DOCUMENTOS DE TRABAJO


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1 DOCUMENTOS DE TRABAJO Calvo Wages Vs. Search Fricions: a Horse Race in a DSGE Model of a Small Open Economy Markus Kirchner Rodrigo Tranamil N.º 778 Febrero 216 BANCO CENTRAL DE CHILE
2 DOCUMENTOS DE TRABAJO Calvo Wages Vs. Search Fricions: a Horse Race in a DSGE Model of a Small Open Economy Markus Kirchner Rodrigo Tranamil N.º 778 Febrero 216 BANCO CENTRAL DE CHILE
3 BANCO CENTRAL DE CHILE CENTRAL BANK OF CHILE La serie Documenos de Trabajo es una publicación del Banco Cenral de Chile que divulga los rabajos de invesigación económica realizados por profesionales de esa insiución o encargados por ella a erceros. El objeivo de la serie es aporar al debae emas relevanes y presenar nuevos enfoques en el análisis de los mismos. La difusión de los Documenos de Trabajo sólo inena faciliar el inercambio de ideas y dar a conocer invesigaciones, con carácer preliminar, para su discusión y comenarios. La publicación de los Documenos de Trabajo no esá sujea a la aprobación previa de los miembros del Consejo del Banco Cenral de Chile. Tano el conenido de los Documenos de Trabajo como ambién los análisis y conclusiones que de ellos se deriven, son de exclusiva responsabilidad de su o sus auores y no reflejan necesariamene la opinión del Banco Cenral de Chile o de sus Consejeros. The Working Papers series of he Cenral Bank of Chile disseminaes economic research conduced by Cenral Bank saff or hird paries under he sponsorship of he Bank. The purpose of he series is o conribue o he discussion of relevan issues and develop new analyical or empirical approaches in heir analyses. The only aim of he Working Papers is o disseminae preliminary research for is discussion and commens. Publicaion of Working Papers is no subjec o previous approval by he members of he Board of he Cenral Bank. The views and conclusions presened in he papers are exclusively hose of he auhor(s) and do no necessarily reflec he posiion of he Cenral Bank of Chile or of he Board members. Documenos de Trabajo del Banco Cenral de Chile Working Papers of he Cenral Bank of Chile Agusinas 118, Saniago, Chile Teléfono: (562) ; Fax: (562)
4 Documeno de Trabajo N 778 Working Paper N 778 CALVO WAGES VS. SEARCH FRICTIONS: A HORSE RACE IN A DSGE MODEL OF A SMALL OPEN ECONOMY Markus Kirchner Banco Cenral de Chile Rodrigo Tranamil Banco Cenral de Chile Absrac Mos exising DSGE models used for moneary policy analysis and forecasing assume ha he labor marke always clears a a sicky nominal wage (`a la Calvo) hrough variaions along he inensive margin of labor supply (i.e. hours), wih no role for he exensive margin (i.e. employmen). The laer conrass wih research on he macroeconomics of labor markes ha has emphasized he relevance of he exensive margin and employmen flucuaions using search and maching heory. Agains his background, in his paper we conduc a horse race of a labor marke specificaion wih Calvo wages versus a search and maching specificaion wih endogenous separaions in an oherwise sandard New Keynesian small open economy model, esimaed wih Chilean daa. We conclude ha he search and maching specificaion wins by a wide margin as i significanly improves he model s abiliy o explain and predic boh labor marke daa and oher macroeconomic variables. Resumen La mayoría de los modelos DSGE que se uilizan para el análisis de la políica monearia y proyecciones macroeconómicas asumen que el mercado laboral iende a equilibrio con un salario nominal rígido (a la Calvo) a ravés de variaciones del margen inensivo de la ofera laboral (horas rabajadas), sin ningún rol para el margen exensivo (empleo). Eso úlimo conrasa con esudios sobre la macroeconomía del mercado laboral los cuales han hecho hincapié de la relevancia de las flucuaciones del empleo uilizando la eoría de búsqueda y emparejamieno. En ese conexo, el presene rabajo hace compeir dos ipos de fricciones en el mercado laboral: salarios rígidos a la Calvo frene a búsqueda y emparejamieno con separaciones endógenas, en un modelo neo Keynesiano esándar para economías pequeñas y abieras que se esima con daos de Chile. Se concluye que la especificación usando fricciones de búsqueda se desempeña significaivamene mejor en érminos de la capacidad del modelo para explicar y predecir ano los daos del mercado laboral y oras variables macroeconómicas. We would like o hank Javier GarcíaCicco, Elías Albagli, Albero Naudon and seminar paricipans a he Cenral Bank of Chile for useful commens. The views expressed are hose of he auhors and do no necessarily represen official posiions of he Cenral Bank of Chile or is Board members. s: y
5 1 Inroducion Calvoype wage sickiness remains he dominan labor marke fricion in New Keynesian dynamic sochasic general equilibrium (DSGE) models used for policy analysis and forecasing a cenral banks and oher policy insiuions. 1 Under monopolisic wage seing à la Calvo, he labor marke always clears a he sicky nominal wage hrough variaions of labor inpu along he inensive margin (i.e. hours per worker), bu here is no role for adjusmens along he exensive margin (i.e. employmen). The laer sands in sark conras o academic research ha has emphasized he role of labor marke flows based on search and maching heory. According o ha lieraure, search fricions and maching can successfully explain several relevan labor marke facs such as he exisence of involunary unemploymen and he dynamics of job creaion and job desrucion (see Pissarides, 211). 