Worker flows and matching efficiency

Transcription

1 Worker flows and maching efficiency Marcelo Veraciero Inroducion and summary One of he bes known facs abou labor marke dynamics in he US economy is ha unemploymen and vacancies are srongly negaively correlaed an empirical relaionship called he Beveridge curve 1 In recen imes however large deviaions from he Beveridge curve have been observed In paricular vacancies have increased quie significanly since mid-2009 bu his phenomenon has no been accompanied by a subsanial decrease in he unemploymen rae (see figure 1) This failure of he Beveridge curve has surprised many economiss and has been inerpreed as evidence of mismach ha is of increased fricions in he process hrough which workers mee job opporuniies (for example Kocherlakoa 2010) The purpose of his aricle is o provide a measure of mismach in US labor markes and o assess is imporance in deermining he behavior of he unemploymen rae and oher labor marke oucomes since he sar of he laes recession The framework ha I use is a simplified version of he Morensen and Pissarides (1994) model Since my purpose is o use i as a ool for organizing and inerpreing daa I will absrac from any explici decision making and focus on he essenial srucure of he model The basic srucure of he Morensen and Pissarides model has hree main componens Firs i has an aggregae maching funcion ha summarizes he process hrough which unemployed workers and employers wih open vacancies search for each oher and mee I funcions very much like a sandard producion funcion wih unemployed workers and vacancies enering as inpus of producion and he number of maches formed appearing as oupu The second elemen is a free-enry condiion for he creaion of vacancies In paricular i is assumed ha here is a fixed cos o pos a vacancy and ha employers creae vacancies up o he poin a which he expeced discouned value of a filled job equals his fixed cos The expeced value of a job is given by he probabiliy of filling he job which is deermined by he aggregae maching funcion and by he value of a job In a full-blown version of he model he value of a job is endogenously deermined by he expeced revenues ha he job will generae and by he bargaining power of he worker However in he simplified version considered in his aricle I am silen abou he explici process hrough which he value of a job is deermined The hird main componen is a simple accouning relaionship ha saes ha he oal flows in and ou of each labor marke sae mus be equal A sandard approach in he lieraure is o allow only for wo labor marke saes (employmen and unemploymen) and o assume ha he model is always a is seady sae (ha is is long-run equilibrium) However I consider more flexible specificaions in his aricle I use his simple version of he Morensen and Pissarides model o measure mismach and evaluae is consequences during he pos-2007 recession period This is no he firs aricle o do his Two closely relaed papers are Barlevy (2011) and Barnichon and Figura (2010) Barlevy follows he sandard approach by posulaing wo labor marke saes assuming a consan separaion rae (ha is he rae a which workers ransi from employmen ino unemploymen) and by assuming ha he model is always a is long-run seady sae On he conrary Barnichon and Figura incorporae a hird labor marke sae (nonparicipaion) and allow he ransiion raes beween he hree labor marke saes o vary over ime However similar o Barlevy Barnichon and Figura assume ha he model is always a is seady sae and ha only unemployed workers ener he maching funcion 2 Marcelo Veraciero is a senior economis in he Economic Research Deparmen of he The auhor is graeful for commens from Gadi Barlevy Andy Neumeyer and Juan Pablo Nicolini as well as seminar paricipans a he and he Universidad Torcuao Di Tella He also hanks Hao Zou for research assisance 147

2 Given he differen assumpions made in he lieraure I use my model o evaluae how sensiive he resuls are o he differen specificaions I consider he following dimensions Firs I assess he imporance of allowing he separaion rae o vary over ime insead of assuming i o be consan Second I evaluae he consequences of specifying hree labor marke saes insead of wo Third I assess he consequences of assuming ha he model is always a is seady sae insead of allowing for ransiionary dynamics Fourh I evaluae he consequences of allowing nonparicipans o ener he maching funcion insead of assuming ha he maching funcion solely applies o unemployed workers I find ha he resuls are exremely sensiive o he alernaive specificaions However in he preferred scenario (which has hree labor marke saes variable ransiion raes ransiionary dynamics and nonparicipans enering he maching funcion) I obain he following findings 3 Firs he maching efficiency has been quie volaile hroughou he whole sample period (2001:1[January] 2011:2[February]) Second he maching efficiency has been drifing down since he sar of he las recession Third he value of filled jobs plummeed beween 2007:12 (he sar of he laes recession) and 2009:6 bu i has recovered quie significanly since hen Fourh condiional on he observed pahs for he value of a job and all ransiion raes he drop in maching efficiency since he sar of he recession has had only a moderae impac on he unemploymen rae: The curren unemploymen rae would be 1 percenage poin lower if he maching efficiency had sayed unchanged Fifh he bulk of he increase in he unemploymen rae since he sar of he recession is accouned for by changes in he ransiion raes across labor marke saes Sixh he maching efficiency he value of a job he ransiion raes and he search inensiy of nonparicipans all have significan effecs on he dynamics of nonparicipaion Since hey deemphasize he imporance of maching inefficiencies in explaining he large increase in he unemploymen rae since he sar of he las recession he resuls in his paper are consisen wih a greaer role for policy in achieving improvemens in labor marke condiions In he nex secion I consider he case of wo labor marke saes In he following secion I consider he case of hree labor marke saes and a maching funcion wih only unemployed workers Then I consider he case of hree labor marke saes bu allow for nonparicipans o ener he maching funcion Readers solely ineresed in learning abou he relaive conribuions o unemploymen dynamics should jump o he las secion of he paper which uses he vacancies figure 1 Unemploymen rae vs vacancies unemploymen 2001: : : :02 Noe: Vacancies and unemploymen are normalized by oal labor force Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey preferred scenario The firs wo secions repor resuls using alernaive bu less saisfacory mehodologies The case of wo labor marke saes There are wo ypes of agens: firms and workers Each firm has one job available which can eiher be filled or vacan The expeced discouned value of profis generaed by a filled job is equal o J unis of he numeraire Posing a vacan job requires k unis of he numeraire There is an infinie number of poenial firms Workers can be in eiher of wo saes: employed or unemployed Employed workers ge separaed from heir curren jobs wih probabiliy λ Unemployed workers and posed vacancies deermine he oal number of new maches ha are formed according o he following maching funcion: 1 1) M = AU V where M is he oal number of new maches U is he oal number of unemployed workers V is he oal number of posed vacancies A is he produciviy of he maching funcion and 0 < < 1 Normalizing o one he oal number of workers in he economy he evoluion of unemploymen over ime can be described by he following equaion: 148 4Q/2011 Economic Perspecives

