Wage bargaining, union membership, and the organization of unemployment insurance

Labour Economics 6 Ž1999. 397–415 www.elsevier.nlrlocatereconbase

Wage bargaining, union membership, and the organization of unemployment insurance Bertil Holmlund a

a,)

, Per Lundborg

b,1

Department of Economics, Uppsala UniÕersity, Box 513, S-751 20 Uppsala, Sweden b FIEF, Wallingatan 38, S-111 24, Stockholm, Sweden Received 10 June 1998; accepted 18 December 1998

Abstract The paper offers a theoretical analysis of a labor market institution known as the Gent system, which is a system where unions run unemployment insurance ŽUI. through government-subsidized UI funds. This system is practiced in four Nordic countries with comparatively very high unionization rates. The analysis shows that the Gent system is more conducive to unionization than a compulsory UI system if the Gent system is heavily subsidized by the government or if workers are strongly risk averse. Moreover, a rise in the share of benefits financed by union members is likely to reduce wages as well as union membership. q 1999 Elsevier Science B.V. All rights reserved. JEL classification: J50; J65; J68 Keywords: Wage bargaining; Union membership; Unemployment insurance

1. Introduction There are huge and persistent differences in unionization rates among industrialized countries. Union density, i.e., trade union membership as a percent of the number of employees, varied in the early 1970s between 20% in countries like the United States and France and 60–70% in Denmark, Sweden and Iceland. The past 2 decades have seen increasing divergence in union density across countries. ) 1

Corresponding author. E-mail: [email protected] E-mail: [email protected].

0927-5371r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 5 3 7 1 Ž 9 9 . 0 0 0 1 0 - X

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During the 1980s union density fell precipitously in a number of countries, whereas it remained stable or increased in other countries. By 1990 union density had dropped to 15% in the United States and to 10% in France, while it had increased by 10–20 percentage points in all Nordic countries except Norway. On average union density among OECD countries stood at 43% in 1970 and had increased to 47% in 1980. By 1990, it had fallen back to 41% ŽOECD, 1994.. Four Nordic countries—Denmark, Finland, Iceland and Sweden—had the highest unionization rates in the early 1990s. These countries had membership rates exceeding 70%, with Sweden in the top with density over 80%. Union density in Norway, on the other hand, was only around 55%. The difference between Norway and Sweden is remarkable considering the marked similarities between the two countries in other dimensions. It is also noteworthy that union density is much higher in Belgium than in the Netherlands ŽOECD, 1994.. The four countries with the highest union membership rates organize their unemployment insurance ŽUI. systems through trade union affiliated funds with voluntary membership. These funds are generously supported by the governments. The practice of organizing unemployment insurance through government subsidized but union administered UI funds is often referred to as the ‘Gent system’ after the Belgian town where it was first introduced in 1901. Unemployment insurance in most other OECD countries is based on compulsory rather than voluntary systems. Belgium practices an intermediate system with compulsory UI but union involvement in the benefit administration. These observations suggest that there may be a connection between the organization of unemployment insurance and cross-country differences in unionization rates. Indeed, several empirical studies indicate that the Gent system may account for a substantial part of the difference in unionization rates across countries ŽRothstein, 1990; Western, 1993, 1994.. A number of social scientists have discussed the determinants of union density, but the functioning of the Gent system does not seem to have been subject to a formal theoretical analysis. 2 It may seem obvious that a system where unions run unemployment insurance is bound to raise unionization. This conclusion is not self-evident, however, since the organization of UI affects wage setting as well as the demand for union services. The analysis must accordingly recognize the interactions between membership demand and wage determination. Our paper presents a model of wage bargaining with endogenous union membership in order to examine theoretically how the organization of unemployment insurance affects wage behavior and union membership. Olson Ž1965. argued that unions need to offer selective benefits in order to retain and recruit members. To the extent that the unions offer services that have

2

See Naylor and Cripps Ž1993. for a recent review of some of the explanations of why workers join unions. Earlier contributions include Wallerstein Ž1989., Pedersen Ž1990. and Neumann et al. Ž1991..

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public goods features, there is an obvious free rider problem. A safer workplace, say, benefits members and non-members alike, and the same may hold true for higher wages because of the widespread practice—sometimes enforced by labor law—of paying members and non-members the same wage in the firm. The selective benefits may appear in many guises, such as access to grievance procedures or health insurance. The provision of unemployment insurance through the trade unions can be seen as a device whereby unions are able to recruit and retain members through the creation of benefits that are exclusive to the members. An investigation of the Gent system is important not only for understanding why union density varies across countries and over time, but also for understanding wage determination. Government subsidies, and in particular the degree to which the subsidies are tied to union members’ unemployment rates, are likely to influence wage negotiations through the effects on incentives for wage increases ŽHolmlund and Lundborg, 1988, 1989.. 3 Government subsidies to UI may also affect union membership. A comparison between Sweden and Norway is relevant here. In 1950, when the subsidization rate of the Swedish UI system was around 55%, union density in Sweden exceeded that in Norway by around 15 percentage points. In 1990, when the Swedish UI system was subsidized at a rate around 95%, the difference in union density between the two countries was around 25 percentage points ŽD’Agostino, 1992; OECD, 1994.. Section 2 presents the basic model of an economy with industry level bargaining between employers and unions, where each union runs its own UI scheme. Section 3 proceeds to an equilibrium analysis of the effects of alternative modes of financing UI systems of the Gent variety. Section 4 is devoted to a comparison between a compulsory UI system and a Gent system with respect to the wage and membership outcomes.

