Monopolistic Competition and Di erent Wage Setting Systems.

Transcription

1 Monopolistic Competition and Di erent Wage Setting Systems. José Ramón García Universitat de València Valeri Sorolla y Universitat Autònoma de Barcelona July 20, 200 Abstract In tis paper we matc te static disequilibrium unemployment model witout labor market frictions and monopolistic competition wit an in nite orizon model of growt. We compare te wages set at te rm, sector and national (centralized) levels, teir unemployment rates and growt in economic variables, for te Cobb- Douglas production function, in order to see under wic conditions te inverse U ypotesis between unemployment and te centralization of wage bargaining is con- rmed. We also analyze te e ect of an increase in monopoly power on employment and growt in te tree wage setting systems. Keywords: Disequilibrium Unemployment, Monopolistic Competition, Growt, Wage Setting Systems. JEL number: E24, O4. García is grateful to te Spanis Ministry of Education for nancial support troug grant SEJ y Departament d Economia i d Història Econòmica, Universitat Autònoma de Barcelona, Edi ci B - Campus UAB, 0893 Bellaterra, Spain; tel.: ; fax: ; valeri.sorolla@uab.cat. Corresponding autor. Sorolla is grateful to te Spanis Ministry of Science and Innovation for nancial support troug grant ECO and to te Generalitat de Catalunya for nancial support troug grant 2009 SGR 578.

2 Introduction Te nancial and economic crisis tat started in 2008 as generated strong growt in te unemployment rate in many countries of te OECD. More speci cally, te average unemployment rate increased by 3 percentage points in OECD countries between 2007 and te rst quarter of 200. Te increase in te unemployment rate as been dramatic in countries like Spain, were it rose from 8.3 % to 9 %. Tese results ave begun to encourage important debates at political and academic level on possible reforms of te labor market in te OECD countries most a ected by tis problem. It as been suggested to modify te system of wage negotiation in tose countries caracterized by wage bargaining at sector level to models of negotiation tat generate iger wage moderation tat can give rise to employment. Tese proposals are based on te seminal article by Calmfors and Dri ll (988), were te worst result, in terms of employment, was obtained in a model were te wage was negotiated at te sector level. In tis context, our article considers a wide range of variables at te moment of wage negotiation tat do not appear in Calmfors and Dri ll (988), paying special attention to te role tat market power as on producing iger unemployment wen te wage is set at sector level. Moreover, we consider te e ects tat te unemployment rate as on long-term economic growt. We matc te static disequilibrium unemployment model witout labor market frictions in a monopolistic competition set up ( Arnsperger and De la Croix (990), Layard, Nickell and Jackman (99), Dutt and Sen (997), Blancard and Giavazzi (2003), Spector (2004)), wit te in nite orizon model of growt (see Galí (996) for te full employment version). We compare te wages set at te rm, sector and national (centralized) levels, teir unemployment rates and growt in economic variables for te Cobb-Douglas production function in order to see under wic conditions te inverse U ypotesis between te unemployment rate and te degree of centralization, postulated by Calmfors and Dri ll (988), olds for te unemployment rate and oter variables. We use te monopolistic competition set up because it is te natural framework for di erent labor demand elasticities wit respect to te real wage wen wages are set at te rm, sector and national (wage set for all sectors togeter) levels, te elasticity is greater at sector level tan rm and centralized levels. Tis is because te e ect of te wage on prices is only taken into account at sector level. Tis iger elasticity, combined wit oter variables, will normally produce iger wages and, ceteris paribus, a lower employment rate at te sector level. Te existence and consideration of product market power is te reason tat usually produces te inverse U ypotesis in tis paper. Te idea tat canging from sector to centralized level results in a decrease in labor demand elasticity appears in Layard, Nickell 2

3 and Jackman (99), but tey also justify te existence of full employment wen wages are set at te national level. We upgrade te Layard, Nickell and Jackman set up by adding rm level wage setting and, more importantly, by introducing oter institutional caracteristics tat also a ect wage determination, suc as te size and structure of social expenditures, public sector ine ciencies, te degree of internalization of te contribution of labor income to te provision of social services and labor taxes. From a teoretical point of view, it is interesting to analyze under wat circumstances tese variables may cange te inverse U e ect, due to te di erent labor demand elasticities, and full employment at national level. Neverteless, te important point is tat, as we will see in te next section, te values of some of te institutional variables tat we introduce in te model are really di erent across countries. Tis means tat trying to ceck te inverse U ypotesis by looking only at te level of centralization, witout controlling for all te oter variables, may result in te inverse U ypotesis not appearing in te data. Finally, te introduction of growt allows us to ceck weter te inverse U ypotesis olds for oter variables. Te market power explanation for te inverse U form is di erent from te original one given by Calmfors and Dri ll because tere is no market power in teir model. Te inverse U form arises because of te assumption tat, as centralization increases, te goods produced by sectors wose unions set te wage togeter are closer substitutes. Tere is anoter paper tat combines monopolistic competition, (non frictional) unemployment and growt. Brauninger (2000) presents an OLG growt model wit monopolistic competition, Cobb-Douglas production function, unemployment, wages set at sector level and a rule (constant replacement rate) tat implies a constant employment rate. Te paper analyzes ow unemployment a ects income per capita in te long run. Tere are more papers tat combine perfect competition, (non frictional) unemployment and growt: Daveri and Tabellini (2000) present an OLG growt model wit perfect competition, Cobb-Douglas production function, unemployment, wages set at national level and te rule tat implies a constant employment rate. Tey analyze ow labor taxes a ect employment and long run growt wen tere is an externality in production. Doménec and García (2008), using an IH growt model, introduce te institutional caracteristics presented in tis paper and analyze ow tey a ect te employment rate. All tese papers make assumptions tat imply a constant unemployment rate derived via te wage equation. Te di erent assumptions used are discussed in Rauric and Sorolla (2008) and, because of te use of te wage equation, te constant unemployment rate is neutral wit respect to canges in capital and total factor productivity. All tese papers also use a Cobb-Douglas production function. Kaas and von Tadden (2003) present an OLG growt model wit perfect competition, disequilibrium unemployment and a CES production function. Te cange of production function results in constant real wages and a capital labor ratio instead of a constant employment rate. 3

