Unemployment Insurance Savings Accounts and Collective Wage Determination

Transcription

1 DISCUSSION PAPER SERIES IZA DP No. 34 Uemploymet Isurace Savigs Accouts ad Collective Wage Determiatio Laszlo Goerke November 007 Forschugsistitut zur Zukuft der Arbeit Istitute for the Study of Labor

2 Uemploymet Isurace Savigs Accouts ad Collective Wage Determiatio Laszlo Goerke Uiversity of Tübige, CESifo ad IZA Discussio Paper No. 34 November 007 IZA P.O. Box Bo Germay Phoe: Fax: Ay opiios expressed here are those of the author(s) ad ot those of the istitute. Research dissemiated by IZA may iclude views o policy, but the istitute itself takes o istitutioal policy positios. The Istitute for the Study of Labor (IZA) i Bo is a local ad virtual iteratioal research ceter ad a place of commuicatio betwee sciece, politics ad busiess. IZA is a idepedet oprofit compay supported by Deutsche Post World Net. The ceter is associated with the Uiversity of Bo ad offers a stimulatig research eviromet through its research etworks, research support, ad visitors ad doctoral programs. IZA egages i (i) origial ad iteratioally competitive research i all fields of labor ecoomics, (ii) developmet of policy cocepts, ad (iii) dissemiatio of research results ad cocepts to the iterested public. IZA Discussio Papers ofte represet prelimiary work ad are circulated to ecourage discussio. Citatio of such a paper should accout for its provisioal character. A revised versio may be available directly from the author.

3 IZA Discussio Paper No. 34 November 007 ABSTRACT Uemploymet Isurace Savigs Accouts ad Collective Wage Determiatio * Uemploymet Isurace Savigs Accouts (UISAs) etitle workers to uemploymet beefits at the expese of future pesio paymets. Therefore, such accouts make uemploymet less attractive, itesify job search, ad raise employmet. I the preset paper the wage ad employmet cosequeces of UISAs are ivestigated i a model of collective wage determiatio. I the basic set-up, UISAs iduce a trade uio to lower wages. This effect ca also arise if () balaced-budget repercussios are take ito accout, () idividual job search is icorporated, ad (3) wage-depedet pesios are allowed for. However, the requiremets for egative wage effects to arise become stricter tha i the base model. Thus, collective bargaiig creates additioal impedimets for the positive employmet cosequeces of UISAs. JEL Classificatio: J38, J5, J65, J68 Keywords: employmet, trade uio, uemploymet accouts, uemploymet beefits, wages Correspodig author: Uiversity of Tübige Departmet of Ecoomics Melachthostr. 30 D-7074 Tübige Germay laszlo.goerke@ui-tuebige.de * I am grateful for helpful commets by participats of semiars at the uiversities of Dortmud, Köl, Müche, of a CESifo Area coferece o Employmet ad Social Protectio, the aual meetig of the Verei für Socialpolitik i Zürich, ad the 37 th Ottobeure semiar. Special thaks to Volker Meier ad Mafred Stadler. The paper was completed durig a visit to the Departmet of Fiace ad Maagemet Sciece at the Norges Hadelshøyskole i Berge. I would like to thak the NHH for its hospitality. Obviously, I bear the resposibility for all errors ad iadequacies. The research was supported by the Germa Sciece Foudatio (DFG SPP 069).

4 . Itroductio The primary objective of social isurace systems is to reduce the cosequeces of ecoomic ucertaity. Such isurace systems, however, etail two major disadvatages: Firstly they cause moral hazard problems sice a direct lik is abset betwee the beefit obtaied ad the costs this trasfer causes to society. Secodly, i order to pay for ecompassig social security systems, usually madatory, wage-related cotributios are levied, which will distort decisios with respect to icome geeratig activities. Give these disadvatageous features, curret fiacial problems i may coutries have stregtheed the iterest i efficiecyehacig reforms of social isurace systems. Oe such alterative are idividual welfare savigs accouts. Their basic idea is the followig: Social security cotributios are credited to a persoal accout. If a idividual becomes uemployed, ill, icurs a disability or is otherwise i eed of support, he is etitled to trasfers or beefits i kid, which are ofte assumed to be of the same level as prescribed by the traditioal social security system. The respective expediture reduces the balace i the accout. If there is a positive balace, for example at the ed of the workig life, the pesio will icrease. Moreover, to warrat the isurace feature of the system, the govermet guaratees that idividuals who have ru dow their accouts prior to retiremet will cotiue to receive tax-fiaced trasfers if i eed. Idividual welfare savigs accouts are argued to be beeficial maily for three reasos. Firstly such accouts icrease cosumer choice sice idividuals ca decide whether to obtai paymets or ot. I a traditioal social isurace system there is o real choice because the refusal to obtai trasfers, i geeral, etails o gai to the potetial recipiet. Secodly idividual welfare savigs accouts reduce the above metioed iefficiecies associated with the social isurace activities of the govermet. Thirdly the extet of icome smoothig provided by social isurace systems ca be preserved. Because uemploymet is still a pressig problem i may coutries, welfare savigs accouts have bee discussed most itesively as a complemet to or partial substitute for a traditioal uemploymet isurace (UI) system. Uemploymet Isurace Savigs Accouts (UISAs) already exist i Chile (cf. Scheider et al. 004, p. 43 f, Acevedo et al. 006, Sehbruch 006), while other Lati America coutries also kow variats of such schemes (Vodopivec ad Rejec 00, Ferrer ad Riddell 004, Vodopivec 006). A system of comprehesive welfare savigs accouts ca be foud, for example, i Sigapore, kow as Cetral Providet Fud (Asher 994, p. 33 ff). I Europe,