2. The model 2.1. The sequence of decision-making The sequence of events in the model can be described in a stylized fashion as follows. First, at the beginning of the period, wages are set in the industry with inherited membership taken as given. Second, firms’ demand for labor are revealed; labor demand will be a function of the bargained wage. The chosen wage 3

A.C. Pigou conjectured in the early 1930s that if ‘‘the unemployed members of trade union have to be cared for exclusively by that union, so that heavy unemployment means a heavy drain on union funds, this fact will act as a check upon claims for higher wages. If, however, unemployed members are cared for, in the main, at the expense of other people, the union’s contribution being no larger when there are many unemployed than when there are few, this check does not operate.’’ ŽPigou, 1933, p. 254..

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will also, through its effect on labor demand, determine the UI premium required to fulfill the budget restriction of the UI fund. Third, workers’ membership decisions are taken by comparing the costs and benefits of joining a union, given knowledge of labor demand and UI premiums. Fourth, employment is allocated by random draw among all workers in the industry. Finally, production starts. Fig. 1 illustrates the two relationships of interest in the wage Ž w . and membership Ž m. space. Equilibrium obtains when membership decisions are consistent with wage setting decisions, i.e., at the intersection between the membership schedule ŽMS. and the wage setting schedule ŽWS.. As drawn, the MS-schedule is steeper than the WS-schedule; this will in fact turn out to be a condition for stability. We consider an economy with industry-wide bargaining between an open-shop trade union and an employer organization that represents a number of perfectly competitive firms. Employment Ž N . is determined by profit-maximizing firms once the wage Ž w . is set. Employment is thus given by the labor demand function N s N Ž w ., where the exogenous output price is normalized to unity. The negotiated wage is valid for all employed workers in the industry, irrespective of whether they are union members or not. This kind of ‘contract extension’ is prevalent in continental Europe and in the Nordic countries. It may to some extent be the result of implicit union-employer agreements, but it is also enforced by legislation in a number of countries Žsee OECD, 1994.. The allocation of employment over workers is determined by random draw among all workers. The employment probability, n, is thus the same for members and non-members and given by n s NrL, where L is the fixed labor force in the industry. For notational simplicity, and without loss of generality, we will in the

Fig. 1. Membership demand and wage setting.

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subsequent exposition normalize the labor force to unity, i.e., L s 1, so we have n s N. Union density, i.e., the number of union members relative to the labor force, is denoted m. A consequence of the normalization is that m represents union density as well as the number of union members. 2.2. Membership demand

4

Consider the worker’s decision whether to join or not to join the union. We assume that union membership involves compulsory membership in the UI fund, an assumption that fits the facts for the Gent-countries. To generate variations among workers in the demand for union membership some heterogeneity has to be introduced. Therefore, assume that the valuation Ž V . of regular union services vary among individuals according to a uniform distribution on the interval w0,V x. The value of joining the union is given by the expected utility of being a member:

L m s nU Ž w y c y a . q Ž 1 y n . U Ž B . q V .

Ž 1.

The employed worker’s consumption is given by his wage Ž w . minus the UI premium Ž c . and the regular membership fee Ž a.. Unemployed workers receive unemployment benefits Ž B . but do not pay UI premiums or regular union fees. The utility function UŽ.. is increasing in consumption and concave. For notational simplicity we have normalized the consumer price to unity and ignored income taxes; no results hinge on these simplifications as long as consumer prices and the income tax rate are constant. 5 The regular membership fee is taken as fixed throughout the analysis. The UI fund’s budget restriction is given as:

Ž 1 y n . mB s cnm q S.

Ž 2.

The left-hand side is total outlays on benefits and the right-hand side includes contributions from the employed members and the subsidies from the government. For simplicity we take the government subsidy scheme to be linear: S s Gm q Ž 1 y a . Ž 1 y n . mB.

Ž 3.

G is a fixed grant per union member and Ž1 y a . is the marginal increase in subsidies produced by an increase in outlays on benefits. The random draw 4 Our analysis of membership demand draws on Booth and Chatterji Ž1995.. We have incorporated institutional details of existing Nordic UI systems into the analysis, which leads to a somewhat different membership demand relationship than the one analyzed by Booth and Chatterji. Cf. also Booth and Chatterji Ž1993., Naylor and Cripps Ž1993., and Naylor and Raum Ž1993.. 5 The implicit assumption is that the government’s expenses on unemployment compensation are financed through a general tax on profits. Such a tax does not affect workers’ membership decisions; nor does it affect wage setting in the model that we adopt.

