T-MDS2

Theophilos Papadimitriou
Periklis Gogas
Democritus University of Thrace
Department of Economics
Komotini, Greece
T-MDS:
a new methodology for monitoring Economics networks

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Nodes
Edges
Graph G=(N,E)
N is the set of nodes
E is the set of edges

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7Economic
Entities
Similarity
Graph G=(N,E)
N is the set of nodes
E is the set of edges

Representation Goal:
a) Identify a reduced version of the initial network
b) retaining the necessary information
c) to control and analyze the network.
Current Solution:
Minimum Spanning Tree + Heuristics

Th. Papadimitriou, P. Gogas, B.M. Tabak, "Complex
Networks and Banking System Supervision", Physica
A, Vol. 392, pp. 4429-4434, 2013.

Dominating Set:
A subset of nodes in which every node is
a) a member of the Dominating Set (dominant node)
b) adjacent to a dominant node

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Dom. Node
Dom. Node
Dom. Node
Adjacent
Adjacent
Adjacent
Adjacent

Minimum Dominating Set:
The Dominating Set with the minimum cardinality
Application:
Ad Hoc Communication Networks

𝑥𝑖 =
1 if node 𝑖 ∈ DS
0 if node 𝑖 ∉ DS
𝑖 = 1,2, … , 𝑛Membership variable
min
𝐱
𝑓(𝐱) =
𝑖=1
𝑛
𝑥𝑖 subject to
𝑥𝑖 +
𝑗∈B 𝑖
𝑥𝑗 ≥ 1 𝑖 = 1,2, … , 𝑛
Bi neighborhood of node i
Minimum
Cardinality
Case 1: xi = 1, i is a Dominant Node
Case 2: xi = 0, some j in the Neighborhood is a Dominant Node
In both cases the left hand side is ≥ 1

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𝑥𝑖 +
𝑗∈B 𝑖
𝑥𝑗 ≥ 1 𝑖 = 1,2, … , 𝑛

• Not all edges are important
• Can be misleading
Solution: Threshold
Remove all uninformative edges

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0.34
0.2
0.8
0.44
0.35
0.88
0.9
0.91
0.75
Isolated Node
Isolated Node

T-MDS is a two step methodology:
1. Threshold imposition on the network
2. Identification of the MDS
In order to
1. Keep just the essential edges
2. Find the most representative nodes

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Edges
T-MDSNodes
Threshold Level
T-MDS Edges

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0.88
0.9
0.91
0.75

min
𝐱
𝑓(𝐱) =
𝑖=1
𝑛
𝑤𝑖 𝑥𝑖
𝑥𝑖 +
𝑗∈B 𝑖
𝑥𝑗 ≥ 1 𝑖 = 1,2, … , 𝑛
Node weight
Node importance
Disadvantage for Temporal Analysis

2 3Binary AND
Threshold 1
Threshold 2
Threshold 3
Variable 1
Variable 2
Variable 3

2 3
Threshold 1
Variable 1
Variable 2
Variable 3
z-scores

Goal: Monitoring a banking system through a small subset of banks
Nodes: Banking Institutions
Edges: Correlation
Case 1
Selected Variable: Interbank Loans
Dataset: 200 largest American banks based on their Interbank Loans
Strategy 1 2 3 4 6
Threshold 0.4 0.5 0.6 0.75 0.8
Dominant Nodes 7 10 15 22 26
Isolated Nodes 0 2 4 14 21
T-MDS Nodes 7 12 19 36 47
Total Edges 1390 1047 730 351 268

Edges: Correlation
Case 2
Selected Variable: Assets & Interbank Liabilities
Dataset: 50 Brazilian Banks
Strategy 1 2 3
Threshold 0.6 0.7 0.8
Dominant Nodes 6 8 5
Isolated Nodes 8 10 25
T-MDS Nodes 14 18 30
Remaining Edges 209 131 51

