Documents de travail. «How can the labor market accounts for the effectiveness of fiscal policy over the business cycle?» Auteurs

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1 Documen de ravail «How can he labor marke accoun for he effecivene of fical policy over he buine cycle?» Aueur Thierry Bei, Thoma Couder Documen de Travail n Juin 2015 Faculé de cience économique e de geion Pôle européen de geion e d'économie (PEGE) 61 avenue de la Forê Noire F Srabourg Cedex Secréaria du BETA Géraldine Del Fabbro Tél. : (33) Fax : (33)

2 How can he labor marke accoun for he effecivene of fical policy over he buine cycle? Thierry BETTI, Thoma COUDERT June 9, 2015 Abrac We develop a new-keyneian model wih a wo-ecor earch and maching labor marke framework. We inveigae he fir and econd order effec of fical policy on labor marke and on oupu. The model include four fical inrumen: a labor income ax, a ocial proecion ax paid by firm, public wage and public vacancie. Fir-order imulaion of he model indicae ha whaever inrumen i ued, fical expanion ignificanly increae oal employmen and reduce unemploymen. We explici he differen ranmiion channel a work. The main conribuion i o ue a econd-order approximaion of he model o inveigae he effec of fical hock for wo ae of he economy: a low unemploymen ae (6%) and a high unemploymen ae (12%). For he four fical inrumen, repone of employmen i greaer when he eady-ae unemploymen rae i high. We alo emphaize a new channel for explaining a larger oupu fical muliplier in period of economic downurn: he wage channel ha play a crucial role for explaining he non-linear effec of fical policy. JEL claificaion: E62, J38. Keyword: Labor Marke Search, Wage Bargaining, Public Wage, Buine Cycle, Fical Policy, Second Order. BETA, Univeriy of Srabourg (France), bei@unira.fr. LaRGE, Univeriy of Srabourg (France),.couder@unira.fr 1

3 1 Inroducion Recen lieraure indicae ha he poiion over he buine cycle grealy influence he ize of he fical muliplier. Empirical udie how ha he oupu fical muliplier i in period of economic downurn 1. However, he heoreical mechanim behind hi reul ill need o be evidenced. If ome inuiive mechanim could uppor hi reul 2, explanaion baed on heoreical framework are ill rare. The aim of our paper i o conribue o hi heoreical lieraure. More preciely, our analyi focue on he repone of he labor marke o fical policy auming differen value of he eady-ae unemploymen rae, hu o differen poiion of he economy over he buine cycle. Epecially, we aemp o how ha he labor marke dynamic, and epecially he repone of real wage, can explain differen oupu fical muliplier according o he unemploymen rae a he eady ae. Sim and Wolff (2013) and Michailla (2014) have aemped o inveigae he non-linear effec of fical policy heoreically. Sim and Wolff (2013) inveigae in a andard DSGE model he effec of fical policy on privae conumpion for differen poiion of he economy over he buine cycle. Since a fir verion of heir model doe no include invemen, he ize of he muliplier (around 1) only depend on he repone of privae conumpion. Afer he eimaion of he model a he fir-order, auhor compue he oupu fical muliplier for each poiion over he buine cycle. Their main finding i ha he marginal uiliy of conumpion i greaer during economic downurn ( of conumpion i lower), hu he crowding-ou effec of public pending on privae conumpion i reduced. Thi explanaion of a greaer fical muliplier in he rough of he economic cycle i an inereing fir ep. However, oher apec of an economy in a period of economic downurn mu be aken ino accoun, includind he preence of non-ricardian houehold 3 or he poenial differen dynamic of he labor marke. Michailla (2014) focue on he repone of he labor marke following a rie in public employmen in a DSGE model wih a earch and maching labor marke. The main 1 See Auerbach and Gorodnichenko (2012) and Creel e al. (2011) among oher 2 We could expec a higher price ickine during economic downurn ha produce greaer real effec of pending expanion or a higher hare of non-ricardian houehold ha diminih he crowding ou effec of public conumpion on privae conumpion. 3 See for inance Coenen and Sraub (2005) for dicuion abou he impac of he preence of non-ricardian houehold on fical muliplier. 1

4 reul i ha when he unemploymen rae i high (8% in he paper), a rie in public employmen ha a greaer effec on oal employmen han in he cae of a low unemploymen rae (4%). By conrucion he model produce a crowding-ou effec of public employmen on privae employmen, a ha been hown in empirical udie and noably in Ramey (2011). In Michailla (2014), he crowding-ou effec i baed on a lower pool of unemployed earching for a job in he privae ecor following he rie in public vacancie. When he pool of job eeker i high a he eady ae, hi crowding ou effec i hen lower. However, he auhor doe no conider he role of he wage channel ince he real wage law of moion i aumed a exogenou. Our work follow Michailla (2014) by focuing on he effec of fical policy on he labor marke according o he eady-ae value of he unemploymen rae. In comparion o hi paper, we inroduce a Nah efficien bargaining proce ha deermine he law of moion of real wage. Thi i of fir imporance ince our main reul i baed on he repone of he real wage. Alo, Michailla (2014) inroduce only non-ricardian houehold while we inroduce boh opimizing and hand-o-mouh houehold. Moreover, we how ha he inroducion of Ricardian houehold i neceary o produce higher oupu fical muliplier. In hi paper we conruc a new-keyneian model wih a earch and maching framework for he labor marke. Worker can find a job in boh he privae and he public ecor. Our modelling of he dual labor marke i cloe o oher paper like Afono and Gome (2014) and Brückner and Pappa (2012). Four fical inrumen are inroduced: a labor income ax, a ocial proecion ax paid by firm, he public wage and finally he public vacancie. The fir par of he paper i dedicaed o analyzing he effec of hee four fical inrumen on he labor marke. To achieve hi inveigaion, we ue a fir-order approximaion of he model. A main reul i ha he four fical expanion generae a drop in unemploymen and a drop in privae real wage, expec for he cu in ocial proecion ax. We dienangle he differen ranmiion channel pecific o each fical inrumen. The main conribuion of he paper i o olve he model a he econdorder in order o analyze he non-linear effec of fical policy according o wo differen eady-ae level of unemploymen, in he piri of Michailla (2014). A fir reul i ha he four fical inrumen rigger a larger rie 2

