Fiscal multipliers in a two-sector search and matching model

Transcription

1 Fiscal mulipliers in a wo-secor search and maching model Konsaninos Angelopoulos Universiy of Glasgow Wei Jiang Universiy of Ken James Malley Universiy of Glasgow and CESifo January 29, 215 Absrac This paper evaluaes he effecs of policy inervenions on secoral labour markes and he aggregae economy in a business cycle model wih search and maching fricions. We exend he canonical model by including capial-skill complemenariy in producion, labour markes wih skilled and unskilled workers and on-he-job-learning OJL) wihin and across skill ypes. We firs find ha, he model does a good job a maching he cyclical properies of secoral employmen and he wage-skill premium. We nex find ha vacancy subsidies for skilled and unskilled jobs lead o oupu mulipliers which are greaer han uniy wih OJL and less han uniy wihou OJL. In conras, he posiive oupu effecs from cuing skilled and unskilled income axes are close o zero. Finally, we find ha he secoral and aggregae effecs of vacancy subsidies do no depend on wheher hey are financed via public deb or disoring axes. Keywords: fiscal mulipliers, secoral labour markes, search and maching JEL Classificaion: E24, E32, J63, J64, J68 We would like o hank Jagji Chadha, Pedro Gomes, Amanda Gosling, Miguel León- Ledesma, Mahan Sachi, Fabien Posel-Vinay and paricipans a he Compuing in Economics and Finance, 214 conference in Oslo and he Universiy of Ken MaGHiC Workshop on Labour Marke, Public Policy and he Business Cycle for helpful commens and suggesions. Corresponding auhor: w.jiang@ken.ac.uk.

2 Non-echnical summary of he paper This paper exends he canonical search-and-maching model which has only a represenaive worker by including fragmened labour markes for skilled and unskilled workers. The producion is characerised by capial-skill complemenariy: he elasiciy of subsiuion is higher beween capial equipmen and unskilled labour han beween capial equipmen and skilled labour. The produciviy of workers increases during heir employmen as a resul of on-he-job-learning OJL) wihin and across skill ypes. Our ineres in skilled and unskilled labour markes is moivaed by empirical evidence on he imporance of he differences beween hese wo labour markes regarding boh wage and employmen raes. In paricular, wage inequaliy beween skilled and unskilled labour has increased in recen decades o is highes levels in a cenury. Employmen differs significanly beween he wo secors wih unskilled employmen more volaile han skilled alhough boh closely racking cyclical oupu. The model is calibraed o mach seady-sae aggregae and secoral labour marke daa in he U.S. We find ha he model does a good job of maching he cyclical properies of secoral labour markes. Consisen wih he daa, he model predics ha he volailiy of unskilled employmen is abou wice as large as ha of skilled employmen, and a measure of he skill premium whose volailiy is less han oupu and is correlaion wih oupu is around zero. Moreover, our paper predics an employmen volailiy which ranges around 7-8% of ha in he daa, whereas in he canonical models his raio is ypically only abou 25%. We hen use he model o evaluae he effecs of emporary fiscal inervenions in erms of increasing vacancy subsidies or cuing income axes. The resuls sugges ha vacancy subsidies for skilled and unskilled jobs can lead o fiscal mulipliers on oupu which are greaer han uniy wih OJL bu less han uniy when here is no OJL. These large mulipliers under OJL are deermined by he crowding-in of privae invesmen, which follows he increases in employmen and labour produciviy. Wihou OJL, he labour produciviy channel is absen and causes he mulipliers o fall o abou.6. In conras, he posiive oupu effecs from cuing skilled and unskilled income axes are close o zero. This is because income axes affec employmen indirecly, by working via he disored labour marke, i.e. Nash bargaining, which implies ha par of he benefis of increasing employmen are los. We finally find ha he effecs of boh skilled and unskilled vacancy subsidies do no depend on wheher deb or disoring axes are used o finance hem. This finding suggess ha his ype of inervenion may be paricularly useful under he deb ceilings ha many governmens now face in he wake of he financial crisis. 2

3 1 Inroducion Equilibrium unemploymen models wih search and maching fricions have been exensively used in macroeconomic analyses of unemploymen see e.g. Shimer 21) and Rogerson and Shimer 211) for an analyical overview of his research). Among oher exensions, his lieraure has considered he imporance of boh differences in workers skills and he poenial for skill erosion due o unemploymen see e.g. Cahuc e al. 26), Krause and Lubik 26 and 21), Dolado e al. 29), Hagedorn e al. 21), Doppel 214) and Laureys 214)). In his paper, we conribue o his lieraure by examining unemploymen over he business cycle in an economy wih fragmened labour markes for Universiy educaed or skilled) and non- Universiy educaed or unskilled) workers, when he producion srucure is characerised by capial-skill complemenariy and workers produciviy decreases wih unemploymen. Our ineres in labour markes and unemploymen for skilled versus unskilled workers is moivaed by empirical evidence on he imporance of he differences beween hese wo labour markes, regarding boh wage and employmen raes. We summarise some key differences using quarerly daa for he U.S. over he period of for secoral employmen and for wage inequaliy. 1 Firs, he lieraure on he skill premium has demonsraed ha here are significan differences in he wages across he wo secors. In paricular, wage inequaliy beween skilled and unskilled labour has increased in recen decades o is highes levels in a cenury see e.g. Goldin and Kaz 28) and Acemoglu and Auor 211) for a discussion of longer ime series and hisorical daa). This is demonsraed in he subplo 1,1) of Figure 1, which plos he skill premium, defined as he raio of skilled o unskilled wage, using he quarerly series from Casro and Coen-Pirani 28). Second, wage inequaliy varies in business cycle frequencies, alhough less han oupu and is no srongly correlaed wih oupu see also e.g. Lindquis 24) and Pourpourides 211)). This is capured in subplo 2,1) which shows HP-filered oupu and he skill premium. In paricular, he relaive o oupu volailiy of he skill premium is.87 and is oupu 1 The daa sources for he skilled and unskilled wage daa ) are from he daase of Casro and Coen-Pirani 28). Secoral employmen/unemploymen daa ) are from he Curren Populaion Survey, Table A-4. We use daa on he employmen saus of he civilian populaion 25 years and over by educaional aainmen see Finally, per capia quarerly oupu daa ) are from he U.S. NIPA. 3

