Flexible and Committed Profit Sharing with Wage Bargaining

Transcription

1 ömmföäflsäafaäsflassflassflas ffffffffffffffffffffffffffffffffffff Discussion Papers Flexible and Committed Profit Sharing ith Wage Bargaining Erkki Koskela University of Helsinki, RUESG and HECER and Rune Stenbacka Sedish School of Economics, RUESG and HECER Discussion Paper o. 60 May 2005 ISS HECER Helsinki Center of Economic Research, P.O. Box 7 (Arkadiankatu 7), FI 0004 University of Helsinki, FILAD, Tel , Fax , E mail info hecer@helsinki.fi, Internet.hecer.fi

2 HECER Discussion Paper o. 60 Flexible and Committed Profit Sharing ith Wage Bargaining Abstract In this paper the relationship beteen profit sharing, employee effort and age formation is analysed under different relative timings for the determination of base age and profit sharing. We sho that the optimal profit share, decided by firms, under commitment exceeds that under flexibility. This holds true, because by committing itself to a profit share the firm can induce age moderation, hich adds to the returns from using the profit sharing instrument. If the profit share is negotiated it depends positively on the relative bargaining poer of trade unions and it has both effort enhancing and age moderating effects. JEL Classification: J5, J4, J33. Keyords: Wage bargaining, profit sharing, employee effort. Erkki Koskela Rune Stenbacka University of Helsinki Sedish School of Economics Department of Economics Department of Economics P.O.Box 7 (Arkadiankatu 7) Arkadiankatu 7 FI 0004 University of Helsinki 0000 Helsinki FILAD FILAD e mail: erkki.koskela@helsinki.fi e mail: rune.stenbacka@hanken.fi The authors thank the Research Unit of Economic Structures and Groth (RUESG) at the University of Helsinki and the Yrjö Jahnsson Foundation for financial support.

3 I. Introduction Profit sharing refers to performance related remuneration mechanisms consisting of a base age plus a share of profits of firms. It is an empirically important phenomenon in many OECD countries. The OECD Employment Outlook (995) reports cross country evidence on profit sharing in OECD countries. Pendleton et. al (200) present more recent and detailed data on the large proportion of orkplaces ith financial employee participation, in particular in the form of profit sharing schemes, in countries. For further detailed evidence regarding profit sharing e refer to DICE database collected by CESifo, As profit sharing schemes are noadays commonly used, it is important to study their implications. Weitzman (985, 987) conjectured that profit sharing systems ould both dampen the business cycle fluctuations of employment and reduce equilibrium unemployment. Holmlund (99) formally explored the relationship beteen profit sharing and equilibrium unemployment. He argued that profit sharing ill reduce (increase) equilibrium unemployment if and only if the elasticity of substitution beteen labour and capital exceeds (falls short of) one, hile it ill have no effect on equilibrium unemployment hen the elasticity of substitution beteen labour and capital is equal to one. Layard and ickell (990) sho a similar neutrality result in the case of a Cobb Douglas production function and efficient bargaining. In all these contributions the profit sharing instrument is negotiated and assumed to have no incentive effect on the orkers effort decisions. But this does not lie in conformity ith empirical evidence according to hich profit sharing enhances effort provision and thereby productivity (see e.g. Wadhani and Wall (990), Cahuc and Dormont (997) and Booth and Frank (999)). In this paper e first incorporate the productivity effect of profit sharing into our model in an environment ith firms facing revenue uncertainty by focusing on a production technology ith unit elasticity of substitution beteen employment and effort. This combines and unifies elements from union bargaining and efficiency age theories so that e can explore the implications of profit sharing in a more realistic ay, hich Furthermore, in many countries profit sharing is embedded in a legal setting, hich requires the profitsharing schemes to be independent of the age agreements (see, for example, Cahuc and Dormont (997) or Pendleton et al. (200)).

