Lecture 5: Labour Economics and Wage-Setting Theory

Transcription

1 Lecture 5: Labour Economics and Wage-Setting Theory Spring 2017 Lars Calmfors Literature: Chapter 7 Cahuc-Carcillo-Zylberberg:

2 1 Topics Weakly efficient bargaining Strongly efficient bargaining Wage dispersion Bargaining over working time

3 2 Efficient contracts Bargaining over the wage only and letting employers determine employment (right to manage) is not efficient. An efficient solution can be found by bargaining over both the wage and employment. Max w, L [ ] 1 ( ) [ ν( ) ν( )] γ γ γ R L wl w w L s.t. 0 L N and w w Interior solution R'( L) w γ (1 γ) + 0 (I) RL ( ) wl L L γν '( w) (1 γ) + 0 (II) RL ( ) wl ν( w) ν( w) Eliminate γ between the two equations to get w R'( L) ν( w) ν( w) ν '( w) (III)

4 3 This is the equation of a contract curve (Pareto-efficient combinations of w, L) connecting tangency points of indifference and isoprofit curves. The same equation would be obtained by maximising [ ] L ν( w) ν( w) s.t. π π Differentiation of the contract curve equation gives: dw R"( L) dl ν "( w) w R '( L) [ ] γ 0 R '( L) w according to (I) R '( L) w ν( w) ν( w) and w w according to (III) Hence the contract curve starts on the labour demand schedule at w If w R'( L) > and workers are risk averse, i.e. ν " < 0, then dw / dl > 0 for w > R '( L). w γ 0 gives the competitive level of employment L Lw ( ) With γ > 0, the union uses its bargaining power to raise both the wage and employment over the competitive levels. dw If workers are risk-neutral, then ν " 0 and. Hence the contract dl curve is vertical. Employment is at the competitive level.

5 4 Overemployment if workers are risk-averse weak efficiency as R '( L) < w due to employment being higher than L defined by R'( L ) w c c

6 5 Strongly efficient contracts Efficiency gain for union if utility of employed and unemployed are equated Incentive to bargain with firm over unemployment benefit paid by the firm Union objective Lν( w) + ( N L) ν( b + w) Firm profit π R( L) wl ( N L) b Max Lν( w) + ( N L) ν( b+ w) w, b w, b s.t. π π 0 [ ] Max Lν( w) + ( N L) ν( b+ w) + λ R( L) wl ( N L) b π 0 FOC Lν'( w) λl 0 ( N L) ν'( b + w) λ( N L) 0 ν '( w) λ ν '( b + w) λ

7 6 Hence: ν '( w) ν'( b + w) w b + w Pareto efficiency requires a wage for the employed that is equal to the income as unemployed. The firm pays a benefit b to all unemployed. It pays a wage w + b to the employed. Employment does not matter to the union, since members are insured against unemployment. The bargaining problem Max b FOC: 1 γ [ R( L*) wl* bn] [ ν( w + b) ν( w) ] [ ] ν( w + b) ν( w) γ R( L*) wl* bn ν'( w+ b) 1 γ N with w w+ b γ R'( L*) w Employment equals the competitive level Union members appropriate a share of the firm s profit without this having negative effects on employment

8 7 Diagrammatical illustration Indifference curves: ν ν 1 1 υ s dw dw dl dw dl ν( w) The indifference curves are horizontal lines. Isoprofit curve π R( L) wl bn R( L) wl N( w w) dπ 0 R'( L) dl wdl Ndw dw R '( L) w dl N Tangency points between isoprofit curves and indifference curves give a vertical contract curve (at the competitive level of employment) Bargaining over wages, employment and unemployment benefits from firms is strongly efficient.

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10 9 Collective bargaining and wage dispersion Heterogeneous workers Collective bargaining reduces wage dispersion Two types of workers, indexed by i 1, 2 Revenue of the firm R(L 1, L 2 ) Type -1 workers are more productive with a higher reservation w > w wage 1 2 N i workers of type i in the firm s labour pool The union utility function 2 υ υ υ L ( w ) + ( N L ) ( w + b ) L N s i i i i i i i i i1 Strongly efficient bargaining over employment, wages and unemployment benefits Optimal contract implies w w + b i i i

11 10 Bargaining problem γ 2 2 RL (, L) ( wl bn) N { ( w b ) ( w )} ν + ν i i i i i 1 i 1 Max i i i i b, b, L, L γ s.t. 0 L N i 1, 2 i i FOCs (11) (12) RL (, L) L ν'(w + b ) w i 1 γ i i 2 γ γ 2 i1 [ ν( ) + ) ν( )] N w b w i i i i RL (, L) ( wl + bn) 1 2 i 1 i i i i Equation (11): Productive efficiency, i.e. the marginal productivity of each type of worker equals the reservation wage. This implies the competitive level of employment. Equation (12): RHS is independent of i. Hence the same wage for the two types of labour. Wage equality follows from the assumption of a utilitarian union and identical preferences.