3 2) U +1 = U M + (1 U )λ Tha is he oal number of workers ha will be unemployed omorrow U +1 is equal o he oal number of currenly unemployed workers ha do no find a mach U M plus he oal number of currenly employed workers ha ge separaed from heir jobs (1 U )λ Since firms are profi maximizers he following free-enry condiion mus be saisfied: M 3) k = V J Tha is he cos of posing a vacancy k mus be equal o he probabiliy of filling a vacancy M /V imes he expeced discouned value of profis generaed by a filled job J If his condiion was no saisfied he oal number of vacancies creaed would be eiher zero or infiniy depending on he direcion of he resuling inequaliy Observe ha he produciviy of he maching funcion A he separaion rae λ and he expeced discouned profis generaed by a filled job J are exogenous o he model Given he oal number of workers unemployed a dae zero U 0 he model generaes an endogenous pah for M V U { } + 1 = 0 Seady sae Assuming a consan maching produciviy A a consan separaion rae λ and consan expeced discouned profis generaed by a filled job J a seady sae of he model economy can be defined as an iniial unemploymen level U 0 = U such ha he endogenous pah for { M V U+ 1 } ha he model generaes is = 0 consan over ime Tha is ha M = M V = V and U = U for every 0 A seady sae (M V U ) can be inerpreed as he oal maches vacancies and unemploymen ha he economy will converge o in he long run From equaions 1 3 we have ha he condiions a seady sae mus saisfy are he following: 4) M = AU V 1 5) M = (1 U )λ M 6) k = J V Subsiuing equaion 5 in equaions 4 and 6 gives he following simplified seady-sae condiions: 7) λ U = λ + ( ) ( ) A V U 8) k A U V J = 1 Equaion 7 defines a negaive relaionship beween unemploymen and vacancies and for his reason is called he Beveridge curve Equaion 8 defines a posiive linear relaionship beween unemploymen and vacancies and since i is defined by a free-enry condiion o he posing of vacancies i is called he job creaion curve The Beveridge and job creaion curves are depiced in figure 2 The inersecion of hese curves deermines he seady sae (U * V * ) I is paricularly imporan o deermine wha causes shifs in each of hese wo curves I is possible o show ha an increase in he separaion rae λ shifs he Beveridge curve up an increase in he expeced discouned profis from a filled job J does no affec he Beveridge curve and an increase in he maching efficiency parameer A shifs he Beveridge curve down In urn he separaion rae λ has no effec on he job creaion curve bu an increase in eiher J or A roaes he job creaion curve clockwise Given hese shifs in he Beveridge and job creaion curves we can now deermine how changes in λ J and A affec he seadysae pair (U * V * ) In paricular we can conclude ha ha an increase in λ increases boh vacancies V and unemploymen U ha an increase in J increases V and reduces U and ha an increase in A reduces V The effecs of an increase in A on U are unclear from he figure bu subsiuing equaion 8 in equaion 7 gives ha λ U = λ + A ( ) 1 J 1 k Thus we can safely conclude ha an increase in A reduces U To he exen ha he ransiionary dynamics in response o a change in eiher λ A or J are fas business cycle flucuaions in unemploymen and vacancies can be sudied by performing he seady-sae analysis described in he previous paragraph Assuming ha his is he case we can make he following enaive 149

4 hypohesis Firs since here is a srong negaive empirical relaionship beween vacancies and unemploymen beween 2001:1 and 2007:12 flucuaions in he value of a filled job J ogeher wih a relaively consan separaion rae λ and a relaively consan maching produciviy A are he mos likely scenario for explaining his period Second significan changes in A and/or λ are necessary for explaining he subsanial deviaions from he Beveridge curve observed afer 2007:12 especially afer 2009:6 (see figure 1) A key issue will be o deermine he behavior of he maching efficiency parameer A during his laer period Anoher key issue will be o evaluae he conribuion of changes in A λ and J o he unemploymen and vacancy dynamics observed during his laer period Addressing hese issues will be he focus of he nex wo subsecions Before proceeding i will be convenien o rewrie equaions 7 8 as follows: 9) U = λ λ V + A ( U ) ( ) 10) k A U = V J 1 This makes explici he assumpion ha he economy a any monh can be safely described by he seadysae equaions 7 8 an assumpion ha will be mainained hroughou he res of his secion Consan separaion rae Shimer (2005) has argued ha he separaion rae λ does no play an imporan role in generaing unemploymen flucuaions For his reason I follow Barlevy (2011) and consider in his secion ha he separaion rae λ is consan over ime Under his assumpion I use he model described by equaions 9 10 o measure he ime pahs for he efficiency parameer A and he value of a job J In wha follows I se he separaion rae λ o 0042 which is equal o he average employmen-o-unemploymen ransiion rae plus he average employmen-ononparicipaion ransiion rae beween 2001:1 and 2007:12 From equaion 9 we have for any wo monhs i and j ha λ λ 11) 1 j i = ln λ ln λ U j U i U U i j / ln ln V i V j vacancies figure 2 Beveridge and job creaion curves V* 5 U* unemploymen Beveridge Job creaion Wihin he period 2001:1 2007:12 (which is a period wih relaively consan maching produciviy A) we can hus selec he monh i wih he larges U/V raio and he monh j wih he smalles U/V raio and use hem o ge an esimae for from equaion 11 4 These monhs happen o be i = 2003:6 and j = 2001:1 The esimaed value of urns ou o be Equaion 9 can also be used o measure he maching efficiency a monh as follows: 12) 1 λ U λ U V A = Using he above value of and averaging he values of A beween 2001:1 and 2007:12 obained from equaion 12 gives an esimae of A = 106 Using his consan value for A we can hen use equaion 9 o consruc he vacancies prediced by he model economy (condiional on he observed unemploymen rae) as follows: 13) 1 1 λ 1 V = λ U U A The prediced vacancies are shown by he red line in figure 3 We see ha under a consan maching efficiency parameer A he model does a good job a reproducing he behavior of vacancies beween 2001:1 and 2007:12 However beginning in 2009 he model 150 4Q/2011 Economic Perspecives

