Dual labour markets with search costs

Transcription

1 Inernaional Labour Organizaion European Union Inernaional Insiue for Labour Sudies Dual labour markes wih search coss EC-IILS JOINT DISCUSSION PAPER SERIES No. 7

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3 DUAL LABOUR MARKETS WITH SEARCH COSTS

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5 DUAL LABOUR MARKETS WITH SEARCH COSTS INTERNATIONAL LABOUR ORGANIZATION INTERNATIONAL INSTITUTE FOR LABOUR STUDIES

6 Absrac This paper is par of a series of discussion papers ha have been prepared by he Inernaional Insiue for Labour Sudies IILS) wihin he framework of he join projec Addressing European labour marke and social challenges for a susainable globalizaion, which has been carried ou by he European Commission EC) and he Inernaional Labour Organizaion ILO). The discussion paper series provides background informaion and in-deph analysis for wo concluding synhesis repors ha summarize he main findings of he projec. This paper relaes o firs par of he projec Addressing he shor- and medium-erm labour marke and social challenges of he curren economic and financial crisis and he concluding synhesis repor Building a susainable job-rich recovery. General equilibrium models wih non-compeiive labour marke accouning for he dynamics of wages and employmen have become increasingly used. For he mos par, however, hese general equilibrium models have been applied o advanced economies while he case of developing economies wih dual labour marke has been mainly addressed in parial equilibrium framework. This paper models an economy wih an informal labour marke along he line of he search and maching framework and revisis hree main issues. The firs issue is he dynamics of he informal secor over he business cycle. The second issue is he impac of informaliy on economic volailiy. A hird issue is he exen o which he ineracion beween dual labour markes modifies he sandard properies of search models.

7 TABLE OF CONTENTS Main findings 1 1 Inroducion 2 2 The Model 4 Unemploymen, Vacancies and Maching Households Firms Nash bargaining in he formal labour marke Labour marke ransiion and macro closure Equilibrium condiions Numerical simulaions 16 Calibraion Comparaive saics Dynamics Conclusion 23 i

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9 DUAL LABOUR MARKETS WITH SEARCH COSTS Main findings This paper develops a model of an economy wih dual labour markes o undersand he dynamics of he informal secor over he business cycle, as well as o analyze he implicaion of dualiy for he volailiy of oupu and he persisence of employmen. The informal labour marke is compeiive while he formal labour marke is characerized by search coss. The size of each labour marke segmen depends on labour demand by firms as well as paricipaion decisions of households. The paper shows ha he informal secor plays he role of a buffer, expanding in periods of recessions and shrinking when recovery ses in. This resul is in line wih he view of informaliy as a buffer. This resul confirms ha here is a deerioraion of he qualiy of jobs during recessions. I also calls for specific policy measures argeing he mos vulnerable in period of crisis. A second resul is ha workers swiching beween he wo labour marke increases he volailiy of oupu. In oher words, economies wih labour marke segmenaion are more volaile han economies wih limied segmenaions. In periods of crisis, segmened economies may be less resilien o exernal shocks. 1

10 1 Inroducion General equilibrium models wih non-compeiive labour marke accouning for he dynamics of wages and employmen have become increasingly used. Mos of hese models have been based upon he search and maching framework where unemploymen arises in seady sae due o maching fricions. For he mos par, however, hese general equilibirum models have been applied o advanced economies while he case of developing economies wih dual labour marke has been mainly addressed in parial equilibrium framework 1. More generally, labour marke segmenaion has played only a limied role in he business cycle debae and remains confined o cerain limied academic circles 2. This paper models an economy wih an informal labour marke along he line of he search and maching framework and revisis hree main issues. The firs issue is he dynamics of he informal secor over he business cycle. The radiional view of informaliy argues ha informaliy acs as a buffer for he formal secor conracing in he upurn and expanding in he downurn 3. Anoher view on informaliy poins o he volunary naure of he enry in he informal secor linked wih new opporuniies during period of economic prosperiy 4. Empirical sudies are mixed bu end o favour he view ha informal labour markes ac as a buffer agains aggregae shocks. The second issue is he impac of informaliy on economic volailiy. The volailiy of oupu is direcly linked o he dualiy of he labour marke, which involves workers ransiing beween labour markes. Conesa e al. 22) provides empirical evidences showing ha counries wih small raios of employmen o populaion experience higher volailiy of oupu. They also model an underground economy, 1 See Sao 24), Zenou 28) or Albrech e al. 27) for insance 2 Examples include Sain-Paul 1996) Conesa e al. 22), Baini e al. 29), Arbex and Turdaliev 28) or Fiess e al. 26) 3 For a recen review of he lieraure on he ineracion beween informaliy and volailiy seebacchea e al. 29) 4 This approach argues ha he informal secor is made of self employed, small firms, who prefer o operae informaly o escape axaion and regulaion Maloney 24). 2

