JOB COMPETITION, CROWDING OUT, AND UNEMPLOYMENT FLUCTUATIONS

Transcription

1 Macroeconomic Dynamics, 16, 2012, Prined in he Unied Saes of America. doi: /s ARTICLES JOB COMPETITION, CROWDING OUT, AND UNEMPLOYMENT FLUCTUATIONS SERIF KALIFA California Sae Universiy, Fulleron This paper aemps o deermine he facors generaing he persisence of unemploymen over he business cycle. The observaions show ha he oal unemploymen rae is highly persisen, and ha he persisence of he unemploymen rae of unskilled workers is higher han ha of skilled workers. To accoun for hese observaions, he paper develops a framework ha feaures search fricions. Individua are eiher high educaed or low educaed, and firms pos wo ypes of vacancies: he complex, which can be mached wih he high educaed, and he simple, which can be mached wih he high and he low educaed. On-he-job search for a complex occupaion is underaken by he high educaed in simple occupaions. A negaive aggregae echnological shock induces he high educaed unemployed o compee wih he low educaed by increasing heir search inensiy for simple vacancies. As he high educaed occupy simple vacancies, hey crowd ou he low educaed ino unemploymen. This downgrading of jobs in a cyclical downurn, or he increase in he labor inpu of he high educaed in simple occupaions, and he subsequen crowding ou of he low educaed ino unemploymen, provide a possible explanaion for unemploymen persisence. Keywords: Unemploymen, Business Cycle, Search and Maching 1. INTRODUCTION This paper aemps o deermine he facors generaing he persisence of unemploymen over he business cycle. To his end, he paper derives a se of sylized facs ha capure no only he high persisence of he oal unemploymen rae, bu ao he higher persisence of he unemploymen rae of unskilled workers compared o ha of skilled workers. In addiion, he observaions capure he cyclical allocaion of labor inpu in a labor marke wih heerogeneous agens across educaional leve. These addiional observaions reflec a lagged cyclical upgrading of jobs by he college-educaed, or a lagged cyclical increase in heir labor inpu from jobs ha do no require college educaion o ones ha do. This provides a possible explanaion for unemploymen persisence, as in a cyclical I hank Thomas Lubik, Louis Maccini, Rober Moffi, Michael Krause, Olga Vashuk, and wo anonymous referees. Remaining errors are my own. Address correspondence o: Sherif Khalifa, Seven G. Mihaylo College of Business and Economics, Deparmen of Economics, California Sae Universiy, Fulleron, CA 92834, USA, skhalifa@fulleron.edu. c 2010 Cambridge Universiy Press /10 1

2 2 SERIF KALIFA downurn he skilled workers compee wih he unskilled workers for unskilled jobs, and hus crowd ou he unskilled ino unemploymen. This inuiion, based on job compeiion across skil and he consequen crowding ou of he unskilled ino unemploymen, is used o develop a model ha is capable of reproducing he observed unemploymen persisence. Using he Ougoing Roaion Group of he Curren Populaion Survey for he period from 1979 o 2008, he paricipans are divided ino hose employed and hose unemployed. The wo groups are furher divided ino hose high and low educaed, where he former are hose wih a leas some college educaion. The employed ypes are furher divided ino hose working in complex and in simple occupaions, where he former are jobs ha require a leas some college educaion. Therefore, a monhly daa se is compiled, including measures of employmen and oal hours of he high educaed in complex and in simple occupaions and employmen and oal hours of he low educaed in simple occupaions, besides he unemploymen raes of he high and he low educaed, as well as a measure of he crowding ou of he low educaed by he high educaed in occupying simple jobs. The observaions sugges ha an economic expansion is accompanied conemporaneously by an increase in he employmen and oal hours of all labor ypes employed in simple occupaions, followed wih a lag by an increase in he employmen and oal hours of hose employed in complex occupaions and a decrease in he unemploymen of he wo ypes of labor, and he crowding-ou effec. These observaions reflec possible lagged cyclical upgrading of jobs by he high educaed, hrough increasing heir level of employmen and heir hours of work in complex occupaions. This ao implies a lagged downgrading of jobs and a consequen crowding ou of he low educaed ino unemploymen afer an adverse shock, which provides a possible explanaion for he persisence of unemploymen. The paper develops a model o idenify he underlying marke ineracions ha are criical in generaing he observed behavior along he lines of his inuiion. These ineracions are capured in a dynamic sochasic general equilibrium model ha feaures search fricions. ouseholds are divided ino high educaed and low educaed workers. Firms pos wo ypes of vacancies: he complex, which can be mached wih he high educaed, and he simple, which can be mached wih boh he high and he low educaed. The high educaed in simple occupaions are allowed o search on he job for a complex occupaion. An adverse aggregae echnological shock induces he high educaed unemployed o compee wih he low educaed, as hey increase heir search inensiy for simple vacancies. As he high educaed occupy simple vacancies, hey crowd ou he low educaed ino unemploymen. This downgrading of jobs, or he increase in he labor inpu of he high educaed in simple occupaions, and he subsequen crowding ou of he low educaed ino unemploymen, provide a possible explanaion for unemploymen persisence. This paper adops a differen approach han previous sudies ha aemped o explain he persisence of unemploymen. For insance, Eseban-Preel (2005)

