The role of Social Networks in the
projection of international migration
flows: an Agent-Based approach
Carla Anjos (University of Aveiro)
Pedro Campos (Statistics Portugal and
University of Porto)
Work Session on Demographic Projections - April, 29, 2010, Lisbon
Contents


Motivation, goals
The context
◦ Demography and migrations
◦ Social Networks
◦ The Multi-agent System

The Model
◦ Variables
◦ Gravitational Model
◦ Simulation/Parameters


Results
Final Remarks
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2
Demography and Migrations

Population estimates (Comp. Method)
Pt  Pt 1  N  M  I  E






Pt
Pt-1
N
M
I
E
= population at time t
= population at time t-1
= number of births between Pt-1 and Pt
= number of deaths between Pt-1 and Pt
= number of imigrants between Pt-1 and Pt
= number of emigrants between Pt-1 and Pt
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Motivation

Population Projections
◦ Need to elaborate social policies

Importance of studies in migration flows
◦ More accurate demographic forecasts
◦ Lack of information of migration flows

“New” approaches based on Agent-Based
Computational Demography (ABCD)
◦ bottom-up approach
(Billari et al. (2003a); Billari and Prskawetz (2005))
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Interaction between social
mechanisms
Situacional
Mechanism
Macro
Level
Transformational Mechanism
Micro Level
Mechanism of formation
Interaction between social mechanisms - Billari e Prskawetzy (2005)
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Main goals

Verify the effect of the structure of social
networks on the migration flows
◦ Social network analysis
 Density
 Degree centralization
 Input
 Output
 General
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Social Networks
Relationships and individuals
 Agents or actors – “vertices”
◦ Graph theory
◦ Organized within a society
 Well defined structure (or not?)
◦ A set of units
 Social
 Economic
 Cultural

Links between individuals
◦ Oriented – “arcs”
 Directed transmission of something (goods,
services,information).
◦ Non oriented– “links”
 Undirected links between pairs of agents
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Indicators of Social Networks

Agents
◦ Degree – Number of adjacent agents
 Non oriented networks  Total number of links
 Oriented networks:
 Indegree – number of links received that an agent “receives”
 Outdegree – number of links received that depart from an agent
 General – number of adjacent agents (total Indegree+Outdegree)

Networks
◦ Density
 Proportion between the number of existent links and the number
of possible links among all the agents
 More links  More cohesion Estrutura  Higher denisy
◦ Degree centralization
 Evaluates the structure of the communication in the network
 More variation in agents centrality  More centralized networks
 Indegree, Outdegree, General
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Multi-Agent Systems

Agent
◦ Entity that lives in a certain environment, having the
capacity to interact with other agents

Characteristics:
◦ Action and interaction
 Agents interact with other agents and with the environment
◦ Communication
◦ Individual goals and autonomy
 Agents are oriented towards specific goals
◦ (Limits of) Perception
 “Limited Racionality” – Limited computational resources
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Our study: the Variables
variable
Description
Domain
y
Age of the agent
{1, …, 95}
e
Educational level of the agent
{1, 2, 3}
r
Income of the housheold ($/1000)
[2; +∞[
p
Number of individuals in the household
{1, 2, …, 15}
s
Number of individuals in the agents’ social network
Labour status (working situation: working/not
working)
{2, …, 20}
w
Anjos & Campos, 2010
{0,1}
10
Gravitational Model, Ma
M a  CM  Fm  PM 
Ma= propensity of an agent to migrate
CM – Migration cost
Fm –Force of migration
PM - Propensity to migrate

