Department of Economics Working Paper 2016:14

Transcription

1 Deparmen of Economics Working Paper 2016:14 The maching process: Search or mismach? Nils Gofries and Karolina Sadin

2 Deparmen of Economics Working paper 2016:14 Uppsala Universiy November 2016 P.O. Box 513 ISSN SE Uppsala Sweden Fax: THE MATCHING PROCESS: SEARCH OR MISMATCH? Nils Gofries and Karolina Sadin Papers in he Working Paper Series are published on inerne in PDF formas. Download from hp:// or from S-WoPEC hp://swopec.hhs.se/uunewp/

3 THE MATCHING PROCESS: SEARCH OR MISMATCH?* Nils Gofries # and Karolina Sadin ## 24 November 2016 We examine he maching process using monhly panel daa for local labour markes in Sweden. We find ha an increase in he number of vacancies has a very weak effec on he number of unemployed workers being hired: unemployed workers appear o be unable o compee for many available jobs. Vacancies are filled quickly and here is no (or only weak) evidence ha high unemploymen makes i easier o fill vacancies; hiring appears o be deermined by labour demand while fricions and labour supply play small roles. These resuls indicae persisen mismach in he Swedish labour marke. Keywords: srucural unemploymen, fricional unemploymen, maching funcion, labour demand, labour supply JEL codes: J23, J62, J63, J64 *This paper builds on Chaper II in Sadin (2014). We are graeful for helpful commens on earlier versions from Timo Boppar, Mikael Carlsson, Per-Anders Edin, Anders Forslund, Håkan Gusavsson, John Hassler, Beril Holmlund, Erik Mellander, Eran Yashiv, Johnny Zeerberg and seminar paricipans a Jönköping Universiy, Nordic Summer Insiue for Labor Economics, Raio, he Riksbank (GSMG), and Uppsala Universiy. We also wan o hank employees a he Public Employmen Service (Arbesförmedlingen) for providing us wih daa and helpfully answering quesions. Financial suppor from he Jan Wallander and Tom Hedelius Foundaion and Marianne and Marcus Wallenberg Foundaion is graefully acknowledged. # Deparmen of Economics, Uppsala Universiy, UCLS, CESifo and IZA, nils.gofries@nek.uu.se ## Raio and Uppsala Cener for Labor Sudies, karolina.sadin@raio.se 1

4 1. Inroducion Vacancies and unemploymen coexis in he labour marke. In good imes, here are many vacancies and unemploymen is low, while in bad imes here are few vacancies and unemploymen is high. The sandard explanaion of hese observaions is ha here are search and maching fricions: i akes ime for workers and firms o find each oher. Normally, search fricions are modelled wih he help of a maching funcion, which is a reduced-form relaionship; he underlying microeconomic mechanisms are usually no spelled ou. 1 The word search suggess ha fricions arise because of imperfec informaion. Workers are imperfecly informed abou jobs, and i akes ime o conac firms and invesigae job opporuniies. If vacancies and job seekers are rying o find each oher wihin a finie space, more vacancies should make i easier for unemployed workers o find jobs, and high unemploymen should make i easier o fill vacancies. To his we can add heerogeneiy and mismach. Suppose ha here are wo ypes of jobs, A and B, and wo ypes of workers, A and B, and only A-workers can do A-jobs while only B- workers can do B-jobs. Then, wih a given probabiliy of meeing, and equal numbers of each ype of worker and job, he flow of hiring will be half as large. If mos workers are of ype A while mos jobs are of ype B, his will furher reduce hiring for given socks of unemploymen and vacancies. So, wihin his framework, changes in heerogeneiy and mismach are expeced o shif he maching funcion in a similar way as changes in search inensiy. In he sandard search-maching lieraure, mismach is ypically hough of as one facor ha may cause a shif he maching funcion and he Beveridge curve; see, e.g., Daly, Hobijn, Sahin and Vallea (2012) and Håkanson (2014). 1 For surveys of his lieraure, see Perongolo and Pissarides (2001), Yashiv (2007) and Elsby, Michaels and Raner (2015). 2

5 However, his way of hinking abou heerogeneiy and mismach is sill fundamenally based on imperfec informaion. Wih perfec informaion, he A-workers will queue up for he A- jobs, he B-workers will queue up for he B-jobs, and here will be excess supply, balance, or excess demand in each submarke. In his paper we invesigae he maching process using a monhly panel from he Public Employmen Service (Arbesförmedlingen) covering all 90 local labour markes in Sweden 1992:1-2011:12. Our focus is on how he hiring of unemployed workers and he filling of vacancies are relaed o socks of unemploymen and vacancies a he beginning of he monh as well as o he inflows of vacancies and unemployed workers during he monh. As a background o our empirical sudy, we presen wo simple models of he labour marke. One is he sandard maching funcion. The oher is a model wih perfec informaion where unemploymen is caused by persisen mismach beween supply and demand. In he laer case, we assume ha each local labour marke consiss of a mixure of submarkes, wih excess supply in some and full employmen in oher submarkes. Such a model is moivaed by he observaion ha in many markes ypically hose for less skilled workers here appears o be consan excess supply while oher markes have (close o) full employmen ypically hose for highly qualified workers. We derive he implicaions of hese wo models for he relaions beween he socks and flows of vacancies and unemploymen in a local labour marke. Compared o a sandard maching funcion, a model wih persisen mismach has very differen implicaions for he relaions beween socks and flows. Firs, if a large fracion of he vacancies arise in markes wih full employmen, an increase in vacancies will have a limied effec on he job prospecs for unemployed workers. Second, and mos imporanly, higher unemploymen will no increase he rae a which vacancies are filled. The reason is simple: in markes wih unemploymen, workers are queuing for he jobs and in markes wih full employmen here is, by definiion, no unemploymen. 3