4 Our results sow tat a ig degree of market power produces te inverse U form for unemployment postulated by Calmfors and Dri ll (988), but tey also illustrate tat an increase in employment is possible considering, alternatively, oter types of reforms in te labor market. Tis is because te unemployment rate depends on a complex sample of variables, one of wic corresponds to te system of wage negotiation. Te paper is structured as follows: In section 2 we present te stylized facts concerning some variables tat appear in te model. Section 3 derives labor demand wit monopolistic competition. Section 4 introduces te government budget constraint. Section 5 derives te wage set at te sector level and Section 6 te employment rate at te rm and sector levels. Section 7 computes te wage and employment at national level and section 8 includes te growt equations and results. Te paper concludes wit a summary of te main results. 2 Te stylized facts for some OECD countries. Many of te articles tat ave been written in te last few decades about unemployment focus on explaining te substantial di erences in te level and evolution of te unemployment rate across OECD countries. Te poor performance of te unemployment rate is explained by socks and di erences in institutions or te interaction of bot. It is important to note tat te collective bargaining system appears as a key element in all tese explanations. As pointed out by Calmfors and Dri ll (988), igly centralized (at national or multi-industry level) and decentralized (at te rm level) bargaining systems perform better tan intermediate ones (at te sector/industry level) on wage demands. At rm level, te competitive pressure from oter rms in te same industry (producing closer substitutes) provides strong incentives to moderate wage demands. At national level, te central union federation will internalize externalities tat would be ignored by negotiators in decentralized bargaining structures. Consequently, it is predicted tat more centralized collective bargaining arrangements will produce lower wage demands and unemployment rates. Tis paper explores from a teoretical point of view te link between te unemployment and economic growt rates wit te collective bargaining systems at te rm, industry and national levels. Neverteless, our analysis is deeper because we add oter institutional features, rigidities and macroeconomic parameters tat also a ect wage bargaining. We include te size and structure of social expenditures, public sector ine ciencies, te labor force participation rate, labor taxes and te degree of competition of te output market. We sow tat te employment rate depends on all tese variables togeter, wic means tat empirical researc based only on canges in one variable usually yields poor results. Wen one analyzes, for example, te in uence of taxes on unemployment it seems tat An excellent survey on tese issues can be found in Blancard (2006). 4

5 oter elements must be taken into account in order to explain te data. Te empirical evidence presented by Daveri and Tabellini (2000) supports te view tat in more corporate and decentralized countries, labor taxes are less distortionary tan in countries wit an intermediate level of wage bargaining. Taking into account a broader set of variables tan te wage bargaining system o ers an explanation for te lack of robustness of te ump-saped curve predicted by Calforms and Dri ll (988) 2. Te group of countries tat belong to a certain wage bargaining system may di er in te composition of labor taxes, te ine ciency of teir governments, te degree of competition in te goods market, etc.. and all tese variables also a ect wage determination. However, as we will see, some caracteristics are correlated, wic sometimes implies good results witout considering all variables. Table presents te classi cation of many OECD countries by teir wage negotiation system in tree groups tat we ave named ANGLO, EUCON and NORDIC. For tis country classi cation we use te product of bargaining level, union density and bargaining coordination relative to te value for Finland 3. 2 See Aidt and Tzanatos (2008), for a excellent survey of tese issues. 3 Source: Database Nickell (2006). 5

6 Table Some labour markets institutional indicators in OECD countries Bargaining Union Coordination Relative level Coverage Product ANGLO USA Canada Japan UK New Zealand EUCON France Switzerland Greece Australia Italy Denmark Neterlands Spain Germany Belgium Portugal Ireland NORDIC Sweden Norway Austria Finland Source: Database Nickell (2006). In Tables 2 and 3 we add an average value of di erent institutional indicators and rigidities for te period Te teoretical study below investigates more closely te mecanism troug wic te variables tat re ect te institutional framework a ect te unemployment rate. In Tables 2 and 3 we add an average value of di erent institutional indicators and rigidities for te period Te teoretical study below investigates more closely te mecanism troug wic te variables tat re ect te institutional framework a ect te unemployment rate. Te rst variable presented in Table 2 is te armonized unemployment rate from 6

