On-the-job Search, In ation Dynamics and Welfare Cost of In ation

Transcription

1 On-he-jo Search, In aion Dynamics and Welfare Cos of In aion Yahong Zhang January 4, 2010 Asrac This paper examines he implicaions of on-he-jo search for oh shor-run dynamics of in aion and long-run welfare coss of in aion in a sicky price model wih laour marke search fricions. Boh unemployed workers and workers wih ad jos can search. Firms can adjus laour a oh inensive and exensive margins. On-he-jo search gives rise a srong propagaion of moneary policy shocks hrough he exensive margin since on-hejo search opens up an exra channel of employmen. However, on-he-jo has lile e ec on in aion on impac since in he rs period rms can only adjus inensive margin, which is very cosly. The welfare coss of in aion generaed y he model wih on-he-jo search and he model wih he on-he-jo search mechanism eing shu down are similar as ha generaed y he sandard New Keynesian model, suggesing ha he srucure of laour marke is irrelevan o he welfare coss of rend in aion unless exra nominal rigidiies are added o he model. JEL: classi caion: E24; E31; E32 Keywords: On-he-jo search, search and mach, in aion dynamics, welfare cos of in aion Canadian Economic Analysis Deparmen, Bank of Canada, 234 Wellingon S., Oawa (ON), Canada, K1A 0G9; yzhang@ankofcanada.ca. 1

2 1 Inroducion The main ask of cenral anks is o mainain price sailiy y conrolling inzaion, hus i is imporan o undersand wha drives he dynamics of inzaion. Empirical evidence suggess ha afer an expansionary moneary policy shock, here is a large and persisen rise in oupu and a sluggish response in in aion. The sandard New Keynesian models (NK hereafer) have di culies in replicaing his join responses of oupu and in aion. One of he key reasons is ha he sandard NK model assumes a fricionless compeiive laour marke, which asracs from he unemploymen. Firms can only adjus hours o mee he demand, which is very cosly unless a very high elasiciy of laour supply is assumed. Real wages in he NK models are very volaile, leading o a larger price adjusmen han he daa sugges. In aion is very responsive and shor-lived, hus moneary policy shocks are unale o yield persisen e ecs on real economic aciviy. Recen lieraure has aemped o inegrae he sandard NK model wih laour marke search and maching model in order o generae a less responsive real wage, in urn, a less responsive real marginal cos. Since he real wage implied y he aseline search and maching model is sill oo volaile o mach he daa, some degree of real wage rigidiy is ofen added o he aseline model. However, Krause and Luik (2007a) shows ha alhough inroducing an exogenous wage rigidiy ino a laour marke helps he dynamics of vacanies and unemploymen, i has only minor e ecs on he dynamics of real marginal coss. This is ecause wih a fricional laour marke, real marginal coss are no only deermined y real wages u also deermined y an addiional componen, he so called cos of long-erm employmen relaionship. This is he cos of hiring a worker ne of he expeced saving of fuure hiring coss. Krause and Luik (2007a) shows ha afer imposing real wage rigidiy, real marginal cos can sill e very volaile due o cos of long-erm employmen relaionship. Thus hey quesion he relevance of adding search fricions ino he sandard NK model. A recen sudy y van Zandweghe (2009) emeds an on-he-jo search mechanism o an oherwise sandard NK model wih a laor marke search. He shows ha unlike he exogenously imposed real wage rigidiy, on-he-jo search no only dampens he response in real wages, u 2

3 also dampens he response of he cos of long-erm employmen relaionship. Thus he search fricions in he laour marke endogenously generae rigidiy in real marginal cos. On-he-jo search gives rise o a srong propagaion of moneary shocks ha increases oupu persisence. His ndings are in sark conras wih Krause and Luik (2007a). This is ecause on-he-jo search allows workers o search for more producive jos and hese employed jo seekers ecome a source of employmen growh in addiion o unemployed workers. During he oom, laour marke is less igh due o on-he-jo search. This reduces workers ouside opion, hus he real wages rise y less. The rise in cos of employmen relaionship is also eing dampened since hiring coss rise y less. However, van Zandweghe (2009) only considers he exensive margin, i.e. he change in employmen. Given ha in he daa he cyclical ucuaions in oal hours resul from oh changes in employmen and changes in hours, i seems naural o consider oh margins insead of aking his exreme and polar assumpion. Moreover, considering laour adjusmen a wo margins will generae implicaions for dynamics of hours per worker over he cycle as well as he dynamics of employmen and he ineracions eween he wo margins. More imporanly, when rms can adjus laour a wo margins, he deerminaion of real marginal coss is di eren, hence he deerminaion of in aion. Adjusmen a he hours margin is curren looking, while he adjusmen a he employmen margin has he long-erm employmen relaionship componen, which is forward-looking. Afer moneary shocks, he wo margins will o adjus o mee he demand so ha heir marginal coss are equalized. Given he poenial imporance of considering oh margins, i is surprising ha he sandard NK model only considers he inensive margin while he aseline search and mach model only consider he exensive margin. In fac, ignoring one margin can lead misleading resuls. Thus in his paper, I consider a dynamic general model ha inegrae a fricional laour marke wih a sandard NK model. For workers, hey can search for jos when hey are unemployed or search for eer jos when hey have ad jos. For rms, hey can adjus laour eiher a he inensive or he exensive margin. Following Krause and Luik (2007) and van Zandweghe (2009), search on he jo is moivaed y he presence of wo ypes of jos, which di ers in erms of pro ailiy and hus he reurns o working. I show ha he 3

