Labor Mismatch, Skill Obsolescence, and Unemployment Persistence

Transcription

1 Labor Mismach, Skill Obsolescence, and Unemploymen Persisence Sherif Khalifa California Sae Universiy, Fulleron February 20, 2011 Absrac This paper aemps o assess he impac of skill loss by boh he unemployed and he mismached workers on he persisence of unemploymen. The observaions show ha he oal unemploymen rae is highly persisen, and ha he persisence of he unemploymen rae of he unskilled workers is higher han ha of he skilled workers. A framework ha feaures search fricions is developed, where labor are eiher high educaed or low educaed. Firms pos complex and simple vacancies ha can be mached wih he high and he low educaed. The high educaed lose heir skil if unemployed, and if employed 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, and he subsequen skill mismach and obsolescence, allow he model o capure he observed unemploymen persisence. Keywords: unemploymen, skill loss, business cycle, search and maching. JEL Classificaion: E24, E32, J64. I hank Thomas Lubik, Louis Maccini, Rober Moffi, Michael Krause, and paricipans in he Easern Economic Associaion Annual Conference Remaining errors are my own. Deparmen of Economics, California Sae Universiy, Fulleron, CA, 92834, USA. skhalifa@fulleron.edu. 1

2 1 Inroducion This paper aemps o assess he impac of skill loss and obsolescence on he persisence of unemploymen over he business cycle. The paper argues ha in a cyclical downurn, as he probabiliy of unemploymen increases, skilled workers compee wih unskilled workers for unskilled occupaions. As he skilled occupy unskilled jobs, hey crowd ou he unskilled ino unemploymen. Accordingly, here is a mismach beween he educaional qualificaions of he skilled workers, and he educaional requiremens of he unskilled jobs hey occupy. Skilled workers lose heir skil no only while unemployed for an exended period of ime, bu ao when employed in occupaions ha do no require heir specific skil. The unemployed skilled workers lose heir skil because hey are no applying heir skil in he working place. The skilled workers, mismached wih unskilled occupaions, lose heir skil because he jobs hey are occupying do no require he applicaion of heir skil in he working place. As he mismached skilled workers lose heir skil, and become unskilled, hey are more likely o be crowded ou of unskilled jobs due o heir higher separaion raes. These mismached workers, who lose heir skil and flow ino unemploymen as unskilled unemployed, in addiion o he unemployed skilled workers, who lose heir skil and become unskilled unemployed, are less aracive o poenial employers. This lowers he probabiliy of employmen, and causes unemploymen o exhibi persisence. Even hough few sudies considered he aspec of skill loss of he skilled unemployed, his paper exends he analysis o consider he skill obsolescence of he mismached labor as well. The exension allows he paper o succeed in capuring he observed unemploymen persisence. To his purpose, he paper derives a se of sylized facs ha capures no only he high persisence of he oal unemploymen rae, bu ao he higher persisence of he unemploymen rae of he unskilled workers compared o ha of he skilled workers. In addiion, he observaions capure he cyclical allocaion of labor inpu in a labor marke wih heerogeneous agens across educaional leve. 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 daase is compiled including measures of employmen of he high educaed in complex and in simple occupaions, employmen of he low educaed in complex and in simple occupaions, besides he oal unemploymen rae, and he unemploymen raes of he high educaed 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. 2

3 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 all 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 a possible lagged downgrading of jobs and a consequen crowding ou of he low educaed ino unemploymen afer an adverse shock. The labor mismach, besides he skill obsolescence of he high educaed unemployed and of he high educaed employed in simple occupaions, provide 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. The labor force is divided ino high educaed and low educaed workers. Firms pos wo ypes of vacancies: he complex ha can be mached wih he high and he low educaed, and he simple ha can be mached wih he high and he low educaed. Thehigheducaedinsimpleoccupaionsareallowedosearchon-he-jobforacomplexoccupaion. The high educaed lose heir skil if unemployed, and if employed in simple occupaions. The low educaed in complex occupaions acquire raining o become high educaed. 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 skill loss, allow he model o capure he observed unemploymen persisence. This paper adops a differen approach compared o previous sudies ha aemped o explain he persisence of unemploymen. For insance, Eseban-Preel (2003) and Eseban-Preel and Faraglia (2005) include he aspec of skill loss by he high educaed if unemployed for an exended period of ime. 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. 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 an iniial job 3

