Hiring and Investment Frictions as Inflation Determinants

Transcription

1 Hiring and Invesmen Fricions as Inflaion Deerminans Renao Faccini Queen Mary, Universiy of London and Cenre for Macroeconomics LSE) Leonardo Melosi Federal Reserve Bank of Chicago Eran Yashiv Tel Aviv Universiy, Cenre for Macroeconomics LSE) and CEPR November Absrac We embed convex hiring and invesmen fricions in a New Keynesian DSGE model wih inrafirm wage bargaining. We show ha hese fricions have crucial implicaions for he response of marginal coss, and consequenly inflaion, and for he co-movemen of inflaion wih real variables. We elucidae how he presence of hiring and invesmen fricions affecs he ransmission mechanism of moneary and echnological shocks by means of impulse responses. We find ha hiring fricions are a key deerminan of curren period marginal coss; invesmen fricions also maer, by affecing expecaions of fuure marginal coss. Esimaing he model wih privae-secor US daa shows ha boh hiring fricions and invesmen fricions help explain inflaion dynamics. Smoohed esimaes of marginal coss are radically differen in models wih and wihou hiring fricions. Our resuls indicae ha hiring fricions explain around 50% of he variaion in marginal coss, he real wage componen explains around 35% while he remain 15% is accouned for by an inrafirm bargaining componen. These esimaes rely only on moderae levels of he relevan fricions. Keywords: Inflaion, hiring and invesmen fricions, New-Keynesian model, moneary policy. JEL codes: E22, E24, E31, E32, E37 r.faccini@qmul.ac.uk yashiv@pos.au.ac.il We hank Leonardo Melosi for many commens and suggesions. We are graeful o Francesco Bianchi, Haroon Mumaz, Michel Juillard, and seminar paricipans a Tel Aviv Universiy, he London Macro Workshop 2012 a LBS), Uppsala Universiy, SED 2012, SED 2014, and he second Mannheim workshop in quaniaive macroeconomics 2014) for helpful commens on previous versions. Any errors are our own. The graphs in his paper are bes viewed in color.

2 1 Inroducion New Keynesian models posi ha inflaion dynamics are driven by curren and expeced fuure real marginal coss. Because real marginal coss are proporional o he labor share of income, he labor marke is implicily given a key role in driving inflaion. However, he characerizaion of he labor marke in he sandard model absracs from fricions. Krause, Lopez-Salido and Lubik 2008), have shown ha he explici modelling of labor marke fricions along he lines of Diamond Morensen and Pissarides adds a new erm in he expression for real marginal coss, and hereby poenially generaes an independen role for fricions o affec inflaion. However, hese auhors find ha his addiional componen is unlikely o quaniaively affec he ransmission of shocks o inflaion dynamics. Gali 2010) finds similar resuls, and concludes ha such fricions are oo small o affec he behavior of marginal coss as well as he co-movemen of inflaion wih oher variables. His argumen is simple: because hiring coss only accoun for abou 1% of GDP, while he labor share is around 66% of GDP, fricions canno maer, a leas in he absence of implausibly large flucuaions in ne hiring coss relaive o wages. So he boom line is ha modelling labor marke fricions explicily, complicaes he model wihou affecing inflaion dynamics. In his paper we revisi his issue in a new way. We embed convex hiring and invesmen fricions as in Merz and Yashiv 2007) and Yashiv 2014) ino a very simple New Keynesian DSGE model wih inrafirm wage bargaining. We underake wo exploraions. Firs, in he spiri of Gali 2010) we look a how fricions affec he impulse responses of marginal coss and inflaion, or he co-movemen wih oher real variables. Our reference framework is Gali 2010), from which we depar by explicily modelling capial. This allows us o exend he analysis beyond hiring fricions: our fricions coss funcion allows for hiring and invesmen fricions o be shu down one a a ime, so as o disenangle heir separae role and heir general equilibrium ineracion in he propagaion of shocks. We show ha inroducing hiring fricions ino a fricionless New-Keynesian model smoohs he response of real wages and hereby reduces he elasiciy of he labor share o he underlying shocks. This endogenous rigidiy in he response of real wages operaes hrough he response of he marginal rae of subsiuion and he marginal revenue produc of labor. However, wage sickiness magnifies he response in he discouned value of jobs, boosing he response of he fricional componen of marginal coss. These wo effecs counerac each oher; wheher he ne effec is null, posiive or negaive, will depend on he paricular calibraion and on he shock. However, even in cases where he response of marginal coss is independen of he presence of hiring fricions, his is no because hiring fricions are o small oo maer and he real wage response is virually idenical in he wo models. In our calibraion, he wage componen and he fricional componen of marginal coss are abou equally imporan in driving marginal coss. Hiring fricions produce a dramaic effec on he co-movemen beween inflaion and real variables. As a resul, models wih and wihou hiring fricions imply radically differen views on 1

3 he propagaion of shocks. As explained in Faccini and Yashiv 2015), hiring fricions offse he mechanism a work in New Keynesian NK) models in a non-rivial way. When hiring fricions are calibraed o iny values ha are mean o capure only vacancy posing coss, as in Gali 2010), he responses of real variables are close o he ones generaed in he fricionless NK benchmark. Bu hese resuls are very sensiive o he precise parameerizaion. When hiring fricions are calibraed o reflec conservaive esimaes of raining coss, moneary policy loses effeciveness o simulae oupu, and he response of employmen o echnology shocks urns posiive. The convenional assumpion ha new capial operaes in producion only wih a one quarer lag implies ha invesmen fricions do no affec curren period marginal coss, bu he expecaions of nex period marginal coss. These fricions also smooh he response of employmen, generaing endogenous rigidiy in he wage componen of marginal coss. In he absence of hiring fricions, curren period marginal coss are essenially driven by he wage componen of marginal coss, so he rigidiy in wages direcly ranslaes ino a dampened response of marginal coss and inflaion. Invesmen fricions also affec he condiional co-movemen beween inflaion and real variables, bu heir impac is less dramaic when compared o hiring fricions. So he boom line of our impulse response analysis is ha labor fricions have firs order implicaions for he co-movemen of inflaion wih real variables, while capial fricions mosly affec he response of inflaion o shocks. In a second exploraion, we ake he DSGE model o he daa and carry ou srucural esimaion of various specificaions of he model, where we resric he fricions coss funcion so as o shu down differen fricions one a a ime. Looking a he marginal daa densiy for he whole model and he condiional marginal daa densiy for he inflaion series, we find ha adding labor fricions o he New Keynesian benchmark grealy helps explain inflaion dynamics, as well as he join behavior of our full se of observables. Adding invesmen fricions separaely also helps fi boh inflaion and he full se of observables, bu less han hiring fricions. Adding boh fricions simulaneously increases saisical fi even furher. Our preferred version of he NK model, which includes boh hiring and invesmen fricions, produces a smoohed series of marginal coss ha is considerably differen from he one generaed by he fricionless benchmark model. In paricular, from he 2000s onwards, marginal coss are esimaed o push up on inflaion, as opposed o he resuls obained in he fricionless benchmark. The difference beween he wo series is largely driven by he behavior of he fricional componen of marginal coss, which is esimaed o be quaniaively more imporan han he wage share of income in driving he flucuaions of curren marginal coss. Our sudy shows ha large flucuaions in ne marginal hiring coss are no implausible, raher, hey are validaed by our esimaion. As we poin ou in he paper, he fricional componen of marginal coss can also be inerpreed as he raio of he marginal profi of a new hire over he marginal produc of labor. A large srand of research, which has exensively invesigaed he deerminans of unemploymen flucuaions wihin search and maching models of he labor marke, has produced many differen mechanisms of amplificaion o produciviy shocks, bu mos 2