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assumption implies that the number of employed union members is given as nm. From Eqs. Ž2. and Ž3., we get c s Ž 1rn . a Ž 1 y n . B y G . Ž 4. The parameter a , with 0 F a F 1, is referred to as the ‘degree of experience rating’ of unemployment benefits; a rise in a means that union members to a larger extent will be responsible for the financing of benefits. 6 When the subsidy scheme is strictly proportional Ž G s 0., a is simply the share of total unemployment benefits covered by union members’ UI premiums. Although c is taken as given by the individual worker, it will be endogenously determined in equilibrium. c is in fact fixed via the budget restriction once the wage is determined since the employment rate depends on the wage, i.e., n s nŽ w .. The change in the UI premium implied by an increase in the wage, i.e., c w s yŽ n w rn2 .Ž a B y G ., will be referred to as the marginal UI premium. The marginal UI premium is analogous to a marginal tax, i.e., the rise in the tax produced by a wage hike. The marginal premium can safely be taken to be non-negative, i.e., c w G 0. In fact, c w G 0 holds so long as c G 0. If the worker does not join the union, there are two other options to consider. The first is to join the UI fund on an individual basis, a possibility that exists in reality; it is referred to as ‘individual membership’. The second option is to reject membership in the UI fund as well as union membership. In general, with worker heterogeneity in some dimension, we would expect to find some workers choosing the first option whereas others would choose the second. However, to simplify the analysis we will focus on the special case where only the second of these options is chosen. To illustrate, consider the expected utilities of the two non-union options. Let the value of joining the UI fund as individual member be given as L UI s nU Ž w y cˆ . q Ž 1 y n . U Ž B . , Ž 5. where cˆ is the fee for individual membership. We assume cˆ ) c, which is realistic. Individual membership is more costly to administer, which can be a motive for charging higher premiums for individual members. By assumption, non-members receive the same wage as members, but they do not pay union fees. The expected utility of rejecting membership in both the union and the UI fund is given as L n m s nU Ž w . q Ž 1 y n . U Ž b . . Ž 6. These workers pay no insurance premiums and no regular union fees as employed. In case of unemployment they receive unemployment assistance b, where b - B. 6 The terminology is motivated by a system in the United States. In the US, contribution to unemployment through premiums paid by union members and through its wage demands.

loose analogy with experience rating as practiced in the UI there is a tax on firms that is higher for firms with a higher layoffs. In our case, there is a connection between the UI the extent to which the union contributes to unemployment

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A comparison between options Ž5. and Ž6. reveals that, absent any heterogeneity in worker preferences, the outcome is either that all workers prefer the UI fund or that they all prefer to stay out of the fund. A sufficiently large cˆ will induce all workers to reject the UI fund alternative relative to the option of staying out. We assume this condition to be fulfilled, which is consistent with the fact that few workers have chosen individual membership. The fact that few workers have chosen this option is presumably also due to social norms that add psychic costs to individual membership. The demand for union membership is then given by a comparison between Eqs. Ž1. and Ž6.. The worker chooses membership if L m G L n m . The marginal worker is indifferent between joining and not joining the union. The marginal worker’s valuation, V U , of union services satisfies M Ž . . 'n Ž w . U Ž w y c Ž w . y a . q Ž 1 y n Ž w . . U Ž B . q V U Ž m . yn Ž w . U Ž w . y Ž 1 y n Ž w . . U Ž b . s 0.

Ž 7.

U

Workers with V G V join the union. Union density is thus given as m s Ž V y V U .rV, and hence V U Ž m. s Ž1 y m.V. Implicit differentiation of Eq. Ž7. yields the slope of the membership schedule in Fig. 1 as ŽEwrEm. MS s VrMw , where Mw s U Ž w y c y a . y U Ž w . n w q U Ž b . y U Ž B . n w q n Ž w . U X Ž w y c y a. Ž 1 y cw . y U X Ž w . .

Ž 8.

The slope of the membership schedule is positive if Mw ) 0, a condition that almost certainly holds for realistic parameter values. A sufficient Žbut not necessary. condition is that the marginal UI premium is close to zero. The existing Gent systems in Denmark and Sweden are subsidized to an extent that has eliminated virtually all connections between employment rates and premiums in the UI funds, so c w f 0. Note also that V captures heterogeneity among workers concerning valuation of union services; the more dispersion in this respect there is, the steeper the membership schedule Žsince the slope is given by VrMw .. Why is the membership schedule ŽMS. positively sloped, as illustrated in Fig. 1? Consider the three terms in Eq. Ž8.. A wage increase reduces the employment rate which implies a utility loss for both members and non-members. This utility loss is smaller for members because they have lower consumption than non-members when employed Žthe first square bracket. and higher consumption than non-members when unemployed Žthe second square bracket.. The induced reduction in employment produced by a wage increase thus works unambiguously towards higher membership. An increase in the wage also affects membership through the utility value of consumption Žthe third square bracket.. If the marginal UI premium Ž c w . is negligible, it holds that a wage increase has a larger positive impact on the utility of consumption for a union member than for a non-member as long as members pay something for their membership, i.e., as long as Ž c q a. ) 0; this follows from the concavity of the utility function. A large

