 Smes and Wouers, 2007 for he US. However, mcro and macro evdence s no easly reconcled and lead o very dfferen values of he Frsch elascy. Bayoum e al menon ha mcro sudes gve a range for σ l from 3 o as large as 20. In alernave scenaros for he GEM model, Bayoum e al. 2004; Everaer and Schule 2006 se σ l = 6 or 7 for Europe or France specfcally. We calbrae MELEZE n lne wh Smes and Wouers 2005 n order o work wh a medum range value of he Frsch elascy, ha s σ l = 2.0. For he nverse of he neremporal consumpon elascy σ c, he debae s less ferce and values range from 0.5 n Bayoum e al for EU counres o 2 as n Traband and Uhlg 20 EU and France. The dfferen versons of Smes and Wouers gve σ c =.3 n Smes and Wouers 2003, σ c =.3 n Smes and Wouers 2005 boh for he EU and σ c =.4 n Smes and Wouers 2007 for he US. We choose o mach Smes and Wouers 2005 calbraon wh σc =.3. Anoher weakly denfed parameer, ofen esmaed usng Bayesan esmaon mehods or smply calbraed wh "exper" nsghs, s he share of non-rcardan households µ. In GEM, hs share s esmaed o be 35% for France and 45% n he Euro area, whereas sands o 40% for boh n QUEST III. However, mcro-sudes hghlgh ha hese esmaed shares mgh be over-evaluaed as only a few agens are srcly banned from fnancal markes. Indeed, a large number of agens, desgnaed as wealhy hand-o-mouh, do possess a large llqud wealh, such as housng, so ha her shor-erm consumpon s hghly correlaed o her curren ncome. However, n he long-erm, hs concluson mgh dffer as asses can be raded. Kaplan e al. 204 compue values for he share of wealhy hando-mouh agens around 20% for France. Close o Kaplan e al. 204, Marn and Phlppon 204 focus on he fracon of households wh lqud asses represenng less han 2 monhs of oal gross ncome and calbrae her model o a 46.6% share of non-rcardan agens n France. We choose o calbrae our model o esmaed values n QUEST III. 34

36 Las, he calbraon of he wegh of publc consumpon n he uly s based on McGraan e al. 997, Bouakez and Rebe 2007 and Coenen e al Esmang a CES publc-prvae consumpon aggregaon, hey denfy a share of prvae consumpon of 0.8 η. In order o smplfy he model, we resor o a Cobb-Douglas aggregaon and herefore assume an elascy of subsuon of one. However, hs leraure revew s no enough o oban a realsc calbraon so ha we proceed o an nverse nference. Indeed, n order o properly mach he argeed observed levels or raos n our model, a specfc se of parameers needs o be opmzed upon and canno be se freely. For hese parameers, we verfy ex-pos ha hey reman n he range denfed n he leraure. Table compares for man srucural levels and raos her levels observed n he daa wh hose generaed by he model wh our calbraon. Targes based on observables are compued as averages over he perod o purposely exclude he crss perod. Frs, he weghs of lesure n he uly κ and he level of TFP n each counry ζ allow o replcae value added levels n each counry Ȳ, he erms of rade T and hours worked L. Second, he Cobb-Douglas parameer α and he marke power of frms θ mply he dsrbuon of oupu beween he remuneraon of capal and dvdends Gross Operang Surplus and wages. There s however an mprecson n he daa on GOS whch ncludes mxed ncome,.e. ncome of ndependen workers. Consderng hs and he wde range of mark-up raes n he leraure we have no nroduced dfferences across counres along hs lne. Inflaon s calbraed hrough he cenral banker s arge. The nomnal neres rae s endogenous and clears he demand and supply of fnancal asses unon-wde. Fnal demands o GDP rao are well replcaed by he model. These raos are endogenous: publc consumpon depends on he fscal polcy of boh governmens and balances her neremporal budge consran; nvesmen depends on oher parameers hrough equaon STEADY.5 and s acually lle sensve o he deprecaon rae. Consumpon clears he marke once he rade balance s known. The rade balance s relaed o he ne fnancal asse poson hrough aggregae naonal budge consrans. I can no be szeable whou much greaer mbalances n erms of asse holdngs. However, prces can dffer across counres because of households preferences for domesc goods. These preferences are se such ha we replcae he rade beween France and s parners n he Euro Area and prces appear hgher n France han for s parners n accordance wh purchasng power pares daa. 35