7 OECD statistical (U). Column 2 sows te degree of e ciency of te public sector (GE) 4. Tis variable was been constructed by Kaufmann et. al. (2009). Tese autors de ne government e ciency as an aggregate governance indicator tat measures perceptions of te quality of public service provision, te quality of te bureaucracy and te competence of civil servants among oter elements related to te government. Tis variable is relevant for wage determination wen te government nances a given level of social expenditure. Te more ine cient te government is te iger te tax rates necessary to nance a given government expenditure and, terefore, te greater te e ects on employment. Column 3 sows te degree of rigidity in te goods market (PMR) 5. Many autors stress te relationsip between rigidities in te goods markets and wage setting 6.Wen te price elasticity of goods demand is ig, rms ave more market power and te elasticity of labor demand wit respect to wages is also ig and workers ask for a iger wage. Tus, altoug product market competition is assumed to not ave a direct in uence on union bargaining power, it does ave an indirect impact troug te elasticity of labor demand and tereby on te resulting wage rate. Finally, Column 4 of Table 2 sows te average labor force participation rate elaborated by te OECD (LBPR) tat we assume a ects te amount of social services tat an active worker receives. 4 See Doménec and García (2008) for an in-dept discussion of tis variable. 5 Te indicator of product market regulations (PMR) is de ned in Conway et. al. (2005). Te source of te database is te webpage ttp: 6 For a more detailed discussion of tese issues see, for instance, Nickell (999), Boeri et.al (2000), Blancard and Giavazzi (2003) and OECD (2002) capter ve. 7

8 Table 2 Rigidities and institutions U GE PMR LBPR ANGLO USA Canada Japan UK New Zealand average std desv EUCON France Switzerland Greece Australia Italy Denmark Neterlands Spain Germany Belgium Portugal Ireland average std desv NORDIC Sweden Norway Austria: Finland average std desv Table 3, Column sows social expenditures wit respect to GDP (SE). Tese expenditures are basically nanced by social security contributions paid by workers and employers. Imposition on labor revenues and oter taxes play a minor role (See OECD 8

9 (2007)) 7. Tus, a very close relationsip can be observed between te nancing of social policy expenditure and te unemployment rate, troug te social security contributions in te labour market. Columns 2 to 5 report average tax wedges (TW), income tax (IT) and employees and employers social contributions (WSC and ESC respectively). Te tax wedge is computed as te sum of labor income tax, and social security contributions paid by workers and employers 8. As can be seen from te Table 3, tere are large di erences in te composition of te tax wedge across OECD countries over te period In general, countries wit te igest labor tax are also tose tat tend to ave te igest social contributions paid directly by employers. Te most striking results tat emerge from te data for EUCON countries wit respect to te rest of countries are te following. For nancing social expenditures, we nd tat te social security contribution paid by employers (Table 3 ESC) in some countries is prominent (e.g. France, Italy and Spain). Anoter relevant fact is tat, on average, tey are te most ine cient (Table 2, GE average.57), ave a more regulated goods market (Table 2, PMR average.68) and te lowest labor participation rate (Table 2, LBPR average 72.46). Tese tree caracteristics are important, since tey interrelate wit te imposition on te labor market and, terefore, wit unemployment. Unfortunately, tese series are relatively recent and it is not possible to obtain a longer sample period tat allows regressions to be performed. Tese factors may explain te relatively good/poor empirical estimations found by di erent autors over time. 7 Only Australia, Denmark and N. Zealand do not nance social policy expenditure wit social security contributions. 8 All te e ective tax rates ave been computed, as suggested in Boscá, García and Taguas (2005), using te metodology proposed by Mendoza et. al (994). 9

10 Table 3 Social expenditure and te tax structure SE TW IT WSC ESC ANGLO USA Canada Japan UK New Zealand average std desv EUCON France Switzerland Greece Australia Italy Denmark Neterlands Spain Germany Belgium Portugal Ireland average std desv NORDIC Sweden Norway Austria: Finland average std desv Te stylized facts presented above suggest tat te Eucon countries ave te institutional caracteristics tat can generate a iger unemployment rate tan te rest of countries. Table 4 presents te simple correlation using cross-country data between all relevant variables over te period Since a correlation does not imply in any 0

11 sense causality, te existence of signi cant correlation suggests tat te mecanism relating te variables to labor market performance is not so simple. Table 4 sows tat te tax rates paid by employers seem to be positively related to te unemployment rate (0.663). At te same time, tere is a positive correlation between government e ciency and te labor force participation rates in OECD countries (0.676). It is interesting to notice tat tere is a strong negative correlation between government e ciency and te product market regulation (-0.636). Finally, social expenditure and tax paid by employers are igly correlated (0.63). All tese correlations led us to consider a teoretical framework, in te next sections, in wic all tese variables appear and determine te unemployment rate. Table 4 Correlations between institutions and social expenditure GE LBPR PMR SE TW ESC U * ** 0.546* * 0.663** GE 0.676** ** * LBPR -0.56** ** PMR * 0.63** SE 0.860** 0.607** TW 0.83** ** Te correlation is signi cant at 0.0 level ** Te correlation is signi cant at 0.0 level 3 Labor demand in sector j wit monopolistic competition in te goods market We assume J 2 [0; ] sectors wit one rm per sector tat produces a di erent good, Y j (t), using te same production Cobb Douglas tecnology, tat is: Y j (t) = AK j (t) L j (t). () Te demand function facing rm J is Y j (t) = Pj (t) Y(t), (2) P (t) were > is te constant elasticity of demand of product J wit respect to its price, Y(t) Y (t) is total real expenditures on consumption and investment, P P (t) j(t) is price of product j, P (t) is a price index wit te abitual properties and Y j (t) is te corresponding quantity demanded of te consumption and investment good produced by rm j 9. 9 For more details see Appendix A.

