UNEMPLOYMENT FLOWS, PARTICIPATION AND THE NATURAL RATE FOR TURKEY

Transcription

1 KOÇ UNIVERSITY-TÜSİAD ECONOMIC RESEARCH FORUM WORKING PAPER SERIES UNEMPLOYMENT FLOWS, PARTICIPATION AND THE NATURAL RATE FOR TURKEY Gonul Sengul Mura Tasci Working Paper 1404 February 2014 This Working Paper is issued under he supervision of he ERF Direcorae. Any opinions expressed here are hose of he auhor(s) and no hose of he Koç Universiy-TÜSİAD Economic Research Forum. I is circulaed for discussion and commen purposes and has no been subjec o review by referees. KOÇ UNIVERSITY-TÜSİAD ECONOMIC RESEARCH FORUM Rumelifeneri Yolu Sarıyer/Isanbul

2 Unemploymen Flows, Paricipaion and he Naural Rae for Turkey Gonul Sengul Mura Tasci Cenral Bank of Turkey Federal Reserve Bank of Cleveland February 7, 2014 Absrac This paper measures flow raes ino and ou of unemploymen for Turkey and uses hese raes o esimae he unemploymen rae rend, ha is he level of he unemploymen rae he economy converges o in he long-run. In doing so, he paper explores he role of he labor force paricipaion in deermining he rend unemploymen. We find an inverse V-shaped paern for he unemploymen rae rend over ime in Turkey, currenly sanding beween 8.5 and 9 percen, wih an increasing labor marke urnover. We also find ha allowing for an explici role for paricipaion changes he resuls subsanially, reducing he naural rae a firs, bu hen geing closer o he baseline over ime. Finally, we show ha his parsimonious model can be used for forecasing unemploymen in Turkey wih relaive ease and accuracy. 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 seminar a he Isanbul School of Cenral Banking, he Turkish Labor Marke Research Nework Conference, and he Inernal Conference of he Cenral Bank of he Republic of Turkey. Isanbul School of Cenral Banking, Cenral Bank of he Republic of Turkey. Gonul.Sengul@cmb.gov.r. ResearchDeparmen, FederalReserveBankofCleveland. Mura.Tasci@clev.frb.org 1

3 1 Inroducion The rae of unemploymen in he long-run, or he underlying rend, has araced a lo of aenion since he Grea Recession. In an environmen where a lo of developed counries as well as developing ones face excepionally high levels of unemploymen, policy makers and economiss focused on idenifying he level of he unemploymen rae ha is feasible in he long-run, i.e. he naural rae, o gauge he exen of he labor marke slack. In an effor o face his challenge, recen sudies approached he problem by esimaing he unemploymen rae rend using he underlying flow raes. For insance, Tasci (2012) uses daa on flows beween employmen and unemploymen and, in he conex of he U.S. labor markes, argues ha his mehod provides an esimae of he naural rae ha has several desirable saisical feaures while being heoreically very close o he language of he modern heory of unemploymen. In his paper, we adop his mehodology o esimae he naural rae of unemploymen for Turkey. We believe ha his exercise no only is valuable in is own righ, bu also allows us o highligh usefulness of he approach aken by Tasci (2012) in he face of ineresing challenges posed by various srucural issues experienced by many economies. For insance, many developing counries, Turkey included, have a very limied daa span ha covers subsanial changes in he aggregae economy. Turkey has gone hrough significan changes in he moneary policy environmen followed by a sharp decline in inflaion in he early 2000s. 1 The radiional approach of esimaing a naural rae by focusing on he relaionship beween he labor marke variables and he price level, ha is NAIRU, will no necessarily inform us abou he underlying dynamics of he Turkish labor marke. Secion 4.1 shows ha naural rae esimaes exraced using he NAIRU mehod imply an almos invarian level of unemploymen, which is he average of he sample period, while our mehod reveals variaion over ime. Moreover, our mehod implies recen values of he naural rae of unemploymen ha are below he sample period average. Moreover, he mehod developed by Tasci (2012) is flexible enough o be modified o incorporae differen labor marke srucures of economies. As such, when we implemen he same approach for Turkey, we need o ake ino accoun he ac- 1 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 he moneary policy in Turkey. 2