5 vacancies 0040 figure 3 Prediced Beveridge curve 015 figure 4 Maching efficiency (2 saes consan separaion rae) unemploymen Noe: Vacancies and unemploymen are normalized by oal labor force Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Noe: The log of A is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey fails o keep rack of he daa using a consan A This suggess ha he maching efficiency parameer A may have experienced subsanial changes in his laer period To show ha his could be he case figure 4 repors he values for A (in logs) measured from equaion 12 for he whole sample period (he verical line corresponds o 2007:12 ha is o he sar of he pas recession) We see ha he maching efficiency was relaively sable before 2008:1 However saring in 2008:1 he maching efficiency has flucuaed quie subsanially In paricular we see ha afer an iniial increase he maching efficiency has been decreasing coninuously reaching a cumulaive drop of 175 percen by 2010:11 Normalizing he cos of posing a vacancy k o one and using he pah for A already found equaion 10 can be used o consruc a ime series for he value of a job J In paricular we have ha 14) J k V = A U ( ) Figure 5 repors he evoluion of he value of a job beween 2001:1 and 2011:2 (in logs) We see ha J dropped quie subsanially during he recession: Beween 2007:12 and 2009:8 he value of a job declined by 68 percen 6 I now urn o evaluae he conribuions of changes in A and J o he dynamics of unemploymen and vacancies since he beginning of he recession In order o do his I compue adjused unemploymen U * and adjused vacancies V * using equaions 9 10 under he assumpion ha A = A 2007:12 for every monh Tha is I le he value of a job J evolve as in figure 5 (ha is as in he daa) bu fix he maching produciviy o he value ha i had a he sar of he recession For his reason U * and V * measure he unemploymen raes and vacancies ha would have been obained had he maching produciviy remained consan a is December 2007 level bu he pah for he value of a job J had remained he same Observe ha in a fullblown model (in which J is endogenously deermined) a change in he pah for A would generally affec he * * pah for J As a consequence comparing ( U V ) wih (U V ) canno be sricly inerpreed as describing he oal effecs of variaions in A ; i should be inerpreed as describing he condiional effecs of A (ha is condiional on he observed pah for J ) In a full-blown model he variaions in A would have o be accompanied by variaions in oher variables (for example in he bargaining power of workers) in order o obain an unchanged pah for J 7 Figure 6 shows he pah for U * (labeled consan A ) and for U (labeled variable A ) We see ha hrough 2009:1 he produciviy of he maching funcion did no play an imporan role in he unemploymen dynamics observed (boh pahs are quie similar) However saring in mid-2009 we see ha he decline in maching produciviy repored in figure 4 played a significan role in generaing a significanly larger unemploymen 151

6 figure 5 Value of a job (2 saes consan separaion rae) figure 6 Effecs on unemploymen rae (2 saes consan separaion rae) Noe: The log of J is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Variable A Consan A Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey rae In paricular we see ha by February 2011 he unemploymen rae would have been 75 percen insead of 89 percen had he maching produciviy remained consan a is beginning-of-recession level Figure 7 repors he pahs for V * (labeled consan A ) and for V (labeled variable A ) We also see ha hrough 2009:1 changes in he produciviy of he maching funcion had negligible effecs on vacancies However by mid-2009 boh pahs sar o diverge and we see ha by February 2011 vacancies would have been 16 percen insead of 19 percen had he maching produciviy remained consan a is 2007:12 level Variable separaion rae In his secion I allow he separaion rae o vary over ime Figure 8 repors he separaion rae beween 2001:1 and 2011:2 ha is obained from he Bureau of Labor Saisics Curren Populaion Survey (CPS) daa (once again he verical line depics he beginning of he las recession) We see ha early on in he recession he separaion rae increased quie significanly reaching 49 percen by 2009:1 bu ha i subsequenly rended down oward is pre-recession level Given he daa on U and V and he separaion rae λ repored in figure 8 I compue he maching efficiency A from he following equaion: 15) 1 λ U A = λ U V which is analogous o equaion 12 excep ha λ is allowed o vary over ime The resuling pah for he maching produciviy A is repored in figure 9 We see ha conrary o figure 4 we now observe large flucuaions in A previous o he sar of he recession Anoher difference is ha here is a sharp increase in maching produciviy early on in he recession ha compensaes for he 2009:1 spike in he separaion rae Also we see ha saring in 2009:2 he maching produciviy rends down much more sharply han in figure 4 The value of filled jobs J is compued from equaion 14 using he A values obained from equaion 15 The resuling pah is repored in figure 10 We see ha his pah is no very differen from ha in figure 5 Figures 11 and 12 explore he condiional conribuion o unemploymen and vacancies dynamics of he maching produciviy A he separaion rae λ and he value of a job J In paricular I compue adjused unemploymen U * and adjused vacancies V * using equaions 9 10 under he assumpion ha A = A 2007:12 and λ = λ 2007:12 for every monh Tha is I le he value of a job J evolve as in figure 10 (ha is as in he daa) bu I fix he maching produciviy o he value ha i had a he beginning of he recession A 2007:12 and fix he separaion rae o he value ha i had a he beginning of he recession λ 2007:12 In oher words U * and V * measure he unemploymen raes and vacancies ha would have been obained had he maching produciviy and he separaion rae remained consan a heir December 2007 levels 152 4Q/2011 Economic Perspecives