12 Te rm in sector j maximizes te wealt of its sareolders subject to te demand function (2). Eac rm pays a payroll tax, f, in order to nance social services. Te rst order condition in terms of te real wage 0 is: ( )AK j L j A K j L j = ( + f )m! j, (3) Y(t) were te parameter m represent te monopoly degree or te (price) markup m ( ) = and! j (t) W j(t) P (t) is te real wage in sector j: Te labor demand, in terms of te real wage, is, ten: L d j(t) = ~ L d j(! j (t)) = A ( ) +( ) K(t) +( ( + ) Y(t) f ) +( ) (m ( )! +( ) j(t)), (4) were te elasticity of te labor demand wit respect to te wage is constant and given by: " L d j ;! ~ L d j(! j j! j ~L d j (! j) = + ( ) = + ( ). (5) Note tat te elasticity of labor demand depends positively on te product market elasticity wit te property tat te greater te te lower " L d j ;! j and always " L d j ;! j <, meaning tat an increase in te real wage always decreases te wage bill! j ~ L d j (! j ). In te case of perfect competition we ave = and elasticity is equal to. 4 Government budget constraint Before describing wage bargaining, we need to introduce te government budget constraint. Te government nances te unemployment bene ts paid to unemployed workers and social services. To generate revenue, at eac period t te government imposes a at-rate tax. More speci cally, L denotes te tax rate paid by employees on wages. Tis tax includes income tax plus te social security contribution paid by employees. We assume tat given a level of taxes collected, more ine cient governments will produce a lower level of transfers and social services. It can be assumed tat tis level of ine ciency will be proportional to te administrative cost of managing tax revenues. 0 Tis expression comes from equation (50) in te appendix. Alternatively, forcing te model because we assume only one rm per sector, we can consider te perfect competition situation te case were te rm takes P j (t) as given. Ten, te rst order condition in terms of Wj(t) P j(t) is F L = + f W j(t) P j(t), labor demand is: Ld j elasticity wit respect to Wj(t) P j(t), " L d j ;( W j P j ) =. = ~ L d j ( Wj P j ) = ( )A (+ f ) W j P j! K j and te 2

13 Te parameter stands for te level of ine ciency of te government to nance its public expenditure 2. From all tis, it follows tat te government s ow budget constraint in real terms is: ( + ) (S(t) + (N(t) L(t))B(t)) = L + f!(t)l(t), (6) were S(t) are social services in real terms, B(t) te unemployment bene t in real terms and N(t) te inelastic labor supply (active population). We assume, tat a part of te tax revenues is used to nance social services (suc as education, social security system, pensions etc.) and anoter part is cannelled to nancing te unemployment bene ts of unemployed workers in eac period, so tat te following equalities old: ( + )S(t) = L + f!(t)l(t), (7) ( + )B(t)(N(t) L(t)) = ( ) L + f!(t)l(t), (8) were te parameter captures te relative weigt of te expense in social services decided by te government wit respect to tax revenues. Rewriting te last two equations we get: and S(t) = L + f!(t)l(t) ( + ) (9) Note tat, because we assume L and f L + f!(t)l(t) B(t) = ( ) ( + )(N(t) L(t)). (0) are invariant, te last two equations imply tat an increase in te wage always reduce S(t)and B(t), wen employment is given by labor demand, because its elasticity wit respect to te real wage is less tan. We include te level of public services, S(t), in te utility function of trade unions, re ecting te fact tat te welfare of workers depends on te level of social services tey receive 3. If we add equation (9), we also assume tat workers ave perceptions about ow canges in te wage a ect te amount of public services. 2 A similar assumption is made by Doménec and García (2008). 3 For a more extensive discussion, see Mares (2004). 3

14 5 Wage setting at te sector level We assume tat te basic teoretical structure takes into account a tree-stage game. In te rst stage, te rms decide te level of capital stocks anticipating teir e ects on wage setting and labor demand. In stage two, te wage rate is determined troug a process of bargaining between employers and trade unions. Finally, in stage tree, te rm unilaterally determines te employment level once te conditions of te wage negotiations and investment decisions ave been settled. 4 It is assumed tat te labor force is completely unionized. Tere are J unions (one for eac industry) wose objective is to maximize te income of a worker working in te sector wit respect to te alternative income of working outside te sector, R j (t), times employment. Additionally, we assume tat te union takes into account tat social services a ect te welfare of workers and tat te revenues obtained from te wage bill of te sector may contribute to nance social services 5. Te speci cation of te j t union utility function is given by V j = ( L )! j (t) R j (t) L d j(t) + s ( L + f )! j (t)l d j(t). () ( + ) We introduce te parameter s wic measures te ability of te trade union in sector j to internalize te contribution of te wage bill in sector j,! j L d j, to te provision of social services. It is reasonable to assume tat tis parameter is determined by two factors. Te rst is te degree of centralization of wage bargaining. Tere as been some consensus in recent literature on te importance of te degree of centralization of wage bargaining system on te unemployment rate. It is very usual in te literature to classify wage setting regimes by teir degree of centralization into tree types. Higly centralized systems, suc as national level bargaining, intermediate levels of centralization, were te bargaining process is carried out at industry level and, nally, negotiation at te rm level. We assume tat te degree of internalization is positively related wit te level of centralization of wage bargaining. Te second factor tat will a ect te value of parameter is te sare of active labor force wit respect to te inactive population in te economy. We suppose tat te same level of social services is available to te labor force and te inactive population. Note tat te social services for te non active population are nanced by taxes levied on te active population. Terefore, if te unions care only about te social services of te active population, te iger te inactive population receiving social services, te lower te ability of trade unions to internalize te provision of services and te lower te value of parameter s 6. We also assume tat te union considers no 4 For a more details over tis issue see, for example, Koskela et. al (2009) 5 Details of tese ypoteses are given in Mares (2004). 6 In a more formalized way: our active population is N(t) and total population P (t) = ( + )N(t). 4