5 in employmen in he cae of a high eady-ae unemploymen rae (12% in our paper, in comparion wih a lower unemploymen rae of 6%). The explanaion for hi reul i cloe o he one highlighed in Michailla (2014). A larger pool of job eeker a he eady ae generae more job creaion following he fical hock. Thi higher rie in privae employmen i he aring poin for explaining a larger oupu fical muliplier during economic downurn. Thi ronger effec on employmen when unemploymen i high engender a larger degradaion of marginal produciviy of labor and hen a larger degradaion of real wage. The greaer drop in real wage implie a lower conumpion for he non-ricardian. However i alo implie a lower marginal co, inflaion and a lower rie in inere rae. In hi cae, conumpion of Ricardian houehold i le reduced han in he cae of a low unemploymen rae a he eady ae. The oal effec on aggregae demand depend on he relaive rengh of hee wo oppoie effec on privae conumpion. Under our andard calibraion, he higher conumpion of Ricardian houehold prevail over he lower conumpion of non-ricardian houehold. I finally induce a larger oupu fical muliplier in he cae of a high eady-ae unemploymen rae. Thu, hi paper aemp o offer a new heoriical explanaion for variaion of he oupu fical muliplier over he buine cycle. Sim and Wolff (2013) argue for a larger oupu fical muliplier during economic downurn due o a larger marginal uiliy of conumpion. I i imporan o noe ha our model doe no include hi ranmiion channel. On he conrary, he definiion of eady-ae value for boh ype of conumpion implie a lower marginal uiliy of conumpion for he Ricardian houehold during economic downurn. The wage channel we highligh in hi paper i no in conradicion wih he explanaion found in Sim and Wolff (2013). However, he coexience of hee wo effec could parly explain he izeable difference found in he lieraure abou he ize of he oupu fical muliplier according o he poiion of he economy over he buine cycle. The re of he paper i organized a follow: ecion 2 preen he model, ecion 3 preen he calibraion, he eady-ae calculaion and he econd-order oluion of he model. Secion 4 highligh he main reul of he paper and ecion 5 conclude. 3

6 2 Model The model ued in hi paper feaure nominal rigidiy on price and maching fricion on he labor marke. Since he focu i on he effec of he public ecor on he economy, wo ecor coexi on he labor marke, namely a public and a privae ecor. We make explici he choice o work in he privae ecor or in he public ecor. Alo, we inroduce an efficien Nah wage bargaining in which he public wage direcly affec he deerminaion of he privae wage and hu employmen in boh ecor. The model feaure alo a rich fical ide, wih everal ype of expendiure/axe in order o inveigae he econd-order effec of fical policy on he labor marke according o he fical ool conidered. On he expendiure ide, we conider he effec of a rie of he public wage and of he public vacancie. On he axe ide, we inveigae he effec of a labor revenue ax cu and a ocial proecion ax cu. 2.1 Definiion and he maching proce Le u fir define he non-employed pool 1 (1 ρ)e o 1 (1 ρ)e o uch a: = U + ρe o, (2.1) where E o denoe he employed worker and U he pool of unemployed worker. The derucion rae ρ i aumed o be exogenou. Moreover, he pool of job eeker S i expreed a S = U + ρe o. (2.2) Alo, in he piri of Trigari (2006), auming ha a new job become producive only in he following period and auming ha a mach can be inananeouly broken, employmen in a paricular ecor E i can be expreed a: E i = (1 ρ)e i 1 + p i 1(1 ρ)s 1, (2.3) wih i = p, g ha denoe boh he public and privae ecor. Thee definiion are common o boh ecor. The job-finding probabiliy in he ecor 4

7 i, p i, i defined laer on. Wih hee definiion, i i imporan o noe ha oal employmen i a predeermined variable. Finally, he dynamic of job eeker i given by S = (1 p p 1 p g 1)S 1 + ρ(p p 1 + p g 1)S 1 + ρ(e p 1 + E g 1). (2.4) According o equaion (2.4), he number of job eeker in he curren period i equal o he number of job eeker who did no find a job eiher in he privae ecor or in he public ecor in he previou period plu he number of job eeker i increaed by he number of job which are deroyed in he previou period. Finally, we aume ha here i a kind of rial period: a worker can mach a firm in he beginning of he period bu he relaionhip can be broken a he end of he period exogenouly. Le u now define he maching proce occurring on a pecific labor marke, uch a: M i = κ i e(s ) ϕi (V i ) (1 ϕi), (2.5) where κ i e denoe he maching echnology in a paricular ecor while ϕi denoe he elaiciy of employmen for a upplemenary unemployed worker. V i i he number of vacancie in he ecor i. We can herefore e he following uual definiion: p i = M i S, (2.6) and q i = M i V i (2.7) wih p i he job finding probabiliy in he ecor i a previouly inroduced; q i i he probabiliy for a firm o fill he poed vacancy. The labor marke ighne (LMT hereafer) can be defined a θ i = V i S = pi. (2.8) q i 5

8 2.2 Houehold deciion In hi model wo differen ype of agen are inroduced. We aume a hare µ of non-ricardian (hand-o-mouh) houehold and a hare (1 µ) of Ricardian houehold. The difference beween boh ype of houehold i heir abiliy o paricipae in financial marke. Non-Ricardian can neiher loan nor ave o ha hey imply conume heir dipoable income in each period. On he conrary, Ricardian houehold can hold a rikle ae ha allow hem o opimize heir conumpion iner-emporally. Alo, Ricardian houehold inve in phyical capial ha hey hen loan o firm. Boh ype of houehold formulae imilar labor marke deciion Ricardian houehold A repreenaive Ricardian houehold maximize i lifeime uiliy and i uiliy funcion i defined a: u(c o, C o 1, G, e i ) = (Co HC o 1) 1 σc 1 1 σ c + M o (e j ) (2.9) where C o denoe conumpion of Ricardian houehold. Addiively eparable preference of conumpion and labor are inroduced in an uual manner wih σ c he iner-emporal elaiciy of ubiuion for conumpion. The conumpion deciion i ubjec o a degree H of habi formaion. The funcion M o (e j ) repreen he amoun of leiure in erm of uiliy wih regard o he preence of he houehold member on he labor marke. Following Ravn (2005, 2008), e j wih j = n, u, l denoing he level of leiure according o he au of he houehold on he labor marke i.e. e n for an employed worker, e u for an unemployed worker and e l for an inacive houehold uch a: e n = 1 h, (2.10) e u = 1, (2.11) e l = 1, (2.12) where h denoe hour worked ha we aume a exogenou and a fixed co in he paricipae o labor marke. 6