6 Our empirical findings poin in he direcion of persisen mismach raher han informaion problems as he main explanaion of unemploymen. More vacancies do lead o more unemployed workers being hired, bu he effec is surprisingly weak; i appears ha only a small fracion of vacancies are filled by unemployed workers. Higher unemploymen does no increase he rae a which vacancies are filled or i has a weak effec in some specificaions. Our empirical resuls are in line wih some recen empirical sudies on macro and micro daa. Chrisiano e al. (2011) esimaed a macro model where he recruimen cos per hired worker could poenially depend on labour marke ighness. However, hey found no evidence ha recruimen coss depend on labour marke ighness. Michailla (2012) simulaed a model wih wage rigidiy and showed ha, wih reasonable parameer values, search fricions play a small role in bad imes bu may be more imporan in a igh labour marke. Michailla and Saez (2015) found ha flucuaions in employmen are mosly due o aggregae demand shocks. Carlsson, Eriksson and Gofries (2013) and Sadin (2015) used firm-level daa and found ha higher unemploymen does no make firms hire more workers. Alhough many researchers have esimaed maching funcions, hey have ypically used more limied daa han we use and hey have ofen imposed relaively igh specificaions. Many sudies use aggregae daa and assume he exisence of a consan reurns-maching funcion. Thus, hey relae he job finding rae o labour marke ighness and since boh variables are pro-cyclical hey find a posiive regression coefficien. We do no impose CRS à priori; insead we invesigae he separae roles of vacancies and unemploymen using panel daa for local labour markes. In our baseline esimaion, we include fixed effecs and ime dummies o reduce he risk of spurious correlaions. Following he sock-flow maching lieraure, we invesigae he separae roles of inflows and iniial socks, and we esimae idenical equaions wih he filling of vacancies and he hiring of unemployed workers as dependen variables. 4

7 We find ha he filling of vacancies and he hiring of unemployed workers are very differen variables; here is no such hing as a sable maching funcion ha explains boh of hese flows. Vacancies are filled quickly and, i appears, ofen by a worker who already had a job (or was no in he labour force). Unemployed workers appear o be unable o compee for many of he vacancies. We discuss previous empirical resuls in Secion 6 and show ha qualiaively similar resuls have, in fac, been found in oher sudies when similar empirical sraegies were used. Shimer (2007) brough renewed aenion o heerogeneiy and mismach by explicily allowing for many separae submarkes and perfec compeiion wihin each submarke, so ha he number of maches is deermined by he shor side in each marke. 2 In Shimer s model, here is high mobiliy: jobs and workers move randomly beween markes every ime hey close/qui and because of his high random mobiliy, each worker has some chance of maching wih each vacancy. As a resul, he wo socks are complemens in he maching process, and Shimer s model produces a reduced-form relaionship beween socks and flows, ha is similar o a Cobb-Douglas maching funcion (Shimer 2007, page 1093). We go o he opposie exreme compared o Shimer (2007) and assume ha workers canno move beween markes and ha here is consan excess supply in some markes and consan full employmen in oher markes. Thus, our model highlighs, sarkly, he implicaions of a persisen mismach problem in erms of skills and experience. Our simple model yields a differen and esable predicion: vacancies will no be filled more quickly if here is high unemploymen, and his is also wha we find in our empirical analysis. Obviously, a more realisic model would allow for some mobiliy beween markes and also for some markes o swich from excess supply o balance or excess demand, bu if heerogeneiy is relaed o skills and experience, his will be a slow process. 2 Shimer (2007) reviews some earlier work in his radiion. The model by Lagos (2000) is closely relaed. 5

8 So how can here be unemploymen in some submarkes and full employmen in oher submarkes? Clearly, here mus be limied mobiliy among submarkes, and wage rigidiy may also play a role. In Shimer s (2007) model, wages are flexible and adjus o clear each submarke. If here are fewer jobs han workers in a paricular submarke, wages fall o he reservaion wage and some workers are volunarily unemployed. If here are more jobs han workers, wages rise o equal produciviy and all workers are employed. However, wages play no role in he allocaion of jobs and workers across submarkes; insead, he allocaions of jobs and workers are deermined by exogenous random processes. 3 Alernaively, we can hink of a model where wages affec he allocaion bu where hey do no adjus enough o clear each submarke. As in Lagos (2000), some markes are characerized by excess supply (involunary unemploymen) while here is balance or a shorage of workers in oher markes. Figure 1 illusraes hese wo models of mismach. In his paper, we do no ake a sand on wha drives labour demand, how wages adjus, or wheher unemploymen is volunary or involunary. The purpose of our simple model is o ry o undersand how labour marke socks and flows are relaed when unemploymen is caused by persisen mismach raher han imperfec informaion. In Secions 2 and 3, we use a sandard maching funcion and a simple model of mismach unemploymen o derive equaions for he hiring of unemployed workers and he filling of vacancies. In Secion 4, he daa and he esimaion mehod are presened, and we also illusrae he relaions beween socks and flows graphically. Secion 5 conains he resuls of he baseline economeric analysis, and in Secion 6 we compare wih previous sudies. In secion 7 we consider alernaive funcional forms, and Secion 8 concludes. 3 In an exension, Shimer (2007) allows for limied endogenous mobiliy, bu his does no change he basic mechanism of he model. 6

9 Figure 1. Models of Mismach Shimer (2007) L L D A W B D B W A U Wage rigidiy L L W B W A D B D A U 7

10 2. Fricional Unemploymen In his secion, we specify a maching funcion ha we esimae on monhly panel daa from he Public Employmen Service. We ake he effecive number of job seekers o be + + where U is he number of unemployed workers who are regisered a he 1 U λu E in 1 in beginning of he monh, u is he inflow during he monh and E is he number of job searchers who are no regisered a he Public Employmen Service. The parameer λ reflecs he imporance of he inflow for he formaion of maches. Wih random maching we would expec λ o be smaller han uniy because workers who ener during he period are available for a shorer ime han he workers who are looking for jobs already a he beginning of he monh. Wih sock-flow maching we may insead expec λ o be larger han uniy so he inflow maches a a higher rae han he iniial sock. The sock-flow maching argumen is ha he new inflow of workers can mach wih boh he sock and he inflow of vacancies, while he workers who were unemployed a he beginning of he monh have already exploied all maching possibiliies wih he vacancies ha were available a he beginning of he monh. 4 E is unobserved and consiss of wo groups: job seekers wihou jobs who were no regisered as unemployed wih he Public Employmen Service and employed workers searching on he job. 5 in Similarly, we ake he effecive sock of vacancies o be V + 1 θv +Ω where V 1 is he sock in of vacancies ha are regisered a he beginning of he monh, v is he inflow of new vacancies during he monh and Ω is he number of vacancies ha are no regisered a he Public Employmen Service. Using a similar argumen as above, θ may be larger or smaller 4 Sudies of sock-flow maching include Coles and Smih (1998), Gregg and Perongolo (2005), Coles and Perongolo (2008) and Ebrahimy and Shimer (2010). 5 Allowing he wo ypes of job searchers o have differen search inensiies would no change he conclusions. 8