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marginal premium may conceivably offset this effect, although a complete offset is unlikely provided that workers are sufficiently risk averse. 7 2.2.1. ComparatiÕe statics— partial equilibrium Consider how the membership schedule responds to changes in the UI parameters, i.e., b, B,G and a . A shift to the right Žleft. of the schedule is referred to as an increase Ždecrease. in membership demand. From inspection of Eq. Ž7., it is immediately clear that a rise in unemployment assistance Ž b . reduces membership demand; the provision of higher unemployment income to uninsured workers makes workers less inclined to join the union in order to obtain UI. A rise in unemployment benefits Ž B . will, in general, increase membership demand. The direction of the effect is determined by the sign of MB s Ž 1 y n . U X Ž B . y a U X Ž w y c y a . G 0,

Ž 9.

which is always non-negative and typically positive; the sign is positive if workers are risk-averse andror a - 1 since w y c y a ) B must hold as a ‘participation constraint’. An increase in the lump-sum subsidy G makes membership more attractive because it allows lower UI premiums. A reduction in a has the same effect. Summarizing these partial equilibrium results we have: m s m Ž w ;b, B,G, a . , where m w ) 0, m b - 0, m B G 0, m G ) 0, and ma - 0. 2.3. Wage setting The wage is determined in a Nash bargain, where the objective is to maximize the product

V Ž w . s G Ž w . y G0

b

P Ž w. yP0

1y b

,

Ž 10 .

where 0 - b F 1. G Ž w . y G 0 is the union’s contribution to the bargain and P Ž w . y P 0 is the employer’s contribution. We assume that the union wishes to 7 Consider a utility function of the constant relative risk aversion form, with d 'yŽ w y cy Y X a.U Ž..r U Ž.. being a measure of relative risk aversion. The terms in the third square bracket of Eq. Ž8. can then be written as H Ž.. 'U X Ž w y cy a.Ž1y c w .yU X Ž w . sU Y Ž w . wŽ1yca.y d Ž1y c w .y1x, where ca' Ž cq a.r w is the relative cost of joining the union, expressed as a fraction of the wage. H Ž.. is increasing in relative risk aversion and takes a positive sign as long as workers are strongly risk averse and the union’s share of the financing of benefits is not ‘too high’. To illustrate, suppose that Gs 0, in which case c w s Ž Br w . a´ r n, where Br w is the replacement ratio and ´ 'y wn w r n is the wage elasticity of labor demand. If cas0.1, d s 4, Br w s 0.8, a s 0.4 and ´ r nf1 we get X H Ž.. s 0.03U Ž w . ) 0.

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maximize the expected utility of the median member, where workers are ranked according to their valuation of union services. The union is thus concerned with

G Ž w . s nU Ž w y c y a . q Ž 1 y n . U Ž B . q V me ,

Ž 11 .

me

where V is the median member’s valuation of the benefits provided by the union. To determine the union’s threat point, G 0 , we need to specify the members’ incomes during a conflict. We assume that a fraction of the members receive strike support whereas the rest receive unemployment benefits. To simplify matters we set the strike support equal to the exogenous benefit level. The threat point relevant for the union is then given as

G 0 s U Ž B . q V me ,

Ž 12 .

and we get the union’s utility surplus from an agreement as: R Ž w . ' G Ž w . y G0 s n Ž w . U Ž w y c Ž w . y a. y U Ž B . .

Ž 13 .

Firms care about profits, P Ž w . s QŽ n. y wn, where QŽ n. is a strictly concave production function. Union membership is treated as given in the wage bargain. We also assume that the employer’s threat point, P 0 , depends on inherited membership. The more non-members there are, the easier for the firm to produce during a conflict. This assumption reflects institutional features of Nordic Žand some other European. labor markets. Union and non-union workers are often employed in the same firm. Should a conflict occur, the non-members remain working in the firm. The firm will not typically be able to replace striking workers with non-members, but the mere fact that some non-members will be working in the firm if a conflict occurs strengthens the employer’s hand in the bargain. We thus assume that P 0 is decreasing in membership, i.e., E P 0rEm - 0. Maximization of Eq. Ž10. yields the first-order condition as W Ž w . ' b P Ž w . y P 0 Ž m . R w Ž . . q Ž 1 y b . R Ž w . P w Ž w . s 0,

Ž 14.

where P w s ynŽ w .. RŽ w . is given by Eq. Ž13. and hence: R w Ž .. s U Ž w y c Ž w . y a. y U Ž B . n w q n Ž w . U X Ž w y c Ž w . y a. Ž 1 y cw . .