4 ive role of he paricipaion margin in he labor marke. The role of paricipaion rae in esimaing he long-run rend for unemploymen becomes very eviden in he Turkish daa, a counry whose paricipaion rae is hree imes more volaile hen he U.S. s (see Sengul (2014)). Using flow raes o idenify a rend rae for unemploymen provides us wih a way o carefully address he problem in a counry where he persisence in unemploymen is quie differen from a developed counry, where labor markes are relaively more dynamic. Building on Tasci (2012), we esimae he unemploymen rae rend for Turkey from 2001 o 2012, exending he mehodology o include labor force paricipaion. In doing so, we also exploi he work by Sengul (2014), which esimaes monhly flow raes from 2005 o 2012 for Turkey, including he flows from nonparicipaion o unemploymen. We firs esimae quarerly flow raes from 2001 o 2012, following Sengul (2014). 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, ha is he naural rae, implied by he seady sae descripion of he unemploymen rae in a sandard labor marke search model ha relies on hese flow raes. Our resuls show a disinc paern for he rend unemploymen. As such, he rend unemploymen increases during he firs wo hirds of he sample period, and hen sars declining, which occurs afer he recession. This paern holds regardless of allowing for a ime varying labor force paricipaion explicily. However, wih an explici role for labor force paricipaion, he esimaed unemploymen rend says significanly below he level implied by he baseline, where we assume a consan paricipaion rae over ime. Moreover, we find ha his paern is led by a similar paern by he inflow rae ino unemploymen - firs increasing and hen declining by and a secular rise in he ouflow rae from unemploymen over he whole sample. Taken ogeher, hese findings imply ha Turkish labor markes look a lo more dynamic a he end of 2012 relaive o We also highligh anoher poenially useful feaure of our framework; improving unemploymen forecas accuracy in he shor erm, even hough i is no designed for his purpose. In a counry where unemploymen daa releases lag by more han wo monhs, his is an imporan addiional benefi of he framework discussed in he paper. The res of he paper proceeds as follows: In he nex secion, we lay ou 3

5 he baseline model wih he assumpion ha labor force paricipaion does no move over ime. Afer describing he mehodology for measuremen of he flow raes and he esimaion of he rends, we exend he baseline model o incorporae variaions in he paricipaion rae in Secion 3. Secion 4 presens 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. 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 Baseline Model We firs presen our approach for idenifying an unemploymen rend for Turkey under he simplifying assumpion ha workers can only move beween wo labor marke saes, employmen and unemploymen, and he labor force paricipaion does no move beween wo consecuive periods. These simplificaions no only allow us o implemen he approach proposed in Tasci (2012) for Turkey wih relaive ease, bu also illusraes he main ideas behind our mehodology in a simpler way. Laer in Secion 3, we exend he model o include movemens in and ou of he labor force, hough he basic premise of using underlying flow raes and a measure of he business cycle o disinguish he cyclical movemens from he rend flucuaions in unemploymen is common in boh cases. Following Tasci (2012), we wrie down a simple reduced form unobserved componens model ha incorporaes he comovemen of flows ino and ou of unemploymen ino previous aemps a esimaing he naural rae, such as Clark (1987, 1989) and Kim and Nelson (1999). The reduced form model assumes ha real GDP - or any oher measure of he aggregae business cycle - has boh a sochasic rend and a saionary cyclical componen, where only real GDP is observed by he economerician. We also assume ha boh unemploymen ouflow and inflow raes (F and S, respecively) have a sochasic rend as well as a saionary cyclical componen. Furhermore, he sochasic rend follows a random walk, bu he cyclical componen in he flow raes depends on he cyclical componen ofreal GDP.More specifically, le Y belog real GDP, ȳ beasochasic rend componen, and y be he saionary cyclical componen. Similarly, le F (S ) be he quarerly ouflow (inflow) rae, f ( s ) be is sochasic rend componen, and f (s ) be is saionary cyclical componen. Then we consider he following 4

6 unobserved componens model: Y = ȳ +y, y = φ 1 y 1 +φ 2 y 2 +ε yc, ȳ = r 1 +ȳ 1 +ε yn, r = r 1 +ε r, (1) where r is a drif erm in sochasic rend componen of oupu, which is also a random walk, and cyclical componen of oupu follows an AR(2) process, as in Ozbek and Ozlale (2005). The ime series behavior of flow raes similarly 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, (2) and S = s +s, s = s 1 +ε sn, s = θ 1 y +θ 2 y 1 +θ 3 y 2 +ε sc. (3) We assume ha all he error erms are independen whie noise processes. As equaions (2) and (3) show, we also assume ha he cyclical componen of he inflow and ouflow 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. 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). We are agnosic abou he exisence of any co-movemen beween 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 away from i as, given he shor sample we are working wih, any more complicaion in he form of anoher 5