4 of hem rely on he abiliy o generae large flucuaions in marginal hiring profis o an underlying produciviy shock. So he role of marginal hiring profis has been found o be cenral in almos any heory ha can successfully accoun for unemploymen flucuaions a business cycle frequencies. By incorporaing labor fricions ino a New-Keynesian model, we are able o exend he imporance of flucuaions in marginal hiring profis o inflaion dynamics. Secion 2 presens a shor review of he relevan lieraure. Secion 3 presens he model. Secion 4 inspecs he mechanism by which fricions affec marginal coss and he co-movemen of inflaion wih real variables, making use of calibraion and impulse responses. Secion 5 inroduces esimaion of he full DSGE model, including discussion of he daa, and he mehodology. The resuls are presened and discussed in Secions 6. The full derivaion of he model is relegaed o he Appendix. 2 Lieraure This paper relaes o hree srands of lieraure: i) New Keynesian DSGE models see Woodford 2003), Gali 2008) and Chrisiano e al 2010) for surveys and discussions which offer a model of inflaion as a funcion of curren and fuure expeced marginal coss. ii) Search and maching models of he labor marke, which feaure dynamic, opimal hiring decisions by firms in he face of fricions; see Pissarides 2000), Yashiv 2007) and Rogerson and Shimer 2011) for overviews and surveys. Hiring coss and ime lags are he expression of fricions in hese models. Wihin his lieraure, here is a srand ha invesigaes he role of inrafirm wage bargaining in macroeconomic models of he labor marke. In an applicaion of he bargaining model proposed by Sole and Zwiebel 1996) o search and maching models, Cahuc and Wasmer 2001) have shown ha when firms are large, in he sense ha hey employ a posiive measure of workers, and wages are negoiaed hrough Nash bargaining, he firm should anicipae he impac of is hiring policy on he negoiaed wage. This modificaion of he sandard bargaining problem is known as inrafirm bargaining. Cahuc, Marque and Wasmer 2008) have furher shown ha accouning for inrafirm bargaining can have imporan implicaions for he equilibrium in he labor marke. iii) Models of fricions in invesmen, following he seminal conribuions of Lucas and Presco 1971) and of Tobin 1969) and Hayashi 1982). The idea in hese models is ha coss are key o he undersanding of invesmen behavior. We noe wo imporan exensions in he curren conex: Firs, In recen years, various sudies have embedded fricional models of he labor marke ino he sandard New-Keynesian framework o shed ligh on he channels by which he modelling of unemploymen could affec inflaion dynamics. Early work by Walsh 2005) and Trigari 2009) sparked some enhusiasm abou he possibiliy ha explicily modelling search fricions could help undersand inflaion dynamics. Boh sudies found ha accouning for unemploymen increases 3

5 inflaion persisence. However, he robusness of hese resuls have been quesioned by Gali 2010), while Heer and Maußner 2010), have found ha hey fade ou when capial is inroduced in he model. As shown in Krause, Lopez-Salido and Lubik 2008), he explici modelling of labor marke fricions adds a new erm in he expression for real marginal coss, which can poenially affec inflaion. However, hese auhors find ha his addiional componen is unlikely o quaniaively affec he ransmission of shocks o inflaion dynamics. Gali 2010) finds similar resuls, and concludes ha such fricions are oo small o affec he behavior of marginal coss. Second, a body of evidence, reviewed by Yashiv 2014), has documened he exisence of fricions boh in he capial and in he labor marke. Work by Merz and Yashiv 2007) and Yashiv 2014) has shown he imporance of accouning for heir ineracions in explaining he join behavior of hiring and invesmen as well as he behavior of sock prices. Mumaz and Zanei 2015), provide addiional evidence in his direcion by means of Bayesian esimaion of a DSGE model. While Mumaz and Zanei 2015) are ineresed in he esimaion of he convexiies in facor adjusmen coss and heir abiliy o fi asse prices, our ineres is undersanding he role of hiring and invesmen fricions for inflaion dynamics. 3 The Model 3.1 The Se-Up We inroduce convex hiring and invesmen fricions in he spiri of Lucas and Presco 1971), and following he specificaion in Merz and Yashiv 2007), ino a benchmark New-Keynesian model. The model is an exension of Faccini and Yashiv 2015), o which we refer for a deailed exposiion of he mechanism a work. 3.2 Households The represenaive household, indexed by he subscrip j, comprises a uni measure of workers searching for jobs in a fricional labor marke. The mass of workers who are unemployed a he beginning of he period is denoed by Uj, 0, and each unemployed worker finds a job by he end of he period wih probabiliy x. The law of large numbers implies ha he measure of new hires in each period is given by x Uj, 0. Assuming ha a he end of each period workers lose heir job wih probabiliy δ N, he sock of employed workers N j, obeys he law of moion: N j = 1 δ N )N j, 1 + x U 0 j,. 1) The household enjoys uiliy from he aggregae consumpion index C j, and disuiliy from he measure of workers in employmen, N j,. The discoun facor of he household is denoed by β. Each period, he household receives a nominal wage income W j, from employed workers, dividends 4