Migration Level (ML)
◦ If ML is greater than the value Ma, then the agent remains in the country of origin. Otherwise,
the agent will migrate or stay in U.S. We assumed that three different levels of ML may occur
(low, medium and high). These values are defined as 1,5, 4,0 and 5,0 respectively
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Gravitational Model
M a  CM  Fm  PM 
f EUA  f O
PM 
h 100
fEUA - per capita income of USA
h – Geographical distance between two
countries
fO - per capita income of the country of origin
CM
U(0,5;0,9)  From the Country of origin to USA
U(0,1;0,4)  From USA to country of origin
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Gravitational Model
M a  CM  Fm  PM 
M N ma
Fm  G
2
d
Fm – Force of migration
ma – Agente mass
MN - Mass of social network
d – Average distance between
agents
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M N ma
Fm  G
d2
Gravitational Model
da – average distance
between agents
ma – Agent’s mass
log(r )  p
ma 
w
 y / 10
da 
d a ,i  ...  d a , s
s
MN – mass of the social network
log(rN )  mediana p N 
MN 
 wN
 y N / 10
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The data
IPUMS (Integrated Public Use Microdata
Series, Ruggles et al, (2009))
 The extracted database contains data of
migration flows to the United States
between 2001 and 2008.
 Four communities in the U.S. were
considered with origin in four different
countries (Portugal, Mexico, China and
Germany)

Anjos & Campos, 2010
Parameters of the simulation

Countries
◦
◦
◦
◦

Germany
China
Mexico
Portugal
Three different continents
◦ Different terrritorial and social dynamics


Different development stages
Different migration flows
◦ migrantes have different characteristics in the USA
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Parameters of the simulation

Initial considerations
◦ The majority of the individuals migrate to the
communities created by other individuals of the
same nationality.
◦ Simulated population is proportional to the
population in database IPUMS
◦ Individuals are created within the scope of three
clusters that were found in the original population
◦ Simulação: 2000 to 2008
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Simulation

2000
◦ Agents are created (respecting the clusters found in IPUMS)

2001 to 2008
◦ Ageing of agents in USA
 Agents decide their situation as migrants
◦ Creation of potential new migrants according to original migrants
 Agents decide to migrate to USA or to stay in their country of origin

Three different scenarios (with 15 runs in each)
◦ Simulation I (ML=1.5)
 Migration level is Low, number of agents is high
◦ Simulation II (ML=4.0)
 Migration level is medium, low number of agents
◦ Simulation IIII (ML=5.0)
 Migration level is high, low number de agentes
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Validation

Stability of the model according to the variability of the means
in the 15 runs

Simulated data are similar to reality for the following variables:
Country
Variable
Simularion
Z*
p-value
Country of origin
Variable
Scenario
Z*
p-value
Germany
Working situation (w)
I
-1,718
0,0858
China
HH Income (r)
I
-1,362
0,1731
Working situation (w)
I
-0,889
0,3743
HH Income (r)
I
-1,362
0,1731
Hh Income (r)
II
-1,244
0,2135
Mexico
* Wilcoxon test, p<0,05
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Density and Centrality degree
Porto, 15 de Março de 2010
Density
Mexico – Simulation I
Porto, 15 de Março de 2010
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Final Remarks

Trends between 2000 and 2008
◦ Variables
 Number of individuals in household and age have different trens when
comparing simulated to real data
 Income and working condition are similar for some scenarios
◦ Density
 The greater the diameter of the networks, tjhe lower the density
 Links disappear
◦ Centralization
 Indegree – the importance of the arrival of information to the agents in the
network is high in the first periods, and stabilizes in the following.
 Agents in USA are important to the arrival of new agents
 Outdegree – the importance of the information that leaves from every
agent decreases during the period
 Os agentes nos EUA tendem a perder a sua ligação aos outros agentes da rede
 General - has the same trend as indegree
 In general, the communicaton in the network is higher in the first years and stabilizes
subsequently
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Limitations and further work

The model is not able to preview the trend
of evolution of the main variables in the
simulation
◦ It should be important to introduce a calibration
procedure in a intermediate period (2004?)

The structure of the networks is important
has some influence in the flow of migrants
Anjos & Campos, 2010
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Some references
Billari, F. C., F. Ongaro, et al. (2003a), "Introduction: AgentBased Computational Demography", in Agent-Based
Computational Demography: Using Simulation to Improve Our
Understanding of Demographic Behaviour, F. C. Billari e A.
Prskawetz (editores), Contributions to Economics, pp.1-15,
Heidelberg: Physica- Verlag.
 Billari, F. C., A. Prskawetzy (2005), "Studying Population
Dynamics from the Bottom- Up: The Crucial Role of AgentBased Computational Demography", International Union for
the Scientific Study of Population XXV International Population
Conference, Tours, France.
 Carrilho, M. J. (2005), "Metodologias De Cálculo Das
Projecções Demográficas: Aplicação Em Portugal", Revista de
Estudos Demográficos, Vol. 37, pp. 5-24.

