What drives movements in the unemployment rate?

Transcription

1 Wha drives movemens in he unemploymen rae? Regis Barnichon Federal Reserve Board Andrew Figura Federal Reserve Board 06 April 2010 Absrac We use a Beveridge curve framework and micro daa o decompose unemploymen rae movemens ino: (1) a componen driven by changes in labor demand (2) a componen driven by changes in labor supply and (3) a componen driven by changes in he e ciency of maching unemployed workers o jobs. We nd ha, hisorically, cyclical movemens in unemploymen are dominaed by changes in labor demand, alhough changes in he e - ciency of maching can also plays a role. Secular changes in unemploymen are dominaed by changes in labor supply. The mos recen labor marke downurn appears o be adhering o he hisorical paern: Changes in labor demand appear o explain he large majoriy of he increase in unemploymen since 2007, hough decreases in maching e ciency have been paricularly imporan. JEL classi caions: J6, E24, E32 Keywords: Gross Worker Flows, Job Finding Rae, Employmen Exi Rae, Maching Funcion. Preliminary. Commens welcome. The views expressed here do no necessarily re ec hose of he Federal Reserve Board or of he Federal Reserve Sysem. Any errors are our own. 1

2 1 Inroducion The unemploymen rae is an imporan indicaor of economic aciviy. Undersanding is movemens is useful in assessing he causes of economic ucuaions and heir impac on welfare, as well as assessing in aionary pressures in he economy. To help undersand he forces driving ucuaions in he unemploymen rae, we use a Beveridge curve framework and micro daa o decompose unemploymen rae movemens ino: (1) a componen driven by changes in labor demand (2) a componen driven by changes in labor supply and (3) a componen driven by changes in he e ciency of maching unemployed workers o jobs. We nd ha, hisorically, cyclical movemens in unemploymen are dominaed by changes in labor demand, alhough changes in he e ciency of maching also play a role. Secular changes in unemploymen are dominaed by changes in labor supply. The mos recen labor marke downurn appears o be adhering o he hisorical paern: Changes in labor demand appear o explain he large majoriy of he increase in unemploymen since 2007, hough decreases in maching e ciency have been paricularly imporan. We accomplish our decomposiion by rs decomposing unemploymen rae movemens ino a componen responding o changes in unemploymen in ows and a componen responding o changes in unemploymen ou ows, as in Fujia and Ramey (2009) and Elsby, Michaels and Solon (2009). Then we decompose he ou ow componen ino a componen driven by changes in labor demand and a componen driven by changes in he e ciency of maching workers o jobs. To do his, we esimae an aggregae maching funcion ying levels of vacancies and unemploymen o ransiions from unemploymen ino employmen. The demand driven componen can be represened as movemens along a sable Beveridge curve, while he mach e ciency componen can be represened as a shif in he Beveridge curve. We inroduce our approach wih a simple framework ha sideseps workers heerogeneiy and movemens in and ou of he labor force, bu we successively relax hese wo assumpions. Firs, because changes in he composiion of he unemploymen pool could a ec our maching funcion esimaes, we use micro daa o conrol for individual characerisics and beer 2

3 undersand he naure of he changes in maching e ciency. Using average ransiion raes could hide some shifs in he underlying characerisics of he unemployed ha may lead o changes in maching e ciency. We nd ha shifs in he composiion of he unemploymen pool are indeed imporan, accouning for mos of he shifs in he maching funcion unil 2006 and half of he apparen decline in maching e ciency in he recession. This composiion e ec is mosly due o wo facors: (i) a higher concenraion of unemployed workers in saes wih disressed labor markes and lower han average job nding rae, and (ii) a larger fracion of unemployed workers on permanen layo s. Second, because changes in unemploymen in ows (and shifs in he Beveridge curve) could be caused by changes in labor demand as well as changes in demographics or labor supply, we generalize our decomposiion by disinguishing layo s from quis and by allowing for movemens in and ou of he labor force. Tha way, we can decompose unemploymen ucuaions ino a labor demand componen and a labor supply componen. We idenify he labor demand componen from movemens along he Beveridge curve and from shifs in he Beveridge curve due o layo s. We idenify he labor supply componen from quis and movemens in and ou of he labor force. We nd ha labor demand and labor supply conribue approximaely equally o unemploymen s variance. However, hese wo forces play very di eren roles a di eren frequencies. A business cycle frequencies, labor demand accouns for wo hirds of unemploymen s variance. In conras, a low frequencies, mos of unemploymen movemens are caused by changes in labor supply, in paricular he aging of he baby boom, he increase in women s labor force paricipaion and he increasing aachmen of women o he labor force. Our paper is relaed o wo srands in he lieraure. The rs srand invesigaes he relaive responsibiliy of unemploymen in ows and ou ows in accouning for changes in unemploymen. We ake his lieraure one sep furher by decomposing in ows and ou ows ino economically meaningful componens ha allow us o say somehing abou he economic forces driving movemens in unemploymen. Our use of an aggregae maching funcion and he Beveridge curve o accomplish his decomposiion harks back o an earlier srand in he 3

4 lieraure (e.g. Lipsey, 1965, Abraham, 1987, Blanchard and Diamond, 1989) ha relied on he Beveridge curve o disinguish beween changes in labor demand (movemens along he Beveridge curve) and shifs in secoral reallocaion (shifs in he Beveridge curve). We build on his lieraure by using unemploymen in ows and ou ows and an aggregae maching funcion o beer idenify causes of Beveridge curve shifs. Furher, we use micro daa o beer disinguish beween movemens along he Beveridge curve and shifs in he Beveridge curve due o a changing composiion of unemploymen, as well as o separae Beveridge curve shifs due o changing in ows ino a componen likely driven by labor demand and a componen driven by long-erm demographic and behavioral changes. The nex secion lays he heoreical groundwork for our decomposiion. Secion 3 esimaes an aggregae maching funcion, which we use o decompose unemploymen ou ows ino movemens along he Beveridge curve due o changes in labor demand, shifs in he Beveridge curve, and changes in he maching funcion. Secion 4 uses micro daa o provide a more precise disincion beween shifs in and movemens along he Beveridge curve, as well as o race some of he shifs in he Beveridge curve o changes in he composiion of he labor force. Secion 5 exends he Beveridge curve framework o include ows o and from ou of he labor force, which is paricularly imporan in explaining long-erm changes in he unemploymen rae. Secion 6 concludes. 2 A basic Beveridge curve decomposiion In his secion, we presen a mehod o sudy quaniaively movemens in he Beveridge curve. We decompose unemploymen ucuaions ino hree caegories; movemens along he Beveridge curve due o changes in labor demand, shifs in he Beveridge curve due o unemploymen in ows, and srucural shifs due o shocks o maching e ciency. 4