9 We conider he cae of a repreenaive worker in he piri of Merz (1995), o ha he funcion M o (e i ) conain he differen poible aue of a worker on he labor marke, uch a: M o (e i ) = [(Eop + E og )(1 h ) 1 ζ + S o (1 ) 1 ζ + (1 (E op 1 ζ + E og ) S o )] where 1/ζ define he Frich elaiciy of labor upply and S o i he hare of Ricardian eeking employmen in period. E op denoe employmen of Ricardian houehold in he privae ecor while E og denoe employmen of Ricardian houehold in he public ecor. The opimizaion problem for he repreenaive Ricardian houehold i expreed a: ubjec o max E C o,ko,b,eo,so,io = β u(c o +, C o 1+, G +, e + ). (2.14) (1 + τ c )C o + B + I o R P 1K k 1 + R 1B 1 + b(s o ) P +(1 τ w )[W g he og + W p he op ] (2.15) K o = (1 δ k )K 1 o + [1 A(I o /I 1)]I o o (2.16) E op E og = (1 ρ)e op 1 + p p 1(1 ρ)s 1 o (2.17) = (1 ρ)e og 1 + p g 1(1 ρ)s 1 o (2.18) S o = (1 p p 1 p g 1)S o 1 + ρ(p p 1 + p g 1)S o 1 + ρ(e op 1 + E og 1) (2.19) ha can be reduced o he following Bellman equaion: { (C Ω o (K o, E o, B, I o o ) = max HC 1) o 1 σc + ζ gg 1 σc 1 C o,ko,so,no,b,i 1 σ c 1 σ c + [(Eop + E og )(1 h ) 1 ζ + S o (1 ) 1 ζ + (1 (E op + E og } ) S o )] 1 ζ +βω o +1(K+1, o E+1, o B, I o ), (2.20) (2.13) 7

10 ubjec o he previou e of conrain wih β he dicoun facor. Equaion (2.15) i he budge conrain for he houehold. The opimizing houehold ha acce o perfec financial marke and can hu hold a rikle ae B. Furhermore, he houehold inve I o in phyical capial K o and loan i o he firm a a rae R k. δ k define he depreciaion rae of capial, R he nominal inere rae equal o 1 a he eady ae and b he unemploymen benefi. W g and W p are he real wage repecively in he public β and he privae ecor. P define he conumer price index (CPI hereafer). We noe he appearance of wo axe, a conan VAT τ C and a labor revenue ax τ w. Equaion (2.16) repreen he law of moion of capial accumulaion. We inroduce an adjumen co o invemen change wih A(I o /I 1) o = κ 2 (Io /I 1 o 1) 2 imilarly o Chriiano e al. (2005) or Sme and Wouer (2007) among oher wih κ a conan co aociaed o invemen deciion. Fir order condiion wih repec o repecively C o, B, I o, K o, E op and S o yield: E og λ rio = [Co HC 1] o σc βhe {[C+1 o HC o ] σc } (2.21) 1 + τ [ ] c λ rio +1 = r βe, (2.22) λ rio π +1 wih π +1 = p +1 /p defining he CPI inflaion rae. 1 = Q [1 A(I /I 1 )] (2.23) [ ] λ rio +1 Q = βe [(1 δ k )Q +1 + R k ] (2.24) λ rio, λ Eop = (1 τ w )λ rio W p 1 (1 h )1 ζ h 1 ζ +βe [(1 ρ)(λ Eop +1 λ So +1) + λ So +1] (2.25) λ Eog = (1 τ w )λ rio W g 1 (1 h )1 ζ h 1 ζ +βe [(1 ρ)(λ Eog +1 λ So +1) + λ So +1] (2.26) 8

11 λ So = bλ rio 1 (1 )1 ζ 1 ζ +(1 p p p g )βe [λ So +1] + ρ(p p + p g )βe [λ So +1] +(1 ρ)βe [p p λ Eop +1 + p g λ Eog +1] (2.27) wih λ rio he marginal uiliy of conumpion for Ricardian, λ Eop uiliy of working in he privae ecor, λ Eop in he public ecor and λ So he marginal he marginal uiliy of working he marginal uiliy o be currenly a job eeker. Equaion (2.25) define he value of a job for a Ricardian houehold in he privae ecor while equaion (2.26) deermine he value of a job in he public ecor. Alo, equaion (2.27) deermine he deciion for a Ricardian worker o paricipae in he labor marke Hand-o-mouh conumer Non-Ricardian houehold do no maximize conumpion iner-emporally and hen imply conume heir dipoable income in each period. For a repreenaive non-ricardian houehold, ne VAT conumpion i given by: (1 + τ c )C r = (1 τ w )[W g he g + W p he p ] + bs r (2.28) wih C r he conumpion level for non-ricardian. The choice made by hi cla of houehold concerning he labor marke i imilar o he Ricardian cae. Similarly o Ricardian houehold, he uiliy funcion for hi cla of houehold i expreed a: wih u(c r, C 1, r G, e i ) = (Cr HC 1) r 1 σc 1 + ζ gg 1 σc + M r (e j ) (2.29) 1 σ c 1 σ c M r (e i ) = [(Erp + E rg )(1 h ) 1 ζ + S r (1 ) 1 ζ + (1 (E op 1 ζ 9 + E rg ) S r )] (2.30)