5 the Daish Ecoomic Coucil, for example, has suggested that part of the social isurace system be replaced by madatory idividual savigs accouts (see Boveberg et al. 007b). Boss et al. (007) provide a proposal for itroducig UISAs i Germay. The attractiveess of social security savigs accouts i geeral ad of UISAs i particular is based o the chage i icetives such schemes cause. However, previous aalyses have bee simplified by assumig costat factor prices. Clearly, this presumptio is questioable i the case of UISAs. If such accouts reduce uemploymet, wages are likely to chage as well. The commo argumet explicitly put forward or implicitly assumed to justify the presumptio of give factor prices is that their edogeisatio would ot add isights. However, if UISAs alter the icetives to supply labour, equilibrium wages will chage ad this, i tur, will affect the icetives to rely o the social security system. Such a likage ca be especially proouced i imperfectly competitive labour markets due to the promiet role of uemploymet beefits for wage determiatio. Therefore, to ivestigate the wage effects of UISAs, the process of wage determiatio eeds to be modelled explicitly. Give a collective bargaiig coverage i OECD coutries ofte i the rage of 70%, this paper looks at a ecoomy i which a utilitaria trade uio determies wages. The first objective of this cotributio is to aalyse the impact of UISAs o collective bargaiig outcomes. The secod objective, based o this kowledge, is to evaluate whether the assumptio of exogeous factor prices, ad wages i particular, affects the coclusios with respect to the advatageousess of UISAs. The etire ivestigatio is based o the assumptio that there is a give coverage ad a give level of uemploymet beefits ad, hece, igores issues of optimal UI schemes. This simplificatio allows focussig o the icetive effects of UISAs. I additio, it clarifies that the employmet cosequeces of UI systems ca be improved without impairig its isurace features. The further paper is structured as follows: Sectio surveys the literature o UISAs, while Sectio 3 sets up the basic model ad derives the mai effects of UISAs i a world with collective wage determiatio. It is show that UISAs raise employmet sice the utility differetial betwee employed ad uemployed workers is icreased, therefore reducig the trade uio's gai from raisig wages. Sectio 4 evaluates the robustess of this cetral Sørese's (003, p. 3) evaluatio is programmatic i this respect: "For simplicity, pre-tax factor prices are take as costat, sice edogeous factor price dyamics oly complicate the aalysis without addig aythig of substace." I geeral, however, the assumptio of give wages is ot justified at all. As exceptios, Boveberg et al. (007b) briefly discuss the wage effects of idividual savigs accouts ad surmise that they would stregthe their positive employmet impact, while Brow et al. (007) recogise the ucertai wage effects of UISAs but explicitly wat to exclude them from their aalysis.

6 fidig. A further argumet besides the chage i labour supply icetives, ofte put forward i support of UISAs, is the reductio of tax paymets due to less uemploymet. The aalysis i Sectio 4. shows that UISAs will cotiue to raise employmet i the presece of a budget costrait if higher taxes improve the budgetary situatio of the govermet, that is, if the ecoomy is located o the upward-slopig brach of a Laffer-curve. I Sectio 4., job search of those workers is allowed for who do ot fid a job at the uio wage. Uder some more restrictive assumptios regardig the search techology, the wage mitigatig effects of UISAs cotiue to arise. All ivestigatios up to this poit i the paper assume pesios to be determied oly by the employmet history of a worker. I Sectio 4.3 pesios are the modelled as beig (positively) affected by previous earigs as well. I such a settig, the employmet cosequeces of UISAs become ucertai. This is because the wage reductio caused by UISAs i the basic model etails additioal costs i the form of lower pesios. Relative to the basic sceario, the trade uio's costs of a wage reductio rise. Sectio 5 summarises ad takes a look at the distributive cosequeces of UISAs. Furthermore, it briefly restates the argumets supportig the evaluatio that, firstly such a scheme substatially affects collective bargaiig outcomes ad that, secodly the edogeisatio of wages via collective bargaiig outcomes may limit the positive employmet cosequeces of UISAs. Some formal derivatios are relegated to a appedix.. Survey of the Literature Uemploymet isurace savigs accouts (UISAs), apparetly first proposed by Topel (990, p. 9 ff), Grubel (995), Cortázar (996) ad Fölster (997), have bee aalysed theoretically by, for example, Brow et al. (007), Boveberg ad Sørese (004), Orszag et al. (999), Orszag ad Sower (999, 00), Sørese (003), ad Stiglitz ad Yu (005) ad empirically, iter alia, by Feldstei ad Altma (007), Fölster et al. (003), ad Vodopivec ad Rejec (00). Boveberg et al. (007a) ad Ferrer ad Riddell (004) provide thorough o-techical discussios of the ratioale for idividual savigs accouts. Orszag ad Sower (00) set up a two-period model, based o Phelps (994, pp. 5-65) ad similar to the oe used by Orszag ad Sower (999), Orszag et al. (999), ad Brow et There are a umber of further studies i which Fölster (999a, 999b, 00) looks i detail at various aspects of UISAs or, more geerally, welfare savigs accouts. Kugler (005) ivestigates the wage ad employmet cosequeces of severace pay savigs accouts empirically for Colombia ad theoretically i the cotext of a matchig model. Such severace pay savigs accouts differ from UISAs sice workers caot prevet paymets from the former by alterig their effort or wage. 3

7 al. (007), i which both the probability of retaiig the job ad the probability of fidig oe if uemployed positively deped o effort. 3 Uemploymet is volutary i that workers choose a isufficiet effort level. Moreover, Orszag ad Sower (00) presume that the price of labour is give. UISAs raise the secod period icome of a worker who was employed i period oe above the icome of someoe who was uemployed i the first period. Moreover, losig the job at the ed of period oe etails a icome reductio i period two. I such a settig, Orszag ad Sower (00, p. ) ca show that i the presece of UISAs workers "stad to lose more from beig uemployed" tha uder a traditioal UI system (see also Brow et al. 007, p. 0). Accordigly, workers search more itesively for a job whe uemployed ad try harder ot to lose their job. Both behavioural chages reduce uemploymet. Calibratig the model for Germay, Brow et al. (007) fid that replacig the traditioal UI by UISAs reduces uemploymet substatially (see also Orszag ad Sower 00). Sørese (003) sets up a model with overlappig geeratios of workers who ca be ivolutarily uemployed i the first period ad select their retiremet date withi the secod. A tax-fiaced social security system geerates icetives to retire before the ed of the secod period. The aalysis is performed i a small ope ecoomy settig with a costat returs-to-scale productio fuctio. Sørese (003) shows that the balaced-budget itroductio of savigs accouts ca raise the expected utility of youg workers ad future geeratios while curretly old workers are uaffected. Boveberg ad Sørese (004) exted the approach of Sørese (003) by, iter alia, itroducig additioal worker heterogeeity ad differetiatig explicitly betwee idividual retiremet accouts ad UISAs. They show that the itroductio of idividual (uemploymet isurace) savigs accouts, holdig costat the utility of all workers, raises the preset value of govermet reveues. Give separability of the idividuals' utility fuctios, the ehaced supply of public goods fiaced by the additioal reveues costitutes a Pareto improvemet (see also Boveberg et al. 007b). Whereas Sørese (003) ad Boveberg ad Sørese (004) ivestigate the potetial for a welfare improvig itroductio of idividual savigs accouts, Stiglitz ad Yu (005) focus o the questio of what is the ex-ate optimal combiatio of uemploymet beefits ad 3 The positive relatioship betwee fidig a job ad effort is justified o the basis of a search approach, while the respective likage for the probability of a job loss ad effort is derived from a isider-outsider based model of learig o the job. Alteratively, a shirkig framework may be utilised to justify a egative impact of effort o the probability of beig fired (cf. Orszag ad Sower 00, Brow et al. 007). 4