5 2.1 Seady-sae unemploymen Denoe u and e he number of unemployed and employed individuals as a share of he labor force a insan 2 R +. Assume ha all unemployed workers nd a job according o a Poisson process wih arrival rae UE and ha all employed workers lose heir job according o a Poisson process wih arrival rae EU. There are no movemens in and ou of he labor force. In his conex, he unemploymen rae sais es _u = UE e EU u (1) As rs argued by Shimer (2007), he magniudes of he wo hazard raes is such ha he half-life of a deviaion of unemploymen from is seady sae value is abou a monh. As a resul, a a quarerly frequency, he unemploymen rae is very well approximaed by is seady-sae value u ss so ha u ' EU EU + UE u ss (2) 2.2 Modeling UE wih a maching funcion The job nding rae is de ned as he raio of new hires o he sock of unemployed, so ha he job nding rae can be wrien as UE = m u wih m he number of new maches a insan : By modeling m wih a consan reurns o scale Cobb-Douglas maching funcion, a speci caion widely used in he search and maching lieraure (see e.g. Pissarides, 2001), we can express m as m = m 0 u v 1 wih m 0 a posiive consan, v he number of job openings and u he number of unemployed. In his conex, we can model he job nding rae UE as ln UE = (1 ) ln v u + m 0 + : (3) 5

6 2.3 Decomposing movemens in he Beveridge curve Wriing he seady-sae approximaion for unemploymen (2) and modeling he job nding rae wih a maching funcion, we can wrie u ss EU EU + UE ' EU EU + m 0 v u ss 1 (4) Expression (4) is he heoreical underpinning of he Beveridge curve, he downward sloping relaion beween unemploymen and vacancy posing. Seady-sae unemploymen moves along he Beveridge curve as rms adjus vacancies. In conras, he Beveridge curve shifs when he unemploymen in ow rae EU moves. However, while he maching funcion (3) is remarkably successful a modeling he job nding rae, he relaion is no exac, and he labor marke may emporarily deviae from is average maching e ciency. To separae movemens along he Beveridge curve from shocks o he maching funcion, we de ne u ss;bc, he seady-sae unemploymen rae implied by a sable Beveridge curve, i.e. by a sable maching funcion. Formally, u ss;bc u ss;bc = EU EU + m 0 v u ss;bc is de ned by 1 : (5) Denoing ^ UE = m0 he job nding rae prediced by a sable maching funcion, we can rewrie (2) as v u ss;bc 1 u ss = EU EU + ^ UE e " (6) where " = ln UE UE ln ^ capures deviaions of he job nding rae from he value implied by a sable Beveridge curve, i.e. a sable relaionship beween unemploymen and vacancies. 6

7 Log-linearizing (6) around he mean of EU UE, ^ h d ln u ss = (1 u ss ) d ln EU = d ln u bc + d ln u shifs and ", we ge i UE d ln ^ d" + (7) + d ln u eff + where d ln u bc (1 u ss UE )d ln ^ represens movemens along he Beveridge curve, d ln u shifs (1 u ss )d ln EU represens shifs in he Beveridge curve due o changes in unemploymen in- ows, and d ln u eff (1 u ss )d" capures he shifs in he Beveridge curve caused by changes in maching e ciency. The residual erm corresponds o he rs-order approximaion error. We can hen assess he separae conribuions of he di eren movemens of he Beveridge curve by noing as Fujia and Ramey (2009) ha V ar (d ln u ss ) = Cov(d ln u ss so ha, for example, ; d ln u cyc Cov(d ln ubc ;d ln uss ) var(d ln u ss o movemens along he Beveridge curve: )+Cov(d ln u ss ; d ln u bc )+Cov(d ln u ss ; d ln u eff )+Cov(d ln u ss ; ): ) measures he fracion of unemploymen s variance due While a rs-order approximaion is very good on average, becomes non-negligible wih he high level of unemploymen in he early 80s and in he recession. Moreover, i will be ineresing o decompose unemploymen ucuaions relaive o an arbirary base year for which he rs-order approximaion can be more problemaic. Insead, we will use (8) a second-order approximaion of seady-sae unemploymen. Forunaely, he expression remains simple because in pracice all cross-order erms are negligible compared o d 2 ln EU and 7

8 d 2 ln UE : As a resul, an excellen working approximaion is given by he simple expression d ln u ss = (1 u ss )d ln EU = d ln u bc 1 2 (1 uss2 )d 2 ln EU (9) (1 u ss UE )d ln ^ (1 uss ) 2 d 2 ln (1 u ss )d" d ln u shif EU UE ^ UE EU + UE 2 d"2 + ~ + d ln u eff + ~ : An imporan advanage of being able o log-linearize around he mean or around an arbirary dae is ha we do no need o derend he daa. Tha way, we will be able o sudy he high-frequency as well as he low-frequency movemens in unemploymen. 3 Some rs resuls 3.1 Measuring individuals ransiion raes To idenify he individuals ransiion raes, we consider a general mehod valid for any number of labor marke saes belonging o he se S. A worker can be in di eren saes, for example employed and unemployed. To idenify he ransiion raes, we use CPS gross ows measuring he number of workers moving from sae A 2 S o sae B 2 S each monh. To accoun for ime aggregaion bias, we consider a coninuous environmen in which daa are available a discree daes and proceed as in Shimer (2007). Denoe N AB () he number of workers who were in sae A a 2 N and are in sae B a + wih 2 [0; 1] and de ne n AB () = N AB he share of workers who were in sae A a. P () N AX () X2S Assuming ha AB, he hazard rae ha moves a worker from sae A a o sae B a + 1, is consan from o + 1, n AB () sais es he di erenial equaion _n AB () = X C6=B n AC () CB n AB () X BC, 8 A 6= B: (10) C6=B 8