4 correlaion is.86. [Figure 1 here] Third, employmen differs significanly beween he wo secors. For example, he daa in subplo 1,2), show ha unemploymen is wice as high for unskilled compared wih skilled workers. 2 Moreover, as demonsraed in subplo 2,2), unskilled employmen is more volaile han skilled, alhough boh closely rack cyclical oupu. In paricular, he volailiy of he HP-filered unskilled employmen is 1.8 imes higher han ha of skilled workers, whereas heir oupu correlaions are abou.93. The lieraure has documened furher differences beween he skilled and unskilled secors. Cahuc e al. 26) find ha skilled workers have higher bargaining power, while Pissarides 1994), Acemoglu 21) and Krause and Lubik 26 and 21) sugges ha he flow cos of posing a vacancy is higher in good jobs. Moreover, in business cycle frequencies, here is no much movemen beween he skilled and unskilled secors. In ligh of he above, we build a business cycle model wih search and maching fricions ha lead o secoral unemploymen. To capure he above empirical observaions, we firs assume ha unskilled workers canno become skilled. Insead, skilled workers work in skilled jobs and, if unemployed, search for employmen in he skilled secor. Similarly, unskilled workers work in unskilled jobs, and if unemployed, search for employmen in he unskilled secor. Second, we assume ha he producion srucure allows for skillbiased echnical change and, in paricular, is characerised by capial-skill complemenariy. This seup has been shown o explain key characerisics of he skill premium in he daa, boh in erms of is evoluion over he pas several decades see e.g. Kaz and Murphy 1992), Krusell e al. 2) and He 212)) as well as over he business cycle Lindquis 24) and Pourpourides 211)). The search and maching mechanism for employmen creaion ha we employ follows he benchmark Morensen-Pissarides framework wih he wage being deermined via Nash bargaining. Moreover, our seup allows for differeniaion beween he wo labour markes, such as differences in relaive bargaining power, job separaion raes and job posing coss o reflec he empirical observaions oulined above. Moivaed by heories of labour augmening echnical progress driven by on-he-job learning OJL), we allow skilled and unskilled workers produciviies o be posiive funcions of employmen. Alernaively, since he secoral produciviies are decreasing funcions of unemploymen, hey can equivalenly capure skill erosion due o no working. We consider wo possibiliies 2 Fallick and Fleischman 24), Hagedorn e al. 21), and Pilossoph 212) also documen higher job separaion raes for unskilled versus skilled workers. 4

5 for OJL where boh skill ypes learn from heir own and he oher skill ype. The firs follows he lieraure ha proposes learning-by-doing LBD) as a propery of he producion echnology a he aggregae level and generaes knowledge spillovers. I hus works as an exernal effec for he individual see e.g. Romer 1986) and Barro and Sala-i-Marin 1994)). In his case he workers labour produciviy depends on average employmen, so ha LBD is aken as given a he level of he workers. The second follows more closely he lieraure on skill erosion ha is due o unemploymen see e.g. Laureys 214) and Doppel 214)). In his insance we allow he workers of each ype o inernalise he effec of heir own employmen on heir labour produciviy. However, we mainain he assumpion ha he employmen of he oher worker ype is aken as given. The model is calibraed o mach he seady-sae of aggregae and secoral labour marke daa in he U.S., following he calibraion sraegy in Shimer 21). We find ha he calibraion does a good job a maching he second momens in he secoral labour marke daa. In paricular, he model predics a volailiy for unskilled employmen ha is abou wice as big as ha of skilled employmen. Moreover, i predics a series for he skill premium whose volailiy is less han oupu and is correlaion wih oupu is around zero. Consisen wih he resuls in Shimer, he model under predics quaniaively he volailiy of employmen, bu he gap is no very big. In paricular, he model varians considered predic an employmen volailiy which ranges from 69% o 81% of he volailiy of employmen in he daa, whereas in he canonical models, e.g. Shimer 21), his raio is ypically abou 25%. Since he model wih and wihou OJL gives a relaively similar fi o he daa, we presen resuls below for policy inervenions using boh specificaions. Our policy analysis evaluaes he effecs of emporary inervenions on he secoral labour markes and he aggregae economy. We consider vacancy subsidies and axes, since as is demonsraed in Monacelli e al. 21), pure fiscal spending effecs on oupu are rivial and even negaive in search and maching models. We find fiscal mulipliers on oupu from he subsides o skilled and unskilled vacancies, which are greaer han uniy when OJL is exernal and near uniy when i is inernal. These large mulipliers are deermined by he crowding-in of privae invesmen, which follows he increases in employmen and labour produciviy. Wihou OJL, he labour produciviy channel is absen and causes he oupu mulipliers o fall o abou.6. In conras o he vacancy subsidies, he posiive oupu effecs from cuing skilled and unskilled income axes are near zero, irrespecive of he presence, or model, of OJL. We finally find ha he effecs of he wo vacancy subsidies do no depend on wheher deb or disoring axes 5

6 are used o finance hem. This is paricularly good news, and suggess ha his ype of inervenion may be useful under he deb resricions ha many governmens now face in he wake of he financial crisis. The res of he paper is organised as follows. Secion 2 ses ou he model srucure. Secion 3 presens he calibraion and cyclical properies of he model. Secion 4 underakes he fiscal muliplier analysis and Secion 5 concludes. 2 The model 2.1 Capial-skill complemenariy There are N firms which operae in compeiive produc markes. To produce a single oupu, firms use capial, which hey lease from he household, and skilled and unskilled workers. The producion echnology is characerised by capial-skill complemenariy see e.g. Goldin and Kaz 28) for hisorical evidence on he empirical relevance of his echnology in he 2h cenury). In paricular, a represenaive firm produces oupu y f, using a consan elasiciy of subsiuion CES) specificaion following e.g. Krusell e al. 2): y f = A {θ l f,u ) α [ ) ν + 1 θ) ρ k f + 1 ρ) l f,s ) ν ] α } 1 α ν 1) where A > is he level of oal facor produciviy TFP); α, ν < 1 are he parameers deermining he facor elasiciies, i.e. 1/ 1 α) is he elasiciy of subsiuion beween capial and unskilled labour and beween skilled and unskilled labour, whereas 1/ 1 ν) is he elasiciy of subsiuion beween capial and skilled labour; and < θ, ρ < 1 are he facor share parameers. In his specificaion, k f is he quaniy of capial used by he firm, whereas and l f,u denoe he quaniies of skilled and unskilled labour respecively. l f,s 2.2 Skilled and unskilled workers There is a represenaive household whose members include skilled or unskilled workers. The workers are disinc unis and can offer eiher skilled or unskilled services in he labour markes. They can find a job wihin he skill secor in which hey belong or remain unemployed. In he laer case, hey search for a job for he nex ime period wihin heir skill secor. In oher words, in business cycle frequencies workers canno change heir skill saus. This assumpion is moivaed by empirical evidence suggesing ha over he 6