Ž 15 .

Note that R w must be positive at an interior solution, which implies that the marginal UI-premium c w cannot be ‘too high’. We proceed under the assumption that there is an interior solution to the Nash bargain. The slope of the wage setting schedule in Fig. 1 is given as ŽEwrEm. WS s yWm rWw , where Wm s yŽ1 y b . nŽE P 0rEm. G 0, and Ww - 0 by the secondorder condition. The wage-setting schedule is thus in general positively sloped; the larger is membership, the higher the negotiated wage. A larger membership means that fewer workers are available for work during a conflict, with a weaker bargaining position for the employer as a consequence. A special case involves

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b s 1; the wage is independent of membership when all bargaining power rests with the union. 2.3.1. ComparatiÕe statics— partial equilibrium It is clear from Eqs. Ž14. and Ž15. that a policy that raises the marginal UI premium, holding constant the leÕel of the premium, has an unambiguously negative effect on the negotiated wage Žat a given size of membership.. The intuition is that a rise in the marginal premium, analogous to a rise in the marginal tax rate, reduces the gain to the union of a wage increase Žthe second term in Eq. Ž15... 8 Unemployment assistance Ž b . does not belong to the wage setting schedule since it does not affect union members’ utility. The partial equilibrium comparative static prediction with respect to a parameter of interest—G, say—is given by the sign of WG , since Ww - 0. We refer to an upward Ždownward. shift of the wage setting schedule as an increase Ždecrease. in wage pressure. Differentiation of Eq. Ž14. yields: WG s y Ž 1 y b . nU X Ž w y c y a . q b Ž P y P 0 . U Y Ž w y c y a . Ž 1 y c w . F0.

Ž 16 .

Wage pressure is, in general, reduced by a rise in the lump-sum subsidy. The reasons are that a rise in G increases the union’s rent from an agreement by reducing the UI premium Žthe first term in Eq. Ž16.., and that the marginal gain to the union of a wage increase is reduced Žthe second term in Eq. Ž16... The wage setting schedule is not affected by the lump-sum subsidy in the special case when the worker is risk-neutral ŽU Y Ž.. s 0. and the union has unrestricted power to set the wage Ž b s 1.. A rise in the degree of experience rating Ž a . has, in general, ambiguous effects on wage pressure. The wage response, holding membership constant, takes the sign of Wa s b Ž P y P 0 . U X Ž w y c y a . Bn w y Ž 1 y n . BWG .

Ž 17 .

There are two effects involved in Eq. Ž17.; the first works through the marginal UI premium and the second through the level of the premium. The former effect Žthe first term. is unambiguously negative, whereas the latter Žthe second term. is non-negative and corresponds to the rise in the premium level produced by a higher a . We may think of the first effect as a ‘substitution effect’ whereas the second can be interpreted as an ‘income effect’. The wage response is unambiguously negative in the monopoly union case with risk-neutral workers, in which case WG s 0. 8

Analogous results are available concerning the effects of progressive taxes; see, for example, Lockwood and Manning Ž1993..

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We can rewrite Eq. Ž17. as Wa s BU X Ž . . w bg  dÕ Ž 1 y n . y n ´ 4 q Ž 1 y b . n Ž 1 y n . x ,

Ž 17a.

where d is the measure of relative risk aversion, g ' Ž P y P 0 .rw ) 0, and Õ ' Ž1 y c w .rŽ1 y ca . ) 0. Note that g lies in the unit interval under the plausible assumption that the ratio between profits and the wage bill is less than unity. 9 Note also that Õ is a measure of the elasticity of the net wage Ž wn ' w y cŽ w . y a. with respect to the gross wage, i.e., dlnwnrdlnw s Õ; this is analogous to the measure of tax progressivity known as residual income progression that relates after-tax income to pre-tax income Žsee Jakobsson, 1976.. Risk aversion must be quite high, although not extremely high, in order to make Eq. Ž17a. positive. 10 The more risk-averse workers are, the stronger is the income effect that tends to increase wage pressure when the level of the UI premium is raised. There remains a need to look at the effects of higher unemployment benefits. The derivative of interest is: WB s Ž 1 y b . n2 y b Ž P y P 0 . n w U X Ž B . q Ž arB . Wa .

Ž 18 .

The first term captures the conventional wage increasing effect of higher benefits, whereas the last term captures the effect of the concomitant increase in the UI premium. As the latter effect is in general ambiguous in sign, it can offset or reinforce the conventional effect. The net effect is always positive, however. By using Eqs. Ž16. and Ž17. together with Eq. Ž18., we obtain WB s yb Ž P y P 0 . n w U X Ž B . y a U X Ž w y c y a . q F Ž . . ) 0, X

X

where wU Ž B . y a U Ž w y c y a.x G 0 and F Ž.. ) 0. equilibrium effects on wage setting we have:

11

Ž 18a.