4 ampli caion and propagaion e ecs of on-he-jo search come mainly from he exensive margin insead of inensive margin. This is ecause ha i is less cosly for rms o adjus numer of workers. In conras o he ndings in van Zandweghe (2009) ha on-he-jo search reduce he response in in aion on impac y half, I nd ha on-he-jo search has lile e ec on in aion dynamics on impac, alhough i dampens he response of in aion in he susequen periods. This is due o ha i akes ime for he newly hired workers o ecome producive, on impac rms can only adjus hours, which is very cosly. Once rms are ale o adjus exensive margin, on-he-jo search will dampen oh real wage and cos of long-erm employmen relaionship, hus dampens he real marginal coss and in urn in aion. Finally, since he welfare coss of in aion are likely o e sensiive o assumpions regarding he srucure of he laour marke, I use he caliraed values descried aove o examine he seady-sae welfare for he hree models, he NK model, he on-he-jo search model and he model wih on-he-jo search eing shu down for in aion rae of 0 percen, 1 percen, 2 percen and 4 percen. I show ha as in he NK model, he opimal rend in aion is zero percen in he model wih he laour marke feauring search fricions. This is no surprising since he fricions in laour marke are real fricions; he only nominal rigidiy in he model comes from he saggered price seing ehavior of he rms. Using he consumpion equivalen measure of welfare, I show ha he welfare cos of 2 percen in aion is 0.1 percen of consumpion. The reminder of he paper is organized as follows. Secion 2 descries he model; Secion 3 persens he caliraion; Secion 4 descries he role of on-he-jo search on in aion dynamics; Secion 5 presens he implicaions of laour marke fricions on he welfare coss of rend in aion. Finally Secion 6 o ers some conclusion remarks. 2 Model In his secion I illusrae he model. The model is a convenional New Keynesian model wih a fricional laor marke feauring on-he-jo search. The model has four ypes of agens: households, inermediae good producers, nal good producers and a moneary auhoriy. Households solve for he sandard consumpion/saving prolem. Households supply laor o 4

5 wholesale rms, which produce inermediae goods in compeiive markes using laor as heir only inpu, and sell heir oupu o nal good producers who are monopolisically compeiive and sujec o sicky prices. Households consume nal goods. 2.1 The laor marke In order o capure jo-o-jo ransiions, I follow Krause and Luik (2007) o characerize he laor marke wih heerogenous rms. There are wo classes of rms: "good" and "ad", which di er in heir coss of creaing new jos. "Good" jos can e inerpreed as capialinensive jos. Since a rm wih a "good" jo has already sunk is more expensive invesmen, i is forced o argain o a higher wage. This wage di erenial moivaes workers in "ad" jos o search for employmen in high-wage jos. All workers wih low-wage jos search for highwage jos, and he inensiy of he on-he-jo search is endogenous. Workers in high-wage jos have no incenive o search since i is cosly and does no o er higher reurns o heir curren employmen. Unemploymen workers can search eiher jos. However, workers decide which ype of jo hey wan o apply ex ane, hus in he equilirium he value o an unemployed worker for eiher ype of jo mus e equal. The process of maching workers and rms is summarized y a maching funcion, which is consan reurns o scale and homogeneous of degree one. For ad jos, he oal per period new maches is given y m = (u ) (v ) 1 (1) where u is he measure of unemployed workers searching for ad jos, v he measure of ad jo vacancies. 2 (0; 1) is he unemploymen elasiciy of new maches. is he scale parameer ha re ec he e ciency of he maching process. For good jos, he numer of maches is given y m g = (ug + e ) (v g )1 (2) where u g is he measure of unemployed workers searching for good jos, e is he measure of e ciency unis of search y workers wih ad jos n, who search wih endogenous inensiy s. e = (1 )n s : The proailiies o ll a vacancy for ad jos and good jos are given 5