11 han uniy depending on he maching echnology. The maching funcion is specified as follows: ( in ) α in 1 ( 1 ) M = φ U + λu + E V + θv +Ω (1) β where M is he oal number of maches and we assume ha a and β are smaller han uniy. We do no impose consan reurns o scale because we see no compelling reason o do so. 6 The variable φ represens variaions in maching efficiency, which may be due o changes in incenives, efficiency of he public employmen service, and mismach. Wih his specificaion, he job-finding rae for someone who is unemployed a he beginning of he = + + and hiring from regisered unemploymen is in period is F M / ( U 1 λu E) α ( 1 ) ( 1 ) ( 1 ) ou in in in β u = F U + λu = U + λu V + θv ε (2) α 1 E Ω where ε = φ in + in U 1+ λu V 1+ θv β in The rae a which vacancies are filled is Q M / ( V 1 θv ) vacancies ha are filled during he monh is = + +Ω so he number of regisered α ( 1 ) ( 1 ) ( 1 ) ou in in in β = + = + + v Q V θv U λu V θv h β 1 E Ω where h = φ in + in U 1+ λu V 1+ θv α (3) 6 If unemployed workers and firms search in a limied space we would expec increasing reurns o scale in he meeing echnology, bu as poined ou by Perongolo and Pissarides (2006) reservaion wages may respond in such a way ha an esimaed maching funcion shows consan reurns o scale. 9

12 The ouflows of regisered unemployed and vacancies are posiively relaed o he regisered socks, and he inflows and ε and model we esimae log-linearized versions of hese equaions: η are he unobserved pars. To es he predicions of he lnu = a lnu + a ln u + a lnv + a ln v + ln ε (4) ou in in lnv = a lnu + a ln u + a lnv + a ln v + lnη (5) ou in in αu αλu βv βθv U + λu U + λu V + θv V + θv in in where a11 = a21 =, a12 = a22 =, a13 = a23 = and a in in in 14 = a24 = in. Values wihou ime indexes denoe seady-sae values. We chose o esimae a log-linear specificaion as baseline because i is easy o undersand and gives us a clear idea of how he differen variables are correlaed. Noe ha a11 + a12 = a21 + a22 = a and a13 + a14 = a23 + a24 = β so he deep parameers a and β could poenially be inferred from he esimaes. 7 However, unregisered job searchers and vacancies ener he error erms, and hus he esimaed parameers may no correspond o hose of he underlying maching funcion. The bias depends on how he unobserved variables co-vary wih regisered unemploymen and vacancies. If on-he-job in search is eiher consan or pro-cyclical, E / ( U 1 λu ) + will fall when unemploymen increases and since α 1< 0 his means ha he esimaed effec of unemploymen on he ouflow from regisered unemploymen will be larger, i.e. he sum of he esimaes a11 + a12 will be larger han α. Furhermore, if E increases when vacancies increase (pro-cyclical 7 Alernaively, we can hink of hese equaions as log-linear approximaions of he maching funcions ha arise in he sock-flow maching model see equaions 7-13 in Coles and Perongolo (2008). 10

13 on-he job search), he ne effec of vacancies on he ouflow from regisered unemploymen will be smaller; he sum of he esimaes a13 + a14 will be smaller han β. 8 The effecs of pro-cyclical on-he-job search on he coefficiens in equaion (5) go in he opposie direcion: he effec of regisered unemploymen on he vacancy ouflow will be smaller and he effec of vacancies increases. Thus, we see ha pro-cyclical on-he-job search changes he inerpreaion of he coefficiens, bu we would sill expec all coefficien esimaes o be posiive. For he effec of unemploymen on he vacancy ouflow o be zero, an increase in unemploymen would have o be fully counered by a decrease in on-he-job search (see equaion (1)), and his is unlikely. 9 Simulaneiy and measuremen problems are discussed in Secion Mismach Unemploymen In his secion we presen an alernaive model wih persisen mismach of workers and jobs. The basic idea is ha each local labour marke consiss of many submarkes wih specific job characerisics and skill requiremens. In some submarkes (ype A), here are more workers willing and able o work han here are jobs, and in oher markes (ype B) here is full employmen. We ake demand for labour as given; wha we aemp o undersand is how labour marke socks and flows are relaed when unemploymen is caused by persisen mismach raher han search coss and informaion problems. 8 These biases are discussed in Perongolo and Pissarides (2001). Wheher search on he job is procyclical is no clear; Elsby, Michaels and Raner (2015) consruc a measure of on he job search and find i o be slighly counercyclical 9 If workers searching on he job face convex search coss and weigh he marginal benefis of search agains he marginal coss, an increase in unemploymen will make hem search less, bu no so much less ha he effecive number of job seekers decreases. 11