9 We hen solve his sysem of di erenial equaions numerically o obain he ransiion raes. In he simpler case of only wo labor force saes E and U, he sysem of six equaions simpli es o a sysem of wo equaions in _n UE and _n EU ha we solve for EU and UE. We use daa from he CPS covering 1967M6 2009m12 and calculae he quarerly series for he ransiion raes over 1967Q2-2009Q4 by averaging he monhly series Esimaing a maching funcion We esimae a maching funcion over by regressing ln UE = (1 ) ln v u + c + (11) using our measure of he job nding rae UE as he dependen variable. We esimae (11) wih monhly daa using he composie help-waned index presened in Barnichon (2010) as a measure of vacancy posing. We use non-derended daa over 1967:Q1-2009:Q4 and allow for rs-order serial correlaion in he residual. To ake ino accoun movemens in he size of he labor force, we rescale he composie help-waned index by he size of he labor force. Table 1 presens he resul. Firs, we disregard he behavior of he labor marke in he curren recession and use daa from 1967 unil 2006 only. The elasiciy is precisely esimaed a 0:64, a value inside he plausible range 2 [0:5; 0:7] ideni ed by Perongolo and Pissarides (2001). A legiimae concern wih his regression is ha equaion (3) may be subjec o an endogeneiy bias. We hen esimae (3) using lagged values of v and u as insrumens. As column (2) shows, he endogeneiy bias appears o be small as he elasiciy is lile changed a 0:62. We hen urn o he behavior of he labor marke in he recession. In column (3), we use he whole sample While he OLS poin esimae declines only slighly a 0:62, he maching funcion canno explain he magniude of he drop in he job nding 1 Before 1976, he microdaa are no publicly available so we use he ransiion raes calculaed by Shimer(2007) using Joe Rier s abulaion of he gross ows from June 1967 o December The daa are available a hp://sies.google.com/sie/robershimer/research/ ows. 9

10 rae in 2008 and Figure 1 plos he residual of equaion (3) esimaed over While he maching funcion appears relaively sable over ime, a esimony of he success of he maching funcion, he residual urns negaive in 2008 and remains below zero unil he end of he period. In he hird quarer of 2009, he residual reached an all ime low of hree sandard-deviaions. While he maching funcion previously reached large negaive values in 1979 or in he mid-80s, he residual averaged wo sandard-deviaion below zero hroughou In column (4), we esimae a maching funcion over only and nd ha he elasiciy wih respec o unemploymen is signi canly lower a 0:49: These resuls poin owards a change in maching e ciency, and in he res of his secion, we will explore he quaniaive implicaions of his change for equilibrium unemploymen. 3.3 Decomposing movemens in he Beveridge curve In his secion, we decompose unemploymen ucuaions in he Beveridge curve space. Using he Taylor expansion (9), we decompose unemploymen ucuaions ino: (i) movemens along he Beveridge curve, (ii) shifs in he Beveridge curve, and (iii) shocks o he maching funcion. Imporanly, in all exercises, none of he daa are derended. To beer visualize he conribuion of each caegory in hisory, we log-linearize unemploymen around he base year Tha base year is aracive because i corresponds o he highes reading for vacancy posing per capia as well as he lowes value for ln u shif. 2 Figure 2 plos (log) unemploymen and is componens relaive o heir 1969 values. We rs consider he impac of maching funcion shocks on he Beveridge curve. The shocks generally have a small impac on he equilibrium unemploymen rae, a corollary of he success of he maching funcion in modeling he job nding rae. However, Figure 2 shows some marked decrease in maching e ciencies in he afermah of he 74 and 82 peaks in unemploymen. Wihou any loss in maching e ciency, he unemploymen would have 2 Thus, 1969 corresponds o he year wih he mos lefward Beveridge curve also corresponds o a poin where he maching funcion shock is very close o zero. In all, he base year 1969 is aracive because i can be used as a benchmark from which we can quickly visualize he rise and fall in rend unemploymen as well as he cyclical ucuaions over he las 40 years. 10

11 been more han 50 basis poins lower over and 25 basis poins lower over The recession is unique in he conribuion of shocks o he maching funcion. The large decrease in maching e ciency previously documened is responsible for abou 25 percen of he increase in unemploymen since 2006Q4. This is more han wice as much as wha happened during he early o mid 80s episode of double-digi unemploymen. Had he maching funcion remained sable, he unemploymen rae would have been 150 basis poins lower in 2009, he larges shock o maching e ciency since Comparing movemens along he Beveridge curve and shifs in he Beveridge curve, Figure 2 suggess ha boh conribue roughly equally o unemploymen s ucuaions. A variance decomposiion exercise following (8) con rms his resul. As shown in Table 2, movemens along he Beveridge curve and shifs in he Beveridge curve accoun for respecively 48 and 42 percen of unemploymen s variance. However, his resul lumps ogeher cyclical and secular movemens. Figure 2 suggess ha shifs in he Beveridge curve play a more imporan role a low frequencies. To separae rend and cyclical unemploymen, we furher decompose changes in unemploymen ino a rend componen (from an HP- ler, = 10 5 ) and a cyclical componen. Table 2 presens a variance decomposiion exercise for each componen. Shifs in he Beveridge curve accoun for more han 60 percen of unemploymen s secular rend, bu he siuaion is reversed a business cycle frequencies. 4 Conrolling for individuals characerisics The previous secion suggess ha a leas 50 percen of cyclical unemploymen ucuaions are due o movemens along he Beveridge curve, i.e. o changes in labor demand. However, our framework is silen abou he sources of Beveridge curve shifs, which play a non-rivial role a business cycle frequencies. In paricular, some of he Beveridge curve shifs are caused by changes in labor demand as rms can shed workers during recessions, while ohers are caused by changes in quis, i.e. movemens in labor supply. Moreover, our framework is silen abou he sources of changes in maching e ciency. For 11