12 The correponding Bellmann equaion and conrain for hi opimizaion program i herefore: { (C Ω r r = max HC 1 ) 1 σc S r,er,eg 1 σ c + [(Erp + E r,g )(1 h ) 1 ζ + S r (1 ) 1 ζ + (1 (E rp + E rg } ) S r ))] 1 ζ +βω r +1 (2.31).. (1 + τ c )C r (1 τ w )[W g he rg + W p he rp = (1 ρ)e rp E rp E rg ] + bs r (2.32) 1 + p p 1(1 ρ)s 1 r (2.33) = (1 ρ)e rg 1 + p g 1(1 ρ)s 1 r (2.34) S r = (1 p p 1 p g 1)S r 1 + ρ(p p 1 + p g 1)S r 1 + ρ(e rp 1 + E rg 1) (2.35) Fir order condiion wih rappor o E rp, E rg and S yield: λ Erp = (1 τ w )λ rir W p 1 (1 h )1 ζ h 1 ζ +βe [(1 ρ)(λ Erp +1 λ Sr +1) + λ Sr +1] (2.36) λ Erg = (1 τ w )λ rir W g 1 (1 h )1 ζ h 1 ζ +βe [(1 ρ)(λ Erg +1 λ Sr +1) + λ Sr +1] (2.37) λ Sr = bλ rir 1 (1 )1 ζ 1 ζ +(1 p p p g )βe [λ Sr +1] + ρ(p p + p g )βe [λ Sr +1] +(1 ρ)βe [p p λ Erp +1 + p g λ Erg +1] (2.38) 10

13 wih λ Erp he marginal uiliy of working in he privae ecor for a non- Ricardian houehold, λ Erg imilarly in he public ecor and λ Sr he marginal uiliy for a non-ricardian o eek employmen on he labor marke. Equaion (2.36) define he value of a job in he privae ecor for a non-ricardian houehold while (2.37) define he value of a job in he public ecor. Alo, equaion (2.38) relae o he deciion of a non-ricardian worker o eek a job. Even if non-ricardian houehold do no maximize conumpion ineremporally, maximizaion of (2.31) wih rappor o C r allow o obain heir marginal uiliy of conumpion uch a: 2.3 Firm λ rir = (Cr HC r 1) σc βe [H(C r +1 HC r ) σc ] 1 + τ c (2.39) For he purpoe of he model, we need o inroduce hree kind of firm a in Trigari (2006). Fir, ome firm we refer a "producer" produce good wih labor and privae capial in a compeiive environmen. The producer hen ell heir aggregae good o "inermediae firm", ranforming he aggregae good on a coninuum of differeniaed good in a monopoliic compeiion environmen. The inermediae firm are he price-eer and e heir opimal price ubjec o nominal rigidiy a in Calvo (1983). Finally, a coninuum of "final good firm" in a compeiive environmen purchae he differeniaed inermediae good and package hem o ell i o conumer. Thi diociaion beween producer and inermediae firm i neceary becaue inroducing he price-eing a he producer level would grealy complicae he deciion of hee firm on he labor marke. However, hi implifying aumpion ha no imporan conequence eiher on he price dynamic or on he labor marke dynamic 4. 4 For more deail, Chrioffel e al. (2009a) made a urvey on he implicaion of hi aumpion. In he piri of Kueer (2010), Sveen and Weinke (2007) and Thoma (2011), Chrioffel e al. (2009b) demonrae ha he diociaion aumpion no only ha no puriou conequence bu alo help he andard Keyneian model o mach ylized fac in erm of inflaion reacion o moneary hock. 11

14 2.3.1 The producer Since he producer evolve in a compeiive environmen, hey all behave imilarly and we can conider he following opimizaion program wih a repreenaive firm, uch a:.. where τ p max K,E p,v E 0 =0 β,+1 {Y R k K (1 + τ p )W p E p h κ v V } (2.40) Y = ɛ A (K 1) g αg [ K ] α [E p h] 1 α (2.41) E p = (1 ρ)e p 1 + q 1V p p 1 (2.42) in equaion (2.40) denoe a ax on labor paid by he firm for +1 λ rio ecuriy proecion purpoe. The dicoun facor i β,+1 = β λrio. Moreover, he producer ake he probabiliy of filling a vacancy q p a given. V denoe he vacancie poed by he producer and κ v he uniary co of vacancy poing. We aume ha he accumulaed capial become effecive for producion afer one quarer K = K 1. The Toal-Facor Produciviy (TFP hereafer) ɛ A i driven by he following AR(1) proce ( ) ( ) ɛ A ɛ A ρɛ = 1 exp(ε a ), ɛ A ɛ A where ɛ A and for he TFP a he eady-ae, exp(ε a ) i a iid exogenou diurbance and ρ ɛ he duraion of he hock. Equaion (2.41) repreen he producion funcion of he repreenaive producer. Equaion (2.42) repreen he dynamic of employmen in he producer poin of view. The problem (2.40) can be repreened a a Bellman equaion uch a: +1 λ rio V (Ω ) = max {Y R k,e p k k (1 + τ p )W p E p h κ v V + β λrio V (Ω +1 )},V (2.43) 12

15 Under he free enry condiion, he fir order condiion wih repec o vacancy poing and employmen yield: κ v q p +1 λ rio = β,+1 λ rio λ E f = (1 α) Y E p λ E f +1 (2.44) (1 + τ p )W p +1 λ rio h + (1 ρ)β,+1 λ rio λ E f +1 (2.45) Equaion (2.44) define he value of a poed vacancy and (2.45) he value of a job for a producer. Co minimizaion ubjec o equaion (2.41) implie he following facor demand condiion, R k = αy K mc (2.46) x = (1 α)mc Y E p h p (1 + τ )W p h, (2.47) where mc repreen he level of producer marginal co. Equaion (2.46) characerize he demand of capial by he producer and equaion (2.47) define he marginal co of labor x Inermediae firm, final good firm and Calvo price-eing There i a coninuum j of inermediae firm ha purchae he homogeneou good from he producer a heir marginal co ince he producer are in a compeiive environmen. The inermediae firm hen ranform he homogeneou good on a coninuum j of differeniaed good and ell hem a he final good firm. Final good firm produce a package of he inermediae differeniaed good according o: Y = 1 0 Y j ε 1 ε ε ε 1 dj, (2.48) 13