11 in which populaion swiching beween he wo secors amplifies he response of regisered oupu. Higher flucuaions depend on he movemen of households beween he wo secors, which is driven by he opporuniy coss of no paricipaing in he marke he wage differenial beween regisered and non regisered aciviies). On he conrary, Baini e al. 29) poin o he fac ha informaliy is poenialy a source of lower oupu volailiy. A benefi aached o informaliy is he increased flexibiliy of he economy relaed o he exisence of a non-regulaed labour marke segmen. Informal wages adjus quickly o shocks and reduce business cycle oscillaions. Along his line of argumen, a sandard resul of search and maching models is he increase in oupu volailiy wih search coss 5. A hird issue is he exen o which he ineracion beween dual labour markes modifies he sandard properies of search models. On he one hand, he formal labour marke segmen is characerized by a search and maching funcion. Wages are he resul of a Nash bargaining and are no fully flexible. On he oher hand, he informal segmen is compeiive. The model herefore combines boh an RBC labour marke and a New Keynesian labour marke. The exising lieraure on search and maching models pus forward ha search and maching models have a higher explanaory power han RBC models, as hey accoun for he empirically observed volailiy of employmen. The presence of search coss limis wage volailiy and generaes persisence in employmen dynamic, conrary o RBC models wih compeiive labour markes 6. The main quesion of ineres is he impac on employmen volailiy of ineracing dual labour markes. The model developed in his paper considers informaliy o increase wihin firms raher han across secors. The radiional approach o informaliy is linked o a secoral view of informaliy. Informal workers belong o he agriculure secor, while formal workers are in ciies working in manufacuring secors. In such a framework, he main issue is o undersand under wha condiions he manufacuring secor can absorb he flow of informal workers migraing ino ciies Harris and Todaro, 197). Over he pas decades however, informaliy has evolved and is now increasingly presen wihin he manufacuring secor iself see Chen, 27). Informal workers 5 See Andolfao 1996) for an early example 6 see Merz 1995); Andolfao 1996); Gerler and Trigari 29); Ravenna and Walsh 28) 3

12 are employed alongside formal workers in he same producion plans. We ackle his issue by modelling a single firm using hree inpus capial, formal labour and informal labour, o produce a homogeneous good. The las disincive aspec of he model is he formulaion of an equilibrium condiion for he ransiion beween he wo labour markes. Following Zenou 28), he ransiion from he informal labour marke o he formal labour marke segmen akes place hrough a period of unemploymen. Informal workers compare he expeced value of a formal job wih informal wages. In conras o Zenou 28), we consider he exisence of swiching or ransiion coss ha may ac as a barrier o formal employmen. The res of he paper is organized as follows. The model is presened in secion 2, which focuses especially on households heerogeneiy and he mechanism deermining he relaive size of he labour markes. Secion 3 presens he calibraion of he main parameers and he implied seady sae values. I also examines he properies of he seady saes, and he dynamics of he economy using numerical simulaions. Comparaive saics concerns he impac of swiching coss and search coss on he seady sae values of he models. The dynamics of he economy following a produciviy shock is assessed wih respec o wo benchmark models: a RBC model wih compeiive labour markes and a search and maching model wih single labour marke. Concluding remarks are in secion 4. Lasly, he appendix provides he equaions of he complee model and he seady saes. 2 The Model The formal labour marke is characerized by search coss following he approach used in Ravenna and Walsh 28). There has been lile aemp o model a dual labour marke wih maching funcion. In Baini e al. 29), he formal wage is equal o he informal wage augmened by an insiuionally given premium. Wages are se by union in Fiess e al. 26), while wages are flexible in Arbex and Turdaliev 28). In his model, labour adjuss along he exensive margin i.e. he number of jobs), while mos models also allow for adjusmens along he inensive margin i.e. hours worked). The former approach enables o focus on labour fricions. The laer 4