7 business cycle, he share of college educaed or skilled populaion has low volailiy and is effecively uncorrelaed wih oupu. In paricular, using he daa in Acemoglu and Auor 211), we find ha he sandard deviaion of he cyclical componen of he skilled populaion share, relaive o ha of oupu, is.29, while is correlaion wih oupu is This implies ha skilled workers can eiher work in skilled jobs or remain unemployed and search for skilled jobs), whereas unskilled workers can eiher work in unskilled jobs or remain unemployed and search for unskilled jobs). Following he lieraure on search fricions and unemploymen in macroeconomic DGE models since Merz 1995), we assume ha he head of he household makes all decisions on behalf of is members and provides complee consumpion insurance. In oher words, all workers consume he same amoun of goods, irrespecive of heir labour marke saus, i.e. regardless of wheher hey are employed in skilled or unskilled jobs or hey are unemployed. The numbers of skilled and unskilled members for he represenaive household are denoed as N s and N u, respecively. The oal size of he household is normalised o be N and is hus given as: N = N s + N u. The respecive populaion shares of skilled and unskilled members wihin a household are defined as: n s = N s /N and n u = N u /N. We assume ha populaion and is composiion remain consan. For each skill ype of household members, i = s, u, he number of members/workers can be furher decomposed ino employed and unemployed members, such ha: N i = N i,e + N i,s 2) where i = s, u for skilled and unskilled labour; and N i,e is he number of employed members and N i,s is he number of unemployed members, who are searching for a job. By normalising by N i, we have: 1 = e i + s i 3) where e i N i,e is he employmen rae and s i N i N i,s N i rae or he share of workers searching for a job. is he unemploymen 2.3 Search and maching There are wo labour markes, for skilled and unskilled workers respecively. Each unemployed worker needs o search for a job in he skilled or unskilled 3 This is obained using annual daa for he share of college educaed populaion measured in effi ciency unis, , from Acemoglu and Auor 211) and GDP per capia daa from he U.S. Naional Income and Produc Accouns NIPA). The cyclical componen of he series is obained using he HP-filer wih a smoohing parameer of 1. 7

8 secor, given her skill level, and can be mached wih a firm ha poss vacancies in ha secor. As in he sandard search-and-maching lieraure see e.g. Pissarides 1986) and Blanchard and Diamond 1989)), he maching echnology is represened by a Cobb-Douglas CD) funcion for boh skilled and unskilled labour: M i = χ ) i S i η i ) V i 1 η i 4) where, M i is he aggregae new maches a ; 4 S i = N i s i denoes he aggregae number of unemployed searching in labour marke i; V i = Nv i denoes he aggregae number of job vacancies creaed by firms in labour marke i; χ i > represens he consan effi ciency of maching for labour ype i; < η i < 1 denoes he elasiciy of searches for labour ype i. In addiion, we define he vacancy-o-unemployed raio, z i = V i /S i = v/ i n i s i ), as he ighness of ype i labour marke. The smaller he raio of z, i he igher he labour marke and herefore he harder for unemployed workers o mach wih job vacancies. The probabiliy a which aggregae job searches lead o a new job mach in ype i labour marke is given by: p i = M i S i = χ ) i S i η i 1 ) V i 1 η i ) = χ i z i 1 η i 5) and is inverse, 1/p i, measures he duraion of ype i search. The probabiliy a which a job vacancy can be mached wih an unemployed household member is calculaed by: q i = M i V i = χ ) i S i η i ) V i η i ) = χ i z i η i 6) and is inverse, 1/q i, measures he duraion of ype i job vacancy. 2.4 Household There is a represenaive household comprised of skilled and unskilled individuals whose head makes all decisions on behalf of is members by guaraneeing equal consumpion o each of hem, wih he objecive of maximising household welfare. 4 In wha follows, we use upper case leers for aggregae quaniies and lower case leers for per capia quaniies. 8

9 2.4.1 Problem The represenaive household maximises discouned lifeime uiliy, U : U = E = β u 7) where E is he condiional expecaions operaor a period ; and < β < 1 denoes he consan rae of ime preference. The insananeous uiliy funcion of he household is given by see e.g. Shimer 21)): u = lnc ) n s ξe s n u ξe u 8) where ξ > is he preference parameer ha measures he disuiliy cos of employmen and c is he household s average or per capia) privae consumpion. As is common in he lieraure, he disuiliy cos capures he reducion in he ime available for home producion when a member finds employmen. Hence, he specificaion in 8) assumes ha all members consume c and ha if a member is unemployed, her uiliy is given by lnc ), whereas if a member is employed, her uiliy is given by lnc ) ξ i, so ha u measures average uiliy for he household. The budge consrain of he household is: c + i + b +1 = [ r τ k r δ) ] k + π + +R b b + 1 τ s ) n s w s e s Z s + 1 τ u ) n u w u e u Z u 9) where i is household s average privae invesmen; b +1 is he value of governmen bonds bough a period ; r is he gross reurn o physical capial; τ k is he ax rae on capial income; < δ < 1 is he consan depreciaion rae of physical capial; k is he average physical capial held by he household a he beginning of ; π is average dividends received from he firms; R b = 1 + r) b is he gross reurn o bonds; τ i is he labour income ax; w i is he gross wage rae; and Z i represens labour augmening echnology driven by OJL. This echnology posiively depends on he level of employmen. Alernaively, Z i can be inerpreed as a decreasing funcion of unemploymen and capures skill erosion due o no working. 5 We allow for boh skill ypes o learn on-he-job from heir own and he oher skill ype. We consider wo possibiliies for OJL. The firs follows he lieraure ha proposes learning-by-doing LBD) as a propery of he producion echnology a he aggregae level. This seup generaes knowledge spillovers a he 5 See, for example, Davis and von Wacher 211) and Pollack 213) for he effecs of unemploymen on labour produciviy and Laureys 214) and Doppel 214) for search and maching models wih skill depreciaion due o unemploymen. 9