16 where ε i he elaiciy of ubiuion acro inermediae good. Demand for each inermediae good i of he form: ( ) ε Pj Y j = Y, (2.49) P wih he following definiion for he CPI P : [ 1 ] 1 P = P 1 ε 1 ε j dj, (2.50) and wih P j he price of good j in he period. 0 Following Calvo (1983), inermediae firm are allowed o re-opimize heir price only wih a probabiliy θ p [0, 1) in each period. Thi probabiliy i aumed o be independen from he re-opimizaion deciion aken in he la period. Inermediae firm eek o maximize heir lifeime profi according o heir own price level uch a: [ ] E (βθ p ) λrio + Pj, mc λ rio + Y j,+, (2.51) P + k=0 ubjec o he demand funcion expreed in he equaion (2.49). The fir order condiion yield: P j = ε ε 1 + λ rio E =0 (βθ p) λrio E =0 (βθ p) λrio [mc + P ε +Y + ] + λ rio [P ε 1 + Y + ] (2.52) where Pj ε i he opimal price of he inermediae firm j and he deired ε 1 (naural) mark-up. The law of moion for aggregae price i given by P = [(1 θ p )P 1 ε + θ p P 1 ε 1 ] 1 1 ε. (2.53) Equaion (2.52) and (2.53) yield he New-Keyneian Phillip Curve once log-linearized and afer ome mahemaical rearrangemen. 14

17 2.4 Wage bargaining Following Sähler and Thoma (2012) he union uiliy correpond o he mean of he urplu on employmen of all i member. Wih µ he hare of non-ricardian houehold, le u expre he union uiliy Υ a: Υ = (1 µ)[λ Eop λ So ] + µ[λ Erp λ Sr ] (2.54) Le u now decribe he urplu for boh or of houehold. The urplu for a Ricardian houehold o ay employed and accep he wage level agreed during he wage bargaining raher han eek for a new job in boh ecor i, afer ome re-arrangemen and calculaion: λ Eop λ So = (1 τ w )λ rio W p h λ rio b + (1 h )1 ζ (1 ) 1 ζ 1 ζ +βe [(1 p )(1 ρ)(λ Eop +1 λ So +1) p g (1 ρ)(λ Eog +1 λ So +1)](2.55) and for he non-ricardian worker: λ Erp λ Sr = (1 τ w )λ rir W p h λ rir b + (1 h )1 ζ (1 ) 1 ζ 1 ζ +βe [(1 p )(1 ρ)(λ Erp +1 λ So +1) p g (1 ρ)(λ Erg +1 λ Sr +1)](2.56) Nah produc and efficien bargaining Under he free enry condiion, he Nah produc can be expreed a: wih η he union bargaining power. N = Υ η [λ E f ] 1 η, (2.57) In he cae of efficien bargaining, firm and union joinly deermine he real wage bu no he hour worked in our model ince we aume hem a exogenouly fixed. Maximizaion of he Nah produc wih repec o he privae real wage lead o he following opimal rule for he urplu allocaion: η Υ W p λ E f = (1 η) λef W p Υ (2.58) 15

18 Afer everal calculaion ep (fully decribed in appendix C.4.1), we finally obain hi rule for he privae real hourly wage (ne of he income ax): (1 τ w )W p h = η (1 α)(1 τ w ) (1 + τ p ) E p +(1 η) [b + (1 ] )1 ζ (1 h ) 1 ζ ) (1 ζ)(µλ rir + (1 µ)λ rio { [ +η(1 ρ)e β,+1 1 (1 p p ) (1 τ ] } +1) w (1 + τ+1) Λ p +1 λ E f +1 +(1 η)(1 ρ)p g βe [Λ (λ Erg +1 λ Sr +1) + (1 Λ )(λ Eog +1 λ So +1)], Y (2.59) wih Λ = µλ rir µλ rir + (1 µ)λ rio in he conumer pool and Λ = µλrir he relaive par of non-ricardian conumer + (1 µ)λ rio 1 + (1 µ)λ rio µλ rir Moneary and fical policie In each period, he moneary auhoriy e he nominal inere rae according o he following andard Taylor rule: R R = ( R 1 R ) α r ( Y Ȳ ) αy ( π ) α π π (2.60) wih α r he degree of ineria of he nominal inere rae and α y and α π he relaive weigh given by he moneary auhoriy o he abilizaion of oupu and inflaion. The budge conrain in each period for he governmen equal o: τ c C + (τ w + τ p )(W p E p h) + D = W g E g h + C g + I g + bs (2.61) The governmen i allowed o creae a defici D o finance upplemenary expendiure or deerioraion of he ax bae. I g denoe public invemen. Public wage and public vacancie are conidered a an AR(1) proce uch a: 16

19 W g W = g V g V = g ( W g ) ρ g 1 W g ) ρ g ( V g 1 V g exp(ξ W g ) (2.62) exp(ξ V g ) (2.63) where ρ g denoe he duraion of he hock. The erm ξ i he whie noie aociaed o he hock. Each ax i alo conidered a an AR(1) proce uch a: τ w τ w ( τ w = 1 τ w ) ρ g exp(ξ τ w ) (2.64) τ p τ p ( τ p = 1 τ p ) ρ g 2.6 Aggregaion and marke clearing exp(ξ τp ) (2.65) In order o clear he model, oal demand addreed by boh governmen and houehold o firm i expreed a: Y = C + I + C g + I g (2.66) Given he previou decripion, aggregaion yield E o = E p + E g, (2.67) E g = (1 µ)e og + µe rg, (2.68) E p = (1 µ)e op S = S o + S r (2.70) + µe rp, (2.69) θ = θ p + θ g (2.71) 3 Calibraion, eady-ae calculaion and econdorder oluion We calibrae our model o a quarerly frequency. Some parameer are choen o ha long-run argeed value are reproduced. Table (1) preen he 17