15 e ect of te wage bill in sector j on alternative income because, altoug it is true tat te wage will nance te unemployment bene t in tis sector, te weigt of te unemployment bene t on alternative income is small, because it is also comprises te wages of all te oter sectors. Turning to wage bargaining, we assume tat employers negotiate te sector wage wit te trade union taking into account tat rms retain teir rigt-to-manage power and determine employment (and capital) after te wage as been set. Te outcome of wage bargaining is determined by te Nas-bargaining solution, wic maximizes te Nas product (V j ) j j : Were denotes te bargaining power of te trade union. Te fall-back position for te rm is given by j = r t K j : For an interior solution, te maximization of te logaritm of te generalized Nas criterion gives te rst order condition: were and V j! V j = " V j! + ( ) j j! = 0, (2) V j j j # L d j j! j ( L ) + ( L + f j ( + ) R d j (3) ( ) j j! = ( ) j j! j (m( ) ). (4) Substituting expressions (3) and (4) into te rst-order condition (2) yield, after some rearrangement, te following Nas bargaining solution for te wage rate set by union J! j (t) = ( ) + m ( L ) + s ( L + f ) (+) ir j (t). (5) Note tat in tis case an increase in market power increases te wage as empasized by Layard, Nickell and Jackman (99) (P. 27) and Spector (2004). Note also tat an increase in, and f produces wage moderation and an increase in L and an increase in wage demands. If te rm beaves competitively we ave, on te one and, m =, wic gives te labor demand elasticity ; on te oter and, we assume te internalization parameter to be zero because tere are many rms and many sectors, te wage bill of one rm being negligible in regard to te total wage bill tat nances social services. Ten te wage is: Ten social services per person are S(t) P (t) and te social services of active population, te term tat enters in utility function of te union, S(t) P (t) N(t) = S(t) (+). 5

16 ! f (t) = ( ) + R ( L j (t), (6) ) aving tat! f (t) <! j (t) if m is ig enoug (m > + ( ) + ( ) ( L ) s ( L + f ) ): (+) Tis is because te positive e ect of te reduction in monopoly power will dominate te negative e ect of te elimination of te internalization parameter and, ten, tere will be wage restraint. If we interpret te wage set in te competitive case as wage setting at rm level, because te union takes into account te labor demand of a small competitive rm 7, ten we will ave wage restraint at rm level. 6 Te alternative income and te constant employment rate at te rm and sector level. In te sort run partial equilibrium presented above, te wage bargaining process takes te alternative income of working outside te sector (or te rm) as given. Neverteless, in te sort run general equilibrium, all sectors set te same price and wages in all rms and sectors are set in a similar way. As a result R(t) becomes endogenous. In tis model we assume tat te alternative income a worker gets if e does not work in rm or sector j is given by 8 R j (t) = l(t)( L (t))! e (t) + ( l(t))b(t); (7) were l(t) is te employment rate of te economy i.e. min(l d (t); N(t)) and L d (t) = Z 0 l(t) L(t), were L(t) = N(t) L d j(t)dj,! e (t) is te alternative wage of working outside ( rm) sector j and B(t) is te unemployment bene t tat an unemployed worker gets. In a symmetric equilibrium! j (t) =! e (t) =!(t). We assume tat te unemployment bene t is nanced by te employed workers revenues and determined by te budget constraint of te government once it as decided te constant tax rates, ten from (0), it is: B(t) = ( ) ( + ) ( L + f )!(t)l(t), (8) ( l(t)) taking into account tat! e (t) =!(t) and combining equations (5), (7) and (8) we obtain: 7 In tis case te utility function of te union would be V f;j = ( L ) Wj P R j i ~L d j ( Wj P j ) were te union cooses W j, and, one can sow tat te solution is te above expression. 8 In a similar way Romer (2006) p.454 assumes: R t = ( bu t )! t. 6

17 !(t) =!(t)l(t) ( ) + m i ( L ) + ( ) ( L + f ) (+) i. (9) ( L ) + s ( L + f ) (+) And te employment rate wen wages are set at te sector level is: l(t) = ( ) + m ( L ) + s ( L + f ) (+) ( L ) + ( ) ( L + f ) (+) i i = l SL. (20) Tis means tat te wage equation plus te unemployment bene t budget constraint equation gives, for te Cobb-Douglas production function, a constant employment rate. We can nd a similar expression for a constant employment rate derived via a wage equation plus an unemployment bene t budget constraint equation in a monopolistic competition set up wit a Cobb-Douglas production function and were wages are set at national level (see next section) in Braüninger (2000). Layard, Nickell and Jackman (99) P. 27 also derive a constant unemployment rate using a wage equation plus a constant exogenous replacement rate B. Tere are oter ways of obtaining constant employment rates: wit! perfect competition and a Cobb-Douglas production function, Daveri and Tabellini (2000) assume B(t) = Y (t) and Doménec and García (2008) do te same. Rauric and Sorolla L(t) (2008) discuss di erent ways of obtaining a constant employment rate wen te wage is a mark-up over te reservation wage. Tis constant unemployment rate depends crucially on te use of (0), wic, as we said before, means tat wage increases produce a reduction in te unemployment bene t 9. Papers tat assume a constant unemployment bene t are, for example, Pissarides (998) but in our opinion tis assumption in an economy wit growt is worse tat assuming constant taxes. Looking at lsl it is easy to see tat tere is unemployment wen wages are set at te sector level m is ig enoug or s is low enoug, tat is, iger monopoly power or a lower proportion of social services or lower perceptions produce unemployment. < 0 and tat neiter canges in capital K nor total factor productivity A a ect employment, tat is capital and productivity are neutral wit respect to unemployment or growt does not a ect employment. Te reason is tat wit tis wage setting rule an increase in Kor A decreases unemployment, but ten te unemployment bene t increases and also te wage, completely crowding out te positive e ect of Kor A on labor demand. Koskela, Stenbacka and Juselius (2009) wit a particular production function obtain an employment rate tat depends on capital. Tere is also empirical evidence tat K a ects employment on te sort run (Karanassou et. al. (2008) and Driver and Muñoz-Bugarin (2009)). 9 One may argue tat real governments do not reduce te unemployment bene t wen unemployment increases, but, as we said, a similar result is obtained using B(t) = Y (t) L(t) : 7

