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

Anjos & Campos, 2010 Demography and Migrations Population estimates (Comp. Method) P t = population at time t P t-1 = population at time t-1 N= number of births between P t-1 and P t M = number of deaths between P t-1 and P t I = number of imigrants between P t-1 and P t E = number of emigrants between P t-1 and P t 3

Anjos & Campos, 2010 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)) 4

Anjos & Campos, 2010 Interaction between social mechanisms 5 Interaction between social mechanisms - Billari e Prskawetzy (2005) Situacional Mechanism Mechanism of formation Transformational Mechanism Macro Level Micro Level

Anjos & Campos, 2010 Main goals Verify the effect of the structure of social networks on the migration flows Social network analysis Density Degree centralization Input Output General 6

Anjos & Campos, 2010 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 7

Anjos & Campos, 2010 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 8

Anjos & Campos, 2010 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 9

Anjos & Campos, 2010 Our study: the Variables variableDescriptionDomain 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} w Labour status (working situation: working/not working) {0,1} 10

Anjos & Campos, 2010 Gravitational 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 11 F m –Force of migration C M – Migration cost P M - Propensity to migrate Ma = propensity of an agent to migrate

Anjos & Campos, 2010 Gravitational Model 12 h – Geographical distance between two countries f EUA - per capita income of USA f O - per capita income of the country of origin U(0,5;0,9) From the Country of origin to USA U(0,1;0,4) From USA to country of origin

Anjos & Campos, 2010 Gravitational Model 13 M N - Mass of social network m a – Agente mass d – Average distance between agents F m – Force of migration

Anjos & Campos, 2010 Gravitational Model 14 m a – Agents mass M N – mass of the social network d a – average distance between agents

Anjos & Campos, 2010 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 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 16

Anjos & Campos, 2010 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

Anjos & Campos, 2010 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 18

Anjos & Campos, 2010 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: 19 CountryVariableSimularionZ*Z* p-value Country of originVariableScenarioZ*p-value GermanyWorking situation (w)I-1,7180,0858 ChinaHH Income (r)I-1,3620,1731 Working situation (w)I-0,8890,3743 MexicoHH Income (r)I-1,3620,1731 Hh Income (r)II-1,2440,2135 * Wilcoxon test, p<0,05

Porto, 15 de Março de 2010 Density and Centrality degree

Porto, 15 de Março de Density Mexico – Simulation I

Anjos & Campos, 2010 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 22

Anjos & Campos, 2010 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 23

Anjos & Campos, 2010 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

Anjos & Campos, 2010 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

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

Anjos & Campos, 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)) 27

Anjos & Campos, 2010 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. 28

Anjos & Campos, 2010 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.

Anjos & Campos, 2010 Parâmetros da simulação Idade (y) 1 y 95 Atribuição de y Distribuição normal, N(y, y ) 30 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 ( min e,max e ) Rendimento do agregado familiar (r) r = [2; +[ Atribuição do rendimento Distribuição normal, N(r, r )

Anjos & Campos, 2010 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 31 Número de pessoas do agregado familiar (p) 1 p 15 Atribuição de p Distribuição aleatória uniforme, U ( 1º quartil p,3ºquartil p ) 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,max s )

Anjos & Campos, 2010 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 32

Anjos & Campos, 2010 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 33

Porto, 15 de Março de Estabilidade do modelo Variável 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