8 UISAs. They assume that workers ca lose their job with a exogeous probability oce i their lifetime. Hece, a trasfer durig a spell of uemploymet ca ehace welfare if workers are strictly risk-averse. Moreover, the probability that a uemployed worker fids a ew job depeds positively o search effort. Agai, wages are exogeous. Workers caot borrow agaist future earigs due to capital market imperfectios. Stiglitz ad Yu (005) show, iter alia, that i a secod-best situatio i which idividuals determie their search behaviour, optimal UI beefits decrease with the search elasticity with respect to trasfers ad rise with the Arrow-Pratt measure of absolute risk-aversio. The reverse relatioship applies for paymets from UISAs. UISAs ca icrease welfare, relative to a traditioal UI system, sice such accouts effectively alleviate capital market imperfectios. Furthermore, the authors demostrate that UISAs etail greater welfare gais, the earlier o durig workig life a uemploymet spell takes place. This is because a later spell may cause egative balaces i UISAs ad, thus, dilutes search icetives. These theoretical aalyses of UISAs are complemeted by empirical ivestigatios. Boveberg et al. (007a) estimate that o average about three-quarters of the taxes levied i Demark to fiace social security, flow back to the respective taxpayer over the life cycle. The greater this fractio is, the lower the iterpersoally redistributive elemet of idividual savigs accouts ad the more proouced the reductio i moral hazard owig, for example, to the itroductio of UISAs will be. Boveberg et al. (007a), furthermore, refer to studies idicatig that the extet of iterpersoal redistributio of social security systems over the life cycle is also limited i other coutries. Feldstei ad Altma (007) ivestigate whether idividuals would accumulate sufficiet savigs via UISAs to fiace their ow uemploymet beefit paymets "or whether the cocetratio of uemploymet amog a relatively small umber of idividuals implies that the UISA balaces would typically be exhausted, forcig idividuals to rely o govermet beefits with the same adverse effects that characterize the curret UI system." (p. 56) The authors simulate five variats of UISAs for the Uited States, usig data from the PSID (Pael Study of Icome Dyamics) o heads of households i 960, followig their employmet history util 99 ad assumig o behavioural chages, such as for example of search behaviour. They fid that aroud 5% of the sample would ed up with egative balaces i the accout. Vodopivec ad Rejec (00) ask basically the same questios for Estoia as Feldstei ad Altma (007) pose for the Uited States ad also employ a similar framework. Usig data 5

9 from the Estoia Labour Force Survey for the years , they compute that betwee 8% (low uemploymet sceario) ad 7% (high uemploymet sceario) of those who retire do so with a egative balace i their accout. Hopehay ad Hatchodo (00) complemet the accoutig exercise of Vodopivec ad Rejec (00) by calibratig the ex-ate welfare effects of alterative specificatios of UISAs i a simple life cycle model for Estoia, employig data from the Labour Force Survey. Workers obtai a fixed wage ad icur a fixed level of effort but ca decide whether to quit a job if employed or whether to accept oe whe uemployed. Hopehay ad Hatchodo (00) show that UISAs may geerate outcomes close to those of a optimal UI system. Moreover, for moderate degrees of relative risk-aversio a give utility level of workers ca be obtaied most cost-effectively if replacemet rates are low while workers cotribute a comparatively high share of their icome to UISAs. Fially, Fölster et al. (003) employ a logitudial data set for Swede to aalyse comprehesive welfare accouts, icludig ot oly uemploymet beefits but also other elemets of the welfare state, such as paretal leave ad housig subsidies, sickess ad child beefits ad pesios. For this more extesive accout system, Fölster et al. (003) fid that about % of people would ed up with egative balaces i their accouts. Moreover, they observe that the budgetary costs of welfare accouts deped strogly o the uemploymet rate. Accordigly, they regard the iclusio of the uemploymet beefit system ito a comprehesive scheme of idividual welfare accouts as a importat elemet. I summary, the aalyses by Feldstei ad Altma (007), Vodopivec ad Rejec (00), ad Fölster et al. (003) idicate that a great majority of the labour force would reduce its pesios by the receipt of uemploymet beefits i the presece of UISAs. Sice this egative likage is their basis for the welfare ehacig effects, UISAs promise a substatial improvemet i the efficiecy of labour markets. 3. Model ad Cetral Result The theoretical ad empirical aalyses surveyed above presume a give wage. However, oe of the theoretical predictios which ca be derived from almost every model of uemploymet is that alteratios i beefit levels affect wages. Sice UISAs effectively reduce the trasfer resultig from the receipt of uemploymet beefits, oe of the mai cosequeces of such a scheme may have bee eglected, with accordig implicatios for its evaluatio. To ivestigate this cojecture, UISAs are itegrated ito a model of uio wage settig. 6