2 Some of ha disconnec beween labor marke research and labor marke specificaions in pracical policy models may be due o he fac ha he usefulness of search fricions in mediumscale quaniaive DSGE models for moneary policy analysis and forecasing is no ye sufficienly well undersood. Hence, in his paper we le search fricions compee wih Calvo wages in a DSGE framework. In paricular, we assess wheher and how he inclusion of a search and maching specificaion à la Diamond (1982), Morensen (1982) and Pissarides (1985) wih boh margins of labor supply and endogenous separaions following Morensen and Pissarides (1994), Cooley and Quadrini (1999) and den Haan, Ramey, and Wason (2) improves he empirical fi and forecasing performance of an oherwise sandard New Keynesian small open economy (NKSOE) model. The analysis is conduced using Bayesian echniques and Chilean daa. While our paper forms par of several recen sudies ha have invesigaed he usefulness of labor marke search and maching in macroeconomic models, as we discuss below, we are among he firs o analyze he benefis of search fricions in a small open economy conex. In addiion, only few relaed sudies have examined he relevance of endogenous separaions wih boh margins of labor supply in esimaed DSGE models. As we show, he laer has several relevan implicaions for he dynamics of our model. The shorcomings of labor marke specificaions in sandard DSGE models, boh for closed and open economies, become clear from a brief review. In paricular, exogenous labor marke 1 Examples of DSGE models used a cenral banks and oher policy insiuions ha incorporae Calvoype wage sickiness or some oher form of wage sickiness ha gives rise o a wage Phillips curve, e.g. due o wage adjusmen coss à la Roemberg, are discussed in Brubakk and Sveen (29), Burgess e al. (213), Chung, Kiley, and Lafore (21), de Casro, Gouvea, Minella, dos Sanos, and SouzaSobrinho (211), Del Negro e al. (213), Dorich, Johnson, Mendes, Murchison, and Zhang (213), Erceg, Guerrieri, and Gus (26), González, Mahadeva, Prada, and Rodríguez (211), Lees (29), Medina and Soo (27), Rao, Roeger, and in Veld (29), Schorfheide, Sill, and Kryshko (21), and Smes, Chrisoffel, Coenen, Moo, and Rosagno (21). 2 See also Krause and Lubik (214). 1
6 shocks are ypically found o be imporan drivers of aggregae dynamics in hose models: in he Smes and Wouers (23) euro area model, labor supply preference shocks are he mos imporan drivers of oupu while wage markup shocks are responsible for he bulk of variaions in real wages; whereas in he Smes and Wouers (27) U.S. model where here is no separae labor supply shock, wage markup shocks accoun for mos of medium o longerm flucuaions in oupu and inflaion. In Adolfson, Laséen, Lindé, and Villani s (27) NKSOE model, labor supply shocks are also among he mos imporan shocks o explain oupu, wage and inflaion dynamics in Sweden. The fac ha exogenous labor marke shocks are so imporan in sandard DSGE models seems unsaisfacory, no only because heir underlying deeper deerminans are hard o idenify, bu also because one migh expec ha labor marke oucomes are o a large exen consequences of more srucural shocks such as moneary or fiscal policy shocks or, in open economies, foreign shocks (i.e. shocks o foreign ineres raes, foreign demand, commodiy prices, ec.). In addiion, all of he above models rely on relaively large real wage elasiciies of individual hours worked o mach flucuaions in oal hours, which is known o be a odds wih micro evidence (see Chey, Guren, Manoli, and Weber, 211). Due o he above shorcomings, recen model developmens using search and maching heory have aemped o improve labor marke specificaions and generae sronger endogenous propagaion properies of DSGE models. For insance, Chrisiano, Traband, and Walenin (211) describe he labor marke in an NKSOE model using a search and maching framework wih variaions on boh margins of labor supply. 3 Their esimaion resuls for Swedish daa show ha he labor supply shock becomes unimporan in explaining oupu, he esimaed elasiciy of individual hours is relaively low, and no wage markup shock is needed. However, he labor supply shock is sill he mos imporan shock for boh oal hours and real wages, and basic foreign shocks are relaively unimporan for aggregae dynamics. 4 An earlier sudy by Krause, LopezSalido, and Lubik (28) based on a closed economy model wih search and maching esimaed wih U.S. daa also found a relaively low elasiciy of individual hours and a small role for labor supply shocks. However, in his model price markup and (ad hoc) mach efficiency shocks are he dominan force in labor marke flucuaions. 5 Par of he failure of his model o explain he flucuaions of boh labor marke variables and oher macroeconomic variables such as oupu and inflaion hrough more srucural shocks may be due o he absence of endogenous separaions, in line wih he resuls of Sedláçek (214). Indeed, many sudies 3 See also Adolfson, Laséen, Chrisiano, Traband, and Walenin (213). 4 This is relaed o he problem ha NKSOE models end o have difficulies in accouning for he subsanial influence of foreign shocks idenified in many ime series sudies (see Jusiniano and Preson, 21). 5 Similar resuls were obained by Alberini, Kamber, and Kirker (212) in a New Keynesian small open economy model esimaed wih daa for New Zealand. 2
7 have found ha endogenous separaions are imporan for undersanding labor marke flows and heir ineracion wih oupu and inflaion (e.g. Trigari, 29). 6 Hence, he success of search fricions in quaniaive DSGE models has so far been mixed. Our resuls shed some addiional ligh on his issue. In paricular, we find ha he daa srongly favors he model wih search fricions over he model wih Calvo wages, as refleced by a significanly higher marginal daa densiy (especially when labor marke daa and oher macroeconomic variables are o be explained joinly), as well as a significanly beer abiliy of he model wih search fricions o mach he majoriy of he second momens of he observed daa. The forecasing performance of he model for labor marke variables as well as oher key variables such as oupu and inflaion is also significanly improved by he search fricions. Our paper herefore provides furher evidence ha search fricions are useful o explain aggregae dynamics in quaniaive DSGE models for small open economies. The res of he paper is organized as follows. Secion 2 presens our NKSOE model wih search fricions and maching, while he varian of he model wih Calvo wages is described in Secion 3. 7 Secion 4 describes he calibraion and esimaion sraegy, while Secion 5 compares he fi of he model under he wo labor marke fricions, discusses he role of search fricions in amplifying and propagaing various ypes of shocks, and provides an analysis of he forecasing performance of he differen models. Finally, secion 6 concludes. 2 An NKSOE Model wih Search and Maching This secion presens our NKSOE model wih nominal and real rigidiies, and search and maching à la Diamond (1982), Morensen (1982) and Pissarides (1985) wih endogenous separaions in he labor marke, following Cooley and Quadrini(1999) and den Haan e al. (2). Thecore model shares he srucure of he baseline NKSOE model presened in GarcíaCicco, Kirchner, andjusel(215). 8 Domesic goodsareproducedwihcapial andlabor, hereishabiformaion in consumpion, here are adjusmen coss in invesmen, firms face a Calvopricing problem wih parial indexaion, and here is imperfec exchange rae passhrough ino impor prices in he shor run due o local currency price sickiness. The economy also expors an exogenous endowmen of a commodiy good, which capures he imporance of commodiy expors in many small open economies including Chile. The economy is subjec o shocks o preferences, mach 6 A few recen sudies have invesigaed he implicaions of search fricions in an emerging marke conex, including Boz, Durdu, and Li (215) and Medina and Naudon (212). However, hese sudies are based on calibraed models ha absrac from nominal rigidiies as well as he inensive margin and endogenous separaions, unlike in our paper. 7 The equilibrium condiions and he sraegy for he seady sae for boh models are provided in he appendix. 8 The model is a shrinkeddown version of he Medina and Soo (27) model used for policy analysis and forecasing a he Cenral Bank of Chile. 3