3 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 3 and Eseban-Preel and Faraglia (2005) include he aspec of skill loss by he high educaed if unemployed for an exended period of ime, in order o explain he persisence of unemploymen. When he economy suffers an adverse shock, unemploymen increases and he creaion of vacancies declines, hus lenghening unemploymen spel. The increase in he duraion of unemploymen causes workers o lose heir skil, which leads o an increase in he unemploymen of he unskilled. The increase in he unemploymen of he unskilled, who have a lower probabiliy of finding a job, raises he average duraion of unemploymen in he economy, and accordingly he persisence of unemploymen. In addiion, Pries (2004) argues ha even hough unemployed workers find jobs quickly, due o he high job-finding rae, following a shock ha riggers a burs of job loss, he newly found jobs ofen las only a shor ime. Afer iniial job loss, a worker may experience several shor-lived jobs before seling ino more sable employmen. This recurring job loss conribues o he persisence of unemploymen. Eriksson and Gofries (2005) argue ha employers use informaion on wheher he applican is employed or unemployed as a hiring crierion, because he perceived produciviy of an unemployed worker may be lower han ha of an employed worker, as human capial is los in unemploymen. This ranking of job applicans by employmen saus increases he level and persisence of unemploymen. Eriksson (2006) exends his framework o argue ha long-erm unemployed workers do no compee well wih oher job applicans because hey have los he abiliies ha employers find aracive. In a model wih shor-erm and long-erm unemployed workers, firms prefer o hire he unemployed who have no los heir human capial. This ranking of job applicans resu in a lenghy adjusmen process and is capable of generaing persisence afer an adverse shock. This paper, however, argues ha unemploymen persisence can be reproduced in a model wihou he aspecs of skill loss, recurring job loss, or ranking of job applicans. The success of his model is aribued o he addiional dynamics ha i inroduces, such as compeiion beween hose disinguished by heir educaional leve for a job wih a paricular educaional requiremen, he crowding ou of he unsuccessful by he successfully mached, and he possibiliy of a mismach beween he educaional level of he successful and he educaional requiremens of he job hey occupy. This downgrading of jobs can explain unemploymen persisence. The remainder of he paper is organized as follows: Secion 2 presens he sylized facs, Secion 3 develops he model, Secion 4 discusses he calibraion, Secion 5 analyzes he resu and he sensiiviy analysis, and Secion 6 concludes. The Appendix includes he daa and derivaions. 2. OBSERVATIONS To derive he business cycle paerns of labor marke variables ha reflec agen heerogeneiy in educaional leve and he educaional requiremens of jobs hey are occupying, a ime series is compiled from he Ougoing Roaion Group of

4 4 SERIF KALIFA he Curren Populaion Survey CPS. 1 This Survey provides monhly informaion from January 1979 unil December 2008 on he paricipans employmen saus, level of educaion, ype of occupaion, and hours of work. To compile a ime series ou of his survey, he labor marke paricipans in each monhly file are divided ino hose employed and hose unemployed. Each group is furher divided ino hose high and low educaed, where he former are hose who obained a leas some college educaion. Each of he wo employed groups is furher divided ino hose working in a complex occupaion and hose working in a simple occupaion, where he former is a job ha requires a leas some college educaion. This provides four employed and wo unemployed ypes: he high educaed employed in a complex occupaion, he high educaed employed in a simple occupaion, he high educaed unemployed, he low educaed employed in a complex occupaion, he low educaed employed in a simple occupaion, and he low educaed unemployed. The low educaed employed in a complex occupaion are dropped from he sample due o heir insignifican proporion ou of all he low educaed, and ou of all hose employed in complex occupaions. Leve of employmen are calculaed for he hree employed ypes, and leve of unemploymen are calculaed for he wo unemployed ypes. Using he weighed average weekly hours of work of each group and he level of employmen, he oal hours of each group are derived. The proporion of each unemployed ype ou of he oal sample is ao calculaed. Finally, a crowding-ou variable is defined as he proporion of he oal hours of he high educaed among he oal hours of all hose employed in simple occupaions, such ha is increase reflecs an increase in he crowding-ou of he low educaed by he high educaed in occupying his ype of job. Therefore, he variables compiled and used in he analysis are (1) he employmen level, he average weekly hours, and he oal hours of he high educaed employed in complex occupaions, (2) he employmen level, he average weekly hours, and he oal hours of he high educaed employed in simple occupaions, (3) he employmen level, he average weekly hours, and he oal hours of he low educaed employed in simple occupaions, (4) he proporion of he high educaed unemployed, (5) he proporion of he low educaed unemployed, and (6) he crowding-ou effec. This monhly ime series is ransformed ino quarerly daa by aking hree-monh averages. The daa average during he period under sudy of he proporion of he high educaed in complex occupaions ou of he oal labor force is 0.23, and ha of he high educaed in simple occupaions is 0.25, whereas ha of he low educaed in simple occupaions is The daa average of he proporion of he high educaed unemployed is 0.02, and ha of he low educaed unemployed is 0.04, which gives a oal unemploymen rae of 6%. The cross-correlaion coefficiens beween real gross domesic produc in period and each of hese variables in lag and lead periods are displayed in Table 1. These paerns demonsrae ha he employmen level and average hours of he high educaed in complex occupaions are procyclical wih a lag. Therefore, he oal hours of he high educaed in complex occupaions are procyclical and lags

5 TABLE 1. CPS daa momens: sandard errors in () calculaed by boosrapping Cross correlaions of oupu() and x( + i) x x( 4) x( 3) x( 2) x( 1) x() x( + 1) x( + 2) x( + 3) x( + 4) N (0.1018) (0.1083) (0.1051) (0.1201) (0.1182) (0.1158) (0.1189) (0.0956) (0.0830) (0.0944) (0.0830) (0.0843) (0.0782) (0.0793) (0.0745) (0.0853) (0.0834) (0.0877) T (0.1032) (0.0960) (0.1043) (0.1126) (0.1035) (0.1051) (0.0931) (0.0827) (0.0805) N (0.1017) (0.1004) (0.1030) (0.0826) (0.0971) (0.1054) (0.1272) (0.1185) (0.1019) (0.1077) (0.0896) (0.0793) (0.0832) (0.0770) (0.0804) (0.0926) (0.1000) (0.0896) T (0.1074) (0.0955) (0.0891) (0.0764) (0.0870) (0.0988) (0.1186) (0.1167) (0.1031) N (0.0845) (0.0923) (0.0821) (0.0713) (0.0585) (0.0612) (0.0731) (0.0831) (0.0819) (0.0990) (0.0926) (0.0812) (0.0772) (0.0643) (0.0661) (0.0785) (0.0820) (0.0915) T (0.0887) (0.0923) (0.0810) (0.0714) (0.0519) (0.0591) (0.0774) (0.0867) (0.0847) JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 5