14 Demand, Supply, and Turnover To mach he empirical daa, we le he period lengh be one monh. There is a represenaive firm and an exogenous labour force L in each marke, and we le A N and B N denoe employmen a he end of he period in he wo ypes of markes. In a marke of ype A, labour demand is always smaller han L, firms can hire as many workers as hey wan and unemploymen is U = L N. (6) A A In he B-markes, all workers are employed, so B N B = L and U = 0. A he beginning of each period, some fracions s A and s of he employed workers qui heir B jobs, or hey are fired for exogenous reasons, and some fracions A B z and z of he employed workers decide o apply for oher jobs and qui if hey ge new jobs. Then, firms in boh markes announce new vacancies v A and v resignaions and hires occur, and workers B remain employed or unemployed unil he end of he period. Vacancies remaining a he end of a period are denoed A B V and V. Markes wih Unemploymen (ype A) We assume ha a vacancy ha exiss a he beginning of he period generaes Q hires during a monh and a vacancy ha is announced during he monh generaes q hires during he monh, so hires in a marke wih unemploymen are h = QV + qv. (7) A A A 1 12

15 We ake he raes Q and q as exogenous, reflecing pracical delays in collecing applicaions and deciding whom o hire. I akes some ime o hire a worker, bu his ime is independen of he level of unemploymen. We expec q o be smaller han Q because he new vacancies ener during he period and hus have less ime o be filled. All workers who were unemployed a he beginning of he period and hose who qui exogenously search for jobs ogeher wih he workers who are rying o swich jobs. Firms hire randomly among he job applicans, so he probabiliy ha a job searcher finds a job during he monh is F A A = A A A A A A U 1+ s N 1+ z s N 1 h ( 1 ). (8) Markes wih Full Employmen (ype B) Even if here is full employmen in markes of ype B, i is normally possible o hire workers because here are workers who are ready o swich jobs. Vacancies can be filled by hose who B have already qui ( ) B B (( 1 s ) z L) s L and hose who have no ye qui bu are applying for oher jobs. Assuming ha B B QV + 1 qv workers are hired if here are applicans o all jobs, hiring in he ypical B-marke is ( 1 ( ( ) ) ) B B B B B B h = min QV + q v, s + 1 s z L. (9) If here are enough applicans for all jobs, hiring will be equal o B B QV + 1 qv, bu here could also be congesion if here are no enough workers willing o swich jobs. This funcion is kinked and concave. Wih some heerogeneiy across markes, hires will be a smooh concave funcion of he effecive number of vacancies. 13

16 Ouflow from Unemploymen The above equaions describe a simple model of persisen mismach. Bu we do no have daa for individual submarkes, so we need o undersand he implicaions of he model for daa on a local labour marke consising of many submarkes. Thus, we assume ha here is a coninuum of submarkes and ha a fracion λ of he markes are markes wih full employmen (ype B). Then, aggregae unemploymen a he end of he period is U ( 1 λ ) = U, (10) A he inflow ino unemploymen is u ( 1 λ ) s N 1 = (11) in A A and he ouflow from unemploymen is ( 1 λ ) ( 1 1) u = F U + s N. (12) ou A A A A Using (10), (11), (12), (8) and (7) we can wrie he ouflow from unemploymen as ( 1 ) A A ( 1 λ )( QV 1 + qv ) ( λ ) ( 1 ) ou A in u = F U + u =. (13) A A in 1 z + z 1 L/ U + u The ouflow from unemploymen increases wih he iniial sock and wih he inflow ino unemploymen and he funcion is concave because unemployed workers compee wih each oher for jobs. 10 As in he fricional model, hiring from unemploymen increases wih unemploymen, bu no because more unemployed workers can locae more jobs. Raher, he reason is ha he unemployed ge some of he jobs ha would oherwise have gone o he job swichers. 10 in As U + 1 u approaches is maximum, ( λ ) A A, he ouflow approaches ( 1 λ )( QV 1 qv ) 1 L +. 14

17 The ouflow from unemploymen increases wih he number of vacancies bu only if he vacancies appear in he markes where he unemployed workers are. Vacancies in markes wih full employmen ( B and B V 1 v ) will no increase he job chances of unemployed workers. Thus, he effec of an increase in oal vacancies on he ouflow from unemploymen will depend on where he vacancies appear. Ouflow of Vacancies The ouflow of vacancies is (( ) ) ( 1 λ)( ) λmin Q q, ( 1 ) 1 1 v = QV + qv + V + v s + s z L (14) ou A A B B B B The ouflow of vacancies will increase wih he inflow and he iniial sock of vacancies, and his funcion may be linear or concave depending on wheher here are enough workers willing o swich jobs. An imporan implicaion of his model is ha variaions in unemploymen have no effec on he rae a which vacancies are filled. Inuiively, his follows from wo observaions: in markes wih unemploymen, vacancies are filled a given raes; in markes wih full employmen, here is, by definiion, no unemploymen. This predicion differs markedly from he implicaions of he maching funcion. If unemploymen is due o informaion fricions, he presence of more unemployed job seekers should always increase he rae a which vacancies are filled. 15

18 4. Daa and Esimaion Mehod We wan o invesigae how he hiring of unemployed workers and he filling of vacancies during a monh are relaed o he socks of unemploymen and vacancies a he beginning of he monh as well as he inflows of unemployed workers and vacancies during he monh. We begin by esimaing equaions (4) and (5), which are approximaions of he maching funcion. Alernaive funcional forms are considered in Secion 7. Daa We use regiser daa from he Public Employmen Service (Arbesförmedlingen) for he period 1992:1-2011:12. Daa from he Public Employmen Service are available a he municipaliy level a a monhly frequency. We aggregae he daa o obain a daase wih variables for local labour markes, which consis of one or more municipaliies and are consruced by Saisics Sweden based on commuing paerns. Local labour markes are consruced o be geographical areas ha are as independen as possible from he res of he world wih respec o labour demand and labour supply. 11 The sock of unemploymen, U, is measured as he number of openly unemployed workers ha are regisered a he Public Employmen Service a he end of he monh. There is a srong incenive o regiser because doing so is required o qualify for unemploymen benefis. In he baseline esimaion, workers in labour marke program paricipans are no included because earlier research indicaes ha hey conribue o maching o a significanly smaller exen han do openly unemployed workers; see Forslund and Johansson (2007). (We include program paricipans in a robusness check.) The inflow ino unemploymen, in u, is measured as he 11 The 90 local labor markes are lised in he Appendix. Johansson and Persson (2000) repored ha percen of all hired workers came from he local labor marke area where he firm was locaed. Survey daa for vacancies and unemploymen are no sufficienly large o allow panel esimaion based on local labor markes. 16