37 Dscoun facors β and β g are se o mach observed deb-asse o GDP raos n boh counres see equaons STEADY.. Frs noe ha s no necessary for hese facors o be lower han one, hs condon apples o her ranformaon β + g Kocherlakoa, 990 and s verfed by our calbraon. Also, n a closed moneary unon, s no possble o replcae hese raos exacly as he Euro area s ndebed vs-à-vs he res of he world. We choose o mpue he dscrepancy o non French Euro Area resdens who hus hold more asses n he model han n he daa. In he end, he ne fnancal asse posons of boh counres mrror each oher n he model and are raher small. Taxes are se o he mplc ax raes on consumpon and labour compued by Eurosa. Tax revenues from consumpon are hgher han n he daa, bu our models ax base does no dscrmnae beween consumpon and nvesmen. Tax revenues from labour are lower han n he daa, bu our model does no rea he case of ndependen workers whch may explan par of he dscrepancy. As for capal, we only ax capal ncomes n he model reurn on capal, dvdends and fnancal dvdends as opposed o capal sock. The ax raes on hese hree bases are supposed dencal and se o approach capal ax ncome whou prejudce on he nvesmen o GDP rao. These ax raes mply a ax revenue o GDP rao close bu lower han n he daa, however, mssng ems n our smplfed budge for he general governmen may accoun for hs dscrepancy. 4 Model dynamcs We analyse he shor erm properes of our model hrough he compuaon of IRFs for shocks occurrng n France. We frs plo he IRFs o sandard shocks producvy, preference, moneary polcy, hen o ransory fscal shocks VAT and governmen spendng. A dealed analyss of fscal shocks n MELEZE ncludng permanen ones, s gven n Campagne and Possonner 206a. 4. IRFs o sandard shocks Producvy shock In Fgure 2, producvy n France s ncreased by one percen wh auocorrelaon se o 0.9. Ths producvy shock mples an ncrease n oupu wh margnal posve spllovers o he res of he unon. Prces drop n France bu no n he res of he Euro area, so ha he cenral banker does no reac much o hs dosyncrac shock and he real neres rae n France ncreases. Relave o fnancal savngs, capal reurns also benef from he hgher producvy. Hence nvesmen ncreases o he dermen of fnancal savngs. Prvae asses drop and symmercally publc deb as well, n France bu no n he res of he Euro Area. The drop n domesc prces s favourable o he erms of rade. However, he rade balance margnally deprecaes as domesc demand s spurred whle 36

38 y- axs n p.p. devaon from seady sae Fgure 2: IRFs o a one percen producvy shock auocorrelaed 37

39 demand addressed from he res of he Euro Area s relavely unchanged. Ths s n par due o he lower rade openness of he Eurozone wh respec o France compared o he openness of France wh respec of he res of he Eurozone. In comparson wh a closed economy model Smes and Wouers, 2003, 2005, labour only emporary decreases he frs year as becomes more producve. Smulaons wh a large wegh of counry one n he moneary unon show ha dfferences are manly due o he reacon of he cenral banker who only slghly lowers s rae n comparson wh a unon wde producvy shock. Preference shock In Fgure 3, he dscoun facor n France s ncreased by one percen.e. more paen households or a negave demand shock wh auocorrelaon se o 0.9. As a consequence, Rcardan households pospone consumpon and ncrease her fnancal and physcal savngs. Prces n France drop o lm he fall n fnal demand, so much so ha he res of he Euro Area follows hough wh delay and o a lesser exend, and he cenral banker ses an accommodave moneary polcy. The ncrease n nvesmen more han compensaes for he drop n consumpon sarng from he second year afer he shock. The drop n domesc demand relavely o he res of he Euro Area s benefcal o he rade balance, an effec magnfed by he ncrease n he erms of rade. Moneary polcy shock In Fgure 4, he moneary polcy rae s ncreased by 00 bass pons. Ths large shock o moneary polcy symmercally mpacs boh France and he res of he Euro Area. The only dfference sems from he fnancal asse holdngs n boh regons and her consequences on he rade balance and he erms of rade. Such a large ghenng of moneary polcy markedly deprecaes oupu unon-wde. Prces plumme and gradually decrease boh n France and n he res of he Euro Area, so much so ha he endogenous behavour of he cenral banker leads o a slgh decrease n s neres rae, parally offseng s nal shock. Oupu reacs srongly negavely as he forwardlookng governmen cus spendngs reacng o he hgher fnancng cos. A less adverse reacon s observed when mplemenng a budge rule nsead, as can be seen on Fgure 9. These resuls are n lne wh exbook smulaons Galí, 2008, Chaper 6. Publc spendng Followng a percenage pon auocorrelaed ncrease n publc spendng Fgure 5, oupu ncreases n France. Wh our Euler-ype modellng of governmen consumpon, hs ncrease n publc spendng s fnanced hrough publc deb, mrrored by prvae asses. Prces margnally adjus upwards o hs demand shock and he cenral banker s reacon o hs dosyncrac shock s mnmal. The demand shock s, by assumpon, only addressed o domesc producon and parally crowds ou nvesmen. As a consequence, he demand addressed o he res of he Euro Area ncreases bu due o prce developmens, he compeveness of France deeroraes and he rade balance emporarly and 38

40 y- axs n p.p. devaon from seady sae Fgure 3: IRFs o a one percen preference shock auocorrelaed 39

41 y- axs n p.p. devaon from seady sae Fgure 4: IRFs o a 00 bass pons moneary polcy shock 40

42 y- axs n p.p. devaon from seady sae Fgure 5: IRFs o a one percen governmen spendng shock auocorrelaed 4