6 y q = m, and q g v = mg v g respecively. The proailiies o nd a ad and good vacancy are given y p = m u and p g = mg u g +e respecively. The ighness in he maching marke for ad jos is de ned as = v, and for good jos g u = vg u. +e The evoluion of period employmen in each ype of jo is given y n g = (1 )(ng 1 + mg 1 ); (3) n = (1 )(n 1 + m 1 s 1 p g 1 n 1): (4) where is exogenous separaion rae. The laws of moion imply ha in he eginning of a period, a proporion 2 (0; 1) of exising maches are desroyed. The newly mached workers have o wai for one period o ecome producive. The produc of s 1 p g 1 gives he proailiy of a qui. The oal size of he laor force is normalized o 1, and he oal numer of joless searchers is given y u = 1 (1 )n 1 : where u = u g + u ; n = n g + n : 2.2 Inermediae good producers Bellman equaions Before descriing rms vacancy posing decisions and he deerminaion of real wages and hours, I descrie he ellman equaions ha characerize he prolem of rms and workers. I assume ha cos of posing a vacancy for a good jo, g, and he cos for a ad jo is, and g > : The value of a mached good jo is given y J g = z x g f(hg ) wg hg + E [(1 )J g +1 + V g +1 ]; (5) 6

7 where x g and wg denoe, respecively, he relaive price of he inermediae good and he hourly real wage rae from he high-wage rms. The value of he high-wage jo is he curren pro s z x f(h ) wh plus he coninuaion value. Nex period, wih proailiy (1 ) he mach is no severed, wih proailiy he mach is desroyed. The value of a mached ad jo is given y J = z x f(h ) w h + E [(1 )(1 s p g )J +1 + ( + (1 )s p g )V +1]; (6) which shows ha ad jos face he addiional risk of workers leaving o good jos. The higher he search inensiy s, he lower he likelihood of he ad jo remaining mached in he nex period. The value of a vacancy for oh ypes of jos is given y V j = j + E ;+1 [(1 )q j J j +1 + (1 (1 )qj )V j +1 ]; j = ; g: (7) Once he vacancy is eing lled, i ecomes producive he nex period. The value of an employed worker wih a good jo is given y W g = w g hg g(h g )= + E ;+1 [(1 )W g +1 + U g +1 ]; (8) where g(h g )= is he disuiliy from supplying hours expressed in erms of curren consumpion. The value of an employed worker wih a ad jo is given y W = max s (w h g(h )= (s )+E ;+1 [(1 )(1 s p g )W +1 +(1 )s p g W g +1 +U j +1 ]): (s ) denoes he sricly convex cos of search inensiy s ; wih k(0) = 0; k 0 > 0 and k 00 > 0. Taking as giving he wage, workers chose he opimal search inensiy. The opimal search (9) inensiy is given y: 0 (s ) = 1 pg (g q g q ); (10) which suggess ha search inensiy rises wih he proailiy of nding a good jo, and wih he di erence eween he value of good and ad jos. 7

8 Finally, he values of unemployed workers searching for jos for ype j = g; are U j = u + E ;+1 [(1 )p j W j +1 + (1 (1 )pj )U j +1 ]; (11) where u is he unemploymen ene Vacancy posing Free enry condiion implies ha he values of vacancies are driven o zero a any poin in ime, i.e. V = V g = 0 for all : Given his free enry condiion, he numer of vacancies is deermined y he following jo creaion condiions: q g q g = E ;+1 (1 )[x +1z +1 f(h +1) w+1h +1 + (1 s +1 p g +1 ) q+1 ] (12) = E ;+1 (1 )[x g +1 z +1f(h g +1 ) wg +1 hg +1 + g q g ] (13) +1 The jo creaion condiions relae he expeced cos of a posed vacancy o he expeced ene. Since U g = U, i implies ha p g g q g = p q : (14) I suggess ha he relaive marke ighness for oh ypes of jos are deermined y he relaive vacancy coss Bargaining wages and hours. Boh real wages and hours of work are deermined y Nash argaining eween rms and workers. Tha is, he rms and he workers choose he real wage w and he hours of work, h, o maximize he Nash produc (W j U j ) (J j V j )1 ; (15) 8

9 where 2 (0; 1) is he workers argaining power, he rs erm in rackes is he workers surplus, and he second is he rm s surplus. Firms and workers argaining simulaneously aou real wages and hours, hus he wage is no allocaive, ha is, hours are chosen o maximize he join surplus of he mach, while he wage is se o spli he surplus according o he argaining power parameer. The rs order condiions wih respec o wages give he surplus spliing rules, J j = (1 )W j, which resul in he following wage equaion w h = [x z f(h ) + (1 s )p q ] + (1 )[ + (s ) + g(h )= ]; (16) and w g hg = [xg z f(h g ) + pg g q g ] + (1 )( + g(h g )= ): (17) The workers are rewarded for a fracion of he rms s revenues and he savings of hiring coss and compensaed for a fracion 1 of he disuiliy from supplying hours of work and he foregone unemploymen ene s. For workers who have a ad jos, hey are also compensaed for he search cos. The hours of works are chosen y he following rs order condiion g 0 (h j ) = x j z f 0 (h j ); j = ; g (18) where he values of he marginal produc of laor and he marginal rae of susiuion eween consumpion and leisure. This rs order condiion for hours is he same as in a compeiive laor marke. This is ecause in he model he cos of hours o he rms is no he wages, u he marginal rae of susiuion. This means ha wages are no allocaional for hours. The funcional form for he producion funcion is assumed as f(h j ) = h h. Given ha g(h j ) = (h j )1+ h h 1+, he hours for oh good jo and jo jo secors are h h j = ( x j z h ) h h +1 ; j = ; g (19) h 1 9

