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Income distribution, efficient bargaining and market structure
Economics Letters 40 (1992) 181-185 North-Holland
181
Income distribution, efficient bargaining and market structure Martin J. Conyon * The Queen3 College, Oxford, UK Institute of Economics and StattXcs, Oxford, UK
Received 28 July 1992 Accepted 15 October 1992
We present an efftcient bargaining model in which wage share is negatively associated with product market structure and varies positively with union bargaining strength. The model is tested using data from a panel of U.K. manufacturing industries. Instrumental variables estimates corroborate a positive (negative) union’bargaining strength (concentration) effect on labour’s income share.
1. Introduction
Using a Cournot modelling strategy both Cowling and Molho (1982) and Henley (1987) have demonstrated the existence of a negative relationship between production worker wage share and concentration. Although both models introduce empirically a role for trade union bargaining strength to influence wage share the union effect has not been modelled formally. Furthermore the actual empirical tests relating wage share to unionism have yielded ambiguous results. To resolve this irregularity we present an efficient bargaining model which illustrates that wage share varies positively with union bargaining strength and negatively with product market structure. Using generalised instrumental variable methods we then test the model using a sample of U.K. manufacturing industries in the early 1980s.
2. Theory 2.1. Income distribution and market structure Consider the case where wages are predetermined or exogenous. The firm has a profit function ri = PjY;:- wiLi where pi is firm profits, wi is the wage and Li is direct employment. Following the Correspondence to: Martin J. Conyon, The Queen’s, College, Oxford University, oxford, OX1 4AW, United Kingdom. * I would like to thank Keith Cowling, Jonathan Haskel and Mike Waterson for valuable discussions. Errors remain my own. Part of this research was completed with the financial assistance from the Economic and Social Research Council Award ROO428824041. 0165-1765/93/$06.00
8 1993 - Elsevier Science Publishers B.V. All rights reserved
182
M.J. Conyon / Income distribution,
efficient bargaining and market structure
strategy employed by Haskel and Martin (1992) Y, is a value added production function such that yi = A,LqKf where Ai is a positive technology constant, K is capital (which is also assumed to be predetermined in the short run), and (Yand p are positive scale return fractions. P,<.) is the price in industry j which is a negative function of industry output, 5 (= CY,). The firm chooses labour input to maximise profits, subject to the production constraint, which yields a familiar first-order condition,
wi=c&-
Y I Li
i
l-
M&(1 +Ai) rl
I’
where MS, (= YJY;.) is market share of firm i, hi [ = S
$=(1-a)+
Msit~+I\‘)),
I 1
(2)
When (Y= 1 this produces the familiar Cowling and Waterson (1976) result and the usual caveats when interpreting their model also apply here. The left-hand side of eq. (2) is the margin and is conditioned by monopoly power factors. For present purposes what is important is that the derived margins equation provides no obvious rationale for trade unions since wages are predetermined [see the discussion in Dowrick (199O)l. Recognising that labour’s share of value added wiLi/qyi can be written as 1 - (ri/PjY) then the labour income distribution equation can be written as WiLi
-=(Y &
li
MS,( 1 + Ai)
77
I*
Eq. (3) states that production worker wage share is conditioned by product market factors alone with no apparent role for labour market effects such as trade union bargaining power. Under reasonable specifications of the conjectural variation term, as.discussed by Conyon and Machin (1990, the model with predetermined wages predicts that wage share will be lower the higher is market share. More generally, illustrated by Cowling and Molho (1982), wage share varies inversely with concentration. 2.2. Income distribution and efficient bargaining We now relax the assumption that wages are predetermined and introduce a direct role for unions in shaping production worker wage share. We consider a strongly efficient bargaining model where both employment and wages are bargained over simultaneously to solve the asymmetric Nash bargain A = U.e~!l-e). The firm’s profit function remains rri = PjY;:- wiLi where for analytical simplicity the fali hick position is set at zero. Union preferences over employment and wage are captured by the utility function Vi = (wi - b)L, where b is the alternative wage. This functional form for union preferences assumes that the union is a utilitarian one and also that union members are risk neutral. Such a specification has been widely used in the literature, see Haskel and Martin (1992) and Lockwood and Manning (1989), and for our purposes is convenient for establishing a role for unions in the determination of income distribution. The term 8 is the bargaining strength
M.J. Conyon / Income distribution, eficient bargaining and market structure
183
parameter (0 < 8 < 1). The closer to unity is 0 the more bargaining strength the union has. Maximising the Nash bargain with respect to employment yields a first-order condition,
-
aT,/aL, i q/sLi
e
I=(1-8)$
which can be readily solved and rearranged to give an expression for production worker wage share as WiLi
-=/3+a(l-8) q:.y,
MS,( 1 + hi) li
77
I*
(5)
The efficient bargain wage share equation (5) demonstrates: (i) that union bargaining strength enters directly into the determination of production worker wage share. When 8 = 0 eq. (5) collapses to eq. (31 and the problem reduces to that identified by Cowling and Molho (1982). The model predicts that for positive values of 0 wage share will be higher compared to the case where wages are predetermined. (ii) that efficient bargained wage share is lower the higher is market share.