7 figure 7 Effecs on vacancies (2 saes consan separaion rae) figure 8 Separaion rae Variable A Consan A Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey and Job Openings and Labor Turnover Survey Noe: The separaion rae is equal o he sum of he employmen-o-unemploymen and employmen-ononparicipaion ransiion raes Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 9 Maching efficiency (2 saes variable separaion rae) 015 Noe: The log of A is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 10 Value of a job (2 saes variable separaion rae) 100 Noe: The log of J is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey I also compue adjused unemploymen U ** and adjused vacancies V ** using equaions 9 10 under he assumpion ha A = A 2007:12 for every monh (bu I le he separaion rae λ vary as in he daa) Tha is I le he value of a job J evolve as in figure 10 and he separaion rae λ evolve as in figure 8 bu fix he maching produciviy o he value ha i had a he beginning of he recession A 2007:12 In oher ** ** words U and V measure he unemploymen raes and vacancies ha would have been obained had he maching produciviy remained consan a is December 2007 level In figure 11 U * is labeled consan A consan λ U ** is labeled consan A variable λ and U 153

8 figure 11 Effecs on unemploymen rae (2 saes variable separaion rae) Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 12 Effecs on vacancies (2 saes variable separaion rae) 0 Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey is labeled variable A variable λ We see ha U * increases in he early par of he period and decreases during he second par mirroring he evoluion of he value of a job J described in figure 10 In urn U ** increases much more han U * early on in he recession because of he early increase in he separaion rae λ depiced in figure 8 bu as he separaion rae revers oward is beginning-of-recession level U ** sars o behave very much like U * Finally since he difference beween U ** and U is solely due o changes in he maching produciviy we see ha he large increase in maching produciviy early on in he recession (repored in figure 9) played an imporan role in keeping unemploymen relaively low However he large drop in maching produciviy since early 2009 significanly conribued o mainaining an unemploymen rae of more han 9 percen In urn figure 12 shows ha he maching produciviy doesn play a crucial role in vacancy dynamics However he large increase in he separaion rae in he early par of he recession played a noiceable role in keeping vacancies relaively high early on in he recession The case of hree labor marke saes The model used in he previous secion had wo labor marke saes: employmen and unemploymen In his secion I allow workers o be in a hird labor marke sae: nonparicipaion (ha is ou of he labor force) A main reason for doing his is ha in he CPS daa beween 2001:1 and 2007:12 he oal number of people ransiioning from nonparicipaion o employmen is almos wice as large as he oal number of people ransiioning from unemploymen o employmen (see figure 13) alhough he differences have become much smaller since he sar of he pas recession By considering only wo marke saes he analysis in he previous secion compleely missed hese ransiions Anoher reason for inroducing hree labor marke saes ino he model is ha wih wo labor marke saes i is no clear wha separaion raes o consider: separaions ino unemploymen or separaions ino boh unemploymen and nonparicipaion? Explicily inroducing hree labor markes saes avoids his ype of issue More generally inroducing hree labor marke saes allows me o address worker flows daa in a more saisfacory way In his secion I follow Barnichon and Figura (2010) and assume ha he maching funcion solely describes ransiions from unemploymen ino employmen In paricular I assume ha he maching funcion is given by 16) M = AU V 1 where M are he oal flows from unemploymen ino employmen U is unemploymen V are vacancies and 0 < < Q/2011 Economic Perspecives