19 number of workers who are newly regisered as unemployed during he monh and hires from unemploymen, u, are measured as he number of workers who lef regisered ou unemploymen, reporing o he employmen service ha hey found jobs. V is he sock of vacancies regisered a he Public Employmen Service a he end of he monh, and in v is he inflow of new vacancies during he monh. We measure he ouflow of vacancies as he inflow of new vacancies over he monh minus he change in he sock: ( V ) v = v - V -. (15) ou in -1 A weakness of hese daa is ha we do no know if all vacancies are filled. Firms may abandon heir recruimen effors wihou acually hiring a worker and if he fracion of firms ha does his varies in a sysemaic way we may draw incorrec conclusions. 12 In our sample, unemploymen was, on average, 7.2 percen of he labour force, he monhly inflow ino unemploymen was 0.97 percen of he labour force and he ouflow from unemploymen o jobs was 0.92 percen of he labour force; some of hose who deregisered did no repor ha hey found a job. Vacancies were on average 0.53 percen of he labour force, and he monhly inflows and ouflows of vacancies were boh 0.82 percen of he labour force. 13 Thus, he flows are similar bu he sock of vacancies is more han en imes smaller han he sock of unemployed workers. No all unemployed workers are regisered a he Public Employmen Service. According o Aranki and Löf (2008), vacancies repored o he Public Employmen Service corresponded o percen of oal hirings in he 1990s and 2000s. Thus, we should view our measures of 12 A recruimen survey, which is issued irregularly by he employer s federaion, shows ha abou 4/5 of all aemps o recrui resul in hiring. 13 These are unweighed means across local labor markes. If we insead consider aggregae numbers, we find ha unemploymen was, on average, 6.2 percen and he monhly inflow ino unemploymen was 0.45 percen of he labor force, while vacancies were 0.54 percen and he monhly inflow of new vacancies was 0.42 percen of he labor force. 17

20 unemploymen and vacancies as imperfec measures of he oal socks and flows of unemployed workers and vacancies in he economy as a whole. An imporan quesion, hen, is how represenaive regisered unemployed workers are of he oal populaion of unemployed workers. We have no direc evidence on his, bu Figure 2 shows ha, for Sweden as a whole, unemploymen regisered a he Public Employmen Service has flucuaed in a similar way as unemploymen according o he labour force survey conduced by Saisics Sweden (AKU). However, he number of unemployed workers ha are regisered a he Public Employmen Service has declined over ime compared o he survey measure. 14 The lower panel in Figure 2 shows ha aggregae vacancies regisered a he Public Employmen Service (AF) are closely correlaed wih available jobs according o a survey conduced by Saisics Sweden ha began in he year 2001 (excep for he firs year of he survey). The survey daa are oo limied o do analysis on he local labour marke level. Thus we see ha, a he aggregae level, hese measures vary similarly o he alernaive measures; hey appear o be sufficienly broad and represenaive o make i worh sudying how socks and flows are relaed. The long-erm rend in he fracion of unemployed workers ha regiser a he employmen service makes i imporan o accoun for underlying rends and srucural changes in he esimaion. 14 Regiser daa from he public employmen service (AF) covers all persons regisered a AF while he labour force survey (AKU) is a survey of abou persons. The difference beween he differen unemploymen measures has been analysed by Saisics Sweden (Saisics Sweden 2016, Table 3). In 2015, persons were unemployed according o AKU. Of hese, SCB esimaes ha were no regisered a AF and were paricipaing in labour marke programs wih aciviy suppor so hey were no openly unemployed according o AF. On he oher hand, persons who were regisered as unemployed a AF would coun as ou of he labour force according o AKU, e.g. because hey did no fulfil he job search requiremen. There were also differences in he crieria used o coun a person as employed, where AKU has sricer crieria, leading o a ne difference of In 2015, persons were openly unemployed according o he public employmen service:

21 Figure 2. Alernaive Measures of Unemploymen and Vacancies q1 1992q4 1993q3 1994q2 1995q1 1995q4 1996q3 1997q2 1998q1 1998q4 1999q3 2000q2 2001q1 2001q4 2002q3 2003q2 2004q1 2004q4 2005q3 2006q2 2007q1 2007q4 2008q3 2009q2 2010q1 2010q4 2011q3 U (AKU) U (AF) q1 2002q1 2003q1 2004q1 2005q1 2006q1 2007q1 2008q1 2009q1 2010q1 2011q1 2012q1 2013q1 Vacancies (AF) Vacancies (SCB) Noe: The upper panel shows unemploymen according o he labour force survey (AKU) age 15-74, (series obained from Konjunkurinsiue) and openly unemployed workers who are regisered a he Public Employmen Service (AF). The lower panel shows job openings (lediga jobb) according o a survey conduced by Saisics Sweden (SCB) and vacancies regisered a he Public Employmen Service (AF). The series are seasonally adjused. 19