4 lies in conformity ith empirics. Second, e analyse the folloing unexplored issue. Ho does the time sequence beteen base age formation and profit sharing impact on both the negotiated age and the optimal profit share and its determinants? Section II presents the basic structure of the model and various time sequences for the profit sharing decision. The determination of effort by employees and the employment decision by firms are presented in section III, hile section IV investigates the determination of the compensation scheme under flexibility versus commitment in terms of the profit sharing decision as ell as the case here the profit share and the base age are negotiated simultaneously. Finally, e present a brief conclusion. II. Basic Frameork We consider a representative firm operating in an environment ith revenue uncertainty. In conformity ith the efficiency age hypothesis e assume that the output depends not only on the number of orkers employed, but also on the effort supplied by each orker, i.e. productivity. By employing L units of labour, each providing effort, a, the revenues accruing to the firm are given by ( ) R( a,, here denotes a random revenue shock ith a cumulative distribution function F ( ), and a density function ( ) f, ith the support [ min, max ] R+. We assume that the production function R ( a, satisfies the conventional properties: R 0, R < 0, R > 0, R < 0 and > 0. a > aa L LL R al The profit share,, determines hat fraction of the firm s profits is transferred to employed orkers as part of the contract. The firm unilaterally determines the employment level and the employee the effort level once ages and profit sharing have been determined. As the trade union is formed by homogenous agents and as intraorganizational agency issues ithin the union are outside the scope of our analysis, the union is assumed to be able to enforce the effort provision by the representative union 2

5 member so as to eliminate the potential free rider problems. 2 We summarise the various alternative timing of decisions made by the firm, the union and the union members in Figure. (I) (II) Stage Stage 2 Stage 3 Stage 4 c f ( L, ( L, (III) Stage Stage 2 Stage 3 (i) (, ) ( L, s (ii) (, ) ( L, Figure : Alternative time sequences of decisions in terms of employment L, effort a, profit share, base age and resolution of uncertainty. The timing structure (I) captures the idea that the negotiated base age serve as a commitment, hich the firm takes as given hen it makes its profit maximizing profitsharing decision. Subsequent to the profit sharing decision, the firm unilaterally determines employment and the union members effort provision. Finally, once all these decisions are made, uncertainty is resolved. The timing structure (II) exchanges the relative timing of the determination of profit sharing and age negotiations. This timing highlights a scenario here the firm commits to the profit share in anticipation of the base age. Finally, the timing structure (III) captures simultaneous determination of profit shares and base ages. In order to compare the results e explore to versions of this relative timing: simultaneous determination of profit shares and ages, here the profit share is negotiated or here the firm sets it. III. profits Labour Demand and Effort The risk neutral firm decides on employment L so as to maximize the expected 2 If e ere to apply an alternative formulation here individual efforts ere not directly observable and orkers ere heterogenous, group punishment or reard schemes ould have to be used for enforcement (see e.g. Holmström (982)). This is an important issue for further research. 3

6 (2) ( a, max ( R( a, f ( ) d min Conditional on the negotiated base age and profit share the risk neutral representative employed union member makes the effort decision in order to maximize the expected utility (3) Eu( a, ( R( a, f ( ) d g(, max + L min here the disutility of effort, g (, is an increasing ( g '( > 0 ) and convex ( g ''( > 0) function of effort. The optimal employment and effort provision is determined by the system of first order conditions (4) max min R L ( a, f ( ) d 0 and max (5) Ra ( a, f ( ) d g'( 0. L min According to (4) the firm chooses the employment level so as to equalize the expected marginal return from labour to the age cost, hile (5) characterizes the determination of effort by a representative employee so as to equalize the expected marginal benefit from effort to the marginal disutility of effort. In order to make the comparison of results ith the earlier literature more transparent, e make the folloing to parametric specifications for the functional forms of the production technology and the disutility of employee effort. Assumption R: The technology is assumed to satisfy the concave production function α ( a R ( a, ith 0 < α <. α Assumption G: The increasing and convex disutility of effort belongs to the class of isoelastic functions γ g ( a ith 0 < γ <. γ 4