4 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, since he perceived produciviy of an unemployed worker may be lower han ha of an employed worker. 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 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 recurring job loss, or ranking of job applicans, and improves upon he sudies ha focused only on he skill loss of he unemployed by considering he addiional aspec of skill obsolescence of mismached labor. 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 requiremen of he job hey occupy. This downgrading of jobs, and he subsequen labor mismach and skill obsolescence, 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, secion 6 concludes, secion 7 includes he daa and derivaions appendices. References, ables and figures are included hereafer. 2 Observaions 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 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. 1 Deailed daa descripion is included in appendix

5 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. Leve of employmen are caulaed for all he employed ypes, and leve of unemploymen are caulaed for he wo unemployed ypes. Theproporionofeachunemployedypeouofhe oal sample is caulaed. Using he weighed average weekly hours of work of each group and he level of employmen, he oal hours of each group is derived. Finally, a crowding ou variable is defined as he proporion of he high educaed amongs all hose employed in simple occupaions, such ha is increase reflecs an increase in he crowding ou process 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 low educaed employed in complex occupaions, (3) he employmen level, he average weekly hours, and he oal hours of he high educaed employed in simple occupaions, (4) he employmen level, he average weekly hours, and he oal hours of he low educaed employed in simple occupaions, (5) he proporion of he high educaed unemployed, (6) he proporion of he low educaed unemployed, and (7) he crowding ou effec. This monhly ime series is ransformed ino quarerly daa by aking hree mon averages. The daa average during he period undersudy of he proporion of he high educaed in complex occupaions of he oal labor force is 0.23, and ha of he high educaed in simple occupaions is 0.25, while ha of he low educaed in complex occupaions is 0.01, and 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 an average 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 able 5. These paerns demonsrae ha he oal hours of he high educaed in complex occupaions is procyclical and lags he cycle by 3 quarers, as he cross correlaion coefficien wih oupu reaches which is saisically significan wih a p-value of zero. 5

6 The oal hours of he low educaed in complex occupaions is procyclical and lags he cycle by 4 quarers, as he cross correlaion coefficien wih oupu reaches which is saisically significan. The 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 where he cross correlaion coefficien wih oupu reaches and is saisically significan, while he proporion of he low educaed unemployed is counercyclical where he cross correlaion coefficien wih oupu of is ao saisically significan. The oal unemploymen rae is counercyclical where he cross correlaion coefficien of 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 oal hours of he high educaed in complex occupaions is procyclical wih a lag. (2) The oal hours of he low educaed in complex occupaions is procyclical wih a lag. (3) The oal hours of he high educaed in simple occupaions is procyclical. (4) The oal hours of he low educaed in simple occupaions is procyclical. (5) The unemploymen rae of he high educaed is counercyclical wih a lag. (6) The unemploymen rae of he low educaed is counercyclical. (7) The oal unemploymen rae is counercyclical. (8) The crowding ou effec is counercyclical wih a lag. Table 6 shows he counercyclical paern of he aggregae unemploymen rae exraced from he Bureau of Labor Saisics BLS. This observaion is consisen wih hose on he disaggregaed daa exraced from he Curren Populaion Survey CPS. Table 7 displays he serial correlaions of he oal unemploymen rae, and ha 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 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. Evidence on he cyclical upgrading of jobs is provided by Devereux (2000, 2004) who used he Panel Sudy of Income Dynamics for he period 6