Anjos & Campos, 2010
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The role of Social Networks in the
projection of international migration
flows: an Agent-Based approach
Carla Anjos (University of Aveiro)
Pedro Campos (Statistics Portugal
and University of Porto)
Work Session on Demographic Projections - April,
29, 2010, Lisbon
Anjos & Campos, 2010
IMPORTÂNCIA DAS REDES SOCIAIS
NOS FLUXOS MIGRATÓRIOS:
Aplicação de Sistemas Multi-agente
Carla Anjos
Mestrado em Análise de Dados e Sistemas de Apoio à Decisão
Orientador: Doutor Pedro Campos
Faculdade de Economia da Universidade do Porto
Porto, 15 de Março de 2010
Migração

“Deslocação de uma pessoa através de um
determinado limite espacial, com intenção
de mudar de residência de forma
temporária ou permanente. A migração
subdivide-se em migração internacional
(migração entre países) e migração interna
(migração no interior de um país).”
Instituto Nacional de Estatística (INE, (2003a))
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Redes sociais – Medidas Agentes

Grau (degree)
◦ Redes não orientada
 É igual ao número de vértices adjacentes
◦ Redes orientadas:
 Indegree - ligações que são recebidas pelo vértice
 Outdegree - as ligações que saem do vértice
 Geral - número de vértices adjacentes

Centralidade
◦ Proporção entre o número de ligações do agentes e o número
total de ligações.
 Centralidade do grau (degree centrality)
 Número de conexões directas de cada agente num grafo
 Centralidade de proximidade (closeness centrality)
 Medida do comprimento do caminho mais curto que liga dois agentes
 Centralidade de intermediariedade (betweenness centrality)
 Proporção de todos os caminhos geodésicos entre um par de vértices que
incluem um determinado vértice, e o número total possível.
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Algorithm
◦
Age(y) – if the age in year t (yt)


◦
Educational level (e) – depends on variable age:




◦
If et = 1 and 1 ≤ yt+1 ≤ 14, then et = et+1 = 1;
If et = 1 e 15 ≤ yt+1 ≤ 18, então et+1 = U(1, min(2, maxe));
If et = 1 e 19 ≤ yt+1 ≤ 94, então et+1 = U(1, min(2, maxe))
If et = 2 e 19 ≤ yt+1 ≤ 94, então et+1 = U(2, min(3, maxe));
Income (r) varies in [2;+∞[, and depends on the inflation rate of USA
(equal to 3 %). In t+1, the value of r is given by: rt+1=rt+[U(-1,1)x0,03].
Labour status (w) depends on variable age:
◦


◦
If 1 ≤ yt+1 ≤ 15 then w t+1 = 0;
If 16 ≤ yt+1 ≤ 94 then w t+1 = Bernoulli(k), being k the fraction w of working
people in USA.
Number of individuals in the household (p):



◦
yt ≤ 94 then yt+1 = yt +1;
yt = 95 then the agent die.
If pt = 1, then p t+1 = pt + U(0,1);
If pt = 15, then p t+1 = pt + U(-1, 0);
If 2 ≤ pt+1 ≤ 14 then p t+1 = pt + U(-1,1);
The Number of individuals in the agents’ social network (s) varies
according to the value of MN in the previous year.
Anjos & Campos, 2010
Parâmetros da simulação
Idade (y)
 1 ≤ y ≤ 95
 Atribuição de y
◦ Distribuição normal, N(y,y)
Educação (e)
 Valor possível de e
◦ 1 - Menos de 9 anos de frequência escolar
◦ 2 - Entre 9 e 12 anos de frequência escolar
◦ 3 - Mais de 12 anos de frequência escolar