7 laen variable will subsanially reduce he precision of he esimaes we ge in his unobserved componens model. Tasci (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 long-run maching efficiency of he labor markes, which will be more imporan in deermining he seady sae of unemploymen. One can express he empirical model laid ou in equaions (1) hrough (3), in a convenien sae-space represenaion as Y F S y y 1 0 = 0 τ 1 τ 2 τ y 2 + ε fc, (4) 0 θ 1 θ 2 θ r ε f sc s ȳ y 0 φ 1 φ y y 2 = r f s ȳ ȳ 1 y 1 y 2 y 3 r 1 f 1 s 1 ε yn ε yc 0 + 0, (5) ε r ε fn 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}. We use he Kalman filer o filer he unobserved componens and wrie he log-likelihood 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. These ime-varying rend 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 ε sn ū = s s + f, (6) 6

8 which is consisen wih he search heory of he labor marke. Tasci (2012) inerpres he unemploymen rae rend expressed in (6) 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 unemploymen in he long run, o which he acual unemploymen rae would converge. The inuiion behind his equaion as well as how we measure he observed flow raes, F and S, are described in he following subsecion. Before proceeding o compuaion of he flow raes, we would like o discuss an issue ha needs o be ackled in esimaing he model. The model, as spelled ou in equaions (4)-(5), has hree observable series and seven 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 Compuing he Flow Raes Firs sep in esimaing our measure for he rend unemploymen requires us o obain quarerly flow raes, F and S. There is now an exensive lieraure on he imporance of he flow raes in accouning for unemploymen flucuaions. 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)). In paricular, we follow he mehodology presened in Elsby e al. (2013), which focuses on compuing flow raes for a sample of he OECD counries. They exend he earlier work, as in Shimer (2012) and Elsby e al. (2009) o explicily accoun for low flow hazard raes as no doing so will bias he esimaes of he flow raes in some of he counries in heir sample. In wha follows, we assume ha ime is coninuous, and he daa is available a discree monhs. Hence, period refers o he inerval [,+1). Le L +τ, U +τ, and U <1 (τ) be he number of labor force, he number of unemployed, and he number of unemployed for less han 5 weeks a ime +τ, respecively. In his secion we assume ha all worker ransiions are from unemploymen 7

9 ino and ou of employmen. People become unemployed because hey separae from heir employmen and leave unemploymen because hey find a job. Le S and F be he job-separaion (inflow) and job-finding (ouflow) raes during period. We can wrie he law of moion for unemploymen as follows: U +τ = (L +τ U +τ )S U +τ F. (7) Solving equaion (7) 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, (8) S +F 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. (9) If here is a rend in he underlying flow raes, hen we ge he expression in equaion(6) as he ime-varying rend esimae of he unemploymen rae. This simple accouning framework forms he foundaion of he measuremen exercise, which relies heavily on exploiing he changes in he sock of unemployed a differen duraions across ime o infer he high-frequency flow raes. To compue he flow raes, we also need he law of moion for shor-erm unemployed, unemployed for less han five weeks, which is: U <1 (τ) = (L +τ U +τ )S U <1 (τ)f. (10) The change in he number of shor-erm unemployed consiss of workers separaing from heir jobs and workers who became unemployed afer he las ime daa were available and did no leave unemploymen, respecively. Subracing equaion(10) from equaion (7) yields: U +τ = U <1 (τ) (U +τ U <1 (τ))f. (11) Solving he differenial equaion above provides us wih a simple measuremen 8

10 equaion for he ouflow hazard: where u denoes he unemploymen rae in period. u = e F u 1 +u <1, (12) 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 (12) can be rewrien as ˆF = 1 u u <1. (13) u 1 The inuiion behind (13) is ha we infer he average ouflow probabiliy, jobfinding probabiliy, by measuring he size of he decline in he unemploymen pool who is a no shor-erm unemployed. The monhly ouflow probabiliy relaes o associaed monhly ouflow hazard rae, F <1, hrough he following equaion: F <1 = ln(1 ˆF ). (14) Equaion (13) 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 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 As before, we can calculae he ouflow raes as ˆF d = 1 u u <d. (15) u d F <d = ln(1 ˆF d )/d, (16) 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 unem- 9