8 efficiency, echnology (neural and invesmenspecific), commodiy producion, governmen expendiures, moneary policy, foreign demand, foreign inflaion, foreign ineres raes and he inernaional price of he commodiy good. 2.1 Households There is a coninuum of infiniely lived households normalized o one wih idenical asse endowmens and idenical preferences. Household members can be eiher employed or unemployed. All members pool heir asses so as o ensure equal consumpion, ha is, here is perfec insurance of unemploymen risk. Each member has he following separable uiliy funcion wih habi formaion: 9 u(c,č 1) g(h ) = 1 [ (C ] 1 σ ςč 1) 1 A 1 σ 1 σ 1 κ h 1+φ 1+φ, where C is individual consumpion of a final good, Č is aggregae consumpion, h is hours per worker, κ is an exogenous shock o he disuiliy of labor supply, and A is an economywide sochasic rend (see below). 1,11 The parameers σ, φ and ς are he inverse elasiciy of ineremporal subsiuion, he inverse Frisch elasiciy of hours worked, and he degree of habi formaion, respecively. The welfare funcion of a represenaive household over ime is hen given by 12 E β s +s [ ( u C+s,Č+s 1) n+s g(h +s ) ], (1) s= where β (,1) is he ineremporal discoun facor, is an exogenous preference shock and n is he number of employed household members. Noe ha, in equilibrium, C = Č for all. Households save and borrow by purchasing domesic currency denominaed governmen bonds(b )andby radingforeign currencybonds(b ) wih foreign agens, bohbeingnonsae coningen asses. They also purchase an invesmen good (I ) which deermines nex period s physical capial sock (K ). Le r, r and r K denoe he gross real reurns on B 1, B 1 and K, respecively. The employed members earn a real wage of W per hour, while unemployed 9 Throughou, uppercase leers denoe variables conaining a uni roo in equilibrium (eiher due o echnology or o longrun inflaion) while lowercase leers indicae variables wih no uni roo. Real variables are consruced using he domesic consumpion good as he numeraire. In he appendix we describe how each variable is ransformed o achieve saionariy in equilibrium. Variables wihou ime subscrip denoe nonsochasic seady sae values in he saionary model. 1 We assume exernal habi formaion insead of inernal habi formaion as in GarcíaCicco, Kirchner, and Jusel (215) o simplify he analysis. 11 The disuiliy of work is muliplied by A 1 σ 1 o mainain a balanced seadysae growh pah. 12 Under separable preferences and exernal habi formaion, (1) resuls from he general specificaion E [ ( ) s= βs +s n+su C ( )] +s,č+s 1 n n+sg(h +s)+(1 n +s)u C +s,č+s 1 u since, in equilibrium, C n = C u for all. 4
9 members earn an amoun b u of unemploymen benefis, which is paid ou by he governmen. 13 Le rer be he real exchange rae (i.e. he price of foreign consumpion goods in erms of domesic consumpion goods), le T denoe real lumpsum ax paymens o he governmen and le Σ collec real dividend income from he ownership of firms. The periodbyperiod budge consrain of he household is hen given by C +I +B +rer B +T = W h n +(1 n )b u +r B 1 +rer r B 1 +r K K 1 +Σ. (2) The physical capial sock evolves according o he law of moion: K = (1 δ)k 1 +[1 Γ(I /I 1 )] I, δ (,1], (3) where I denoes invesmen expendiures and ( ) I Γ = γ ( ) 2 I ā, γ, ā 1, I 1 2 I 1 are convex invesmen adjusmen coss. The variable is an invesmen shock ha capures changes in he efficiency of he invesmen process. 14 The household chooses C, I, K, B, and B o maximize (1) subjec o (2)(3), aking W, h, n, r, r, r K, rer, T, Σ, B 1, B 1 and K 1 as given. The household s labor supply choice (h and n ) is deermined as he oucome of a bargaining process over hours and wages (see below). The nominal ineres raes are implicily defined as r = R 1 π 1, r = R 1ξ 1 (π ) 1, where π = P /P 1 and π = P /P 1 denoe he gross inflaion raes of he domesic and foreign consumpionbased price indices P and P, respecively. The variable ξ 1 denoes a counry premium given by (see SchmiGrohé and Uribe, 23): ξ = [ ψ ξexp rer B/A 1 rer b rer b + ζo ζ o ζ o + ζu ζ u ] ζ u, ψ >, ξ 1, where ζ o and ζ u are exogenous shocks o he counry premium, where we assume ha ζ o is observable while ζ u is unobservable. The foreign nominal ineres rae R whereas he domesic cenral bank ses R. evolves exogenously, 13 We allow unemploymen benefis o grow proporionaely wih A 1 in order o mainain a balanced seadysae growh pah. Then, b u = ba 1 wih b. 14 See Greenwood, Hercowiz, and Krusell (1997) and Jusiniano, Primiceri, and Tambaloi (211). 5
10 2.2 Labor Marke Labor Marke Flows The labor marke is subjec o DiamondMorensenPissaridesype search fricions and maching. In order o form new employmen relaionships (maches), workers mus search and firms mus pos vacancies. We assume ha all unemployed workers look for jobs. The number of maches in period is given by he maching funcion M = m v 1 µ (u s )µ, where u s is he number of searching workers, v is he number of vacancies posed, m is an exogenous mach efficiency parameer and µ (,1) is he mach elasiciy. The iming of he model is as follows. 