3. Modelling strategy and empirical results We can test the non-linear wage share equation (5) using a panel of 95 U.K. industries ’ over the time period 1983 to 1986 in the following standard estimating equation: WSj, = (~g+ (Y~CON~~,+ (~2DENSj, + Ejt,
(6)
where WS is production worker wage share (i.e. operative wage bill over value added) in industry j at time t, CONC is the five-firm concentration ratio, DENS is industry density and E a random error. CONC is used as a proxy for product market power and DENS approximates union bargaining strength. This is consistent with the recent empirical literature [e.g. Macpherson (1990)]. To relate the estimating equation (6) to the model in eq. (5) all continuous variables are in natural logarithms to account for the interactive nature of the theoretical model. The efficient bargaining wage share model would predict (pi < 0 and (Ye> 0. Estimates of eq. (6) are presented in table 1. Data definitions and variable means are presented in table 2. All models are estimated by generalised instrumental variable methods. A clear systematic empirical relationship emerges. A negative and significant concentration effect on wage share is isolated in column (1) of table 1. This is consistent with previous empirical evidence [e.g. Macpherson (199011 and with the efficient bargaining model presented earlier. In column (2) a significantly positive union density effect on wage share is unearthed. In column (3) the impact on wage share of both market concentration together with union density is examined. The reported point estimates suggest that the effect of a 10 percent increase in product market concentration is to depress wage share by approximately 2.3 percent. Conversely, a 10 percent rise in union density predicts a rise in labour’s income share of approximately 6.1 percent. The sign and significance of ’ This is the data set used by Conyon and Machin (1991) where more details are given.
184
M.J. Conyon / Income distribution, efficient bargaining and market structure
Table 1 Estimates of the impact of market structure and bargaining strength on wage share in 95 U.K. manufacturing industries 1983-1986. a,b,c
(2)
(1) Constant
4.223 (0.099)
CONC
(3)
1.629 (0.401)
1.865 (0.408)
- 0.192 to.050)
- 0.227 (0.027
DENS Residual sum of squares Time dummies ,y2 (3) test d
0.464 (0.097)
0.609 (0.103)
47.41
49.54
43.03
Yes 0.685
Yes 0.128
Yes 0.167
Estimated models use data from 1983-1986 with data from 1980 retained as instuments. Dependent variable is operative wage share - WS - operative wage bill/value added. Models estimated by generalised instrumental variable methods: potential instruments available in 1983 are all predetermined variables together with endogenous variables dated 1980, 1981, and 1982, in 1984 endogenous variables from 1980 to 1983 are available and so on. As the panel becomes more advanced so more instruments become available. CONC and DENS are treated as endogenous using instruments: CONC,_ 1 back to CONC,_s, DENS,_, back to DENS,_6. Heteroscedastic consistent standard errors are reported in parentheses. A chi squared Wald test with 3 degrees of freedom is reported of the significance of the time dummies.
