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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