12 example, changes in he composiion of he pool of unemployed could be responsible for some of he movemens in maching e ciency. If a given caegory of he populaion wih a lower han average job nding rae becomes overrepresened in he unemploymen pool, he average job nding rae will decline because of a composiion e ec. Thus, i is imporan o conrol for worker heerogeneiy when esimaing a maching funcion. To address hese issues, his secion exends our analysis by conrolling for workers heerogeneiy in wo ways. Firs, we proceed as in Secion 3 bu disaggregae he labor marke ows by demographic groups and reason for unemploymen (layo or qui). Second, we use micro daa on ransiions across labor force saes o esimae he probabiliy of exiing or enering unemploymen. This second approach allows us o conrol for a larger range of individuals characerisics han is possible wih macro daa. 4.1 Disaggregaing worker ows In his secion, we generalize our approach from Secion 3 o di eren caegories of workers ordered by sex, age and reason for unemploymen Demographics To allow for changes in he demographic composiion of he labor force, we use CPS daa o spli workers ino N = 8 caegories; male vs. female in he hree age caegories 25-35, 35-45, 45-55, and male and female ogeher for ages and over 55. Since he di erenial equaions (10) governing labor marke ows hold independenly for each age-sex caegory i 2 [1; N], we can esimae he hazard raes AB ;i hazard raes used in Secion 3 can hen be decomposed as using he mehod described in Secion 3. The aggregae 8 >< >: UE = EU = U i U UE i ' E i E EU i ' u i i u ss UE i 1 u i i 1 u ss EU i (12) 12

13 where! i = LF i LF is he share of group i in he labor force and u i he unemploymen rae of group i. The seady-sae unemploymen rae for caegory i sais es u ss i = di erenial equaion (1) holds independenly for each demographic group. Log-linearizing (12), we ge EU i EU i + UE i since he 8 >< >: d ln UE = d ln EU = u i UE i u ss i UE 1 u i EU i 1 u ss i EU d ln UE i u + d ln i i u ss = d ln ~ UE i + d ln UE;demog d ln EU 1 u i + d ln i i 1 u ss = d ln ~ EU i + d ln EU;demog (13) The rs erm in boh equaions corresponds o movemens in ~ UE = 1 u i i 1 u EU ss i second erm, d ln UE;demog u i i u UE ss i or ~ EU =, he hazard rae ha holds he share of each demographic group consan. The u i UE i u ss i u d ln UE i i u ss or d ln EU;demog 1 u i EU i 1 u ss i EU d ln! i 1 corresponds o he composiion e ec, due o movemens in he relaive size of he labor force in each group! i, as well as changes in he share of each group in he unemploymen pool ( uss i u ) ss or in he employmen pool ( 1 uss i 1 u ). To illusrae he imporance of conrolling for changes in ss demographics, Figure 3 compares EU rend in EU and ~ EU, and shows ha a signi can fracion of he can be accouned for by demographics. Since young individuals have a higher urnover rae han older workers, he aging of he baby boom generaion (which led o a decline in he share of young individuals in he labor force) explains some of he secular decline in he job separaion rae. u ss i 1 u ss, Separaing quis, emporary layo s and permanen layo s Layo s and quis are di eren labor marke evens ha lead o shifs in he Beveridge curve. To separae hese wo conceps, we use he CPS micro daa and classify jobless workers according o he even ha led o heir unemploymen saus: a permanen layo p, a emporary layo, or a qui q. 13

14 There are hree unemploymen raes by reason: u p ; u and u q and hree ses of hazard raes f pe ; Ep ; qe ; E ; E ; Eq g as a job leaver may no have he same unemploymen exi rae as a job loser. Afer obaining he mached gross ows fn pe ; N Ep ; N qe ; N E ; N E ; N Eq g from CPS daa, we correc for ime aggregaion bias using a version of (3) as in Secion 3 o obain he six ransiion raes. Figure 4 plos he resul and shows ha he hazard raes by reason for unemploymen display a lo of heerogeneiy. Job separaion due o permanen or ransiory layo s do no display any evidence of a rend while job separaion due o quis appear o follow a downward rend since he early 90s. Transiory layo s seem o play a diminishing role in oal separaion and he recession is sriking in his respec. While Ep rapidly o a record level, E increased remained 20 percen below is early 80s level. No surprisingly, quis and especially emporary layo s have a higher unemploymen exi rae han permanen layo s. As in Secion 3, in seady-sae, he aggregae unemploymen u = X (2) wih he average ransiion raes given by j2fp;;qg u j rae sais es and where n and u ss;j u ss;j o n seady-sae, j2fp;;qg UE = X j2fp;;qg EU = X j2fp;;qg u ss;j u ss je (14) Ej : is he seady-sae unemploymen rae for reason j. To solve for uss X u j ), 8 j 2 fp; ; qg so ha in, noe ha u j sais es _uj = UE (1 u ss;j j2fp;;qg Ej u j oj2fp;;qg is he soluion of he sysem given by n _u j = 0 oj2fp;;qg.3 Expression (14) highlighs he imporance of he composiion e ec on movemens in he average job nding rae. The average job nding rae depends on each group s job nding rae X Y 3 Formally, a lile bi of algebra gives us u ss = 14 X j2fp;;qg j2fp;;qg Ej Y j6=i Ej j6=i je + je Y j2fp;;qg je and u ss;j =

15 bu also on he composiion of he unemploymen pool. If he share of permanen job losers (he ones wih he lowes unemploymen exi rae) increases more han usual in a recession (as i appears o be he case in he curren recession), he average job nding rae will decline more han usual, and an approach ha does no conrol for composiion will inerpre his resul as lower maching e ciency. Log-linearizing (14), we ge d ln X j2fp;;qg u j;ss u ss je = X u j;ss u ss j2fp;;qg je d ln je UE + X j2fp;;qg u j;ss u ss je UE d ln uj;ss u ss (15) The rs erm is he job nding rae holding he share of each unemploymen rae consan, and he second erm is he composiion e ec. Afer a bi of algebra, we can rewrie he composiion e ec as d ln UE;reason = X j2fp;;qg u j;ss u ss je UE 1 d ln Ej + X X j2fp;;qg i6=j u j;ss u ss ie UE 1 d ln je The rs erm of (16) capures he e ec of movemens in he job separaion rae of a subgroup ha di ers from he average job nding rae by je UE UE (16). An increase in he job separaion rae of permanen job losers lowers he average job nding rae because his caegory of unemployed has a lower han average job nding rae je UE < 0. The second erm capures he impac of a change in he job nding rae. If he job nding rae of a job leavers increases, his will lower he fracion of unemploymen due o quis and may lower he job nding rae as he share of oher caegories (wih a lower han average job nding rae) increases. UE u ss To illusrae he imporance of conrolling for composiion changes, Figure 5 compares and ~ UE, he job nding rae holding he share of each unemploymen rae (by reason) X Ej j2fp;;qg Y j6=i Ej je Y j6=i : je 15