6 TABLE 1. Coninued. Cross correlaions of oupu() and x( + i) 6 SERIF KALIFA x x( 4) x( 3) x( 2) x( 1) x() x( + 1) x( + 2) x( + 3) x( + 4) U h (0.0671) (0.0699) (0.0659) (0.0554) (0.0494) (0.0431) (0.0516) (0.0570) (0.0733) U l (0.0917) (0.0875) (0.0768) (0.0461) (0.0242) (0.0363) (0.0590) (0.0875) (0.1032) U (0.0861) (0.0813) (0.0742) (0.0460) (0.0359) (0.0363) (0.0513) (0.0750) (0.0891) Crowding (0.0914) (0.0861) (0.0999) (0.0818) (0.0923) (0.0939) (0.0947) (0.0826) (0.0840) Noes: T : oal hours of he high educaed in complex occupaions; T : oal hours of he high educaed in simple occupaions; T : oal hours of he low educaed in simple occupaions.

7 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 7 he cycle by hree quarers, as he cross-correlaion coefficien wih oupu reaches , which is saisically significan wih a p-value of zero. The employmen level and average hours of he high and low educaed employed in simple occupaions are procyclical. Thus, he oal hours of he high and he low educaed in simple occupaions are posiively correlaed wih conemporaneous oupu, wih cross-correlaion coefficiens of and , respecively, ha are saisically significan wih p-values of zero. The proporion of he high educaed unemployed is counercyclical and lags he cycle, wih a cross-correlaion coefficien wih oupu ha reaches and is saisically significan, whereas he proporion of he low educaed unemployed is couner-cyclical wih a crosscorrelaion coefficien wih oupu of ha is ao saisically significan. The oal unemploymen rae is counercyclical, wih a cross-correlaion coefficien of ha is saisically significan. Finally, he crowding-ou effec is counercyclical wih a lag, as he fourh lagged cross-correlaion coefficien of is saisically significan. These paerns are summarized as follows: (1) The employmen level of he high educaed in complex occupaions is procyclical wih a lag. (2) The average hours of he high educaed in complex occupaions are procyclical wih a lag. (3) The oal hours of he high educaed in complex occupaions are procyclical wih alag. (4) The employmen level of he high educaed in simple occupaions is procyclical. (5) The average hours of he high educaed in simple occupaions are procyclical. (6) The oal hours of he high educaed in simple occupaions are procyclical. (7) The employmen level of he low educaed in simple occupaions is procyclical. (8) The average hours of he low educaed in simple occupaions are procyclical. (9) The oal hours of he low educaed in simple occupaions are procyclical. (10) The unemploymen rae of he high educaed is counercyclical wih a lag. (11) The unemploymen rae of he low educaed is counercyclical. (12) The oal unemploymen rae is counercyclical. (13) The crowding-ou effec is counercyclical wih a lag. Table 2 shows he cyclical paerns of he aggregae unemploymen rae and hours of work exraced from he Bureau of Labor Saisics (BLS). The observaions show ha he unemploymen rae is counercyclical, and he hours of work are procyclical. These observaions are consisen wih hose on he disaggregaed daa exraced from he Curren Populaion Survey (CPS). Table 3 displays he serial correlaions of he oal unemploymen rae, and of he unemploymen raes of he high and he low educaed. The observaions from he CPS daa show he high persisence of oal unemploymen, and ha he persisence of he unemploymen of he low educaed is higher han ha of he high educaed. The persisence of he aggregae unemploymen rae from he BLS daa is similar o ha from he CPS daa. The approach of his paper is he use of he cyclical behavior of he variables peraining o he allocaion of labor inpu o ascerain inuiively he facors behind

8 8 SERIF KALIFA TABLE 2. BLS daa momens: sandard errors in () calculaed by boosrapping Cross correlaions of oupu() and x( + i) x x( 4) x( 3) x( 2) x( 1) x() x( + 1) x( + 2) x( + 3) x( + 4) AggU (0.0889) (0.0838) (0.0724) (0.0436) (0.0248) (0.0314) (0.0548) (0.0803) (0.0972) Agg (0.0880) (0.0856) (0.0628) (0.0414) (0.0434) (0.0756) (0.1076) (0.1069) (0.1086) Noes: AggU: aggregae unemploymen rae; Agg : aggregae weekly hours of work.

9 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 9 TABLE 3. Unemploymen serial correlaions Variable ρ(x,x 1 ) ρ(x,x 2 ) ρ(x,x 3 ) ρ(x,x 4 ) ρ(x,x 5 ) CPS daa U BLS daa U Benchmark U No-crowding U No-skil U CPS daa Benchmark No-crowding CPS daa Benchmark No-crowding U h U h U h U l U l U l he business cycle paern of unemploymen and is persisence. For insance, he lagged increase in he oal hours of he high educaed in complex occupaions revea a possible lagged procyclical upgrading of jobs hey are occupying. Evidence on he cyclical upgrading of jobs is provided by Devereux (2000, 2004), who used he Panel Sudy of Income Dynamics for he period and found ha in a recession he skilled occupy jobs ha would normally be occupied by he unskilled. Thus, in a downurn, as he high educaed compee wih he low educaed in occupying simple jobs, hey crowd ou he low educaed ino unemploymen, which conribues o he persisence of oal unemploymen, and he higher persisence of he unemploymen of he low educaed compared o ha of he high educaed. 3. MODEL Consider an economy where ime is infinie and discree. The populaion is of measure 1, and here is a consan fracion δ of households ha are ex ane high educaed and (1 δ) ha are low educaed. The represenaive firm poss complex and simple vacancies. The complex vacancies are mached wih he high educaed only, whereas he simple vacancies are mached wih boh he high and he low educaed. The firm ao chooses he proporion of simple vacancies direced oward he high educaed and ha direced oward he low educaed. An explanaion could be ha here are differen newspapers for he high educaed and for he low educaed, so ha companies can direc heir adverisemens abou available vacancies o paricular newspapers. A high educaed worker in a simple occupaion is allowed o coninue searching on he job for a complex occupaion. This is jusified, as he wo ypes of vacancies differ according o heir creaion coss, and hese coss generae rens ha give rise o equilibrium wage differenia beween occupaion ypes.

