3. 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
4. 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
5. 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
11. 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.
13. 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
15. …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
16. 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
17. 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
18. 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
20. …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