15 A he beginningof each period, before new maches are formed, a fracion ρ x of exising maches erminae for exogenous reasons. Then, maching akes place. The jobs ha do no separae exogenously and new maches may separae endogenously, before producion sars, if he firm s operaing cos c is greaer han an endogenously deermined hreshold c. 16 This operaing cos is assumed o be i.i.d. across firms and ime wih c.d.f. F( ). The endogenous separaion rae is herefore ρ n = Pr( c > c ) = 1 F(c ), implying he job desrucion or oal separaion rae ρ = ρ x +(1 ρ x )ρ n. The evoluion of aggregae employmen is hen given by n = (1 ρ )n 1 +(1 ρ n )M, and he number of unemployed workers a he end of period is u = 1 n. This is differen from he number of searching workers which is given by u s = u 1 + ρ n 1. The probabiliy ha a searching worker is mached o a new job is hen s = (1 ρ n )M /u s, while he probabiliy ha a firm fills a vacancy is e = (1 ρ n )M /v Bargaining over Wages and Hours Real wages and hours per worker are deermined hrough Nash bargaining. On he firm side, he value of an open vacancy V V is given by an exogenous vacancy posing cos ω, plus he value of filling he vacancy wih probabiliy e condiional on having he job no severed endogenously or, oherwise, he discouned coninuaion value of an open vacancy in he nex period: V V = ω +e c V J ( c ) df( c ) F(c ) +(1 e )E Ξ,+1 V V +1, (4) whereξ,+1 is he firm s sochasic discoun facor for real payoffs. 17 The value of a filled job V J given a draw c is equal o he firm s currenperiod profi generaed by he worker (i.e. revenue 15 Our iming assumpions are such ha employmen may adjus insananeously along all relevan margins, as in Chrisoffel e al. (29). 16 We assume addiive idiosyncraic operaing coss as in Cooley and Quadrini (1999) o avoid excessive crosssecional heerogeneiy in hours per worker, which would resul from a specificaion as in den Haan e al. (2) wih a muliplicaive idiosyncraic produciviy shock in he producion funcion. 17 As he firms are owned by he households, he sochasic discoun facor saisfies Ξ,+s β s ( +s/ )(Λ +s/λ ), for s. 6
11 minus producion coss), plus he discouned coninuaion values of having he job is severed nex period (wih probabiliy ρ +1 ) or having i is no severed (wih probabiliy 1 ρ +1 ): V J ( c ) = p m mpn W n ( c )h A 1 c +E Ξ,+1 (1 ρ +1) c +1 V+1 J ( c +1) df( c +1) F(c +1 ) +ρ +1 V+1 V, (5) where p m is he relaive price of wholesale goods in erms of he final good, mpn is he marginal produc of he worker and W n is he negoiaed wage. On he worker side, he value of being employed in a job V E wih idiosyncraic operaing cos c is equal o he worker s currenperiod benefi from he job (i.e. he wage paymen plus he marginal rae of subsiuion beween n and C ), plus he discouned coninuaion values of remaining on he job or being separaed and finding a new job in he nex period (wih probabiliy 1 ρ +1 (1 s +1 )) or being separaed and remaining unemployed nex period (wih probabiliy ρ +1 (1 s +1 )): V E ( c ) = W n ( c )h g(h ) Λ +E Ξ,+1 (1 ρ +1(1 s +1 )) c +1 V+1 E ( c +1) df( c +1) F(c +1 ) +ρ +1 (1 s +1 )V+1 U, (6) where Λ is he household s marginal uiliy of consumpion. The value of being unemployed V U is equal o he curren unemployed benefi, plus he discouned coninuaion values of finding a job condiional on having he mach no severed nex period wih probabiliy s +1 or, oherwise, remaining unemployed: V U = b u +E Ξ,+1 [ s +1 c+1 V+1( c E +1 ) df( c ] +1) F(c +1 ) +(1 s +1)V+1 U. (7) A free enry condiion applies for firms, which implies V V = for all. Thus, we obain from (4) and (5) respecively ha c V J ( c ) df( c ) F(c ) = ω e, (8) and V J ( c ) = p m mpn W ( c )h A 1 c +E Ξ,+1 (1 ρ +1 ) ω +1 e +1. (9) Firms and workers choose he real wage W n ( c ) and hours h o maximize he Nash produc: max(v W n E ( c ) V U )ϕ (V J ( c )) 1 ϕ,,h where he firs erm is he worker s surplus and he second is he firm s surplus, while ϕ (,1) is he worker s relaive bargaining power. The firsorder condiions for W n ( c ) and h imply 7
12 ha p m mpn h = g (h ) Λ. This equaion implicily defines he amoun of hours per worker. I shows ha in equilibrium he marginal produciviy of an exra workerhour is equal o he marginal rae of subsiuion beween h and C. Now, he firsorder condiion for W n ( c ) implies ha (1 ϕ)(v E ( c ) V U ) = ϕv J ( c ). (1) Using (6)(9) in (1), aking expecaions condiional on having c c and using s /e = v /u s yields he wage equaion of an individual worker: [ ] ( W n ( c )h = ϕ p m v +1 mpn A 1 c +E Ξ,+1 (1 ρ +1 )ω +1 u s +(1 ϕ) b u + g(h ) ). (11) +1 Λ I expresses he wage paymen o he worker as a weighed average, according o he relaive bargaining power of he worker and he firm, beween he marginal produc of he worker minus operaing coss plus he cos of replacing he worker if ha worker survives he exogenous job desrucion shock (weighed by he relaive probabiliy of finding a job and replacing he worker, i.e. labor marke ighness), and he ouside opion of he worker. coss: The aggregae real Nash wage is he average of (11) over he disribuion of idiosyncraic [ ] ( W n h = ϕ p m v +1 mpn H(c )+E Ξ,+1 (1 ρ +1 )ω +1 u s +(1 ϕ) b u + g(h ) ) +1 Λ where H(c ) is he average operaing cos. In order o allow for some degree of nominal wage sickiness hrough indexaion, following Hall (25), we assume ha he effecive nominal wage paid o he worker is a weighed average of he inflaionindexed pas nominal wage and he Nash wage, wih weighs κ W [,1) and 1 κ W respecively: 18 P W = κ W Γ W 1 P 1W 1 +(1 κ W )P W n, where Γ W is a wage indexaion variable ha saisfies Γ W = (A /A 1 ) α W π ϑ W π 1 ϑ W, where π is arge inflaion. 19 The criical hreshold a which jobs are desroyed endogenously is implicily 18 Hall (25) considers real wage ineria while we consider nominal wage ineria wih indexaion o accoun for he imporance of inflaion indexaion of nominal wages in many emerging marke economies including Chile. In order o keep he model simple, we do no adop a more sophisicaed specificaion of wage sickiness as Gerler and Trigari (29) and Gerler, Sala, and Trigari (28) or Chrisiano, Eichenbaum, and Traband (215). 19 The parameer α W conrols wheher wages are indexed o he sochasic rend (α W = 1), as is ypically he 8
