Unemployment Flows, Participation and the Natural Rate of Unemployment: Evidence from Turkey

Transcription

1 Unemploymen Flows, Paricipaion and he Naural Rae of Unemploymen: Evidence from Turkey Gonul Sengul Mura Tasci Cenral Bank of Turkey Federal Reserve Bank of Cleveland January 28, 2016 Absrac The level of he unemploymen rae he economy converges o in he long-run has long been a major concern for policy makers. This quesion is radiionally addressed by exploiing he co-movemen beween inflaion (nominal variables) and unemploymen in he conex of a Phillips curve. In developing counries and emerging markes, which go hrough srucural changes and major ransiions, relying on such a framework becomes more challenging. Moreover, labor marke size in developing counries also changes, adding o he challenge of using radiional measures. This paper uses labor marke flow raes, aking paricipaion ino accoun explicily, o esimae he unemploymen rae rend, using Turkish economy as a laboraory. The paper finds ha naural rae of unemploymen esimaed using unemploymen flows gives a differen picure han he esimaes using nominal variables. Moreover, aking paricipaion rae explicily ino accoun changes he value of naural rae esimae, while preserving is paern. JEL Classificaion: E24, E32, J64. Keywords: Unemploymen, Unemploymen Flows, Labor force Paricipaion, Turkey. The views expressed herein are hose of he auhors and no necessarily hose of he Cenral Bank of he Republic of Turkey, Federal Reserve Bank of Cleveland or he Federal Reserve Sysem. We would like o hank he paricipans of he Turkish Labor Marke Research Nework Conference and he Cenral Bank of he Republic of Turkey Inernal Conference. Isanbul School of Cenral Banking, Cenral Bank of he Republic of Turkey. Gonul.Sengul@cmb.gov.r. Research Deparmen, Federal Reserve Bank of Cleveland. muraasci@gmail.com 1

2 1 Inroducion The long-run rae of unemploymen (he underlying rend) has araced a lo of aenion since he Grea Recession. In an environmen where many developed counries and emerging marke economies face excepionally high levels of unemploymen, policy makers and economiss focused on idenifying he unemploymen rae ha is feasible in he long run, i.e, he naural rae, o gauge he exen of labor marke slack (see, for insance, Daly e al. (2012) and Weidner and Williams (2011)). This quesion is radiionally addressed by exploiing he co-movemen beween inflaion (nominal variables) and unemploymen in he conex of a Phillips curve. In developing counries and emerging markes, which go hrough srucural changes and major ransiions, relying on such a framework becomes more challenging. Even for developed marke economies, a sable relaionship beween inflaion and unemploymen migh be somewha enuous. 1 Our main conribuion in his paper is o provide a framework ha could be useful even for economies where we canno rely on radiional Phillips-curve based approaches. We hink Turkey provides a unique laboraory in his respec. The counry has gone hrough significan changes in is moneary policy environmen, followed by sharply declining inflaion in he early 2000s. 2 The radiional approach of esimaing a naural rae by focusing on he relaionship beween labor marke variables and he price level (NAIRU) will no necessarily inform us abou he underlying dynamics of he Turkish labor marke. 3 We show ha naural rae esimaes exraced using he NAIRU mehod imply an almos invarian level of unemploymen, in spie of subsanial movemens in he daa and significan changes in he labor marke in he sample period. Essenially, price level movemens do no seem o be informaive abou an aggregae unemploymen rae ha could be susained in he long run, in he absence of high-frequency shocks. 1 See for insance Knoek and Zaman (2014). 2 The Cenral Bank of Turkey implemened implici inflaion argeing from 2002 o 2006, and has been officially argeing inflaion since hen. Please see Kara (2006) and Kara and Orak (2008), among ohers, for more informaion regarding Turkey s moneary policy. 3 For a recen discussion regarding NAIRU see Fizgerald and Nicolini (2013). 2

3 Turkish case provides anoher imporan challenge o evaluae he usefulness of an approach for esimaing he naural rae. In addiion o major srucural changes in Cenral Bank objecives, labor force paricipaion increased sharply from 46 percen o 51 percen wihin a 5-year span in our sample, mosly led by rising female labor force paricipaion. Hence, any aemp o undersand he long-run poenial of he labor marke canno ignore he paricipaion margin for Turkey. Even hough his margin has been relaively sable (and hence ignored) in developed economies, here is now some evidence ha he Grea Recession migh have recenly changed his as well (Elsby e al. (2013) and Erceg and Levin (2013)). This paper confrons boh challenges and develops a mehod o esimae he rae of unemploymen in he long run wihou relying on variaions in he general price level and aking ino accoun changes in he labor force paricipaion rae. We esimae our model using daa on Turkey, where he labor force paricipaion rae has increased sharply since 2003 and is hree imes more volaile han he US paricipaion rae (see Sengul (2014)). To face hese challenges, we need a framework ha relies exclusively on labor marke feaures. A recen example of such a framework is Tasci (2012) which approaches he problem by esimaing he unemploymen rae rend using he underlying flow raes. Tasci (2012) builds an unobserved-componens mehod and uses daa on flows beween employmen and unemploymen for he US. and argues, in he conex of US labor markes, ha his mehod provides an esimae of he naural rae ha has several desirable saisical feaures and comes very close o he language of he modern heory of unemploymen. In his paper, we adop his mehodology o incorporae labor force changes and o esimae he naural rae of unemploymen for Turkey. Exending his work, we esimae he unemploymen rae rend for Turkey from 2001 o 2013, aking ino accoun flows from inaciviy. In doing so, we also draw on he work of Sengul (2014), which esimaes Turkey s monhly flow raes from 2005 o 2011, including flows from nonparicipaion o unemploymen. We firs esimae quarerly flow raes from 3

4 2001 o Then, using a parsimonious unobserved-componens mehod, as in Tasci (2012), we decompose he flow raes ino heir rend and cyclical componens. Once we infer he rend componens, we provide an esimae of he unemploymen rae rend, i.e., he naural rae, implied by he seady-sae descripion of he unemploymen rae in a sandard labor-marke search model. To assess he effecs of paricipaion on he unemploymen rae, we also esimae he rend unemploymen rae while resricing flows o hose beween employmen and unemploymen. Our resuls show a disinc paern for rend unemploymen: The rend unemploymen increases during he firs wo-hirds of he sample period and sars o decline afer he recession. This paern holds, wheher or no one explicily allows for ime-varying labor force paricipaion. However, if an explici role is given o labor force paricipaion, he esimaed unemploymen rend varies somewha relaive o he level implied by he model where we assume a consan paricipaion rae over ime. The larges discrepancy occurs in he afermah of he las recession, which coincides wih he beginning of he secular rise in paricipaion. Moreover, we find ha his paern for he naural rae is led by a similar paern for he inflow rae ino unemploymen, firs increasing and hen declining in , and a secular rise in he rae of ouflow from unemploymen over he whole sample. Taken ogeher, hese findings imply ha Turkish labor markes looked far more dynamic a he end of 2013 han in We also highligh anoher poenially useful feaure of our framework. I improves he accuracy of he unemploymen forecas in he shor erm-even hough i is no designed for his purpose. This is an imporan addiional benefi of he framework discussed here, in a counry where unemploymen daa releases have a wo-monh lag. Our paper is he firs sudy ha relaes general oupu dynamics o he underlying labor marke flows for Turkey in order o consruc an empirically useful naural rae measure. We believe ha his exercise is valuable, no only in is own righ bu also becauseiallowsusohighligh heusefulness ofourapproachinhefaceofheineresing 4