22 Esimaion Mehod To invesigae how ransiion raes are relaed o socks, we rely on differences in he variaion over ime across local labour markes. Thus, we include ime dummies and fixed effecs for local labour markes in our baseline specificaion. We include fixed effecs because geography, densiy, and indusry srucure affec he maching process in differen labour markes. We include ime dummies in he baseline specificaion for wo reasons. Firs, cycles are highly correlaed across local labour markes, so alhough we have a panel wih 90 local labour markes, he resuls of a regression wihou ime dummies will be driven mainly by he aggregae business cycle. Then, here will be a risk ha he resuls are affeced by some unobserved macroeconomic shocks ha affeced all local labour markes in he same way. When we use differences in variaion over ime across labour markes, i is much less likely ha he resuls are affeced by some specific unobserved shocks. The second reason o include ime dummies is ha we have daa for a long ime period, and here have clearly been srucural changes in he labour marke during his period. As discussed above, here has been a decline in he fracion of unemployed workers ha are regisered a he Public Employmen Service. Addiionally, formal rules and firms behaviour wih respec o he posing of vacancies may have changed. By including ime dummies, we can accoun for changes in rules and behaviour provided ha hey had similar effecs across local labour markes A number of srucural changes have been noed in repors from he Public Employmen Service: i) Unil 2007, i was mandaory for all employers o announce heir vacancies a he Public Employmen Service, and his is sill mandaory for he governmen. Alhough many vacancies wen unrepored before 2007, i is likely ha his rule change affeced firms behavior. ii) Around , here was an increased endency for firms o pos he same job several imes, bu from 2008 onward, such behavior was policed by he Public Employmen Service. iii) In recen years, increased use of IT sysems has led o a dramaic increase in auomaic ransfers of job posings o he PES regiser, and his appears o have increased he share of job posings ha are regisered wih he PES. iv) Vacan summer jobs are posed earlier in he year in he laer par of he period. 20

23 We also include seasonal dummies ineraced wih dummies for he local labour markes. We do his o accoun for differences in seasonal paerns depending on he imporance of secors such as agriculure and ourism. Finally, we include local linear and quadraic ime rends o accoun for long-erm srucural changes in specific labour markes. Table 1 shows ha here is considerable variaion remaining in he explanaory variables afer removing fixed effecs, common ime effecs, and local seasons and rends. Table 1. Sandard Deviaions of Explanaory Variables Variaion removed: Fixed effecs for llm, local seasons Fixed effecs for llm, local seasons, ime dummies Fixed effecs for llm, local seasons, ime dummies, linear and quadraic local ime rends lnu lnv lnuin lnvin Noe: Socks are measured on he las day of he previous monh and in relaion o he labour force. The inflows during he monh are also measured in relaion o he labour force in each local labour marke. We esimae equaions (4) and (5) by ordinary leas squares (OLS) and insrumen variable esimaion (IV). In he IV esimaion, we use five lags of he inflows and he socks from six monhs ago as insrumens. By insrumening, we can alleviae wo problems. Firs, here may be purely random variaion in he fracions of all unemployed workers and all vacancies ha regiser wih he employmen service. We can hink of his as pure measuremen errors ha will lead o biased esimaes. 16 Second, a simulaneiy problem may arise because persisen shocks o he maching funcion ( φ ) may be correlaed wih he variables included on he righ hand side. Suppose ha here is a persisen increase in mismach (e.g., because of a 16 The sign of his bias is unclear. If some addiional vacancies are randomly regisered and deregisered wihin he monh, he inflow and ouflow of vacancies will boh increase. If some addiional vacancies are randomly regisered bu no deregisered wihin he monh, he inflow of vacancies will increase bu no he ouflow. If some vacancies are randomly deregisered, he ouflow will increase bu no he inflow. 21

24 large inflow of immigrans) so ha he ypical unemployed worker maches wih fewer jobs. This means ha as φ falls, he ouflow from unemploymen decreases and he sock of unemploymen increases over ime. Persisen mismach shocks of his ype imply reverse causaion ha will make he coefficien on he iniial sock of unemployed smaller. To address hese problems, we use lagged socks and inflows as insrumens because hey should be more exogenous o he maching process in a given period han recen socks and curren inflows. 17 A Look a he Daa Figure 3 shows vacancies, unemploymen and he ouflow from unemploymen for he hree larges local labour markes: Sockholm, Göeborg and Malmö. The graphs for vacancies and unemploymen mirror each oher and are fairly similar for he differen local labour markes; o a large exen, vacancies and unemploymen reflec he general business cycle. The ouflow from unemploymen is posiively correlaed wih unemploymen, bu i is hard o see how i is relaed o he number of vacancies. Figure 4 shows he same daa, aggregaed o quarerly frequency, bu here we have unemploymen on he horizonal axis and vacancies on he verical axis, and he size of he bubbles reflecs he ouflow from unemploymen. By comparing he bubbles in he horizonal direcion, we can examine how he hiring of unemployed workers is relaed o he sock of unemployed holding he sock of vacancies consan. We see clearly ha he ouflow from unemploymen is higher when unemploymen is high. Comparing he sizes of he bubbles in he verical direcion, holding unemploymen consan, we see only a weak posiive relaion beween he number of vacancies and he ouflow from unemploymen. 17 Unforunaely, we have been unable o find more exogenous insrumens. We ried o exploi he indusry srucure of differen local labor markes, using inpu-oupu ables o consruc exogenous shocks. Such an approach was used successfully by Carlsson, Eriksson and Gofries (2013) for firm-level daa. This approach was unsuccessful, however. Because of srong inpu-oupu linkages beween differen secors, here urned ou o be very lile difference beween he exogenous shocks calculaed for differen local labor markes. 22

25 Figure 3. Ouflow from Unemploymen lnu&lnv Sockholm lnuou 1990m1 1995m1 2000m1 2005m1 2010m1 lnu lnv lnuou lnu&lnv Göeborg lnuou 1990m1 1995m1 2000m1 2005m1 2010m1 lnu lnv lnuou Malmö lnu&lnv m1 1995m1 2000m1 2005m1 2010m lnuou lnu lnv lnuou Noe: Monhly regiser daa from he Public Employmen Service, seasonally adjused. 23

26 Figure 4. Bubble Scaer Plos for Hiring from Unemploymen Larger bubble = larger ouflow from unemploymen Uou-bubbles Sockholm lnv lnu lnv Uou-bubbles Göeborg lnu lnv Uou-bubbles Malmö lnu Noe: Quarerly averages of monhly regiser daa from he Public Employmen Service, seasonally adjused. 24