13 defined by V J (c ) =. 2 Using his condiion wih (9) and (11), we obain A 1 c = p m mpn b u g(h ) +E Ξ,+1 (1 ρ +1 ) 1 ϕs +1 ω +1. Λ 1 ϕ e +1 Noe ha a higher marginal produc of he worker increases c (i.e. ρ n decreases) while an increase in he worker s ouside opion decreases c (i.e. ρ n increases). 2.3 Firms Thereare differen ypes of firmsha are all owned by he households. Thereis ase of perfecly compeiive wholesale firms ha produce differen varieies of a home good wih labor and capial as inpus, a se of monopolisically compeiive reail firms ha buy and resell hose varieies, a se of monopolisically compeiive imporing firms, and hree groups of perfecly compeiive aggregaors: one packing differen varieies of he home good ino a composie home good, one packing impored varieies ino a composie foreign good, and anoher one ha bundles he composie home and foreign goods o creae a final good. This final good is purchased by households (C,I ) and he governmen (G ). 21 In addiion, here is a se of compeiive firms producing a homogeneous commodiy good ha is expored abroad. A proporion of hose commodiyexporing firms is owned by he governmen and he remaining proporion is owned by foreign agens. The oal mass of firms in each secor is normalized o one. Throughou, we denoe producions/supply wih he leer Y and inpus/demand wih X Final Goods A represenaive final goods firm demands composie home and foreign goods in he amouns X H and X F, respecively, and combines hem according o he echnology [ Y C = (1 o) 1 ( ) η X H η 1 η +o 1 η ] ( ) X F η 1 η η 1 η, o (,1), η >. (12) Le p H and p F denoe he relaive prices of X H and X F in erms of he final good. Subjec o (12), he firm maximizes is profis Π C = Y C p H X H p F X F over he inpu demands X H and X F aking p H and p F as given. case in models wih Calvo wages, or no (α W = ). 2 The join surplus of a mach is given by V S ( c ) = V J ( c )+V E ( c ) V U. A mach is endogenously separaed whenever V S ( c ) which is equivalen o V J ( c ). 21 The final good is also used o pay vacancy posing and operaing coss. 9
14 2.3.2 Home Composie Goods A represenaive home composie goods firm demands home goods of all varieies j [,1] in amouns X H (j) and combines hem according o he echnology Le p H [ 1 ] ǫ H Y H = X H ǫ H 1 ǫ H 1 ǫ (j) H dj, ǫh >. (13) (j) denoe he price of he good of variey j in erms of he home composie good. Subjec o (13), he firm maximizes is profis Π H = p H Y H 1 ph ph (j)xh (j)dj over he inpu demands X H (j) aking he relaive prices p H and p H (j) as given, which yields he inpu demand funcions X H (j) = p H (j) ǫ H Y H, for all j. (14) Wholesale Goods of Variey j and he Job Creaion Condiion Wholesale goods of variey j are produced according o he echnology Y H (j) = z K 1 (j) α [A n (j)h (j)] 1 α, α [,1), (15) where z is an exogenous saionary neural echnology shock, while A (wih a A /A 1 ) is a nonsaionary laboraugmening echnology rend, boh common o all varieies. The wholesale firmschooseshowmuchcapial orenandhowmuchlaborohire, subjecoaidenical vacancy posing cos of ω per vacancy and firmspecific operaing cos per worker c (j) (hese coss are assumed o be paid in erms of final goods). Leing p m (j) denoe he relaive price of wholesale good j in erms of he final good, firm j s profi is given by Π m (j) = pm (j)y H (j) r K K 1(j) W h (j)n (j) C (j) L (j), where C (j) = n (j)a 1 κ c c (j) c (j) df( c (j)) F(c (j)) = n (j)h(c (j)), is he oal operaing cos of firm j condiional on working wih κ c, while L (j) = ω v (j) is he vacancy posing cos wih ω = ωa 1, ω. 22 The firm s workforce evolves over ime as he number of workers whose jobs do no ge erminaed plus new hires: n (j) = (1 ρ )n 1 (j)+e v (j). (16) 22 We allow operaing coss and vacancy posing coss o grow proporionaely wih he echnology rend o mainain a balanced seadysae growh pah. 1
15 Since oday s choice of v (j) affecs omorrow s workforce, he firm faces an ineremporal decision problem o maximize expeced discouned profis. Hence, he firm chooses K 1 (j), n (j) and v (j) o maximize E s= Ξ,+sΠ m +s(j) subjec o (15) and (16). The firsorder condiions for his problem yield he job creaion condiion: 23 ω e = p m mpn H(c ) W h +E Ξ,+1 (1 ρ +1 ) ω +1 e +1. Tha is, firms pos vacancies o expand employmen unil he effecive cos of posing an addiional vacancy (ω imes he expeced duraion of he vacancy 1/e ) equals he marginal produc of an exra worker plus he producion coss plus is expeced reurn from he reducion of vacancy posing coss if he job survives job desrucion in period Reail Goods of Variey j Reail firms buy and disribue wholesale goods. There is one reailer associaed wih each variey of he wholesale good. The reailer disribuing variey j saisfies he demand given by (14) bu i has monopoly power for is variey. Given nominal marginal coss P H mc H (j) = P p m (j) = P p m, he firm chooses is price P H (j) o maximize profis. 24 In seing prices, he firm faces a Calvoype problem, whereby each period i can change is price opimally wih probabiliy 1 θ H, and if i canno opimally change is price, i indexes is previous price according o a weighed produc of pas and seady sae inflaion wih weighs ϑ H [,1] and 1 ϑ H Foreign Composie Goods A represenaive foreign composie goods firm demands foreign goods of all varieies j [, 1] in amouns X F (j) and combines hem according o he echnology [ 1 ] ǫ F Y F = X F ǫ (j) F 1 ǫ F 1 ǫ F dj, ǫf >. (17) Le p F (j) denoe he price of he good of variey j in erms of he foreign composie good. Subjec o (17), he firm maximizes is profis Π F = p F Y F 1 pf p F (j)x F (j)dj over he inpu demands X F(j) aking he relaive prices pf and p F (j) as given. The firsorder condiions yields he inpu demand funcions: X F (j) = p F (j) ǫ F Y F, for all j. (18) 23 We drop subscrips j due o symmery. 24 Noe ha mc H (j) is real marginal cos expressed in erms of home composie goods prices. 11
16 2.3.6 Foreign Goods of Variey j Imporing firms buy an amoun M of a homogenous foreign good a he price P F in he world marke and conver his good ino varieies Y F (j) ha are sold domesically, where M = 1 Y F (j)dj. The firm producing variey j saisfies he demand given by (18) bu i has monopoly power for is variey. As i akes one uni of he foreign good o produce one uni of variey j, nominal marginal coss in erms of composie goods prices are P F mc F (j) = P F mc F = S P F, (19) where S is he nominal exchange rae (defined as he price of one uni of foreign currency in erms of domesic currency). Given marginal coss, he firm producing variey j chooses is price P F (j) o maximize profis. In seing prices, he firm faces a Calvoype problem, whereby each period i can change is price opimally wih probabiliy 1 θ F, and if i canno opimally change is price, i indexes is previous price according o a weighed produc of pas and seady sae inflaion wih weighs ϑ F [,1] and 1 ϑ F. In his way, he model feaures delayed passrough from inernaional o domesic prices Commodiies A represenaive commodiy producing firm produces a quaniy of a commodiy good Y Co in each period. Commodiy producion evolves exogenously according o he process log(y Co /A 1 ) = (1 ρ y Co)log(ȳ Co )+ρ y Co log(y Co 1/A 2 )+ε yco, ρ y Co [,1), ȳ Co >. The enire producion is sold abroad a a given inernaional price P Co. The real foreign and domesic prices are denoed as p Co and p Co, respecively, where p Co is assumed o evolve exogenously. The real domesic currency income generaed in he commodiy secor is herefore equal o p Co Y Co. The governmen receives a share χ [,1] of his income and he remaining share goes o foreign agens. 2.4 Fiscal and Moneary Policy Thegovernmenconsumesanexogenoussreamoffinalgoods(G ), paysunemploymenbenefis, levies lumpsum axes, issues oneperiod bonds and receives a share of he income generaed in he commodiy secor. We assume for simpliciy ha he public asse posiion is compleely denominaed in domesic currency. Hence, he governmen saisfies he following periodby 12