18 We can explore te e ect of te weigt of social services, te imposition on te employee L and f on te employment rate. Te di erentiation of te employment rate (20) wit respect to yields a positive relationsip. Te e ect of te imposition on employment in bot cases depends on te sign of te following expression [ s ( )] More speci cally, > 0 > 0 f s > : Our ndings concerning te determinants of unemployment, under sort run general equilibrium, sow te importance of te relationsip between te parameters of te model. Wen te wage is set at te rm level, te employment rate is equal to ( L ) l(t) = i = l ( ) + ( L ) + ( ) ( L + f ) F L < (2) (+) and tere is always unemployment. Note tat te employment rate does not depend on m. Tis may seem strange because from (6), it is te wage wat does not depend on m. Te explanation is tat an increase in m does not initially cange te wage and, via labor demand, increases unemployment, but, if unemployment increases, te unemployment bene t is reduced, implying, via a wage equation, a decrease in te wage in suc a way tat, nally, employment is not a ected. Note nally tat, as we argued before, if m is ig enoug, we will ave a iger employment rate at rm level. Tis result gives te condition for te rst part of te inverse U ypotesis to be true, if market power is ig enoug te unemployment rate will be iger if wages are set at te sector level tan if tey are set at te rm level. Tis fact is due to te iger wage set at sector level iger elasticity of te labor demand to take into account te output demand function. 7 Wage setting at national level Following Layard, Nickell and Jackman (99), P.5, in a symmetric equilibrium P j (t) = P (t) for all j and ten te aggregate price index is also P (t), tus te labor demand in sector j becomes 20 : F L (K j (t); L j (t)) = m( + f ) W j(t) P (t) = ( + f )m! j (t), moreover in tis symmetric equilibrium K j (t) = K(t), L j (t) = L(t) and ten te aggregate labor demand Z 0 demand is given by te equation: L j (t)dj is also L j (t) and! j (t) =!(t). Tis means tat aggregate labor 20 Tis assumption implies tat product demand and ten market power disappears from te program of te rm. 8

19 F L (K(t); L(t)) = ( + f )m!(t), (22) expression tat implies te aggregate labor demand function L d (t) = L ~ d ((+ f )m!(t); K(t)) were L ~ (+ f )m! < 0 and L ~ K > 0: More speci cally, for te Cobb-Douglas production function aggregate labor demand is: L d (t) = ( ) A (( + f )m!(t)) K(t), wit elasticity wit respect to te wage equal to < market power, m, as is te case wen te rm acts competitively., tat also does not depend on Now we assume tat in a centralized wage setting system, te national union maximizes te utility function given by were V = ( L )!(t)l(t) + (N(t) L(t))B(t) + n ( L + f )!(t)l(t) ( + ) L(t) = min(n(t); L d (t)). (23) We assume, as argued before, tat n > s. It is easy to ceck tat te solution obtained from tis program is te same as te one obtained if te national union also maximizes () considering tat te alternative income R(t) is te unemployment bene t B(t), because tere is no alternative sector. Ten te wage set by te national union is! n (t) = ( ) + ( L ) + n ( L + f ) (+) ib(t). (24) Note now tat te wage markup over te alternative income is lower at te national level tan at te sector level because ( ) + i < ( L ) + n ( L + f ) (+) ( ) + m ( L ) + s ( L + f ) (+) due to te presence of te price markup in te sector level wage setting system, moderation tat is reinforced by te assumption tat in te wage setting system te value of is iger. Now considering (8) we ave tat te employment rate is: l(t) = ( L ) + n ( L + f ) (+) i ( L ) + n ( L + f ) (+) i + ( ) + i ( )( L + f ) (+) = l NL. (25) Note tat as long as < ten l NL <, tat is tere is always unemployment wen 9