7 , 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. The skill loss of he mismached workers 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 represenaive firm poss complex and simple vacancies. The complex vacancies are mached wih he high and he low educaed, and he simple vacancies are mached wih he high and he low educaed. The firm ao chooses he proporion of complex and simple vacancies direced owards he high educaed and ha direced owards he low educaed. An explanaion can be ha here are differen newspapers for he high educaed and for he low educaed, where 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 which give rise o equilibrium wage differenia beween occupaion ypes. The seup ao feaures skill loss by he high educaed unemployed, and by he high educaed in simple occupaions. Finally, he low educaed in complex occupaions acquire raining o become high educaed. Figure 11 shows he model flows ino and ou of employmen and unemploymen. 3.1 ouseholds Le N ij denoes he number of workers of educaion ype i in occupaion ype j, wherei (h, l) for high and low educaed workers, respecively, and j (c, s) for complex and simple occupaions, respecively. Le U i denoes he number of he unemployed of ype i. Assume ha he high educaed unemployed lose heir skil wih probabiliy σ, and ha he high educaed in simple occupaions lose heir skil wih probabiliy θ. Therefore, he high educaed unemployed, excluding hose who los heir skil, are denoed U h =(1 σ). U h The low educaed unemployed, including he high educaed unemployed who los heir skil, are denoed U l = σ U h + U l. The high educaed in simple occupaions, excluding hose who los heir skil, are denoed N =(1 θ). N The low educaed employed in simple occupaions, +θ N. including he high educaed in simple occupaions who los heir skil, are denoed N = N The high educaed in complex occupaions, including he low educaed who compleed heir raining in 7

8 complex occupaions, are denoed N = N excluding hose who compleed heir raining, are denoed N + δ N. The low educaed in complex occupaions, =(1 δ). N The variables wih he sars denoe employmen and unemploymen before skill loss and acquisiion. The labor force is normalized o one. In his conex, he high and he low educaed household members are divided ino hose employed and hose unemployed as follows N + N + N + N + U h + U l =1 (1) Time for all ypes is normalized o one. A high educaed unemployed, excluding hose who los heir skil, uses a porion S occupaion, and 1 S of is ime o search for a complex occupaion, a porion S o search for a simple S for leisure. A low educaed unemployed, including he high educaed unemployed who los heir skil, uses a porion S porion S of is ime o search for a simple occupaion, and 1 S of is ime o search for a complex occupaion, a S for leisure. A high educaed worker in a complex occupaion, including he low educaed who compleed heir raining, spends a porion hours a work and 1 for leisure. A high educaed worker in a simple occupaion, excluding hose who los heir skil, spends 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 in complex occupaions, excluding hose who compleed heir raining, spends a porion hours a work and 1 for leisure. The low educaed in a simple occupaion, including he high educaed in a simple occupaion who los heir skil, spends a porion hours a work and 1 for leisure. As differen employmen hisories amongs 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, who 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 following value funcion Γ = Γ N, N, N, N, he opimizaion problem of he household can be wrien in he following recursive form Γ = Max {C,S,S,O,S,S } f (C )+U h Ω h + UΩ l l + N Ω + N Ω + N Ω + N Ω ª + βe Γ +1 (2) where E is he expecaion operaor condiional on he informaion se available in period, β is he dis- 8

9 S and Ω l = Ω l 1 S S coun facor and f (C ) is he uiliy of period consumpion of he household C. Ω h = Ω h 1 S denoe he uiliy of period leisure of he high and he low educaed unemployed, respecively. Ω = Ω 1, Ω = Ω 1 O, Ω = Ω 1, and denoe he uiliy of period leisure of he employed ypes. This is subjec o he Ω = Ω 1 following budge consrain C = N W + N W + N W + N W + D ϕδn (3) where W ij is he period wage for labor ype ij, D is he dividends disribued by firms, and ϕ is he cos of raining. 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 comprised 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, who did no lose heir skil N+1 = 1 χ N + P S U h + O N (4) where P = M S U h+o N occupaion, and M is he probabiliy ha a high educaed searcher is mached wih a complex = M Z c V c,s U h + O N represens he number of complex maches. Z c is he proporion of complex vacancies direced o he high educaed. Similarly, he high educaed workers in simple occupaions in period +1are comprised of hose of ha ype, who did no lose heir skil, and 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 pool of he high educaed unemployed, who did no lose heir skil = M S U h N+1 = 1 χ O P N + P S U h (5) where P is he probabiliy ha a high educaed searcher is mached wih a simple occupaion, and M = M Z sv s,s U h represens he number of simple maches wih he high educaed. Z s is he proporion of simple vacancies direced o he high educaed. Similarly, he low educaed workers in complex occupaions in period +1 are comprised of hose of ha ype who are no separaed from complex occupaions exogenously in period according o he separaion rae χ, in addiion o he new maches from he searchers pool of he low educaed unemployed 9