5 challenges posed by various srucural issues ha many economies face. As we argued above, for insance, many developing counries, Turkey included, have a very limied span of daa ha covers subsanial changes in he aggregae economy. The framework we provide in he paper is flexible enough o incorporae labor force paricipaion-in spie of daa limiaions- for a relaively less dynamic labor marke ha goes hrough major srucural changes, which in urn makes radiional Phillips curve-based measures raher uninformaive. Theresofhepaperproceedsasfollows: Inhenexsecion, welayouheunobservedcomponens model wih he assumpion ha labor force paricipaion moves over ime. Since he model wih a consan labor force assumpion is nesed in our model, we describe ha model in he appendix. Afer describing he mehodology for measuring he flow raes and esimaing he rends, we presen he daa and he esimaion resuls for boh consan and ime-varying labor force models in secion 3. A more deailed discussion of he naural rae concep we develop here in conjuncion wih he more convenional measures of he naural rae used in he lieraure, including a NAIRU, is in Secion 4. We also address he robusness of he esimaion in his secion. Secion 5 presens he forecasing performance of he model. The las secion concludes. 2 Model wih Paricipaion We now describe our approach for idenifying an unemploymen rend for Turkey under he assumpion ha workers can move beween hree labor marke saes; employmen, unemploymen, and inaciviy. To esimae he long run unemploymen rae while allowing for variaions in he labor force paricipaion rae, we exend he unobserved componens model described in Tasci (2012). This exended model ness wo-sae model of Tasci (2012) as a special case. When we discuss he resuls of our model, we compare he model wih paricipaion o is alernaive wo-sae model. We compue he long run unemploymen rae as he seady sae descripion of un- 5

6 employmen based on rend inflow and ouflow raes. Hence, we need labor marke flow raes o esimae he unemploymen rae rend. We begin wih describing he esimaion procedure for he flow raes. 2.1 Measuremen of Flow Raes To measure flow raes, we rely on he aggregae daa. This is because we use quarerly daa o esimae unemploymen rae rend o have a larger sample size and household level daa for Turkey is only available annually. There is now an exensive lieraure on measuring he flow raes using aggregae daa. Mos of his lieraure uses a simple unemploymen duraion based measuremen o infer hese raes (i.e., Shimer (2012), Elsby e al. (2009), Fujia and Ramey (2009), Elsby e al. (2013), Perongolo and Pissarides (2008)). We follow he mehod used in Sengul (2014), which exends he mehod used by Elsby e al. (2013), Shimer (2012) and Elsby e al. (2009), o allow for changes in labor force beween wo consecuive periods. Inwha follows, we assume haime isconinuous, andhedaa is availablea discree monhs. Hence, period refers o he inerval [, + 1). Le N +τ be he number of populaion and le he populaion grow a a rae ρ and he paricipaion rae (he raio of he labor force o he populaion) grow a a rae G. Laws of moion for he populaion and he paricipaion rae are Ṅ+τ = ρ N +τ and P +τ = G P +τ, respecively. P +τ is he paricipaion rae and i is compued as he raio of he labor force o he populaion (P +τ = L +τ /N +τ ), where L +τ is he number of labor force. Furhermore, le U +τ, and U <1 (τ) be he number of unemployed and he number of unemployed for less han 5 weeks a ime + τ, respecively, while A is he fracion of he inacive populaion (N +τ L +τ ) ha decide o look for a job. People become unemployed because hey separae from heir employmen or hey ener labor force as unemployed, and hey leave unemploymen because hey eiher find a job or leave he labor force. Le S and F be he job-separaion and unemploymen exi (ouflow) raes during period. We can wrie he law of moion for unemploymen as 6

7 follows: U +τ = (L +τ U +τ )S U +τ F +(N +τ L +τ )A. (1) We are limied in our abiliy o disinguish beween exis from unemploymen ino employmen or ino inaciviy in he daa due o lack of daa availabiliy a a high frequency. Hence, F absorbs exis from unemploymen, regardless of heir desinaion. Since some of he ouflow may be due o he inaciviy, F is he unemploymen exi rae, no necessarily he job-finding rae. This way of modeling does no affec our analysis as he focus of he paper is o measure and esimae he flows ino and ou of unemploymen. We do no need o have specific informaion abou he naure of he exi from unemploymen per se. Noe ha if he labor force is consan, hen we have ρ = 0 and G = 0 and A = 0. In his case, he equaion above is he same as he equaion of Elsby e al. (2013), which assumes consan labor force beween wo consecuive periods. 4. We solve equaion (1) and ierae i hree monhs o ge he evoluion of he unemploymen rae based on observed daa in discree inervals as: 5 u = u 3 (1 λ )+ λ S + λ ( A (θ +G )(1 e 3θ ) ) 1, (2) θ +G θ +G P θ λ where λ = (1 e 3(S+F+ρ+G) ) is he quarerly convergence rae and θ = S +F +ρ for noaional convenience. One can use equaion (2) and wrie he seady sae unemploymen rae as u ss = S + A ( (θ +G )(1 e 3θ ) ) 1. (3) θ +G θ +G P θ λ Noe ha inroducing variable labor force affecs he seady sae unemploymen hrough muliple channels. Firs we need o accoun for he fracion of he inacive populaion who sar looking for a job and become unemployed, i.e. A /(θ +G ). Second we have o ake ino accoun he fac ha he size of he labor force changes wih paricipaion, as well as he populaion growh (θ +G ). Lasly, change in paricipaion also changes he size 4 We derive flow equaions under his assumpion in he appendix. 5 We use quarerly daa. 7

8 of he inacive pool, which affecs he flows from inaciviy o unemploymen. To see his las poin, suppose G = 0, hen he coefficien of A becomes coefficien of A /(θ +G ) in he equaion above becomes (N /L 1). To compue he flow raes, we also need he law of moion for shor-erm unemployed, i.e. unemployed for less han five weeks: U <1 (τ) = (L +τ U +τ )S U <1 (τ)f +(N +τ L +τ )A. (4) The change in he number of shor-erm unemployed consiss of workers enering unemploymen, workers separaing from heir jobs and workers who became unemployed afer he las ime daa was available and did no leave unemploymen, respecively. Subracing equaion (4) from equaion (1) resuls in U +τ = U <1 (τ) (U +τ U <1 (τ))f. (5) Wedo no observe A in(5) explicily. This is no because paricipaion does no affec he law of moion for unemploymen, bu because he fracion of inacive populaion enering o unemploymen is already presen in U <1 he labor force. and F also covers unemployed workers leaving Solving he differenial equaion above and he laws of moion for he populaion and he paricipaion rae (and rewriing he equaion in erms of raes) yields: where u denoes he unemploymen rae in period. u = e F ρ G u 1 +u <1. (6) Assuming unemploymen exi occurs wih a Poisson process wih parameer F, he probabiliy of exiing unemploymen wihin a monh is ˆF = 1 e F. Therefore, equaion (6) can be rewrien as ˆF = 1 u u <1. (7) e G ρ u 1 The inuiion behind (7) is ha we infer he average ouflow probabiliy by measuring he size of he decline in he unemploymen pool who are no shor-erm unemployed. 8

9 Noice ha ρ + G is he labor force growh rae, as labor force varies due o changes in populaion and he paricipaion decisions. The equaion above akes ino accoun he change in he size of he labor force o ge he average ouflow probabiliy. The monhly ouflow probabiliy relaes o associaed monhly ouflow hazard rae for he shor-erm unemployed, F <1, hrough he equaion F <1 = ln(1 ˆF <1 ). Equaion (7) works well o esimae he ouflow probabiliy in labor markes for which he flow rae ou of unemploymen is high(duraion of unemploymen is low). For counries wih longer duraions, like Turkey, here are relaively few people in u <1 a any ime since exi raes are low. Hence, he variance of he esimae will be higher (ˆF will be noisy). We follow Elsby e al. (2013) and Sengul (2014) and use addiional duraion daa o increase he precision of he esimae of ˆF. Based on he unemploymen daa by duraion, we can calculae he probabiliy ha an unemployed worker exis unemploymen wihin d monhs as ˆF d u u <d = 1 e d 1. (8) j=0 (G j+ρ j ) u d Subsequenly, we can calculae he ouflow raes as F <d = ln(1 ˆF d )/d for differen duraions, d = 1,3,6,9,12. This rae is inerpreed as he rae a which an unemployed worker exis unemploymen wihin he subsequen d monhs. If he exi rae from unemploymen is independen of he duraion of unemploymen, henf <d fordifferen values ofdwouldnobemuch differen fromeachoher, andwehave he monhly ouflow hazard rae as F <1. However, if he exi rae from unemploymen depends on he duraion of unemploymen, hen he F <1 rae would no be a consisen esimae of he average ouflow rae. We formally es he duraion dependence by esing he hypohesis ha F <1 = F <3 = F <6 = F <9 = F <12. 6 The approach in general is o derive he asympoic disribuion of unemploymen raes and unemploymen raes for differen duraions, and hen o apply he Dela mehod o compue he join asympoic 6 Formal deails of he es can be found in Elsby e al. (2013) wih he only difference being ha his paper has an exra erm, he duraion d < 9. 9