10 10 SERIF KALIFA The model is an exension of Gauier (2002) in a general equilibrium framework, and focuses on he dynamics of he model o explain some aspecs of he business cycle. This paper exends ha framework ino one where employmen is considered in he inensive and exensive margins. The paper uses he observed cyclical behavior of he variables peraining o he allocaion of labor inpu o ascerain inuiively he facors behind he business cycle paern of unemploymen and is persisence. Accordingly, he Gauier (2002) framework is exended o a dynamic sochasic general equilibrium framework ha incorporaes he aspecs of job compeiion beween workers of differen educaion leve on jobs of differen educaional requiremens. In his framework, he maching process deermines he level of employmen in every occupaion, and he hours of work are deermined endogenously. This allows he endogenous deerminaion of labor inpu, which generaes he crowding ou of he low educaed by he high educaed in simple jobs in a downurn. Therefore, i is he inuiion derived from he observaions ha jusifies he deviaion from he Gauier (2002) framework. The oher deviaion from he Gauier (2002) framework is ha direced search is assumed in he model, insead of random search, o capure he disincion beween he creaion of simple vacancies for he high educaed and he low educaed. This clarifies he dynamics of job compeiion and crowding ou. As he proporion of jobs creaed for he high educaed increases, he crowding-ou effec increases. In his conex, we expec he proporion of vacancies direced o he high educaed o increase in a downurn, and o decrease in an economic expansion due o he cyclical upgrading of jobs. The maching in Gauier (2002) is beween one firm and one worker, whereas his paper depars from his assumpion o allow complemenariies in he producion funcion ouseholds In his conex, he high and he low educaed household members are divided ino hose employed and hose unemployed as follows: N N + N + U h = δ, (1) + U l = 1 δ, (2) where N ij denoes he number of workers of educaion ype i in occupaion ype j, where i (h, l) for high and low educaed workers, respecively, and j (c, s) for complex and simple occupaions, respecively. U i denoes he number of he unemployed of ype i. Time for all ypes is normalized o one. A high educaed unemployed person uses a porion S of is ime o search for a complex occupaion, a porion S o search for a simple occupaion, and (1 S S ) for leisure. A low educaed unemployed person uses a porion of is ime o search for a simple occupaion and (1 S ) for leisure. A high educaed worker in a complex occupaion spends a porion hours a work and (1 ) a leisure. A high educaed worker in a simple occupaion spends S

11 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 11 a porion hours a work, a porion O o search on he job for a complex occupaion, and (1 O ) for leisure. The low educaed worker in a simple occupaion spends a porion hours a work and (1 ) a leisure. As differen employmen hisories among members of a household can lead o heerogeneous wealh posiions, we follow he lieraure in assuming ha each household is hough of as an exended family whose members perfecly insure each oher agains variaions in labor income due o employmen or unemploymen. Remaining wihin he confines of complee markes allows solving he program of a represenaive household, which chooses consumpion and search inensiies o maximize he expeced discouned infinie sum of is insananeous uiliy which is separable in consumpion and leisure. Assuming he household has he value funcion Ɣ = Ɣ ( N, N, N ), he opimizaion problem of he household can be wrien in he recursive form Ɣ = Max {C,S,S,O,S } { (C ) + U h h + U l l + N + N + N } + βe Ɣ +1, (3) where E is he expecaion operaor condiional on he informaion se available in period, β is he discoun facor, and (C ) is he uiliy of period- consumpion of he household C. h = h (1 S S ), and l = l (1 S ) denoe he uiliy of period- leisure of he high and he low educaed unemployed, respecively. = (1 ), = (1 O ), and = (1 ) denoe he uiliy of period- leisure of he employed ypes. This is subjec o he budge consrain C = N W + N W + N W + D, (4) where W ij is he period- wage for labor ype ij, and D is he dividends disribued by firms. The households ao ake ino consideraion he employmen dynamics of he hree ypes of workers. The high educaed workers in complex occupaions in period ( + 1) are composed of hose of ha ype who are no exogenously separaed in period according o he separaion rae from complex occupaions χ, in addiion o he new maches from he searchers pool, wheher hey are high educaed unemployed or on-he-job searchers, N+1 = (1 χ )N + P ( S U h + O N ), (5) where P = M /(S U h + O N ) is he probabiliy ha a high educaed searcher is mached wih a complex occupaion, and M = M (V c,s U h + O N ) represens he number of complex maches. Similarly, he high educaed workers in simple occupaions in period ( + 1) are composed of hose of ha ype who are neiher separaed from simple occupaions exogenously in period according o he separaion rae χ, nor are mached wih complex occupaions as a resul of on-he-job search, in addiion o he new maches from he searchers

12 12 SERIF KALIFA pool of he high educaed unemployed, N+1 = (1 χ ) ( 1 O P ) N where P = M /S U h mached wih a simple occupaion, and M + P ( S U h ), (6) is he probabiliy ha a high educaed searcher is = M (Z V s,s U h) represens he number of simple maches wih he high educaed. Z is he proporion of simple vacancies direced o he high educaed. Finally, he low educaed workers in simple occupaions in period ( + 1) are composed of hose of ha ype who are no exogenously separaed in period according o he separaion rae χ, in addiion o he new maches from he searchers pool of he low educaed unemployed, where P = M /S U l wih a simple occupaion, and M N+1 = (1 χ )N + P ( S U l ), (7) is he probabiliy ha a low educaed searcher is mached = M (1 Z )V s,s U l represens he number of simple maches wih he low educaed. The consan separaion raes are jusified by all (2005), who concludes ha over he pas fify years job separaion raes have remained almos consan in he Unied Saes, and by Shimer (2005), who demonsraes ha separaion raes exhibi acyclicaliy. The maching funcions are consan reurns o scale homogeneous funcions of degree one of he number of corresponding vacancies, V c and V s, and effecive searchers. The represenaive household chooses consumpion such ha he marginal uiliy of consumpion equa he Lagrange muliplier λ, (C ) = λ. (8) C The household chooses he opimal proporion of ime he high educaed unemployed allo o searching for a complex occupaion S, such ha he disuiliy from increasing search by one uni is offse by he discouned expeced value of an addiional high educaed worker in a complex occupaion, h Ɣ S + βp E +1 N+1 = 0. (9) The household chooses he opimal proporion of ime he high educaed unemployed allo o searching for simple occupaions S, such ha he disuiliy from increasing search by one uni is offse by he discouned expeced value of an addiional high educaed worker in a simple occupaion, h Ɣ S + βp E +1 N+1 = 0. (10) The household chooses he opimal proporion of ime he low educaed unemployed allo o searching for a simple occupaion S, such ha he disuiliy from