Restrições
◦ y ≤ 14  e=1 e 15 ≤ y ≤ 18  e=1 ou e=2

Atribuição de e
◦ Distribuição aleatória uniforme , U(mine,maxe)
Rendimento do agregado familiar (r)
 r = [2; +∞[
 Atribuição do rendimento
◦ Distribuição normal, N(r,r)
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Parâmetros da simulação
Condição perante o trabalho (w)
 Valor possível de w
◦ w = 0, se o agente não está a trabalhar
◦ w = 1, se o agente está empregado (y>15)

Atribuição do rendimento
◦ Distribuição Bernoulli(k),
◦ k=fracção de indivíduos a trabalhar nos
EUA
Número de pessoas do agregado familiar (p)
 1 ≤ p ≤ 15
 Atribuição de p
◦ Distribuição aleatória uniforme , U(1º quartilp,3ºquartilp)
Número de indivíduos da rede social do agente (s)
 2 ≤ s ≤ p+10, mas no máximo s=20
 Atribuição de s
◦ Distribuição aleatória uniforme , U(p,maxs)
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Redes sociais – Medidas Redes

Clustering (transitivity)
◦ Probabilidade de dois vizinhos de um dado vértice estarem ligados

Densidade
◦ Proporção entre o número de relações existentes e o número de relações
possíveis.
 Orientada o número de relações possíveis é igual ao número de vértices N
multiplicado por N-1.
 Rede não for orientada, o número de relações possíveis é dado por N(N1)/2

Comprimento médio de um caminho
◦ Número médio de ligações no caminho mais curto entre qualquer dois
pares de vértices

Diâmetro
◦ Número máximo de ligações no caminho mais curto entre qualquer dois
vértices

Grau de centralização (degree centralization)
◦ Variação centralidade que existe na rede
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Recursos utilizados

Base de dados
◦ IPUMS – recolha de dados reais de migrações

Software
◦ SPSS – tratamento de dados
◦ Repast – execução da simulação do modelo
◦ Pajek – análise das redes sociais
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Estabilidade do modelo
Variabilidade das médias das 15 simulações
Alemães - Simulação I
Variável
2000
2001
2002
2003
2004
2005
2006
2007
2008
Agregado
familiar
2,40±0,03
(1,4%)
2,73±0,07
(2,5%)
2,90±0,06
(2,2%)
3,01±0,06
(1,9%)
3,11±0,06
(1,8%)
3,17±0,04
(1,3%)
3,23±0,05
(1,6%)
3,27±0,05
(1,6%)
3,30±0,05
(1,5%)
Idade
43,8±0,7
(1,6%)
39,4±1,1
(2,7%)
38,0±0,8
(2,0%)
37,4±0,8
(2,2%)
37,1±0,6
(1,7%)
37,1±0,6
(1,5%)
37,2±0,6
(1,7%)
37,6±0,6
(1,6%)
38,0±0,6
(1,5%)
Rede social
7,85±0,21
(2,7%)
7,31±0,14
(1,9%)
7,39±0,13
(1,8%)
7,57±0,15
(2,0%)
7,79±0,14
(1,8%)
8,02±0,14
(1,7%)
8,22±0,15
(1,8%)
8,39±0,16
(1,9%)
8,53±0,15
(1,8%)
Rendimento
65,5±1,5
(2,2%)
61,9±1,6
(2,5%)
61,4±1,7
(2,8%)
61,1±1,7
(2,8%)
61,0±1,7
(2,7%)
61,1±1,8
(2,9%)
61,5±1,8
(2,9%)
61,4±1,7
(2,7%)
61,4±1,5
(2,4%)
Fracção de 0,476±0,023 0,552±0,017 0,504±0,022 0,473±0,016 0,465±0,017 0,460±0,011 0,455±0,010 0,457±0,014 0,460±0,010
(4,9%)
(3,1%)
(4,4%)
(3,3%)
(3,7%)
(2,3%)
(2,3%)
(3,1%)
(2,2%)
trabalhadores
Porto, 15 de Março de 2010
34