11 ploymen, hen F <d for differen values of d would no be much differen from each oher, and we have 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. 2 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 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. Once, we compue F, we use equaion (8) and daa on u o back ou he inflow rae S. 2.2 Daa and Esimaion Resuls Before discussing he resuls, we describe our daa sources and he reamens we have o implemen o address some concerns before geing he desired flow raes a a quarerly frequency. We hen presen our resuls for he baseline model. The daa used in esimaing he flow raes is from he Turkish Saisical Agency (TurkSa). 3 We have quarerly daa from 2000:Q1 o 2012:Q4 on he number of workers in he labor force, and unemployed persons for less han d monhs, where d {1,3,6,9,12}. 4 Unforunaely, he 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, due o a change in populaion projecion mehods. 5 TurkSa updaed quarerly daa unil 2005:Q1 and yearly daa unil To correc he daa prior o 2005, we make use of he availabiliy of unadjused quarerly and 2 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. 3 For more informaion go o hp:// 4 d = 1 corresponds o he number of workers unemployed for less han five weeks and his daa is provided by TurkSa upon reques. 5 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. 10

12 adjused 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 and he average of he new quarerly daa for 2004 is he same as he adjused 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. 6 To correc for his, we assume ha he growh rae of he share of unemployed wih a duraion of d monhs among all unemployed from 2003:Q4 o 2004:Q1 is he average 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. 7 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. Finally, we also use he aggregae real GDP daa from he TurkSa. 8 Table 1: Flow Raes u F S (0.014) (0.022) (0.003) Noe: Sandard deviaions are in parenheses. Once we make necessary adjusmens o he daa, we compue he aggregae flow raes following our discussion in he preceding secion. Table 1 presens he basic momens of he daa. Average unemploymen in Turkey has been abou 6 This break may resul from sample redesign in 2004, which may have allowed a beer measuremen of unemploymen wih differen duraions. 7 There wasalsoan anomalyin he unemployedfor 6-7monhs daa for2003:q2and 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. 8 Expendiure based, in 1998 prices. 11

13 10.5 percen over our sample 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 as we have here. 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 also look a how he compued flow raes move wih he GDP. To compare our resuls wih oher sudies, we use cyclical componens exraced using HP filer. 9 As expeced, we see ha unemploymen is counercyclical and persisen (Table 2). The unemploymen rae in Turkey is more counercyclical and less persisen compared wih he U.S. daa. 10 The unemploymen exi rae is persisen and procyclical while he enry rae is counercyclical and no as persisen. Shimer (2005) shows ha unemploymen and exi raes are negaively correlaed wih labor produciviy while job-finding rae is posiively correlaed for he U.S. Though cyclical properies of flow raes for Turkey are qualiaively similar o hose of he U.S., here is more persisence in he U.S. daa compared o he flow raes in Turkey. Table 2: Business Cycle Properies GDP F S u σ σ/σ Y corr(x,y) corr(x,x 1 ) Noes: All series are quarerly and are log-derended wih HP filer and a smoohing parameer of 98. Sandard deviaions are in absolue erms. is significance a %1 and is significance a %10. Using he flow raes described above, we esimae he model expressed in (4)- 9 We se he smoohing parameer o 98, as suggesed by Alp e al. (2011). 10 Shimer (2005) repors ha he correlaion beween unemploymen and produciviy is and he quarerly auocorrelaion of unemploymen is

14 (5) via maximum likelihood. The poenial idenificaion issue appears o be no 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 ha he drif erm for he rend oupu for his ime-period in Turkey 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 an average of 4.9 percen annualized quarerly growh rae for he rend oupu. The normalizaion we find o be opimal for he flow raes in his baseline 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 follows Tasci (2012) and is explained in deail in Secion 4. Table 3: Esimaion Resuls: 2001:Q1-2012:Q4 Esimae Sd Esimae Sd φ (0.2379) σ yn (0.0024) φ (0.1881) σ yc (0.0034) τ (0.1104) σ fn (0.0005) τ (0.1022) σ sn (0.0002) τ (0.0879) r ( ) θ (0.0448) θ (0.0643) θ (0.0355) Noes: Log-likelihood is , γ f = 0.75, and γ s = Sandard deviaions are in parenheses. 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, iniiaing 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 he firs eigh quarers of he daa in our esimaion. We discuss he poenial effecs of his exclusion resricion in Secion 4. In Figure 1, 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 13