13 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 13 increasing search by one uni is offse by he discouned expeced value of an addiional low educaed worker in a simple occupaion, l S Ɣ + βp E +1 N+1 = 0. (11) The household chooses on-he-job search inensiy O, such ha he disuiliy from increasing search by one uni is offse by he difference beween he discouned expeced value o he household from an addiional high educaed worker in a complex occupaion and ha of an addiional high educaed worker in a simple occupaion, O Ɣ + P βe +1 Ɣ N+1 P βe +1 N+1 (1 χ ) = 0. (12) From he envelope heorem, an addiional high educaed worker mached wih a complex occupaion accrues a value o he household ha is given by Ɣ N = ( 1 ) h ( 1 S + β ( 1 χ P S ) Ɣ +1 E N+1 S ) + λ W Ɣ βp S E +1 N+1. (13) Similarly, an addiional high educaed worker mached wih a simple occupaion accrues a value o he household ha is given by Ɣ N = ( 1 + β (1 χ ) ( 1 O P + β ( P O P O ) h ( 1 S ) P S ) Ɣ +1 E N+1 S S Ɣ +1 E N +1 ) + λ W. (14) Finally, an addiional low educaed worker mached wih a simple occupaion accrues a value o he household ha is given by Ɣ N = ( 1 + ( 1 χ P ) l ( 1 S ) + λ W S ) Ɣ +1 E N+1. (15)

14 14 SERIF KALIFA Subsiuing he envelope condiions ino he firs order condiions yields he following represenaive household s opimal condiions: τ h βp = τ h ( E 1 S +1 ) S +1 + E ( 1 +1 ) + E +1 W +1 C +1 E τ h S +1, τ h βp (1 + E χ P+1 ) ( ) τ h S +1 P+1 = τ h ( E 1 S +1 ) S +1 + E ( 1 +1 O ) +1 + E +1 W +1 C +1 + E τ h ( O +1 S+1 ) ((1 + E χ ) ( 1 O +1 P+1 ) ) ( P τ h +1 S +1 P+1 τ l βp (16) ), (17) = τ l ( ) E 1 S +1 + E ( 1 +1 ) + +1 W +1 E C +1 (1 + E χ P+1 ) ( τ l S +1 P+1, (18) where τ h and τ l are he marginal uiliies of leisure of he high and he low educaed unemployed, respecively. ) 3.2. Firms The represenaive firm chooses he number of complex and simple vacancies o pos, besides he proporion of he simple vacancies direced o he high educaed, in order o maximize he discouned expeced infinie sum of is fuure profi sreams. The profi funcion is given by he difference beween he value of is producion, where he price of one uni of oupu is normalized o one, and he oal cos incurred for creaing he wo ypes of vacancies, as well as he wages of he hree labor ypes. Assuming he firm has he value funcion Ɣ F = Ɣ F ( N, N, N ), he opimizaion problem can be wrien in he recursive form { Ɣ F = Max N {V s,v c,z } W Y ω s V s ω c V c N W N W } λ+1 + βe Ɣ+1 F, (19) λ

15 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 15 where ω c is he cos of creaing a complex vacancy, and ω s is he cos of creaing a simple vacancy. The discoun facor of firms is such ha i effecively evaluaes profis in erms of he values aached o hem by households, who ulimaely own he firms. Thus, he uiliy-based and ime-varying discoun facor used by firms is given by (βλ +1 /λ ). The maximizaion is subjec o he producion funcion, which is a composie of he complex occupaion oupu ( occupaion oupu ( N + N ), Y = Y A, ( N ) (, N + N ) and he simple N ), (20) where A is he aggregae echnology. The maximizaion problem of he firm is ao subjec o he employmen dynamics: where q M /Z V s N+1 = (1 χ )N + q V c N+1 = (1 χ ) ( 1 O P ) N, (21) + q Z V s, (22) N+1 = (1 χ )N + q (1 Z ) V s, (23) = M /V c is he probabiliy of filling a complex vacancy, q is he probabiliy ha a simple vacancy is filled by a high educaed = worker, and q = M /(1 Z )V s is he probabiliy ha a simple vacancy is filled by a low educaed worker. The firm chooses he opimal level of complex vacancies o pos, V c, such ha he expeced marginal cos of posing his ype of vacancy is equal o he discouned expeced value for he firm of an addiional high educaed worker in a complex occupaion, ω c λ +1 Ɣ+1 F q = βe λ N+1. (24) The firm chooses he opimal level of simple vacancies o pos, V s, such ha he cos of posing a simple vacancy is equal o he discouned expeced value of creaing an occupaion from his vacancy, wheher i is filled by a high or a low educaed worker, ω s = q λ +1 Ɣ+1 F Z βe λ N+1 + q λ +1 Ɣ+1 F (1 Z ) βe λ N+1. (25) The firm chooses he opimal proporion of simple vacancies direced o he high educaed, Z, so ha he discouned expeced value of an addiional high educaed worker in a simple occupaion is equal o he discouned expeced value of an addiional low educaed worker in a simple occupaion: q λ +1 Ɣ+1 F E λ N+1 = q λ +1 Ɣ+1 F E λ N+1. (26)