13 approach implies ha marginal coss are mainly driven by he inensive margin and ha he properies of hese models is sensiive o he marginal rae of subsiuion beween leisure and consumpion. In our se-up labour marke segmenaion is no relaed o a secor approach as in Baini e al. 29), where wo firms are assumed o operae in wo differen secors, using eiher formal labour or informal labour. In our model, here is a single firm producing a homogeneous goods using wo ypes of labour inpus. Our approach also differs from models ha assume ha formal employmen are salaried workers, while informaliy is characerized self employmen, as in Conesa e al. 22) and Fiess e al. 26). This paper relies on Conesa e al. 22) as well as Baini e al. 29) o model heerogeneiy. Assuming a perfecly insured marke, he compeiive equilibrium is characerized by agens purchasing an infinie sequence of loeries. This approach is similar o assuming ha a represenaive household spends a share of his ime on he informal labour marke and a share of his ime on he formal labour marke. Conrary o Conesa e al. 22), however, he paricipaion on each labour markes does no only depend on households decision bu also depends on labour demand. Lasly, he relaive size of informal employmen is relaed o wo facors. Firs informaliy depends on he labour demand by firms, which subsiues he hree inpus depending on he relaive coss and produciviy. Second, households paricipaion ino he labour markes is a decision based on relaive wages and employmen opporuniies in boh labour markes. We here follow Zenou 28), which specifies an equilibrium condiion for he ransiion beween he wo markes. The equilibrium condiion includes swiching coss which affec he degree of labour marke segmenaion. Paricipaion in he informal secor is no a pure choice variable as in Conesa e al. 22) and does no resul from a ax evasion sraegy as in Arbex and Turdaliev 28). Unemploymen, Vacancies and Maching There are wo labour marke segmens wih differen characerisics. The informal labour marke is compeiive, while he formal labour marke is characerized by nonclearing wages. The acive populaion is spli beween informal employmen n, i for- 5

14 mal employmen n f and unemploymen u in he formal secor; is size is normalized o 1. u = 1 n f n i The number of formal workers equals he exising sock of employmen a he beginning of he period ρn f 1 plus new maches m. The rae of job desrucion is a consan 1 ρ): n f = ρn f 1 + m 1) New maches m depend posiively on he number of unemployed workers searching a formal jobs s and he number of vacancies v. The funcion of new maches is similar o a Cobb-Douglas producion funcion, wih σ he subsiuion elasiciy. The parameer σ m reflecs he efficiency of he maching process. m = σ m s σ v 1 σ For convenience, we use he raio θ = v s o measure labour labour marke ighness. The probabiliy of firms o fill up a vacancies is denoed qθ ) and is equal o he raio of maches over he number of vacancies: q = m = σ m θ σ v Similarly, he probabiliy of an unemployed workers o find a formal job is given by he raio of new maches over he number of unemployed searching workers: p = m s = σ m θ 1 σ 6

15 Given he above definiions, new formal maches can be expressed as he probabiliy of filling a vacancy imes he exising number of vacancies: n f = ρn f 1 + q v Households There is a represenaive household wih hree ypes of members depending on heir employmen saus: formal workers, informal workers and unemployed workers: max L = E,c,c i u,k,x c f β = n f c f ) 1 σ 1 σ + ni [ +λ x r k 1 n f w f w u 1 n f n i [ +λ ϕ k 1 δ)k 1 x ) c i 1 σ ) 1 σ + 1 n f c n i u ) 1 σ 1 σ 1 η k 2 x [ + µ n f ρn f 1 p 1 ρn f 1 ni 1 ) nw i i + n f c f ) )] 2 1 x 1 )]} + n i c i + Households heerogeneiy is inegraed in a represenaive agen framework, wih composiional effecs in he welfare and budge funcion arising from changes in he relaive size of he informal economy see Conesa e al. 22) and Baini e al. 29) for a similar se-up). The size of he formal and informal labour marke segmens eners he uiliy funcion as well as consumpion. Similarly, he oal labour income of he represenaive households is he sum of he wage bill in boh secors. The similariy beween he wo households simplifies he formulaion of he ransiion beween he wo labour markes. 7 Firs order condiions imply ha c f = c i = c u a he 7 Alernaives are much more complex or much less saisfacory. In Fiess e al. 26), self employed mus dis-accumulae heir sock of capial before ransiing o he formal salaried secor. Galí e al. 27) specify wo households, one opimizing and one hand o mouh household. The relaive size of he wo groups of households is however fixed, as agens wih financial asses canno shif auomaically in he group of households wih zero savings and asses. ] 1 n f n )c i u Π 7

