F. HASHEMI585
Consider a region consisting of a constant number of
countries with different levels of wages. The set of
wages forms a distribution which evolves over time.
Fierce competition in labor markets generates some sta-
tionary equilibrium distribution of real wages with a cer-
tain mean and variance, towards which the ensemble of
countries considered tend. The equilibrium is a result of
tension between counteracting forces of convergence and
divergence. Convergence is a result of adjustment of
capital-labor ratios to common steady-state levels,
starting from different initial values [9,10]. Call this the
drift spread, driven by diminishing returns to capital. A
counteracting diffusion spread is at work, driven by
bottlenecks in the flow of labor and capital and by
random effects, which cause a spread of wages from high
density towards lower density. Diffusion of knowledge
and learning [11-16] is limited by the presence of
obstacles in the form of trade barriers and the like.
Consistent with the above, the following drift-diffu-
sion model is proposed to express the wage adjustment
process with noise, describing diffusion of shocks across
space:
2
2
f
usf
ts
where
denotes probability density, denotes the
mean of the stationary equilibrium distribution,
u
de-
notes wages,
the wage adjustment rate, and
a di-
ffusion parameter2.
3. Empirical Analysis
The empirical analysis uses Williamson’s data [1] which
consists of purchasing power parity adjusted real wage
rates for unskilled labo r recorded from 1830 - 1988. The
data is for the following 15 countries3: Argentina, Aus-
tralia, Belgium, Canada, Denmark, France, Great Britain,
Germany, Ireland, Italy, Netherlands, Norway, Spain,
Sweden and USA.
The evidence presented by Williamson suggests that
there have been four distinct global labor market ‘regi-
mes’ since 1830. In this paper, we adopt Williamson’s
four regimes: (1) 1830-1869, (2) 1870-1913, (3) 1914-
1945, and (4) 1946-1988. The first is associated with
early industrialization in Belgium, Denmark, France,
Great Britain, Germany, Ireland, Italy, Netherlands, No r-
way, Spain and Sweden, settlement in Australia, Argen-
tina, Canada and the United States, international migra-
tions, high transport costs on commodity trade, and ba-
rriers to trade. The second covers the age of industria-
lization and free international migration, the Victorian
boom amidst an age of imperialism, and a general world
boom under free trade and the gold standard. The third
covers the two World Wars and the interwar period when
world commodity and factor markets break down. The
fourth is the po s t W orl d Wa r II period.
The evolution of the distribution of real wages for the
15 countries across the four time periods has been
investigated. Table 1 reports the descriptive of the four
phases (regi mes).
It can be observed that in general, real wages rose
sharply, especially in regime 4. At the same time, the
distribution of real wages became more heterogeneous.
Table 1 reports a lower mean wage (M = 58.28) as com-
pared with the reported mean wage of Phase 2 (M =
90.95), Phase 3 (M = 124.38), and Phase 4 (M = 280 .49) .
However, although Phase 1 displays a lower mean, it dis-
plays less fluctuations, suggesting a relatively stable
labor market. In what follows, we test the reliance of
these developments on five parameters: the initial mean
wage 0, the initial standard deviation 0
u
, the mean
wage at stationary equilibrium , the velocity of con-
vergence to stationary equilibrium
u
, and the diffusion
parameter
.
3.1. Estimation
The model has been fitted to the log real wage distri-
bution of the four populations as a function of time,
using the non-linear least-squares estimation using a
two-step procedure. First, the values for 0, and uu
were estimated using the first moment of the distribution.
In the second step, the values for
and 0
were
computed using the second moment. Tables 2-5 report
estimates for the five model parameters, along with the
standard errors and t-values for the four phases respec-
tively.
Table 1. Descriptive of the four Phases.
N MinimumMaximum Mean Std. Deviation
Phase 14048.38 67.58 58.28 4.02
Phase 24464.93 126.67 90.95 15.96
Phase 32591.93 141.47 124.38 15.99
Phase 443144.23 417.53 280.49 97.60
Table 2. Phase 1 Parameter estimates.
Parameter Value Std Error t-value
λ 1.24 1.02 0.02
u 1.27 0.03 3.43
u0 1.15 0.03 5.31
σ0 1.07 0.04 2.31
ε 0.57 0.05 4.53
2For an elaboration of this model see [17-21] and the Appendix.
3Williamson [1] reports data for 11 countries. We are grateful to Wil-
liamson for data on the remaining countries, which were collected and
received post-publication.
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