17 period consrain G +b u u +r B 1 = T +B +χp Co Y Co. Moneary policy is carried ou according o a Taylor rule of he form R R = ( R 1 R ) ρr [ (π ) ( ) απ Y /Y αy ] 1 ρr 1 exp(ε R ), π where R is he moneary policy rae in he longrun, π is arge inflaion and ε R is an n.i.d. shock ha capures deviaions from he rule. a Res of he World Foreign agens demand home composie goods and buy he domesic commodiy producion. There are no ransacion coss or oher barriers o rade. The srucure of he foreign economy is idenical o he domesic economy, bu he domesic economy is assumed o be small relaive o he foreign economy. The laer implies ha he foreign producer price level P F o he foreign consumpionbased price index P. Furher, le P H is idenical denoe he price of home composie goods expressed in foreign currency. Given full radabiliy and compeiive expor pricing, he law of one price holds separaely for home composie goods and he commodiy good, i.e. P H = S P H and P Co = S P Co. Tha is, domesic and foreign prices of boh goods are idenical when expressed in he same currency. Due o local currency pricing, a weak form of he law of one price holds for foreign composie goods, i.e. P F mc F = S P F from (19). The real exchange rae rer herefore saisfies rer = S P = S P F P P = PF mc F P = p F mcf, and he commodiy price in erms of domesic consumpion goods is given by p Co = PCo = S P Co P P = S P p Co = p F p Co. P We also have he relaion rer /rer 1 = π S π /π,where π S = S /S 1. Furher, foreign demand for he home composie good X H is given by he schedule X H ( ) P = o H η P Y, o (,1), η >, where Y denoes foreign aggregae demand or GDP. Boh Y and π evolve exogenously. 13
18 2.6 Aggregaion and Marke Clearing Taking ino accoun he marke clearing condiions for he differen markes, we can define he rade balance in unis of final goods as TB = p H X H +rer p Co Y Co rer IMP, Furher, we define real GDP as follows: Y C +I +G +X H +Y Co IMP. Then, he GDP deflaor (p Y, expressed as a relaive price in erms of he final consumpion good) is implicily defined as p Y Y = C +I +G +TB. Finally, we can show ha he ne foreign asse posiion evolves according o rer B = rer r B 1 +TB (1 χ)rer p Co Y Co. 2.7 Driving Forces For each exogenous variable in he model, we assume a process of he form log(x / x) = F x log(x 1 / x)+ε x, F x [,1), x >, forx = {,κ,m,,z,a,ζ o,ζ u,r,π,p Co,y Co,y,g}, whereheε x aren.i.d. shocks. Wefurher assume ha he idiosyncraic shock c is lognormally disribued wih mean and sandard deviaion σ c The Model wih Calvo Wages This secion briefly describes he model wih monopolisic wage seing à la Calvo, following SchmiGrohé and Uribe (26, 27). Mos of he model is idenical o he model wih search fricions. The differences are discussed below. 25 Several alernaive disribuions of he idiosyncraic shock have been used in he lieraure. Morensen and Pissarides (1994) use a uniform disribuion on he inerval [ 1, 1] for he idiosyncraic shock. Den Haan e al. (2) and Walsh (25) use a lognormal disribuion wih mean. Guerrieri (28) considers shocks disribued according o uniform, Pareo and lognormal disribuions and finds no significan difference. Similarly, Tororice (213) finds ha here is very lile difference when using he uniform disribuion in comparison o he lognormal disribuion. Hence, we simply follow mos of he lieraure and use a lognormal disribuion. 14
19 3.1 Households Expeced discouned uiliy of a represenaive household is given by [ E β+s +s s 1 1 σ (C +s ςc +s 1 ) 1 σ κa 1 σ s= The periodbyperiod budge consrain of he household is given by +s 1 h 1+φ +s 1+φ ]. (2) C +I +B +rer B +T = W h +r B 1 +rer r B 1 +r K K 1 +Σ. (21) The household chooses C, I, K, B, and B o maximize (2) subjec o (21) and he capial sock level, aking r, r, r K, rer, T, Σ, B 1, B 1 and K 1 as given. 3.2 Labor Union Following SchmiGrohé and Uribe (26, 27), labor decisions are made by a cenral auhoriy, a union, which supplies labor monopolisically o a coninuum of labor markes indexed by i [, 1]. Households are indifferen beween working in any of hese markes. In each marke, he union faces a demand for labor given by h (i) = [W n(i)/wn ] ǫ W h d, where Wn (i) denoes he nominal wage charged by he union in marke i, W n is an aggregae hourly wage index ha saisfies (W n ) 1 ǫ W = 1 Wn (i) 1 ǫ Wdi, and h d denoes aggregae labor demand by firms. The union akes W n and h d as given and, once wages are se, i saisfies all labor demand. In addiion, he oal number of hours allocaed o he differen labor markes mus saisfy he resource consrain h = 1 h (i)di. Wage seing is subjec o a Calvoype problem, whereby each period he household (or union) can se is nominal wage opimally in a fracion 1 θ W of randomly chosen labor markes, and in he remaining markes, he pas wage rae is indexed o a weighed produc of pas and seady sae inflaion wih weighs ϑ W [,1] and 1 ϑ W. 3.3 Wholesale Goods of Variey j Wholesale goods of variey j are produced according o he echnology Y H (j) = z K 1 (j) α [A h d (j)]1 α, α [,1). (22) Firm j s profi is given by Π m (j) = p m (j)y H (j) r K K 1 (j) W h d (j). The firm chooses K 1 (j)andh d (j)omaximize Π m (j)subjeco (22). From helabormarke clearing condiions we hen obain ha h = h d W in equilibrium, where W is a wage dispersion erm. 15