7 Under assumptions R and G the equilibrium condition (4) ith respect to the employment decision can be ritten as follos (6) η η η L a, here denotes the expected value of revenue shock and η ( α) > is the direct age elasticity of labour demand. Labour demand depends negatively on the base age and positively on the effort of employee. Analogously, by substituting assumption G into (5) e find that the optimal effort is given by (7) γ [ ], 0 < < a γ. Hence the optimal effort depends positively on the base age as ell as on profit sharing. We can no summarize our characterization of the optimal combination of employment and effort provision in Proposition : Labour demand depends negatively on the base age and positively on the effort of employees, hile effort by employees depends positively on the profit share as ell as on the base age. Equation (6) suggests that labour demand does not directly depend on profit sharing, hich lies in conformity ith empirical evidence (see e.g. Wadani and Wall (990)) and Cahuc and Dormont (997)). Profit sharing enhances productivity by stimulating effort provision. 3 3 Some aspects of the interactions beteen age bargaining and efficiency age considerations have been previously analysed e.g. in Lindbeck and Snoer (99), Sanfey (993) and Garino and Martin (2000). In contrast to our analysis, in these papers the effort function as not derived from the employee s objective function. 5

8 IV. Wage Bargaining ith Flexible and Committed Profit Sharing IV.. Base Wage and Profit Share Flexibility We first analyse the timing structure (I) (see Figure ), here the firm is flexible by deciding on the profit share after the base age negotiation. Hence at stage 2 the firm decides on the profit share in order to maximize the expected net profit subject to (6) and (7) and by taking the base age as given according to (8) Max { ( ) η ( ) ( a η L It is shon in Appendix A that the optimal profit share, hen it ill be decided after age negotiation, is ( ) γ (9) 0 < f <, + ( ) γ a here γ. Hence, profit sharing depends positively both on γ and on so that a e have Proposition 2: Under flexible profit sharing the optimal profit share depends positively on both the elasticity of effort ith respect to profit sharing (γ ) and the elasticity of labour demand ith respect to effort ( ). At stage the base age is negotiated. We apply the ash bargaining solution, according to hich employment and profit sharing are unilaterally determined by the firm, hereas effort is provided subject to the discretion of employees. In line ith (3), the objective function of the trade union can be ritten as ˆ L + + ( b L g( L, here the first term captures the benefits from employment to employed orkers, the 6

9 second term the benefits for unemployed union members and the last term denotes the disutility of effort for employed union members. We assume that the threat points of the union and the firm are o o b and 0, respectively. The calculation of the union s expected rent captures the idea that all the orkers have incentives to seek employment. Union members, ho are left unemployed, have the outside option b. Thus the rent of the union,, is calculated to be () ˆ 0 ( a, L ) L b + ( a, L ) g( a L ). Applying the traditional ash bargaining solution the negotiating parties decide on in order to solve Max { Ω [ ] [( ) π ] ( 2) E ( ) subject to the labour demand (6) and the effort determination (7), here and describes the relative bargaining poer of the union and the firm, respectively. The ash bargaining solution has to satisfy the folloing first order condition ( 3) + ( ) 0 here the subscript denotes the partial derivatives ith respect to the age rate. We assume that the sufficient second order condition for the ash bargaining solution (3) holds. The determinants of the negotiated base age implicit representation (4) + + b + + can be expressed through the g( a ), 7

10 here L η η ( ) γ denotes the total age elasticity of labour demand, L hich incorporates both the direct negative employment effect and the indirect positive effect via effort provision. Hence profit sharing has to opposite effects on the negotiated base age: (i) it tends to induce age moderation as part of the compensation is shifted to the performance related profit share and (ii) the effort enhancing effects of profit sharing ill also increase the costs of effort provision and thereby increase the individual rationality constraint of each union member, hich ill have a positive effect on the age rate, ceteris paribus. By substituting the optimal effort (7) into (4) the ash bargaining solution can be expressed in explicit form (see Appendix B) as follos (5) + + b. γ η The age rate increases ith the outside option and the bargaining poer of the union, and decreases as a function of the total age elasticity of labour demand. Under the assumption that the age moderating effect of profit sharing dominates relative to the cost of effort provision, i.e. if ( ) γ <, e can no summarize our analysis in Proposition 3: The negotiated age is proportional to the outside option available to the union, increasing in the bargaining poer of the union, and decreasing in the total age elasticity of labour demand. Furthermore, profit sharing ill moderate the negotiated base age if ( ) γ <. The negotiated base age equation (5) represents a generalization relative to the traditional ash bargaining solution. 4 4 Our analysis associated ith the ash bargaining solution (5) simultaneously includes profit sharing and efficiency age considerations. Altenburg and Straub (999), Bulkley and Myles (996), Lindbeck 8