27 Figure 5 shows vacancies and unemploymen for he hree larges labour markes ogeher wih he ouflow of vacancies. The ouflow of vacancies is very closely correlaed wih he number of vacancies, bu i is difficul o see wheher he ouflow of vacancies is relaed o unemploymen. In Figure 6 we again have unemploymen on he horizonal axis and vacancies on he verical axis, bu now he size of he bubbles reflecs he ouflow of vacancies. By comparing he sizes of he bubbles in he verical direcion, holding unemploymen consan, we see ha more vacancies are associaed wih a bigger ouflow of vacancies. Comparing he sizes of he bubbles in he horizonal direcion, holding vacancies consan, we see no obvious relaion beween unemploymen and he ouflow of vacancies. Our graphical examinaion indicaes srong own effecs in he sense ha high unemploymen leads o a high ouflow from unemploymen and more vacancies lead o more vacancies being filled. The cross effecs appear weak, however. Hiring from unemploymen is only weakly relaed o he number of vacancies, and we see no clear relaion beween unemploymen and he rae a which vacancies are filled. Noe, however, ha his graphical examinaion exploied he ime series variaion in individual labour markes, so he resuls may be driven by common unobserved shocks and srucural changes. By including ime dummies in our panel esimaion we can eliminae he effecs of common shocks, and his should make he resuls more reliable. By IV esimaion we can reduce he effecs of measuremen errors and simulaneiy. 25

28 Figure 5. Ouflow of Vacancies lnu&lnv Sockholm lnvou 1990m1 1995m1 2000m1 2005m1 2010m1 lnu lnv lnvou Göeborg lnu&lnv lnvou 1990m1 1995m1 2000m1 2005m1 2010m1 lnu lnv lnvou Malmö lnu&lnv lnvou 1990m1 1995m1 2000m1 2005m1 2010m1 lnu lnv lnvou Noe: Monhly regiser daa from he Public Employmen Service, seasonally adjused. 26

29 Figure 6. Bubble Scaer Plos for he Ouflow of Vacancies Larger bubble = larger ouflow of vacancies Vou-bubbles Sockholm lnv lnu lnv Vou-bubbles Göeborg lnu lnv Vou-bubbles Malmö lnu Noe: Quarerly averages of monhly regiser daa from he Public Employmen Service, seasonally adjused. 27

30 5. Resuls Table 2 shows OLS and IV esimaes of equaions (4) and (5) wih he ouflow from unemploymen and he ouflow of vacancies as dependen variables. Table 2. Deerminans of Ouflows of Unemployed Workers and Vacancies (1) (2) (3) (4) lnuou OLS lnuou IV lnvou OLS lnvou IV lnu 0.576*** 0.585*** (0.023) (0.053) (0.022) (0.071) lnuin *** (0.013) (0.060) (0.019) (0.083) lnv 0.009*** 0.013* 0.415*** 0.487*** (0.003) (0.007) (0.009) (0.018) lnvin 0.038*** 0.111** 0.462*** 0.821*** (0.005) (0.043) (0.013) (0.065) Observaions 20,394 19,725 20,391 19,722 R-squared Number of llm Hansen (p-value) Kleibergen-Paap (p-value) Noe: Robus sandard errors (clusered on local labour marke) in parenheses; *** p<0.01, ** p<0.05, * p<0.1. Fixed effecs for local labour markes, ime dummies, local seasons and linear and quadraic local ime rends are included in all specificaions. Insrumens for IV are five lags of inflows plus he socks in -6. Unemploymen Ouflow Equaion According o he OLS esimaes in column 1 of Table 2, unemploymen and vacancies boh have saisically significan effecs on he ouflow from unemploymen, bu he sock of unemployed workers has a quaniaively much larger effec han he effec of vacancies. There is no effec of he inflow of newly unemployed workers. In column 2 we accoun for measuremen errors and simulaneiy by insrumening all he variables on he righ hand side wih five lags of he inflows and he socks lagged six monhs. The es saisics show ha his insrumen se is boh valid and relevan. One concern, which was raised above, is ha 28

31 mismach shocks may creae a simulaneiy problem ha affecs he coefficiens for he socks, bu his does no appear o be an imporan problem; he coefficiens for he socks are roughly similar as we go from OLS o IV. The coefficiens for he inflows increase, however, and become quaniaively imporan when we esimae by IV. One possible inerpreaion is ha esimaion by IV reduces he effecs of measuremen errors wih respec o he inflows. As discussed above, esimaion by IV should be a good way o address measuremen errors. In he IV esimaion, he sum of he coefficiens for he sock and inflow of unemploymen is abou 0.8, so a 10 percen increase in he sock and he inflow ino unemploymen will raise he ouflow by approximaely 8 percen. A en percen increase in (new and old) vacancies increases hiring from unemploymen by only 1.2 percen. The sum of he four coefficiens in column 2 is and we canno rejec consan reurns o scale a convenional levels of significance. The signs of he effecs are qualiaively in line wih he implicaions of he maching funcion, bu he effec of vacancies on he hiring of unemployed workers is surprisingly weak. Vacancy Ouflow Equaion Column 3 in Table 2 shows he OLS esimae of equaion (5) wih he ouflow of vacancies as he dependen variable. We see ha he iniial sock and he inflow of new vacancies boh conribue o he ouflow of vacancies, bu neiher he iniial sock of unemploymen nor he unemploymen inflow have significan effecs on he rae a which vacancies are filled. The IV esimaes are shown in Column 4, and again he es saisics show ha he insrumens are boh valid and relevan. Compared o OLS, we find a much bigger effec of he vacancy inflow, while he effec of he vacancy sock is somewha larger. As discussed above, his difference beween OLS and IV could be due o measuremen errors. Again, we see no effec of unemploymen on he vacancy ouflow. 29