20 3.4 Driving Forces The Calvo wages model absracs from maching shock (m ). 4 Paramerizaion Sraegy Our empirical sraegy combines boh calibraed and esimaed parameers. The calibraed parameers and argeed seady sae values are presened in Table 1. For mos of he parameers no relaed wih he search fricions we draw from relaed sudies for Chile, as indicaed in he able, while ohers are endogenously deermined in seady sae o arge some firs momens ( π, κ, o, ḡ and ȳ Co ). The parameers ha deserve addiional explanaion are hose relaed o he search fricions: ω (he vacancy posing cos), b (he unemploymen benefi), µ c and κ c (he parameers of he sochasic operaing cos), ρ x (he exogenous separaion rae), and ϕ (he workers bargaining weigh). The values of hose parameers are eiher chosen o mach observed saisics and available evidence for Chile, or following relaed sudies for oher counries. [Table 1 here.] We derive he vacancy posing cos(ω) from he seady sae calculaions o mach an average unemploymen rae (u) of around 8 percen beween 1987 and The implied vacancy cos o GDP raio is approximaely 4 percen, which is close o he value in Trigari (29). The unemploymen benefi ( b) is se o based on OECD daa. 27 Following Cooley and Quadrini (1999), den Haan e al. (2) and oher relaed sudies, we se he probabiliy of filling a vacancy in seady sae (e) o.7 and derive he average mach efficiency parameer m from he seady sae calculaions. The resuling value of m is approximaely.5. We furher fix he oal separaion rae in seady sae (ρ) based on evidence repored by Jones and Naudon (29), who calculae quarerly labor saus ransiion probabiliies from micro survey daa for Chile and find a probabiliy of changing saus from employed o unemployed, p E,U, of abou.4 as well as a probabiliy of changing saus from unemployed o employed, p U,E, of abou.47. These probabiliies imply a value for ρ of approximaely 7.5 percen, which is a he lower end of he range of quarerly U.S. worker separaion raes of 8 o 1 percen repored by Hall (1995) and he values ypically used in he lieraure. 28 Following den Haan e al. (2), he exogenous separaion rae (ρ x ) is hen se o wo hirds imes he oal separaion rae. We furher normalize he lognormal mean of he firm s operaing cos o and derive he scaling 26 The average unemploymen rae over he sample period from 21Q3 o 215Q2 was also abou 8 percen. 27 See hps://daa.oecd.org/socialexp/publicunemploymenspending.hm. 28 The value of ρ is calculaed from (6) which implies ha p E,U = ρ(1 p U,E ) in seady sae, such ha ρ = p E,U /(1 p U,E )
21 parameer κ c from he seady sae calculaions in order o mach he argeed value of ρ. The workers bargaining weigh (ϕ) is se o.5, following he relaed lieraure. We also calibrae he parameers characerizing hose exogenous processes for which we have a daa counerpar. In paricular, for g we use linearly derended real governmen consumpion, for y Co we use linearly derended real mining producion in he copper secor, for R we use he 3monh U.S. dollar London Inerbank Offered Rae, for y we use linearly derended real GDP of commercial parners while for π we use CPI inflaion (in dollars) of commercial parners (boh radeweighed), and for p Co we use he price of refined copper a he London Meals Exchange (in dollars) deflaed by he same price index used o consruc π. 29 The oher parameers of he model were esimaed using Bayesian echniques, solving he model wih a loglinear approximaion around he nonsochasic seady sae. The lis of hese parameers and he priors are described in columns one o five of Table 4. 3 Because we esimae wo differen versions of he model, we used differen daa ses for each model. In boh cases, he following variables were used (all for he inflaion argeing sample from 21Q3 o 215Q2): he growh raes of real GDP, privae consumpion and invesmen, he CPI inflaion rae, he moneary policy rae, he mulilaeral real exchange rae, he growh rae of real wages, oal hours worked (hours per worker imes employmen divided by he labor force) and he EMBI Chile (which we mach by he endogenous componen of he counry premium ξ plus he observed shock o he counry premium ζ o ). We also include as observables he variables used o esimae he exogenous processes previously described. 31 In addiion, for he model including search fricions, we also use as observable he unemploymen rae. Overall, we use 16 observed variables in he esimaion. Our esimaion sraegy also includes i.i.d. measuremen errors for all observables. The variance of he laer was se o 1% of he variance of he corresponding observables. 5 Resuls In his secion, we firs assess he goodness of fi of he model under he differen labor marke specificaions, in order o undersand if and how he presence of search and maching helps o improve he abiliy of he model o accoun for he dynamics observed in he daa. We hen discuss he differences in he inferred parameers and compare he variance decomposiion o find ou which shocks are he mos imporan drivers of he dynamics under Calvo wages 29 The daa source is he Cenral Bank of Chile s saisical daabase; see hp://si3.bcenral.cl/siee. 3 The prior means were se o represen(whenavailable) heesimaes of relaed papers for hechilean economy (e.g. Medina and Soo, 27). 31 While he parameers of hese exogenous processes were calibraed, including hese variables in he daa se is informaive for he inference of he innovaions associaed wih hese exogenous processes. 17
22 and under search fricions. In addiion, we analyze he impulse responses o seleced shocks o undersand he propagaion properies of he differen labor marke fricions. Finally, we compare he forecasing performance of he wo model varians agains each oher and agains reducedform Bayesian vecor auoregressive (BVAR) benchmark forecasing models. 5.1 Goodness of Fi To have an overall measure of goodness of fi, we compue he marginal daa densiy implied by he poserior disribuion of he parameers for each model. Since he models where esimaed wih differen daa ses, he marginal daa densiies for he esimaion samples are no comparable. We herefore compue, based on he poserior disribuion for he model wih search fricions, he marginal daa densiies of a differen se of variables, excluding from he full daa se (X T ) he unemploymen rae (u T ). The values for he marginal daa densiies for he daa se excluding he unemploymen rae are indeed comparable. In addiion, we are ineresed in he fi of each model for he daa wihou he remaining wo labor marke variables, i.e. oal hours worked (h T n T ) and real wage growh ( logw T ). Thus, we have also compued he marginal daa densiies for hose daa ses. Finally, since he model wih search fricions has an addiional shock, he mach efficiency shock (m ), which may give his model addiional degrees of freedom o mach he daa compared o he model wih Calvo wages, we have also compued he marginal daa densiy for he model wih search fricions shuing down his shock. 