10 Collective bargaiig is assumed because it is the most widespread mechaism of wage determiatio i a large majority of OECD coutries. Gross uio desity varied betwee 0% (Frace), 79% (Swede) ad 84% (Icelad) i the OECD i 000, its uweighted average amoutig to 34%. However, the (uweighted) average collective bargaiig coverage was substatially higher ad equalled 60% i 000, reachig or eve exceedig 80% i umerous coutries (OECD 004, Europea Commissio 004). To focus o the price, i. e. wage effects of UISAs, the iitial ivestigatio does ot iclude idividual labour supply decisios. Istead, ad i lie with virtually all models of collective wage determiatio, it is assumed that every worker who is offered a accordig job will work at the uio wage. I additio, i this sectio workers who do ot obtai a job at the collectively agreed wage are presumed to remai uemployed. Therefore, idividual job search is ot allowed for. The double moral hazard problem metioed i the itroductio is evertheless preset, sice there is decetralised wage determiatio ad the trade uio does ot take ito accout the repercussios of its wage decisio o the budget of the UI system. I additio, taxes are employed to fiace uemploymet beefits. Suppose idividuals live for three periods. They ca work durig the first two ad are retired i the fial period. For simplicity, future paymets are ot discouted. At the begiig of periods oe ad two, a utilitaria trade uio represetig all employees i the respective sector sets a wage. There are may idetical sectors i the ecoomy such that the results for the trade uio uder ivestigatio ca be geeralised. Accordigly, the trade uio is small relative to the size of the ecoomy. Workers are risk-averse ad ca be characterised by a cocave (idirect) utility fuctio u, u' > 0, u'' 0, defied over et icome, where u is separable over time. Give the wage set by the moopoly trade uio, the firm determies employmet. Employmet declies with the wage at a o-decreasig rate but does ot vary over time for a give wage. Each period, workers are radomly selected from the pool of available employees, the size of which is ormalised to uity. Ay worker who is ot employed at the uio wage obtais a exogeously give level of uemploymet beefits w, which is always less tha the et wage. That is, uemployed idividuals are ot allowed to refrai from the receipt of beefits. I lie with this assumptio, workers are uable to trasfer icome from oe period to aother, that is, savigs ad debts are ot feasible. The otio of UISAs is captured by makig actual pesio paymets deped o the legth of the uemploymet spell ad o the magitude of beefit paymets. The pesios of workers who have always bee employed amout to P, while pesios of those who experieced oe 7

11 period of uemploymet, the short-term uemployed, are give by P = P - α w > 0, 0 α. The parameter α measures the percetage by which a paymet of of uemploymet compesatio reduces future pesios. Pesios of workers who are without a job for two periods, the log-term uemployed, are give by P, P = P (α + β) w > 0, 0 β. The parameter β idicates whether a secod period of uemploymet implies a reductio i the pesio, beyod that caused by a oe-period spell of uemploymet, ad will be zero if, for example, P already equals a legally bidig miimum pesio. 4 To fiace uemploymet beefits ad pesios, employed workers have to pay a liear icome tax or social security cotributio rate t, 0 < t <, which is costat over time. Cotributios do ot ear a rate of retur. UISAs may be based o a pay-as-you-go or a fuded system. 5 As log as the returs of the two schemes coicide, which they do i the preset settig, the choice betwee fudig ad PAYG ca be separated from the aalysis of the icetive effects of UISAs. The timig is as follows: First, the govermet determies the (time-ivariat) tax rate t, aticipatig the outcome of the subsequet wage settig process. Afterwards the trade uio selects wages w i at the begiig of period i. The model is solved by backward iductio to obtai a subgame-perfect Nash-equilibrium. Deotig the gross wage i period i, i =,, by w i ad the resultig employmet level by N i (w i ), where the argumet w i will be omitted if feasible without loss of iformatio, while the et wage is give by w i := w i ( t), the expected utility two of a worker who has bee employed i period oe ca be expressed as: U e at the begiig of period U e = N N u(w) u(p (w ) u(w ) u(p) ( ) (w )) () If the worker is also employed i the secod period, this takig place with the probability N, he will obtai a et wage w ad the full amout of pesios P i period three. If the worker is uemployed i period two, this beig the case with probability ( N ), he will receive beefits w ad a pesio of P i period three. 4 Modellig the effects of UISAs ot as a fall but as a icrease i pesios for those workers who experiece o (or less) uemploymet would raise the costs of the pesio system. I a balaced-budget settig (cf. Sectio 4.), this would etail higher taxes ad lower employmet, for a give wage chage. The approach pursued here will, thus, result i a positive employmet bias if balaced-budget repercussios are take ito accout. 5 See, for example, Sørese (003, p. 33, 30f), Vodopivec ad Rejec (00), Orszag ad Sower (00), ad Brow et al. (007). 8

12 If a worker who has bee without a job i period oe does (ot) fid a job i the followig period, he will receive a pesio P (P ). The expected secod-period utility U u is: U u = N N u(w) u(p (w ) u(w ) u(p ) ( ) (w )) () The trade uio maximises the expected utility of its members U = N e U + ( N ) U u with respect to the wage i period two. Rearragemet of the first-order coditio U / w = 0 for the uio's maximisatio problem yields: N ) u(p )) N u(p u'(w )( t) + N ' u(w ) u(w) + ( N )(u(p + (u(p) )) = 0 (3) While the first term i equatio (3) depicts the uio's gai from a higher wage, which N members obtai, the secod ad third term describe the costs of a wage icrease. I additio to the differece betwee the utility resultig from the et wage w ad from uemploymet compesatio w, the costs of a wage icrease also iclude the impact o pesios. If the wage is raised margially i period two, all those ( N ) workers who have already bee uemployed i period oe will see their pesio fall from P to P. Moreover, a fractio of N workers who had bee employed i period oe will experiece a declie i their pesios from P to P. Therefore, the costs of a wage icrease are greater tha i the absece of UISAs ad the optimal wage will be lower, ceteris paribus. The (sufficiet) secod-order coditio for the uio's maximisatio problem is warrated if the labour demad fuctio N is weakly cocave, give risk-averse workers. Turig to the trade uio's problem i period oe, it should be oted that the choice of the wage w ot oly affects the payoff i period oe, but also iflueces the expected utility U via the variatio i N, ad the esuig adjustmet i the secod period wage w. The expected first period utility of the uio, hece, is give by: U = N (w )u(w ) + ( N (w ))u(w) + U ( w (w ), N (w )) (4) Maximisatio of U with respect to the wage w, makig use of U / w = 0, yields: N ' N u(p )) ( N ) u(p u'(w )( t) + N u(w ) u(w) + (u(p) + )(u(p )) = 0 (5) 9