10 aggregae level which work as an exernal effec for he individual see e.g. Romer 1986) and Barro and Sala-i-Marin 1994)). In his case, we allow he worker s labour produciviy o depend on average employmen, so ha LBD or, alernaively, skill erosion) is aken as given a he level of he worker. This case is represened as follows: Z s Z s,x = Ω s e s ) ζs e u ) 1 ζs 1) Z u Z u,x = Ω u e s ) ζu e u ) 1 ζu 11) where a bar over a variable refers o average quaniies; Ω i > are learning produciviy parameers; and < ζ i < 1, are he elasiciies of OJL wih respec o skilled employmen for skilled and unskilled workers. We will proceed wih he model soluion below using 1) and 11). However, we will also presen and discuss resuls using a second possibiliy for he deerminaion of Z i, following more closely he lieraure on skill erosion ha is due o unemploymen see e.g. Laureys 214) and Doppel 214)). This alernaive assumes ha workers inernalise he effec of employmen on heir labour produciviy. Hence, in his case we allow he worker of each ype o inernalise he effec of heir own employmen on heir labour produciviy. However, we mainain he assumpion ha he employmen of he oher worker ype is aken as given: 6 Z s Z s,n = Ω s e s ) ζs e u ) 1 ζs 12) Z u The capial sock evolves according o: Z u,n = Ω u e s ) ζu e u ) 1 ζu. 13) k +1 = 1 δ) k + Ãk i 14) The capial evoluion equaion allows for an exogenous process, Ãk, capuring an invesmen-specific echnological IT) change, which has been shown o conribue o oupu flucuaions see e.g. Greenwood e al. 2), as well as he changes in he skill premium see e.g. Krusell e al. 2), Lindquis 24), and Pourpourides 211)). The sochasic process for invesmenspecific echnology, Ã k is: ) Ã k 1 ρa k +1 = Ãk ) Ã k ρa k e ε Ak +1 15) where Ãk > ; < ρ A k < 1; and ε Ak +1 iidn [, σ A k) 2]. 6 Noe ha in boh specificaions examined, labour produciviy is increasing and concave wih respec o employmen and bounded beween zero and Ω i, where i = s, u. 1

11 By using equaion 14) and defining as A k 1, we can rewrie he à k budge consrain of household: c + A k k +1 + b +1 = r k + π + +R b b + 1 τ s ) n s w s e s Z s + 1 τ u ) n u w u e u Z u 16) where r = r τ k r δ) + A k 1 δ), is he ne reurn o physical capial afer depreciaion and ax. Noe ha A k 1 measures he effecive price à k of invesmen, since A k unis of invesmen are needed o creae one uni of capial in he nex period. Employmen for ype i = s, u worker evolves according o: e i +1 = p i s i + 1 γ i ) e i 17) where < γ i < 1 is he rae of job separaion for ype i labour. The sochasic process for he job separaion rae, γ i, is: γ i +1 = γ i) 1 ρ g ) i γ i ρgi e εgi +1 18) [ where γ i > ; < ρ g i < 1; and ε gi +1 iidn, ) ] σ i 2 g. The household s opimizaion problem is o choose {c, k +1, b +1 } = o maximise 7) subjec o he consrains 3) and 16) aking facor prices {w s, w u, r, r} b =; profis {π } = ; he evoluion of employmen {ei } = ; he exogenous variables { A k, γ} i ; policy variables { } τ k =, τ s, τ u and iniial = condiions for k, b as given Firs-order condiions FOCs) The recursive form of he household s problem is: V k, b, e s, e u ) = max {ln c n s ξe s n u ξe u ) + c,k +1,b +1 +βe V ) 19) k +1, b +1, e s +1, e u +1 } where V.) is he value funcion. consrain 16) gives: Replacing c making use of he budge V k, b, e s, e u ) = max [ ln[ r k A k k +1 b +1 + π + R b k +1,b +1 b τ s ) n s w s e s Z s + 1 τ u ) n u w u e u Z u ] n s ξe s n u ξe u + +βe V k +1, b +1, e s +1, e u +1)]. 2) The envelope condiion for capial sock, k is: V k k, b, e s, e u ) = r c 21) 11

12 and he firs order condiion for k +1 is: βe V k k+1, b +1, e s +1, e u +1 ) = A k c 22) which equaes he discouned expeced marginal benefi o he marginal cos of invesmen. Finally, subsiuing he one-period lead of he envelope condiion 21) ino he firs-order condiion for capial 22) gives he consumpion Euler: E β c ) r +1 = A k 23) c +1 which shows ha he expeced, discouned reurn on invesing in capial mus equal is price. Noe ha he reurn is discouned using he sochasic discoun facor β c c +1. The envelope condiion for governmen bonds, b is: and he firs order condiion for b +1 is: V b k, b, e s, e u ) = Rb c 24) βe V b k+1, b +1, e s +1, e u +1 ) = 1 c. 25) Subsiuing he one-period lead of he envelope condiion 24) ino he firs-order condiion for governmen bonds 25) gives he bonds Euler, which has a similar inerpreaion as he Euler for capial: E β c )) 1 + r b +1 = 1 26) c +1 The FOCs for he household s problem are given by 16), 23) and 26). These { deermine } he pahs for {c, k +1, b +1 } = given exogenous variables A k, γ i ; policy variables { } τ k =, τ s, τ u ; iniial condiions, {k =, b }; and he pahs for variables ha are exogenous o he household s problem, i.e. hose deermined a he aggregae level, { π, r, r, b e+1} i and by wage bargaining, {w} i = =. 2.5 Firms There is a represenaive firm which leases capial from he household and employs skilled and unskilled workers o produce a single good, wih he objecive of maximising profis. 12

13 2.5.1 Problem To hire workers, he firm needs o pos vacancies one period before he jobs are required. In paricular, he evoluion of he number of workers per skilled ype employed by he firm is given by he job ransiion funcion which links he fuure number of filled jobs, l+1, f,i o he ne hiring, qv i, i plus he curren sock of filled jobs, 1 γ i ) l f,i : l f,i +1 = qv i i + ) 1 γ i l f,i. 27) Given ha posing vacancies is cosly, he profi funcion of he firm is: π f = y f r k f w s l f,s 1 τ v,s ) ϕ s v s w u l f,u 1 τ v,u ) ϕ u v u 28) where ϕ s, ϕ u > sand for he consan resource coss of opening a new skilled and unskilled vacancy respecively; and τ v,i refer o he vacancy subsidies. The employmen evoluion equaions in 27) imply ha profi maximisaion is ineremporal, since expendiure on posing vacancies oday will increase profis omorrow. Therefore, he objecive of he firm a ime period = is o maximise he presen value of is lifeime profis, which is given by: y f r k f wl s f,s 1 τ v,s ) ϕ s v s wl u f,u 1 τ v,u ) ϕ u v u + +E r 1 i {y f r k f w s l f,s 1 τ v,s ) ϕ s v s w u l f,u =1 i=1 1 τ v,u ) ϕ u v u } 29) where y f and y f are given by he CES producion funcion in 1) a ime and respecively. Since profis are reurned o he household, + 1 reurns are convered o presen value erms by he sochasic discoun facor from { he household s } opimisaion problem, 23). For i = s, u, he firm chooses k f, v, i l f,i +1 = o maximise 29) subjec o 27), aking facor prices {w, i r } = ; maching probabiliies {q} i = ; exogenous job separaion raes {γi } = ; economic policy { } τ v,i ; and iniial condiions for {lf,i = } as given. The variable, A is deermined by he following sochasic process: A +1 = A) 1 ρ A A ) ρ A e εa +1 3) where A > ; < ρ A < 1; and ε A +1 iidn [, σ A ) 2]. 13