10 disribuion of he ouflow rae esimaes. For Turkey, he hypohesis ha here is no duraion dependence (i.e., he hypohesis ha F <d is he same for all d) can be rejeced a 95 percen confidence level. We use he asympoic disribuion o compue an opimally weighed esimae of ouflow rae ha minimizes he mean squared error of he esimae. We discuss compuaion of A series below when we describe he daa, as we infer he series direcly from he daa. Given F, u and A series, he equaion (2) gives us he separaion rae daa we need o proceed wih our esimaion. 2.2 Esimaing Trend Unemploymen Rae Afer discussing he measuremen of flow raes, we now presen our approach for idenifying an unemploymen rend in he presence of varying labor force paricipaion. In doing so, we exend he model used in Tasci (2012) o include paricipaion. Tasci (2012) uses a simple reduced form unobserved componens model ha incorporaes he comovemen of flows beween employmen and unemploymen ino previous aemps a esimaing he naural rae, such as Clark (1987, 1989) and Kim and Nelson (1999). OurreducedformmodelassumesharealGDP-hemeasureofheaggregaebusiness cycle we use- has boh a sochasic rend and a saionary cyclical componen, where only real GDP is observed by he economerician. The sochasic rend follows a random walk while he cyclical componen is an auoregressive process. More specifically, le Y be log realgdp,ȳ beasochasicrendcomponen, andy behesaionarycyclical componen. Then we consider an unobserved componens model saring wih he process for he GDP as, Y = ȳ +y, y = φ 1 y 1 +φ 2 y 2 +ε yc, ȳ = r 1 +ȳ 1 +ε yn, (9) r = r 1 +ε r, 10

11 where r is a drif erm in sochasic rend componen of oupu, which is also a random walk, and he cyclical componen of oupu follows an AR(2) process, as in Ozbek and Ozlale (2005). The model also assumes ha boh unemploymen exi and job separaion raes (F and S ) have a sochasic rend as well as a saionary cyclical componen. Furhermore, he sochasic rend in hese flow raes follows a random walk while heir cyclical componen depends on he cyclical componen of real GDP. Le f and s be he sochasic rend componens, and f and s be saionary cyclical componens of F and S, respecively. The ime series behavior of hese flow raes ake he following form: F = f +f, f = f 1 +ε fn, f = τ 1 y +τ 2 y 1 +τ 3 y 2 +ε fc, (10) and S = s +s, s = s 1 +ε sn, s = θ 1 y +θ 2 y 1 +θ 3 y 2 +ε sc. (11) We assume ha all he error erms are independen whie noise processes. As equaions (10) and (11) show, we also assume ha he cyclical componen of he ouflow and separaion raes move wih he aggregae cycle. This idea capures he empirical paern ha recessions are imes when a subsanial number of maches dissolve because hey cease o be producive enough and significanly fewer new maches are formed because firms do no demand as much labor anymore. Hence, a priori, we expec a negaive co-movemen beween he cyclical componens of he flow raes, s and f and cyclical componen of real GDP. 7 This basic descripion of he comovemen beween flow raes and he aggregae cycle can be easily reconciled wih he exensions of he basic labor marke search model wih endogenous separaions, as in Morensen and Pissarides (1994). Tasci 7 We are agnosic abou he exisence of any co-movemen among he rends of he flow raes, if any, as long as hey are no correlaed wih he aggregae oupu. Even hough such ineracion is possible, we absrac from i. Given he shor sample we are working wih, any more complicaion in he form of anoher laen variable will subsanially reduce he precision of he esimaes we ge in his unobserved componens model. 11

12 (2012) argues ha he low-frequency movemens in he rends, f and s, will capure he effecs of insiuions, demographics, ax srucure, labor marke rigidiies, and he longrun maching efficiency of he labor markes, which will be more imporan in deermining he seady sae of unemploymen. Afer modeling unemploymen exi and separaion raes, we are lef wih he ime series behavior of paricipaion rae, inaciviy-o-unemploymen flow rae and populaion. Due o he lengh of our sample and he addiional number of parameers ha arise wih an addiional variable in our unobserved componens model, we canno fully model all he flow raes ha deermine he seady sae unemploymen rae. Hence, we need o make some assumpions. We begin by assuming ha he populaion growh ρ has a rend and a cycle ha are independen of he GDP, and we idenify hese componens using HP filer. 8 We also subjec A series o he same procedure. Even hough one expecs he cyclical componen of flows from inaciviy o unemploymen o depend on he overall cycle (in GDP), we canno model i ogeher wih he paricipaion rae and is growh as we run ou of degrees of freedom. Since A is measured indirecly, we hink including P and G in our model can be more informaive. Given hese assumpions, we hen model paricipaion as having a cyclical componen and poenially a sochasic growh componen in is rend: P = p +p p = µ 1 y +µ 2 y 1 +µ 3 y 2 +ε pc p = p 1 +g 1 +ε pn g = g 1 +ε g (12) The model described by equaions (9) hrough (12) can be represened in a sae-space form in he following way: much. 8 We also fi an AR process o he populaion growh and see ha rend we exrac does no change 12

13 Y F S = 0 τ 1 τ 2 τ θ 1 θ 2 θ P 0 µ 1 µ 2 µ ȳ y y 1 y 2 r g p f s φ 1 φ = ȳ y y 1 y 2 r g p f s ȳ 1 y 1 y 2 y 3 r 1 g 1 p 1 f 1 s ε fc ε sc, (13) ε pc + ε yn ε yc 0 0 ε r ε g ε pn ε fn ε sn. (14) where all error erms come from an i.i.d. normal disribuion wih zero mean and variance σ i, such ha i = {yn,yc,r,g,fn,fc,sn,sc,pn,pc}. We use he Kalman filer o filer he unobserved componens and wrie he loglikelihood funcion o esimae he model via maximum likelihood. Since we are ineresed in he unobserved sochasic rend and cyclical componens, once we esimae he model, we use he Kalman smooher o infer hem over ime. Then, we obain he unemploymen rae rend using he flow seady sae equaion and evaluae a he curren rend levels of he variables: ū = ( s ā ) s + f + ρ +g + ā(1 e 3( s+ f+ ρ) ) p ( s + f + ρ ) λ, (15) where λ = 1 e 3( s+ f + ρ +g ). Recall ha ρ and ā are no esimaed hrough he model, bu compued separaely as he rend implied by he HP filer. Tasci (2012) inerpres he unemploymen rae rend expressed in (15) as he seady sae unemploymen rae ha is implied by he curren rend esimaes of he flow raes. Noe ha, since rend flow raes are random walks, curren rend esimaes are also he bes esimaes for fuure rend values. Hence, we inerpre his rae as he rae of 13