12 11 N N N N ν( w ) + ν( w ) ν w + w N + N N + N N + N N + N Because of concavity the union is better off with a wage N N 1 2 w + N + N N + N w for everyone than with separate wages w 1 and w 2.

13 12 Two-stage bargaining over employment (Manning 1987) Stage 1: Bargaining over the wage Stage 2: Bargaining over employment Different bargaining strengths in the two negotiations Bargaining over employment (given the wage) Max L 1 [ ] [ ν ν ] γ γ γ L L L R( L) wl ( w) ( w) L s.t. 0 L N The solution gives L L( γ, w, w) L Bargaining over the wage (takes the outcome of second-stage bargaining over employment into account) Max w s.t. 1 [ ( ) ] [ ν( ) ν( )] R L wl w w L L L( γ, w, w) and w w L γ γ γ Different cases γ 0 and γ > 0 gives the right-to-manage model L γ γ gives (weakly) efficient bargain model L Otherwise solution on neither labour-demand schedule nor contract curve

14 13 Motivations Efficient bargaining is complex Wage bargaining precedes employment bargaining Wage bargaining is often at more centralised level Strongly efficient bargaining is improbable because of moral hazard problems: unemployed being fully insured will not search effectively for jobs - argument for partial insurance - individual firm (sector) offering full insurance would be swamped by labour inflow One does not find many examples of contracts with unemployment benefits paid by firms Unclear empirical results on right-to-manage model and (weakly efficient) bargaining

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16 15 Bargaining over hours Real-world bargaining appears often to be about both wages and working time Ω wage income T time allocation H hours worked Ω wh Utility function of a worker is υ(ω, H) e (H) productivity of a worker L number of workers Revenue of the firm [ ( ) ] [ ( ) ] / [ 0, 1] ReHL ehl α α α e η He '( H ) / e( H ) > 0 is the elasticity of worker H productivity w.r.t. hours. eh ( )/( H ) the productivity per hour. It increases with the e number of hours if η > 1. H Bargaining about the hourly wage and hours only Union utility [ ν ] V ( Ω, T H) + (1 ) ν( w, T) Min (1, L/N) s

17 16 Firm profit π 1 α [ eh L] a ( ) ΩL (24) Right-to-manage assumption Firm determines employment from profit maximisation. w and H or equivalently Ω and H are taken as given. π Set / L 0 and solve for L: [ ] /(1 ) 1/( 1) L(, H) e( H) α α α Ω Ω (25) If L( Ω, H) < N, we can plug (25) into profit equation (24). π 1-α eh ( ) ( Ω, H ) Ω α Nash bargaining solution If no agreement: Employee gets ν( wt, ) Firm gets zero profit γ α/(1 α) L( Ω, H) Max (, ) (, ) (, ) Ω, H N γ [ ν Ω T H ν w T ] [ π Ω H ] s.t. L( Ω, H) N and H H H is legal constraint on hours (maximum hours allowed by legislation).

18 17 Interior solution Take logs and differentiate w.r.t. Ω and H. FOCs γν ( Ω, T H) α(1 γ) + γ 1 ν( Ω, T H) ν( w, T) (1 α) Ω (26) γν ( Ω, T H) α eh '( ) 2 ν( Ω, T H) ν( w, T) (1 α) e( H) (27) Divide (26) by (27): 2 [ ] ν ( Ω, T H) α(1 γ) + γ (1- α) eh ( ) 1 ν ( Ω, T H) (1 α) Ω α e'( H) [ α(1 γ) + γ] eh ( ) H H[ α(1 γ) + γ] (28) e α e'( H) H Ω Ω αη η e H He '( H ) / e( H ) H Equation (28) defines the MRS between income and leisure as a function of the e wage w Ω/H and the elasticity of employee productivity w.r.t. H, η. h

19 18 Assume Cobb-Douglas utility function: ν μ 1 μ ( Ω, ) ( Ω) ( ) μ (0, 1) Then: T H T H ν 1 μω ( T H) μ 1 1 μ ν 2 2 μ (1- μ)( T H) Ω ν μ 1 1 μ Ω ( T H) ν 1-μ 1-μ μ ( T H) Ω Assume that e(h) H, then η e H e'( H) 1 and e'( H) H / e( H) 1. (28) then simplifies to: μ ( T H) H α(1 γ) + γ Ω Ω 1 μ α H * μα (29A) [ ] (1- μ) γ + α(1 γ) + μα