14 2.5.2 Firs-order condiions The firm s problem is wrien in recursive form as: ) J l f,s, l f,u = max [y f k f r k f w s l f,s,vs,vu w u l f,u 1 τ v,u ) ϕ u v u ] + E r γ s ) l f,s +1Jq s v s +, q u v u + 1 γ u ) l f,u ) 1 τ v,s ) ϕ s v s 31) where J.) is he value funcion. The FOCs for k f, v s and v u are: r = 1 { ) α [ ) ν ) ν ] α } 1 α A θ l f,u + 1 θ) ρ k f + 1 ρ) l f,s α 1 ν 1 θ) α ν [ ) ν ρ k f + 1 ρ) l f,s ) 1 τ v,s ) ϕ s = E r +1q 1 s J l f,s l+1, f,s l f,u +1 ) 1 τ v,u ) ϕ u = E r +1q 1 u J l f,u l+1, f,s l f,u +1 ) ν ] α ν 1 ) ν 1 ρν k f mpl k 32) 33) 34) saing respecively ha he marginal cos of capial is equal o is marginal benefi and ha he marginal coss of creaing skilled and unskilled vacancies are equal o he expeced reurn of hiring one addiional skilled and unskilled worker nex period. The envelope condiion for skilled employmen, l f,s ) J l f,s l f,s, l f,u where mpl s = A {θ 1 θ) [ ρ k f = mpl s w s + 1 γ s ) E r 1 +1J l f,s ) α [ l f,u + 1 θ) ρ ) ν + 1 ρ) l f,s for he coninuaion value, r +1J 1 l f,s for v s in 33) his condiion becomes: J l f,s l f,s, l f,u ) ν k f + 1 ρ) ) ν ] α ν 1 1 ρ) is: l+1, f,s l f,u +1 l f,s ) 35) ) ν ] α } 1 α 1 ν ) ν 1. l f,s Afer subsiuing ) l+1, f,s l f,u +1, using he firs-order condiion ) = mpl s w s + 1 γ s) ϕs 1 τ v,s q s ). 36) Finally, o obain he FOC for he firm, we firs lead 36) by one period and subsiue i ino 33) o obain: [ 1 τ v,s ) ϕs = E r 1 q s +1 mpl+1 s w+1 s + ) 1 γ s ϕ s +1 1 τ v,s q +1) ] 37) +1 s 14

15 Working, similarly for unskilled employmen, we have: 1 τ v,u ) ϕu q u = E r 1 +1 where mpl u = A {θ l f,u [ mpl+1 u w+1 u + ) 1 γ u ϕ u +1 1 τ v,u q +1) ]. 38) +1 u ) α [ ) ν + 1 θ) ρ k f + 1 ρ) l f,s ) ν ] α } 1 α 1 ν ) α 1. θ l f,u These condiions equae he marginal cos of posing a job vacancy o he expeced discouned marginal benefi for skilled and unskilled jobs respecively. The benefi is comprised of wo elemens. Firs, he increase in profis associaed wih hiring an exra worker, mpl+1 u w+1, u and he saving associaed wih no having o pos a job vacancy in he nex period, ) 1 γ u ϕ u +1. q+1 u For i = s, u, he FOCs for he firm s problem{ are given by }27), 28), 32), 37) and 38), which deermine he pahs for l+1, f,i π f, k f, v i, given exogenous processes, {A, γ i } = ; variables ha are deermined a he aggregae level, {r, q} i =, or by wage bargaining {wi } = ; and iniial condiions for {l f,i }. 2.6 Wage Bargaining We assume ha once a worker/household member is mached wih a firm, he household and he firm bargain over he wage rae. The equilibrium wage is deermined by a Nash bargain. In paricular, he equilibrium wage rae maximises he Nash produc: = ) [Ṽe ] φ i [ ) ] 1 φ i i w i Jl f,i w i 39) where φ i measures he power of he household/worker relaive o he firm in he Nash bargain; Ṽe i wi ) is he value of a successful bargain a wage w i for he household and J l f,i w i ) is he value of a successful bargain a wage w i for he firm Household s valuaion of employmen The valuaion of he household for an addiional member being employed a wage w i is given by he envelope condiions of 2) for e s and e u respecively: V e s k, b, e s, e u ) = 1 τ s )ns w szs c n s ξ + 1 γ s p s ) 4) βe V e s k+1, b +1, e s +1, e+1) u 15

16 V e u k, b, e s, e u ) = 1 τ u )nu w uzu c n u ξ + 1 γ u p u ) 41) βe V e u k+1, b +1, e s +1, e+1) u. We nex consider he marginal value o a household of allowing a small number of is members, ɛ s >, o be paid an arbirary wage, w s, in period, assuming ha he wage revered o he equilibrium wage w s +1 from nex period. In hese circumsances he value funcion of household in equaion 2) becomes: V w s, ɛ s ) = max { ln r k A k k +1 b +1 + π + R b k +1,b +1 b τ s ) n s w s e s Z s + 1 τ s ) n s w s ɛ s Z s + 1 τ u ) n u w u e u Z u ) n s ξ e s + ɛ s ) n u ξe u } + βe V {k +1, b +1, [p s 1 e s ɛ s ) γ s ) e s + ɛ s )], [p u 1 e u ) + 1 γ u ) e u ]}. 42) Differeniaing V w s, ɛ s ) wih respec o ɛ s and evaluaing he derivaive a ɛ s = o derive he marginal value of a skilled worker employed a an arbirary wage, w s : V ɛ s w s, ) = 1 τ s )ns w szs c n s ξ + 1 γ s p s ) 43) βe V e s k+1, b +1, e s +1, e+1) u. If we combine he expression for Ṽe s ws ) V ɛ s w s, ) wih he envelope condiion for e s in equaion 4) we obain: Ṽ e s w s ) = 1 τ s ) n s c w s w s ) Z s + V e s k, b, e s, e u ). 44) Equivalenly, we can derive he marginal value of an unskilled worker employed a an arbirary wage, w u : Ṽ e u w u ) = 1 τ u ) n u Firm s valuaion of employmen c w u w u ) Z u + V e u k, b, e s, e u ). 45) We work similarly o obain he firm s valuaion of agreeing o employmen a a wage w. i Assume ha he firm pays a small fracion, ψ s >, of employed workers an arbirary wage w s a ime period, and ha he wage rae will reurn o he equilibrium wage w+1 s from he nex period. The value funcion of firm, 31) can be modified o: ) Ĵ w s, ψ s ) = max{y f v s r k f w s l f,s + w s ψ s 1 τ v,s ),vu ϕ s v s w u l f,u l s,f 1 τ v,u + ψ s )], [q u v u + 1 γ u ) l f,u ) ϕ u v u + E r +1J[q 1 s v s + 1 γ s ) ])} )