6 from ownership of firms Υ j, and pays lump sum governmen axes T j,. Wealh akes he form of nominal governmen bonds B j,, and can be ransferred ino he fuure a he presen discouned value B j,+1 /R, where R is he gross nominal ineres rae. The ineremporal problem of he households is o maximize he discouned presen value of curren and fuure uiliy: max {C +s } s=0 [ E β s s=0 subjec o he budge consrain and he law of moion of employmen 1). ] η p +s ln C j,+s ϑc +s 1 ) ηl +sχ 1 + ϕ N 1+ϕ j,+s C j, + B j,+1 R = W j N j + B j + Υ j T j,, 2) The parameers ϕ denoes he inverse Frish elasiciy of labor supply, χ is a scale facor on he disuiliy of work and ϑc is an index of exernal habis in consumpion. The variables η p and η l denoe preference and labor supply shocks, respecively. Denoing by λ j, he Lagrange muliplier associaed wih he budge consrain, he firs order necessary condiions and co-saes are: V N j, = W j, λ j, = η p C j, ϑc 1 ), 1 R = βe λ j,+1 λ j,, 3) ηl ϕ χnj, x Vj, N + E Λ,+1 1 δ N ) V λ j, 1 x j,+1, N 4) where Λ,+1 = β λ j,+1 1 λ j, +1 = R /π +1 denoes he real discoun facor and π +1 = +1 /. The value of a job for he household expressed in unis of he numeraire good equals he real wage ne of he opporuniy cos of work ηl χn ϕ j, λ j,, and a re-employmen value j,, plus he coninuaion value. In a model wih no fricions, where employmen generaes no rens and hus V N j, = 0, he marginal rae of subsiuion equals he real wage: W labor supply. 3.3 Firms, x 1 x V N = η l χn ϕ j, /λ j,, which governs We assume hree ypes of firms: inermediae good producers, final good producers and reailers. Inermediae producers hire labor and inves in capial o produce a homogeneous produc, which is hen sold o final producers in perfec compeiion. Final producers ransform each uni of he homogeneous produc ino a uni of a differeniaed produc facing price rigidiies a la Roemberg 5

7 1982). We also assume ha reailers buy a bundle of differeniaed goods from he final producers and ransform i ino homogeneous consumpion and invesmen goods. In urn, hese goods are sold in perfec compeiion o he households, he governmen and he inermediae firms. Firms: Reailers We assume ha idenical and compeiive reailers produce a homogeneous good Y, using he echnology: Y = 1 0 Y i) ɛ 1)/ɛ di ɛ/ɛ 1) Reailers choose he specialized inpus Y i) so as o maximize profis: 1 Y 0 Y i)di,. 5) subjec o he echnology in 5). The oucome of he maximizaion problem is a demand funcion for each specialized produc: ) P i) ɛ Y i) = Y. 6) The reailers ransform he oupu good Y ino a consumpion good or an invesmen good. I is assumed ha one uni of he oupu good can be urned ino one uni of he consumpion good, and one uni of he oupu good can be ransformed ino 1/η q unis of he invesmen good. ηq is he relaive price of he invesmen good, which is assumed o follow an exogenous AR1) sochasic process. Inermediae Goods Producers A uni measure of inermediae firms combine capial and labor in order o produce a homogenous, inermediae oupu good, denoed by Z, which is sold o final producers in perfec compeiion. The consan reurns o scale producion funcion is fa, N, u, K 1 ) = a A N ) α u K 1 ) 1 α, where K 1 denoes physical capial and u is uilizaion rae. We assume ha η A labor-augmening sochasic rend ha follows he process = A /A 1 is a ln η A = 1 ρ A) ln η A + ρ A ln η A 1 + ς A 1, 7) where η A denoes a seady-sae value ha equals he economy s growh rae µ. We furher assume ha a denoes a ransiory shock o he level of echnology: ln a = ρ a ln a 1 + ς a. We assume a fricions coss funcion g, capuring he disrupion in economic aciviy ha is 6

8 associaed wih hiring and invesmen. As discussed in deails in Faccini and Yashiv 2015), his funcion is mean o capure all he fricions involved in geing newly employed workers o work and capial o operae in producion, including worker raining coss, organizaional coss, implemenaion coss, financial premia on cerain projecs, capial insallaion coss, learning he use of new equipmen, ec. So our noion of fricions exends beyond, say, jus capial adjusmen coss or vacancy coss. Following Merz and Yashiv 2007) and Yashiv 2014) we assume ha he fricions coss funcion is consan reurns o scale and is increasing in each of he firm s decision variables. In paricular, we assume he following explici funcional form: ga, A, I, K 1, H, N ) = [ ) e 2 1 I + e 2 2 u K 1 2 H N ) 2 ] a A N ) α u K 1 ) 1 α, 8) where he quadraic adjusmen coss funcion is consisen wih esimaes in Yashiv 2014). 1 The ne oupu of a represenaive firm a ime is: Z = fa, A, N, u, K 1 ) ga, A, I, u, K 1, H, N ). In every period, he exising capial sock depreciaes a he rae δ K and is augmened by new invesmen: K = 1 δ K )K 1 + I, 0 δ K 1, 9) Togeher wih he producion funcion, his law of moion implies, following a convenion in DSGE modelling, ha newly insalled capial only becomes effecive wih a one period quarer) lag. Similarly, he number of a firm s employees decreases a he rae δ N and i is augmened by new hires H. The law of moion for employmen reads: N = 1 δ N )N 1 + H, 0 δ N 1, 10) which implies ha new hires are immediaely producive. The ineremporal maximizaion problem of he firm is o maximize he presen discouned value of cashflows: max E Λ,+j {mc +j [fa +j, A +j, N +j, u +j, K +j 1 ) ga +j, A +j, I +j, u +j, K +j 1, H +j, N +j )] j=0 W } +ji +j, u +j, K +j 1, H +j, N +j ) N +j η q +j P [I +j + ν u )], +j 1 A raionale for he use of such funcional forms, emphasizing consisency of aggregae employmen and capial dynamics wih hiring and invesmen decisions a plan level is provided by King and Thomas 2006) and Kahn and Thomas 2008), respecively. 7