13 Ispectio of equatios (3) ad (5) demostrates that wages ad employmet do ot vary over time. The ituitio is the followig: Give idetical labour demad fuctios for both periods, the absece of discoutig, 6 employmet probabilities which are idepedet of previous employmet histories, ad a utilitaria trade uio, the oly icetive to chage wages over time could arise from the pesio system. However, the worker's expected utility from the pesio system is symmetric i employmet i both periods i that ay expected utility level from pesio paymets resultig from hypothetical employmet levels N ad N, N N, i periods oe ad two, ca also be obtaied if employmet levels are exactly reversed. Give that there is a first period wage w which uiquely maximises uio utility U such that the optimal secod period wage w is also uiquely determied, the oly combiatio of wages compatible with optimal choices of the trade uio is w = w. For the subsequet aalysis with the exceptio of Sectio 4. the distictio betwee period oe ad period two variables is omitted. Rewritig the optimality coditio for N = N = N ad w = w = w yields: Ψ = Nu '(w )( t) + N' ρ(w, w, P, α, β) = 0, (6) where ρ is defied as: ρ ( w, w, P, α, β, t) : = u(w ) u(w) + N[u(P) u(p )] + ( N)[u(P ) u(p )] > 0 (7) A weakly cocave labour demad fuctio (N' < 0, N'' 0) is a sufficiet coditio for Ψ w < 0 to hold (see Appedix A.). To simplify the expositio, a costat labour demad elasticity ε ot less tha uity, ε = - N'w/N, is presumed. The respective optimality coditio is give by Y := wψ/n = 0. I a stadard moopoly trade uio model, a labour demad elasticity of uity or more guaratees the sufficiet secod-order coditio, as equatio (8) below clarifies for P = P = P. However, i the presece of pesios which deped o the employmet status, this requiremet may ot suffice to assure Y w < 0. This is the case because employmet-related pesios alter the costs of a wage icrease i two ways: first, a higher wage causes a fall i 6 If the uio discouted future payoffs, wages would declie over time sice the icetives to reduce wages because of their impact o pesios would be lowered. Therefore, also the impact of UISAs would become less proouced. More geerally, the assumptio of o discoutig has two mai cosequeces: first, it greatly reduces the aalytical complexity of the ivestigatio. Secod, issues of icome variability due to ucertai discout rates ca be eglected. For a discussio of the latter issue i the cotext of idividual retiremet accouts, see Feldstei ad Raguelova (00), iter alia. 0

14 pesios from P to P sice fewer idividuals are employed for two periods. Secod, if more people suffer a loss i pesios from P to P, fewer idividuals icur a reductio i pesios from P to P. The combied effect depeds o the curvature of the utility fuctio ad o pesio levels. Yw = ( t)c εn'[u(p) + u(p ) u(p )] for c : = u' '(w )w + u'(w )( ε) < 0 (8) To rule out the possibility that the assumptio of a costat labour demad elasticity affects the wage impact of variatios i the beefit system, Y w < 0 is presumed also for a exogeously give value of ε. This presumptio will obviously be warrated aalytically if UISAs are itroduced, because the ambiguous effects o Y w are ot preset for P = P = P. The impact of a chage i the parameters α ad β of the savigs accouts system o the optimality coditio Y = 0 ca be computed as: Y w ( N)[u'(P ) u'(p )] Nu'(P ) α = ε < 0 (9a) Y β = εwu' (P )( N) < 0 (9b) Equatios (8) ad (9) yield: 7 Propositio If UISAs reduce the pesios of either log-term uemployed or all uemployed, such accouts will iduce a trade uio to lower wages. If the pesios of short-term uemployed are curtailed, N > 0.5 is a sufficiet coditio for wages to declie. Propositio shows that UISAs, which retai the level of uemploymet beefits but lower pesios of all workers who receive such trasfers, reduce wage claims by a moopoly trade uio. The ituitio is the followig: A reductio i pesios pealises the uio sice a uemployed worker ot oly loses wage icome, obtaiig uemploymet beefits istead, but also icurs a cutback i pesios. Thus, the costs of a wage icrease rise, relative to a settig without UISAs, ad the uio is cotet with a lower wage. However, this reasoig does ot ecessarily apply to short-term uemployed, sice a margial decrease i their pesios icreases the costs of a job loss from u(p) to u(p ) for N people, while it decreases the respective costs from u(p ) to u(p ) for - N uemployed. Accordigly, pealisig short- 7 Note that the sigs of (9a) ad (9b) are uaffected by the assumptio of a costat labour demad elasticity.

15 term uemployed makes log-term uemploymet more attractive at the margi. If the employmet rate exceeds 50% i the preset two-period model, more people icur a relative utility loss tha a gai ad a combiatio of (9a) ad (9b) shows that the trade uio lowers wages. Nevertheless, the fidigs for short-term uemployed idicate that the wage reducig effects of UISAs will oly uambiguously arise if such accouts dimiish the expected payoffs of workers at each relevat margi. Propositio furthermore clarifies that UISAs are likely to have a positive employmet impact eve i the absece of effects o idividual job search behaviour because such schemes ted to reduce the icetives for wage icreases i a moopoly uio framework. While a trade uio may, i extreme situatios, be able to actually set a wage, i geeral, it will bargai with a couterpart such as a firm or a employer associatio. Assumig that the bargaiig outcome ca be approximated by the Nash-solutio, the qualitative impact of UISAs o wages is ulikely to be affected. The Nash-solutio maximises the product of the gai from a bargai for the uio ad, say, the firm. The firm's payoff i the case of a agreemet are its profits ad the payoff i the absece of a agreemet, for example, the costs due to a iterruptio of the productio process. Neither of these payoffs is directly affected by UISAs. The trade uio's payoff from a agreemet is give by its utility U, while the payoff i the absece of a agreemet may be the utility its members obtai either i a ouio job or from uemploymet. Uless this payoff i the absece of a agreemet is affected by UISAs more strogly tha uio utility U, the trade uio's gai from a higher wage will chage i qualitatively the same way as i a moopoly uio settig. Therefore, the icetives to alter wages are affected by UISAs i the same basic maer irrespective of whether there is bargaiig or uilateral wage settig. Apart from the wage settig power of the trade uio it may also be questioed whether the uio oly represets workers who live for three periods. A alterative assumptio is that a ew geeratio of workers of the same size is bor i every period, which the lives for three periods. It ca the be show that a utilitaria trade uio sets the same wage as defied by equatio (6). The ituitio for this irrelevace is as follows: The optimal wage results from the maximisatio of the sum of the expected utility of workers who just bega their workig lives, labelled youg workers, ad the expected utility of workers who have already had a period of labour market experiece, amely the old workers. Sice the wage is decided upo i each period, wages i period τ + ca oly be iflueced idirectly i period τ via the choice of employmet. Thus, the gai from a higher wage for youg workers results from a greater icome for the employed, while the costs of a wage icrease are determied by the

