The Evolution of the
International Trade
Network
Tim Kastelle
IBUS2302 – 5 June 2009

Question
• Globalisation has changed
everything, right?

A transformation, or a change in
degree?
Exports/GDP 1820-2001
0.200
0.180
0.160
0.140
0.120
0.100 Exports/GDP
0.080
0.060
0.040
0.020 Source: Maddison, 1997, 2001, 2003
0.000
1800 1820 1840 1860 1880 1900 1920 1940 1960 1980 2000 2020
Year

What is Network Analysis
• Analytical tool for measuring network structure
consisting of actors (people, firms, etc.) and the
connections between them (social, financial
exchange, technical collaboration, etc.)
• Draws from Social Network Analysis (sociology,
psychology) and Complex Network Analysis
(physics, economics)
• Theoretical justification in evolutionary
economics

Data Set
• IMF Trade data, every 10 years from
1938-98, and 2003 (8 sets)
• Calculate significant trade relations to
build adjacency matrix
• If there is a significant trade flow from
country A to country B, a 1 is recorded,
otherwise the value is 0

1938 Network

1968 Network

1998 Network

Convergence?

Or divergence?

Degree Distribution
• The degree of a node is the number of
edges that connect to it. An important
characteristic of most graphs is the mean
degree k, the average number of
connections per node. The degree
distribution of a graph is the measure of
degree frequencies, in other words, it is a
count of how many nodes have degree = k
for each possible value of k.

Degree = 9
Average degree = 254/256 = 1.0

The Degree of a Node Roughly
Correlates with GDP
1000
100
log Imports ($US billion)
10
1
0.1 1 10 100 1000
0.1
0.01
log In Degree
Consequently, the degree distributions of the network
should be able to tell us whether GDP is converging or not

Frequency
0
2
4
6
8
10
12
14
16
18
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
Degree (k)
In Degree Histogram
95
10
0
10
5
11
0
11
5
histogram…
12
0
12
5
13
0
13
5
14
0
14
5
The degree distribution
15
0
15
5
16
0
16
5

…is Converted to a Cumulative
Distribution Function
1938 In Degree Distribution
1
1 10 100
0.1
Cumulative Distribution
Cumulative Distribution
0.01
0.001
Log Degree

Expected Changes
2003 Random Graph Data
1
1 10 100 1000
0.1
Cumulative Distribution
Normal Distribution
x^-1
x^-0.5
0.01
Economic convergence will lead to a normal degree distribution,
while divergence will lead to a power law distribution
0.001
Log Degree

Actual Distributions
1
1 10 100 1000
Cumulative distribution - Pc(k)
0.1
1938
1948
1958
1968
1978
1988
1998
2003
0.01
0.001
Degree - k

Results
• All of the CDFs are best described by a log-
normal distribution with a power law tail
• The only change is that the curve has shifted to
the right as the size of the network has
increased over time
• This suggests that the reason that neither
convergence nor divergence has gained
overwhelming empirical support is that neither is
actually happening

However, it is
actually
a James Dean
network:
Calm on the
outside….

…but seething underneath the
surface
• Even though the overall network structure has
been stable, we know that the roles of individual
countries within the network have changed over
time
• For example, China, Singapore, South Korea
and Taiwan have become much more highly
connected, while countries such as Portugal and
Argentina have become less connected

Rank Clock Data – In Degree
Country 1938 1948 1958 1968 1978 1988 1998 2003
United States 1 1 2 3 2 1 1 1
United Kingdom 2 2 2 1 4 4 4 4
Germany 3 8 1 2 1 3 2 2
France 4 3 5 5 3 2 3 3
Netherlands 5 4 4 4 6 7 6 6
Belgium 6 6 7 8 8 8 8 10
Italy 7 5 6 6 5 5 5 5
Japan 8 21 8 7 7 6 9 9
Sweden 9 7 9 12 11 13 23 25
Argentina 10 17 23 34 47 59 61 96
Norway 11 18 21 17 28 28 38 41
South Africa 12 14 14 20 52 55 34 34
Poland 13 18 15 16 17 34 21 19
India 14 10 11 22 23 21 18 14

Rank Clock - International Trade Network 1938-2003
1938
100
90
80 1948
70
60
50
40
30
20
2003 1958
10
0
1998 1968
1988 1978

Rank Shift Dynamics 1938-2003
1938
100
90
80 1948
70 Singapore
60 United States
50 Argentina
40 Ireland
30 China - Mainland
2003 20 1958
10
0
1998 1968
1988 1978

Conclusions
• The overall structure is stable
• Changes at the country level reflect the
impact of policy – and these are quite
substantial