14 unemploymen in he long run, o which he acual unemploymen rae would converge in he limi. 3 Daa and Esimaion Before proceeding o he esimaion, we describe our daa sources and he reamens we have o implemen o address some concerns. Then we presen he esimaion resuls for he flow raes and he long-run unemploymen rae implied by hese raes for Turkey. To beer undersand he conribuion of incorporaing changes in he labor force o he unemploymen rae rend, we also esimae he model wih he assumpion ha he labor force does no change beween wo consecuive quarers. Since our model already ness he consan labor force model, we leave he explici discussion of he model wihou variable labor force o he appendix. The daa used in esimaing he flow raes is from he Household Labor Force Survey conduced by Turkish Saisical Agency (TurkSa). 9 We have quarerly daa from 2000:Q1 o 2013:Q4 on he populaion, he number of workers in he labor force, and unemployed persons for less han d monhs, where d {1,3,6,9,12}. 10 The raw daa requires some adjusmens due o breaks prior o consrucion of he flow hazard raes, F and S. Firs, here is a break in he 2005:Q1 daa. This break is due o a change in populaion projecion mehods ha ook place in TurkSa updaed quarerly daa prior o he break unil 2005:Q1 and yearly daa unil To correc he daa prior o 2005, we make use of he availabiliy of unadjused quarerly and adjused 9 For more informaion go o hp:// Household labor force survey is he main daa source for labor force saisics in Turkey. The survey began in 1988 and conduced a biannual frequency unil In 2000, he survey was exended o include a larger sample and more quesions. Also is frequency increased allowing for quarerly aggregae resuls. In 2004, he sample size increased furher o allow for saisics for 26 regions, compared o 9 regions of previous surveys. Microdaa is available a annual frequency since d = 1 corresponds o he number of workers unemployed for less han five weeks and his daa is provided by TurkSa upon reques. 11 In 2007, Turkey implemened an address-based populaion regisraion sysem (ADNKYS), which allows yearly daa for populaion. Turksa was using populaion numbers based on projecions from census daa prior o his change, and i realized a discrepancy beween he projecions and he acual numbers delivered by ADNKYS. 14

15 annual values for As such, we updae he unadjused quarerly values for 2004 such ha quarerly growh raes wihin 2004 are he same for adjused and unadjused series andheaverage ofhenew quarerlydaafor2004ishesame asheadjused annual value repored by TurkSa. Once we adjus he quarerly series of 2004, we also updae he daa prior o 2004 such ha he quarerly growh raes are he same as in he unadjused series. In addiion, here is a break in 2004 in he daa for unemployed wih differen duraions. 12 To correc for his, we assume ha he growh rae of he share of unemployed wihaduraionofdmonhs amongall unemployed from2003:q4o2004:q1isheaverage of he growh rae of he same quarer of he wo previous and he following years shares. Then, we back up he new shares for periods prior o 2003:Q4 from he new growh raes, and readjus all duraion daa so ha he shares add up o 1. We adjus he number of unemployed for less han one monh such ha heir share among unemployed for less han hree monhs (in unadjused series) remains he same. 13 All hese reamens are unforunaely dicaed by he concerns we have due o daa breaks, survey redesign, and mehodological changes. However, he fac ha here was no major aggregae economic shock hiing he economy around his ime reassures us ha he impac of our reamens on he esimaion resuls will be nonsubsanial. 14 Finally, we also use he aggregae real GDP daa from he TurkSa. 15 Figure 1 shows he unemploymen and he paricipaion rae hroughou he sample. The Turkish unemploymen rae hoovered around 10 percen during he sample period, wih he excepions of he rise during he global crisis. Paricipaion rae was around In 2004, he sample size of Household labor force survey increased. Regional resuls were available for 9 regions prior o Wih he increased sample, TurkSa began o release resuls for 26 regions. This increase in sample size migh have allowed beer esimaes of unemployed wih differen duraions. 13 There was also an anomaly in he unemployed for 6-7 monhs daa for 2003:Q2 and 2003:Q3, which generaed a level shif in he seasonally adjused daa. We replace he growh raes of shares from 2003:Q1 o 2003:Q2 and from 2003:Q2 o 2003:Q3 wih he average of he growh rae of he same quarer of he wo previous and he following years shares. 14 We also used some oher impuaion mehods for his break. The resuls show no significan change. 15 Expendiure based, in 1998 prices. 15

16 percen unil 2007 and i increased o around 50 percen by In addiion o he daa described above, we make use of he daa on unemploymen by reason o consruc A series. Figure 2 displays he series. Ideal compuaion would require daa on labor marke ransiions of enrans who will be unemployed for less han one monh. The raio of his pool o he inacive populaion would be A. However, daa on he number of unemployed for less han one monh by reason of unemploymen is no available. Thus, we use daa on unemploymen by reason for a duraion less han hree monhs and assume ha he fracion of enrans among unemployed for less han hree monhs (he shores duraion for which we have daa) is he same as he fracion of enrans among unemployed for less han one monh. The assumpion implies ha Ue,<1 U <1 Ue,<3, where U e,<d U <3 denoes labor marke enrans who are unemployed for less han d monhs. Noe ha U e,<1 U <1 and we have daa for he righ-hand side of his approximaion. Hence, we compue A as U <1 U e,<3 /(N U <3 L ). Before proceeding o he esimaion and resuls, we would like o discuss an issue ha needs o be ackled in esimaing he model. The model, as spelled ou in equaions (13)- (14), has four observable series and en shock parameers ha needs esimaing, and hence is subjec o a poenial idenificaion problem. The soluion involves normalizing he sandard deviaion of he cyclical componen of a variable relaive o is rend componen, hereby reducing he number of parameers o esimae. We address his issue in more deail and describe he process in Secion 3.2. U e,<3 U <3 3.1 Resuls for Consan Labor Force Model Once we make necessary adjusmens o he daa, we compue he aggregae flow raes following our discussion in he preceding secion. We sar wih he resriced model which assumes ha he labor force is consan, which is effecively equivalen o resricing assumpion ha we have ρ = 0 and G = 0 and A = 0 in our model. We sar wih his simplified case o presen an easier benchmark. Table 1 presens he basic momens of he daa. Average unemploymen in Turkey was abou 10.5 percen over our sample 16

17 period, rising from around 7.5 percen o more han 14 percen in he middle of he las recession. We are in a sense forunae o have unemploymen move around his much, as i helps o idenify he movemens in he rend and cycle componens in he flow raes even wihin a shor sample. Observed flow rae levels in Table 1 show ha he Turkish labor marke also feaures very low raes of urnover, similar o some OECD counries. As such, our approach o use more duraion daa o compue he average flow hazards is clearly warraned. Similar o he paern we observe in oher counries, ouflow hazard, F, is a leas six imes more volaile han he inflow hazard, S. We esimae he unobserved componens model wih consan labor force via maximum likelihood using he flow raes described above. 16 The poenial idenificaion issue discussed above appears no o be a major one for he daa a hand. The log-likelihood funcion urns ou o be well behaved and quie variable, such ha we can avoid he normalizaion for he GDP componens ha Tasci (2012) relies on for he U.S. daa. The same is no rue for he flow raes, which implies ha we esimae he process for boh ε yn and ε yc, bu we resor o normalizaion for he flow raes. Our esimaion resuls sugges hahedrif erm forherendoupu for hisime-periodinturkey was consan, ha is σ r = sd(ε r ) = 0. Hence, we impose his resricion in our esimaion, obaining r = for he sample period. This rae ranslaes ino a 4.9 percen average annualized quarerly growh rae for he rend oupu. The normalizaion we find o be opimal for he flow raes in his resriced model esimaion implies ha γ f = σ fn σ fc = 0.75 and γ s = σsn σ sc = The procedure o choose parameer values for γ s and γ f is explained in deail in Secion 4. In our esimaion, we rely on he Kalman filer o generae he log-likelihood funcion and o obain he smoohed unobserved saes. Because we have several variables following a random walk, iniializing he Kalman filer requires saring wih a diffuse prior, which requires us o exclude some of he quarers a he beginning of he sample. We exclude 16 This version of he model is expressed in (A.25)-(A.26) in he appendix. 17

18 he firs eigh quarers of he daa in our esimaion. We discuss he poenial effecs of his exclusion resricion in Secion 4. In Figure 3, we plo he esimaed unobserved rend componens as well as he daa on he flow raes, unemploymen rae, and he rae of convergence, λ. The upper panel of Figure 3 shows ineresing changes in he underlying rends for he flow raes. In paricular, he ouflow rae, rae a which an average unemployed would find a job in a given monh, has increased over he course of he decade by essenially doubling from 0.06 o 0.12, implying a monhly probabiliy of roughly 11 percen by he end of he sample. In a somewha similar fashion, he inflow rae also rended up over he sample period, ripling from is level o Since he end of he las recession, he rend changed course and has sared o decline owards a level of These rend changes ogeher imply a relaively sable paern for he unemploymen rae rend early on in he sample period, wih he excepion of he firs recessionary episode. Then, rend unemploymen gradually declines from is recession era highs of 12 percen o around 9 percen a he end of he sample. In he firs par of he sample, rend changes in F and S offse each oher o some exen as hey push rend unemploymen in opposing direcions. However, since he end of he las recession, changes in direcion of he rend behavior of S reinforced he decline in he unemploymen rae rend ha is implied by he gradual increase in he ouflow rae, F, over ime. A more imporan observaion is ha overall reallocaion in he labor markes have experienced a seady increase in Turkey. The picure on he lower-righ panel plos he reallocaion measure we look a, λ, which governs he rae a which unemploymen approaches is flow seady sae. The magniude of he changes over ime implies ha he half-life of a cyclical gap in he unemploymen rae declined from more han five quarers in early 2000s o around hree quarers by he end of he sample. Hence, our resuls no only sugges a declining rend for he unemploymen rae, bu also more churning in he labor marke implying faser adjusmens in response o cyclical changes in he 18