16 wage loss relative to uemploymet beefits ad the alteratio i pesio etitlemets for all those who lose their job due to the wage icrease. The gais ad loses from a higher wage for old workers cosist of the same basic compoets. If the employmet probabilities of youg ad old workers coicide for a give wage, the objective of a utilitaria uio will be the same as i a world with oly oe geeratio of workers. Accordigly, wage demads ad the impact of UISAs o employmet are idepedet of the time horizo uderlyig the aalysis. As a fial commet o the applicability of the aalysis, it may be assumed that workers are allowed to save or to icur debts, which have to be paid off by the ed of period three. Such possibility would ot ivalidate the basic mechaism iducig the trade uio to mitigate its wage claims i the presece of UISAs. This is because the primary effect of UISAs i the preset set-up is to lower the expected icome of a uemployed worker over his workig life. The distributio of the etire icome over time, however, which may be affected by the possibility to save, is ot determiig outcomes. Havig established that UISAs systematically affect collective bargaiig cotracts i a admittedly simplified settig, the ext sectio cosiders formal extesios ad determies the coditios uder which the egative wage cosequeces will also arise if the assumptios uderlyig the basic model of collective wage determiatio are relaxed separately. 4. Extesios I Sectio 4., the budgetary effects of UISAs are take ito accout. Such a aalysis is useful ad ecessary because the reductio i (margial) tax rates caused by UISAs is oe of the mai argumets i favour of such a scheme. At first sight it may appear that the budgetary effects of UISAs must stregthe their (positive employmet) impact because lower beefit paymets reduce the budgetary requiremets so that taxes ca be decreased. However, this coclusio may be premature because lower wages imply a fall i tax paymets ad a rise i employmet etails higher pesio paymets. Sectio 4. icorporates these couteractig iflueces. I Sectio 4., job search is added to the basic model of Sectio 3. Workers without uemploymet experiece who do ot obtai a job at the wage set by the trade uio, are ow presumed to search for a job i a competitive sector of the ecoomy, tradig off search costs ad the expected icrease i utility due to a higher moetary icome. Sectio 4., therefore, combies the labour market effects of UISAs traditioally ivestigated, for example by Boveberg ad Sørese (004) ad Brow et al. (007), with collective wage determiatio. The aalyses up to Sectio 4. presume that the maximal level of pesios P is 3

17 exogeous. However, pesios are ofte related to cotributios. I the curret framework, such a relatioship is equivalet to wage-related pesios, which are looked at i Sectio 4.3. Wage-related pesios mitigate the icetives to accept lower wages. The positive employmet impact of UISAs the depeds o whether the fall i pesios due to uemploymet more tha compesates their reductio owig to lower wages. 4. Balaced-Budget Reforms Assume that UISAs lower wages ad raise employmet i a uioised ecoomy. Give a labour demad elasticity i excess of uity, the payroll rises. If the budget therefore experieces a surplus, taxes ca be lowered which, i tur, provides a further icetives for the uio to reduce wages. However, a icrease i employmet raises pesio paymets. To ivestigate if the positive budgetary impact of lower uemploymet beefits domiates the egative cosequeces of higher pesio etitlemets, let the govermet operate a comprehesive budget, fiaced by the liear wage tax t, from which uemploymet beefits w ad pesios P, P ad P are paid. Sice employmet does ot vary over time, the balaced-budget costrait B = 0 ca be writte as: B = wtn P w( N)[ α( + N) β( N)] = 0 (0) As metioed above, the trade uio igores the repercussios of its wage settig o the budget B because there are so may trade uios that their idividual impact o B is egligible. Normalisig the umber of trade uios to uity to avoid additioal otatio, the derivatives of the budget costrait B, assumig a costat labour demad elasticity ε, are give by: B w = tn( ε) + wn' γ < 0, (a) for γ := - Nα - β( - N) 0, as 0 α, β, N. B t = wn > 0 (b) B α = w( N ) > 0 (c) B w( N) β = > 0 (d) B α d( α+β) = 0 = w( N) > 0 (e) 4

18 For the subsequet aalysis, the wage w ad the tax rate t represet the edogeous variables. The wage cosequeces of a more proouced reductio i pesios for all uemployed i the presece of a ecompassig balaced-budget restrictio are: dw dα db= 0 B Yt Y = α αbt D < 0 () if D < 0, sice B α, B t, Y t = -wc > 0 (from equatios (6) ad (8)) ad Y α < 0, where: D : = wnc( t w / w) wn N'[u(P) u(p ) u(p YwBt BwYt = ε εγ ε + )] (3) Furthermore, the effects of chagig pesios for log-term ad short-term uemployed are: dw dβ db= 0 Nεu'(P ) ( N)c = ww( N) < 0, if D < 0 (4) D dw dα d( α+β) = 0 db= 0 ε(n )u' = wwn (P ) D ( N)c < 0, if D < 0 ad N > 0.5 (5) The determiat D of the system will be egative if a higher wage tax rate t gives rise to a budget surplus, takig ito accout adjustmets i wages ad employmet, i.e. if the requiremet of a positively sloped (budgetary) Laffer-curve is warrated (see Appedix A.). It ca be oted, though, that i the absece of UISAs, etailig γ = ad P = P = P, ad for a labour demad elasticity ε of uity or more as suggested by the model, a margial tax rate t ad a (gross) replacemet rate w / w which together exceed a value of uity suffice to violate the Laffer-curve coditio. Therefore, the restrictio of D < 0 caot be iferred from the model. However, give D < 0, the wage chages of UISAs are uaffected by a balacedbudget restrictio. The fidigs may accordigly be summarised i: Propositio If icreasig the tax rate t geerates a budget surplus, takig ito accout adjustmets i wages ad employmet, UISAs which reduce pesios of all or log-term uemployed raise employmet i the presece of a balaced-budget costrait. The same effect will uambiguously arise for a cut i pesios of short-term uemployed if N 0.5. Takig ito accout the budgetary effects of UISAs, o the oe had, stregthes the positive employmet cosequeces because of lower uemploymet beefit paymets. However, o the other had the budget costrait also aggravates the employmet performace of the 5