9 subjec o he laws of moion for capial 9) and labor 10), where Λ,+1 = λ j, λ j, = R /π +1 is he real discoun facor of he households who [ own he firms, ] mc P Z / is he relaive price of he inermediae firm s good and ν u ) = A u 1+ξ u 1+ξ / 1 + ξ) is a convex cos funcion for he uilizaion of capial. This funcional form implies ha seady-sae uilizaion coss ν u) are zero. Noice ha when choosing facors of producion and he uilizaion of capial, he firm correcly anicipaes he impac of is decisions on he negoiaed wage bill. The firs-order necessary condiions and co-saes for dynamic opimaliy are: mc f u, g u, ) = W u, N + η q ν u ) 11) [ Q K = E Λ,+1 mc +1 f K,+1 g K,+1 ) W ) ] K,+1 N δ K )Q K +1, 12) +1 Q K = mc g I, + W I, N + η q, 13) Q N = mc f N, g N, ) W W N, N + 1 δ N )E Λ,+1 Q N +1, 14) Q N = mc g H, + W H, N, 15) where Q K and Q N are he Lagrange mulipliers associaed wih he capial and he employmen laws of moion, respecively. One can label Q K as Tobin s Q for capial or he value of capial and Q N as Tobin s Q for labor or he value of labor. For an exensive discussion of heir economic significance, see Yashiv 2014) and Faccini and Yashiv 2015). In a New Keynesian model wih no fricions and no bargaining, hese four equaions boil down o wo sandard firs order condiions, which equae he real wage o he marginal revenue produc of employmen W / = mc f N,, and he opporuniy cos of capial o he marginal revenue produc of capial: η q = E 1 [ mc+1 f K, δ K )η q ] +1. R /π +1 Final good producers There is a uni measure of monopolisically compeiive final good firms indexed by i [0, 1]. Each firm i ransforms Zi) unis of he inermediae good ino Y i) unis of a differeniaed good, where Zi) denoes he amoun of inermediae inpu used in he producion of good i. Monopolisic compeiion implies ha each final firm i faces he demand reailers demand funcion 6). 8

10 We assume price sickiness à la Roemberg 1982), meaning firms maximize curren and expeced discouned profis subjec o quadraic price adjusmen coss. We assume ha adjusmen coss depend on he raio beween he new rese price and he one se in he previous period, adjused by a geomeric average of seady sae inflaion and pas inflaion. Final good firms maximize he following expression: max E Λ,+s P s=0 +s ) 2 +s i) +s mc +s ) Y +s i) ζ +s i) 2 π +s 1 ) ψ π) 1 ψ +s 1 i) 1 +sy +s, subjec o he demand funcion 6) from he reailers. The opimaliy condiion is: ) P i) ɛ ) P i) ɛ 1 +s i) +s mc +s Y ɛ Y ) i) ζ π 1 ) ψ π) 1 ψ 1 i) 1 Y π 1 ) ψ π) 1 ψ 1 i) ) +1 i) +E Λ,+1 ζ +1 π ) ψ π) 1 ψ i) 1 π ) ψ π) 1 ψ +1 i) +1 Y +1 [ ] 2 = 0. π ) ψ π) 1 ψ i) Since all firms se he same price and herefore produce he same oupu in equilibrium, he above equaion can be rearranged as follows: ) π π 1 ) ψ π) 1 ψ 1 π π 1 ) ψ π) 1 ψ = 1 ɛ + ɛ ζ ζ mc [ 1 π +1 +E R /π +1 π ) ψ π) 1 ψ 1 ) π +1 Y +1 π ) ψ π) 1 ψ Y ]. 16) This equaion specifies ha inflaion depends on marginal coss as well as pas and expeced fuure inflaion. Solving forward equaion 16), i is possible o show ha inflaion depends on he expeced marginal cos sequence. In urn, an expression for curren marginal coss can be obained by rearranging he dynamic opimaliy condiion for employmen in 14): mc = W W N, P + N + QN 1 δ N )E Λ,+1 Q N +1, 17) f N, g N, f N, g N, f N, g N, while he dynamic opimaliy condiion for capial 12) can be solved o obain a cross-equaion resricion for E mc +1 : 9

11 W K,+1 +1 N +1 1 Q K Λ,+1 1 δ K )Q K +1 E mc +1 = E + E. 18) f K,+1 g K,+1 Λ,+1 f K,+1 g K,+1 For a deailed discussion of he erms in he wo equaions above we refer o Faccini and Yashiv 2015). Recen work by Gali 2010) has raised he quesion wheher he fricional componen of marginal coss, i.e., he las erm in equaion 17) maers for marginal coss and inflaion. Before geing ino he quaniaive analysis, an inuiive way o approach his quesion is o noice ha he erm Q N 1 δ N )E Λ,+1 Q N +1 in equaion 14) equals he marginal flow profi of a mach: Π = mc f N, g N, ) W W N, N, so he fricional componen of marginal coss in equaion 17) equals he raio of marginal hiring profis o he marginal produc of labor. A large lieraure ha sared following he work by Shimer 2005), has developed a range of models o overcome he inabiliy of he sandard exbook search and maching model o mach he volailiy of unemploymen a business cycle frequencies. While here is ye no consensus on wha model is mos appropriae o explain unemploymen dynamics, fricional models of he labor marke can accoun for he volailiy of unemploymen only if he volailiy of marginal profis is suffi cienly high, or oherwise incenives for job creaion would no flucuae enough over he cycle. A benchmark paper in his lieraure, Hagedorn and Manovskii 2008), generaes cyclical flucuaions in he raio of marginal hiring profis o he marginal produc of labor, wih a sandard deviaion ha is over fory imes as large as ha of he labor share. 2 A rule of humb calculaion based on his resul suggess ha he imporance of he fricional componen in driving marginal coss should be around 60% ha of he labor share. In his new ligh, we would find i surprising if hiring fricions didn maer for inflaion dynamics Wage bargaining Wages are assumed o maximize a geomeric average of he household s and he firm s surplus weighed by he parameer γ, which denoes he bargaining power of he households: { V ) N γ ) W = arg max Q N 1 γ }, The firs order condiion o his problem leads o he Nash sharing rule: 2 Auhors calculaions based on Hagedorn and Manovskii s 2008) calibraion, as illusraed in heir Table 2, page Gali 2010) shows ha a log linearizaion of he marginal coss yields: mc = 1 Φ) ŝ +Φ ˆf, where s denoes he labor share, f denoes he fricional componen, a ha denoes percenage deviaions from seady-sae and Φ = f f+s assuming ha a he seady sae s is abou 66% of GDP and f is roughly 1% of GDP. However, if ˆf 40ŝ, hen he conribuions of he fricional componen relaive o he labor share is approximaely 40Φ/ 1 Φ) 61%. 10