10 where P = M S U l N+1 = 1 χ N + P S U l (6) is he probabiliy ha a low educaed searcher is mached wih a complex occupaion, and M = M (1 Z c ) V c,s U l represens he number of complex maches wih he low educaed. Similarly, he low educaed workers in simple occupaions in period +1 are comprised of hose of ha ype, including he high educaed in simple occupaions who los heir skil, 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, including he high educaed unemployed who los heir skil where P M = M S U l N+1 = 1 χ N + P S U l (7) is he probabiliy ha a low educaed searcher is mached wih a simple occupaion, and = M (1 Z s ) V s,s U l represens he number of simple maches wih he low educaed. Finally, he high educaed unemployed in period +1are comprised of hose of ha ype who did no mach wih a complex or a simple occupaion in period, in addiion o he high educaed separaed from complex or simple vacancies U+1 h = 1 P S P S U h + χ N + χ N (8) The consan separaion raes are jusified by all (2005), who concludes ha over he pas fify years job separaion raes 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 of degree one funcions of he number of corresponding vacancies, V c dynamic equaion for U+1 l is given by (1). and V s, and effecive searchers. The The represenaive household chooses consumpion such ha he marginal uiliy of consumpion equa he Lagrange muliplier λ f (C ) C = λ (9) The household chooses he opimal proporion of ime he high educaed unemployed, who did no lose heir skil, allo o search 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 in a complex occupaion 10

11 Ω h Γ S + βp E +1 N +1 Γ βp E +1 U+1 h =0 (10) The household chooses he opimal proporion of ime he high educaed unemployed, who did no lose heir skil, allo o search for a simple occupaion S, such ha he disuiliy from increasing search by one uni is offse by he discouned expeced value of an addiional high educaed in a simple occupaion Ω h Γ S + βp E +1 N +1 Γ βp E +1 U+1 h =0 (11) The household chooses he opimal proporion of ime he low educaed unemployed, including he high educaed unemployed who los heir skil, allo o search 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 low educaed in a complex occupaion Ω l Γ S + βp E +1 N +1 =0 (12) The household chooses he opimal proporion of ime he low educaed unemployed, including he high educaed unemployed who los heir skil, allo o search for a simple occupaion S, such ha he disuiliy from increasing search by one uni is offse by he discouned expeced value of an addiional low educaed in a simple occupaion Ω l Γ S + βp E +1 N +1 =0 (13) 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 Ω O Γ + P βe +1 Γ N+1 P βe +1 N+1 =0 (14) From he envelope heorem, an addiional high educaed mached wih a complex occupaion accrue a 11

12 value o he household ha is given by Γ N = Ω 1 Ω l 1 S S +λ W + β 1 χ Γ E +1 Γ N+1 + βχ E +1 U+1 h Γ βp S E +1 Γ N+1 βp S E +1 N+1 (15) Similarly, an addiional high educaed mached wih a simple occupaion accrues a value o he household ha is given by Γ N = Ω 1 O Ω l 1 S +β 1 χ O P Γ +1 E Γ +βχ E +1 U+1 h βp S N +1 S E Γ +1 + λ W + βo P E Γ +1 N+1 N+1 βp S E Γ +1 N +1 (16) Similarly, an addiional low educaed mached wih a complex occupaion accrues a value o he household ha is given by Γ N = Ω 1 Ω l 1 S +β 1 χ E Γ +1 N +1 S + λ W λ ϕδ βp S E Γ +1 N +1 Γ βp S E +1 N+1 (17) Similarly, an addiional low educaed mached wih a simple occupaion accrues a value o he household ha is given by Γ N = Ω 1 Ω l 1 S Γ βp S E +1 N+1 βp S + 1 χ Γ E +1 N+1 Γ E +1 S + λ W N+1 (18) 12

13 Finally, an addiional high educaed unemployed accrues a value o he household ha is given by Γ U h = Ω h 1 S Γ +βp S E +1 S Ω l 1 S N+1 βp S E Γ +1 N +1 S + βe Γ +1 U h +1 + βp βp S E Γ +1 N +1 1 P S Γ S E +1 N+1 P S (19) Subsiuing he envelope condiions ino he firs order condiions yields he following represenaive household s opimal condiions τ h βp = τ E W +1 E C +1 1 χ +τ h E P+1 1 (20) τ h βp = τ E W +1 E C +1 1 χ +τ h E P+1 1 (21) τ l βp = τ E E +τ l E 1 χ P W+1 C +1 µ ϕδ 1 E C +1 (22) τ l βp = τ E E +τ l E 1 χ P +1 1 τ = τ h 1 P P +1 W+1 C +1 (23) (24) where τ ij is he marginal uiliy of leisure of labor ype i in occupaion j. 13