19 ecoomy because higher pesios etitlemets have to be fiaced ad thus lead to higher taxes ad wage claims, ceteris paribus. Assumig a upward-slopig Laffer curve effectively supposes that the first impact domiates. Propositio, therefore, clarifies that the positive employmet effects of UISAs do ot occur because of exteralities i the process of wage determiatio via the govermet budget. It should be emphasised, however, that UISAs reduce pesio paymets (cf. the defiitio of P ad P ) i the preset settig. The adverse balaced-budget repercussios may accordigly be more proouced if UISAs iduce a rise i pesios. 4. Addig Job Search Oe of the mai effects of UISAs is that o idividual job search icetives (see Sectio ). This impact has bee eglected thus far. To itegrate job search ito the collective bargaiig framework, a umber of additioal assumptios are required. Presume, therefore, that a worker who has o prior uemploymet experiece ad does ot get a job at the uio wage w i i period i ca search for a job i the competitive labour market i that period. For simplicity, therefore, the co-existece of etirely uioised ad completely competitive labour markets is presumed. The decisive feature of this extesio is that o-employmet i the uioised labour market is ot automatically equivalet to uemploymet. The itesity of search i the o-uioised competitive labour market is deoted by s i, 0 s i, ad results i a probability θ(s i ) of fidig a job for that period at the costat competitive et wage w c. If the worker does ot have a job, he will receive uemploymet beefits w, w w c. The separable utility loss resultig from search equals C(s i ), C(0) = 0 < C', C''. I additio, if a worker is employed at the competitive istead of the uio wage, pesios will ot be curtailed. Assume fially, that a worker who has bee uemployed i the first period will ot icur a further reductio i pesios below P, implyig β = 0, ad as idicated above that such a worker will ot exped search effort i the secod period. The timig of decisios is the followig: First, the trade uio determies the wage w. The a worker lears whether he will be employed i the first period at the uio wage. If ot, he will work at the competitive wage with the probability θ(s ) ad be uemployed with probability ( - θ(s )). At the begiig of the secod period, the uio determies w ad a worker with work experiece i the first period but without a uio job i the followig 6

20 period agai searches for a competitive job. He succeeds with probability θ(s ). The uio takes ito accout search behaviour whe determiig wages ad also icorporates the repercussios which the choice of the first period wage w has upo its payoff resultig from the wage w i the secod period. Idividual workers, i cotrast, take wages as give whe determiig their search itesity. As optimal search itesities i both periods differ, so will wages. Therefore, the approach of Sectio 3 i which the trade uio ca igore the time dimesio of its optimisatio problem caot be applied here. Istead, the trade uio's objective is treated explicitly as a fuctio of both wages, U ~ = U ~ (w,w ). Note that to differetiate the expected payoffs i this sectio from those of other parts of the paper they are characterised by a tilda (~). A worker has bee uemployed i the first period with probability - N ~ := (N + ( - N )θ(s )), where N = N (w ). Give the above assumptios, his expected payoff U ~ u i period two equals = 0. With the probability N ~ U u as defied i equatio (), where P has bee replaced by P because β a worker has bee employed either at the uio or the competitive wage i the first period ad obtais a expected secod period utility U ~ e. With probability ( - N ) he does ot obtai a uio job i period two. His probability of fidig a competitive job, prevetig a drop i pesios, amouts to θ(s ). Accordigly, by: U ~ e is give U ~ e = N [u(w ) + u(p)] + ( N )A (6) where A : = θ(s c ) u(p)] ( (s u(p )[u(w + + θ ))[u(w) + )] C(s ) The optimal search itesity s * i the secod period is defied by U ~ e / s = 0 or, equivaletly by: A s = θ'(s )[u(w c ) + u(p) u(w) u(p )] s = 0 (7) Optimal search effort s * is idepedet of wages w, w because a worker will oly search i the competitive sector if he has ot obtaied a uio job. Thus, the icome level of the job ot obtaied has o effect o the icetives or costs of fidig aother job. 7

21 Subsequetly, it is presumed that the probability θ(s i ) is liear i s i ad give by θ(s i ) = s i / s, s > s i, while the cost fuctio C(s i ) is quadratic ad equals C(s i ) = (s i ) /. These assumptios esure, iter alia, that the secod-order coditio ( A/ (s *) < 0) is satisfied. Note, i additio, that optimal search effort s * rises with the parameter α, because A/( s * α) = θ'(s *)u'(p ) > 0 holds. Accordigly, UISAs have the proclaimed effect of mitigatig the moral hazard impact of a UI system by itesifyig search of uemployed workers. Substitutig the first-order coditio (7) ito equatio (6), utilisig the simplifyig assumptios o C(s i ) ad θ(s i ), the term A ca be expressed as: A (s *) = u(w) + u(p ) + C(s *) (8) The expected utility U ~ resultig i the secod period cosists of the expected payoff U ~ e if havig bee employed i the first period with probability N ~ ad the expected payoff U ~ u if havig bee uemployed i period oe with the opposite probability. Takig ito accout that N ~ depeds o θ(s ) ad usig equatio (8), the expected utility U ~ ca hece, be expressed as: U ~ (w, w s = N ~ + + N *),s *) N ) u(p)] ( [u(w )A(s + ( N ~ ) + u(p )] + ( N + u(p ) N [u(w )[u(w) )] (9) The expected overall payoff U ~ of the trade uio cosists of the expected payoff i the first period, i additio to the expected utility U ~ (w,w s,s * ) resultig i period two. U ~ (w, w s,s *) = Nu(w ) + ( N) θ(s)u(w c ) + ( θ(s))u(w) + N N ~ *) u(w ) ( N ) u(w) u(p ) C(s (s ) + N + ) N ~ ( N ~ u(p) )u(p (0) 8

