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Title: The role of Social Networks in the projection of international migration flows: an Agent-Based approach


1
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

2
Contents
  • Motivation, goals
  • The context
  • Demography and migrations
  • Social Networks
  • The Multi-agent System
  • The Model
  • Variables
  • Gravitational Model
  • Simulation/Parameters
  • Results
  • Final Remarks

3
Demography and Migrations
  • Population estimates (Comp. Method)
  • Pt population at time t
  • Pt-1 population at time t-1
  • N number of births between Pt-1 and Pt
  • M number of deaths between Pt-1 and Pt
  • I number of imigrants between Pt-1 and Pt
  • E number of emigrants between Pt-1 and Pt

4
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))

5
Interaction between social mechanisms
Interaction between social mechanisms - Billari
e Prskawetzy (2005)
6
Main goals
  • Verify the effect of the structure of social
    networks on the migration flows
  • Social network analysis
  • Density
  • Degree centralization
  • Input
  • Output
  • General

7
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

8
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
    IndegreeOutdegree)
  • 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

9
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

10
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 8
p Number of individuals in the household 1, 2, , 15
s Number of individuals in the agents social network 2, , 20
w Labour status (working situation working/not working) 0,1
11
Gravitational Model, Ma
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

12
Gravitational Model
fEUA - per capita income of USA
h Geographical distance between two countries
fO - per capita income of the country of origin
U(0,50,9) ? From the Country of origin to USA
U(0,10,4) ? From USA to country of origin
13
Gravitational Model
Fm Force of migration
ma Agente mass
MN - Mass of social network
d Average distance between agents
G 1
14
Gravitational Model
da average distance between agents
ma Agents mass
MN mass of the social network
15
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)

16
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

17
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

18
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 (ML1.5)
  • Migration level is Low, number of agents is high
  • Simulation II (ML4.0)
  • Migration level is medium, low number of agents
  • Simulation IIII (ML5.0)
  • Migration level is high, low number de agentes

19
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
Mexico HH Income (r) I -1,362 0,1731
Hh Income (r) II -1,244 0,2135
Wilcoxon test, plt0,05
20
Density and Centrality degree
21
Density
Mexico Simulation I
Ano 2008, n 2476
Ano 2000, n 404
22
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

23
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

24
Some references
  • Billari, F. C., F. Ongaro, et al. (2003a),
    "Introduction Agent-Based 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 Agent-Based 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.

25
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

26
IMPORTÂNCIA DAS REDES SOCIAIS NOS FLUXOS
MIGRATÓRIOSAplicação 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

27
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))

28
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.

29
Algorithm
  • Age(y) if the age in year t (yt)
  • yt  94 then yt1  yt 1
  • yt  95 then the agent die.
  • Educational level (e) depends on variable age
  • If et  1 and 1  yt1  14, then et  et1  1
  • If et  1 e 15  yt1  18, então et1  U(1,
    min(2, maxe))
  • If et  1 e 19  yt1  94, então et1  U(1,
    min(2, maxe))
  • If et  2 e 19  yt1  94, então et1  U(2,
    min(3, maxe))
  • Income (r) varies in 28, and depends on the
    inflation rate of USA (equal to 3 ). In t1, the
    value of r is given by rt1rtU(-1,1)x0,03.
  • Labour status (w) depends on variable age
  • If 1  yt1  15 then w t1  0
  • If 16  yt1  94 then w t1  Bernoulli(k),
    being k the fraction w of working people in USA.
  • Number of individuals in the household (p)
  • If pt  1, then p t1  pt  U(0,1)
  • If pt  15, then p t1  pt  U(-1, 0)
  • If 2  pt1  14 then p t1  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.

30
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 ? e1 e 15 y 18 ? e1 ou e2
  • Atribuição de e
  • Distribuição aleatória uniforme , U(mine,maxe)
  • Rendimento do agregado familiar (r)
  • r 2 8
  • Atribuição do rendimento
  • Distribuição normal, N(r,?r)

31
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 (ygt15)
  • Atribuição do rendimento
  • Distribuição Bernoulli(k),
  • kfracção 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 p10, mas no máximo s20
  • Atribuição de s
  • Distribuição aleatória uniforme , U(p,maxs)

32
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(N-1)/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

33
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

34
Estabilidade do modelo
Variabilidade das médias das 15 simulações
Alemães - Simulação I
Variável 2000 2001 2002 2003 2004 2005 2006 2007 2008
Agregado familiar 2,400,03 (1,4) 2,730,07 (2,5) 2,900,06 (2,2) 3,010,06 (1,9) 3,110,06 (1,8) 3,170,04 (1,3) 3,230,05 (1,6) 3,270,05 (1,6) 3,300,05 (1,5)
Idade 43,80,7 (1,6) 39,41,1 (2,7) 38,00,8 (2,0) 37,40,8 (2,2) 37,10,6 (1,7) 37,10,6 (1,5) 37,20,6 (1,7) 37,60,6 (1,6) 38,00,6 (1,5)
Rede social 7,850,21 (2,7) 7,310,14 (1,9) 7,390,13 (1,8) 7,570,15 (2,0) 7,790,14 (1,8) 8,020,14 (1,7) 8,220,15 (1,8) 8,390,16 (1,9) 8,530,15 (1,8)
Rendimento 65,51,5 (2,2) 61,91,6 (2,5) 61,41,7 (2,8) 61,11,7 (2,8) 61,01,7 (2,7) 61,11,8 (2,9) 61,51,8 (2,9) 61,41,7 (2,7) 61,41,5 (2,4)
Fracção de trabalhadores 0,4760,023 (4,9) 0,5520,017 (3,1) 0,5040,022 (4,4) 0,4730,016 (3,3) 0,4650,017 (3,7) 0,4600,011 (2,3) 0,4550,010 (2,3) 0,4570,014 (3,1) 0,4600,010 (2,2)
Simulação II lt 10 Simulação III
Simulação I lt 5
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