19 unemploymen rae. 3.2 Resuls for Variable Labor Force Model Nex we urn o he case wih variable labor force paricipaion, which is our main focus. We begin wih he descripive saisics for flow raes under he assumpion ha measuremen akes ino accoun variaion in he labor force paricipaion over ime. Table 1 shows he average levels of flow raes for boh cases; wih consan and varying labor force assumpions. We observe ha relaxing consan labor force assumpion affecs boh he levels and he sandard deviaions of flow raes. Resuls for he esimaion of he exended model wih paricipaion are displayed in Table 3. Some of he individual parameer esimaes lose significance, however, overall he model is preferable o he one wih hese parameers excluded and o he model wih no paricipaion, as he improvemen in log-likelihood is significan. Conrary o he sochasic growh rae for he oupu rend, labor force paricipaion indeed has a ime-varying growh rae in is rend. Consisen wih he cyclical behavior of F and S, we observe ha τ 1 is posiive while θ 1 is negaive. We see ha τ 3 is no independenly significan, bu he model is preferable o he one wihou τ 3. Our esimaes of he model wih varying labor force sugges ha he impac on he unemploymen rae could be subsanial. Figure 4 plos he unemploymen rae rend from he resriced model ogeher wih he esimaed rend from he exended model of his secion. According o our esimaes, for mos of he early par of he sample, he difference beween wo models are quie subsanial, and he difference is smaller owards he end of he sample. For insance, we observe as much as a 2.5 percenage poin difference beween wo rend esimaes in he middle of he sample and 0.5 percenage poin difference a he end of he sample period. To beer undersand he effec of including variable labor force, firs noice hrough equaion 3 ha including flows from inaciviy has posiive effec on he seady sae unemploymen rae. However, he increase in unemploymen rae due o flows from in- 19

20 aciviy per se is small (see Figure A.11). As flow rae from inaciviy o unemploymen is high a he earlier episodes of he sample, we observe a larger conribuion from he second erm of equaion 3 compared o he laer par. 17 The major difference across he unemploymen raes wih consan vs. variable labor force sems from he fac ha including paricipaion in he model affecs he esimaed rend values of he flow raes. As Figure A.12 shows, alhough modeling he flows from inaciviy does no affec he esimaed flow raes much, i affecs he rend esimaes of flow raes. Figure 5 displays all of he imporan unobserved componens for he exended model wih variable labor force paricipaion rae. Even hough he implied rend esimaes for F and S change somewha, resuls confirm he secular rends we obained from he resriced model. More imporanly, he paricipaion rae rend implied by he esimaion (righ figure in middle panel) shows ha here has been an imporan rend growh change. The paricipaion rae has been growing in Turkey over his period, and our model idenifies par of his as a rend increase. This is no unlike he behavior in he U.S. where paricipaion hardly responds o he business cycle, if a all. Taken ogeher, he convergence rae now reflecs he added impac of an increasing growh rae in he labor force paricipaion, which is picured in he lower panel. 4 Discussion and Robusness We have proposed and esimaed a naural rae for Turkey using a relaively parsimonious model purely relying on he flow raes in and ou of unemploymen. We view his concep in line wih Tasci (2012) and perceive i as he seady sae unemploymen rae ha is implied by he curren rend esimaes of he flow raes. Pracically, his means ha i is he rae of unemploymen in he long-run, o which he acual unemploymen rae would converge. This view comes as a sark conras o he alernaives ha he lieraure focuses on, 17 Our measuremen of A implies a level of a he beginning of he sample, umbling laer by more han 75 percen over he nex 12 years, mos of which happened in he firs five quarers. 20

21 such as Gordon (1997) and Saiger e al. (1997, 2001). These sudies are concerned wih a naural rae concep ha relaes price pressures o a level of unemploymen ha is consisen wih consan inflaion rae. As we argued in he inroducion, here were some srucural changes in he case of Turkey, ha renders such a concep uninformaive. In his secion, we address his issue and compare our esimaes o some alernaives, including a NAIRU. Furhermore, we address some of he robusness issues of he underlying esimaion we employed, such as he normalizaion implied by γ s and γ f, as well as he exclusion resricions for he early par of he sample in he maximum likelihood esimaion. 4.1 Alernaive Naural Raes and Filers In his secion, we presen a basic comparison beween our measures of he naural rae and some alernaives proposed in he lieraure. One of hese alernaives is a NAIRU. One can also ake a differen approach and use an unobserved componens mehod wihou using he flow raes, bu insead focusing on he unemploymen rae. We will refer o his alernaive as he bivariae unobserved componens model wih unemploymen rae (UC-UR). Finally, we will also address wheher purely saisical filers could be good subsiues for our proposed naural rae. We view our approach as an alernaive ha solely relies on he daa from labor markes and he real economy in deermining long-run rend for he unemploymen rae. There is a widespread use of similar erminology in he lieraure, as nicely discussed in Rogerson (1997). Geing ino he deails of his discussion will be ou of he scope of his paper. The NAIRU esimaion akes a simple form, relaing he curren inflaion o lagged inflaion and he unemploymen gap (Gordon (1997)), using quarerly changes in headline CPI a an annualized rae for he measure of inflaion. 18 The bivariae model we have in mind is similar o he flow model, bu only uses daa onhe acual unemploymen raeand 18 More specifically, we assume ha, π = β π π 1 + β u [u ū ] + ε π, where π and u denoe acual inflaion and unemploymen rae, respecively. The naural rae, ū, follows a random walk, whereas he unemploymen gap, u c = u ū, is assumed o follow an AR (2) process; u c = θ 1 u c 1 +θ 2 u c 2+ ε u. 21

22 real oupu as in Clark (1987, 1989) and Kim and Nelson (1999). 19 In boh frameworks, one can use he Kalman filer o infer he unobserved rends in he unemploymen rae much like we do for he unobserved rends in he flow raes. Our comparison relies on hese unobserved rends, which are inerpreed as alernaive naural raes. 20 Figure 6 presens hese alernaives along wih he flow-based esimaes of he naural rae from he resriced and he exended models. Boh esimaed NAIRU and UC-UR are almos consan a around 10.5 percen over he enire sample period. 21 There is virually no variaion a all. 22 For NAIRU, i is very easy o undersand why his is he case. Turkey experienced a sharp drop in he consumer inflaion over he early par of he sample period, caused by he aggressive effors by he newly independen cenral bank ha effecively insiued an inflaion arge. This will undoubedly affec he saisical relaionship beween inflaion and he unemploymen rae, ha any NAIRU esimae will rely on. Inflaion umbled from levels of more han 60 percen per year o single digis in a relaively shor period, while unemploymen only increased modesly and sayed a hose levels for some ime. This, in urn, renders he relaive variaion in inflaion wih respec o unemploymen uninformaive. Thus, we obain a fla NAIRU. I is imporan o keep in mind ha we do no resric he unobserved NAIRU o be consan in our empirical esimaion. The bivariae model, UC-UR, also implies an almos consan naural rae over our sample period. This model explois he variaion in he observed unemploymen relaive o he cyclical changes in he real GDP o idenify he naural rae. Firs, we observe ha here are wo major episodes of business cycle conracions in our sample; he firs one 19 Oupu is modeled asin equaion(9). The observedunemploymen has cyclicaland rend componens such ha he rend componen follows a random walk and he cyclical componen depends on he cyclical componen of he real oupu, much like he flow raes. 20 Boh alernaive models are esimaed using maximum likelihood esimaion and resuls are available upon reques. 21 Though our NAIRU esimaion assumes ime-invarian parameers, we do no resric he naural rae iself o be consan over ime. 22 Us (2014) esimaes NAIRU for Turkey using ime-varian parameers, her findings is inline wih our esimaions under he consan labor force assumpion. 22