20 wages are set in a centralized way. Wen = we ave l(t) =, tat is, if tere are only social expenditures and not unemployment bene ts te national union cooses te competitive wage. Tis is because in tis case te utility function of te union becomes: V = ( and, as te elasticity of labor demand in tis case is L )!(t)l(t) + n ( L + f )!(t)l(t), (26) ( + ) < reduces!(t)l(t) and te union cooses te competitive wage. Wen = 0, te employment rate is: l(t) = ( L ) ( L ) + ( ) + ( L + f ) (+), an increase in te wage = l NL < (27) tat means tat wen only unemployment bene ts are paid we ave unemployment wen wages are set in a centralized way. For aving lnl > l SL we need: > i ( L ) + n ( L + f ) (+) i ( L ) + n ( L + f ) + ( ) + (+) i ( L ) + s ( L + f ) (+) ( ) + m ( L ) + ( ) ( L + f ) (+) ( )( L + f ) (+) i. (28) An educated look at tis expression sows tat te rst term is always greater tan te second one if m is ig enoug or s low enoug, assuming all te oter parameters are equal. Tis means tat for all te oter parameters equal tere is wage restraint at national level if market power is ig enoug or te degree of internalization of te sector union low enoug. Tis may be surprising because we saw tat te wage markup is always lower wen wages are set in a centralized way, but te reason is tat alternative income is di erent. Of course, wen one considers di erent countries wit di erent parameters it may be te case tat even if te degree of market power is ig enoug or te degree of internalization of te sector union low enoug tere is more unemployment at national level. One may alternatively consider tat te national union also as perceptions about ow te wage will a ect te unemployment bene t in a similar way it considers it a ects social expenditures. In tis case, te national union believes tat canging te wage, te wage bill and te amount of employment will cange and ten also te unemployment bene t according to te equation: 20

21 ( ) B(t) = ' ( + ) ( L + f )!(t)l(t) (N(t) L(t)) wit 0 < ' 5 2. Wit a Cobb-Douglas utility function, tis means tat te union now considers tat an increase in te wage bill reduces te unemployment bene t because!(t)l(t) decreases and (N(t) L(t)) increases. Now te utility function of te union becomes: (29) V B = ( L + ['( ) + n] ( L + f ) )!(t)l(t) (30) ( + ) and in tis case it is obvious tat it cooses te competitive wage because te elasticity wit respect to te wage is equal to and an increase in te wage always reduces te wage bill!(t)l(t). In tis case, terefore, tere is full employment, tat is, lnl;s = and l NL;S > l S if m is ig enoug or s is low enoug. One may nally consider te opposite case: tat in a centralized wage setting system te national union also as perceptions about te e ect of wages on taxes. More specifically, it may tink tat if te wage increases ten te unemployment bene t and te tax rate on employers will remain invariant and ten te tax rate on employed workers is going to cange. Tis means tat, in tis case, te national union now adds te following restriction to its program: L = ( + )S(t)(N(t) ' L(t))!(t)L(t) were 0 < ' 5 re ects te union s belief about ow canges in te unemployment bene t are going to a ect workers taxes 22. Te case ' = 0, is te rst one presented in tis section and Layard, Nickell and Jackman (99) on P. 30 consider te case ' = =, f = = f = Now te objective function of te union becomes: V L = ( + f )!(t)l(t) + ( '( + ) + ')S(t)(N(t) L(t)) and for 0 < ' 5 te wage is:! n; L(t) = Ten te employment rate is: ( ) + i ( '(+)+') ( + f ) B(t). (3) 2 Tis is te case wen te union considers, in part, exactly wat te government does. 22 Te alternative assumption is tat te union tinks tat if te wage increases, ten te tax rate will (t)!(t)l(t) (N(t) L(t)). remain invariant and, ten, te unemployment bene t is going to cange according to s(t) = In tis case te objective funcion of te union becomes ( + )!(t)l(t) 23 In tis case, watever te union considers is going to appen wen employment canges, te objective function of te union is!(t)l(t). 2

22 l(t) = ( + f ) + ( + f ) ( ) + i = l ( '(+)+') NL;. (32) L Note tat in tis case tere is unemployment if te term '( + ) is low enoug and in te speci c case consider by Layard, Nickell and Jackman (99) we ave full employment, l(t) =. In order to ave l NL; > l L SL we need: ( + f ) + ( + f ) i > ( ( ) + '(+)+') ( ) + m ( L ) + s ( L + f ) (+) and, again, l NL; L > l S if m is ig enoug or s is low enoug. ( L ) + ( ) ( L + f ) (+) Terefore, obtaining unemployment or full employment in te centralized wage setting system depends eavily on wat te union assumes is going to appen wen te wage it sets increases. If it tinks tat neiter te unemployment bene t nor taxes on employed workers will cange, ten tere is unemployment. If it tinks tat an increase in te wage will decrease te unemployment bene t ten we ave full employment. If it tinks tat an increase in te wage will increase workers taxes we ave, in general, unemployment. Note also tat a iger degree of market power does not a ect any of te employment rates obtained wen wages are set at national level for te same reason as wen tey are set at rm level. In all tree cases we ave a iger employment rate wen wages are set at national level tan wen wages are set at sector level if i i (33) m is ig enoug or s is low enoug. Hence, we sould expect te inverse U relationsip between unemployment and te degree of centralization of wage setting wen te degree of market power in te product market is ig enoug. Tis is due to te iger labor demand elasticity at sector level because of considering market power at tis level. Tis argument is similar to Calmfors and Dri l s assumption tat te elasticity of labor demand decreases wit te degree of centralization, but we ave a strong argument for tis assumption: te consideration of market power wen wages are set at te sector level. Note nally, tat tis relationsip occurs wen all te oter parameters do not cange. Terefore, it is not surprising tat if one cecks for te inverse U ypotesis witout controlling for te oter parameters tat a ect te employment rate, te relationsip does not appear. 22