17 We differeniae Ĵ ws, ψ s ) wih respec o ψ s and evaluae i a ψ s = o ge he marginal profi of employing a skilled worker a w s : ) α ) ν Ĵ ψ s w s, ) = A {θ l f,u + 1 θ) [ρ k f + 1 ρ) ) ν [ ) l f,s α 1 ν ) ν ] α ] ν } α 1 1 θ) ρ k f + 1 ρ) l f,s ν 1 47) ) ν 1 ) 1 ρ) l f,s w s + 1 γ s ) E r +1J 1 l l f,s f,s +1, l f,u +1. We hen combine his wih he envelope condiion for l f,s in 36) o ge he marginal profi of employing a skilled worker a an arbirary wage, w s, a ime, and he equilibrium wage hereafer: J l f,s w s ) = w s w s + J l f,s l f,s ), l f,u 48) where J l f,s w s ) Ĵψ s w s, ). Similarly, we can derive he respecive condiion for unskilled workers: ) J l f,u w u ) = w u w u + J l f,u l f,s, l f,u. 49) Nash) equilibrium wage The firs-order condiion of he Nash bargain 39) wih respec o w s is: = φ s [Ṽe s w s )] φ s 1 [ Jl f,s w s ) + 1 φ s φs [ ) [Ṽe s w )] s Jl f,s w s ) ] 1 φ s Ṽ e s w s ) + w s ] φ s J f,s w l s) w s. 5) Subsiuing he derivaives of 44) and 48) wih respec o w s as well as he expressions for Ṽe s ws ) and J l f,s w s ) from 44) and 48) respecively ino 5) and evaluaing a w s = w s gives: φ s 1 τ s ) n s J c l f,s l f,s ), l f,u Z s = 1 φ s ) V e s k, b, e s, e u ). 51) Working as described in deail in Appendix A, we can derive he wage equaions A3) - A4), which can alernaively be wrien as: [ ] 1 τ s ) Z s w s = φ s {1 τ s ) Z s mpl s + 1 γ s ) ϕs 1 τ v,s q s ) ) 52) 1 γ s p s ) E 1 τ s +1 Z s +1 A k 1 τ v,s )} + 1 φ s ) ξc. ϕ s q s 17

18 1 τ u ) Z u w u = φ u {1 τ u ) Z u 1 γ u p u ) E 1 τ u +1 ) Z u +1 A k [ mpl u + 1 γ u ) ϕu ϕ u q u 1 τ v,u ] 1 τ v,u ) q u 53) )} + 1 φ u ) ξc ϕ i q i These equaions are generalisaions of wage equaions under Nash bargaining obained in he lieraure see e.g. Shimer 21)). For i = s, u, he reurn of an addiional worker o he household is given by 1 τ i ) Zw i, i i.e. he afer-ax effecive or produciviy-adjused) wage. In equilibrium, his is equal o a weighed average of he effecive [ marginal produc of labour ) ] under search and maching, i.e. 1 τ i ) Z i mpl i + 1 γ i ) ϕi q 1 τ v,i i ) 1 τ v,i, and he marginal rae of sub- ) 1 γ i p i ) E 1 τ i +1 Z i +1 A k siuion beween consumpion and leisure, MRS i, i.e. ξc, wih he weighs given by he bargaining power of he worker. The MRS i follows he common definiion of he raio of he marginal uiliy of leisure, ξ, over he marginal uiliy of consumpion, 1/c. The effecive marginal produc of labour measures he addiional afer-ax produciviy-adjused oupu generaed by moving a worker from unemploymen o employmen. I is comprised of i) he direc afer-ax increase in oupu provided by an addiional skilled worker, mpl; i ii) he addiional savings in erms of resources ha would be ) required o pos a vacancy if he mached job survives, 1 γ i ) ϕi q 1 τ v,i i, where 1 γ i ) is he probabiliy ha a worker will remain in place in he 1 τ v,i nex period and ϕi q i duraion ha he job needs o be posed, 1 q i ) is he cos per job posing muliplied by he ; 7 iii) he increase in job-posing coss for he firm implied by he decrease in fuure successful ) maches due o ) he increase in employmen, 1 γ i p i ) E 1 τ i +1 Z i +1 A k ϕ i q 1 τ v,i i. Noe ha an increase in curren employmen increases fuure unemploymen and hus he requiremen for he firm o pos a vacancy o fill he los job) by s +1 e = 1 γ i p i ), because here is reducion in he number of workers who search for jobs. Furhermore, noe ha hese coss need o be discouned by he price of ransferring resources beween periods, A k, which equals, from 23), expeced fuure reurns o invesmen discouned by he sochasic discoun facor. The above wage equaions hold when here is no OJL and under purely exernal OJL. If we employ he alernaive OJL mechanism which inernalises own employmen on labour produciviy, he righ hand side of he 7 Noe ha from 37) - 38), ϕi q i firm from posing a job. 1 τ v,i ) is also equal o he expeced benefi o he 18

19 above equaions respecively are muliplied by he erm: ) ) 1 φ i Z i φ i + e i Z i 1 e + i, i = s, u where Zs e s Z i = ζ s Ω s e s ) ζs 1 e u ) 1 ζs ; and Zu e u = 1 ζ u ) Ω u e s ) ζu e u ). These exra erms: i) collapse o uniy under exernal OJL, i.e. when Zi = ; e i ii) are less han one, 8 implying ha inernalising OJL creaes a channel ha ends o reduce he Nash bargained wage, relaive o he cases of no or exernal OJL. When he workers inernalise he effec of employmen on heir produciviy and hus on heir reurns, hey are willing o work for a lower wage rae. 2.7 Governmen budge and marke clearing The governmen budge consrain is: g + τ v,s ϕ s v s + τ v,u ϕ u v u + Rb b = = b +1 + τ k r δ) k + τ s n s w s e s Z s + τ u n u w u e u Z u 54) where g is he per-capia governmen consumpion. The capial markes clear when he supply is equal o he demand for capial per capia: k = k f. 55) In he skilled and unskilled labour markes, he equaliy of per capia labour supply and demand is given by: n s e s Z s = l f,s 56) and n u e u Z u = l f,u. 57) Moreover, dividends paid o he household mus equal profis: π = π f. 58) Finally, in he goods markes, he economy s per capia resource consrain is saisfied: y f = c + A k k +1 A k 1 δ) k + g + ϕ s v s + ϕ u v u. 59) 8 To see his, firs noe ha Z ) Z i +ei Z i e i Z i > 1, since e i Z i e i >. Then, noe ha φ i + 1 φ i) Z > 1 φ i + Z φ i Z 1 > ) ) [ Z 1 φ i Z 1 > 1 > φ i, which is rue. Hence, φ i + 1 φ i) 1 Z] < 1. 19