16 16 SERIF KALIFA From he envelope heorem, he value for he firm of an addiional high educaed worker in a complex occupaion is given by he difference beween is marginal produciviy and he wage, in addiion o he discouned expeced value of he mach in case he worker is no exogenously separaed, Ɣ F N = Y N W + (1 χ λ +1 )βe λ Ɣ F +1 N +1. (27) Similarly, he value for he firm of an addiional high educaed worker in a simple occupaion is given by he difference beween is marginal produciviy and he wage, in addiion o he discouned expeced value of he mach in case he worker is neiher exogenously separaed nor mached wih a complex occupaion as a resul of on-he-job search, Ɣ F N = Y N W + (1 χ ) ( 1 O P ) λ +1 βe λ Ɣ F +1 N +1. (28) Finally, he value for he firm of an addiional low educaed worker in a simple occupaion is given by he difference beween is marginal produciviy and he wage, in addiion o he discouned expeced value of he mach in case he worker is no exogenously separaed, Ɣ F N = Y N W + (1 χ λ +1 )βe λ Ɣ F +1 N +1. (29) Subsiuing he envelope condiions ino he firs-order condiions yields he represenaive firm s opimal condiions, { } ω c λ +1 Y +1 q = βe λ N+1 +1 W +1 + (1 χ ) ωc q+1, (30) ω s q { λ +1 Y +1 = βe λ N+1 +1 W +1 + (1 χ ) ( } 1 O +1 P+1 ) ω s q+1, (31) ω s q { λ +1 Y +1 = βe λ N+1 +1 W +1 + (1 χ ) ωs q +1 }. (32) 3.3. Wages and ours We follow he lieraure in assuming ha a realized mach share he surplus hrough a bargaining problem. Therefore, he wage of a high educaed worker in a complex

17 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 17 occupaion is given by 2 W = (1 ξ Y ) N + P S ω c q + ξ C h ( 1 S S ) ( 1 ) + S τ h, (33) where ξ is he firm s share of he surplus. The wage is a weighed average of wo erms: he firs indicaes ha he worker is rewarded by a fracion (1 ξ ) of boh he firm s revenues from he worker s produciviy and he discouned expeced value of he mach o he firm. The second erm indicaes ha he worker is compensaed by a fracion ξ for he foregone benefi from he worker s ouside opion or he difference beween he leisure of a high educaed unemployed person and ha of a high educaed worker in a complex occupaion, in addiion o he forgone benefi from being mached wih a simple vacancy. Similarly, he wage of he high educaed worker in a simple occupaion is given by 3 W = (1 ξ Y ) N ( 1 + P S O ) ( O S ω s q + ξ C h ( 1 S S ) ) τ h, (34) where ξ is he firm s share of he surplus. The wage is a weighed average of wo erms: he firs indicaes ha he worker is rewarded by a fracion (1 ξ ) of boh he firm s revenues from he worker s produciviy and he discouned expeced value of he mach for he firm. The second erm indicaes ha he worker is compensaed by a fracion ξ for he ouside opions or he difference beween he leisure of a high educaed unemployed person and ha of a high educaed worker in a simple occupaion, in addiion o he forgone benefi from being mached wih a complex vacancy. Finally, he bargained wage of he low educaed worker in a simple occupaion is given by 4 W = (1 ξ Y ) ( 1 N + P S ω s q + ξ C l ( 1 S ) ), (35) where ξ is he firm s share of he surplus. The wage is a weighed average of wo erms: he firs indicaes ha he worker is rewarded by a fracion (1 ξ ) of he firm s revenues from he worker s produciviy and he discouned expeced value of he mach for he firm. The second erm indicaes ha he worker is compensaed by a fracion ξ for he ouside opions or he difference beween he leisure of a low educaed unemployed person and ha of a low educaed worker in a simple occupaion. The hours of he high educaed in complex occupaions are chosen so ha he disuiliy of leisure from increasing he hours of work by one uni is offse by he

18 18 SERIF KALIFA increase in marginal produciviy due o an increase in hours by one uni, 5 ( ) Y / N ( 1 + λ ) = 0. (36) The hours of he high educaed in simple occupaions are chosen so ha he disuiliy of leisure from increasing he hours of work by one uni is offse by he increase in marginal produciviy due o an increase in hours by one uni, 6 ( ) Y / N ( 1 + λ ) = 0. (37) The hours of he low educaed in simple occupaions are chosen so ha he disuiliy of leisure from increasing he hours of work by one uni is offse by he increase in marginal produciviy due o an increase in hours by one uni, 7 ( ) Y / N ( 1 + λ Finally, he crowding-ou effec is defined as Crowding = N Toal unemploymen is defined as U = U h ) N + N Y = C + ω c V c = 0. (38). (39) + U l. To close he model, we have + ω s V s. (40) 4. CALIBRATION The funcional forms are deermined and he parameers are calibraed in order o solve he model numerically. In his conex, numerical values are assigned o he srucural parameers in order o conduc a quaniaive analysis. Table 4 shows he values chosen for he parameers of he model. In his conex, some of he parameers are se as is sandard in he lieraure. Because informaion may no be available for he oher parameers, heir values are compued in he seady sae sysem of equaions afer values are se for variables quanifiable from he daa. I is worh menioning ha he ime period in he model is a quarer. The seady sae values for cerain variables are calculaed from he averages in he daa se during he period under sudy. For insance, he proporion of he high educaed in he populaion, δ, is se a 0.5, which equa he daa average. Similarly, he proporions of he employed ypes are se a N = 0.23, N = 0.25, N = 0.46 and he unemployed ypes a U h = δ N N = 0.02, U l = 1 δ N = 0.04, and U = 0.06, which are equal o he daa averages during he period under sudy as well.