10 The aggregae producion funcion for he inermediae rms is, y j = (1 )z n j f(hj ), j = ; g (20) where f(h j ) = (hj ) h, z is he produciviy shock which follows an AR(1) process. log(z ) = z log(z 1 ) + z ; z N(0; 2 z): (21) 2.3 Final good producers The nal good marke is characerized y monopolisic compeiion. There is a coninuum of nal good producers of measure 1. Le y (j) e he nal good sold y nal good producer j and p (j) e is nominal price. Each of he nal good producer comines inermediae goods and g produced in ad jo secor and good jo secor ino a di ereniaed good using a Co-Douglas producion echnology y (j) = (y (j)) (y g (j))1 : (22) The nal good producer oain inpu and g from compeiive laor facor markes a price x and x g. I assume ha < 1=2 so ha produciviy of inpu g exceeds ha of : To minimize he cos, rms j s demand for inpu and g are given y y (j) = ( x x )y (j); (23) y g (j) = (1 )( x x g )y (j); (24) where x g, x are he relaive price for inpu g and. The real marginal cos x for each nal good rm is given y x g x = ( x ) ( 1 )1 : (25) 10

11 The nal goods, y, are he composie of individual reail goods: y = [ Z 1 0 y " 1 " j dj] " " 1 ; (26) and he corresponding price index, p, is given y p = [ Z 1 0 p (j) 1 " dz] 1 1 " : (27) The demand funcion faced y each nal good producer is given y y j = ( p j p ) " y : (28) Following Calvo (1983), each nal good producer canno reopimize prices unless i receives a random signal. The proailiy of receiving such a signal is 1. Thus, in each period, only a fracion of 1 of reailers rese heir prices, while he remaining nal good producers keep heir prices unchanged. Given he demand funcion equaion (28), he nal good producer chooses P j o maximize is discoun, expeced real oal pro over he periods during which is prices remain xed. E 1 i=0 i;+i [( p j p +i )y j+i x +i y j+i ]; (29) where ;i i c +i =c is he sochasic discoun facor. Le p e he opimal price chosen y all rms adjusing a ime. The rs order condiion is: p " = ( " 1 )E The aggregae price evolves according o: P 1 i=0 i i;+i x +1 y +i ( 1 p +i ) " E P 1 i=0 i i;+i y +i ( 1 p +i ) 1 " : (30) p = [p 1 " 1 + (1 )(p ) 1 " ] 1 1 " : (31) 11

12 2.4 Households There is a represenaive household wih a coninuum of memers of measure one. Following Andolfao (1996) and Merz (1995), I assume ha family memers are perfecly insured agains he risk of eing unemployed, hus each family memer has he same level of consumpion. The represenaive household maximizes lifeime uiliy. X 1 E 0 u(c ; h g ; h ); (32) =0 where 1 U(c ; h g ; h ) = c1 1 h(n g hg1+ h + n h1+h ); (33) 1 + h 1 + h where h are he weigh on laor supply in he uiliy funcion. The represenaive household derives uiliy from consumpion, c. The household supply laor o wo ypes of jos, su er he disuiliy from supplying laor h g and h. The numer of family memers currenly employed is n = n g + n. The represenaive household is sujec o he following udge consrain p c + = w g p h g ng + w p h n + u (1 n g n ) + 1 r 1 + r : (34) Households have he ownership of nal goods and supply laor o he inermediae good producers. The employed family memers earn real wage w g and w. The unemployed memers receive unemploymen ene u. Thus he income of he household consiss of hree pars: he laour income from oh good jo secor and ad jo secor w g p h g ng + w p h n, he income from unemploymen ene u (1 n g n ), and he share of aggregae pro s from nal good producers r. The aggregae price is p. The household saves y holding a one-period riskless ond. 1 is he ond held eween periods 1 and, and r 1 is he nominal rae of reurn on he riskless ond. The aggregae price is p. The household maximize is expeced lifeime uiliy equaion (32) sujec o equaion (34). 12