Table 2 Data definitions and variable means 1983-1986. a*b
Wage share Concentration Density
ws CONC DENS
1983
1984
1985
1986
1983-1986
36.12 43.58 60.15
36.12 42.44 58.46
35.42 42.31 56.90
35.25 42.56 55.01
35.73 42.72 57.63
a Definitions of variables are as follows: WS - Production worker wage share; CONC-5 firm seller concentration ratio by sales; DENS - industry union density; b Data sources are as follows: WS, CONC - Report on the Census of Production Summary Tables, PA 1002, HMSO. DENS - supplied by Steve Machin from the London School of Economics.
both the product market and labour market strength variables in shaping wage share attest to the importance of these factors in shaping income distribution.
4. Conclusions In the literature which considers the relationship between wage share, market structure and unionism an anomaly has been encountered whereby the role of union bargaining does not enter directly in the theoretical wage share equation. This paper has presented an efficient bargaining model to illustrate that wage share is conditioned by both market structure and union bargaining strength. Instrumental variable estimates of an empirical income distribution equation have demonstrated that both product market and labour market factors are empirically important in shaping income distribution.
M.J. Conyon / Income distribution, efficient bargaining and market structure
185
References Conyon, M. and S. Machin, 1991, The determination of profit margins in U.K. manufacturing, Journal of Industrial Economics 39, 369-382. Cowling, K. and I. Molho, 1982, Wage share, concentration and unionism, Manchester School 50, 99-115. Cowling, K. and M. Waterson, 1976, Price cost margins and market structure, Economica 43, 267-274. Dowrick, S., 1990, Wage pressure, bargaining and price cost margins in U.K. manufacturing, Journal of Industrial Economics 38, 239-267. Haskel, J. and C. Martin, 1992, Margins, concentration and the business cycle: Theory and evidence for Britain, International Journal of Industrial Organisation, forthcoming. Henley, A., 1987, Trades unions, market concentration and income distribution in United States manufacturing industry, International Journal of Industrial Organisation 5, 193-210. Lockwood, B. and A. Manning, 1989, Dynamic wage employment bargaining with employment adjustment costs, Economic Journal 99, 1143-1158. Macpherson, D., 1990, Trade unions and labour’s share in U.S. manufacturing industries, International Journal of Industrial Organisation 8, 143-153.
181
Income distribution, efficient bargaining and market structure Martin J. Conyon * The Queen3 College, Oxford, UK Institute of Economics and StattXcs, Oxford, UK
Received 28 July 1992 Accepted 15 October 1992
We present an efftcient bargaining model in which wage share is negatively associated with product market structure and varies positively with union bargaining strength. The model is tested using data from a panel of U.K. manufacturing industries. Instrumental variables estimates corroborate a positive (negative) union’bargaining strength (concentration) effect on labour’s income share.
1. Introduction
Using a Cournot modelling strategy both Cowling and Molho (1982) and Henley (1987) have demonstrated the existence of a negative relationship between production worker wage share and concentration. Although both models introduce empirically a role for trade union bargaining strength to influence wage share the union effect has not been modelled formally. Furthermore the actual empirical tests relating wage share to unionism have yielded ambiguous results. To resolve this irregularity we present an efficient bargaining model which illustrates that wage share varies positively with union bargaining strength and negatively with product market structure. Using generalised instrumental variable methods we then test the model using a sample of U.K. manufacturing industries in the early 1980s.