12 1 γ)v N = γq N. 19) Subsiuing 30) and 14) ino he above equaion and using he sharing rule 19) o eliminae he erms in Q N +1 and V +1 N one ges he following expression for he real wage: W = γmc f N, g N, ) γ W [ N, η l N + 1 γ) χn ϕ + x γ λ 1 x 1 γ QN The analyic soluion o his parial differenial equaion is provided in he Appendix. ]. 20) 3.5 Closing he model We assume ha he governmen runs a balanced budge: G T = B +1 R B, 21) where G denoes real governmen consumpion expendiures, which are given by: G = 1 1 η G ) Y, and η G is a governmen shock ha follows he sochasic process: ln η G = ρ G ln η G ρ G) ln η G + ς G. The moneary auhoriy obeys a sandard Taylor rule: R R = R 1 R ) ρ r 1 ) 1 ) 1/4 ρ r R 2 2 j= 2 E Π +j R Π φ π 1 1/4 j= 2 Ỹ+j) E Ȳ r y 1 ρ 1 r ρ 2 r where Ỹ Y /A and he bar sign over a variable denoes is seady-sae value, he parameer r s represens ineres rae smoohing, and r y and r π govern he response of he moneary auhoriy o deviaions of oupu and inflaion from heir seady-sae values. The erm η R capures a moneary policy shock. We assume ha he moneary shock is Gaussian and iid whereas he process Π capures persisen deviaions from he inflaion arge ln Π. More specifically, we assume ha ς R, 22) ln Π = 1 ρ π ) ln Π + ρ π ln Π 1 + ς π Finally, consolidaing he households and he governmen budge consrain, and subsiuing 11

13 for he profis of inermediae and final good producers yields he marke clearing condiion: Y 1 η G ) 2 ζ π 2 π 1 ) ψ π) 1 ψ 1 = C + η q [I +j + ν u )] = f g. 23) 4 Fricions and Inflaion Dynamics: an Impulse Response Analysis This secion explores he mechanisms by which fricions affec he response of marginal coss and he co-movemen of inflaion wih real variables. We firs calibrae he seady-sae equilibrium of he model ha allows for boh hiring and invesmen coss. We will hen inspec how fricions affec marginal coss and inflaion by comparing he impulse responses generaed by he unresriced model and hose obained from hree differen versions of he model, where fricions are shu down one a a ime. Specifically, he version of he model wih hiring invesmen) fricions only is obained by resricing e 1 0 e 2 0), while he sandard New Keynesian model wih no fricions corresponds o he case of e 1 = e 2 = 0. In wha follows we look a he calibraed or prior) equilibrium in order o compare models wih he same parameer values excep for he parameers of L and K fricions. Remark 1 In he las paragraph do you mean = 0 or 0? RF: I mean =0 only in he fricionless benchmark. 4.1 Calibraion The model is calibraed o he US economy over he period 1984Q1-2014Q2. The discoun facor β is consisen wih a quarerly nominal ineres rae of 1.34% as measured by he Federal Fund Rae, a quarerly inflaion rae of 0.62%, and an economy s growh rae of 0.50%. Togeher, hese numbers imply a value for β = The job separaion rae δ N is se o reflec separaions from employmen ino eiher unemploymen or inaciviy, while he capial depreciaion rae δ K is se o 0.02 consisen wih evidence in Yashiv 2015). Noice ha his value for he depreciaion rae implies an invesmen o capial raio of 2.5%, which is also consisen wih he daa. 4 The inverse Frisch elasiciy on he exensive margin ϕ is se equal o 3, in line wih he range of esimaes by Domeji and Floden 2006) and in beween he value of 5 used in Gali 2010) and he more sandard value of 1 as in Chrisiano Eichenbaum and Traban 2013) among many ohers. The elasiciy of subsiuion in demand ɛ is se o he convenional value of 11, implying a seady-sae markup of 10%, consisen wih esimaes presened in Burnside 1996) and Basu and Fernald 1997). The elasiciy of oupu o he labor inpu α is se o 0.66, which implies a labor share of income around 2/3. 5 The habi parameer is se o 0.6 as in???. 4 See Appendix B in Yashiv 2015) for deails on he consrucion of hese ime series. 5 In his model he elasiciy of oupu o he labor income does no correspond exacly o he labor share of income, bu hese wo values are close a he calibraed saionary equilibrium. 12

14 Table 1 This leaves us wih only five parameers o calibrae are: he bargaining power γ, he wo scale parameers in he fricions coss funcions, e 1 and e 2, he scale parameer χ in he uiliy funcion and he parameer, which governs he disuiliy of work, and he parameer ξ, which governs he curvaure of he uilizaion cos funcion. These parameers are calibraed o mach: i) marginal hiring coss, g H / [f g)/n], equal o 0.20 as esimaed by Yashiv 2015), which corresponds o nearly four weeks of wages; ii) marginal invesmen coss equal o 5% of he invesmen price as esimaed by Yashiv 2015); iii) an unemploymen rae of 10%, which is consisen wih our measure of he separaion rae ha includes separaion from employmen ino boh unemploymen and inaciviy and is in line wih BLS esimaes; iv) a replacemen raio of he opporuniy cos of work over he marginal revenue produc around 0.75, as advocaed by Cosain and Reier 2015). We emphasize here ha his implies a moderae calibraion of he fundamenal surplus fracion, so our resuls ha fricions maer for inflaion dynamics do no hinge on exremely low values of his noion of surplus; v) a value of he parameer ξ = uv / u) /v u) = 0.7 as esimaed by Gerler Sala and Trigari 2008). Noice ha our calibraion allows labor fricions o accoun for a higher share of marginal coss han in he papers of Krause, Lopez-Salido and Lubik 2008) and Gali 2010). These sudies assume ha average and marginal hiring coss equal nearly 5% of quarerly wages, following empirical evidence by Silva and Toledo 2009) on vacancy posing coss. Our funcional form for fricions coss allows for hiring coss o be inerpreed in a wider sense, which also includes raining as well as all oher sources of forgone oupu associaed wih hiring and discussed in Secion 3.3. As repored by Silva and Toledo 2009), average raining coss are abou 55% of quarerly wages, nearly wo monhs of wages. In he calibraion marginal hiring coss equal approximaely 30% of quarerly wages, approximaely one monh of wages, while average hiring fricion coss are abou half as large, around wo weeks of wages. We consider his value as conservaive in he ligh of he evidence above. Faccini and Yashiv 2015) also show ha he fricions coss funcion implies only a mild degree of convexiy: because marginal hiring coss can be expressed as a funcion of he hiring rae and parameer values using he funcional form in 8), i is possible o compue how he raio of marginal hiring coss over seady sae wages changes wih hiring raes. For a value of he hiring rae equal o 0.161, which is he highes value measured in he daa since hey were firs colleced in 1976Q1, he fracion of marginal hiring fricion coss over wages is only 37% of quarerly wages, implying an upper bound of marginal hiring coss ha is well below he average raining coss repored by Silva and Toledo 2009). 4.2 Impulse responses In wha follows we focus on TFP, invesmen and moneary shocks. This is suffi cien o highligh he following common hemes: 1) he ineracion of boh hiring/invesmen fricions and price fricions 13