20 2.8 Decenralized equilibrium Given he pahs of he exogenous variables { } A, A k, γ s, γ u and iniial = condiions for {k, b, e s, e u }, a decenralized equilibrium is defined as a series of prices, { w s, w u, r, r} b, maching probabiliies, = {ps, p u, q s, q u } { } = and allocaions, c, π, k +1, b +1, e s +1, e u +1, π f, k f, v s, v u, l+1, f,s l f,u +1, such ha = i) households and firms underake heir respecive opimizaion problems, aking aggregae oucomes and economic policy as given, under search and maching in he labour marke as oulined above; ii) wage raes for boh ypes of labour are deermined by a Nash bargain for mached household members and firms; iii) all budge consrains are saisfied; and iv) all markes clear. Finally noe ha in equilibrium, we have e s = e s and e u = e u. Using Walras law we drop he household s budge consrain, so ha he DE consiss of he following equaions: i) he search and vacancy maching probabiliies in 5) and 6); ii) he consumpion and bonds Euler equaions 23) and 26); iii) he firm s opimaliy condiions given by 27) for i = s, u), 28), 32), 37) and 38); iv) he wage equaions A3) and A4); and v) he marke clearing condiions in 55), 56), 57), 58) and 59). 9 3 Quaniaive implemenaion In he following secion we firs discuss he model calibraion followed by he quaniaive predicions of he model regarding he seady-sae and near seady-sae dynamics. We consider hree model varians, depending on he assumpions we make regarding he labour produciviy echnology, as capured by Z i, for i = s, u. In paricular, since we wan o conexualise he poenial imporance of OJL, we firs consider a benchmark case wihou i, so ha Z i = Ω i = 1. We hen choose Ω i in he cases of OJL ha we consider where he employmen effecs are purely exernal, OJL x, and where he own effec is inernalised, OJL n ) so ha he level of labour produciviy in he seady-sae, Z i, is he same across all hree model varians. This furher implies ha he models wihou OJL and OJL x have idenical seady-saes, whereas OJL n is re-calibraed following he same sraegy as he oher wo models so ha is seady-sae is effecively he same. 9 Noe ha when he marke clearing condiions 56) and 57) and he maching probabiliies in equaions 5) and 6) are imposed on he employmen evoluion equaions 17) and 27) he laer become idenical. Hence, we drop he employmen evoluion equaions 17) from he household s problem from he DE. 2

21 3.1 Model Calibraion Table 1 repors he values for he srucural parameers of he model based on a quarerly calibraion. 1 The able indicaes how each parameer is obained by referring o various sources. This includes calculaions using: i) he daa; ii) esimaes and assumpions from oher sudies in he lieraure; and iii) calibraion o arge seady-sae values for he relevan endogenous variables of he model. As explained above, hese refer o he model varians wihou and wih purely exernal OJL. We summarise a he end is his sub-secion he changes in parameers required for he OJL n model. Table 1: Model Parameers Parameer Value Definiion Source < n s < 1.45 populaion share of skilled workers daa τ k < 1.36 ax rae on capial income esimae τ s < 1.35 ax rae on skilled labour income esimae τ u < 1.25 ax rae on unskilled labour income esimae g >.425 per-capia governmen consumpion calibraion < β < 1.99 ime discoun facor calibraion δ 1.22 depreciaion rae of capial sock calibraion capial o skilled labour elasiciy esimae 1 ν capial o unskilled labour elasiciy esimae 1 α < θ < share of composie inpu o oupu calibraion < ρ < 1.82 share of capial o composie inpu calibraion ξ >.1 disuiliy cos of employmen calibraion < γ s < 1.28 skilled job separaion rae calibraion < γ u < 1.45 unskilled job separaion rae calibraion < η s < 1.6 elasiciy of skilled search assumpion < η u < 1.5 elasiciy of unskilled search assumpion < φ s < 1.6 bargaining power of skilled workers assumpion < φ u < 1.5 bargaining power of unskilled workers assumpion ϕ s >.9 uni cos of posing skilled job calibraion ϕ u >.82 uni cos of posing unskilled job calibraion < τ v,s, τ v,u < 1.1 job vacancy subsidy assumpion χ s >.8 skilled maching effi ciency calibraion χ u >.6 unskilled maching effi ciency calibraion < ζ s, ζ u < 1.5 elasiciy of learning assumpion 1 Noe ha, where possible, we follow Shimer 21, see Appendix A) in he choice of ime period ). Noe however, ha he secoral daa employed below are only available from 1992:1-211:4. 21

22 3.1.1 Populaion shares, policy, discoun and depreciaion raes We use daa from Acemoglu and Auor 211) for he period ) o calculae he populaion share of skilled workers, n s =.45. Consisen wih he range used in he lieraure, he ime discoun facor, β =.99, is se o give an annual reurn o capial, ne of depreciaion, of abou 4%. Similarly he depreciaion rae, δ =.22, is calibraed o arge a quarerly seady-sae capial o oupu raio of abou 8 which on an annual basis is consisen wih a raio of around 2. Following Uhlig 21) we se he ax rae on capial income o 36%. Moreover, we choose he wo labour income ax raes o be τ s = 35% and τ u = 25%, which imply a weighed average close o he 28% labour income ax rae used in Uhlig 21). The level of governmen spending is se so ha he deb o oupu raio is.63 or in quarerly erms 2.52 as in Uhlig 21)) Producion The elasiciies of subsiuion beween skilled labour and capial and beween unskilled labour and capial have been esimaed by Krusell e al. 2). We use heir esimaes, so ha ν =.495 and α =.41. To ensure he skill premium and labour share in income are consisen wih he daa, θ and ρ respecively are calibraed o.493 and.82 see, e.g. Lindquis 24), He and Liu 28), Pourpourides 211) and He 212) who use a similar approach o calibraing he producion funcion). The arge value for he skill premium of approximaely 1.68 is obained from Acemoglu and Auor 211) for he period ). We measure he labour income share using daa from Naional Income and Produc Accouns Table 1.1, , which gives a value of approximaely.66. Finally, he parameers capuring seady-sae TFP and invesmen-specific echnical change, i.e. A and A k are normalised o uniy Uiliy funcion and job separaion raes Following Shimer 21) we se he disuiliy of employmen parameer, ξ =.1, o imply an aggregae unemploymen rae of abou 5%. Also noe, ha Shimer 25) repors ha an average employmen exi probabiliy of.34. Given his and he assumpion ha skilled labour has a lower job separaion rae see, e.g. Fallick and Fleischman 24), Hagedorn e al. 21), and Pilossoph 212)) we se he job separaion raes, γ s =.28 and γ u =.45, o approximaely mach he secoral unemploymen raes of 22