9 housands of people figure 13 Flows ino employmen 0 Unemploymen-employmen Nonparicipaion-employmen Source: Bureau of Labor Saisics Curren Populaion Survey The ransiion rae from employmen o unemploymen λ EU he ransiion rae from employmen o nonparicipaion λ EN he ransiion rae from unemploymen o nonparicipaion λ he ransiion rae from nonparicipaion o unemploymen λ NU and he ransiion rae from nonparicipaion o employmen λ NE are assumed o be exogenous o he model The evoluion of workers across labor marke saes is hen given by he following equaions: 1 NE EU EN 17) E = E + AU V + λ N ( λ + λ ) E + 1 EU NU 1 18) U = U + λ E + λ N λ U AU V + 1 (eiher from employmen or unemploymen) minus all ransiions ou of nonparicipaion (eiher o employmen or unemploymen) In wha follows oal populaion will be normalized o one ha is 20) E + U + N = 1 for every period Similar o he previous secion he following free-enry condiion mus be saisfied: 1 NE AU V + λ N 21) k = ( J V ) Observe ha from he poin of view of a firm he probabiliy of filling a vacancy is equal o NE ( M + λ N ) / V because maches can be formed wih workers eiher coming from unemploymen or from nonparicipaion Given he oal number of workers unemployed a dae zero U 0 and he oal number of workers ha are nonparicipans a dae zero N 0 he model generaes an endogenous pah for M V U N { } = 0 Seady sae Assuming a consan maching produciviy A a consan value of a job J and consan ransiion raes λ a seady sae of he model economy can be defined as an iniial unemploymen level U 0 = U and an iniial nonparicipaion level N 0 such ha he endogenous pah for { M V U+ N } ha he model = 0 generaes is consan over ime From equaions we have ha he condiions ha a seady sae (U N V ) mus saisfy are he following: 19) N = N + EN E + NE U NU + 1 λ λ ( λ λ + ) N Equaion 17 saes ha nex-period employmen is equal o curren employmen plus all ransiions ino employmen (eiher from unemploymen or nonparicipaion) minus oal separaions (eiher o unemploymen or nonparicipaion) Equaion 18 saes ha nex-period unemploymen is equal o curren unemploymen plus all ransiions ino unemploymen (eiher from employmen or nonparicipaion) minus all ransiions ou of unemploymen (eiher o employmen or nonparicipaion) Equaion 19 saes ha nex-period nonparicipaion is equal o curren nonparicipaion plus all ransiions ino nonparicipaion EU EN 1 NE 22) ( λ + λ )( 1 U N) = AU V + λ N 23) ( λ NE + λ NU + λ EN ) N = λ EN ( 1 U )+ λ U 24) k = 1 NE AU V + λ N ( ) J V Similar o he previous secion i will be convenien o rewrie hese equaions as: EU EN 1 NE 25) ( λ + λ ) ( 1 U N ) = AU V + λ N 155

10 EN λ ( 1 U ) + λ U 26) N = NE NU EN ( λ + λ + λ ) 060 figure 14 Transiion raes (λs) 27) kv J 1 NE = AU V + λ N 040 This makes explici he assumpion ha he economy a any monh can be safely described by he seady-sae equaions an assumpion ha will be mainained hroughou he following wo subsecions Consan ransiion raes EU EN Figure 14 shows he ransiion raes λ λ λ λ NE and λ NU in logs normalized by heir average value for he period 2001:1 2007:12 We see ha hese ransiion raes were relaively sable prior o 2007:12 However we see ha wih he onse of he recession here was a significan drop in he ransiion rae from nonparicipaion o employmen λ NE a drop in he ransiion rae from unemploymen o nonparicipaion λ a large increase in he ransiion rae from nonparicipaion o unemploymen λ NU and a large increase in he ransiion rae from employmen o unemploymen λ EU In urn he ransiion rae from employmen o nonparicipaion was no significanly affeced Based on figure 14 and similar o he previous secion here I assume ha he ransiion raes EU EN NU λ λ λ λ NE and λ are consan over he period 2001:1 2007:12 Taking simple averages over his period gives he following values: 28) λ = ) A = EU EN NE NU Noe: All ransiion raes are repored in logs and normalized o zero a he sar of he las recession Source: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey 1 U V 1 EN EU EN λ ( 1 U ) + λ U λ + λ 1 U NE NU EN λ + λ + λ EN NE λ ( 1 U ) + λ U λ NE NU EN λ λ λ ) λ EU = ) λ EN = ) λ NE = ) λ NU = Subsiuing equaion 26 in equaion 25 under he assumpion of consan λ values we ge ha Assuming ha A is consan over he period 2001:1 2007:12 we can hen use wo monhs i and j wihin his period o ge an esimae of as follows: 34) 1 1 ij = V Vi j ln( U ) ln( ) i U j EU EN λ λ + EN λ ( 1 Ui ) λ U i 1 U + i NE NU EN {ln λ λ λ + + EN NE λ ( 1 Ui ) λ U i λ + NE NU EN λ λ λ Q/2011 Economic Perspecives

11 vacancies figure 15 Prediced Beveridge curve unemploymen Noe: Vacancies and unemploymen are normalized by oal civilian noninsiuional populaion (16 years and older) Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 16 Maching efficiency (3 saes seady sae consan ransiion raes) Noe: The log of A is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey EN λ 1 U j λ U EU EN + j λ λ + 1 U j NE NU EN λ λ λ + + ln EN λ 1 U j λ U NE + j λ NE NU EN λ λ λ ln U ln ( )} j U i Picking i = 2003:6 and j = 2001:1 which are he monhs wih he larges and smalles V/U raio respecively gives an esimae of = In urn equaion 33 can be used o measure he maching efficiency A a monh Using he above value of and averaging he values of A beween 2001:1 and 2007:12 obained from equaion 33 gives an esimae of A = Using his consan value for A I can hen use equaion 33 o consruc he vacancies prediced by he model economy (condiional on observed unemploymen) as follows: 35) 1 V = AU EU EN λ λ + EN λ ( 1 U ) λ U 1 U + NE NU EN λ λ λ + + EN NE λ ( 1 U ) λ U + λ NE NU EN λ λ λ Figure 15 repors unemploymen as a fracion of oal populaion and vacancies as a fracion of oal populaion beween 2001:1 and 2011:2 (black dos) as well as he vacancies prediced by equaion 35 We see ha he seady sae of he model wih hree labor marke saes consan ransiion raes and a consan A provides a good fi o he daa hrough 2007:12 However since he sar of he laes recession here have been large deviaions from he sable Beveridge curve prediced by he model This indicaes ha he maching efficiency parameer A mus have experienced significan changes since hen Figure 16 shows ha his has been he case I repors he maching efficiency levels obained by equaion 33 beween 2001:1 and 2011:2 We see ha before 2007:12 he maching efficiency had been fairly sable bu i plummeed wih he onse 157

