Title: The role of Social Networks in the projection of international migration flows: an Agent-Based approach
1The 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
2Contents
- Motivation, goals
- The context
- Demography and migrations
- Social Networks
- The Multi-agent System
- The Model
- Variables
- Gravitational Model
- Simulation/Parameters
- Results
- Final Remarks
3Demography 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
4Motivation
- 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))
5Interaction between social mechanisms
Interaction between social mechanisms - Billari
e Prskawetzy (2005)
6Main goals
- Verify the effect of the structure of social
networks on the migration flows - Social network analysis
- Density
- Degree centralization
- Input
- Output
- General
7Social 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
8Indicators 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
9Multi-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
10Our 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
11Gravitational 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
12Gravitational 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
13Gravitational Model
Fm Force of migration
ma Agente mass
MN - Mass of social network
d Average distance between agents
G 1
14Gravitational Model
da average distance between agents
ma Agents mass
MN mass of the social network
15The 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)
16Parameters 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
17Parameters 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
18Simulation
- 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
19Validation
- 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
20Density and Centrality degree
21Density
Mexico Simulation I
Ano 2008, n 2476
Ano 2000, n 404
22Final 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
23Limitations 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
24Some 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.
25The 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
26IMPORTÂNCIA 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
27Migração
- 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))
28Redes 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.
29Algorithm
- 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.
30Parâmetros 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)
31Parâmetros 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)
32Redes 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
33Recursos 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
34Estabilidade 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