14 3.2 Firms The represenaive firm chooses he number of complex and simple vacancies o pos, besides he proporion of he complex and 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 all labor ypes. Assuming he firm has he following value funcion Γ F = Γ F N, N, N, N, he opimizaion problem can be wrien in he following recursive form Γ F = Max {V s,v c,zc,zs } ½ Y ω s V s ω c V c N W N W ¾ N W N W λ+1 + βe Γ F +1 λ 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 given 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 ³ facor used by firms is given by β λ +1 λ. The maximizaion is subjec o he producion funcion which is a composie of he complex occupaion oupu N + N and he simple occupaion oupu N + N (25) Y = Y A, N + N, N + N (26) where A is he aggregae echnology. The maximizaion problem of he firm is ao subjec o he following employmen dynamics N+1 = 1 χ N + q Z c V c (27) N+1 = 1 χ O P N N+1 = 1 χ N + q Z s V s (28) + q (1 Z c ) V c (29) where q = M Z cv c N+1 = 1 χ N + q (1 Z s ) V s (30) is he probabiliy ha a complex vacancy is filled by a high educaed, q he probabiliy ha a simple vacancy is filled by a high educaed, q = M (1 Z c)v c = M Z sv s is is he probabiliy ha a 14

15 complex vacancy is filled by a low educaed, and q = M (1 Z s)v s is he probabiliy ha a simple vacancy is filled by a low educaed. The firm chooses he opimal level of complex vacancies o pos V c, such ha he expeced marginal cos of posing a complex 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 c = q Z c λ+1 Γ F +1 βe λ N+1 + q (1 Z c λ+1 Γ F +1 ) βe λ N+1 (31) The firm chooses he opimal level of simple vacancies o pos V s, such 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 ω s = q λ+1 Γ F +1 Z βe λ N+1 + q λ+1 Γ F +1 (1 Z ) βe λ N+1 (32) The firm chooses he opimal proporion of simple vacancies direced o he high educaed Z c, such ha he discouned expeced value of an addiional high educaed worker in a complex occupaion is equal o he discouned expeced value of an addiional low educaed worker in a complex occupaion q V c λ+1 Γ F +1 E λ N+1 = q V c λ+1 Γ F +1 E λ N+1 (33) The firm chooses he opimal proporion of simple vacancies direced o he high educaed Z s, such 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 V s λ+1 Γ F +1 E λ N+1 = q V s λ+1 Γ F +1 E λ N+1 (34) From he envelope heorem, he value of an addiional high educaed worker in a complex occupaion for he firm 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 Γ F N = Y N W + 1 χ λ+1 βe Γ F +1 λ N+1 (35) Similarly, he value of an addiional high educaed worker in a simple occupaion, who did no lose skil, for he firm is given by he difference beween is marginal produciviy and he wage, in addiion o he 15

16 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 Γ F N = Y N W + 1 χ O P λ+1 βe λ Γ F +1 N +1 (36) Similarly, he value of an addiional low educaed worker in a complex occupaion for he firm 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 Γ F N = Y N W + 1 χ λ+1 βe Γ F +1 λ N+1 (37) Finally, he value of an addiional low educaed worker in a simple occupaion, or a high educaed in a simple occupaion who los skil, for he firm 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 Γ F N = Y N W + 1 χ λ+1 Γ F +1 βe λ N +1 (38) Subsiuing he envelope condiions ino he firs order condiions yields he represenaive firm s opimal condiions ω c µ λ+1 Y+1 q = βe λ N+1 +1W χ ω c q +1 ω s µ λ+1 Y+1 q = βe λ N+1 +1W χ O +1 P+1 ω s q+1 ω c µ λ+1 Y+1 q = βe λ N+1 +1W ω s λ+1 q = βe λ µ Y+1 N+1 +1W χ ω c q χ ω s q +1 (39) (40) (41) (42) 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 occupaion is given by 2 2 Deailed derivaions are included in appendix