12 figure 17 Value of a job (3 saes seady sae consan ransiion raes) Noe: The log of J is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 18 Nonparicipaion (3 saes seady sae consan ransiion raes) Model Daa Noe: Nonparicipaion is normalized by oal civilian noninsiuional populaion (16 years and older) Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey of he recession Observe ha he magniude of he fall is much larger han in figure 4 (p 151) Subsiuing equaion 26 in equaion 27 we ge ha 1 1 NE AU V λ + EN 36) J = kv λ ( 1 U ) λ U + NE NU EN λ λ λ + + Figure 17 repors he pah for J hus measured We see ha i is very similar o ha in figure 5 (p 152) indicaing ha having hree labor marke saes does no significanly affec he measuremen of he value of a job Before decomposing he effecs of he maching efficiency parameer A and he value of a job J I would like o poin ou ha he resuls ha follow should be aken wih a grain of sal While I seleced he pahs for A and J o reproduce he observed pah for U and V (given he resricions imposed by equaions 33 and 36) I made no aemp o reproduce he pah for nonparicipaion N which according o he model is given by EN λ ( 1 U ) + λ U 37) N = λ NE λ NU λ EN ( + + ) Figure 18 repors he pah for nonparicipaion in US daa and he pah for N given by equaion 37 We see ha he model does a reasonable job a reproducing he pah for N before 2007:12 bu ha i largely overpredics nonparicipaion afer ha This suggess ha eiher he assumpion of consan ransiion raes or he assumpion ha he economy is always a he seady sae of he model fails I reurn o his issue in he nex secion Similar o he previous secion I compue adjused unemploymen U * adjused nonparicipaion N * and adjused vacancies V * from equaions under he assumpion ha A = A 2007:12 for every monh Tha is I le he value of a job J evolve as in figure 17 (ha is as in he daa) bu fix he maching produciviy o he value ha i had a he sar of he recession In oher * * * words U N and V measure he unemploymen nonparicipaion and vacancies ha would have been ob- ained had he maching produciviy remained consan a is December 2007 level bu he value of a job had evolved as observed The version of he model wih consan ransiion raes delivers he following resuls 9 Similar o figure 6 (p 152) figure 19 indicaes ha saring in mid-2009 he decline in maching produciviy repored in figure 16 played an imporan role in generaing a large unemploymen rae This version of he model also indicaes ha by February 2011 he unemploymen rae would have been 64 percen insead of 89 percen had maching produciviy remained consan a is beginning-of-recession level Figure 20 shows ha 158 4Q/2011 Economic Perspecives

13 figure 19 Effecs on unemploymen rae (3 saes seady sae consan ransiion raes) figure 20 Effecs on nonparicipaion (3 saes seady sae consan ransiion raes) Variable A Consan A Variable A Consan A Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey he effecs of maching produciviy on nonparicipaion are very similar o hose on unemploymen Finally similar o figure 7 (p 153) figure 21 shows ha he effecs of maching efficiency on vacancies are negligible Variable ransiion raes In his secion insead of assuming ha ransiion raes are consan I allow hem o flucuae as in figure 14 Given daa on U and all ransiion raes I compue maching efficiency as follows: 38) 1 A = U V 1 EU EN λ λ + EN λ ( 1 U ) + λ U 1 U NE NU EN λ λ λ + + EN NE λ ( 1 U ) λ U + λ NE NU EN λ λ λ + + an expression obained from subsiuing equaion 26 in equaion 25 Figure 22 repors he pah for A hus obained We observe huge differences from figure 16 Insead of relaively sable behavior before 2007:12 followed by a large drop we observe significan volailiy hroughou he sample period and a large increase afer 2007:12 These differences indicae ha he predicions of he model rely criically on wheher ransiion raes are assumed o be consan or no The value of a job J is measured as 39) EN 1 NE λ ( 1 U ) + λ U J = kv AU V + λ NE NU EN λ λ λ and repored in figure 23 We see ha he qualiaive behavior is similar o figure 17; however he drop in J afer he sar of he pas recession is now somewha larger Before urning o he decomposiion of he differen effecs I revisi he issue of how well he model is able o reproduce he pah for nonparicipaion a pah ha has no been argeed in he calibraion Figure 24 repors he pah for nonparicipaion in US daa and he pah for N from equaion 26 We see ha conrary o figure 18 he model now does a reasonable job a reproducing he pah for N hroughou he sample period In principle his should be a reason for having more confidence in he resuls obained in his secion In order o decompose he differen effecs I compue adjused unemploymen U * adjused nonparicipaion N * and adjused vacancies V * from equaions under he assumpion ha A =A 2007:12 λ = λ : EU EU λ = λ λ EN λ EN : = λ NE λ NE : = and : NU NU λ λ for every monh Tha is I le he = : 159

14 figure 21 Effecs on vacancies (3 saes seady sae consan ransiion raes) Variable A Consan A Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 22 Maching efficiency (3 saes seady sae variable ransiion raes) Noe: The log of A is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 23 Value of a job (3 saes seady sae variable ransiion raes) Noe: The log of J is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 24 Nonparicipaion (seady sae variable ransiion raes) Model Daa Noe: Nonparicipaion is normalized by oal civilian noninsiuional populaion (16 years and older) Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey value of a job J evolve as in figure 23 (ha is as in he daa) bu fix he maching produciviy and he ransiion raes o he values ha hey had a he beginning of he recession In oher words U N and V measure he unemploymen nonparicipaion and vacancies ha would have been obained had he maching produciviy and ransiion raes remained consan a heir December 2007 levels bu J had evolved as i did 160 4Q/2011 Economic Perspecives