13 The rs-order condiions include c p = r E c +1 p +1 ; (35) 2.5 Moneary auhoriy I assume ha he cenral ank operaes y he sandard Taylor Rule. The cenral ank adjuss he nominal ineres rae, r, in response o deviaions of in aion,, and oupu, y, from heir seady-sae values. r r n = r 1 r r y 1 y y r e m ; (36) where r, and y are he seady-sae values of r, and y, and " m is a moneary policy shock which follows " m i:i:d: N(0; " m): (37) r, and y are policy coe ciens chosen y he cenral ank. 3 Caliraion To compue he welfare cos of in aion in his model, I rs calirae he model o he quarerly U.S. daa. The daa is from 1964 Q1 o 2008 Q1 and i is linearly derened. The aseline caliraion is summarized in Tale 1. The discoun facor is se o e 0.99, which corresponds o he annual risk-free ineres rae of 4%. The ineremporal elasiciy of consumpion is se o e 1. The elasiciy of laor supply is 1= h. Since mos microeconomics sudies sugges ha his elasiciy o e close o 0 and no higher han 0.5, I se h o e 8, which implies ha he laor supply elasiciy of 1/8. I hen se he weigh on leisure h o 1 so ha he average working ime is normalized o 1. I se he Calvo parameer o e equal o 0.67, which implies ha he average ime eween price adjusmens is 3 quarers. I assume ha ha he markup of price on marginal cos is 10 percen. This implies ha " = 11: 13

14 Tale 1: Srucural Parameers Parameer Value Descripion 0.99 Sujecive discoun facor (quarerly) 0.40 Share of ad secor inpu h 1 Coe cien in inermediae good producion secor h 1 Weigh on leisure 8 he inverse of laor supply elasiciy (hours) 1 ineremporal elasiciy of consumpion 0.67 Fracion of rms no seing prices opimally each quarer " 11 Price elasiciy of demand for a speci c good variey 0.4 Elasiciy of maching o unemploymen 0.62 Scale parameer in he maching funcion 0.1 Jo separaion rae (quarerly) 0.02 Jo posing cos in low wage secor g 0.04 Jo posing cos in high wage secor 1.1 Elasiciy of search inensiy o search cos 0.5 Bargaining power of workers R 0.80 Ineres-rae smoohing parameer 1.5 Policy coe cien o deviaions of in aion y 0 Policy coe cien o deviaions of oupu z 0.9 Serial correlaion of he log of echnology shock z Sd. dev. of he innovaion o log of echnology e Sd. dev. of he innovaion o log of moneary policy For he laor marke, I choose a separaion rae of =0.1, which is aken from den Haan and Wason (2000), his value includes oh exogenous jo desrucion as well as quis ino unemploymen or movemens ou of he laor force. I se he unemploymen rae as Krause and Luik (2007), which is 15.4%. This value is higher han ha commonly used in he daa ecause i also includes workers ha are only loosely aached o he laor force, such as discouraged workers or workers engaging in home producion. Also following Krause and Luik (2007), I se jo-o-jo ransiion rae o e 0.06, which measures he fracion of workers in ad jos secor who move on o good jos secor among he oal employmen. This also implies ha 40% of he oal hires are jo-o-jo ransiions. Good jos are di eren from he ad ones due o he di eren jo creaion coss. Following 14

15 Krause and Luik (2007), I assume ha he jo creaion coss g >. The values of g and are pined down y he following consideraions. Jo creaion coss are assumed o consis of recruimen coss, raining coss and hose are mos likely o e proporional o he capial inensiy. Good jo secor is more capial inensive han ad jo secor, hus I se g = 2, which is in line wih he di erence eween he capial inensiy of average high-wage and low-wage jos. The second consideraion for jo creaion coss is ha he coss should resul in reasonale resource loss. I se g = 0:04 and = 0:02 and hose values resuls in 1% of oupu used in jo creaion aciviies. The share parameer is se o e 0.4, which is he value in van Zandweghe (2009). I se he echnology parameer h o e 1, implying ha i is consan reurns o hours per worker. Wih respec o search coss, i is assumed ha hese coss are sricly increasing and convex in he search inensiy. In paricular, I use (s ) = s : The elasiciy of search coss o search inensiy is, which is se o e 1.1. The scale parameer is compued implicily o mach he caliraed seady sae. I consider wo ypes of shocks: echnology shock and moneary policy shock. The echnology shock is assumed o follow an AR(1) process wih an auoregressive parameer z = 0:9 and a sandard deviaion z = 0:006. The moneary policy shock is assumed o follow an AR(1) process wih an auoregressive parameer m = 0 and a sandard deviaion m = 0:0023: z and m are chosen o mach he sandard deviaion of oupu oserved in he U.S. daa, which is 4.04%. Finally for he moneary policy rule, I follow he esimaes in Clarida and Gerler (2000) and se he coe ciens for in aion and oupu gap, and y o 1.5 and 0, and se he ineres rae smoohing parameer r o 0.8. Based on his caliraion, I nd ha in he seady-sae, he cos of posing vacancies is aou 1% of GDP. 40% of jos are ad jos, and he search inensiy is aou one hird. This means ha 12% of he laour force are acively searching on he jo. 15