17 ³ W Y = 1 ξ N + ξ C τ h Ω 1 (43) 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 ³1 ξ of boh he firm s revenues from he worker s produciviy. 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 and ha of a high educaed in a complex occupaion, in addiion o he forgone benefi from being mached wih a simple vacancy. Similarly, he wage of he high educaed in a simple occupaion, who did no lose heir skil, is given by 3 ³ W = 1 ξ Y N O P ω s q + ξ C τ h Ω 1 O (44) 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 ³1 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 and ha of a high educaed in a simple occupaion, in addiion o he forgone benefi from being mached wih a complex vacancy. Similarly, he wage of he low educaed in a complex occupaion is given by 4 ³ W Y = 1 ξ N + ξ C τ l Ω 1 ϕδ + C (45) 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 ³1 ξ of boh he firm s revenues from he worker s produciviy. 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 and ha of a low educaed in a complex occupaion, in addiion o he forgone benefi from being mached wih a simple vacancy. Finally, he bargained wage of he low educaed in a simple occupaion, including he high educaed in 3 Deailed derivaions are included in appendix Deailed derivaions are included in appendix

18 simple occupaions who los heir skil, is given by 5 ³ W Y = 1 ξ N + ξ C τ l Ω 1 (46) 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 ³1 ξ for he firm s revenues from he worker s produciviy. 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 and ha of a low educaed in a simple occupaion, in addiion o he forgone benefi from being mached wih a complex vacancy. The hours of he high educaed in complex occupaions are chosen such 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 ³ Y N µ 1 Ω + λ =0 (47) The hours of he high educaed in simple occupaions, who did no lose heir skil, are chosen such 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 ³ Y N µ 1 Ω + λ =0 (48) The hours of he low educaed in complex occupaions are chosen such 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 8 ³ Y µ N 1 Ω + λ =0 (49) The hours of he low educaed in simple occupaions, including he high educaed in simple occupaions who los heir skil, are chosen such 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 9 5 Deailed derivaions are included in appendix Deailed derivaions are included in appendix Deailed derivaions are included in appendix Deailed derivaions are included in appendix Deailed derivaions are included in appendix

19 Finally, he crowding ou effec is defined as ³ Y µ N 1 Ω + λ =0 (50) Crowding = N N + N (51) Toal unemploymen is defined as U = U h + U l.toclosehemodel,wehave Y = C + ω c V c + ω s V s (52) 4 Calibraion 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. Since informaion may no be available for he oher parameers, heir values are compued in he seady sae sysem of equaions afer seing values for variables quanifiable from he daa. The seady sae values for cerain variables are caulaed from he averages in he daase during he period under sudy. For insance, he proporions of he employed ypes are se a N =0.23, N =0.25, N =0.01, N =0.45 and he unemployed ypes a U h =0.02, U l =0.04, andu =0.06, which are equal o he daa averages during he period under sudy as well. Given he proporion of employmen of all ypes, he wages, W, W, W and W are se equal o he daa average, such ha he seady sae skill premium is 1.52, which is ao equal o he daa average of 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 =0.35 is ao se equal o he daa average of 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 f (C )=ln (C ). The insananeous uiliy funcions of leisure are given by Ω h = τ h 1 S S, Ω l = τ l 1 S S, Ω = τ 1, Ω = τ 1 O, Ω = τ 1, Ω = 19

20 τ 1. The parameers 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 parameers in he uiliy of leisure for he high educaed in complex occupaions τ is given by 2.5, for he high educaed in simple occupaions τ is given by 0.7, for he low educaed in complex occupaions τ is given by 1.5, 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 (Z c V c ) γ 1 γ, S U h + O N M = T (Z s V s ) γ 1 γ, S U h M = T ((1 Z c ) V c ) γ S U l 1 γ and M = T ((1 Z s ) V s ) γ 1 γ, S U l where γ (0, 1) is he elasiciy of maching wih respec o vacancies. T, 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, T and T are given by 0.1. The choice of he level parameers is deermined o arge he separaion raes. In he seady sae, he flows ou of employmen equa he flows ou of unemploymen. This ensures ha he employmen level of every ype says consan. Thus, we have χ N = M, χ + OP N = M, χ N = M and χ N = M in he seady sae. Therefore, he choice of T, T, T and T deermines he maches, and accordingly arges he separaion raes. The separaion raes χ, χ, χ and χ from he complex and simple occupaions are given by 0.01, 0.02, 0.01, and 0.03, respecively. These are seleced such ha he separaion rae from simple vacancies is higher han ha from complex ones, he separaion rae of he low educaed is higher han hose of he high educaed, and ha heir average is close o he weighed average separaion rae caulaed by all (2005) and Shimer (2005). The coss of creaing he complex vacancy ω c and he simple vacancy ω s are given by 2.28 and 0.12, respecively. These values are deermined hrough he seady sae equaions of he opimal number of vacancies. The firm s share of he surplus ξ, ξ, ξ and ξ are all se a 0.5, as is sandard in he lieraure. The bargaining power of he households are 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 probabiliy of skill loss of he high educaed unemployed σ is deermined by muliplying he proporion of long erm unemploymen ou of oal unemploymen, by he proporion of he high educaed 20

