A number of recent papers have been concerned with the labour share. The focus of these works
has been to understand the determinants of either the evolution of the labour share over time in OECD,
or cross-country differences (Blanchard, Nordhaus, and Phelps, 1997; Rodrik, 1999; de Serres, Scarpetta
and de la Maisonneuve, 2002; Bentolila and Saint-Paul, 2003). We present a different perspective, trying to
understand not the determinants but the effects of differences in the rewards to capital and labour across
countries and over time.
The paper is organised as follows. Section 2 presents our theoretical model. Section 3 presents the
data and our results. We then perform a number of simulation exercises. Section 4 concludes.
2. Theoretical considerations
2.1. The determinants of the relative wage and the labour share
2.1.1. Technological determinants
We consider an economy with three inputs, capital, denoted by K , skilled workers, H , and unskilled
workers, L . Output is produced according to a constant return to scale production function
Y = F(K , L, H ) . As is well known, a Cobb-Douglas production function implies constant labour and
capital shares. In order to explain observed variations in labour shares, a more general production
function is needed. We assume that output is produced with a CES production function using capital, K,
and a “labour aggregate”. Production is a CES function of K and the labour aggregate, which is in turn a
Cobb-Douglas function of skilled and unskilled labour. That is, output is produced according to2
Y = [αK-σ +(1 - α)(HβL1-β)-σ
with - 1 ≤ σ < ∞ , 0 < α < 1,0 < β < 1
(1)
This production function allows for different degrees of substitutability across factors. The elasticity of
substitution between skilled and unskilled labour is 1, while that between capital and the labour aggregate
is 1/(1 + σ) . For σ = 0 the production function would be Cobb-Douglas in the three inputs. In line
with existing evidence,3 we assume that the elasticity of substitution between capital and the labour
aggregate is less than one, which requires σ > 0 .
Differentiating the production function we obtain factor demand functions,
-σ -(1+σ) /
r = α(α + (1 - α)x-σ )
(2a)
(2b)
(2c)
wu = (1 -β)(1 -α)(α + (1 -α)xσ) d'σ' σ xσ K
L
nʌ = β(1 -α)(α + (1 -α)xσ)( ) x° —
2 This formulation has been proposed, for example, by Katz and Murphy (1992).
3 This is consistent with the evidence reported in Hamermesh (1993), Rowthorn (1999), Krusell, Ohanian, Rios-Rull,
and Violante (2000), and Antras (2004).