16 opimum. The maximizaion of households can herefore be re-wrien as follows making use of a Bellman equaion): L h = c1 σ 1 σ + βe {H n f,n i,k,x )} + [ +λ x r k 1 n f w f w u 1 n f n i [ +λ ϕ k 1 δ)k 1 x 1 η k 2 [ +µ n f ρn f 1 p 1 ρn f 1 ni 1 x ) ] nw i i + c Π + ) )] 2 1 x 1 )] Households eiher consume c or accumulae capial k hrough invesmen x. The depreciaion rae of capial is δ and capial accumulaion is subjec o adjusmen coss proporional wih he rae of change of invesmen 1 η k x ) ) 2 2 x 1 1 following Chrisiano e al. 25). The employmen consrain eq 1) faced by formal workers can be expressed as a funcion of he number of unemployed workers searching a formal job s = 1 ρn f 1 ni 1. The firs order condiions are as follow: λ = 1 c σ ϕ = E Λ,+1 [r +1 + ϕ +1 1 δ)]) 3) ϕ [1 φ + x )] { ) } 2 φ x+1 = 1 βe ϕ +1 Λ,+1 φ +1 4) x 1 x Equaions 2 and 3give he sandard Euler equaion. Equaion 4 gives he opimal condiions for capial and invesmen, where ϕ is he shadow value of a uni of invesmen. We derive H n, he represenaive household s marginal value of having one of is member hired in he labor marke raher han unemployed, which eners furher below he Nash wage bargaining. H n, increases wih addiional income gains expressed in uiliy from being employed raher han unemployed. H n, also increases wih he expeced uiliy of being sill employed in he nex period. 2) 8

17 H n, = λ w f w u) + βρe { Hn,+1 1 p +1 ) } 5) Firms Firms use hree inpus, capial k 1, formal labour n f and informal labour n i o produce a homogeneous good y, using a Cobb-Douglas producion funcion. Firms increase he formal workforce by posing vacancies v a a cos κ. The rae of maching q imes he number of vacancies give he number of new formal jobs every periods. Firms also pay wages o formal workers w i and informal workers w f as well as he renal rae of capial r o households. The bellman equaion for firms reads as follow: ) F n f 1,ni 1,k 1 a k 1 ) α k,n,k i 1 = max n f +βe {Λ,+1 F n f n f,n i,k )} ) α f ) n i 1 αk α f r k 1 w f n f wn i i κv 6) 7) The lagrangian of he opimizaion problem is: max L = a k 1 ) α k v,n,n i f,k 1 n f + ψ [ n f ρn f 1 q v ] ) α f ) )} n i 1 αk α f r k 1 w f n f wn i i κv + βe {Λ,+1 F n f,n,k i The firs wo order condiions of he firm s opimizaion problem wih respec o capial k 1 and informal labour n i equae he marginal produciviies wih heir respecive prices: r = α k y k 1 8) w i = 1 α k α f ) y n i 9) 9

18 Firms hen choose he opimal quaniy of vacancies ψ = κ q. Then maximizing profis wih respec o formal employmen and making use of he envelope condiion, we ge he equilibrium condiion for formal employmen: κ q = α f y n f w f + βρe { κ Λ,+1 q +1 } 1) The equilibrium condiions wih segmened labour markes reflec he degree of rigidiies of each marke. In he informal marke, wages are flexible and equal he marginal produc of informal labour. Firms increase formal employmen o he poin where he marginal coss of hiring an addiional workers is equal o is benefi. The benefis of an addiional worker is he difference beween he marginal produciviy of his workers and is wage coss augmened by he expeced saving of no having o generae a new mach nex period. In he absence of search coss, i.e. κ =, he equilibrium condiion reduces o ha of a compeiive labour marke. The same occurs if σ m ends o infiniy, i.e. when maching efficiency increases wihou bounds. Equaion 8 is he opimal condiion for he choice of capial wih he renal rae equaing he marginal produc of capial. I is necessary o define he value for a firms of an addiional formal workers F n,, which eners he wage bargaining in he following secion. Using he employmen condiion for employmen and making use of he equilibrium condiion for posing vacancies, we ge ha F n, = κ q. Plugging his definiion ino equaion 1 yields: F n, = α f y n f w f + βρe { Λ,+1 F n,+1 } 11) Nash bargaining in he formal labour marke Each period, he real wage in he formal labor marke is deermined hrough a generalized Nash-bargaining process beween he represenaive firm and he marginal formal worker ha was mached wih he firm. Formally, { w f max H n, ) η F n, ) 1 η}, < η < 1 12) 1