19 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 19 TABLE 4. Calibraion of model parameers Exogenous Value Descripion δ 0.5 Proporion of he high educaed in he populaion β 0.98 ousehold discoun facor η 4 Parameer in he uiliy of leisure χ 0.01 Separaion rae from complex occupaions χ 0.02 Separaion rae of high educaed from simple occupaions χ 0.02 Separaion rae of low educaed from simple occupaions γ 0.5 Elasiciy of maches wih respec o vacancies µ 0.5 Elasiciy of oupu o complex occupaion oupu ξ 0.5 Firm share from bargaining wih a high educaed worker in a complex occupaion ξ 0.5 Firm share from bargaining wih a high educaed worker in a simple occupaion ξ 0.5 Firm share from bargaining wih a low educaed worker in a simple occupaion ρ A 0.9 Auoregressive coefficien of aggregae echnology σ ɛa Sandard deviaion of he aggregae echnology shock Calibraed Value Descripion ω c 2.28 Cos of posing a complex vacancy ω s 0.12 Cos of posing a simple vacancy T 0.1 Efficiency in he complex-occupaion maching funcion T 0.1 Efficiency in he simple-occupaion maching funcion wih he high educaed T 0.1 Efficiency in he simple occupaion maching funcion wih he low educaed τ h 1.7 Parameer in he uiliy of leisure of he high educaed unemployed τ l 0.7 Parameer in he uiliy of leisure of he low educaed unemployed τ 2.5 Parameer in he uiliy of leisure of he high educaed in complex occupaions τ 0.7 Parameer in he uiliy of leisure of he high educaed in simple occupaions τ 0.6 Parameer in he uiliy of leisure of he low educaed in simple occupaions Given he proporion of employmen of all ypes, he hree wages, W, W, and W, are se equal o he daa average, such ha he seady sae skill premium ( N W + N W ) N + N W

20 20 SERIF KALIFA is 1.52, which is ao equal o he daa average in he period under sudy. In addiion, given he proporion of employmen of every ype, he hours of work of every ype is chosen equal o he daa average, such ha Crowding = N /(N + N ) = 0.39 is ao se equal o he daa average. The household s discoun facor β is given by 0.98, which is sandard in he lieraure. The insananeous uiliy funcion of consumpion is represened by he logarihm of consumpion expendiures, (C ) = ln(c ). A nonlinear uiliy funcion of leisure is inroduced o examine he case when workers are risk-averse o flucuaions in hours worked. In his conex, if workers dislike high volailiy in hours, firms find i more appealing o adjus he level of employmen raher han he level of hours. Therefore, he insananeous uiliy funcion of leisure is given by h = τ h (1 S S ) 1 η /(1 η), l = τ l (1 S ) 1 η /(1 η), = τ (1 ) 1 η /(1 η), = τ (1 O ) 1 η /(1 η), = τ (1 ) 1 η /(1 η), such ha η = 4, which implies ha he average individual labor supply elasiciy is 1, which is consisen wih he bulk of empirical esimaes. 2 The parameer in he uiliy of leisure for he high educaed unemployed, τ h,is given by 1.7; for he low educaed unemployed, τ l is given by 0.7. The parameer in he uiliy of leisure for he high educaed in complex occupaions, τ,isgiven by 2.5; for he high educaed in simple occupaions, τ is given by 0.7; and for he low educaed in simple occupaions, τ is given by 0.6. These parameers are solved for in he seady sae equaions for he opimal hours of work, given he proporion of employmen and hours of work of every ype. The maching funcions for he complex and simple occupaions are represened as a Cobb Douglas specificaion wih consan reurns o scale, and are given by M = T (V c)γ (S U h + O N ) 1 γ, M = T (Z V s)γ (S U h)1 γ, and M = T ((1 Z )V s)γ (S U l)1 γ, where γ (0, 1) is he elasiciy of maching wih respec o vacancies. T, T, and T are he level parameers of he maching funcions, which capure all facors ha influence he efficiency of maching. The elasiciy of maches wih respec o vacancies γ is se a 0.5, as is sandard in he lieraure. The level parameers in he maching funcions T, T, and T are given by 0.1. The choice of he level parameers is deermined o arge he separaion raes. In seady sae, he flows ou of employmen equal he flows ou of unemploymen. This ensures ha he employmen level of every ype says consan. Thus, we have χ N = M, (χ + OP χ OP )N = M, and χ N = M in seady sae. Therefore, he choice of T, T, and T deermines he maches, and accordingly arges he separaion raes. The separaion raes χ, χ, and χ from he complex and simple occupaions are given by 0.01, 0.02, and 0.02, respecively. These are seleced so ha he separaion rae from simple vacancies is higher han ha in complex ones, and so heir average is close o he weighed average separaion rae calculaed by all (2005) and Shimer (2005). The coss of creaing he complex vacancy ω c and he simple vacancy ω s are 2.28 and 0.12, respecively. These values are deermined hrough he seady sae equaions for he opimal number of vacancies. The firm s shares of he surplus,

21 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 21 ξ, ξ, and ξ,aresea0.5, 0.5, and 0.5, respecively, as is sandard in he lieraure. The bargaining power of he households is se equal o he elasiciy of maching wih respec o vacancies, which, as shown in osios (1990), implies ha he bargaining process yields a Pareo-opimal allocaion of resources. The echnological consrains faced by he firm is ao represened by a consan reurns o scale Cobb Douglas funcion, Y = A ( N ) µ ( N N ) 1 µ, where µ (0, 1) is he elasiciy of oupu wih respec o he complex + occupaion oupu. The logarihm of he aggregae echnology A is assumed o follow an AR(1) process as follows, log A +1 = ρ A log A + ɛ A +1, (41) where ɛ A +1 is an independenly and idenically disribued random variable drawn from a normal disribuion wih mean zero and sandard deviaion denoed by σ ɛa. The elasiciy parameer in he producion funcion µ is given by 0.5, as in Krause and Lubik (2004). The auoregressive coefficien in he echnological law of moion, ρ A, is given by 0.9. As is common in he lieraure, an innovaion variance is chosen such ha he baseline model s predicions mach he sandard deviaion of he U.S. GDP, which is 1.62%. Consequenly, he sandard deviaion of echnology is se o σ ɛa = ANALYSIS 5.1. Impue Responses The model is solved by compuing he nonsochasic seady sae around which he equaion sysem is linearized. The resuling model is solved by he mehods developed in Sims (2002). The success of he model can be primarily assessed by comparing he serial correlaions of he oal unemploymen rae, and he unemploymen raes of he high and he low educaed produced by he model, referred o as he benchmark model, and hose observed in he daa. Table 3 shows ha he model succeeds in reproducing he high persisence observed in he daa. For insance, he firs lagged serial correlaion of oal unemploymen is in he daa and in he model. The firs lagged auocorrelaion of he unemploymen of he high educaed is in he daa and in he model, whereas ha of he unemploymen of he low educaed is in he daa and in he model. For he remaining lagged serial correlaions of he unemploymen variables, he persisence is higher in he model han in he daa. The impue responses in Figures 1 and 2 show he dynamic evoluion of he variables of ineres, along wih a deviaion of oupu from is long-run rend as a consequence of a negaive aggregae echnological shock. The adverse shock decreases he produciviy of all ypes of workers. This reduces he discouned expeced value o he firm of an addiional worker of any ype. The firm poss complex vacancies so ha he expeced marginal cos of posing a complex vacancy