15 upper panel of Figure 1 shows ineresing changes in he underlying rends for he flow raes. In paricular, he ouflow rae, a which an average unemployed would find a job in a 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 Figure 1: Esimaion Resuls (Consan Labor Force) Noe: Dashed lines are rend and solid lines are acual daa. 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 14

16 S reinforced he decline in he unemploymen rae rend ha is implied by he gradual increase in he ouflow rae 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 unemploymen rae. Figure 2: Variance Decomposiion (Consan Labor Force) Noe: In he lower panel, he solid line shows he movemen of he naural rae, given he ime series of rend flow raes. Dashed lines show he pah he naural rae would have followed if he rend job-finding rae would have sayed consan a is mean and he rend separaion rae would have followed is acual pah. Similarly, he doed line shows he conribuion of he rend job-finding rae o he rend unemploymen rae. Our framework also lends iself o analyzing he conribuions of differen flows o he flucuaions in he unemploymen rae, boh a business cycle frequency and over he long-run. The flow model laid ou in he previous secion gives us he esimaes of cyclical and rend componens in he underlying flow raes, 15

17 hereby enabling us o ease ou he paricular flow ha drives unemploymen flucuaions over he business cycle, as well as in he long-run. Hence, in principle, one can use a similar decomposiion used in Fujia and Ramey (2009) o sudy he conribuion of each flow rae o variaions in he unemploymen rae, boh a he high and he low frequency. Figure 2 shows resuls of decomposing he variance of rend and cycle unemploymen rae o variaions from inflows and ouflows. Trend unemploymen is he unemploymen rae compued using rend flow raes and equaion (9). Conribuions of each rend flow rae o variaion in naural rae is compued using he seady sae unemploymen formula and he average of he rend of he oher flow rae. Then, series are demeaned and ploed for ease of display purposes. The lower panel of Figure 2 shows he decomposiion resul for he rend unemploymen rae. As discussed earlier, we observe ha changes in he rend of he ouflow rae pushes down he long-run unemploymen rend hroughou he sample period, hough he effec is weaker in he laer pars. The separaion rae, on he oher hand, conribued owards increasing he naural rae of unemploymen unil he end of he las crisis, and hen, hrough a decline in is rend, sared o have a dampening effec on he unemploymen rae rend. Hence, as a resul of offseing effecs, we observe a relaively sable unemploymen rae rend unil he end of 2009, followed by a decline in he long-run rae. Analyzing he upper panel of Figure (2), we see ha variaions in he separaion rae capures mos of he small movemens in he cyclical componen of he unemploymen rae. Hence, variaions in inflows in he shor-run are more relevan for he movemens in cyclical unemploymen, while rends in boh flow raes are imporan in deermining he underlying unemploymen rae rend. 3 Model wih Paricipaion We now exend he unobserved componens model described in he previous secion o allow for variaions in he labor force paricipaion rae. We rely on he aggregae daa in his secion as well, since micro household daa for Turkey is only available annually. We are also limied in our abiliy o disinguish beween exis from unemploymen ino employmen or ino inaciviy, due o lack of daa availabiliy a a high frequency. However, since he focus of he paper is o measure and esimae he flows ino and ou of unemploymen, we do no need o 16

18 have specific informaion abou he naure of he exi from unemploymen per se. In he nex subsecion, we describe how o incorporae he change in he labor force ino he esimaion of flow raes. Then, we describe he exended unobserved componens model ha now allows for ime variaion in he labor force paricipaion. 3.1 Measuremen of Flow Raes wih Paricipaion Our firs ask is o consruc he flow raes when one allows for poenial changes in he paricipaion rae. We follow he mehod used in Sengul (2014), which exends he mehod used by Elsby e al.(2013)(described in he previous secion), o allow for changes in labor force. 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, P +τ = G P +τ, respecively, where P +τ is he paricipaion rae (P +τ = L +τ /N +τ ). Furhermore, lea denoehefracionofheinacivepopulaion(n +τ L +τ ) ha decide o look for a job. We can wrie he law of moion for unemploymen as follows: U +τ = (L +τ U +τ )S U +τ F +(N +τ L +τ )A. (17) Noe ha he equaion above is he same as equaion (7), excep for he las erm. However, he inerpreaion of F is differen. In his exension of he model, F capures he flows ou of 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. In equaion (7), F was he job-finding rae, as exi from unemploymen can only be ino employmen under he baseline model. We solve he equaion (17) and ierae i hree monhs o ge he evoluion of 17