19 where η denoes he bargaining power of he formal workers and where he expressions of H n, and F n, are given by 5) and 11), respecively. The firs order condiion of he Nash-bargaining process is given by ηf n, = 1 η) H n, λ 13) where H n, λ represens he household s marginal value of an addiional formal worker expressed in unis of consumpion goods. The oal surplus from an addiional mach in he formal labor marke or surplus for shor), denoed by S n,, is defined as he sum of he firm s marginal value of an addiional formal worker and he household s marginal value of an addiional formal worker defined in unis of consumpion goods: S n, F n, + H n, λ. One can show ha he Nash-bargaining process leads he household and he firm o share ha surplus: F n, = 1 η)s n, and H n, λ = ηs n,. In addiion, he surplus S n, can also be measured by he size of he gap beween firm s reservaion wage w f and he household s reservaion wage w f : S n, = w f w f 14) The household s formal reservaion wage w f defines he minimum value of he real wage for which he household is willing o work in he formal labour marke. In urn, firm s formal reservaion wage w f defines he maximum value of he real wage ha firms are willing o pay a formal worker. The household s marginal value of an addiional worker expressed in unis of consumpion goods becomes zero H n, λ = if he real wage is se equal o he household s reservaion wage w f = w f. In his case, equaion 5) becomes: { } w f = w u H n,+1 βρe Λ,+1 1 p +1 ) λ +1 15) The household s formal reservaion wage, w f, increases wih he replacemen wage, w u. In urn, w f decreases wih he household s expeced fuure coninuaion value 11

20 H of he mach, βe Λ n,+1,+1 λ ρ 1 p ). Similarly, he firm s marginal value of an addiional formal job of a worker is zero F n, =, if he formal real wage is se equal o he firm s reservaion wage, w f = w f. In his case, equaion 11) becomes: w f = α f y n f + βρe { Λ,+1 F n,+1 } 16) Firm s formal reservaion wage, w f, increases wih he curren marginal produciviy of labor and wih he firm s expeced fuure coninuaion value of he mach. This las elemen reflecs ha urn over is cosly for firms. The bargained real wage, w f, is hen obained by aking he average sum of he wo reservaion wages, he weighs being given by he bargaining powers of firms and households: w f = η w f + 1 η)w f 17) Equaion 17 can be rearranged by using equaions 15, 16 ogeher wih F n, = q κ and H n, λ = η 1 η q κ : { } w f y = ηα f n f + 1 η)w u p +1 + ηβρκe Λ,+1 18) q +1 The real wage is a weighed sum of he marginal produciviy of labour and he replacemen income a ime and he he expeced fuure sae of he labour marke a ime + 1. The weighs are made of he bargaining power of firms and workers. We can also compue a recursive expression for he surplus, S n,, by plugging 15) and 16) ino 14) and by using he relaions beween he surplus, S n,, and he marginal values of an addiional labor, H n, and F n, : S n, = α f y n f w u ) + βρe { Λ,+1 S n,+1 1 η p +1 ) } 19) The surplus ha arises from he curren mach is deermined by wo erms appearing in he righ-hand side of equaion 19)). S n, increases wih he gap beween he marginal produciviy of labor and he replacemen wage w u. The curren sur- 12

21 plus also increases wih he expeced nex period surplus, if he curren mach is no broken in he following period, βρe { Λ,+1 S n,+1 }, ne of he expeced nex period household s marginal value of an addiional worker expressed in unis of consumpion goods), derived from a new mach ha would occur in he following period, { } { H βηρe Λ,+1 p +1 S n,+1 = βρe Λ,+1 p n,+1 +1 λ }. +1 Recall ha a fracion 1 η of he surplus goes o firms: F n, = 1 η)s n,. Combining he laer wih equaions for q and aking ino accoun ha F n, = κ q, one ges: κ q = 1 η)s n, 2) By making use of equaions 19) and 2), one can ge a recursive equaion reflecing he dynamic of employmen: κ y = 1 η) α f q n f w u ) + βρe { Λ,+1 } κ 1 η p +1 ) q +1 When eiher he vacancy posing cos parameer becomes close o zero,κ, or he maching efficiency parameer srongly improves, α m +, he marginal produciviy of labor is equal o he replacemen wage in he equilibrium. 21) Labour marke ransiion and macro closure Following Zenou 28), we make wo assumpions abou he mobiliy of workers beween he formal and informal labor markes. 1. An employed worker in he informal labor marke canno move direcly o he formal labor marke. He or she has o become unemployed before seeking a formal job. 2. Formal workers become unemployed if hey lose heir job bu never shifs direcly from a formal o an informal job. Hence, hese wo assumpions regarding possible job ransiions follow from he idea ha each labor marke requires ime and a social nework o ener. These resricions on he mobiliy of workers faciliae he characerizaion of he equilibrium in he labor marke ha includes search and maching fricions. 13