21 unemployed ou of oal unemploymen. The longer he duraion of he spell of unemploymen, he higher he deerioraion of skil. Thus, he unemployed for a long ime are more likely o lose heir skil. According o a Congressional Budge Office paper (2007), he highes proporion of long erm unemploymen ou of oal unemploymen in he period is around 20%. Assuming ha he probabiliy of he high educaed unemployed for a long period is similar o he proporion of he high educaed unemployed ou of oal unemploymen = 1 3, hen he porion of hose who lose skil during he spell of unemploymen are equal o he porion of he high educaed in long erm unemploymen σ = 1 3 (0.2) = Similarly, he probabiliy of skill loss of he high educaed in simple occupaions θ is deermined by muliplying he proporion of long erm mismach by he proporion of he high educaed employed in simple occupaions ou of all hose employed in simple occupaions= = There is no informaion available on long erm mismach. Assume he long erm mismach ou of oal mismached labor is similar o long erm unemploymen=20%, hen θ =( ) (0.2) = The raining parameer δ is se a 0.5. The echnological consrains faced by he firm is ao represened by a consan reurns o scale Cobb- Douglas funcion Y = A N + N µ 1 µ, N + N whereµ (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 loga +1 = ρ A loga + A +1 (53) where A +1is independenly and idenically disribued random variable drawn from a normal disribuion wih mean zero and sandard deviaion denoed by σ A. 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 A =

22 5 Analysis 5.1 Impue Responses The model wih he feaures of labor mismach and skill loss, referred o as he "Mismach/Loss1" model hereinafer, 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 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 of an addiional worker of any ype o he firm. The firm poss complex and simple vacancies such ha he expeced marginal cos of posing a 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. Accordingly, he decrease in he marginal produciviy of workers induces firms o decrease heir posing of complex and simple vacancies. Firms ao reduce he porion of he vacancies direced a he high educaed. Accordingly, he high educaed decrease heir search inensiy for complex occupaions. This causes a decline in he employmen of he high educaed in complex occupaions. As he high educaed unemployed reduce heir search inensiy for complex occupaions, he high educaed in simple occupaions increase heir on-he-job search. This is due o he diminished compeiion from he unemployed searchers. This ao causes an increase in he search inensiy for simple occupaions, which causes a lagged increase in he employmen of he high educaed in simple occupaions. The decline in he employmen in complex occupaions causes an increase in he unemploymen of he high educaed. On he oher hand, he low educaed unemployed reduce heir search inensiy for simple and complex occupaions due o he decline in he proporion of hese vacancies direced o his ype. This causes a decrease in he employmen of he low educaed in simple and complex 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, consisenly wih he observaions. The lagged increase in he high educaed in simple occupaions, and he decrease in he low educaed in simple occupaions cause he crowding ou variable o increase, consisenly wih he observaions. The hours of work of any ype are chosen such ha he disuiliy of leisure from increasing he hours of work by one uni is offse by he increase in he marginal produciviy due o an increase in hours by 22