20 19 Optimal number of hours is increasing in μ (the importance of income relative to leisure) is decreasing in union bargaining power γ - unions want low working time to get leisure and more workers employed - explanation of work sharing: reduction in hours to boost employment Legal maximum of hours H < H Negotiated wage is then given by (26) with H With Cobb-Douglas preferences one obtains: * H μ 1 μ γ(1 α) + α Ω ( T H) ν( w, T) (A) γ(1 μ)(1 α) + α RHS of (A) is a constant. Hence: μ 1 μ Ω ( T H) constant μ nω + (1 μ) n( T H) constant

21 20 Differentiate w.r.t. d nh μ d nω d n( T H) + (1 μ) 0 d nh d nh μ d nω d n( T H) dh + (1 μ) 0 d nh dh d nh μ d nω ( 1) + (1 μ) H 0 d nh T H d nω H(1 μ) η Ω h d nh ( T H) μ The elasticity of wage income w.r.t. hours, Hence wage income falls if hours fall. It falls more if hours are long to begin with. η Ω h, is positive.

22 21 [ ] /(1 ) 1/( 1) L(, H) e( H) α α α Ω Ω (25) Assume again eh ( ) H L H H α α α /(1 ) 1/ 1 ( Ω, ) Ω (B) We want to know what happens to employment L if binding legal maximum H is reduced. - direct effect from change in H - indirect effect from induced change in wage income Ω. Take logs of (B): α 1 nl nh + nω 1 α α 1 Differentiate w.r.t. d nh d nl d nh α α α 1 d nω d nh We use: d nω H(1 μ) d nh ( T H) μ

23 22 d nl α 1 H(1 μ) + d nh 1 α α 1 ( T H) μ d nl α 1 H(1 μ) < 0 if + < 0 d nh 1 α α 1 ( T H) μ This is equivalent to H > Hˆ Hˆ μα (1 μ) + μα T Interpretation A reduction in working time raises employment only if H > Hˆ. From (29A) we have that Ĥ is optimal hours for unions. H * γ 1 μα [ ] (1 μ) γ + α(1 γ) + μα (29A) H * μα (1 μ) + μα

24 23 A reduction in H increases employment only down to the point where H reaches the trade union optimum. Further reductions lower employment.

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26 25 Insiders and outsiders Unions negotiate on behalf of insiders (the already employed those with a strong affiliation to the labour market) Unions do not negotiate on behalf of outsiders (the unemployed in general or the long-term unemployed) An insider-outsider model L O insiders The firm decides on how many insiders L I L O it wants to retain. It also decides on how many outsiders L E it wants to hire. Revenue function R(L I + L E ) The firm s profit: π R(L I + L E ) - w(l I + L E ) Employment of insiders, L I, and of outsiders, L E, is found by maximising profits s. t. L I L O and L E > 0. Define w O by R (L O ) w O. Define L as the employment level such that R (L ) w, where w is the current wage. Labour demand L L and L 0 if w w I E O L L and L L L if w w I O E O O If w w we have L L < L, so some insiders are fired. O I O

27 26 Wage bargaining V expected utility of an insider I V ν( w) + (1 ) ν( w) Min (1, L / L ) I O w the reservation wage 1 γ [ π w ] { [ ν w ν w ]} Max ( ) ( ) ( ) w with π( w) R( L ) wl Let w 1 be the solution when L / L (interior solution O with some unemployed insiders). The solution is the same as in the standard right-to-manage model but with L O N. γ ν( w ) ν( w) γ 1 L wν'( w ) γη + (1 γ) η 1 w π w (10) Solution with 1 L Set η 0 in (10); employment of insiders cannot increase w ν( w ) ν( w) γ 2 π w ν'( w ) (1 γ) η w 2 2

28 27 Different solutions B Nash bargaining product when > L, i.e. some employed outsiders 1 0 B Nash bargaining product when L < L, 2 0 i.e. some unemployed insiders L We have: B w > B w 1 2 Larger gain from wage increase if only outsiders lose their jobs than if also insiders do. Second-order conditions for a maximum 2B 1 ( B 1 / w) w2 w < 2B 2 ( B 2 / w) w2 w < 0 0

29 28 (1) Interior solution with B w B > 0 > 0 w 1 2 (2) Corner solution with w > w and L L 0 0 w w and L L 0 0 B w B > 0 < 0 w 1 2 (3) Interior solution with B w B > 0 < 0 w 1 2 w < w 0

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31 30 Conclusion A fall in the number of insiders results in an unchanged wage or in an increase in the wage Explanation of the persistence of unemployment No incentive to reduce the wage as the union does not care about the unemployed Empirical research has had problems finding that a reduction in lagged employment has a positive effect on the wage.