15 figure 25 Effecs on unemploymen rae (3 saes seady sae variable ransiion raes) Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey figure 26 Effecs on vacancies (3 saes seady sae variable ransiion raes) Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Also I compue adjused unemploymen U ** adjused nonparicipaion N ** and adjused vacancies V ** from equaions under he assumpion ha A = A 2007:12 for every monh (bu leing all λ s ake heir acual values) Tha is I le he value of a job J evolve as in figure 23 and he ransiion raes evolve as in figure 14 (p 156) bu I fix he maching produciviy o he value ha i had a he beginning of he recession ** ** ** A 2007:12 In oher words U N and V measure he unemploymen nonparicipaion and vacancies ha would have been obained had he maching produciviy remained consan a is December 2007 level bu all ransiion raes and J had evolved as hey did Figure 25 shows U / ( E + U ) ( consan A consan λ ) U / ( E + U ) ( consan A variable λ ) and U / (E + U ) ( variable A variable λ ) We see ha despie he large drop in he value of a job J described in figure 23 U / ( E + U ) increased only + moderaely In urn U ( E U ) increases by a huge amoun indicaing ha he large increases in he EU NU λ and λ observed afer 2007:12 in figure 14 had a large negaive impac in he labor marke Acually he unemploymen rae urned o increase only as described by U / (E + U ) because of he large increase in maching efficiency repored by figure 12 (p 154) Figure 26 shows ha he increase in maching produciviy A and he changes in ransiion raes played a noiceable role in keeping vacancies relaively high In urn figure 27 shows ha he increase in maching produciviy A played a crucial role in keeping nonparicipaion (N) relaively low since he changes in ransiion raes would have increased i quie subsanially Transiionary dynamics The previous secion showed ha inroducing variable ransiion raes affecs he resuls quie significanly and ha i allows one o keep rack of he behavior of nonparicipaion much more closely However he analysis of he previous secion suffered wo drawbacks Firs while he calibraion of he maching elasiciy parameer assumed consan maching efficiency and consan separaion raes prior o 2007:12 we see from figures 14 (p 156) and 22 ha his is no quie he case Second he analysis assumed ha he seady sae of he model could be used o describe monhly daa while he large flucuaions in ransiion raes observed in figure 14 (p 156) sugges ha his may no be a good approximaion For hese reasons in his secion I ake a more direc approach o he calibraion of he maching elasiciy parameer and perform he analysis wihou imposing ha he model is always a is seady sae This allows me o evaluae o wha exen his affecs he resuls Observe from equaion 16 ha M U 40) ln = ln A + ln V ( ( ) V ( ) ) 161

16 figure 27 Effecs on nonparicipaion (3 saes seady sae variable ransiion raes) M/V figure 28 Maching funcion Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey U / V Noe: M/V is oal maches per vacancy; U/V is he unemploymen vacancy raio Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey In wha follows I idenify M wih he oal number of workers ha ransiion from unemploymen o employmen beween monhs and + 1 as repored by he CPS Figure 28 plos ln M V ( ) agains ln U ( V ) for he whole sample period We see a srong linear relaion suggesing ha equaion 40 provides a good descripion of he daa wih a relaively consan A Fiing equaion 40 using OLS (ordinary leas squares) over he period 2001:1 2007:12 gives an esimae of = 069 Given his esimaed value of he pah for he maching efficiency parameer A implied by equaion 40 is repored in figure 29 We see ha his pah is compleely differen from ha in figure 22 The maching produciviy is much less variable and conrary o figure 22 displays a large drop afer he sar of he las recession reaching by he end of he sample period a value 12 percen lower han in 2007:12 There is no doub ha measuring A direcly from he maching funcion in equaion 16 gives a very differen picure from measuring i from he seady saes of he model economy Figure 30 repors he value of a job J obained from equaion 27 using he maching efficiencies A obained from equaion 40 and repored in figure 29 The figure is very similar o figure 23 again indicaing ha he pah for he value of a job is robus o he differen ways of measuring i I now urn o evaluaing he relaive conribuions of he value of filled jobs J he maching efficiency parameer A and he ransiion raes EU EN λ λ λ NU λ and λ NE o unemploymen dynamics since he beginning of he recession For his purpose I proceed * * * as before and find a sequence E U N and V * ha saisfies equaions and 21 under he assumpion ha A EU EU = A 2007:12 λ = λ : λ = λ : EN EN λ = λ λ NE λ NE : = and λ NU λ NU : = : for every monh Tha is I le he value of a job J evolve as in figure 30 bu fix he maching produciviy and all ransiion raes o he values ha hey had in 2007:12 (ha is a he beginning of he recession) * * * * Similarly as before E U N and V describe he employmen unemploymen nonparicipaion and vacancies levels ha would have obained if he value of a job had been he only variable changing over ime ** ** ** ** Also I compue he E U N and V ha saisfy equaions and 21 under he assumpion ha A ** ** = A 2007:12 for every monh Tha is E U ** ** N and V describe he employmen unemploymen nonparicipaion and vacancies levels ha would have been obained if he maching produciviy parameer had remained consan a is December 2007 level while all oher variables (ha is J and all he λ values) had changed he way hey did Figure 31 repors he pahs for U / ( E + U ) ( consan A consan λ ) U / ( E + U ) ( consan A variable λ ) and U / ( E + U ) ( variable A variable λ ) From he U / ( E + U ) pah we see 162 4Q/2011 Economic Perspecives