16 consan. We can see ha a sizeable fracion of he dramaic decline in UE in he recession is due o he composiion e ec. Unlike in he early-80s recession, he conribuion of emporary layo s o oal job separaion in is a lo smaller. In conras, he fracion of permanen layo s is a is highes level since Since workers from he laer group have a much lower job nding rae, heir "overrepresenaion" in he unemploymen pool is parly responsible for he lower han usual average job nding rae. The 2001 recession also saw a relaively high conribuion of permanen layo s so ha a sizeable fracion of he decline he average job nding rae is due o a composiion e ec. Since composiion accouns for a non-rivial fracion of movemens in he job nding rae and can exaggerae he e ec of movemens in labor marke ighness on UE, we reesimae a maching funcion on ~ UE. Table 1 shows he resuls of he regression d ln ~ UE = (1 )d ln v u + ". We can see ha he esimaed elasiciy is higher, indicaing ha he characerisics of he unemployed worsen during recessions. Moreover, he composiion e ec appears o explain a sizeable fracion of he decrease in maching e ciency since Figure 5 plos he ed value m 0 v u 1 alongside ~ UE wih he behavior of ~ UE in he job nding rae since and UE. This ime he maching funcion is broadly consisen in he recession and explains a larger fracion of he decline Combining demographics and reason for unemploymen Since each demographic group evolves independenly of he oher, i is relaively sraighforward o simulaneously disaggregae by demographics and reason for unemploymen. The disaggregaion by reason presened above is valid for each group i, so we can wrie 8 >< >: d ln UE i = d ln X j2fp;;qg d ln EU i = d ln X j2fp;;qg u j;ss i u ss je i i Ej i 8 i 2 [1; N] 16

17 Summing across demographic groups and combining (13) wih (15), we ge 8 >< >: and 8 >< >: d ln UE = d ln EU = X j2fp;;qg = d ln ~ UE X j2fp;;qg = d ln ~ EU! i u j;ss i u je i UE d ln je i + + d ln UE;reason 1 u i i Ej 1 u ss i d ln Ej EU i + d ln UE;demog + d ln UE;demog d ln UE;reason i + d ln EU;demog + d ln UE;demog (17) The rs erm in (17) corresponds o movemens in ~ UE = X j2fp;;qg u! j;ss i i u je ss i he job nding rae ha holds he unemploymen share of each demographic group consan as well as he share of each unemploymen rae (by reason) consan. Similarly, ~ EU X 1 u = i i 1 u Ej ss i is j2fp;;qg he job separaion rae ha holds he share of each demographic group consan. 4.2 Using micro daa o esimae labor force ransiions The preceding secion highlighed he imporance of accouning for individual characerisics in order o beer undersand changes in maching e ciency and shifs in he Beveridge curve. While conrolling for demographics and reason for unemploymen helped o explain some of he apparen decline in maching e ciency in he recession, Figure 5 shows ha he maching funcion sill overpredics he job nding rae since To conrol for a larger range of individuals characerisics, we urn o micro daa and explore wheher individuals heerogeneiy can accoun for some of he shifs in he maching funcion as well as some of he movemens along he Beveridge curve. We use micro daa on ransiions across labor force saes from he CPS o esimae which characerisics make exi from unemploymen less likely, and which characerisics make employmen separaion (layo or qui) more likely. Then we esimae wheher he observable characerisics of he unemployed have changed in a way ha could explain he decline in maching e ciency since 17

18 UE Transiion raes We use mached CPS daa o esimae individual s i ransiion probabiliy from unemploymen o employmen UE i. The following explanaory variables appear o be robusly associaed wih an individual s probabiliy of escaping unemploymen: reason for becoming unemployed, unemploymen in he individual s sae of residence, job openings in he indusry in which he individual was previously employed, age, sex, and he curren duraion of unemploymen. The duraion of unemploymen could represen rue duraion dependence due, perhaps, o scarring e ecs; more likely, i represens unobserved heerogeneiy in hazard raes, as individuals wih low unobserved hazard raes become over ime disproporionaely represened in he group of unemployed workers wih relaively long duraions. When esimaing he e ec of duraion on UE ransiion raes, i is imporan o conrol for aggregae labor marke condiions. The abiliy of duraion o proxy for scarring or worker heerogeneiy may be weaker in recessions, when duraions for all workers ends o increase, han in expansions. Thus, in our speci caion we inerac he duraion of unemploymen wih average duraion. We also include a se of monhly dummies o conrol for seasonaliy in exi hazards and a measure of labor marke ighness. We choose he parameerizaion of he laer variable and he funcional form of he esimaing equaion so ha esimaes are comparable wih he esimaes of aggregae maching funcion parameers from previous secions. Speci cally, we use a logi speci caion. The logi funcion has he propery ha he e ec of an explanaory variable on he odds raio is consan and equal o he exponeniaed esimaed parameer of ha variable. Speci cally, O i (X ) = p ex 1 p = 1+e X e 1 X 1+e X = e X 18

19 where O i (X i ; ) is he odds raio for individual i a ime, and X denoes individual i s characerisics. If we choose he measure of labor marke ighness o be he log of he odds raio for he aggregae maching funcion and consrain he logi parameer associaed wih i o equal 1, i.e. X 1; = ln m 0 v u 1 1 m 0 v u 1 wih 1 = 1 (18) we ge ha he change in he odds raio for an individual wih idenical characerisics across di eren labor marke saes is equal o he change in he odds raio as compued using he aggregae maching funcion. O i (X i ; ) O i 1 (X i ; 1) = m 0 v u 1 1 m 0 v u 1 m 0 v 1 u m 0 v 1 u 1 1 In oher words, wih he logi speci caion and he variable re ecing labor marke ighness equal o X 1; in (18), here is a congruence beween he e ec of labor marke ighness on he probabiliy of an individual exiing unemploymen as esimaed using aggregae daa and he same esimae using individual-level daa. To illusrae his poin, we aggregae he individual level unemploymen exis in each monh and esimae a maching funcion using aggregaed daa, weighing each monhly aggregaed observaion by he number of individual observaions underlying i. Then we compare he esimaed parameers from his aggregae regression o he same parameers esimaed using maximum likelihood on he individual level daa wih he labor marke ighness variable de ned as X 1 and is coe cien consrained o equal 1. As shown in Table 3, he esimaed maching funcion parameers are nearly idenical. 19