2. Theory 2.1. Income distribution and market structure Consider the case where wages are predetermined or exogenous. The firm has a profit function ri = PjY;:- wiLi where pi is firm profits, wi is the wage and Li is direct employment. Following the Correspondence to: Martin J. Conyon, The Queen’s, College, Oxford University, oxford, OX1 4AW, United Kingdom. * I would like to thank Keith Cowling, Jonathan Haskel and Mike Waterson for valuable discussions. Errors remain my own. Part of this research was completed with the financial assistance from the Economic and Social Research Council Award ROO428824041. 0165-1765/93/$06.00
8 1993 - Elsevier Science Publishers B.V. All rights reserved
182
M.J. Conyon / Income distribution,
efficient bargaining and market structure
strategy employed by Haskel and Martin (1992) Y, is a value added production function such that yi = A,LqKf where Ai is a positive technology constant, K is capital (which is also assumed to be predetermined in the short run), and (Yand p are positive scale return fractions. P,<.) is the price in industry j which is a negative function of industry output, 5 (= CY,). The firm chooses labour input to maximise profits, subject to the production constraint, which yields a familiar first-order condition,
wi=c&-
Y I Li
i
l-
M&(1 +Ai) rl
I’
where MS, (= YJY;.) is market share of firm i, hi [ = S
$=(1-a)+
Msit~+I\‘)),
I 1
(2)
When (Y= 1 this produces the familiar Cowling and Waterson (1976) result and the usual caveats when interpreting their model also apply here. The left-hand side of eq. (2) is the margin and is conditioned by monopoly power factors. For present purposes what is important is that the derived margins equation provides no obvious rationale for trade unions since wages are predetermined [see the discussion in Dowrick (199O)l. Recognising that labour’s share of value added wiLi/qyi can be written as 1 - (ri/PjY) then the labour income distribution equation can be written as WiLi
-=(Y &
li
MS,( 1 + Ai)
77
I*
Eq. (3) states that production worker wage share is conditioned by product market factors alone with no apparent role for labour market effects such as trade union bargaining power. Under reasonable specifications of the conjectural variation term, as.discussed by Conyon and Machin (1990, the model with predetermined wages predicts that wage share will be lower the higher is market share. More generally, illustrated by Cowling and Molho (1982), wage share varies inversely with concentration. 2.2. Income distribution and efficient bargaining We now relax the assumption that wages are predetermined and introduce a direct role for unions in shaping production worker wage share. We consider a strongly efficient bargaining model where both employment and wages are bargained over simultaneously to solve the asymmetric Nash bargain A = U.e~!l-e). The firm’s profit function remains rri = PjY;:- wiLi where for analytical simplicity the fali hick position is set at zero. Union preferences over employment and wage are captured by the utility function Vi = (wi - b)L, where b is the alternative wage. This functional form for union preferences assumes that the union is a utilitarian one and also that union members are risk neutral. Such a specification has been widely used in the literature, see Haskel and Martin (1992) and Lockwood and Manning (1989), and for our purposes is convenient for establishing a role for unions in the determination of income distribution. The term 8 is the bargaining strength
M.J. Conyon / Income distribution, eficient bargaining and market structure
183
parameter (0 < 8 < 1). The closer to unity is 0 the more bargaining strength the union has. Maximising the Nash bargain with respect to employment yields a first-order condition,
-
aT,/aL, i q/sLi
e
I=(1-8)$
which can be readily solved and rearranged to give an expression for production worker wage share as WiLi
-=/3+a(l-8) q:.y,
MS,( 1 + hi) li
77
I*
(5)
The efficient bargain wage share equation (5) demonstrates: (i) that union bargaining strength enters directly into the determination of production worker wage share. When 8 = 0 eq. (5) collapses to eq. (31 and the problem reduces to that identified by Cowling and Molho (1982). The model predicts that for positive values of 0 wage share will be higher compared to the case where wages are predetermined. (ii) that efficient bargained wage share is lower the higher is market share.
3. Modelling strategy and empirical results We can test the non-linear wage share equation (5) using a panel of 95 U.K. industries ’ over the time period 1983 to 1986 in the following standard estimating equation: WSj, = (~g+ (Y~CON~~,+ (~2DENSj, + Ejt,
(6)
where WS is production worker wage share (i.e. operative wage bill over value added) in industry j at time t, CONC is the five-firm concentration ratio, DENS is industry density and E a random error. CONC is used as a proxy for product market power and DENS approximates union bargaining strength. This is consistent with the recent empirical literature [e.g. Macpherson (1990)]. To relate the estimating equation (6) to the model in eq. (5) all continuous variables are in natural logarithms to account for the interactive nature of the theoretical model. The efficient bargaining wage share model would predict (pi < 0 and (Ye> 0. Estimates of eq. (6) are presented in table 1. Data definitions and variable means are presented in table 2. All models are estimated by generalised instrumental variable methods. A clear systematic empirical relationship emerges. A negative and significant concentration effect on wage share is isolated in column (1) of table 1. This is consistent with previous empirical evidence [e.g. Macpherson (199011 and with the efficient bargaining model presented earlier. In column (2) a significantly positive union density effect on wage share is unearthed. In column (3) the impact on wage share of both market concentration together with union density is examined. The reported point estimates suggest that the effect of a 10 percent increase in product market concentration is to depress wage share by approximately 2.3 percent. Conversely, a 10 percent rise in union density predicts a rise in labour’s income share of approximately 6.1 percent. The sign and significance of ’ This is the data set used by Conyon and Machin (1991) where more details are given.