15 dampens he response of employmen. In urn, his reduces he response of he marginal rae of subsiuion and real wages and implies a smooher response of he wage componen of marginal coss. 2) In models wih labor fricions he smooher response of wages affecs he value of a job Q N in such a way ha he fricional componen of marginal coss offses he response of he wage componen. Depending on he precise parameerizaion, his can resul in a smaller, larger or perfec offse. In he model wih capial fricions insead, his offse does no ake place, so for all shocks here is no couner-effec of Q N and he change in mc is miigaed. Remark 2 This las poin is no clear. RF: Replace he emphasized ex in he very las senence above wih he following senence and foonoe: In he model wih capial fricions only insead, Q N is oo small o maer, so his offse does no ake place, and he change in mc is miigaed. 6 3) Fricions do no offse he sign of he response of marginal coss and inflaion on he impac of shocks, bu hiring fricions, and o a lesser exen invesmen fricions change he sign response of real variables. This implies ha hiring fricions, and o a lesser exen invesmen fricions, affec he condiional co-movemen of inflaion wih real variables Technology Shocks Remark 3 I find he following sub-secion no clear enough; can u use equaions direcly and speak abou heir componens? equaions such as Remark 4 mc = W W N, P + N + QN 1 δ N )E Λ,+1 Q N +1, 24) f N, g N, f N, g N, f N, g N, W K,+1 +1 N +1 1 Q K Λ,+1 1 δ K )Q K +1 E mc +1 = E + E. 25) f K,+1 g K,+1 Λ,+1 f K,+1 g K,+1 Figure 1 repors impulse responses for a se of key variables o a 1% increase in TFP. Figure 2 decomposes he impulse responses of marginal coss and real wages ino conribuions from he various componens on he righ hand side of equaions 17) and 20), respecively. Each figure highlighs he response of he four benchmark parameerizaions discussed above. Figure 1 shows ha marginal coss and inflaion fall in all models, bu less srongly in he presence of capial fricions. Hiring, invesmen, employmen and capial fall in he fricionless NK model on he impac of shocks. This reflecs he sandard mechanism a work in NK models: oupu is demand driven when prices are rigid, herefore following an increase in produciviy, less inpu is needed o produce he same quaniy of goods. Inroducing separaely hiring and invesmen fricions can 6 Noice ha wih capial fricions only, Q N does no equal zero because he inra-firm bargaining erm W H, N P C in equaion 15) is non zero 14

16 reverse some of hese responses. For insance, hiring fricions bu no invesmen fricions) urn he response of employmen o posiive, while eiher hiring or invesmen fricions urn he response of invesmen o posiive. As discussed in Faccini and Yashiv 2015), he ineracion beween hiring or invesmen fricions wih price fricions generaes a relaive price effec on he value of employmen and capial ha offses he mechanism a work in he fricionless NK model. The smooher fall in employmen in he model wih capial fricions, and he increase in employmen in he model wih labor fricions, imply ha he marginal rae of subsiuion falls less, and respecively rises, relaive o he fricionless benchmark see Figure 2). Because real wages increase wih he marginal rae of subsiuion equaion 20), hiring fricions, and o a lesser exen capial fricions, endogenously dampen he fall in he real wage on he impac of he shock. In addiion, in he model wih hiring fricions only, he low bargaining power decrease he impac of he fall in marginal coss on he marginal revenue produc and hence on he negoiaed wage. Relaive o he fricionless model, he response of he marginal revenue produc is dampened also in he presence of capial fricions. As we explain in he nex paragraph, he smooh response of real wages wih capial fricions ranslaes ino a dampened response of marginal coss. This feeds-back o he negoiaed wage, enailing a subdued response of he marginal revenue produc. So he endogenous rigidiy in real wages arises in models wih fricions hrough he endogenous responses of boh he marginal rae of subsiuion and he marginal revenue produc Figure 2). The resilience of wages o echnology shocks implies a dampening effec on Q N, and hereby a fall in he fricional componen of marginal coss. The response of he inrafirm componen of marginal coss is small, alhough no negligible, so he firs-order effec is ha he fricional componen of marginal coss almos enirely offses he response of he wage componen, resuling in a similar response of marginal coss in he fricionless model and in he model wih hiring fricions only. In he model wih capial fricions only insead, mc only depends on he real wage componen. So marginal coss and inflaion will fall by less in his model, relaive o he fricionless benchmark. In he model wih boh hiring and invesmen fricions, he response of marginal coss and inflaion lies in beween he values obained in he parameerizaions where only one fricion is acive. I is worh emphasizing ha in models wih hiring fricions, he conribuion of he fricional componen o changes in marginal coss appears o be abou as imporan as ha of he wage share of income, even if hiring fricions are calibraed o relaively conservaive values Moneary shocks Figures 3 shows ha following a negaive shock o he ineres rae, marginal coss and inflaion increase in all models. Hiring, invesmen, employmen, capial and oupu increase in he fricionless NK model, whereby an expansionary moneary shock engenders a fall in he real rae, which simulaes boh consumpion and invesmen. The same variables increase also in he model wih capial fricions, albei less srongly so, while in he model wih hiring fricions hey barely 15