22 In order o saisfy hese wo assumpions, Zenou 28) defines formally a mobiliy condiion saing ha he household s value for unemploymen mus be equal o he expeced ineremporal sum of he informal real wage see he firs equaliy in equaion 3.2) in Zenou 28) p. 341) plus a sricly posiive) swiching cos ν. Hence, unemployed workers are always beer of han being informal. The swich from informaliy o unemploymen is sluggish and depends on he size of he swiching coss. The mobiliy condiion can be expressed as follows: U f + = E λ j= U f = w i + ν + βe λ β j Λ,+ j w i + j + ν { U f } +1 Λ,+1 λ +1 22) where U f λ denoes he household s value for unemploymen expressed in unis of consumpion goods. The value of a posiion in he unemploymen pool, U f is found by making use of equaion 5 and by aking ino accoun ha he surplus from employmen of a worker is he difference beween he employmen and he unemploymen values: H n, = W f U f. We ge he following expressions for W f and U f : ) W f = λ w f + βe {ρ W f +1 U f +1 { U f = λ w u + βe ρ p +1 W f +1 U f +1 + U f ) +1 } + U f +1 The resource consrain of he arificial economy is derived from he household s budge consrain. In paricular, by combining he household s budge consrain, wih he expression of he firm s profi. The macroeconomic closure equals privae consumpion and invesmen, search coss. Unemploymen benefis also appear in he ressource consrain in line wih Ravenna and Walsh 28): } 14

23 y = c + x + κv w u u Equilibrium condiions The equilibrium condiions of he model are as follow: q = σ m θ σ s p = σ m θ 1 σ s v θ = 1 ρn f 1 ni 1 k = 1 δ)k 1 + x 1 η k 2 ) α y = a k 1 ) α f ) k n i 1 αk α f n f = ρn f 1 + q v λ = 1 ϕ = c σ n f ) ) 2 x 1 x 1 ) λ 2 ) +1 [1 )] x+1 x+1 βe ϕ +1 η k 1 /[ 1 λ x x ) [r +1 + ϕ +1 1 δ)] ϕ = βe λ+1 λ y r = α k k 1 w i = ) y 1 α k α f n i y = c + x + κv w u u w f = ηα f y n f + 1 η)w u + ηβκe { λ+1 λ θ +1 } ) η 2 k x 1 + x ) x η k 1 2 x 1 x 1 x 1 15

24 κ θ σ s σ m = 1 η) y α f U f λ = w i + ν + βe n f { W f = λ w f + βe {ρ w u ) Λ,+1 U f +1 + βρe { λ+1 λ +1 } W f +1 U f +1 λ ) + U f ) U f = λ w u + βe { ρ p +1 W f +1 U f +1 a = ρ a a + 1 ρ a )a 1 + ε a +1 } κ 1 η p +1 )θ σ s σ +1 m } + U f +1 } 3 Numerical simulaions Calibraion Table 1: Values of parameers Discoun facor β.99 Capial depreciaion rae δ.4 Producion funcion capial) α k.26 Producion funcion formal labour) α f.2 Elasiciies of maches o unemploymen σ.5 Maching efficiency parameer σ m.7 Search coss κ.3 Employmen desrucion rae 1 ρ.1 Capial adjusmen coss η k 1.5 Swiching coss ν 1 Bargaining power parameer η.4 Technology auoregressive parameer ρ a.9 The model is calibraed using parameers convenional in he business cycle lieraure see able 1). The discoun facor of households is β =.99, he rae of depreciaion of capial is δ =.4 as in Monacelli e al. 21). The parameers of he producion funcion α k =.26 and α f =.2) are chosen such ha he relaive size of 16