184
M.J. Conyon / Income distribution, efficient bargaining and market structure
Table 1 Estimates of the impact of market structure and bargaining strength on wage share in 95 U.K. manufacturing industries 1983-1986. a,b,c
(2)
(1) Constant
4.223 (0.099)
CONC
(3)
1.629 (0.401)
1.865 (0.408)
- 0.192 to.050)
- 0.227 (0.027
DENS Residual sum of squares Time dummies ,y2 (3) test d
0.464 (0.097)
0.609 (0.103)
47.41
49.54
43.03
Yes 0.685
Yes 0.128
Yes 0.167
Estimated models use data from 1983-1986 with data from 1980 retained as instuments. Dependent variable is operative wage share - WS - operative wage bill/value added. Models estimated by generalised instrumental variable methods: potential instruments available in 1983 are all predetermined variables together with endogenous variables dated 1980, 1981, and 1982, in 1984 endogenous variables from 1980 to 1983 are available and so on. As the panel becomes more advanced so more instruments become available. CONC and DENS are treated as endogenous using instruments: CONC,_ 1 back to CONC,_s, DENS,_, back to DENS,_6. Heteroscedastic consistent standard errors are reported in parentheses. A chi squared Wald test with 3 degrees of freedom is reported of the significance of the time dummies.
Table 2 Data definitions and variable means 1983-1986. a*b
Wage share Concentration Density
ws CONC DENS
1983
1984
1985
1986
1983-1986
36.12 43.58 60.15
36.12 42.44 58.46
35.42 42.31 56.90
35.25 42.56 55.01
35.73 42.72 57.63
a Definitions of variables are as follows: WS - Production worker wage share; CONC-5 firm seller concentration ratio by sales; DENS - industry union density; b Data sources are as follows: WS, CONC - Report on the Census of Production Summary Tables, PA 1002, HMSO. DENS - supplied by Steve Machin from the London School of Economics.
both the product market and labour market strength variables in shaping wage share attest to the importance of these factors in shaping income distribution.
4. Conclusions In the literature which considers the relationship between wage share, market structure and unionism an anomaly has been encountered whereby the role of union bargaining does not enter directly in the theoretical wage share equation. This paper has presented an efficient bargaining model to illustrate that wage share is conditioned by both market structure and union bargaining strength. Instrumental variable estimates of an empirical income distribution equation have demonstrated that both product market and labour market factors are empirically important in shaping income distribution.
M.J. Conyon / Income distribution, efficient bargaining and market structure
185
References Conyon, M. and S. Machin, 1991, The determination of profit margins in U.K. manufacturing, Journal of Industrial Economics 39, 369-382. Cowling, K. and I. Molho, 1982, Wage share, concentration and unionism, Manchester School 50, 99-115. Cowling, K. and M. Waterson, 1976, Price cost margins and market structure, Economica 43, 267-274. Dowrick, S., 1990, Wage pressure, bargaining and price cost margins in U.K. manufacturing, Journal of Industrial Economics 38, 239-267. Haskel, J. and C. Martin, 1992, Margins, concentration and the business cycle: Theory and evidence for Britain, International Journal of Industrial Organisation, forthcoming. Henley, A., 1987, Trades unions, market concentration and income distribution in United States manufacturing industry, International Journal of Industrial Organisation 5, 193-210. Lockwood, B. and A. Manning, 1989, Dynamic wage employment bargaining with employment adjustment costs, Economic Journal 99, 1143-1158. Macpherson, D., 1990, Trade unions and labour’s share in U.S. manufacturing industries, International Journal of Industrial Organisation 8, 143-153.