32 The sum of he coefficiens in column 4 is and we can rejec consan reurns o scale saisically, so insead of congesion we find increasing reurns o scale. One possible inerpreaion is ha his reflecs heerogeneiy among vacancies. There may be some fairly consan ses of vacancies ha are difficul o fill, while he vacancies ha do flucuae are filled a a faser rae. 18 Robusness across Time and Space In Table 3 we invesigae he robusness of he resuls for he unemploymen ouflow across ime and space; all esimaions are performed by IV, including local labour marke fixed effecs, ime dummies, local seasons and local rends. Column 1 repeas our baseline esimae for he whole ime period and all labour markes. In columns 2 and 3 we esimae he equaion for wo periods, and The coefficien esimaes are similar o wha we find for he whole period, bu some coefficiens are more uncerain and no saisically significanly differen from zero. In columns 4-6 we divide he sample ino small, medium and large labour markes, wih one hird of he labour markes placed in each caegory. The resuls are qualiaively roughly similar hose for he whole sample, bu some esimaes are more uncerain. In Table 4 we invesigae he robusness of he resuls for he vacancy ouflow across ime and space. The resuls are robus across ime and space. In no case do we find any saisically significan effec of unemploymen, bu he coefficiens for he sock and inflow of vacancies are sable showing significan, posiive effecs on he ouflow of vacancies. 18 There are a large number of job openings in ele-markeing where paymen is ofen based on commission and firms may simply wan o hire as many as possible. 30

33 Table 3. The Ouflow from Unemploymen: Robusness across Time and Space Dep. variable: lnuou (1) (2) (3) (4) (5) (6) Period Labour markes All All All Small Medium Large lnu 0.585*** 0.844*** 0.668*** 0.718*** 0.568*** 0.483*** (0.053) (0.193) (0.059) (0.095) (0.043) (0.084) lnuin 0.207*** ** 0.278*** (0.060) (0.243) (0.084) (0.104) (0.100) (0.097) lnv 0.013* 0.022* 0.012** *** (0.007) (0.011) (0.005) (0.012) (0.008) (0.013) lnvin 0.111** *** (0.043) (0.090) (0.066) (0.056) (0.069) (0.063) Observaions 19,725 7,317 11,870 6,405 6,660 6,660 R-squared Number of llm Noe: Robus sandard errors in parenheses; *** p<0.01, ** p<0.05, * p<0.1. IV-regressions. Insrumens: five lags of inflows plus he socks in -6. Regressions include fixed effecs for local labour markes, ime dummies, local seasons and local rends. 31

34 Table 4. The Ouflow of Vacancies: Robusness across Time and Space Dep. variable: lnvou (1) (2) (3) (4) (5) (6) Period Labour markes All All All Small Medium Large lnu (0.071) (0.216) (0.075) (0.143) (0.098) (0.122) lnuin (0.083) (0.344) (0.122) (0.174) (0.108) (0.135) lnv 0.487*** 0.428*** 0.536*** 0.498*** 0.479*** 0.446*** (0.018) (0.030) (0.018) (0.026) (0.026) (0.045) lnvin 0.821*** 0.884*** 0.578*** 0.886*** 0.610*** 0.796*** (0.065) (0.119) (0.115) (0.075) (0.123) (0.142) Observaions 19,722 7,317 11,867 6,403 6,659 6,660 R-squared Number of llm Noe: Robus sandard errors in parenheses; *** p<0.01, ** p<0.05, * p<0.1. IV-regressions. Insrumens: five lags of inflows plus he socks in -6. Regressions include fixed effecs for local labour markes, ime dummies, local seasons and local rends. 32

35 These robusness checks show ha our main resuls are no due o some specific shocks ha happened in paricular ime periods or in specific labour markes. If we hink of hese regressions as esimaes of he maching funcion, wo resuls are surprising. The firs is ha he number of vacancies has such a weak effec on he hiring of unemployed workers. The second is ha unemploymen has no effec on he ouflow of vacancies. Boh resuls are consisen wih a model of persisen mismach in he labour marke bu inconsisen wih a sandard maching funcion. Our esimaes ell us somehing imporan abou vacancy daa. There are many vacancies in a boom, bu his is no because heir duraions increase; insead, i is because here is a large inflow of vacancies in boom periods. One may argue ha he laer resul arises mechanically because firms rouinely pos vacancies for a fixed ime and hen collec applicaions and hire he bes applican. However, his is exacly how we would expec firms o behave if hey expec o quickly arac a sufficien number of qualified applicans for mos jobs ha hey announce. Alernaive Trends, Aggregae Daa and Labour marke Programs Table 5 shows regressions where we leave ou eiher he local rends or he ime dummies. The cross effecs become posiive in some cases and negaive in oher cases, bu hey are generally weak. Wihou ime dummies or wihou local rends, higher unemploymen appears o have a posiive effec on he ouflow of vacancies. However, he effec is quie small and of limied economic significance. A one-sandard-deviaion change in boh V and v in has an effec on v ou ha is almos 10 imes larger han he effec of one sandard deviaion changes in boh U and u in Using he sandard errors in he firs row of Table 1 and he coefficiens in he sixh column of Table 5, we ge = for unemploymen and = for vacancies. 33

36 Table 5. Leaving ou Local Trends or Time Dummies (1) (2) (3) (4) (5) (6) Baseline No rend No TD Baseline No rend No TD lnuou IV lnuou IV lnuou IV lnvou IV lnvou IV lnvou IV lnu 0.585*** 0.416*** 0.811*** *** 0.133*** (0.053) (0.041) (0.038) (0.071) (0.037) (0.029) lnu in 0.207*** 0.328*** 0.083** * 0.088*** (0.060) (0.057) (0.038) (0.083) (0.059) (0.031) lnv 0.013* 0.020*** ** 0.487*** 0.488*** 0.453*** (0.007) (0.007) (0.013) (0.018) (0.017) (0.019) lnv in 0.111** *** 0.821*** 0.727*** 0.720*** (0.043) (0.025) (0.048) (0.065) (0.034) (0.041) Time dummies YES YES NO YES YES NO Local rends YES NO YES YES NO YES Observaions 19,725 19,725 19,725 19,722 19,722 19,722 R-squared Number of llm Noe: Robus sandard errors in parenheses; *** p<0.01, ** p<0.05, * p<0.1. IV-regressions. Insrumens: five lags of inflows plus he socks in -6. In baseline ime dummies, local seasonal dummies, linear and quadraic local rends, and fixed effecs for he local labour marke are included. 34