20 The imporance of conrolling for individual-level characerisics We now esimae he aggregae maching funcion parameers using he individual daa and conrolling for he individual-level characerisics described above. We perform his esimaion on hree ses of daa. The rs daa se uses JOLTS job openings o measure vacancies and, hus he ime period is limied o We exclude 2008 and 2009 o preven he aggregae maching funcion parameers from being biased by he apparen ouward shifs in he Beveridge curve over hese years due o changes in he maching funcion ha could be correlaed wih changes in aggregae labor marke ighness. One advanage of he JOLTS daa se is ha i allows us o measure vacancies a he indusry level and conrol for he e ec of he concenraion of unemploymen in sagnan indusries on aggregae maching e ciency. Our second daa se exends back o 1994, when a redesign of he CPS improved he qualiy of labor force ransiions. In his daa se, we use he composie HWI o measure vacancies. Our hird daa se exends back o 1976 and again uses he composie HWI o measure vacancies. Because of changes in he CPS daa due o he 1994 redesign, we esimae separae coe ciens on individual characerisics for observaions before and afer 1994, bu consrain he aggregae maching funcion parameers o be consan hroughou he sample period. Column 1 of Table 4 presens esimaes from he rs daa se. Firs, noe he change in he aggregae maching funcion parameers once we conrol for individual characerisics. The elasiciy of he probabiliy of exi wih respec o he vacancy-unemploymen raio, 1, falls by abou 1=3 relaive o elasiciies esimaed using aggregae daa or using individual daa bu no conrolling for individual characerisics. This resul con rms and exends Secion 4.1 s nding ha changes in he composiion of unemploymen pool can bias maching funcion esimaes. Esimaes of maching funcion parameers using aggregae daa implicily assume ha average characerisics of he unemployed are no correlaed wih he vacancy-unemploymen raio. The e ec of average individual characerisics on average exi probabiliies are subsumed in he error erm of he aggregae esimaing equaion. If hese characerisics change over ime and hese changes 20

21 are correlaed wih changes in he aggregae vacancy-unemploymen raio, hen esimaes of maching funcion parameers using aggregae daa will be biased. Conrolling for a wide range of individuals characerisics lowers 1 signi canly and indicaes ha esimaes of maching funcion parameers using aggregae daa are biased upward because characerisics of he unemployed worsen in recessions. Columns 2 and 3 of Table 4 perform he same esimaion wih he second and hird daases discussed above, respecively. The resuls are qualiaively similar: he maching funcion elasiciy is considerably reduced when esimaion is performed wih individual-level daa because he e ec of individual characerisics on exi hazards is procyclical. Conribuions of individual characerisics Nex, we examine which characerisics of he unemployed are mos responsible for causing composiion e ecs o be procyclical. The prediced average exi rae ^ UE is ^ UE = X i { i UE X i ; ; ^ (19) wih { i he share of unemployed wih characerisics X i and ^ he esimaed parameers. Taking a rs order approximaion of (19), one can decompose E p ino componens aribuable o changes in each of he observable characerisics. For example, if X i is a vecor of J observable characerisics indexed by j, hen he conribuion of characerisic j is ^ UE ' X i ' X j! i 2 4 X j ^ UE;j UE X i ; = ; j i Xi = X X j i X j i + ^ UE; i ^ UE; (20) 3 5 UE;j wih ^ = i ; =! ;^) j X j i i Xi = X i X j UE; i and ^ is he conribuion of he aggregae labor marke ighness. The rs order approximaion does a good job racking he change in he hazard due o unemploymen composiion, suggesing ha he decomposiion 21

22 (20) will be informaive. We use he JOLTS measure of vacancies and decompose he composiion e ec ino ve componens: reason for unemploymen (which capures he increasing share of permanen job losers), demographic e ecs (age and sex), unemploymen duraion, unemploymen in he individual s sae of residence, and concenraion of unemploymen in sagnan indusries (hose wih low raes of job openings). Since he conribuion of demographics is very small, Figure 6 plos he conribuion of he four oher characerisics along wih he oal composiion e ec. The unemploymen rae in he sae of residence is he mos imporan facor, accouning for more han 50 percen of he oal composiion e ec. This is paricularly rue in he recession. Unemployed workers are concenraed in saes wih higher han average unemploymen rae, i.e. in saes wih lower han average job nding probabiliies. These pockes of very high unemploymen rae drive down he average job nding rae. for unemploymen conribues o abou 25 percen of he oal composiion e ec. Reason As we saw in Secion 4:1, he fac ha permanen job losers have become a larger fracion of he unemployed has also lowered he average job nding rae. The higher share of long-erm unemployed also explain some of he composiion e ec. Finally, he increasing concenraion of he unemployed in sagnan indusries can also play a role, accouning for abou 10 percen of he oal composiion e ec in he recession. Can individual characerisics explain he shifs in he maching funcion? Nex, we ask wheher accouning for he characerisics of he unemployed can explain he shifs in he aggregae maching funcion esimaed in Secion 3. 4 Combining (7) wih (20), we can wrie an approximae decomposiion of he shifs in he maching funcion ino (1) a componen due o changes in he composiion of unemploymen (2) shifs no accouned for by composiion changes, and (3) an error erm capuring he di erence beween adjused ows daa (which we use for his decomposiion) and he unadjused daa, 4 Since he esimaion of maching shifs uses aggregaed (unadjused) micro daa bu some of he individual characerisic measures are based on published (adjused) BLS daa, we veri ed ha parameer esimaes were similar using he aggregaed individual level daa (unadjused daa) or he published daa on labor force ows. 22