32 [Table 2 here.] The resuls in Table 2 show ha he overall fi of he model wih search fricions is significanly beer han he fi of he model wih Calvo wages. This resul holds for he daa ses including he differen labor marke variables (see he second and hird rows of he able), as well as he daa se wihou he labor marke variables (see he fourh row), and independenly of wheher he mach efficiency shock is acive or no. The difference beween he marginal daa densiies is larges, more han 5 log poins, for he daa se ha includes hours worked. The difference is sill more han 3 log poins for he daa se ha includes real wage growh as he only labor marke variable. For he daa se wihou he labor marke daa, he difference is smaller, abou 2 log poins. According o he usual scales of inerpreaion, his consiues srong o very srong evidence in favor of he model wih search fricions. 33 Imporanly, he model wih search fricions no only explains he labor marke variables significanly beer han he model wih Calvo wages, bu also he remaining macroeconomic daa. 32 The marginal daa densiies were compued hrough he Laplace approximaion a he mean of he poserior disribuion of he parameers. 33 See Jeffreys (1961) and Kass and Rafery (1995). 18
23 [Table 3 here.] To obain a more deailed view of which variables are beer mached by each model, Table 3 repors he sandard deviaions and firsorder auocorrelaion coefficiens of seleced variables implied by he poserior mean of he parameers, and compares hese saisics wih he corresponding empirical momens. In erms of he sandard deviaions shown in he hird o fifh columns of he able, he model wih search fricions maches mos variables beer (wih a few excepions including real GDP, privae consumpion and he nominal rade balance). The model wih Calvo wages grossly oversaes he sandard deviaion of hours worked, real and nominal wages and he real exchange rae. Likely relaed o he laer, i also oversaes he sandard deviaion of inflaion and he moneary policy rae. The auocorrelaion coefficiens in he sixh o eighh columns of he able show ha he model wih search fricions maches he empirical momens of all variables beer han he model wih Calvo wages. Noe ha he model wih Calvo wages oversaes he persisence of all variables. Overall, his goodnessoffi analysis yields as a main conclusion ha he model wih search fricions performs significanly beer han he model wih Calvo wages in erms of fiing boh labor marke daa and oher macroeconomic daa. We examine nex which properies of he model wih search fricions can explain his difference. 5.2 Esimaed Parameers and Dynamics Columns six o nine in Table 4 display he poserior mean and he 9% highes poserior densiy inervals of he esimaed parameers of he wo model varians. We will commen on hose parameers whose inference is differen beween he models o see how he presence of he differen labor marke specificaions affecs he resuls. [Table 4 here.] One parameer whose esimaed value is differen beween he wo models is he inverse Frisch elasiciy of hours worked (φ), whose poserior mean is almos 3% higher in he model wih search fricions. Hence, he inensive margin seems o be less imporan in ha model compared o he model wih Calvo wages. This resul is in line wih he findings of Chrisiano e al. (211) and oher calibraions of search and maching models wih boh margins of labor supply (e.g. Trigari, 29). I may seem surprising ha he model wih Calvo wages also has a low elasiciy of hours worked, since ha model can only explain he observed variaions in oal hours hrough variaions in individual hours (i.e. he inensive margin). The low elasiciy may 19
24 be due o he need o avoid large counercyclical reacions of hours worked o foreign shocks ha generae srong wealh effecs on labor supply. 34 In erms of he parameers relaed o he nominal rigidiies, boh models rely on relaively large degrees of wage sickiness, as refleced by a high Calvo parameer for wages (θ W ) or a high wage ineria parameer (κ W ). However, he degree of indexaion of nominal wages o pas inflaion (ϑ W )is much larger in hemodel wih Calvo wages. Also, ha model hasasignificanly higher Calvo parameer for home prices (θ H ) as well as a relaively low esimaed reacion of moneary policy o inflaion (α π ). Taken ogeher, hose resuls imply ha boh wages and inflaion end o be highly persisen in ha model (see Table 3). Oher parameers ha differ significanly beween he wo models are he ones ha deermine he real rigidiies. In paricular, he model wih Calvo wages has a significanly higher degree of higher habi formaion (ς) and a higher elasiciy of invesmen adjusmen coss (γ). The laer may explain he relaively large size (i.e. he esimaed innovaion sandard deviaion and auocorrelaion coefficien) of he consumpion preference shock ( ) and he invesmenspecific echnology shock ( ) in ha model. In addiion, he model wih Calvo wages seems o require a relaively large labor supply preference shock (κ). [Table 5 here.] However, insead of comparing he parameers of he exogenous shocks direcly, i is more insrucive o see how he differen shocks explain aggregae flucuaions. To ha end, Table 5 displays he uncondiional variance decomposiion obained for each version of he model for seleced variables, compued a he respecive poserior mean. In he model wih Calvo wages, echnology shocks (and in paricular invesmenspecific echnology shocks) are he dominan driving force for mos variables, followed by foreign shocks. On he oher hand, in he model wih search fricions foreign shocks are he mos imporan driving force for several variables, including consumpion, invesmen, real wages and he unemploymen rae. While labor supply preference shocks are imporan o explain hours worked in ha model, hose shocks are relaively unimporan for he remaining variables. 35 In addiion, mach efficiency shocks explain merelyupo24% of hevariance ofheunemploymen rae. 36 Inaddiion, hemodelwihsearch fricions aribues a larger shock o ransiory TFP shocks (for mos variables) and moneary policy shocks (especially for inflaion). 34 Openeconomy sudies someimes address his issue by assuming preferences wih a low or zero wealh effec of labor supply, such as preferences of he Greenwood, Hercowiz, and Huffman (1988) ype. 35 Since labor supply shocks are no very imporan o explain unemploymen in he model wih search fricions, we may conclude ha labor supply shocks end o explain variaions in individual bu no oal hours worked in ha model. 36 This finding is in line wih he resuls of Sedláçek (214) who shows ha variaions in mach efficiency can be explained by endogenous separaions such as in our model. 2