19 he unemploymen rae based on observed daa in discree inervals as: u = u 3 (1 λ )+ λ (S A ) + A (1 e 3(S+F+ρ) ), (18) S +F +ρ +g P (S +F +ρ ) where λ = (1 e 3(S+F+ρ+G) ) is he quarerly convergence rae. Noe ha if G = 0 and ρ = 0 (and hence A = 0), in oher words if we assume ha he labor force is consan, we ge he original equaions of Elsby e al. (2013), which is equaion (8) in he previous secion. Noe furher ha he effec of paricipaion on law of moion for unemploymen has wo channels. Firs is ha now we have o accoun hrough A for inacive populaion who sar looking for a job, and hence become unemployed. Also, we have o ake ino accoun ha paricipaion also changes he size of he labor force. as One can use equaion (18) and wrie he flow seady sae unemploymen rae u ss = (S A ) + A (1 e 3(S+F+ρ) ). (19) S +F +ρ +G P (S +F +ρ )λ Noe ha he law of moion for he shor-erm unemployed, ha is unemployed for less han five weeks becomes U <1 (τ) = (L +τ U +τ )S U <1 (τ)f +(N +τ L +τ )A. (20) Also noe ha subracing equaion (20) from equaion (17) resuls in U +τ = U <1 (τ) (U +τ U <1 (τ))f. (21) Hence, adding he inaciviy sae o he model does no change he law of moion for he number of he shor-erm unemployed, given he difference in inerpreaion of F. However, 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: u = e F ρ G u 1 +u <1. (22) Assuming unemploymen exi occurs wih a Poisson process wih parameer F, he probabiliy of exiing unemploymen wihin a monh is ˆF = 1 e F. There- 18

20 fore, equaion (22) can be rewrien as ˆF = 1 u u <1. (23) e G ρ u 1 Noice ha ρ + G is he labor force growh rae, as labor force varies due o changes in populaion and he paricipaion decisions. Hence, we modify our inerpreaion of he change in he pool of unemployed who are no shor erm unemployed, o ake ino accoun he change in he size of he labor force as well, in order o ge he average ouflow probabiliy. As saed previously, his las equaion does no work well for counries wih average unemploymen duraions ha are long, like Turkey. We follow Sengul (2014) and use addiional duraion daa o increase he precision of he esimae of ˆF. Basedonheunemploymen daabyduraion, wecancalculaeheprobabiliy ha an unemployed worker exis unemploymen wihin d monhs as As before, we can calculae he ouflow raes as ˆF d u u <d = 1 e d 1. (24) j=0 (G j+ρ j ) u d for d = 1,3,6,9,12. F <d = ln(1 ˆF d )/d, (25) Once again, before esimaing he model, we formally es he duraion dependence by esing he hypohesis ha F <1 = F <3 = F <6 = F <9 = F <12. We use he same procedure as in he previous secion and rejec he hypohesis ha here is no duraion dependence. 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 (18) gives us he separaion rae daa. 3.2 Unobserved Componens wih Paricipaion Margin Dueohelenghofoursampleandheaddiionalnumberofparameershaarise wih an addiional variable in our unobserved componens model, we canno fully model all he raes ha deermine he seady sae unemploymen rae. Hence, we need o make some assumpions. We begin by assuming ha he populaion 19