23 wihin he firs year of he sample by 6 percen and he second one coinciding wih he global recession by abou 15 percen. 23 Even hough he oupu conracions were significanly differen, unemploymen rae increases were almos idenical, by abou 70 percen, in boh episodes. Moreover, he unemploymen rae did no decline a all following he firs recession, demonsraing a loof persisence. 24 These facorsimply a consan naural rae in he UC-UR case. Our mehod, on he oher hand, can address he persisence in he unemploymen rae wihou implying a consan naural rae since we focus on he underlying flow raes, hereby easily accommodaing he non-lineariies. 25 One migh argue ha if our objecive is o derive an empirically useful unemploymen rae rend, a pure saisical unemploymen rae rend migh be more pracical, if unemploymen flows do no seem o provide us wih any addiional informaion. In order o address his issue, we focus on differen saisical filering mehods wih and wihou unemploymen flows o disinguish he role hey play. For he sake of exposiion, we focus on he resriced model. Taking an HP-filer of he unemploymen rae iself has been one approach used in he lieraure o idenify a rend for he unemploymen rae in he conex of he naural rae debae (see Rogerson (1997)). We compare our esimae of he long-run rend for he unemploymen rae wih hose ha could be obained using an HP or a bandpass filer. Figure 7 presens he resuls of his exercise. When we omi he informaion on unemploymen flows and filer he quarerly unemploymen rae (op panel), we find a lo of variaion in he rend and significan diversion across differen filers. For insance, applying an HP-filer wih a high smoohing parameer (1600) gives a relaively smooh rend ha moves closely wih he preferred rend from he flow model. However, a band- 23 Noe ha he firs recession acually sared righ before he beginning of our sample, in 2000:Q4, wih an overall peak-o-rough decline of 10 percen in real GDP. 24 Please see Cerioğlu e al. (2012) for more on he comparison of he unemploymen in wo recessions. 25 Tasci (2012) also compares a varian of our baseline model wih flows o hese alernaives on some oher dimensions, such as he precision of esimaes, required rerospecive revisions wih addiional daa, and predicion accuracy for inflaion and concludes ha he flow-based approach has several desirable properies along hose dimensions as well. 23

24 pass filer or an HP-filer wih a smaller smoohing parameer (98) produces much more variaion in he rend. The op panel also shows he well-known problem relaed o he end poins of he sample in one-sided filers. A relaively differen picure emerges if we include informaion on unemploymen flows and impue an unemploymen rae rend, as we did in he paper, based on he rends of hese underlying flows. As he lower panel of Figure 7 shows, unemploymen rends impued his way do no vary much across differen filers and are much smooher han he rend esimaes based solely on unemploymen rae informaion. Moreover, he flow model, which pus a lo more srucure on he comovemen of flows and real oupu, produces a rend ha moves closely wih hese oher filers. We inerpre his resul as evidence of he imporance of unemploymen flows in undersanding he unemploymen rae rend over he long run. The obvious discrepancy beween various esimaes of he rend wih differen filers when flows daa are ignored makes i harder o ge an empirically consisen, and oherwise useful measure. 4.2 Robusness of he Esimaion When compuing our esimae for he rend unemploymen rae, we rely on equaion (15) where we subsiue he HP filer of he variables A and ρ. We resor o his soluion because of he daa availabiliy, bu we are also mindful of is poenial impac on our resuls. Therefore, we conduc a robusness check where we model he process ha governs A and ρ in a linear AR process and analyze he effec on he rend unemploymen. Noe ha his exercise sill confines o he same model wih paricipaion bu he process ha deermines he rend componens of A and ρ are assum ed o be a produc of a process differen from a basic HP filer. The acual esimae of he rend we back ou assuming AR processes yields virually he same resul. We do no repor hem separaely o save space here 26. In principle, he resuls of our esimaion could be sensiive o he exac values of γ f 26 Resuls are available upon reques. 24

25 and γ s ha we use. In he benchmark esimaion, we use values of 0.75 for boh. These parameers conrol he relaive variaion in he cyclical componens of he flow raes wih respec o heir esimaed rends. Hence, i is reasonable o have differen implied unemploymen rae rends wih differen values. To pin down he exac numbers, we follow he approach proposed in Tasci (2012). This essenially means ha we re-esimae he model over a fine grid for boh γ f, and γ s ; γ f = {0.25,0.375,0.5,...,3.375,3.5} and γ s = {0.5,0.625,0.75,...,3.875,4}. We arge wo momens o mach: one is he maximum loglikelihood over his combinaion of poins, he oher is he maximum correlaion beween he implied naural rae from he esimaion and he rend of he observed unemploymen rae, calculaed using a bandpass filer. Since we do no use he acual unemploymen rae in he esimaion, we are rying o impose some discipline on he esimaion by no leing i diverge oo much from he daa. 27. The objecive here is o maximize he likelihood of he model wihou geing an implied unemploymen rend ha is far from a saisical rend obained by he bandpass filer. We implemen his robusness check exercise using he resriced model wih consan labor force. The effecs on he log-likelihood and he overall objecive funcion responds he same way in he exended model. Figure 8 shows how hese wo momens change across γ f and γ s. The preferred benchmark values maximize he objecive of high log-likelihood and high correlaion, which is clear from Figure 8. For insance, we do no improve he likelihood of he model for higher values of γ f, whereas smaller values do no resul in any reducion. The likelihood value seems more concave in γ f, and he preferred value of 0.75 is close o is global maximum. As γ s declines, he rend of he separaion converges o a sraigh line; hence, he naural rae will be deermined more by he rend of he job-finding rae. The opposie is rue when γ f is small and is rend is close o a sraigh line. Hence, when one flow has a consan rend imposed (low γ i ), and he oher flow has a very small cyclical variaion (high γ j,j i), we miss he low-frequency movemens in he observed unemploymen rae by 27 Noe ha wih he flow raes hemselves, he unemploymen rae does no give any more informaion for our model, hence, i is no par of i. 25

26 a significan margin. Any increase in γ s sharply reduces he correlaion of he saisical filer wih he rend esimae o he exen ha he correlaion poenially changes sign. The objecive funcion deermines he opimal rade-off beween hese wo dimensions by puing more weigh on he more informaive momen, ha is, by using he inverse of he covariance marix as he weighing marix. Finally, for almos all of he values of γ f and γ s, he naural rae implied by he model varies beween 9.5 percen and 11 percen a he end of he sample. Anoher robusness issue arises wih respec o he exclusion resricions. Recall ha, since we model mos of he rend variables as random walks, we had o sar wih a diffuse prior for he Kalman filer. The impac of he diffuse prior someimes can be subsanial for he firs few periods, as he Kalman filer does no converge on a reasonable uncondiional variance for he unobserved saes. This is usually handled by ignoring he iniial several periods in he acual esimaion - by no considering is conribuion o he log-likelihood. Since we have a very shor sample, his migh be somewha ricky and we are concerned abou poenially losing useful informaion ha he Kalman filer can infer from he likelihood funcion for he iniial daa poins, which in his case coincide wih a recession. The radeoff is beween losing valuable informaion from he firs several quarers versus geing poenially noisy esimaes for he uncondiional variance due o he diffuse prior. In order o address his, we have re-esimaed he model several imes, each ime excluding a larger number of quarers from he iniial par of he sample. Our resuls sugges ha afer 8 quarers, he esimaes for he uncondiional variance behave well. Figure 9 plos he esimaed naural raes corresponding o each exclusion case and shows hawihheexcepion ofheexcluded parofhesample, ourresuls donochangemuch. Esimaed parameers repored in Table 3 correspond o he case where he likelihood funcion ignores he firs 8 quarers. Noe ha his does no mean ha he smoohed unobserved variables we presen do no include hem. They include he firs 8 daa poins, 26