Summarizing the partial

w s w Ž m; b, B, G, a . , where wm G 0, w b s 0, wB ) 0, wG F 0, and wa 4 0.

3. Labor market equilibrium Equilibrium is obtained when membership decisions are consistent with wage setting decisions, i.e., at the intersection between the membership schedule and the wage setting schedule in Fig. 1. As drawn, the MS-schedule is steeper than the WS-schedule; this is a condition for stability that we assume to be fulfilled. A 9 We have P r w s n P r wn, where P r wn can safely be taken as less than unity. The fact that P 0 G 0 reinforces the claim that g -1. 10 If ns 0.9, b s 5, Õ s1.1, g s 5 and ´ s1 we have Wa - 0 as long as d -6.5. X X Y 11 F Ž.. ' a Ž1y n.wŽ1y b . nU Ž w y cy a.y b Ž P y P 0 .U Ž w y cy a.Ž1y c w .xqŽ1y b . n2 U Ž B . ) 0.

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sufficiently large variation in individual valuations of union services, as represented by V, guarantees stability. ŽAn Appendix, available on request, gives details.. So far, we have ignored the interactions between the two structural equations. We will now consider the simultaneous determination of membership and wages. It has already been noticed that an increase in unemployment assistance Ž b . induces a shift to the left of the membership schedule whereas it does not directly affect wage setting. The equilibrium outcome is thus a decline in the wage as well as in union membership. An increase in the benefit level Ž B . has also predictable effects. From Eq. Ž9., we know that the membership schedule shifts to the right, whereas Eq. Ž18a. implies that the wage setting schedule is shifted upwards. The equilibrium outcome is thus an increase in the wage as well as an increase in union membership. An increase in G will, in general, affect both the MS- and the WS-schedules and the net effects on wages and membership are ambiguous. The effects of an increase in the degree of experience rating are given as: dw s y Ž 1rD 0 . VWa y Ž 1 y n . BU X Ž w y c y a . Wm Ž 19 . da dm s y Ž 1rD 0 . Ž 1 y n . BU X Ž w y c y a . Ww q MwWa . Ž 20 . da where D 0 ' MwWm y MmWw . Stability requires that the MS-schedule is steeper than the WS-schedule, which implies D 0 - 0. A rise in a has an ambiguous effect on the WS-schedule Žthe first term in Eq. Ž19. and the second term in Eq. Ž20.., whereas it induces a shift to the left of the MS-schedule Žthe second term in Eq. Ž19. and the first term in Eq. Ž20... Since risk aversion must be very high in order to induce substantial wage pressure from an increase in a , the most plausible outcome is that there will a reduction in the wage as well as in the size of membership. The potentially ambiguous effects of an increase in experience rating is due to offsetting income and substitution effects. We will also consider a policy that influences the marginal UI premium while at the same time neutralizing the effect that works through the level of the premium. The policy involves an increase in a with a simultaneous adjustment in G, subject to the restriction that the government’s subsidy per member is fixed at S s G q Ž1 y a .Ž1 y n. B. We thus have three equations, namely the membership equation M Ž w,G,m; a . s 0, the wage equation W Ž w,m,G; a . s 0, and the subsidy rule S s G q Ž1 y a .Ž1 y nŽ w .. B. A rise in a has the following effects: dw s y Ž VrD1 . b Ž P y P 0 . U X Ž w y c y a . Bn w - 0 Ž 21 . da S dm dw s Ž 1rV . Mw q Ž 1 y a . Bn w MG . Ž 22 . da S da S

ž / ž /

ž /

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D 1 —the determinant of the system—is negative by the stability condition. The expression in the square brackets of Eq. Ž21. is negative, implying that the wage response will be negative. A policy that tilts the financing scheme in the direction of a higher marginal UI premium, with a concomitant adjustment of G so as to keep the amount of subsidies constant, is thus conducive to wage moderation. The membership response is in general ambiguous, however. 12 Summarizing the equilibrium effects of alternative UI policies we thus have that a rise in b reduces the wage as well as membership, whereas a rise in B increases both the wage and membership. Changes in a and G have in general ambiguous effects. However, an increase in a with a simultaneous adjustment of G, so as to keep the subsidies fixed, will unambiguously reduce the wage.

4. Compulsory vs. voluntary UI: effects on wages and membership Is a Gent system always more conducive to unionization than a compulsory UI system? We examine this issue by considering the effects of introducing the two alternative UI systems. 13 The initial, pre-UI, situation is one where there are no government unemployment benefits at all. To the extent that workers have some income Ž B0 . when unemployed, this is income from the informal economy Žincluding home production.. Let B denote unemployment income for union members and b income for unemployed non-members, and assume B s b s B0 G 0 in the pre-UI situation. A compulsory system Žsuperscript C. involves a simultaneous increase in b and B, with the following effects: dw

ž / ž /

C

dB

dm dB

s y Ž 1rD 0 . V WBC ) 0

Ž 23 .

s y Ž 1rD 0 . MwWBC ) 0,

Ž 24 .