21 growh ρ has a rend and a cycle ha are independen of he GDP, and we idenify hese componens using HP filer. 11 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 (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. We keep he way we model Y, F, and S as in he previous secion, described inequaions(1)-(3). Wecomplemen hemodel wihheparicipaionraeashe fourh observable, where i has 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 (26) g = g 1 +ε g As in he previous secion, all he error erms are independen whie noise processes and we use he Kalman filer o find he rend componens. The full exended model described by equaions (1), (2), (3), and (26) can be represened in a sae-space represenaion in he following way: Y F S P y y = 0 τ 1 τ 2 τ y 2 0 θ 1 θ 2 θ r ε fc + ε sc, (27) g 0 µ 1 µ 2 µ ε pc p f s 11 We also fi an AR process o he populaion growh and see ha rend we exrac does no change much. ȳ 20

22 ȳ y 0 φ 1 φ y y r = g p f s ȳ 1 y 1 y 2 y 3 r 1 g 1 p 1 f 1 s 1 ε yn ε yc ε r. (28) ε g ε pn ε fn Similar o our approach for he baseline model, we esimae his exended version wih maximum likelihood and use he Kalman filer o infer he unobserved rend and cyclical componens. Then, we ge 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 + ā(1 e 3( s+ f+ ρ) ) + ρ +g p ( s + f, (29) + ρ ) λ 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. ε sn 3.3 Daa and Esimaion Resuls In addiion o he daa described in he previous secion, we make use of he daa on unemploymen by reason o consruc A series. Ideal compuaion would require daa on labor marke ransiions of enrans who will be unemployed for lesshanonemonh. TheraioofhispooloheinacivepopulaionwouldbeA. 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 Ue,<3 U <1, 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 U e,<3 U <3 Hence, we compue A as U <1 and we have daa for he righ-hand side of his approximaion. U e,<3 /(N U <3 L ). 21

23 We begin wih he descripion of he flow raes under he assumpion ha measuremen akes ino accoun variaion in he labor force paricipaion over ime. Table 4 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. Table 4: 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. We also documen he cyclical properies of hese flow raes in Table 5. Wih his measuremen, we now inerpre S and A ogeher as flows ino unemploymen, whereas S is he separaion from employmen o unemploymen. Inflow raes esimaed under he exended model show differen business cycle frequency feaures han he baseline. Due o he significanly procyclical naure of he inflows o unemploymen, we obain a somewha less counercyclical S in he curren measuremen. We see ha paricipaion rae does no have a significan cyclical behavior. However, wih longer daa available a an annual frequency Baskaya and Sengul (2014) show ha he paricipaion rae is counercyclical, which cauions he findings regarding he cyclical behavior wih a relaively shor sample. Table 5: Cyclical Properies (Changing Labor Force) GDP F S A g ρ P u σ σ/σ Y corr(x,y) corr(x,x 1 ) Noes: y is he GDP while x is he variable of ineres. Growh rae series are derended while all oher series are log-derended wih an HP filer. ( ): significance a 1%, ( ): significance a5%. Resuls for he esimaion of he exended model wih paricipaion are displayed in Table 6. Some of he individual parameer esimaes lose significance, 22

24 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. Table 6: Esimaion Resuls: 2001:Q1-2012: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 = 0.75 Our esimaes of he model wih varying labor force sugges ha he impac on he unemploymen rae could be subsanial. Figure 3 plos he unemploymen rae rend from he baseline 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 hedifference issmaller owardsheendofhesample. Forinsance, weobserve as much as a 2 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. The main reason behind he divergence beween wo alernaive rend esimaes in he early par of he sample is he behavior of he flows from he inacive populaion direcly ino he unemploymen pool, A. 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. One possible inerpreaion is ha a he early pars of he sample period here is a movemen from inaciviy o unemploymen, which implies a naural rae 23

25 Figure 3: Unemploymen Rae Trends - Impac of he Variable Paricipaion wih variable paricipaion rae ha is very differen from he one wih consan paricipaion. As A declines, ha is as flows from inaciviy o unemploymen slow down, we see he gap beween wo naural raes closing. However, we suspec ha par of he decline we observe in A could be a measuremen problem in he household survey, or an exraordinary response by he non-paricipans o he firs major recession in our sample. We do no have a convincing way o isolae one or he oher. In any case, he absence of he abnormal behavior in A laer on and he apparen convergence beween he wo alernaives sugges ha his channel is no longer as imporan. Moreover, he implied naural rae wih a varying paricipaion rae is lower han he one implied by he baseline model. However, heir overall paern hroughou he sample, including he urning poins, align very closely wih each oher. Figure 4 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 baseline 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. 24