23 which we use o measure composiion e ecs. Figure 7 plos he decomposiion using he HWI measure of vacancy and shows ha unil 2006, almos all of he cyclical shifs in he maching funcion are due o composiion changes. 5 Afer 2006, composiion explains abou half of he oal decline in maching e ciency EU Transiion raes Nex, we urn o esimaing ransiions from employmen o unemploymen. Because ransiions from employmen o unemploymen resuling from a qui and ransiions resuling from a layo are a eced di erenly by characerisics of workers and by he sae of he aggregae economy, we specify he ransiion as a mulinomial logi wih hree oucome: no ransiion, ransiion o unemploymen via layo and ransiion o unemploymen via qui. Age and sex likely in uence hese ransiion raes as does he level of aggregae labor demand, which we proxy for using he log of he aggregae vacancy rae. Davis, Faberman, and Haliwanger (2006) described a non-lineariy in rms layo funcions. If rms have posive ne employmen growh, layo s decrease slighly as ne employmen growh declines. If rms have negaive ne employmen growh, layo s increase srongly as ne employmen growh declines. To allow for a non-lineariy in layo behavior as a greaer proporion of rms become ne job desroyers, we also include a quadraic erm for he log vacancy rae. The JOLTS daa also enable us o include he deviaion and squared deviaion of he vacancy rae in he workers indusry from he aggregae vacancy rae. Finally, some indusries have persisenly higher urnover han ohers, leading o a persisenly higher level of layo s or quis. We use he average rae of job openings in an indusry o proxy for average urnover. Table 5 shows resuls from he esimaion of he mulinomial logi. Wih he excepion of he average vacancy rae, all variables are signi can a he 5 percen level in predicing a layo ransiion. In conras, only he age variables and he average vacancy rae variable are signi can in predicing quis. The coe cien on he aggregae vacancy raes indicaes ha 5 Resuls are very similar using JOLTS daa. 23

24 layo s are highly counercyclical; quis are mildly procyclical hough he coe cien on he aggregae vacancy rae is no saisically signi can. Conribuions of individual characerisics Nex, using a similar rs-order decomposiion of (19), we decompose movemens of EU ransiions raes ino conribuions from age, sex, indusry demand, and aggregae demand. Consisen wih he ndings from Secion 4:1, he gradual aging of he labor force has pushed he separaion rae lower of he he pas 15 years. Abou 2/3 of he aging e ec has occurred hrough reduced layo s and abou 1/3 hrough lower quis. Given ha quis are abou 1/5 of layo s on average, his implies a larger e ec of aging on quis han layo s. Changes in gender composiion have had very lile e ec on EU ransiions. By far he larges conribuor o changes in EU ransiions is changes in labor demand, as proxied by changes in aggregae and indusry vacancy raes. Resuls using JOLTS daa show ha mos of he demand e ec occurs hrough he aggregae vacancy rae. Alhough indusry-level demand is imporan in predicing individual-level layo s, i is no a signi can conribuor o cyclical increases in layo s. 5 Allowing for enry and exi from he labor force In order o inerpre shifs in he Beveridge curve, i is imporan o include movemens in and ou of he labor force as hose can be a non-negligible deerminan of unemploymen ucuaions, especially a low frequency (see e.g. Abraham and Shimer, 2001). In his secion, we generalize our approach from Secion 3 by allowing for movemens in and ou of he labor force. Firs, we presen a simple decomposiion using average hazard raes. Second, we conrol for worker heerogeneiy (demographics and reason for unemploymen) in a similar fashion o he wo labor marke saes decomposiion. 24

25 5.1 Using aggregae hazard raes We rs ignore worker heerogeneiy and proceed as in Secion 3. Denoe U ; E ; and I he number of unemployed, employed and inacive individuals a insan 2 R +. Denoing AB he hazard rae of ransiing from sae A 2 fe; U; Ig o sae B 2 fe; U; Ig, unemploymen, employmen and inaciviy will saisfy he sysem of di erenial equaions 8 >< >: _U = EU E + IU I ( UE _E = UE U + IE I ( EU I_ = EI E + UI U ( IE + UI )U + EI )E + IU )I (21) Again, Shimer (2007) showed ha he unemploymen rae is seady-sae value ( _ U = _ E = _ I = 0) equal o U LF is very well approximaed by u ss s s + f (22) wih s and f de ned by 8 >< >: s = EI IU f = UI IE + IE EU + IU UE + IU EU + IE UE Similarly o Secion 3; log-linearizing (22) gives us 6 d ln u ss = EI d ln EI + IU d ln IU + EU d ln EU (23) IE d ln IE UI d ln UI UE d ln UE 6 Conrary o he wo labor marke saes, a rs-order Taylor expansion already gives an excellen approximaion of deviaions of unemploymen from is mean. This is due o he fac ha compared o (7), (23) splis d ln u ss ino smaller pieces, which hen deviae less from heir mean. + 25

26 wih AB some posiive consans depending on he mean of AB in he Beveridge curve are given by. 7 In his conex, shifs d ln u shif = EU d ln EU + EI d ln EI + IU d ln IU IE d ln IE UI d ln UI (24) 5.2 Allowing for worker heerogeneiy Using he same logic as in Secion 4, we can re ne (24) by disaggregaing worker ows by reason for unemploymen and demographics. Each demographic group i veri es he sysem of di erenial equaions (21) where he ransiion raes are given by AB i u ss i s i s i +f i wih s i and f i de ned as in (22)., and seady-sae unemploymen of group i is given by To disaggregae by reason for unemploymen, we classify jobless workers according o he even ha led o heir unemploymen saus: a permanen layo p, a emporary layo, a qui q and a labor force enrance o. Formally, for each demographic group i, here are four unemploymen raes by reason: u p i ; u i, uq i and u o i and he associaed hazard raes due o employmen separaion f je i ; Ej i ; ji The aggregae unemploymen rae u ss i g; j 2 fp; ; qg or labor force enrance f oe i saes case, he average ransiion raes can be decomposed as ; Io i ; oi i g. sais es (22) and, similarly o he wo labor marke 8 >< >: UB = EU = IU = X j2fp;;qg X j2fp;;qg i i i i ss Io i u! j;ss i i u ss jb i, e i i e ss Ej i and IU = B 2 fe; Ig and EI = i i i i ss EI i e i i e ss EI i (25) Because Beveridge curve shifs due o job separaion can be caused by labor demand 7 Formally, EI = (1 u ss ) EI IU, UE = IU UE + IE UE, IE = IE EU (1 u ss ) s s+f s UI = UI IE, EU = (1 u ss ) IE EU + IU EU, IU = (1 u ss ) EI IU + IU EU s+f s s IU UE s+f : UI IE + IE UE s+f, 26