20 baeline calibraion for he houehold preference and for he firm producion funcion. Table 2 preen he baeline calibraion for he fical and moneary policie and for he labor marke. The ime-dicoun facor β i e o in order o mach an average annual real rae of 3%. According o Chey e al. (2013) and o Peerman (2012), we e ζ o 1/3 in order o mach he macro eimae of he Frich elaiciy. Thi parameer i lighly higher han he calibraion choen by Sme and Wouer (2007) which i around 2. Following Sme and Wouer (2003) and Sähler and Thoma (2012), we e he value of he rik averion coefficien o σ c = 2. Knowing ha we e h = 0.33, we e he value of he fixed co of paricipaing in he labor marke o = 7.5% of he ime endowmen. Thi value i halfway beween Burnide and Eichenbaum (1996) value and Ravn (2005) value which are repecively equal o 5% and 9.9% of he ime endowmen. Following Sme and Wouer (2003) and Sähler and Thoma (2012), we e H = 0.85.Finally, we e µ = 0.3 which i quie imilar o he choice made by Coenen and Sraub (2005). Regarding he moneary policy parameer, we e he coefficien repone o he oupu gap and o inflaion o he repecive value α y = 0.5 and α π = 1.5 a in Clarida e al. (2000) and Trigari (2006). The nominal inere rae moohing coefficien i e o α r = 0.8 a in Chrioffel e al. (2009a). Following Sähler and Thoma (2012), we e he public ecor capial influence in he privae producion α g = 0.015, he adjumen co parameer κ = The hare of he public ecor in he whole economy i equal o f racpub = Following Afono and Gome (2014) and Sähler and Thoma (2012), we e he elaiciy of mache o unemploymen in he public ecor ϕ g = 0.3 in order o give greaer imporance o vacancie in he public ecor. However, he elaiciy of mache o unemploymen in he privae ecor i equal o ϕ p = 0.5. Finally, in order o aify he Hoio (1990) condiion, we e he bargaining power a equal o he elaiciy of mache o unemploymen in he privae ecor. Regarding he producion ide, we e he elaiciy of ubiuion beween differeniaed good a ε = 7 in order o obain an opimal markup of around 17%. The depreciaion rae of capial i e o δ k = ju a 18

21 in Moyen and Sähler (2010) and Sähler and Thoma (2012). The privae ecor capial influence coefficien follow he choice of Moyen and Sähler (2010) and i i e o α = 0.3. Table 1: Parameer and heir calibraed value I Preference β Time-dicoun facor ζ 1/3 Revere of Frich elaiciy σ c 2 Rik averion h 0.33 Worked hour 0.075h Fixed co of paricipaing in he labor marke H 0.85 Degree of Conumpion habi µ 0.3 Share of non-ricardian worker in he economy Producion ε 7 Elaiciy of ubiuion of good δ k Depreciaion rae of capial α 0.3 Privae ecor capial influence κ v 0.2 Vacancie poing co Regarding he long-run argeed value able 3 preen he differen choice. 19

22 Table 2: Parameer and heir calibraed value II Moneary Policy α r 0.8 Inere rae moohing α y 0.5 Repone coefficien o he oupu gap α π 1.5 Repone coefficien o inflaion Fical Policy ρ g 0.6 Duraion of he fical policy hock Labor marke and wage bargaining κ 2.48 Adjumen co parameer η 0.5 Worker bargaining power ρ 0.06 Job derucion ϕ p 0.5 Elaiciy of mache o unemploymen in he privae ecor ϕ g 0.3 Elaiciy of mache o unemploymen in he public ecor f racpub 0.19 Share of he public ecor in he whole e conomy Table 3: Targeed Value π 1 Inflaion p 1 Price Y 1 Oupu C g 0.2 Public Conumpion I g 0.03 Public Invemen b 0.3Y Unemployemen benefi τ c 0.20 VAT τ w 0.16 Income ax τ p 0.16 Social Proecion ax U 0.08 Unemploymen q p 0.7 Job filling probabiliy in privae ecor q g 0.8 Job filling probabiliy in public ecor 4 The effec of fical policy on he labor marke and oupu We imulae he model wih all fical hock in urn. We begin by uing a fir-order approximaion of he model 20in order o emphaize he ranmiion

23 channel of he differen fical inrumen. Alo, in he cae of he public wage, we compare our reul wih hoe of Afono and Gome (2014). Then, he model i olved a he econd-order in order o analyze he effec of he differen fical hock according o wo eady-ae for he unemploymen rae. The low unemploymen rae ae coni in U = 6% while he labor marke in bad ime i repreened by U = 12%. 4.1 Effec in normal ime The IRF of he fir order are preened in appendix A and B Public wage expanion financed by deb A rie in W g ha a direc poiive impac on conumpion of non-ricardian houehold. Thi effec i amplified by a rie in employmen. On he oher hand, we oberve a drop in privae real wage ha produce downward preure on non-ricardian conumpion. However, oal repone i unambiguouly poiive. Oupu hu increae righ a he momen of he hock. However, he rie in price generae higher inere rae ha progreively crowd ou Ricardian conumpion and invemen. Thi crowding-ou effec on privae aciviy produce a negaive repone of oupu in he mid-erm, a hown in he IRF. In conra wih Afono and Gome (2014), a rie in public wage produce a drop in privae real wage and a rie in employmen. In Afono and Gome (2014), auhor explain higher privae real wage hrough hree differen channel. Fir, a higher public wage increae he value of being unemployed, and we alo hare hi channel. Secondly, heir model generae a rie in marginal produciviy of labor which creae upward preure on privae real wage. In our model, marginal produciviy of labor clearly decreae due o a negaive oal effec on oupu and a clear rie in employmen. Thi imporan apec parly explain he differen dynamic of privae real wage produced by our model following a rie in public wage. Thirdly, Afono and Gome (2014) aume ha he wage bill i enirely financed by a rie in labor income ax. The auhor argue ha hi rie in he labor income ax ha conradicory effec on real wage. In hi imulaion, we aume ha he 21

24 upplemenary pending i financed by deb. Indeed, in our model, all hing being equal, an increae in he labor income ax rigger a raie in privae real wage. Thu, inroducing he labor income ax a financing he wage bill pu upward preure on privae real wage. For comparion purpoe, we imulae a cenario imilar o he one in Afono and Gome (2014) by replacing equaion (2.64) by: τ c (C o + C r ) + τ w W p E p h + τ p E p W p h = C g + I g + (1 τ w )(W g E g h) + bs (4.1) In equaion (4.1), we aume ha τ c and τ p are conan. In hi cae, he degradaion of he public defici i oaly counerbalanced by a raie in he labor income ax. A hown in appendix A, our model reproduce imilar reul in hi cae. Employmen fall, unemploymen rie and privae real wage increae. We conclude ha he rie in privae real wage following a rie in public real wage rongly depend on he aumpion made abou he financing. A hown before, in cae of a deb-baed public wage expanion, our model produce a clear decreae in privae real wage Public vacancie expanion Following Michailla (2014), a rie in public vacancie rigger a poiive effec on oal employmen depie a crowding-ou effec on privae employmen. The hiring of job eeker by he public ecor increae he labor marke ighne and hu rigger le job creaion in he privae ecor. Since in our model a rie in public vacancie i waeful (he public ecor i unproducive), he effec on oupu i clearly negaive becaue of a crowding-ou effec on Ricardian houehold conumpion ince real inere rae increae. Conumpion of non-ricardian houehold increae wih he rie in oal employmen depie he decreae in real wage. For he fir few period, he repone of oupu i poiive, hank o a rie in privae invemen. Thi rie in aggregae demand rigger a rie in privae employmen. However, afer few period he crowding-ou effec of public employmen on privae employmen prevail over he poiive effec induced by he aggregae demand. 22