23 one uni. Figure 2 shows ha he hours of all ypes decline due o he reducion in marginal produciviy. Accordingly, oal hours decline as well. Comparing he momens of he model in able 8 o he daa observaions, he model succeeds in several aspecs. The model succeeds in replicaing he lagged counercyclicaliy of he unemploymen of he high educaed, The firs lag correlaion coefficien of he model is , and is saisically significan. The model, however, produces a lagged counercyclical unemploymen of he low educaed, and a lagged counercyclical oal unemploymen where he firs lag correlaion coefficien equa , is saisically significan. Finally, he model produces a counercyclical crowding ou effec, wihou he lag ha is observed in he daa. The success of he model can be ao 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, and hose observed in he daa. Table 7 shows ha he model succeeds in reproducing he high persisence observed in he daa. For insance, he firs lag serial correlaion of oal unemploymen is in he daa and in he model. The firs lag auocorrelaion of he unemploymen of he high educaed is in he daa and in he model, while 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 ha in he daa. 5.2 Sensiiviy Analysis The robusness of he resu of he model is examined o check wheher he dynamic evoluion of he variables of ineres are sensiive o he feaures of a specific framework. The model wih he feaures of labor mismach and skill loss is considered a benchmark and is referred o as he "Mismach/Loss1" model hereinafer. The "Mismach/Loss1" model is compared o a similar model wih he same feaures, bu wihou he aspec of skill loss of mismached labor where θ =0. In his conex, only he high educaed unemployed lose heir skil. This model is referred o as he "Mismach/Loss2" model hereinafer 10.The "Mismach/Loss1" is ao compared o a similar one wih he same feaures, bu wihou he aspec of skill loss where σ = θ =0. In his conex, neiher he unemployed no he mismached workers lose heir skil. This model is referred o as he "Mismach/No Loss" model hereinafer 11. Table 7 shows ha he serial correlaions are lower in he "Mismach/No Loss" model han in he wo mode wih he aspec of skill loss. This confirms ha inroducing he aspec of skill obsolescence increases he persisence of 10 Figures 3 and 4 show he impue responses of he "Mismach/Loss2" model. 11 Figures 5 and 6 show he impue responses of he "Mismach/No Loss" model. 23

24 unemploymen. In addiion, he serial correlaions of he "Mismach/Loss2" model is higher han hose in he "Mismach/Loss1" model. This is because in he former, he high educaed unemployed lose heir skil, and become low educaed unemployed whose probabiliy of finding a job is low. This causes he persisence of unemploymen o be high. In he laer, he loss of skil of mismached workers, cause he high educaed in simple occupaions o become low educaed. The low educaed in simple occupaions have a higher separaion rae ino unemploymen. As hey become unemployed, his allows an opporuniy o he high educaed unemployed o escape unemploymen ino simple occupaions. This reduces he unemploymen persisence compared o he model wihou he skill loss of he mismached labor. Therefore, he "Mismach/Loss1" performs beer han he "Mismach/Loss2" in capuring he observed persisence of unemploymen. In addiion, we compare he above menioned mode ha feaure labor mismach o one where here is no labor mismach. In his conex, here are wo ypes of workers and wo ypes of vacancies, bu he aspec of job compeiion and crowding ou are assumed away. In his conex, he complex vacancies are filled by he high educaed only, while he simple vacancies are filled by he low educaed only. There is no on-he-job search in his case. This model, wih he aspec of skill loss, is referred o as he "No Mismach/Loss" model hereinafer 12, while he one wihou he aspec of skill loss is referred o as he "NoMismach/NoLoss"modelhereinafer 13. I is obvious from he serial correlaions ha he mode wihou he aspec of labor mismach exhibis higher persisence compared o he mode wih mismached labor. This can be aribued o he observaion ha afer he iniial shock, he recovery of he economy is capured in a faser recovery of he hours of work, raher han in he employmen leve. This causes he unemploymen, in hese mode wih he endogenous choice of he hours of work, o exhibi higher persisence. The mode wih labor mismach are relaively more successful in reproducing he persisence of unemploymen because of he feaure of job compeiion, which allows he employmen of he high educaed in simple occupaions o increase afer he adverse shock. This allows he simple occupaions o absorb a porion of he high educaed, who would have been unemployed oherwise, and accordingly reduce he unemploymen persisence compared o he oher mode wihou ha feaure. 12 The deai of he "No Mismach/Loss" model are available from he auhor upon reques. Figures 7 and 8 show he impue responses of he "No Mismach/Loss" model. 13 The deai of he "No Mismach/No Loss" model are available from he auhor upon reques. Figures 9 and 10 show he impue responses of he "No Mismach/No Loss" model. 24