C

where WBC is given by expression Ž18., evaluated at a s G s 0 and B s B0 , i.e., WBC s wŽ1 y b . n2 q b Ž P y P 0 .xU X Ž B0 . ) 0. A general increase in unemployment income thus increases wage pressure, for the conventional reasons. There is no effect on membership demand; as is clear from the membership demand equation 12

By evaluating Eq. Ž22. at a sGs 0 we obtain: sign Žd m rd a .S ssign wŽ Br w . ´ y1x. The replacement ratio Ž Br w . is below unity whereas estimates of the absolute value of the wage elasticity of labor demand Ž ´ . often falls between one half and unity Žsee, for example, Bean et al., 1986.. There is thus a slight presumption that the equilibrium membership response is negative. 13 We ignore the financing of the government’s subsidies to UI. Since taxes to finance UI can be raised in a number of different ways, it is useful to focus explicitly on the effects of UI without having to specify the details of the financing scheme. An appendix, available on request, examines the case where the government raises proportional income taxes to finance its contributions to UI.

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410

given by Eq. Ž7., a simultaneous increase in b and B does not influence the attractiveness of joining the union. Equilibrium membership will increase, however, as the wage-setting schedule shifts upwards; this is captured by Eq. Ž24. and illustrated in Fig. 2. Consider instead the effects of an introduction of a Gent system Žsuperscript G. with a strictly proportional subsidy scheme. The equilibrium effects are as follows: dw

ž / ž /

G

dB

dm dB

s y Ž 1rD 0 . VWB q Wm MB ) 0

Ž 25 .

s y Ž 1rD 0 . w yWw MB q MwWB x ) 0.

Ž 26 .

G

The first term in the square brackets of Eq. Ž25. captures the effect on wage pressure, which is positive by Eq. Ž18a.. The second term is the effect that works through the increase in membership demand, which induces an increase in the wage as long as the wage-setting schedule is positively sloped ŽWm ) 0.. The wage response is thus unambiguously positive, as illustrated in Fig. 3. There is also an unambiguously positive effect on membership, as stated in Eq. Ž26.. The effect of the increase in membership demand Žthe first term in the square bracket. is reinforced by the rise in wage pressure Žthe second term in the square bracket.. It is thus clear that both compulsory systems and Gent systems tend to increase wages and union membership. Is it possible to say anything regarding the relative magnitudes involved? To compare the two systems we need to compare Eq. Ž23. with Eq. Ž25. and Eq. Ž24. with Eq. Ž26.. We therefore make use of Eq. Ž18. and decompose the wage response to an increase in B into WB s WBC q Ž arB .Wa , where the first term Žthe conventional wage increasing effect. is common to both

Fig. 2. Introduction of compulsory UI.

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411

Fig. 3. Introduction of voluntary UI.

UI systems whereas the second is relevant only in the Gent system. We can then rewrite Eqs. Ž25. and Ž26. as dw

ž / ž /

G

dB

dm dB

s y Ž 1rD 0 . V  WBC q Ž arB . Wa 4 q Wm MB

Ž 27 .

s y Ž 1rD 0 . yWw MB q Mw  WBC q Ž arB . Wa 4 .

Ž 28 .

G

The conditions under which a Gent system produces higher wages and higher membership can thus be stated as: w G ) w C iff F ' V Ž arB . Wa q Wm MB ) 0, G

C

m ) m iff C ' yWw MB q Mw Ž arB . Wa ) 0.

Ž 29 . Ž 30 .

The value of a and the sign of Wa are crucial for these inequalities. As we have argued above, there is a presumption that Wa is negative unless workers’ degree of relative risk aversion d is very high Žcf. Eq. Ž18a... Risk aversion matters because it affects the induced wage response to the increase in UI premiums that is associated with higher benefits in the Gent system. Risk aversion also matters by affecting how membership demand responds to an increase in benefits. The more risk averse workers are, the stronger the rise in membership demand when benefits are raised; this is intuitively appealing and follows from Eq. Ž9.. Finally, the relative bargaining power of the union Ž b . matters since it affects the slope of the wage setting schedule; recall that we have a flat WS-schedule ŽWm s 0. in the monopoly union case. Table 1 presents results that can be deduced from different assumptions concerning three crucial parameters: a , d and b . Consider first the case with a

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Table 1 Gent vs. compulsory UI—effects on wages and membership wG y wC

b s1

a s0 a )0

0 - b -1

a s0 a )0

mG y mC

d Small

d Large

d Small

d Large

0 y Ži. q ?

0 q Žii. q q Živ.

q ?

q q Žiii. q q Živ.

q ?