25 4.1.3 Labor income ax cu Fir, he cu in he labor income ax yield a drop in privae real wage. Thi drop can be explained hank o a direc impac of he labor income ax on he wage dynamic. Indeed, he drop in he labor income ax increae he mach urplu going o he worker. In he bargaining proce, i pu a downward preure on privae ecor wage. I induce a raie in privae ecor employmen. Alo, marginal produciviy of labor i reduced, which caue addiional downward preure on privae ecor wage. Following he increae in privae employmen and depie he drop in privae ecor wage, conumpion of non-ricardian houehold increae. Wih a rie in inflaion and inere rae, Ricardian conumpion drop and hi crowding-ou effec rigger a drop in oupu a he mid-erm Social proecion ax cu Following he cu in ocial proecion ax, he mach urplu going o he firm hike which induce an upward preure on he privae ecor wage. A a conequence, conumpion of non-ricardian rie. There i a limied crowding-ou effec on Ricardian conumpion. On he labor marke, he decreae in τ p rie direcly he preen and fuure value of a job for firm. The marginal produciviy of labor decreae lighly bu he repone of privae real wage remain unambiguouly poiive. Employmen in he privae ecor increae while in he public ecor he rie in privae real wage and he drop in unemploymen reduce employmen. However, oal employmen increae rongly. 4.2 Wha impac over he buine cycle? For all imulaion in hi paper we ue he Dynare program creaed by he CEPREMAP eam. The algorihm ued by Dynare for he econd order approximaion of our model i very cloe o he one developed in Schmi-Grohé and Uribe (2004). In addiion, he imulaion are done by uing he pruning mehod 5, in order o avoid riggering polynomial of increaing degree when imulaing he model. The IRF of he econd order imulaion are 5 See for inance Lombardo and Uhlig (2014) for a preenaion of he pruning mehod. 23

26 preened in appendix C. For all he fical hock conidered, we find a imilar reul: fical policie have a greaer effec on employmen, unemploymen and oupu in he cae of he high eady-ae value for he unemploymen rae. A we will ee hroughou hi ecion, hee reul are driven by wo main elemen: a wider pool of job eeker and he crucial role of he wage channel. The wage channel: The aring poin i ha wih a higher unemploymen rae (U = 12%), he pool of job eeker i wider a he eady ae. In he cae of expanionary fical hock, he rie in privae vacancie generae more mache when he iniial pool of job eeker i wider. Thi channel i very cloe o he reul expounded by Michailla (2014). From hen on, ince employmen increae more when U = 12%, all hing being equal, marginal produciviy of labor alo decreae more harply. Indeed, even if he beer repone of oupu when U = 12% eae hi channel, he repone of marginal produciviy of labor remain ronger when unemploymen i high. I caue larger downward preure on real wage, a hown in he IRF. Effec on oupu fical muliplier: Moreover, he wage channel i a crucial elemen for underanding and comparing he repone of oupu according o differen eady-ae unemploymen rae. We now explore he condiion under which we obain a beer repone of oupu in he cae of a high unemploymen rae, hank o a higher degradaion of real wage. Fir, excep for he ocial proecion ax hock, he greaer degradaion of real wage when U = 12%, principally driven by he decreae in produciviy, ha a direc negaive effec on conumpion of he non-ricardian. Indeed, non-ricardian houehold conumpion increae more when U = 6% han when U = 12%. The cae for he ocial proecion ax hock i differen in he ene ha a decreae in he ocial proecion ax produce a poiive repone of privae wage. However, hi poiive repone i larger when unemploymen i low han when unemploymen i high o he non-ricardian 24

27 houehold conumpion reac in he ame way a previouly. The conequence of he previou reul i he following: if our economy were compoed only of non-ricardian houehold, like in Michailla (2014) for inance, our model would produce higher oupu fical muliplier wih he low eady-ae unemploymen rae. In ha ene, we need o inroduce Ricardian houehold o produce higher oupu muliplier a he bad ae of he economy. A oberved in he IRF, conumpion of he Ricardian i higher when he unemploymen rae i high, which produce beer oupu fical muliplier. Thi i due o he greaer degradaion of real wage, cauing lower inflaion preure for he firm and hu, a lower rie of he inere rae in he medium and long erm. Thu, when U = 12% he larger negaive repone of real wage produce a higher repone of Ricardian conumpion bu a lower non-ricardian conumpion, in comparion wih he imulaion when U = 6%. Toal repone of aggregae conumpion and oupu depend on he rengh of hee wo oppoie effec and of he relaive hare of boh ype of houehold in he economy. Wih a hare of non-ricardian in line wih previou eimae 6, ha i µ = 0.3, he repone of aggregae demand i beer when he unemploymen rae i high. Wih hi model calibraion, he poiive effec of a lower inflaion on Ricardian conumpion when he unemploymen rae i high prevail over he weaker repone of non-ricardian conumpion due o a greaer degradaion of real wage. I i imporan o noice ha he more poiive repone of conumpion of he Ricardian i no due in our model o a higher marginal uiliy of conumpion in economic downurn, a hi i he cae in Sim and Wolff (2013). The auhor highligh hi ranmiion channel for explaining differen oupu fical muliplier over he buine cycle. Thi i no he cae in our model according o he definiion of he eady-ae. The value of Ricardian conumpion a he eady ae i obained reidually wih he eady-ae value of non-ricardian conumpion uch a: 6 See for inance Coenen and Sraub (2005) C o = C µc r 1 µ, (4.2) 25