17 move. As explained in Faccini and Yashiv 2015), his reflecs a relaive price effec on he value of employmen and capial, which offses he mechanism a work in he fricionless NK benchmark. Remark 5 This is no clear wihou he analysis of he ype we did in he oher paper, i.e., wih showing expressions like Q N mc For slighly higher values of hiring fricions, he response of hiring, employmen and oupu can urn negaive, generaing a procyclical marginal cos condiional on moneary shock, in line wih evidence by Nekarda and Ramey 2013). The resul ha moneary policy is neural, if no conracionary, is consisen wih VAR evidence by Uhlig 2005), who, based on an agnosic idenificaion, concludes ha a moneary simulus is jus as likely o increase oupu or o decrease i. Remark 6 I find he res of he sub-secion unclear; i needs direc reference o equaions The smaller rise in employmen in he model wih capial fricions, implies a smooher response in he marginal rae of subsiuion and in real wages. Wih hiring fricions, he response of he MRS is mued, implying an even sronger dampening effec on real wages. In addiion, for he same reasons discussed for echnology shocks, boh hiring and invesmen fricions conain he response of real wages by smoohing also he response of he marginal revenue produc Figure 4). This rigid response of real wages ranslaes ino a dampened response of he wage componen of marginal coss, relaive o he fricionless benchmark. However, in models wih hiring fricions, wage moderaion implies a jump in he value of a job on he impac of he shock, and hus an increase in he fricional componen of marginal coss, which, in he curren calibraion more han offses he smoohing impac of fricions on he wage componen. As a resul, marginal coss increase by more in he model wih labor fricions only, relaive o he fricionless case. In he model wih invesmen fricions only, insead, he wage share of income is he only componen of marginal coss, so he dampening impac of capial fricions on wages direcly ranslaes ino a smooher response of marginal coss and inflaion. In he model wih boh labor and capial fricions, he response of marginal coss and inflaion lies in beween he wo benchmarks wih eiher labor or capial fricions only. In he model wih hiring fricions only, he response of he fricional componen of marginal coss appears o conribue o changes in marginal coss more han he wage componen, while in he model wih boh capial and labor fricions, boh componen seem o be equally imporan Invesmen specific shocks Remark 7 This is clearer bu sill would be helped by equaions Figure 5 shows ha following an expansionary invesmen-specific echnology shock, marginal coss and inflaion increase in all models. In he fricionless NK model, hiring, invesmen, employmen, capial and oupu increase, boh because of he direc effec of he shock on invesmen raes, 16

18 and because of he indirec impac of marginal coss on he marginal revenue produc of capial and labor. Fricions offse his effec hrough a relaive price effec on he values of labor and capial, leading o smooher responses in all real variables. The dampened response of employmen in he models wih fricions smoohs he response of he real wage via he marginal rae of subsiuion and he marginal revenue produc of employmen Figure 6). In urn, he smooher response of real wages ranslaes ino a dampened response of he wage componen of marginal coss, relaive o he fricionless benchmark. Wih hiring fricions, he lower increase in wages generaes an increase in he curren value of a job, and hus an increase in he fricional componen of marginal coss, which more han offses he response of he wage share of income in he case where only hiring fricions are acive. Wih capial fricions only, he wage share of income is he only componen of marginal coss, so he smooher response in wages direcly affecs he response of marginal coss. In he model wih boh capial and labor fricions, he response of marginal coss and inflaion is someway in beween he responses of he wo benchmarks wih eiher fricion acive; in his model boh he wage and he fricion componen appear abou equally imporan in driving marginal coss. 5 Esimaion of he DSGE Model The previous secion has shown ha boh hiring and invesmen fricions have crucial implicaions for he behavior of marginal coss and for he condiional co-movemen of inflaion wih real variables. We now underake esimaion of he full DSGE model o compare how he saisical performance of he NK model changes wih fricions. The quesion we address in empirical work is wha specificaion of he model is mos likely o have generaed he inflaion series, given a common se of observables and disribuions of priors for he parameer values. This secion describes he mehodology, he daa used and he choice of priors. The subsequen secions provide analyses of he resuls. 5.1 Mehodology and Daa We esimae he model using Bayesian mehods. Firs, we ake a firs-order approximaion of he sysem of equaions around a deerminisic seady-sae wih zero inflaion. We hen solve he model and apply he Kalman filer o evaluae he likelihood funcion of he observable variables. The likelihood funcion and he prior disribuion of he parameers are combined o obain he poserior disribuions. The poserior kernel is simulaed numerically using he Meropolis-Hasing algorihm. We firs esimae he full model described in Secion 3 using he priors and he shocks discussed below. Nex, using he same shocks, he same observables and he same priors for all he parameers, we esimae versions of he same model, where we resric he parameers e 1 and e 2 so as o shu 17

19 down one fricion a a ime. We hus esimae hree versions of he model wih fricions coss: he unresriced model, he model ha allows only for hiring coss, resricing e 1 = 0, and he model ha allows only for invesmen coss, resricing e 2 = 0. We will denoe hese hree models by M 1, M 2, and M 3, respecively. Each of hese hree versions is compared o he fricionless New Keynesian model, obained by resricing e 1 = e 2 = 0 and denoed by M 0. We esimae he model using he minimum se of observables and shocks ha are required o assess wheher hiring and invesmen fricions coss help explain inflaion dynamics in he conex of New Keynesian models. Inflaion, oupu and he ineres rae are ypically considered he very minimum se of observables when esimaing any model of inflaion dynamics. Given ha our heoreical mechanism affecs marginal coss hrough he inerplay of hiring and invesmen dynamics, we add series of gross invesmen and gross hiring flows o his se of observables. Finally, o discipline flucuaions in marginal coss we make he labor share of income observable o he esimaion. To keep boh he model and he esimaion as simple as possible, we have absraced from he governmen secor. Our daa se will herefore include only observables peraining o he privae secor in he spiri of Gali and Gerler 1999), hus no confounding he analysis wih governmen oupu, inflaion, hiring and invesmen. The model is esimaed on quarerly US daa over he period 1976 Q1 o 2014 Q2. The daa perain o he U.S. privae secor and have been downloaded from he Federal Reserve Economics Daa FRED) se. We make he following mapping beween model variables and observable daa series: oupu in he model corresponds o non-farm business secor oupu scaled by civilian noninsiuional populaion; inflaion is he implici price deflaor; he ineres rae is he effecive federal funds rae; invesmen corresponds o real gross privae domesic invesmen scaled by civilian noninsiuional populaion; he hiring rae is gross hiring flows scaled by civilian non-insiuional populaion. 7 The inflaion rae and he ineres rae series are demeaned prior o esimaion, while he oupu, invesmen, hiring and labor share series are derended wih an Hodrik-Presco filer wih smoohing parameer 1, Because no assumpion on he wage seing process is unconroversial in models wih fricional labor markes, we include a measuremen error in he observaion equaion for he labor share o capure model misspecificaion. We hen use five shocks o mach he behavior of he remaining five 7 The classificaion codes of he series used in he esimaions are he following: FEDFUNDS for he effecive federal funds rae, IPDNBS for he price deflaor, OUTNFB for oupu, GPDIC96 for invesmen, and CNP16OV for he populaion series. The compuaion of he hiring series firs builds on he flows beween E employmen), U unemploymen) and N no-in-he-labor-force) ha correspond o he E,U,N socks published by CPS. The mehodology of adjusing flows o socks is aken from BLS, and is given in Frazis e al 2005). This mehodology, applied by BLS for he period 1990 onward, produces a daase ha appears in hp:// Here he series have been exended back o The labor share series is derended because i feaures a major rend decline saring in he years 2000s. King and Wason 2012) argue ha real facors migh have influenced he rend in he labor share in ways ha are largely unrelaed o inflaion. Karabarbounis and Neiman 2014) documen ha he decline in he labor share is a global phenomenon and can be aribued o a large exen o he secular decline in he price of invesmen goods. Because our model canno accoun for rends in he labor share we simply remove he low frequency componen. The resuls in his paper are robus o excluding he labor share from he se of observable series. 18

