Y = F(K,θM(P)LM,θF(P)LF)
Firms are profit maximizers and given wage levels wM and wF for managers and front-line workers
respectively, the first order conditions defining the optimal choice of labor inputs provide the equality
condition between wages and marginal productivities for each category of workers as follows:
|
∂Y ⅛" = wM (1) ∂LM ∂Y ∂LF = wF (2) |
Assuming a Cobb Douglas production function with constant returns to scale 4, the production func-
tion is given by:
F(K,θM(P)LM,θF(P)LF)=Kα(θM(P)LM)βM(θF(P)LF)βF
The system of first order condition (3) becomes:
-———— F ( K,Θm ( P ) Lm ,Θf ( P ) Lf ) = Wm (3)
θM (P)LM
βF
F K>∖θ F(K,θM(P)LM ,θF(P)LF) = wF (4)
θF (P)LF
The wage ratio between manager and front-line workers is therefore given by the following equation:
wM = вм Θf ( P) Lf
wF βF Θm (P) Lm
(5)
Taking the log of both sides of this equation provides the empirical equation to be estimated:
log ( Wm ) = log ( βM ) + log ( L' ) + log ( θ' P. ) (6)
wF βF LM θM (P)
Following the literature on skill-biased technological change, it is assumed that the invention associ-
ated with workplace practices toward more employee involvement represents a discrete and exogenous
change in technological opportunities. Some firms have adopted the new workplace practices (P>0,
θ(P) > 1) while others haven’t (P = 0, θ(0) = 1).
The last term of equation (6) represents the effect of the use of workplace practices on wage dis-
persion. The identification of this term will be based on the following reasoning. Among firms not
implementing the practices, the term vanishes because θM (0) = θF (0) = 1. The term will be non
4The use of a Cobb Douglas production function follows the empirical literature on the effect of workplace practices on
firm performance. In particular, Black and Lynch (1997) tested the hypothesis of constant returns to scale based on the
NES data and could not reject it.