Ži. d - Ž n ´ .rŽŽ1y n.n . necessary and sufficient condition. Žii. d ) Ž n ´ .rŽŽ1y n.n . necessary and sufficient condition. Žii. d ) Ž n ´ .rŽŽ1y n.n . sufficient but not necessary condition. Živ. d ) Ž n ´ .rŽŽ1y n.n .yŽŽ1y b . n.rŽ bng . sufficient but not necessary condition.

heavily subsidized Gent system, in the sense that a is close to zero. A Gent-system implies an unambiguously higher unionization rate than a compulsory system when a is strictly zero; this prediction is likely to carry over to the case when a is in a neighborhood of zero. The difference between the two systems is then solely due to the rightward shift of the membership demand schedule; there is no induced effect on wage setting due to experience rating. The Gent-system is also in general associated with a higher wage when a is close to zero. The reason is that the rise in membership strengthens the union’s hand in the wage bargain, thus producing an additional rise in the wage. There is however no differential impact on the wage in the special case with monopoly unions; in this case there is no bargaining and the WS-schedule is flat. The wage effect of the Gent system is in general ambiguous when union members have to finance part of the rise in benefits Ž a ) 0.. There is a strong presumption that the wage will be lower in a Gent system with monopoly unions Ž b s 1. than in the corresponding compulsory system. Consider, as an example that is not unrealistic, the case where n s 0.9, ´ s 1 and Õ s 1. In order to obtain w G ) w C , the degree of relative risk aversion would have to be larger than 9, which is a rather remote possibility. 14 As we have noted, the Gent system always raises the unionization rate provided that the system is heavily subsidized by the government. In the general case with some degree of experience rating, the membership effects are ambiguous. The more risk averse workers are, the more likely that the Gent system raises the unionization rate. Strong risk aversion reinforces the rise in membership demand and weakens wage moderation Žor increases wage pressure.. 14 Estimates of union members’ degree of relative risk aversion are reported by Farber Ž1978., Carruth and Oswald Ž1985. and Forslund Ž1994.. Most of these estimates fall in a range of 1–4, although Forslund’s estimates on Swedish data are somewhat higher.

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5. Concluding remarks The paper has offered an analysis of a labor market institution known as the Gent system, i.e., a system where unemployment insurance is run by union affiliated funds with voluntary membership. We have used a model of an economy with industry-level wage bargaining to examine if the Gent system is conducive to union membership. This was found to be the case under certain conditions. The degree to which the government subsidizes UI is one of the crucial factors. This presumably also explains why unions in the Nordic countries have been actively lobbying against UI reforms that involve less subsidies of the system. Our results suggest that the Gent system reduces the free-rider incentives by creating benefits that are exclusive to union members. Our results are also broadly consistent with the observed differences in unionization rates between Sweden and Norway that we mentioned in Section 1. Some of the existing empirical studies of union density seem to have been loosely guided by a framework broadly similar to ours, although joint estimations of equations for membership demand and wage setting are rare. 15 A recent paper by Pehkonen and Tanninen Ž1995. examines the evolution of union membership in Finland over the past three decades and finds that the relationship between regular unemployment benefits Ž B in our model. and unemployment assistance Ž b in our case. appears as a significant explanatory factor. The authors calculate that union density would fall by some 10 percentage points if the two unemployment compensation schemes were to be equalized. There is however no evidence in that paper on how reforms of the financing system would affect membership demand. We have also examined how the government can affect employment through its choice of financing system for UI. A policy that raises the marginal cost of wage increases, analogous to the effects of a more progressive tax system, is unambiguously good for employment. Such policies can be implemented by making government subsidies less sensitive to changes in unemployment in the UI funds. As is well known, progressive taxes distort labor supply decisions, including decisions to invest in human capital. UI reforms of the kind we have discussed have effects on wage bargaining that are similar to the effects of an increase in tax progressivity, but there is little reason to expect similar distortions of labor supply incentives. The reason for this difference is that the UI policies operate exclusively on collective wage setting, without introducing any direct penalty on individual efforts to increase wages through education and training. To simplify the analysis, we have ignored worker heterogeneity in other dimensions than the valuation of union services. A richer model is required to explain the fact that some workers have chosen individual membership in the UI funds. Such a model is also required to analyze how government policies would 15

A paper using UK data by Booth and Chatterji Ž1995. is an exception in this regard.

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affect incentives for individual UI fund membership and union membership. A more complete analysis would also have to consider how job search behavior among the unemployed is affected by changes in benefit levels and financing systems. One might, for example, expect that a reduction in government subsidies will affect incentives to monitor job search within the unions and their affiliated UI funds. 16 Such an extension of the present analysis would be a valuable contribution with potentially interesting implications also for wage and membership decisions.

Acknowledgements We are grateful for comments from Alison Booth, Monojit Chatterji, Daniele ` Meulders, Jaakko Pehkonen, Peder Pedersen and Dennis Snower as well as from participants at presentations at Uppsala, FIEF, IUI and the 1997 EEA and EALE meetings. This research was initiated while Lundborg was at IUI, Stockholm. Financial support from HSFR is gratefully acknowledged.

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16

See Kiander Ž1993. for an analysis along these lines in a monopoly union model with fixed membership.

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