11 IV.2. Base Wage and Profit Share Commitment ext e analyse the timing structure (II) (see Figure ), here the firm commits to the profit share prior to the base age negotiation. When the firm commits to the profit share, it means that equation (8) is maximized ith respect to subject to labour demand (6), effort determination (7) and the ash bargaining solution for the base age. Using a similar procedure as in Appendix A, the optimal profit share is found to be (6) c ( η ) γ + η γ ( ), for the case hen the firm commits itself to the profit share before the age negotiation (see also Koskela and Stenbacka (2004)). Based on a straightforard comparison beteen (6) and (9) e can conclude that c f >. This means that under commitment the optimal profit share is larger than that associated ith flexibility. Furthermore, under commitment the profit share is increasing as a function of γ, and of the elasticity of base age ith respect to profit sharing ( ). This is summarized as Proposition 4: The optimal profit share under commitment exceeds that under flexibility. Furthermore, the profit share under commitment is increasing as a function of the elasticity of effort ith respect to profit sharing (γ ), of the elasticity of labour demand ith respect to effort ( ) and of the elasticity of base age ith respect to profit sharing ( ). and Snoer (99) and Sanfey (993) analyse related issues, but these models do not include profit sharing as an incentive device. 9

12 Intuitively, under commitment profit sharing has a age moderating effect. This effect adds to the returns from profit sharing. Thus, the optimal profit share under commitment exceeds that associated ith flexibility. IV.3. Base Wage and Profit Share egotiation Finally, e analyse the timing structure (III) (see Figure ), here the profit share and the base age are determined simultaneously. We first study the negotiated profit share (scheme III(i)) and configuration here the firms decides on the profit share simultaneously ith the base age negotiation (scheme III(ii)). With simultaneous negotiation the parties decide on and in order to solve Max { Ω [ ] [( ) π ] ( 7) E (, ) subject to the labour demand (6) and the effort determination (7). This gives a negotiated base age, hich formally looks identical to (5). In terms of profit sharing e have the folloing first order condition (8) + ( ) 0. Solution of equation (8) yields the folloing implicit representation of the negotiated profit share (9) + ( ) γ X + ( ) γ X, 0

13 here 0 < X < ith A + γ A η + A + γ η denoting the mark up hereby the base age exceeds the outside option b (see Appendix C). From (9) e can directly infer that the negotiated profit share is an increasing function of the union s bargaining poer, i.e. > 0. In particular, by allocating the bargaining poer completely to the firm or to the union e obtain the folloing to special cases s ( ) γ (20) 0 < < 0 + ( ) γ and M. From (20) e can observe that the profit share here the firm decides on the profit share simultaneously ith the age negotiation, i.e. s 0, coincides ith that associated ith flexible profit sharing hen the firm decides about it after the base age negotiation. In other ords, the relationship f s holds. Moreover, the negotiated profit share,, is increasing as a function of the trade union s bargaining poer. Furthernore, for each 0 < < presence of the efficiency effect raises the negotiated profit share (see (9) and (20)). We can no summarize our analysis of the timing structure here the profit share is determined simultaneously ith the base age negotiation. Proposition 5: The ash bargaining solution for profit sharing, hen determined simultaneously ith the base age, is increasing in the bargaining poer of the union and is higher in the presence of productivity effect hen the union has some bargaining poer, i.e. 0 < <. Further, hen the firm decides on profit sharing simultaneously ith the age bargaining, the optimal profit share is identical to the profit share under flexibility.

14 V. Brief Conclusion This study has offered a ne unified frameork for analyzing the determination of employment, the effort provided by employed union members, the age, and profit sharing hen firms face uncertainty generated by a stochastic revenue shock. Our analysis focused on the implications for the optimal profit share of the relative timing structure of profit sharing and age bargaining. Most importantly, e demonstrated that the optimal profit share under commitment exceeds that under flexibility. This holds true, because by committing to a profit share the firm can induce age moderation. This age moderating effect promotes profit sharing as it adds to the returns from using the profit sharing instrument. Moreover, hen the firm decides on profit sharing simultaneously ith the age bargaining, the optimal profit share is identical to the profit share under flexibility. Finally, if the profit share is determined through ash bargaining, the profit share is higher in the presence of the productivity effect hen the trade union has some bargaining poer. Appendix A: Derivation of the optimal profit share ith flexibility The first order condition associated ith the maximization of (8) ith respect to and subject to (6) and (7) (for given ) is η η η (A) ( al ) L + ( ) ( a La 0, γ a η η η here a, al aη and L η a al( ). By using these a expressions e can rerite (A) as follos η ( ) γ (A2) a a η hich gives (9). QED 2