27 bu he parameer esimaes are only esimaed using he res of he daa. 5 Forecasing Performance Using flow raes provides us wih a measure of he naural rae for he Turkish economy, which in urn can help policymakers gauge he exen of he labor marke slack. Beyond providing a simple way o measure he unemploymen rae rend in a heoreically meaningful way, anoher useful feaure of his framework has recenly been highlighed by Meyer and Tasci (2013): is forecasing accuracy. Meyer and Tasci (2013) argue ha by essenially disciplining he long-run rends wih he unobserved componens mehod, his modeling framework does a remarkable job in forecasing he evoluion of he unemploymen rae in he shor- and medium-run. Since he framework heavily relies on he flow raes more han he unemploymen rae iself, i is especially very flexible in capuring he non-lineariies around he urning poins in he business cycle. We suspec ha his is even more of a concern for Turkey, where reallocaion raes are much lower relaive o U.S. levels. Moreover, he absence of high frequency, imely informaion abou he unemploymen rae provides he necessary moivaion o come up wih a good forecasing framework for Turkey 28. To evaluae he forecas performance of he framework, we esimae boh he baseline model and he exended version wih he paricipaion rae over ime saring from 2007 fourh quarer and repeaing he exercise for every quarer unil he end of For every esimaion sample, we produce wo-period ahead forecass for he unemploymen rae using he prediced flows and he observed iniial condiion for he unemploymen rae. Noe ha he models produce forecass of he flow raes inernally. However, we rely on he respecive equaion of moion for he unemploymen rae, ha is equaions (A.23) and (2). In order o gauge forecasing performance of he framework, we repor one-period and wo-period ahead roo mean squared forecas errors (RMSFE) relaive o 28 Turkish Saisical Insiue only releases unemploymen rae daa wih more han wo monhs of lag. 27

28 hose generaed from a simple ime series process for he measured unemploymen rae. In paricular, we choose an AR(2) process. 29 I is imporan o remember ha we are no running his numerical exercise wih real-ime daa. Given he changes in he daa collecion and mehodology over he sample period and he sheer lengh of he daa span (or lack hereof), repeaing his experimen in real ime seems like a fuile effor. Table 4 repors RMSFEs for one and wo-quarer ahead forecass from he wo models we used in he paper and he AR process ha does no rely on flow raes a all. As forecas errors sugges, boh models produce more accurae unemploymen rae forecass relaive o he ime series model for he forecas sample period we considered, especially a one-quarer ahead forecas horizon. This relaive improvemen in forecas accuracy over he near-erm could provide a useful ool for policymakers in Turkey. Having esablished a relaive improvemen in forecasing he unemploymen rae wih he unobserved componens models we used in he paper, we finally provide he predicions of hem condiional on he daa we have for he whole sample; 2001:Q1-2013:Q4. Figure 10 presens he forecas pahs for he exended model as well as he resriced model wih consan labor force. Regardless of he model we use, we predic a gradual decline in he unemploymen rae beyond Recall ha he model wih paricipaion implies a lower naural rae in he long-run, herefore yielding a lower pah beyond 2015 relaive o he resriced model. Unforunaely, Turkish Saisical Insiue implemened a mehodological change beginning in 2014, which made he daa prior incomparable. Neverheless, he firs quarer daa which is available confirms he forecas qualiaively, poining a decline in he aggregae unemploymen rae. 6 Conclusion We use a parsimonious unobserved componens model wih unemploymen flow raes, similar o he one used by Tasci (2012) for he U.S., o esimae a ime-varying unem- 29 The AR process we assume akes he form u = κ 1 u 1 +κ 2 u 2 +ǫ u, where daa is quarerly. 28

29 ploymen rae rend for Turkey ha is grounded in he modern heory of labor marke search. We believe ha he specific challenges presened by he Turkish daa makes i a compelling case o consider. One of hese challenges was he imporance of he paricipaion rae behavior, which we handled by exending he basic model o incorporae ime-varying labor force paricipaion. Our resuls sugges ha by he end of 2013, he naural rae for unemploymen, or he underlying rend, is hovering around 9 percen for Turkey. Models wih and wihou he paricipaion margin imply subsanially differen esimaes a he earlier pars of he sample period and he gap narrows over ime, wih he exended model feauring he paricipaion rae predicing a level slighly below 9.5 percen. This is due o a slow down in he rae of flows from inaciviy o unemploymen. More imporanly, we find ha he reallocaion rae, he sum of he inflow and ouflow raes, has been gradually rending up for Turkey suggesing an increasingly dynamic labor marke. Finally, we argue ha he modeling framework we provide here can be used for near-erm forecasing of he unemploymen rae wih relaive ease and accuracy. We are mindful of he main cavea of our paper: he sample size. Our daa covers only 13 years a quarerly frequency. However, he fac ha we have quie a bi of variaion in he variables of ineres over he sample period reassures us ha he lack of longer ime-series daa does no undermine he usefulness of our approach. In fuure work, i would be ineresing o focus on undersanding he secular increase in he reallocaion rae over ime. 29

30 References Cerioğlu, E., H. B. Gürcihan, and T. Taşkın (2012) ve 2008 Krizleri Sonrası İşsizlik Oranı Gelişmeleri. Türkiye Cumhuriye Merkez Bankası Ekonomi Noları Serisi, ( ). Clark, P. K. (1987). The Cyclical Componen of US Economic Aciviy. The Quarerly Journal of Economics 102(4), Clark, P. K. (1989). Trend Reversion in Real Oupu and Usnemploymen. Journal of Economerics 40(1), Daly, M. C., B. Hobijn, A. Şahin, and R. G. Vallea (2012). A search and maching approach o labor markes: Did he naural rae of unemploymen rise? The Journal of Economic Perspecives, Elsby, M. W., B. Hobijn, and A. Sahin (2013). On he imporance of he paricipaion margin for labor marke flucuaions. Unpublished manuscrip. Elsby, M. W., B. Hobijn, and A. Şahin (2013). Unemploymen Dynamics in he OECD. Review of Economics and Saisics 95(2), Elsby, M. W., R. Michaels, and G. Solon (2009). The Ins and Ous of Cyclical Unemploymen. American Economic Journal: Macroeconomics 1(1), Erceg, C. J. and M. A. Levin (2013). Labor force paricipaion and moneary policy in he wake of he Grea Recession. Number Inernaional Moneary Fund. Fizgerald, T. and J. P. Nicolini (2013). Is here a sable relaionship beween unemploymen and fuure inflaion? evidence from us ciies. Technical repor, Working Paper. Federal Reserve Bank of Minneapolis. Forhcoming. Fujia, S. and G. Ramey (2009). The Cyclicaliy of Separaion and Job Finding Raes. Inernaional Economic Review 50(2), Gordon, R. J.(1997). The Time-Varying NAIRU and Is Implicaions for Economic Policy. The Journal of Economic Perspecives 11(1), Kara, A. H. (2006). Turkish Experience wih Implici Inflaion Targeing. Cenral Bank of Turkey Working Paper Series (06/03). Kara, A. H. and M. Orak (2008). Enflasyon Hedeflemesi. Cenral Bank of Turkey. Rerieved from. hp:// Kim, C.-J. and C. R. Nelson (1999). Sae-space Models wih Regime Swiching: Classical and Gibbs-sampling Approaches wih Applicaions. MIT Press. Knoek, E. S. and S. Zaman (2014). On he relaionships beween wages, prices, and economic aciviy. Economic Commenary (Aug). 30