25 informal employmen is comprised beween 5 and 6% of oal employmen, which is repored as being he average size of informal employmen in exising sudies see Johannes e al., 28, Bacchea e al.). The parameers for he maching funcion as well as he search coss are chosen such ha he level of unemploymen is close o 1%. The elasiciy of maches o unemploymen is he average value used in he lieraure σ =.5). Gerler and Trigari 29) repor ha plausible values range beween.4 and.7. σ m is se a.7 and ν a 1, as i conribues o generae a relaive size of informal employmen slighly larger han 5%. Search coss κ =.3 are hen chosen such ha he rae of unemploymen is close o 1%. Lasly, he rae of job desrucion is 1 ρ) =.1, a sandard value in he lieraure, as in Monacelli e al. 21). Table 2: Implied seady sae values Unemploymen rae u.12 Formal employmen n f.31 Informal employmen n i.57 Consumpion oupu raio C y.72 Invesmen oupu raio x y.2 Search coss oupu raio κv y.8 Wage share w i n i +w f n f y.64 Comparaive saics In his subsecion, we perform comparaive saics on he seady sae values of he model o analyse he impac of swiching coss and search coss on he long run level of employmen and producion. The seady saes are deailed in he appendix of he model. The firs se of comparaive saic deals wih he role of swiching coss for he ransiion beween he wo labour markes. In he model, swiching coss ν ener equaion 22 according o which he expeced value of being unemployed equals informal wages plus swiching coss. A he seady sae, swiching coss lower informal wages, which increases informal labour demand hrough he equilibrium condiion on he labour marke. The size of he informal economy increases relaively 17

26 Figure 1: Higher swiching coss 1 Consumpion.2 Invesmen 1 Oupu Wage share Wages - formal Wages - informal Employmen - formal Unemploymen 1 2 Employmen - informal o he formal economy when swiching coss go up. Given ha he informal secor has lower earnings and a lower produciviy, consumpion, invesmen and oupu decrease. Ineresingly, he higher he swiching coss, he higher he wage gap and produciviy gap beween he wo labour markes see figure 1). The second se of comparaive saic analyzes he impac of higher search coss on he seady sae values of he main macroeconomic variables. Similarly o he sandard search model, higher search coss reduce formal) employmen and increase unemploymen. Their effecs on informal employmen is limied, as i increases a firs and hen decreases slighly. The main ransmission channel from he formal secor o he informal secor goes hrough he equilibrium condiion for he ransiion beween he wo labour markes. Lower informal wages have limied effecs on informal employmen as a resul of he higher ransiion coss. In sum, higher search coss increases unemploymen, and he relaive size of he informal employmen. Higher unemploymen reduces he wage share, consumpion and oupu see figure 2). 18

27 Figure 2: Higher search coss 1 Consumpion.2 Invesmen 1 Oupu Wage share Wages - formal Wages - informal Employmen - formal Unemploymen.5 1 Employmen - informal Dynamics Figure 3 illusraes he key dynamics a work in our model. I displays impulse responses o a produciviy shock of one percen of seady sae oupu. Responses are expressed as a percenage deviaion from he seady sae value of he respecive variables. In line wih he resul of a search model wih a single labour marke, he main macroeconomic variables consumpion, invesmen and oupu) are procyclical. The posiive shock on produciviy increases he marginal produciviy of labour and capial and heir respecive prices oo see also correlaions in able 3). The firs resul is ha informaliy is couner-cyclical, in line wih he view of informaliy as a buffer. Increases in ineres rae and formal wages are slower han increases in corresponding marginal produciviies due o capial adjusmen coss and search coss, which foser an increase in he demand for boh inpus. Informal wages increase faser han formal wages in he absence of search coss in he informal secor. Firms herefore subsiue informal wih formal workers. Formal labour increases a he expense of informal labour. Informal labour plays he role of a buffer and decrease in he upurn. In he long-run, formal employmen reurns o is seady sae, as formal wages adjus downward slower han informal wages. 19

28 Figure 3: Informaliy as a buffer: swiching coss.4 C.5 I.1 Y x 1-3 r W_f W_i N_f N_i U Table 3 displays saisics summarizing he characerisics of he business cycle for four differen nesed models. The performances of wo varians of our segmened labour marke model are assessed agains hose of an RBC model and a search model. Column 1 is a measure of volailiy and displays sandard deviaion for he variables considered. Column 2 is anoher measure of volailiy and display he sandard deviaion of a given variable normalized by he sandard deviaion of oupu. Column 3 provides a measure of co-movemen of each variable wih oupu. Table 3: Cycle properies: search coss wih differen level of informaliy σ x) RBC Search model Informaliy swiching coss Informaliy α 1 =.54 σ y) =.5 σ y) =.41 σ y) =.21 σ y) = 2.59 σx) σy) corrx,y) σ x) σx) σy) corrx,y) σ x) σx) σy) corrx,y) σ x) Consumpion σx) σy) corrx,y) Invesmen Formal employmen Unemploymen Informal employmen Formal wages Informal wages I is also worh poining ou ha our wo benchmark models, he RBC and he 2