16 4 Implicaions of on-he-jo search for shor run dynamics In order o evaluae he conriuion of laour marke fricions, especially he on-he-jo search mechanism o shaping he dynamics in he key macro variales, I compare he aseline onhe-jo search model (OJS hereafer) wih a sandard search model y shuing down he on-he-jo search (NoOJS hereafer), and wih a NK model y assuming away search and maching fricions in he laour marke. All oher feaures are kep he same as he aseline model. Tale 2 repors he performance of hese hree models in erms of maching he relaive volailiies of he key variales in he daa. The rs row displays he sandard deviaions of real wages, unemploymen, vacancies and in aion relaive o oupu. OJS model generaes he resuls ha maches he daa he es. Compared o NoOJS model, he model wih he on-he-jo search increases he volailiy in vacancies y 2.6 imes and in unemploymen y 1.8 imes, i also reduces he volailiy in real wages y 33%. Tale 2: Sandard Deviaions of he Key Variales y w u v daa OJS NoOJS NK NoOJS Oupu Figure 1 shows he oupu responses o one sandard deviaion of moneary policy shock in he hree models. Compared o he NK model, he models wih laour marke fricions, OJS and NoOJS models generae a more ampli ed and persisen response of oupu. OJS model generaes a peak increase in oupu of aou 0.27% and i akes around 13 quarers for oupu o come ack o he seady-sae; while he NK model generaes a peak increase of aou 0.22% and oupu goes ack o is seady-sae afer 5 quarers. The NoOJS model lies in eween. In oh OJS and NoOJS models, he oupu responses are more ampli ed and more persis- 16

17 en compared o he NK model. This is mainly due o he changes of employmen raher han hours. The lower panel of Figure 1 shows he impulse responses of hours and employmen and i is clear ha he ampli caion and propagaion come from employmen raher han hours. Afer he moneary policy shock, wih on-he-jo search, he employmen reaches a peak of 0.16 percen and ges ack o he seady-sae afer 13 quarers; while hours drops elow he seady-sae level a he second quarer and comes ack o he seady-sae afer 5 quarers. The inuiions for why on-he-jo search ampli es and propagaes he response of oupu afer a moneary policy shock is as follows. Afer an expansionary moneary policy shock, rms pos more vacancies o mee he rise in demand, and his leads o more jo creaions. The more jo creaion increases he proailiy for workers o nd a jo, and his increases he numer of employed workers n, and oupu. However, wihou he on-he-jo search mechanism, he jo creaion process will ge ack o he seady-sae very fas. This is due o ha he increased numer of vacancies will cause laour marke ighness o rise. The increase in ighness increases wages, hus reduces he incenive of rms o pos vacancies. The increase in ighness also pushes up hiring cos since rms face he less chance o mee workers. Wih he on-he-jo search mechanism, he increased numer of vacancies in he good jo secor will induce workers wih ad jos o increase heir search inensiy, as shown in he following equaion: 0 (s ) = 1 g g (1 g )1 : This equaion is derived from he opimal search inensiy equaion and he arirage condiion for he unemployed workers. An increase in search inensiy will furher feed ack o g as seen from he de niion, g = v g u g + s n : The higher search inensiy will miigae he ighness in he laour marke. Thus, wih onhe-jo search, he increased search inensiy will encourage rms o pos more vacancies and i will lower he ighness in he good jo secor. Due o his, rms in he good jo secor need o increase he vacancies more o mee he jo creaion condiion. This process will end due o he decreasing reurns of search. 17

18 4.2 In aion The second panel of Figure 1 displays he dynamic responses of in aion. On impac, in aion jumps up and peaks in all hree models. The magniudes of he peak in aion response are almos he same for he hree models. In he susequen periods, he in aion responses in he models wih laor marke fricions are dampened. This is di eren from van Zandweghe (2009), which nds ha he on-he-jo search reduces he response in in aion y half on impac. This is due o van Zandweghe (2009) only considers he exensive margin and assumes he conemporaneous hiring, i.e. in response o shocks, rms change numer of employed workers y hiring or exogenous separaion and he new hire ecomes producive insanly. In my model, I assume ha he new hire needs o wai for a period o e producive. Afer a moneary policy shock, on impac, rms can only adjus inensive margin (hours) since hey need ime o adjus he exensive margin (numer of employed workers), and his pushes up he marginal cos he same way as he sandard NK model. To undersand his eer, le us sar wih he NK model. In he NK model, o mee he demand, rms can only adjus hours. Real marginal cos is given y x = w z f 0 (h ) : Real wage is equal o he marginal rae of susiuion, which is very responsive unless he laour supply elasiciy is large. Thus, he sandard NK models usually predic larger price adjusmen han he daa sugges. In he model wih laor marke fricions, rms can adjus oh inensive and exensive margins, i.e. hours worked per worker or numer of workers. However, on impac, since i akes ime o hire a new worker hrough vacancy posing and maching, he sock of currenly employed workers, n, is perdeermined, rms can only adjus hours. Hours are deermined over he e cien argaining, he real marginal coss in oh secors are given y j ) g0 (h x j = z f 0 (h j j = ; g: (38) ); 18