17 figure 29 Maching efficiency (3 saes ransiionary dynamics) figure 30 Value of a job (3 saes ransiionary dynamics) Noe: The log of A is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Noe: The log of J is normalized o zero a he sar of he pas recession Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey ha changes in he value of a job J played a very minor role in unemploymen dynamics: The red line is roughly fla From comparing he pah for U / ( E + U ) wih he pah for U / ( E + U ) I conclude ha changes in he ransiion raes λ played a crucial role in unemploymen dynamics: The gray line is widely differen from he red line In fac we see ha changes in he ransiion raes λ accouned for mos of he unemploymen dynamics observed since he recession: The black line is very close o he gray line indicaing ha he maching produciviy played a minor role in he observed unemploymen rae dynamics In urn figure 32 repors he pah for N * ( consan A consan λ ) N ** ( consan A variable λ ) and N ( variable A variable λ ) From he N * pah we see ha far from accouning for he observed increase in nonparicipaion changes in he value of a job J would have accouned for a decrease in nonparicipaion The bulk of he increase in nonparicipaion is accouned for by changes in ransiion raes since changes in he maching produciviy played a relaively minor role: The gray line is very close o he black line) Finally figure 33 shows ha none of he changes in he maching efficiency parameer A or in he ransiion probabiliies were imporan deerminans of vacancies dynamics: The pah for vacancies was mainly deermined by J Nonparicipans compee for vacancies This secion describes and uses he mos saisfacory specificaion of he model Thus i provides he main resuls of he paper Observe ha he model used in he previous secion had hree labor marke saes bu only unemployed workers were inpus o he maching funcion: Nonparicipans made ransiions o employmen bu wihou going hrough he maching funcion I view his feaure as a weakness of he previous specificaion of he model The workers ransiioning from nonparicipaion o employmen mus be compeing for he same vacancies as he workers ransiioning from unemploymen o employmen and should herefore ener he maching funcion in a similar way This secion addresses his issue by modifying he maching funcion of he previous secion accordingly Inroducing a more saisfacory specificaion for he maching funcion allows me o obain beer measuremens of he maching efficiency The maching funcion is now described as follows: 1 41) M = A ( U + ψ N ) V where M is he oal number of maches U is unemploymen N is nonparicipaion V is vacancies A is he maching efficiency 0 ψ 1 and 0 < < 1 Observe ha ψ can be inerpreed as he fracion of he oal number of workers who repor hey are nonparicipans bu search for jobs anyway Alernaively 163

18 figure 31 Effecs on unemploymen (3 saes ransiionary dynamics) figure 32 Effecs on nonparicipaion (3 saes ransiionary dynamics) Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey ψ can be inerpreed as he search inensiy of nonparicipan workers The ransiion rae from unemploymen ino employmen λ UE is given by: 42) λ UE = M U ( U ) ( U + ψ N ) U ( ) 1 ( ) A U + ψ N V = U + ψ N since a fracion U + ψ N of he oal maches M is formed wih unemployed workers Similarly he ransiion rae from nonparicipaion ino employmen λ NE is given by: 43) λ NE = M ψ N ( N )( U + ψ N ) = ψ A ( U + ψ N ) V U + ψ N 1 ( ) of he oal maches M is since a fracion ψ N U + ψ N formed wih nonparicipan workers The ransiion rae from employmen o unemploymen λ EU he ransiion rae from employmen o nonparicipaion λ EN he ransiion rae from unemploymen o nonparicipaion λ and he ransiion rae from nonparicipaion o unemploymen λ NU are assumed o be exogenous o he model The evoluion of workers across labor marke saes is hen given by he following equaions: 44) E = E + M EU EN ( + + E 1 λ λ ) 45) U = U + EU NU E + UE N + + U 1 λ λ ( λ λ ) 46) N = N + EN E + NE U + NU + N 1 λ λ ( λ λ ) Equaion 44 saes ha nex-period employmen is equal o curren employmen plus all new maches minus oal separaions (eiher o unemploymen or nonparicipaion) Equaion 45 saes ha nex-period unemploymen is equal o curren unemploymen plus all ransiions ino unemploymen (eiher from employmen or nonparicipaion) minus all ransiions ou of unemploymen (eiher o employmen or nonparicipaion) Equaion 46 saes ha nex-period nonparicipaion is equal o curren nonparicipaion plus all ransiions ino nonparicipaion (eiher from employmen or unemploymen) minus all ransiions ou of nonparicipaion (eiher o employmen or unemploymen) 164 4Q/2011 Economic Perspecives

19 figure 33 Effecs on vacancies (3 saes ransiionary dynamics) figure 34 Search inensiy of nonparicipans Variable A variable λs Consan A consan λs Consan A variable λs Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey Sources: Auhor s calculaions based on daa from he Bureau of Labor Saisics Curren Populaion Survey 51) V J k A U N V 1 = ( + ψ ) The free-enry condiion is given by ( ) M 47) k = J V since from he poin of view of a firm he probabiliy of filling a vacancy is now equal o M / V Observe ha using equaions and 43 we can rewrie equaions as follows: Given he oal number of workers unemployed a dae zero U 0 and he oal number of workers ha are nonparicipans a dae zero N 0 he model generaes an endogenous pah for { M V U 1 N 1} + + = 0 Resuls From equaions 42 and 43 we have ha he search inensiy of nonparicipans can be measured as + 1 ( ) ( ) 1 EU EN 48) E = E + A U + ψ N V λ + λ E 52) ψ NE λ = UE λ EU NU 49) U + 1 = U + λ E + λ N 1 A ( U + ψ N ) V ( + λ U + ψ N ) U EN 50) N + 1 = N + λ E + λ U 1 A ( U + ψ N ) V NU ψ + λ N ( U + ψ N ) Figure 34 shows ha he fracion of nonparicipans ha search has increased quie subsanially since he sar of he laes recession From equaion 41 we have ha M U + ψ N ln = ln + ln V V 53) ( A ) In wha follows I idenify M wih he oal number of workers ha ransiion from unemploymen ino employmen beween monhs and + 1 plus he oal number of workers ha ransiion from nonparicipaion ino employmen beween hose same monhs 165