29 search models have convenional properies. In paricular, RBC models are unable o accoun for he observed persisence in employmen σn) σy) is close o zero) as he macroeconomic adjusmen fall compleely on wages. The innovaion of search and maching funcion is ha search coss reduces he volailiy of wages and increase ha of employmen σn) σy) =.13 ). The impac of he informal secor on he persisence of employmen and wages is assessed by comparing he characerisics of he RBC and search models agains he model wih dual labour markes. The model wih dual labour markes is analyzed for wo differen ses of parameers. The firs se of parameers corresponds o he parameers discussed in he calibraion secion. The seady sae level of informal employmen is calibraed by adjusing he swiching coss beween he wo labour markes. Swiching coss ν are se o 1, while he parameers for he elasiciy of capial in he producion funcion α k is equal o.26. The informal secor accouns for 57% of he acive populaion, while he unemploymen rae is 13%. The consumpion o oupu raio also increases o 73%. The corresponding properies of he business cycle following a posiive produciviy shock are displayed in column 3 of able 3. The firs resul is ha oupu volailiy drops o.21, which is wice as low as ha of eiher he RBC or he search model. This resul is consisen wih Conesa e al. 22), who show ha he volailiy of economies wih informal labour is relaed o he ransiion of populaion beween he wo labour markes. In our model, large ransiion coss reduce he populaion swiching effec. The presence of boh search and swiching coss also grealy increase he normalized volailiy of employmen o.24 from.13 in he search model wih single labour marke. The absolue volailiy of wages.13 and.9) is similar o he volailiy of he search model wih single labour marke. The normalized volailiy of wages is however much larger in he model wih dual labour markes. This resul sands in conras wih he conclusion of Baini e al. 29), who argue ha he informal labour marke increases he overall flexibiliy of he economy. In he second se of parameers, he seady sae level of informal employmen is calibraed by increasing capial elasiciy α k =.54, while reducing ransiion coss 21

30 Figure 4: Sensiiviy analysis, swiching coss and employmen persisence Y W f W i N f.4 N i close o zero ν =.18. The informal secor now accouns for 5% of he acive populaion, while unemploymen is smaller a 5%. A firs resul is ha oupu volailiy σ y) = 2.59) is more han five imes larger han ha generaed by he RBC and search models see column 4 of able 3). This resul is consisen wih he previous simulaions, which show ha he ransiion of he populaion beween he wo secors of he economy amplifies he business cycle flucuaions. A second resul is ha he combinaion of a large informal secor wih small ransiion coss reduces he impac of search coss on he persisence of employmen. An economy wih free ransiion of households beween he wo labour markes is similar o an economy wih a single compeiive labour marke. Mos of he adjusmen falls on wages σx) σy) is.43 and.45 for formal and informal wages respecively), while employmen persisence falls o zero. These resuls are in line wih he conclusions of Baini e al. 29), which argue ha he informal secor increases he overall flexibiliy of boh labour markes. Figure 4 performs sensiiviy analysis and displays he sandard deviaion of oupu, wages and employmen for differen values of swiching coss ranging from 5 22

31 o The sensiiviy analysis confirms he resuls found previously regarding he impac of swiching coss on he volailiy of oupu, employmen and wages. Resuls are in line wih he above discussion. Increasing swiching coss reduce oupu volailiy, as volailiy is here generaed by households moving beween he formal and informal labour markes. Similarly, increasing he swiching coss grealy increases he volailiy of employmen, while he volailiy of wages decreases in he informal secor or says mainly consan in he formal secor. 4 Conclusion Applying he search and maching framework o he case of an economy wih dual labour markes allows us o beer undersand he implicaion of informaliy for he dynamics of oupu, employmen and wages in developing economies. We are able o show ha informal employmen plays he role of a buffer for firms, which subsiue informal for formal jobs in periods of economic recessions. We also show ha he dynamics of oupu and employmen no only depend on he level of search coss bu also depend on he barriers beween he wo labour markes. When he ransiion is cosly, he exisence of an unregulaed labour marke does no modify he characerisics of he formal labour marke, which sill behave along he line of a search and maching model. Wages do no adjus insanaenously and employmen akes ime o reurn o is seady sae values. Furhermore, informal employmen also displays persisence despie he fricionless naure of his labour marke segmen. Resuls are reversed when ransiion coss are low. Then, he formal labour marke behaves like a Walrasian marke wih wages absorbing he produciviy shocks and employmen displaying no or very lile persisence. 8 Sandard deviaion for wages and employmen are normalized by he sandard deviaion of oupu. 23

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