23 3% and 7% respecively New maches and bargaining power The values used for he elasiciies of new maches wih respec o search ime, η s =.6 and η u =.5, are wihin he range of economeric evidence repored in Perongolo and Pissarides 21). To ensure ha he Hosios 199) condiion is saisfied we se he relaive bargaining power of worker in he skilled and unskilled secors respecively o φ s =.6 and φ u =.5 see, Cahuc e al. 26) who find ha skilled workers have higher bargaining power) Job posing coss and subsidy Pissarides 1994), Acemoglu 21) and Krause and Lubik 26 and 21) sugges ha he flow cos of posing a vacancy is higher in good jobs. Following hese sudies, we assume ha he job posing for skilled is greaer han ha for unskilled labour, i.e. ϕ s > ϕ u. These parameers are calibraed o ensure aggregae job coss as a share of GDP of abou 2.5% which coheres wih Arseneau and Chugh 212) and aggregae labour marke ighness of abou uniy which is he value used in Pissarides 1998) and Campolmi and Gnocchi 214). Also following Campolmi e al. 211) we se he vacancy subsidy rae o 1% Maching effi ciency and OJL Consisen wih an aggregae unemploymen rae of 5% and an average employmen exi probabiliy of.34, Shimer 21, see p. 67) implies a job finding probabiliy abou.65. Following his approach for each labour marke gives us arge probabiliies of p s =.828 and p u =.591 which we obain by calibraing χ s =.8 and χ u =.6. The finding probabiliies in urn imply unemploymen duraions of abou 1.21 and 1.69 quarers for skilled and unskilled respecively. The calibraion also suggess ha he job filling rae is higher for he skilled versus he unskilled consisen wih Krause and Lubik 26 and 21). As explained above, we presen he models resuls below boh wihou and wih learning. In he former, Z s = Z u = 1 in 1-11). In boh forms of laer i.e. OJL x and OJL n ) we se he exponens ζ s = ζ u =.5 and calibrae Ω s and Ω u so ha in he seady-sae 11 The secoral employmen and unemploymen daa are from he monhly Labor Force Saisics, Curren Populaion Survey for period 1992:1-211:4). I repors daa for civilian non-insiuional populaion 25 years and over by educaional aainmen. Skilled workers are hose wih a Bachelor s degree and higher. 23

24 he Z funcions are equal o uniy as under no learning. This requires ha Ω s = Ω u = Seady-sae The seady-sae implied by he above calibraion is repored in Table 2 for he models wihou and wih purely exernal learning. These resuls show ha grea raios are well in line wih he U.S. daa. Moreover, he remaining values cohere wih he arges discussed in he calibraion above. For he hird model varian, he resuls are quaniaively similar. To ensure ha he model under OJL n implies an analogous seady-sae wih he remaining wo model-varians, we re-calibrae θ =.5, ϕ s = 1.6, ϕ u = 1.52, and g =.41, following he same calibraion sraegy oulined above. Noe ha as discussed in Secion 2.6.3, when workers inernalise OJL, bargained wages end o be lower and hus unemploymen lower. Therefore, o mainain he same level of unemploymen and labour marke ighness in he seady-sae, job-posing coss need o increase. c y k y g y Table 2: Seady-sae b y we y v s s s u s y w s w u r r b z s z u p s p u q s q u Sochasic processes When underaking he model simulaions we draw he four processes discussed above from a mulivariae normal disribuion, denoed x = N x, Σ, ) where x = [ε A, ε Ak, ε gs, ε gu ], x is he vecor of means and Σ is he variancecovariance marix of shocks. The parameers of sochasic processes driving he model are repored in Table 3. The auocorrelaion parameer of TFP is se equal o.95, following Gerler and Trigari 29), and Arseneau and Chugh 212). As in he lieraure, he volailiy parameer, σ A, is calibraed o mach he sandard deviaion of HP-filered oupu,.11. Re- 12 Given he lack of daa for exponens in he learning funcions, we experimen wih some alernaive combinaions. For example, we place more weigh on he own-elasiciy for he skilled, i.e. ζ s =.8 and 1 ζ s ) =.2 while a he same ime keeping weigh of he own-elasiciy for he unskilled: i) he same, ζ u =.5 and 1 ζ u ) =.5; ii) higher, ζ u =.8 and 1 ζ u ) =.2; and iii) lower, ζ u =.2 and 1 ζ u ) =.8. We find ha he resuls repored below, including seady-sae, second-momens, impulse responses and fiscal mulipliers, are robus hese o alernaive parameerisaions. This applies o boh he OJL x and OJL n seups. 24

25 garding invesmen-specific echnical change, we use he esimaes from Pourpourides 211), which implies seing ρ A k, o.615 and σ A k, o.47. Given he lack of secoral daa for he job separaion raes, we apply he same quarerly auocorrelaion, ρ γ s and ρ γu, and sandard deviaion, σ γ s and σ γ u, parameers for skilled and unskilled using daa from he Job Openings and Labor Turnover Survey JOLTS) for he period 21Q1-214Q2. Finally, he correlaion beween job separaion shocks, corε gs, ε gu ), is calibraed o mach he correlaion beween HP-filered skilled and unskilled employmen/unemploymen raes in he daa. 13 Table 3: Sochasic processes Parameer Value Definiion Source σ A.8 SD of TFP calibraion ρ A.95 AR1) coeffi cien of TFP assumpion σ A k.47 SD of IT esimae ρ A k.615 AR1) coeffi cien of IT esimae σ γ s.73 SD of skilled separaion rae daa ρ γ s.74 AR1) coef. of skilled separaion rae daa σ γ u.73 SD of unskilled separaion rae daa ρ γ u.74 AR1) coef. of unskilled separaion rae daa corε gs, εgu ).98 Job separaion rae shock correlaion calibraion 3.4 Soluion and second momens Following Shimer 21), we presen resuls under shocks o TFP and he job separaion raes bu we also consider invesmen-specific echnological change, given he imporance aached o skill-biased echnical change in explaining he behaviour of he skill premium in he lieraure. The resuls for he secoral variables discussed in he Inroducion are presened in Table 4. To obain hese resuls we firs solve a firs-order approximaion of he dynamic sysem of equaions characerising he DE around he seady-sae, by implemening he perurbaion mehods in Schmi-Grohé and Uribe 24). We hen simulae ime pahs under shocks o oal facor produciviy, he job separaion raes and invesmen-specific echnological change, as indicaed. We conduc 1, simulaions of 8 periods i.e. 1992Q1-211Q4) o mach he secoral employmen and unemploymen daa and 1 periods i.e. 1979Q1-23Q4) o mach he skill premium daa, iniialised from he seady-sae in Table 2. For each simulaion, we HP-filer he logged series and hen compue he required momens and repor he means of hese 13 Noe ha no allowing for his correlaion only affecs his arge. 25