Edges: Correlation
Case 3
Selected Variable: Tier 1 capital/ Total Assets & Loan loss allowance/ Total Assets
Dataset: 4030 American banks
Strategy 1
Threshold 0.8
Dominant Nodes 491
Isolated Nodes 589
T-MDS Nodes 1080

96% 95% 94% 92% 91%
Healthy Neighborhoods
97% 95% 94% 93% 92%
Bankrupt Neighborhoods
Healthy Bank Bankrupt Bank

Goal: Test the business cycle convergence of the European economies after the
implementation of a common currency
Case 1
Nodes: 22 EU Countries
Edges: Correlation
Selected Variable: GDP Growth
Dataset: 22 EU Countries, 1986-2011, annual frequency
1986-1998 1999-2011

Pre-euro network
(1986-1998)
Post-euro network
(1999-2011)

Period
Pre-euro
1986-1998
Post-euro
1999-2011
Network Edges 22 115
Network Density 0.095 0.498
Dominant nodes 4 3
Isolated Nodes 7 1
T-MDS 11 4
In the post-euro network (1999-2011):
The number of edges increases
Network density increases
T-MDS size reduces
Evidence of business
cycle convergence

Goal: Describe the inter-temporal patterns of income inequality in the U.S. for the
period 1916-2012
Case 3
Nodes: 48 States (excluding Hawai and Alaska due to data unavailability)
Edges: Correlation
Selected Variable: Top 1% Income Share
Dataset: 48 States, 1916-2012, annual frequency
1916-1929 1930-1944 1945-1979 1980-2012

1916-1929 1930-1944 1945-1979 1980-2012
T-MDS 22 28 15 3
Isolated states 14 22 10 0
Dominant
states
8 6 5 3

Goal: Examine international business co-movements over several periods of
economic globalization
Case 4
Nodes: 27 Countries
Edges: Correlation
Selected Variable: GDP per capita
Dataset: 27 Countries, 1875-2013, annual frequency
1875-1912 1913-1944 1945-1972 1973-2013

1875-1912 1913-1944 1945-1972 1973-2013
T-MDS size 24 10 14 9
Isolated nodes 22 6 8 5
Dominant nodes 2 4 6 4
Number of edges 3 41 28 56
Network Density 0.01 0.12 0.08 0.16
• Heterogeneous pattern of business cycle synchronization
o First period (Golden standard era) associated with the
lowest business cycle synchronization degree
o Second period (Great depression) brings about
convergence
o Third period (Bretton Woods) induces diverging patterns
o Last period of floating exchange rates associated with the
highest degree of business cycle synchronization

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NODEDEGREE
Series1 Series2 Series3 Series4

Goal1: Use the T-MDS methodology to identify the most representative UK CPI classes
Goal2: Construct a new measure of core inflation for the United Kingdom
Nodes: 85 Classes
Edges: Correlation
Selected Variable: Inflation rates
Dataset: 85 Classes, 2002:1-2014:6, monthly frequency
CPI
FOOD
Meat
Gamon
Turkey
Fish
Fresh fish
Alc.
Beverages
Wine
Beer
12 Categories 85
Classes
700
Components

T-MDS application:
• 14 dominant nodes (CPI classes)
• 3 isolated ones
Construction of a new index
using the 14 dominant nodes as
network representatives
T-MDS index as a core inflation
measure.
Criteria:
• Reduced volatility
• Unbiased CPI predictor
• Easy to comprehend by the public
• Requires no extra resources
T-MDS index fulfils the intuitive
criteria of an appropriate core
inflation measure
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CPI
T-MDS

This research has been co-financed by the
European Union (European Social Fund – ESF) and
Greek national funds through the Operational
Program "Education and Lifelong Learning" of the
National Strategic Reference Framework (NSRF) -
Research Funding Program: THALES. Investing in
knowledge society through the European Social
Fund.
Komotini, Greece

Thank you
For further information you can reach me in:
papadimi@ierd.duth.gr
Komotini, Greece

T-MDS2

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