23 8 Houseolds and equilibrium In te IH model we ave a representative family wit N(t) members growing at te constant rate n, wit an inelastic labor supply equal to N(t) tat (see Galí (996) section 2.) cooses aggregate consumption per capita, c(t) order to maximize: Z 0 c j (t)dj, were c j (t) C j(t) N(t), in subject to: Z t=0 e ( n)t c(t) (34) _a(t) = ( )w(t)l(t) + s(t)( l(t)) e(t) + Z 0 (d j (t) + _q j (t))s j (t)dj na(t). (35) were s j (t) te number of sares per capita in rm j eld at time t by te family. A sare in rm j trades at price q j (t) and generates a dividend ow d j (t) at time t. Financial wealt of te family is tus given by A(t) = Z 0 q j (t))n(t)s j (t)dj and ten a(t) A(t) N(t). Note tat te revenues of tis family accrue from total labor income because we assume te family is so big tat it considers all workers, employed and unemployed, Daveri and Ma ezzoli (2000), Eriksson (997) and Rauric, Sala and Sorolla (2006) also make te big family assumption. If we ave eterogeneous agents instead of a big family, te solution does not cange as long as we assume complete competitive insurance markets for unemployment or tat te union pursues a redistributive goal, acting as a substitute for te insurance markets (Ma ezzoli (200) and Benassy (997)). In market equilibrium we obtain (see Galí (996)): _c(t) c(t) = m F K(k(t); l(t)) ( + ), (36) _k(t) = f(k(t); l(t)) c(t) (n + )k(t). (37) Were k(t) is capital per capita and F (k; l) is te production function per capita (see appendix). Assuming a constant employment rate l t = l, tat is wat we obtain wit a Cobb-Douglas production function plus te wage equations in te rm, sector and centralized wage setting systems, plus te assumption of te unemployment bene t budget constraint, tese equations become: 23

24 _c(t) c(t) = m F K(k(t); l ) ( + ), (38) _k(t) = F (k(t); l ) c t (n + )k(t). (39) Because l <, it is clear from (39) tat te rate of growt of capital per capita is lower for a given level of c and k in a model wit unemployment, tat is, employment a ects growt in te sort run. It is also clear, from (38) and (39), tat consumption and capital per capita converge to a steady state wit a zero rate of growt of capital per capita and consumption per capita. Tat means tat tere is no relationsip between growt and unemployment in te long run: te constant rate of unemployment is given by l and te rate of growt in income per capita is zero, or x, if we introduce tecnological progress. It is also easy to see, drawing te pase diagram, tat a decrease in l decreases te long run level of consumption, capital and income per capita, tat is, tere is a positive relationsip between income, capital and consumption per capita and employment in te long run. In oter words, all oter parameters equal, economies wit a iger employment rate will record iger income, capital and consumption per capita in te long run. On te oter and, te level of capital per worker and income per worker in te long run does not depend on te employment rate because we can rewrite (38) as _c(t) c(t) = m f(^k(t)) ( + ), (40) were ^k is capital per unit of labor and f(^k) te production function in intensive form, and, ence, in te long run ^k is given by: 0 = m f(^k) ( + ). (4) Ten, all te oter parameters remaining equal, we also ave a U relationsip between long run income, capital and consumption per capita and te degree of centralization of wage setting wen te degree of market power in te product market is ig enoug and tere is no relationsip between capital and income per worker and te degree of centralization of wage setting. Finally, as we saw, an increase in market power increases unemployment wen te wage is set at sector level, but as no e ect wen it is set at rm and national level. However, in all tree systems it produces a decrease in long run income, capital and consumption per capita and in capital and income per worker. 24

25 9 Main Results We te inverse U relationsip between unemployment and te degree of centralization of wage setting is to be expected in an economy were te product market is non competitive wen te degree of market power of tis product market is ig enoug. Tis is due to te iger labor demand elasticity at sector level because of considering market power at tis level. Note tat tis relationsip occurs wen all te oter parameters do not cange. As a result, it is not surprising tat if one cecks for te inverse U ypotesis witout controlling for te oter parameters tat a ect te employment rate, te relationsip does not appear. We sould also expect a U relationsip between long run income, capital and consumption per capita and te degree of centralization of wage setting wen te degree of market power in te product market is ig enoug and tere is no relationsip between capital and income per worker and te degree of centralization of wage setting. Finally an increase in market power increases unemployment wen te wage is set at sector level but as no e ect wen it is set at rm and national level. However, in all tree systems it produces a decrease in long run income, capital and consumption per capita and in capital and income per worker. Tis paper o ers an explanation for te weak relationsip between te wage bargaining system and te employment rate tat as been explicitly tested in a large number of studies. As we saw in section 2, te empirical evidence reveals strong eterogeneity for te parameters tat determine te rate of unemployment in te teoretical model of tis paper for te sample of countries wit a wage bargaining system at sector level. Tis causes, even inside tis group, te results on te unemployment to be very eterogeneous. Anoter implication of te results presented is tat it may be particularly relevant for policy makers wo plan to implement labor market reforms to reduce unemployment to analyze te speci c caracteristics for every country of te variables tat determine te unemployment rate in te model, suc as for example: social expenditure structure, government e ciency, etc. 0 References Aidt, T. and Tzanatos Z. (2008). Trade Unions, Collective Bargaining and Macroeconomic Performance: a review. Industrial Relations Journal 39(49): Arnsperger, C., and De la Croix, D. (990). Wage Bargaining wit a Price Setting Firm. Bulleting of Economic Researc 42, Benassy, J.P. (997). Imperfect Competition, Capital Sortages and Unemployment Persistence, Scandinavian Journal of Economics 99(): Blancard, O. (2006). European Unemployment: te Evolution of Facts and Ideas. Economic Policy, January,