22 Give the determiatio of the wage i period, a worker ot employed at a uio job maximises his expected utility U ~ with respect to search effort s i period. 8 Φ : = θ' (s c ) u(w ) u(w) + N [u(p) u(p )] + ( N )C(s *) s = 0 () The secod-order coditio for a maximum holds as Φ/ s = < 0. Optimal search effort s * is idepedet of the uio wage i period ( Φ/ w = 0) ad icreases with the parameter α, takig ito accout that s * = s *(α) from (7). Φ α = θ' (s *)u'(p ) N '(s *)s > [ + ( N ) θ *] 0 () The trade uio determies optimal wages i periods ad, takig ito accout that workers who do ot obtai a uio job select their search effort optimally. Utilisig U ~ / s * = 0, so that w does ot affect U ~ via s *, ad the assumptio of a costat labour demad elasticity ε := -N 'w /N = -N 'w /N > 0, the derivatives of U ~ (w,w s *,s *) with respect to w ad w are give by: U ~ Y ~ ) u(w) N ~ u(p) u(p : = = w u'(w )( t) ε u(w + ) C(s *) = 0 w (3) U ~ Y ~ = = ε ) θ(s c ) + C(s *) : w u'(w )( t) u(w *)u(w w + ε( θ(s *)) u(w) N [u(p) u(p )] ( N )C(s *) = 0 (4) 8 Actually, the worker maximises the expected payoff resultig from search, give o uio job i period oe. This expected payoff is give by: c θ ( s )u(w ) + ( θ(s ))u(w) C(s )) + θ(s )[ N (u(w ) + u(p)) + ( N )A(s *)] + θ ( (s N u(p )) ( N u(p )) )) (u(w ) )(u(w) = θ ξ c ( s ) u(w ) u(w) N (u(p) u(p )) ( N )C(s *) C(s )), where ξ is idepedet of s, ad the first term before the equality sigs describes the expected payoff from search i period oe, while the secod ad third term capture the expected payoff i period two, give o uio job i the first period. The maximisatio of this expressio with respect to s leads to the same outcome as the maximisatio of U ~. 9

23 The secod (ow-) derivatives of (3) ad (4) are assumed to be egative, while the crossderivatives ad the effects of a rise i the parameter α, takig ito accout s i */ α > 0 from (7) ad (), ad also () i (7), are give by: Y ~ i = ε( θ(s u(p) u(p ) C(s *))N' j *) w j, i, j =,, i j (5) Y ~ s = ε θ + θ * u' (P )N ~ u(p) u(p ) C(s (s *)) ( N ) '(s *) α ( α *) (6) Y ~ α = ε( θ(s *))N u' (P ) s ε * s ε * ( N )s * s * α α s + εθ * '(s c *) u(w ) u(w) + N u(p α [u(p) )] [ N ( θ(s *)) + ( N ) θ(s *)] 0 + ( N )C(s *) = εu '(P ) < (7) The derivative i (5) will i be egative if UISAs are itroduced (P = P ) because a competitive wage i excess of uemploymet beefits already iduces a positive search effort (s * > 0). Assume, however, that the term i square brackets i (5) is o-egative. For Γ := u(p) u(p ) C(s *) 0, Y ~ / w = Y ~ / w > 0 ad Y ~ / α < 0 hold. Give the sufficiet secod-order coditio for a maximum of U ~, the chage i the wage w owig to a rise i α is foud to be egative. I aalogy, dw /dα < 0 ca be derived. Therefore, wages will declie ad uio employmet will rise with a more proouced reductio of all the uemployed's pesios also i the presece of edogeously determied job search efforts by workers without previous uemploymet experiece if Γ 0 holds. Assumig that UISAs also (weakly) reduce uemploymet by those workers ot lookig for a job i the uio sector, the fidigs ca be summarised as: Propositio 3 Assumig that () workers who do ot obtai a job i the uio sector ad who are without previous uemploymet experiece search for a job i the competitive labour market, () there is o differetiatio of pesios for short-term ad log-term uemployed, ad (3) Γ 0 holds, UISAs will uambiguously reduce wages so that employmet will rise. 0

24 Propositio 3 clarifies that the basic result accordig to which UISAs raise employmet i the presece of collective wage determiatio ca also occur if search effort by workers who do ot fid a job i the uio sector is take ito accout. However, simplifyig assumptios particularly with respect to the probability of fidig a o-uio job ad the treatmet of log-term uemployed ad their search behaviour are required to obtai this result. The reasoig is as follows: If job search is allowed for, this opportuity will oly have a effect o behaviour if search makes a worker better off (at least i expected terms). Therefore, allowig for job search icreases the expected payoff of those workers who do ot obtai a job owig to excessive wages. This effect, ceteris paribus, teds to icrease uio wages ad, as a cosequece, creates various repercussios o optimal search behaviour. The simplifyig assumptios listed i Propositio 3 rule out that these repercussios substatially affect the outcome. The mai, wage mitigatig impact of UISAs, captured by Propositio thus cotiues to determie the outcome. 4.3 Edogeous Pesios Pesios geerally deped o the magitude of cotributios made by employees ad firms. Moreover, these cotributios are usually wage- or icome-related. Accordigly, if wages determie cotributios that, i tur, gover the magitude of pesios, pesio paymets will be affected by wages. It may, therefore, be plausible to assume that pesios P are a liear fuctio of cumulative wage paymets, P = p(w + w ), 0 < p <. Followig the same procedure ad applyig the same argumets as for the model with fixed pesios (cf. Sectio 3), it ca be show that wages do ot vary over time, implyig P = pw. The coditio for the optimal wage ca be expressed as: Ψ ˆ = Nu' (w )( t) + N' ρ + p N u'(p) + N( N)u' (P ) + ( N) u'(p ) = 0 (8) where ρ > 0 is defied i equatio (7) ad the payoffs specific to this sectio are characterised by a hat (^). Relative to the case of a fixed pesio, there are additioal icetives to raise the wage, sice ay wage icrease ot oly makes employed workers better off but also raises everyoe's pesio. I the derivatio of equatio (8) the assumptio of a costat labour demad elasticity imposed previously has ot bee made because such a restrictio would bias the fidigs, as argued i footote 0.