20 observable series. The shocks include a preference shock, a echnology neural shock, a moneary policy shock, a labor supply shock and an invesmen echnology shock. All shocks are assumed o follow a firs-order auoregressive process wih i.i.d. normal errors. 5.2 Parameer priors and poseriors The model conains 13 srucural parameers, excluding he shock parameers. For he parameers ha affec he seady sae, he prior means of he esimaed parameers and he value of he parameers ha are kep fixed in esimaion, are assigned so as o follow he calibraion discussed in Secion 4.1. In erms of he disribuions for our priors, we use he Bea disribuion for priors ha ake values beween zero and one, he Gamma disribuion for parameers resriced o be posiive and he Inverse Gamma disribuion for he sandard deviaion of he shocks. Table 2 repors he parameers ha are kep fixed in esimaion. Table 2 Because he elasiciy of subsiuion ε and he coeffi cien of price sickiness ζ are no joinly idenified, ε is fixed in esimaion. A key feaure of our esimaion sraegy is ha we selec priors of he fricions coss funcion o be igh around he calibraed means. The reason why we do so is because we are ineresed in undersanding wheher conservaive parameerizaions of fricions coss can help explain and predic inflaion in he conex of New-Keynesian models, so we wan o enforce poserior esimaes of fricions coss o remain a he lower end of he range of reasonable values. This sraegy allows us o examine wheher moderae) fricions coss maer for inflaion dynamics. For he same reason, as seen in Table 2, we keep fixed in esimaion a number of parameers ha have a direc impac on he seady-sae, and could herefore change he size of fricions coss relaive o oupu. We can hink abou hese parameers as being esimaed wih infiniely igh priors. A echnical reason for eiher fixing or selecing igh priors for he parameers affecing he seady-sae is ha doing so ensures convergence of he seady-sae non-linear solver, which is only possible if he saring values are no oo far from he soluion. So for hese reasons, he workers separaion rae δ N and he capial depreciaion rae δ K are fixed, as in Gerler, Sala and Trigari 2008), and he priors around he bargaining power parameer γ are igh. We selec looser priors for he parameers ha do no affec he seady-sae, such as he coeffi ciens of he Taylor rule and he auocorrelaion of shocks. We have also esimaed versions of he model where we esimae a larger number of parameers and/or assume looser priors on he parameers affecing he seady-sae. This alernaive esimaion sraegy ends o increase he abiliy of fricions coss o explain inflaion dynamics. However, hese imply larger fricions coss and hence are less suied o address Gali s 2010) poin ha hiring fricions are oo small o maer. 19

21 Tables 3 and 4 fully characerize he priors used for esimaion as well as he poserior esimaes. 9 Tables 3-4 Overall, he poserior esimaes of he parameers appear o be ighly esimaed across all specificaions. The esimaed elasiciy of labor supply ranges from 0.28 o 0.33 in he four esimaed versions of he model, which is somewha below our prior and in line wih he synhesis of micro evidence repored by Chey e al. 2012), poining o Frisch elasiciies around 0.25 on he exensive margin. Anoher resul ha is common across models is ha he degree of ineres rae smoohing in he Taylor rule is esimaed o be lower han he prior mean. Models wih hiring fricions coss end o esimae a lower labor share of income han assumed in he calibraion. In he specificaion ha allows for boh hiring and invesmen fricions coss, an esimaed coeffi cien of α = 0.57 maps ino a labor share of income of 60%. Models wih fricions coss esimae a small sensiiviy of ineres raes o oupu in he Taylor rule, as in Chrisiano, Eichenbaum and Traband 2013), who also esimae a DSGE model wih hiring fricions. Turning o he shocks, all models esimae ha preference shocks are quie persisen. In addiion, boh echnology neural and invesmen-specific shocks are more persisen in models wih fricions, while moneary shocks are persisen only in he fricionless model. 6 Accouning for he Role of Fricions in Inflaion We now evaluae wheher fricions coss affec marginal coss in a way ha is useful o explain inflaion. We also seek o deermine wha specific form of fricions maers. Table 5 shows he esimaed marginal and oal fricions coss for differen specificaions of he fricions coss funcion, evaluaed a he poserior means repored in Tables 3 and 4. Table 5 The fulles model, M 1, has oal fricions coss a 2.4% of GDP and marginal coss a magniudes ha were discussed in Secion 4.1 above. The M 2 model is esimaed o imply similar coss: 1.6% of GDP for oal coss and marginal hiring coss as in M 1. The oher model, M 2 implies somewha lower oal coss, 1% of GDP, and marginal invesmen coss as in M 1. In wha follows we explain wha role hese fricions play in deermining inflaion. 6.1 Marginal Daa Densiy Analysis We rely on he marginal daa densiy MDD) as he measure of fi. The MDD is compued for each model using he modified harmonic mean esimaor inroduced by Geweke 1999). Considering 9 Each esimaion of he model is based on five parallel chains, each one consising of 250,000 draws from he Meropolis algorihm, half of which are discarded as burn-in. Brooks and Gelman 1998) diagnosics provide evidence on convergence. Accepance raes for all he models vary beween 20 and 34 percen. 20