the role of social networks in the projection of international migration flows: an agent-based...

The role of Social Networks in the The role of Social Networks in the projection of international migration projection of international migration

flows: an Agent-Based approach 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

ContentsContentsMotivation, goalsThe context◦ Demography and migrations◦ Social Networks◦ The Multi-agent System

The Model◦ Variables◦Gravitational Model◦ Simulation/Parameters

ResultsFinal Remarks

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Demography and MigrationsDemography and MigrationsPopulation 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

3

EIMNPP tt 1


MotivationMotivationPopulation 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

5

Interaction between social mechanisms - Billari e Prskawetzy (2005)

SituacionalMechanism

Mechanism of formation

Transformational Mechanism

Macro Level

Micro Level


Main goalsMain goalsVerify 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 NetworksSocial NetworksRelationships and individualsAgents 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 NetworksIndicators of Social NetworksAgents

◦ 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 SystemsMulti-Agent SystemsAgent◦ 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 VariablesOur 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 {2, …, 20}

wLabour status (working situation: working/not

working){0,1}

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Gravitational Model, MaGravitational Model, Ma

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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MmMa PFCM

Fm –Force of migration

CM – Migration cost

PM - Propensity to migrate

Ma= propensity of an agent to migrate


Gravitational ModelGravitational Model

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h – Geographical distance between two countries

fEUA - per capita income of USA

100h

ffP OEUAM

fO - per capita income of the country of origin

MmMa PFCM

MC

U(0,5;0,9) From the Country of origin to USA

U(0,1;0,4) From USA to country of origin



2d

mMGF aN

m

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MN - Mass of social network

ma – Agente mass

d – Average distance between agents

Fm – Force of migration

MmMa PFCM



wy

prma

10/

)log(

14

NN

NNN w

y

pmedianarM

10/

)log(

ma – Agent’s mass

MN – mass of the social network

s

ddd saiaa

,, ...

da – average distance between agents

2d

mMGF aN

m


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)


Parameters of the simulationParameters of the simulationCountries◦ Germany◦ China◦ Mexico◦ Portugal

Three different continents◦ Different terrritorial and social dynamics

Different development stagesDifferent migration flows◦ migrantes have different characteristics in the USA

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Parameters of the simulationParameters 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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SimulationSimulation2000

◦ 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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ValidationValidation 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:

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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, p<0,05

Porto, 15 de Março de 2010

Density and Centrality degree

Porto, 15 de Março de 2010 21

DensityDensityMexico – Simulation I


Final RemarksFinal 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 workLimitations and further workThe 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

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Some referencesSome 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.

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The role of Social Networks in the The role of Social Networks in the projection of international migration projection of international migration

flows: an Agent-Based approach 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

IMPORTÂNCIA DAS REDES SOCIAIS IMPORTÂNCIA DAS REDES SOCIAIS NOS FLUXOS MIGRATÓRIOS:NOS FLUXOS MIGRATÓRIOS:

Aplicação de Sistemas Multi-agenteAplicação de Sistemas Multi-agente

Carla Anjos

Mestrado em Análise de Dados e Sistemas de Apoio à Decisão

Orientador: Doutor Pedro CamposFaculdade de Economia da Universidade do Porto

Porto, 15 de Março de 2010


MigraçãoMigração

“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 AgentesRedes sociais – Medidas AgentesGrau (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)

yt ≤ 94 then yt+1 = yt +1; yt = 95 then the agent die.

◦ 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):

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.


Parâmetros da simulaçãoParâmetros da simulaçãoIdade (y) 1 ≤ y ≤ 95 Atribuição de y

◦ Distribuição normal, N(y,y)

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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)


Parâmetros da simulaçãoParâmetros da simulaçãoCondição 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

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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)


Redes sociais – Medidas RedesRedes 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

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Recursos utilizadosRecursos 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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Porto, 15 de Março de 2010 34

Estabilidade do modeloEstabilidade do modelo

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 trabalhadores

0,476±0,023 (4,9%)

0,552±0,017 (3,1%)

0,504±0,022 (4,4%)

0,473±0,016 (3,3%)

0,465±0,017 (3,7%)

0,460±0,011 (2,3%)

0,455±0,010 (2,3%)

0,457±0,014 (3,1%)

0,460±0,010 (2,2%)

Alemães - Simulação I

Variabilidade das médias das 15 simulações

the role of social networks in the projection of international migration flows: an agent-based...

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