22 22 SERIF KALIFA FIGURE 1. Benchmark model impue response funcions o a negaive 1% aggregae echnological shock. is equal o he discouned expeced value for he firm of an addiional high educaed worker. Accordingly, he decrease in he marginal produciviy of workers induces firms o decrease heir posing of complex vacancies. On he oher hand, firms pos simple vacancies so ha he expeced marginal cos of posing a simple vacancy is equal o he discouned expeced value of creaing an occupaion from his vacancy, wheher i is filled by a high or a low educaed worker. Even hough he produciviy of boh ypes of workers declined, he probabiliy ha a simple vacancy is filled by a high educaed worker increases. This causes an increase in he posing of simple vacancies direced o he high educaed. Accordingly, he inensiy of search for simple vacancies by he high educaed increases, and ha of search for complex vacancies decreases. This causes a decline in he employmen of he high educaed in complex occupaions, and an increase in he employmen of he high educaed in simple occupaions. As he decline in he former is smaller han he increase in he laer, he unemploymen of he high educaed increases slighly and hen decreases wih a lag, conrary o he observaions. On he oher hand, he low educaed unemployed reduce heir search inensiy for simple occupaions because of he decline in he proporion of simple vacancies direced o his ype. This causes a decrease in he employmen of he low educaed

23 JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 23 FIGURE 2. Benchmark model impue response funcions o a negaive 1% aggregae echnological shock. in simple occupaions and an increase in he unemploymen of he low educaed. The impue responses show a high persisence of oal unemploymen, and ha he persisence of unemploymen of he low educaed is higher han ha of he high educaed, consisen wih he observaions. The hours of work of any ype are chosen so ha he disuiliy of leisure from increasing he hours of work by one uni is offse by he increase in marginal produciviy due o an increase in hours by one uni. Figure 2 shows ha he hours of work of all ypes in his model increase. This reflecs he risk aversion of workers o flucuaions in hours worked. In his conex, he firms respond o he adverse shock by adjusing he level of employmen and no he hours of work. Due o he increase in he employmen and he hours of he high educaed in simple occupaions, he oal hours of his ype increase. Therefore, he crowding-ou variable increases. This crowding ou of he low educaed by he high educaed conribues o he persisence of unemploymen. Comparing he momens of he model in Table 5 o he daa, he model succeeds in several respecs. The model replicaes he lagged procyclicaliy of he employmen of he high educaed in complex occupaions, and he lagged procyclicaliy of he oal hours of he high educaed in complex occupaions. The model does no succeed in reproducing he procyclicaliy of he employmen and oal hours of

24 TABLE 5. Benchmark model momens: sandard errors in () calculaed by boosrapping Cross correlaions of oupu() and x( + i) x x( 4) x( 3) x( 2) x( 1) x() x( + 1) x( + 2) x( + 3) x( + 4) N (0.0558) (0.0498) (0.0428) (0.0353) (0.0287) (0.0218) (0.0157) (0.0115) (0.0093) (0.0371) (0.0325) (0.0262) (0.0192) (0.0114) (0.0103) (0.0096) (0.0088) (0.0101) T (0.0558) (0.0503) (0.0448) (0.0395) (0.0332) (0.0246) (0.0177) (0.0140) (0.0096) N (0.0550) (0.0486) (0.0406) (0.0341) (0.0285) (0.0223) (0.0147) (0.0110) (0.0089) (0.0218) (0.0199) (0.0160) (0.0111) (0.0009) (0.0125) (0.0210) (0.0270) (0.0281) T (0.0317) (0.0252) (0.0198) (0.0134) (0.0045) (0.0064) (0.0089) (0.0099) (0.0118) N (0.0906) (0.0823) (0.0747) (0.0758) (0.0703) (0.0638) (0.0584) (0.0515) (0.0461) (0.0230) (0.0206) (0.0158) (0.0107) (0.0002) (0.0116) (0.0174) (0.0213) (0.0245) T (0.0910) (0.0911) (0.0788) (0.0803) (0.0726) (0.0670) (0.0624) (0.0594) (0.0500) 24 SERIF KALIFA

25 TABLE 5. Coninued. Cross correlaions of oupu() and x( + i) x x( 4) x( 3) x( 2) x( 1) x() x( + 1) x( + 2) x( + 3) x( + 4) U h (0.0508) (0.0482) (0.0423) (0.0334) (0.0303) (0.0242) (0.0138) (0.0092) (0.0075) U l (0.0885) (0.0833) (0.0799) (0.0784) (0.0697) (0.0626) (0.0568) (0.0529) (0.0460) U (0.0952) (0.0892) (0.0875) (0.0865) (0.0843) (0.0835) (0.0802) (0.0741) (0.0722) Crowding (0.0391) (0.0332) (0.0274) (0.0193) (0.0104) (0.0093) (0.0103) (0.0099) (0.0113) Noes: T : oal hours of he high educaed in complex occupaions; T : oal hours of he high educaed in simple occupaions; T : oal hours of he low educaed in simple occupaions. JOB COMPETITION AND UNEMPLOYMENT FLUCTUATIONS 25