27 movemens (layo s) or labor supply movemens (quis), i is useful o rea hese wo evens X separaely. We furher decompose EU ino EU = Ep + Eq wih Ep u =! j;ss i i u je ss i and Eq = u! q;ss i i u qe ss i : j2fp;g Proceeding as in Secion 4, we can isolae he movemens in he average hazard raes d ln AB due o he composiion e ec. Log-linearizing he average hazard raes, we can wrie 8>< where >: d ln UB d ln EB d ln IB = d ln ~ UB = d ln ~ EB = d ln ~ IB + d ln UB;reason + d ln UB;demog, B 2 fe; Ig + d ln EB;demog, B 2 fp; q; Ig + d ln IB;demog, B 2 fu; Eg n o ~ AB are de ned as in Secion 4 and denoe he ransiion raes ha hold he composiion (demographics and reason for unemploymen) of he unemploymen pool, employmen pool and inaciviy pool consan. Similarly, d ln AB;demog i in Secion 4. 8 and d ln UA;reason i (26) are de ned as 5.3 Inerpreing shifs in he Beveridge curve We now combine secions 5.1 and 5.2 o inerpre he movemens in he Beveridge curve since Combining (24) and (26), we can decompose shifs in he Beveridge curve ino four componens: (i) changes in labor demand (permanen and emporary layo s), (ii) he e ec of demographics on layo s, (iii) changes in labor supply (due o quis and movemens in and ou of he labor force), and (iv) he composiion e ec of movemens in demographics and reason for unemploymen on labor supply. Formally: d ln u shifs = d ln u Ld shifs + d ln u Ld shifs;comp + d ln u Ls shifs 8 See he Appendix for he expressions for ~ AB, d ln AB;demog or d ln UA;reason : + d ln u Ls shifs;comp (27) 27

28 where 8 >< >: d ln u Ld shifs d ln u Ld shifs;comp d ln u Ls shifs d ln u Ls shifs;comp = EU d ln ~ Ep = EU d ln Ep;demog = EI d ln ~ EI + IU d ln ~ IU = EI d ln EI;demog IE d ln IE;demog + EU d ln ~ Eq + IU d ln IU;demog UI d ln UI;reason IE d ln ~ IE + EU d ln Eq;demog + d ln UI;demog UI d ln ~ UI Table 6 presen he resuls of a variance decomposiion exercise for d ln u shifs. Looking rs a he raw daa suggess ha labor demand and labor supply are equally responsible for Beveridge curve shifs, accouning for one hird of he variance each and composiion e ecs accouning for he remaining hird. However, his conclusion changes drasically when one considers high and low-frequency movemens separaely: labor supply is he prime driving force of secular shifs in he Beveridge curve bu labor demand is he main driving force a business cycle frequencies. We now discuss each frequency range separaely. Low-frequency movemens: Labor supply, including he composiion e ec due o demographics, accouns for almos 80 percen of he oal variance in secular Beveridge curve shifs. This resul is due o wo facors: he aging of he baby boom and he increase in women s labor force paricipaion rae. 9 The righ panel of Figure 8 plos he rends in d ln u Ls shifs;comp for six demographic groups and shows ha he decline in he share of young workers (male and female) conribued o he rend in unemploymen. Indeed, younger workers have higher urnover and a higher unemploymen rae han prime age or old workers and a decline in he youh share auomaically reduces he aggregae unemploymen rae. The oher in uenial demographic change, his ime wih a negaive e ec on unemploymen, was he large increase in prime age female s labor force paricipaion rae unil he mid-90s ha dampened he baby boom s e ec. 9 The 18 percen conribuion of d ln u Ld shifs;comp he expense of emporary layo s since early is he resul of he increasing use of permanen layo s a 28

29 The lef panel of Figure 8 plos he rends in d ln u Ls shifs for six demographic groups and highlighs a downward rend in unemploymen caused by a change in he behavior of women. To help undersand his phenomenon, Figure 9 plos he behavior of prime age women s ransiion raes over Two changes are apparen. 10 Firs, he secular increase in IU unil he mid-90s and he secular increase in IE are due o more women joining he labor force, eiher by direcly nding a job (as is increasingly he case) or by going rs hrough he unemploymen pool. Second, women display an increasing aachmen o he labor force as UI and EI follow downward rends since 1976, meaning ha women are increasingly likely o join or remain in he unemploymen pool afer an employmen spell raher han drop ou of he labor force. Finally, he downward rend in quis menioned in Secion 4 can be raced back o a secular decline in he qui rae of women, possibly due o heir increased aachmen o he labor force. 11 Since rends are of consequence for he fuure locus of he Beveridge curve in he years o come, wo more recen labor supply rends are worh menioning. Firs, Figure 10 plos he ransiion raes for women aged over 55. A rend apparen since he lae 90s is he increasing labor force paricipaion of older women as boh IU and IE are following upward rends. We can also noice an increase in labor force aachmen as boh UI and EI are following downward rends. The same resul holds for men over 55. Second, Figure 12 shows ha young workers are less likely o join he labor force ( IE and IU are boh on downward rends since he mid-90s). This could be relaed o he increase in he number of years of educaion as young workers say longer in school before joining he labor force. In conras o labor supply, labor demand plays almos no role a low frequencies (a corrolary of he absence of any signi can rend in he layo rae). However, he aging of he baby boom generaion caused he average layo rae o decline (as younger workers have he highes urnover raes), and explains why d ln u Ld shifs;comp lefward shif in he Beveridge curve. accouns for 18 percen of he secular 10 Abraham and Shimer (2001) were he rs o noice hese wo changes using annual ransiion probabiliies. 11 In conras, men s qui rae displays lile rend. 29