28 whih C o, C r and C repecively he eady-ae value of C o, C r and C. The eady-ae value of non-ricardian conumpion i larger wih U = 12% ince real wage i larger han unemploymen benefi a he eady ae. I rigger a higher marginal uiliy of conumpion for hi cla of houehold bu i ha no impac on heir conumpion behavior ince hey imply conume heir dipoable income. However, a lower level of conumpion a he eady ae for he non-ricardian houehold implie a higher conumpion for he Ricardian. 5 Concluion Thi paper aemp o inveigae he non-linear effec of fical policy over he buine cycle wih a focu on he labor marke. A fir par of he reul ecion i dedicaed o he analyi of he effec of differen fical inrumen on he labor marke and on oupu. We ue a fir-order approximaion of he model in order o dienangle he main ranmiion channel a work. The main reul i ha all fical inrumen increae employmen and decreae unemploymen. Alo, repone of oupu i poiive in he hor erm bu negaive in he medium erm becaue of a rong and permanen crowdingou effec on Ricardian conumpion. Uing a econd-order approximaion of he model, we how ha all fical hock are more effecive when he eady-ae unemploymen rae i high: boh employmen and oupu increae more. Following Michailla (2014), he ronger effec on employmen i due o a larger pool of job eeker when he hock occur. We hen inveigae he aumpion needed o produce a beer repone of oupu. In our model, if we inroduced only non-ricardian houehold, he oupu fical muliplier would be lower when he unemploymen rae i a 12%. The inroducion of Ricardian houehold i neceary o produce a higher oupu fical muliplier a explained in he reul ecion. However, he ranmiion channel i very differen from he one in Sim and Wolff (2013). In our model, i i he wage channel and a lower rie in inere rae ha produce he larger oupu fical muliplier during economic downurn while i 26

29 i a higher marginal uiliy of conumpion during bad ime ha miigae he degradaion of conumpion of he Ricardian houehold in Sim and Wolff (2013). On he conrary, our definiion of he eady ae rigger a lower marginal uiliy of conumpion for he Ricardian when he unemploymen rae i high. We can expec ha when inroducing a higher marginal uiliy of conumpion for he Ricardian during economic downurn a he eady-ae, hi reul would be amplified. 27

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33 A A comparion wih Afono and Gome (2014) Privae Wage Ricardian' marginal uiliy of real income Non Ricardian' marginal uiliy of real income Financing = Taxe Financing = Deb Financing = Taxe Financing = Deb Financing = Taxe Financing = Deb Toal Conumpion Ricardian Houehold' Conumpion Non Ricardian Houehold' Conumpion 2e 04 0e+00 2e 04 4e 04 6e 04 8e 04 1e 03 Financing = Taxe Financing = Deb Financing = Taxe Financing = Deb Financing = Taxe Financing = Deb Oupu Toal Employmen Public Employmen Financing = Taxe Financing = Deb 1e 04 0e+00 1e 04 2e 04 Financing = Taxe Financing = Deb 2.0e e e e e e e 05 Financing = Taxe Financing = Deb 31

34 Privae Employmen Privae Vacancie Unemploymen Financing = Taxe Financing = Deb 0e+00 2e 04 4e 04 6e 04 Financing = Taxe Financing = Deb Financing = Taxe Financing = Deb Inere Rae Inflaion 6e 05 4e 05 2e 05 0e+00 2e 05 4e 05 6e 05 8e 05 Financing = Taxe Financing = Deb 1e 04 5e 05 0e+00 5e 05 Financing = Taxe Financing = Deb B The IRF for he differen hock in he middle of he buine cycle B.1 The Wage Tax Shock Privae Wage Ricardian' marginal uiliy of real income Non Ricardian' marginal uiliy of real income

35 Toal Conumpion Ricardian Houehold' Conumpion Non Ricardian Houehold' Conumpion Oupu Toal Employmen Public Employmen 1e 04 0e+00 1e 04 2e 04 3e 04 4e 04 5e 04 0e+00 1e 04 2e 04 3e 04 4e 04 5e 04 4e 05 3e 05 2e 05 1e 05 0e+00 1e 05 2e 05 Privae Employmen Privae Vacancie Unemploymen 0e+00 1e 04 2e 04 3e 04 4e 04 5e 04 0e+00 2e 04 4e 04 6e 04 8e 04 1e 03 5e 04 4e 04 3e 04 2e 04 1e 04 0e+00 Inere Rae Inflaion

36 B.2 The Public Vacancie Shock Privae Wage Ricardian' marginal uiliy of real income Non Ricardian' marginal uiliy of real income Toal Conumpion Ricardian Houehold' Conumpion Non Ricardian Houehold' Conumpion 8e 04 6e 04 4e 04 2e 04 0e Oupu Toal Employmen Public Employmen 1e 03 8e 04 6e 04 4e 04 2e 04 0e+00 2e 04 4e Privae Employmen Privae Vacancie Unemploymen 1e 03 5e 04 0e+00 4e 04 2e 04 0e+00 2e 04 4e 04 6e

37 Inere Rae Inflaion Privae Invemen 0e+00 1e 04 2e 04 3e 04 4e 04 1e 04 0e+00 1e 04 2e 04 3e 04 4e 04 0e+00 1e 04 2e 04 3e 04 4e 04 5e 04 Renal Rae of Privae Capial Marginal Produciviy of Labor e+00 5e 04 1e 03 B.3 The Social Proecion Tax Shock Privae Wage Ricardian' marginal uiliy of real income Non Ricardian' marginal uiliy of real income

38 Toal Conumpion Ricardian Houehold' Conumpion Non Ricardian Houehold' Conumpion 0e+00 2e 04 4e 04 6e 04 8e 04 1e 04 8e 05 6e 05 4e 05 2e e+00 1e 04 2e 04 3e 04 4e 04 Oupu 0e+00 1e 04 2e 04 3e 04 4e 04 5e 04 Toal Employmen 4e 05 3e 05 2e 05 1e 05 0e+00 1e 05 2e 05 Public Employmen Privae Employmen Privae Vacancie Unemploymen 0e+00 1e 04 2e 04 3e 04 4e 04 0e+00 2e 04 4e 04 6e 04 8e 04 5e 04 4e 04 3e 04 2e 04 1e 04 0e+00 Inere Rae Inflaion