19 Thus he real marginal cos is equal o he marginal rae of susiuion divided y he marginal produc of laour in his secor. This is he same form as in a neoclassical laour marke. Thus on impac, he response in in aion is very similar o ha in he NK model. In addiion o he rise in hours, in oh OJS and NoOJS models, here is a jump in he numer of vacancies on impac since rms expec higher pro in he fuure. The response of vacancies is more pronounced in OJS model. The increase in vacancy posing reduces he availale oupu, causing in aion rises more on impac in OJS model han he oher models. In he susequen periods, rms in he models wih laour marke fricions can adjus oh inensive and exensive margins. Boh wo margins will adjus o mee demand so ha heir marginal coss are equalized. A he opimum he cos of producing he marginal uni of oupu y adding an exra hour of work mus e equal o he hourly cos of producing he marginal uni of oupu y adding an exra worker. Figure 1 shows ha rms mainly rely on adjusing he exensive margin insead of he inensive margin o mee he demand since he adjusmen in he exensive margin is less cosly. Due o his exra margin, he in aion responses in he models wih laor marke fricions are dampened in he models wih laour marke fricions. The in aion is dampened more in he model wih on-he-jo search model. The inuiions for his is as follows. When rms adjus he exensive margin, he marginal cos o he rms consiss of wo componens: x g = wg hg z f(h g ) + J g g =q g z f(h g ) ; x = w h z f(h ) + J (1 s p ) =q z f(h ) : The rs is he ow cos of keeping one addiional worker employed: divided y he average produc of laour. The second erm J l l =q l z f(h l w g hg z f(h g ), he wage cos ) is he cos of an employmen relaionship, which capures he value of a long erm employmen relaionship o he rm, he di erence eween he curren value of having an addiional worker availale J g and he expeced value of lling a new vacancy his period and saring o produce nex period g =q g. Compared o he sandard search model, on-he-jo search dampens he response in oh he wage coss and he cos of an employmen relaionship. Consider rs how on-he-jo search 19

20 a ecs he real wage afer a moneary policy shock. In he search models, real wages are direcly relaed o laour marke ighness. The igher he laour marke, he higher he value of workers ouside opion and he higher he real wages. On-he-jo search opens up an addiional employmen growh, i.e. he addiional jo seekers from he ad jo secor. This reduces he laour marke ighness, and in urn, dampens he response in real wages. On-hejo search also dampens he response of he cos of employmen relaionship. This is ecause on-he-jo search lowers he hiring coss for rms. When laour marke is less igh, rms will have higher proailiy of meeing workers and he vacancies will e lled faser. 5 Implicaions of laour marke fricions for long run welfare cos of in aion Since he welfare coss of in aion are likely o e sensiive o assumpions regarding he srucure of he laour marke, in his secion I use he caliraed values descried aove o examine he seady-sae welfare for he hree models, he NK model, NoOJS model and OJS model for in aion rae of 0 percen, 1 percen, 2 percen and 4 percen. Tale 2 repors he comparison resuls. Tale 3: Welfare Coss of In aion Relaive o 0 Percen Model 1% 2% 4% NK NoOJS OJS As in he NK model, he opimal rend in aion is zero in he model wih he laour marke feauring search fricions. This is no surprising since he fricions in laour marke are real fricions; he only nominal rigidiy in he model comes from he saggered price seing ehavior of he rms. In oh NK model and he model wih laor marke fricions, here are wo ypes of disorions in he model: one is price dispersion disorion, he oher is mark up disorion. The price dispersion disorion in oh model is given y 20

21 ss = (1 )p " ss 1 " : ss while p ss is given y p ss = ( 1 " ss 1 ) 1 1 " : 1 The mark up disorion is given y = " " 1 ( 1 1 " 1 ss 1 " 1 1 " ss 1 " : ss I is easy o see ha if ss = 1, ss = p ss = 1 and = " " 1 : Thus o eliminae he price dispersion disorion generaed y sicky prices, he opimal rend in aion should e se o zero in oh NK and he model wih laour marke fricions. I also compue he welfare cos of rend in aion, i.e. he how much consumpion households are willing o give up a he 0 percen in aion o oain he equivalen level of welfare as for he higher levels of in aion. I nd ha he welfare coss are almos he same across he models. This again suggess ha only nominal fricions maers for welfare coss of in aion. ) 1 6 Conclusions This paper sudies he role of on-he-jo search in explaining he shor-run join responses of oupu and in aion afer moneary shocks. The resuls sugges ha afer an expansionary moneary policy shock, he laour adjusmen are mainly a he exensive margin since i is less cosly for rms o adjus employmen raher han hours. On-he-jo search opens up an exra employmen channel, which furher ampli es and propagaes he response in oupu. In conras o he ndings in van Zandweghe (2009), on-he-jo search does no have much impac on in aion. This is ecause on-he-jo search dampens he real marginal coss when rms adjus he exensive margin u on impac rms can only adjus hours, where on-he-jo search has no much a role o play in his margin. This paper also suggess ha adding real fricions has no e ecs on he welfare coss of in aion. 21