15 Appendix B: Derivation of the negotiated age This appendix develops the expressions for the terms and in the first order condition (3) of the ash bargaining. The optimal employment decision of the firm has α (+ r) to satisfy the first order condition L 0 ( a. By taking this into aη account e find that L a ( + r) ( + r) L [ γ ] < 0, here the η a age elasticity of effort a γ a E π ( /( )) L e can conclude that (B) [ γ ][ η ] < 0 and can be expressed according to (B2) + (( γ )( ) + η ) g( a ) η + L, b + g( a ) L L here η η ( ) γ. Making use of η e can rerite (B2) according to L (B3) ( ) g( a ) + η b L b + g( a ) L. Substituting (B) and (B3) into equation (3) of the text yields (4) and (5). QED Appendix C: Derivation of the negotiated profit share This appendix develops the expressions for the terms and in the first order condition (8) associated ith the ash bargaining for profit sharing and solves it to Laa produce equation (9). We first find that so that by using the properties L of labour demand (6) and effort (7) equations e end up ith E η γ (C) π ( ). 3

16 Differentiating L b + g( ith respect to yields L Lg( [ γ ( ) ] + + L. Using the properties of the labour L demand and the profit function e get ( ) γ g( (C2) + b + g( L o e can re express the first order condition (8) as ( ) γ L( b) ( ) (C3) + 0 ( ) After some manipulation e end up ith (C4) ( ) γ + ( X ), + ( ) γ X here 0 < X < ith A + γ A η + A. QED + γ η References: Altenburg, L. and Straub, M. (998): Efficiency Wages, Trade Unions, and Employment, Oxford Economic Papers, 50, Booth, A.J., Frank, J. (999): Earnings, Productivity, and Performance Related Pay, Journal of Labor Economics, 7(3), Bulkley, G. and Myles, G.D. (996): Trade Unions, Efficiency Wages and Shirking, Oxford Economic Papers, 48, Cahuc, P., Dormont, B. (997): Profit Sharing: Does It Increase Productivity and Employment? A Theoretical Model and Empirical Evidence on French Micro Data, Labour Economics, 4, Garino, G., Martin, C. (2000): Efficiency Wages and Union Firm Bargaining, Economics Letters, 69, Holmlund, B. (99): Profit Sharing, Wage Bargaining, and Unemployment, Economic Inquiry, 28, Holmström, B. (982): Moral Hazard in Teams, Bell Journal of Economics, 3, Koskela, E. and Stenbacka, R. (2004): Profit Sharing and Unemployment: An Approach ith Bargaining and Efficiency Wage Effects, Journal of Institutional and Theoretical Economics, 60(3), Layard, R., ickell, S. (990): Is Unemployment Loer if Unions Bargain over Employment, Quarterly Journal of Economics, 05,

17 Lindbeck, A., Snoer, D.J. (99): Interactions beteen the Efficiency Wage and Insider Outsider Theories, Economics Letters, 37, ickell, S., Wadhani, S. (99): Employment Determination in British Industry: Investigations Using Micro Data, Revie of Economic Studies, 58, OECD Employment Outlook (995): Chapter 4, Profit Sharing in OECD Countries. Pendleton, A., Poutsma, E., van Ommeren, J., Brester, C. (200): Employee Share Onership and Profit Sharing in the European Union, Office for Official Publications of the European Commission, Luxembourg. Sanfey, P.J. (993): On the Interaction beteen Efficiency Wages and Union Firm Bargaining Models, Economics Letters, 4, Wadhani, S., Wall, M. (990): The Effects of Profit Sharing on Employment, Wages, Stock Returns and Productivity: Evidence from U.K. Micro Data, Economic Journal, 00, 7. Weitzman, M. (985): The Simple Macroeconomics of Profit Sharing, American Economic Revie, 75(5), p Weitzman, M. (987): Steady State Unemployment under Profit Sharing, Economic Journal, 97,