1 NETWORK INDICATORS: A NEW GENERATION OF MEASURES? EXPLORATORY REVIEW AND ILLUSTRATION BASED ON ESS DATA Elsa Fontainha ISEG Technical University of Lisbon.

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NETWORK INDICATORS: A NEW GENERATION OF MEASURES?

EXPLORATORY REVIEW AND ILLUSTRATION BASED ON ESS DATA

Elsa Fontainha

ISEG Technical University of Lisbone-mail: [email protected]

Edviges CoelhoStatistics Portugal (INE)

e-mail: [email protected]

Brussels

18-20 February 2009

NTTS 2009

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Aim of Research

To illustrate how to construct indicators of cohesion and convergence across Europe and to identify the roles (e.g. centrality, reciprocity) performed by several entities (countries, regions, institutions, individuals, enterprises, etc.) in European networks mapped by demographic, economic, financial and communication flows or links.

To attain that goal we adopted network analysis, derived from graph theory, to explore data from the European Statistical System (ESS) The proposed indicators can be produced on a regular

basis and complement the current indicators.

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Attribute and Relational Data

Attribute Data

Gross Domestic Product (GDP)

Population growth Student/Teacher ratio

...

Relational Data

Foreign Direct Investment

Immigration Emigration Tourism flows ...

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How to study relational data?

Matrix format Eurostat

• geo/partner• input-ouput analysis

From matrix format to network graph…A

E

D

C

A B C D E

A - 0 1 0 0

B 0 - 0 0 0

C 0 0 - 1 0

D 0 1 0 - 0

E 0 0 0 0 -

B

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From matrix format to network graph…

AE

D

C

A B C D E

A - 0 1 0 0

B 0 - 0 0 0

C 0 0 - 1 0

D 0 1 0 - 0

E 0 0 0 0 -

Links are directed (represented by arrrows)E is an isolated node (ex: country)There are no reflexive links

From adjacency matrix to network graph…

B

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Network AnalysisLinks and Nodes

Network analysis Describes the structure of relations

(represented by links, oriented or not) between agents (represented by nodes/egos)

e.g. Nodes Countries

Links Immigration flows among countries

Applies quantitative techniques to compute measures which improve the knowledge of

the characteristics of the whole network (e.g. EU) the position of nodes (e.g. countries) in the network

structure.

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Network and Node Indicators (computed from flow matrices)

Indicators

Network

Size Centrality Density Cohesion Reciprocity …

Indicators

Node/Ego

In-degree Out-degree Power Isolated …

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Computing Network Indicators from ESS:some illustrations

Data: ESS

Immigration by country of previous residence (migr_immiprv)

Immigration by citizenship (migr_immictz) EU direct investment flows, breakdown by partner

country (bop_fdi_flows) Socrates-Erasmus student and teacher mobilityProblems encountered

Data • (e.g. missing information for some countries

and/or years ( -> imputation ) Methodology: limits imposed by methodology

• (e.g. n x n matrix)

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Methodology: main steps(for each indicator)

1. Selection, filtering and weighting original data (ESS)

2. Construction of the adjacency (association) matrix

3. Construction of network graphs from matrix( all links and only strongest links)

4. Computation of indicators (for nodes and network) from adjacency matrix

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intra-EU Immigration 2002 251 ties, 17 nodes

ATCY

CZ

DE

DK

ES

FI

IT

LT

LV

NL

PL

PT

SE

SI

SK

UK

Blue arrows = reciprocal linksRed arrows=Non reciprocal

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intra-EU Immigration 2006 267 ties, 17 nodes

AT

CY

CZ

DE

DK

ES

FI

IT

LT

LV

NL

PL

PT

SE

SI

SK

UK

Blue arrows = reciprocal linksRed arrows=Non reciprocal

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intra-EU Immigration 200227 ties, 17 nodes (only strong links)

AT

CY

CZ

DE

DK

ES

FI

IT

LT

LV

NL

PL

PT

SE

SI

SK

UK

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intra-EU Immigration 200636 ties, 17 nodes (only strong links)

AT

CY

CZ

DE

DK

ES

FI

IT

LT

LV

NL

PL

PT

SE

SI

SK

UK

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Immigration(residence)

Immigration (ctz)

FD Invest.

Students Teachers

N countries = = = = =

Network size = = = = =

N of Ties

Network Centr. (Outdegree) %

Network Centr.(Indegree) %

Outdegree Mean (StdDev)

Indegree Mean (StdDev)

Network Density

Indicators – NetworksImmigration, Foreign Investment, Teachers and

Students (Year t - 2006)

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Immigration(origin residence)

Foreign D Investment

2006 2002 2006 2002

Size in 16(except CY,

SI)

16(except CY, LT, LV, PL, PT, SI, SK)

NL(10)PT (7)SE (7)

BE (11)SE (11)

Size out 16(except FI, LT, LV, SI)

16AT, DE, ES, NL, PL, SE,

UK

FR (14)NL (9)

AT (13)FR (13)IT (13)NL (13)UK (13)

In-degree DE (1578)UK(1082)ES(577)

DE (1153)UK (298)ES (280)

BE (60)NL (47)

FI (49)NL (46)

Out - degree PL (701)SK(613)

SK (551)PL (310)

FR (48)ES (42)

UK (47)SE (37)

Indicators – Node (Countries)Immigration and Foreign Investment

2002-2006

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Student mobility

2006/7 2004/5

Size in 26BE ES FR IT DE EE

26BE DE ES FR IT PT FI SE UK LV LT AT PL FI25BE CZ DE EE ES FR IT LV LT AT PL FI

Size out 25BE CZ DE EE ES FR IT LV LT AT PL FI

25BE DE ES FR IT NL AT PT FI UK

In-degree ES (26992)FR (20140)DE (16683)

ES (25217)FR (20200)DE (16688)

Out - degree DE (2715)FR (21213)ES (20568)

DE (2715)FR (21213)ES (20568)

Indicators – Node (Countries)Student mobility (Socrates-Erasmus)

2004/5 – 2006/7

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Conclusions and future research

1. It is possible to compute network indicators from the ESS data. They are useful for the understanding of the relations among countries and the network diffusion mechanisms.

2. There is, in general, an increase in the density of the network (EU countries) across time regardless of the phenomena under analysis (migrations, capital flows, etc.). Cohesion is increasing. EU recent enlargements are reflected in that increase.

3. The role of each country inside the network remains stable across time in some cases but changes in others. For example, with regard to immigration, Spain has increased its position as a destination country since 1998.

4. The results suggest that geography and language still matter for several EU networks of people, goods, services, capital and knowledge. Explanation for this is beyond this paper’s goals but could contribute to a greater understanding of EU networks.