22 7 Appendix 7.1 Equaion Sysem 1. Jo creaion condiions: q g q g = E ;+1 (1 )[x +1z +1 f(h +1) w+1h +1 + (1 s +1 p g +1 ) q+1 ] (39) = E ;+1 (1 )[x g +1 z +1f(h g +1 ) wg +1 hg +1 + g q g ] (40) Wage deerminaion: w = f[x z f(h ) + (1 w g = f[xg z f(h g ) + pg s )p q ] + (1 )[u + (s ) + g(h )= ]g=h (41) g q g ] + (1 )[u + g(h g )= ]g=h g (42) 3. Opimal search inensiy: 0 (s ) = s 1 = 1 pg (g q g q ): 4. Evoluion of employmen: n g +1 = (1 )(ng + mg ); (43) n +1 = (1 )(n + m s p g n ): (44) 5.Unemploymen: u = u g + u = 1 n g n : 6. Employed searchers: e = s n : 22

23 7. Maching funcions: m g = M g(u g + e ) (v g )1 ; (45) m = M (u ) (v ) 1 : (46) 8. Firm and worker mach proailiies: q g = mg =vg = M g( g ) 1 ; q = m =v = M ( ) (47) p g = mg =(ug + e ) = M g ( g ) 1 ; p = m =u = M ( ) 1 (48) where g = vg u g+e, and = v u 9. Arirage condiion (U g = U = U ): p g g q g = p q 10. Secoral and aggregae oupu: y g = (1 )z n g f(hg ) g v g (49) y = (1 )z n f(h ) v (50) 11. Prices: P g = (1 ) y y g MC; (51) P = y y MC: (52) 12. Aggregae consumpion: y = c 7.2 Seady-sae m = (u ) (v ) 1 (53) 23

24 m g = (u g + e) (v g ) 1 (54) q = m v (55) q g = mg v g (56) p = m u (57) p g = mg u g + e (58) p g g = p qg q w = f[x f(h ) + (1 s)p q ] + (1 )[u + (s) + g(h )=]g=h (59) w g = f[x g zf(h g ) + p g g q g ] + (1 )[u + (s) + g(hg )=]g=h g (60) s 1 = 1 pg ( g q g q ) m = n (1 (1 )(1 sp g )) (61) m g = n g (62) u = u g + u u = 1 (1 )n g (1 )n x g = x(1 )( n f(h ) n g f(h g )) (63) x = x( ng f(h g ) n f(h ) )(1 ) (64) q = v v g + v q + vg v g + v qg (65) n p g s( n ) = 0:06 (66) + n h j = ( xj h ) h h +1, for j = ; g (67) h 1 24

25 y j = (1 )n j f(h j ) j v j, j = ; g (68) y = (y ) (y g ) 1 =l (69) y = c p = ( 1 " 1 ) 1 1 (70) 1 l = p ( 1 1 ) (71) = " " 1 ( 1 1 " 1 ) 1 1 " 1 " 1 1 " ; References Andolfao, D. (1996). Business cycles and laour marke search. American Economic Review 96, 112. Clarida, R., Gali, J. and Gerler, M. (2000). Moneary policy rules and macroeconomic sailiy: Evidence and some heory. Quarerly Journal of Economics 115, 147. den Haan, W.J., Ramey, G and Wason, J. (2000). Jo desrucion and propagaion of shocks. American Economic Review 90, 482. Krause, Michael and Luik, Thomas. (2007a). The (ir)relevance of real wage rigidiy in he new keynesian model wih search fricions. Journal of Moneary Economics 54, 706. (2007). On-he-jo search and he cyclical dynamics of he laor marke. ECB Working Paper Series No Merz,M. (1995). Search in he laour marke and he real usiness cycle. Journal of Moneary Economics 95, 269. van Zandweghe,W. (2009). On-he-jo search, sicky prices and persisence. FRB Kansas Ciy Working Paper

26 Figure 1: Responses o a posiive moneary policy shock oupu S NoOJS S OJS NK inflaion Quarers Quarers 0.3 hours 0.2 employmen Quarers Quarers 26