26 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. Figure 4: Esimaion Resuls (Variable Labor Force) Noe: Dashed lines are rend and solid lines are original series. When compuing our esimae for he rend unemploymen rae, we rely on equaion (29) where we subsiued 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 conduced a robusness check where we model he process ha governs A and ρ in a more simple linear AR process and analyzed 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 assumed 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 Resuls are available upon reques. 25

27 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, 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, suchashenormalizaionimpliedbyγ s andγ f, aswell asheexclusion 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. The NAIRU esimaion akes a simple form, relaing he curren inflaion o lagged inflaion and he unemploymen gap (Gordon (1997)), where we use quarerly changes in headline CPI a an annualized rae for he measure of inflaion. 13 The bivariae model we have in mind is similar o he flow model, bu 13 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 1u c 1 +θ 2u c 2 + ε u. 26

28 only uses daa on he acual unemploymen rae and real oupu as in Clark (1987, 1989) and Kim and Nelson (1999). 14 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. 15 Figure 5: Alernaive Naural Raes Figure 5 presens hese alernaives along wih he flow-based esimaes of he naural rae from he baseline and he exended models. Boh esimaed NAIRU and UC-UR are almos consan over he sample period a around 10.5 percen. There is virually no variaion a all. 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 14 Oupu is modeled as in equaion (1). The observed unemploymen has cyclical and 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. 15 Boh alernaive models are esimaed using maximum likelihood esimaion and resuls are available upon reques. 27

29 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 consan NAIRU. The bivariae model, UC-UR, also implies a 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 wihin he firs year of he sample by 6 percen and he second one coinciding wih he global recession by abou 15 percen. 16 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, showing a lo of persisence. 17 These facors imply 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. 18 One migh argue ha if our objecive is o derive an empirically useful unemploymen rae rend, a pure saisical rend of he unemploymen rae 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 baseline 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 6 presens he resuls of his exercise. When we omi he informaion on unemploymen flows and filer he quarerly unem- 16 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. 17 Please see Cerioğlu e al. (2012) for more on he comparison of he unemploymen in wo recessions. 18 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. 28

30 ploymen 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 bandpass 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. Figure 6: Alernaive Filers - The Role of Flows A relaively differen picure emerges if we include informaion on unemploymen flows andimpue anunemploymen raerend, aswe did inhe paper, based on he rends of hese underlying flows. As he lower panel of Figure 6 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 29

31 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 In principle, he resuls of our esimaion could be sensiive o he exac values of γ f 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 log-likelihood 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. 19. 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. Figure7shows 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 7. 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 19 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. 30

32 Figure 7: Robusness for γ f, and γ s Correlaion wih BP Trend for UR Log Likelihood γ s γ f 3 4 γ s γ f 3 4 rae by 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 worried 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 31

33 Figure 8: Robusness for Exclusion Resricions 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 8 plos he esimaed naural raes corresponding o each exclusion case and shows ha wih he excepion of he excluded par of he sample, our resuls do no change much. 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, bu he parameer esimaes are only esimaed using he res of he daa. 5 Near-Term Prospecs 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 32

34 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 20. To evaluae he forecas performance of he framework, we esimae boh he baseline model and he exended version wih 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 (8) and (18). 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 hose generaed from a simple ime series process for he measured unemploymen rae. In paricular, we choose an AR(2) process. 21 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 7: Forecas Performance: RMSFEs for 2007:Q4-2012:Q4 AR (2) in UR Baseline Model Exended Model Turkish Saisical Insiue only releases unemploymen rae daa wih more han wo monhs of lag. 21 TheAR processweassumeakeshe formu = κ 1 u 1 +κ 2 u 2 +ǫ u, wheredaaisquarerly. 33

35 Table 7 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. Figure 9: Forecasing Performance of Boh Models 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:Q1-2012:Q4. Even hough our sample ends by he end of 2012, we have acual unemploymen raes unil he end of Augus Hence, we have hree quarers of daa o compare he real-ime forecass from he models. Figure 9 presens he forecas pahs for he baseline model as well as he exended model wih paricipaion. Regardless of he model we use, we predic a sligh increase in he unemploymen rae beyond 2012, which has been confirmed given he daa for he firs hree quarers of Recall ha he model wih paricipaion implies a lower naural rae in he long-run, herefore is higher levels of unemploymen 34