31 Meyer, B. and M. Tasci (2013). Forecasing Unemploymen in he U.S.: Use he Flow Raes, Mind he Trend. Working Paper. Morensen, D. T. and C. A. Pissarides (1994). Job Creaion and Job Desrucion in he Theory of Unemploymen. The Review of Economic Sudies 61(3), Ozbek, L. and U. Ozlale (2005). Employing he Exended Kalman Filer in Measuring he Oupu Gap. Journal of Economic Dynamics and Conrol 29(9), Perongolo, B. and C. A. Pissarides (2008). The Ins and Ous of European Unemploymen. The American Economic Review 98(2), Rogerson, R. (1997). Theory Ahead of Language in he Economics of Unemploymen. The Journal of Economic Perspecives 11(1), Sengul, G. (2014). Ins and Ous of Unemploymen in Turkey. Emerging Markes Finance and Trade (forhcoming). Shimer, R. (2012). Reassessing he Ins and Ous of Unemploymen. Review of Economic Dynamics 15(2), Saiger, D., J. H. Sock, and M. W. Wason (1997). The NAIRU, Unemploymen and Moneary Policy. The Journal of Economic Perspecives 11(1), Saiger, D., J. H. Sock, and M. W. Wason (2001). Prices, Wages, and he US NAIRU in he 1990s. In The Roaring Nineies: Can Full Employmen Be Susained. Russell Sage Foundaion. Tasci, M. (2012). The Ins and Ous of Unemploymen in he Long Run: Unemploymen Flows and he Naural Rae. FRB of Cleveland Working Paper No:12/24. Us, V. (2014). Esimaing nairu for he urkish economy using exended kalman filer approach. Cenral Bank of Republic of Turkey Working Paper Series 14/06. Weidner, J. and J. C. Williams (2011). Wha is he new normal unemploymen rae? FRBSF Economic Leer 5. 31

32 Table 1: Flow Raes u F S A Changing Labor Force (0.014) (0.022) (0.004) (0.0003) Consan Labor Force (0.022) (0.003) - Noe: Sandard deviaions are in parenheses. Table 2: Esimaion Resuls: 2001:Q1-2013:Q4 Esimae Sd Esimae Sd φ (0.2026) σ yn (0.0022) φ (0.1735) σ yc (0.0030) τ (0.0935) σ fn (0.0005) τ (0.0911) σ sn (0.0002) τ (0.0775) r ( ) θ (0.0338) θ (0.0415) θ (0.0224) Noe: Sandard deviaions are in parenheses. Log-likelihood is , γ f = 0.75, and γ s = Table 3: Esimaion Resuls: 2001:Q1-2013:Q4 Esimae Sd Esimae Sd φ ( ) µ ( ) φ ( ) µ ( ) τ ( ) µ ( ) τ ( ) σ yn ( ) τ ( ) σ yc ( ) θ ( ) σ g ( ) θ ( ) σ pn ( ) θ ( ) σ fn ( ) σ sn (0.0001) Noe: Log likelihood is Sandard deviaions are in parenheses. γ f = 0.75, and γ s =

33 Table 4: Forecas Performance: RMSFEs for 2009:Q1-2013:Q4 AR (2) in UR Resriced Model Exended Model Figure 1: Unemploymen and Paricipaion Raes (in %) Figure 2: Unemploymen Enry from Inaciviy and Paricipaion Growh Raes (in %) 33

34 Figure 3: Esimaion Resuls (Consan Labor Force) Noe: Dashed lines are rend and solid lines are acual daa. 34

35 Figure 4: Unemploymen Rae Trends - Impac of he Variable Paricipaion 35

36 Figure 5: Esimaion Resuls (Variable Labor Force) Noe: Dashed lines are rend and solid lines are original series. 36

37 Figure 6: Alernaive Naural Raes 37

38 Figure 7: Alernaive Filers - The Role of Flows 38

39 Figure 8: Robusness for γ f, and γ s Correlaion wih BP Trend for UR γ s γ f 3 4 Log Likelihood γ s γ f 3 4 Figure 9: Robusness for Exclusion Resricions 39

40 Figure 10: Forecasing Performance of Boh Models 40

41 A Appendix In his secion we lay ou he model which absracs from he variaion in he labor force in deail. This is essenially nesed in he benchmark model we presen in he main ex wih he resricion ha rho = 0, G = 0 and A = 0. Flow Raes in Resriced Model: Le us sar wih he flow raes. Since here is no change in he labor force, all flows are beween unemploymen and employmen in his resriced model. Recall ha we need he law of moion for unemploymen and he shor erm unemploymen o compue he flow raes. The law of moion for unemploymen becomes: U +τ = (L +τ U +τ )S U +τ F. (A.16) Noeha he onlydifference beween heequaion above and equaion 1 is ha heformer lacks he erm wih A. The law of moion for shor-erm unemployed, unemployed for less han five weeks is: U <1 (τ) = (L +τ U +τ )S U <1 (τ)f. (A.17) As menioned earlier, his equaion is no affeced by he assumpion regarding labor force direcly, i is he same as equaion 4. However, here F is he job finding rae. Subracing equaion (A.17) from equaion (A.16) yields: U +τ = U <1 (τ) (U +τ U <1 (τ))f. (A.18) Solving he differenial equaion above provides us wih a simple measuremen equaion for he ouflow hazard: u = e F u 1 +u <1, (A.19) where u denoes he unemploymen rae in period. This equaion is he same as 6 wih ρ = 0 and G = 0. Regardless of he assumpion on labor force, if unemploymen exi occurs wih a Poisson process wih parameer F, hen he probabiliy of exiing unemploymen wihin a monh is ˆF = 1 e F. Therefore, equaion (A.19) can be rewrien as ˆF = 1 u u <1. (A.20) u 1 The monhly ouflow probabiliy relaes o associaed monhly ouflow hazard rae, F <1 hrough he following equaion: F <1 = ln(1 ˆF ). We rely on addiional duraion daa o esimae ˆF. Based on he unemploymen daa by duraion, we can calculae he probabiliy ha an unemployed worker exis unemploymen wihin d monhs as ˆF d = 1 u u <d. (A.21) u d As before, we can calculae he ouflow raes as, F <d = ln(1 ˆF d )/d, (A.22) 41

42 for differen duraions, d = 1,3,6,9,12. We follow he procedure described in secion 2.1 o esimae ˆF. Solving equaion (A.16) and ieraing i hree monhs, we ge he evoluion of unemploymen rae in he daa, observed in discree inervals, as: S u = u 3 (1 λ )+λ, S +F (A.23) where λ = (1 e 3(S+F) ) is he quarerly convergence rae. Noe ha his is he original equaion of Elsby e al. (2013). Solving his equaion for he seady sae leads o he definiion of he flow seady sae unemploymen as follows u ss = S S +F. (A.24) Unobserved Componens in Resriced Model: Having he flow raes, we now urn o unobserved componens model. Noe ha modeling labor force does no affec he process he real oupu follows. I is given by equaion 9. Furhermore, he ime series behavior of F and S are also no direcly affeced from he assumpion regarding he labor force, and hence are given by 10 and 11, respecively. However, noe ha now inerpreaion of F is differen. F is he unemploymen exi rae (which could be exi o employmen or o inaciviy) in he benchmark model while F in resriced model is job finding rae as all exis from unemploymen mus go o employmen. Since we have ρ 0, G = 0, and A = 0 we are lef wih no oher flow rae. We can express he empirical in a convenien sae-space represenaion as [ Y F S ] = [ ] τ 1 τ 2 τ θ 1 θ 2 θ ȳ y 0 φ 1 φ y 1 y = r f s ȳ y y 1 y 2 r f s ȳ 1 y 1 y 2 y 3 r 1 f 1 s ε fc, (A.25) ε sc + ε yn ε yc 0 0 ε r ε fn ε sn, (A.26) where all error erms come from an i.i.d. normal disribuion wih zero mean and variance σ i, such ha i = {yn,yc,r,fn,fc,sn,sc}. As in he exended model wih variable paricipaion, we use he Kalman filer o filer he unobserved componens and wrie he log-likelihood funcion o esimae he model via maximum likelihood. Once we esimae he model, we use he Kalman smooher o infer unobserved sochasic rend and cyclical componens over ime. These ime-varying rend 42

43 esimaes for he flow raes, f and s, deermine he unobserved unemploymen rae rend over ime. More specifically, our definiion of he long-run rend for he unemploymen rae is given by ū = s s + f, (A.27) which is consisen wih he search heory of he labor marke. Figure A.11: Unemploymen Rae wih Variable Labor Force Figure A.12: Flow Raes of Differen Models 43