The Role of Social Interactions in Demography: An Agent Based - - PowerPoint PPT Presentation

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Alexia Fürnkranz-Prskawetz

Institute of Mathematical Methods in Economics, Vienna University of Technology Vienna Institute of Demography, Austrian Academy of Sciences Wittgenstein Centre for Demography and Global Human Capital

The Role of Social Interactions in Demography: An Agent Based Modelling Approach

Workshop: Recent Developments and Future Directions in Agent-Based Modelling in Population Studies, KU Leuven 19th September, 2014

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• 1. Introduction
• 2. The gap between theory and techniques in demography
• 3. Three examples

The Wedding Ring - Mate search and marriage Transition to parenthood – Social Interaction and Social networks Family policies – Social Structure

• 4. The potential role of agent-based computational

demography

Structure of the talk

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⇒ ABC uses computational approach to the study of human behavior. ⇒ ABC models do not aim to understand why specific rules are applied by humans BUT pre-suppose rules of behavior and verify whether these micro based rules can explain macroscopic regularities. ⇒ Emphasis on explanation rather than on prediction

• f behavior; models are based on individual agents

(agent-based modeling).

• 1. Introduction

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„Whereas the purpose of induction is to find patterns in data and that of deduction is to find consequences

• f assumptions, the purpose of agent-based modelling

is to aid intuition“ (Axelrod, 1997)

• 1. Introduction

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Two good examples: ⇒ micro-macro link (good theories of behavior and good statistical models but difficult link between them) ⇒ ‘subjective’ aspects (values, norms, psychological aspects, cognition, emotions) of demographic behavior

• 2. The gap between theory and techniques in

demography

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Some reasons for the gap:

• 1. Poor level of precision in theoretical constructs

(especially in sociological-based theories). Sometimes theory is too vague.

• 2. Insufficient theoretical basis of statistical analyses

and data collection.

• 3. Difficult observability of important theoretical pieces

(e.g. values, norms).

• 2. The gap between theory and techniques in

demography

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Why is ABCD advantageous?

• 1. Precision: theoretical statements have to be written in

a precise way to be implemented in a program (including subjective aspects).

• 2. Mathematical tractability is less a limit for formalized

theoretical constructions.

• 3. Bottom-up approach (solving the micro-macro link

allowing for interactions), using micro-based theories.

• 2. The gap between theory and techniques in

demography

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Billari, F., A. Prskawetz, B. Aparicio Diaz and T. Fent (2007) The Wedding-Ring”: An agent-based marriage model based on social interaction, Demographic Research, Vol. 17, 59-82. Aparicio Diaz, B., T. Fent, A. Prskawetz and L. Bernardi (2011) Transition to Parenthood: The Role of Social Interaction and Endogenous Networks, Demography 48, 559-579. Fent, T., B. Aparicio Diaz and A. Prskawetz (2013) Family policies in the context of low fertility and social structure, Demographic Research, Vol. 29, 963-998.

• 3. Examples

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Timing of marriage has been studied from 2 different perspectives: Demographers: Explaining & modeling shape of age-at-marriage curves  mathematical and statistical macro-level models Psychologists and economists: Studying & modeling process of partner search  micro-level models Agent-based modeling: Models that account for macro-level marriage patterns starting from plausible micro-level assumptions and allowing for interactions between potential partners.

Wedding Ring

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Benchmark against which we test our model: shape of the age-at-marriage hazard function

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 18 23 28 33 38 43 48 Romania Women, 1998 Romania Men, 1998 Norway Men, 1998 Norway Women, 1998 Norway Men, 1978 Norway Women, 1978

Wedding Ring

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“observations” on social interaction and marriage homogamy in marriage w.r.t. socioeconomic status, religion, ethnicity, etc. (closeness matters) number of relevant others increases with age during youth and adulthood, and decreases thereafter social learning and social influence may trigger diffusion

• f marriage within social network (share of married

people in social network matters) NOTE: highest incidence of marriage occurs within a social network of a relatively high share of both married and unmarried persons

Wedding Ring

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An agent based model spatial location of each agent: ϕ ∈[0,2π] additional coordinate: age x

availability

• f mates

desirability

• f marriage

Wedding Ring

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Flow diagram

mutual search starting at age 16

Wedding Ring

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Simulation results

Hazard of marriage in a population of simulated agents with alternative settings for social pressure. WOMEN

A: only social pressure, independent of age of agent, determines potential partners B: A + including age dependency of network size C: constant social pressure, ignores increase of social pressure with age D: linear instead of S-shaped social pressure

Wedding Ring

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The macro-level shape of the age-at-marriage pattern emerges from the bottom up as an outcome of individual behavior and social interactions Including the age dependency of network size is a key determinant to obtain the emergence of the hazard function as empirically verified !

Wedding Ring

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Transition to Parenthood

• Fertility behavior of individuals depends not only on family

background variables and life course paths but also on the behavior and characteristics of other individuals (social networks)

• Social multiplier effects and multiple equilibria can be explained

through social network effects

• Within social networks:

exchange information about childbearing choices learn about other’s preferences feel induced to conform to other’s norms, ….

• Variation of network by marital and parental status

 introduce agent-based model to study endogenous network structure

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Transition to Parenthood

Model implementation

Agents One sex model (only female agents) Age x Intended Education ie Parity p Social Network (peer group)

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Transition to Parenthood

Initial population

Age Structure: Austrian female age distribution Intended Education: Austrian education distribution at age 30 Parity: Austrian distribution by age, education and parity Social Network: probability of a link based on similarity of individuals

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Transition to Parenthood Micro-level dynamics

Agent´s Individual Probability of having a Child

) , ( p x bpr

t

i

si

empirical/average age- and parity specific birth probability at time t multiplier to take social influence into account Age of youngest child, g(.) monotonically decreases

i

xc

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Transition to Parenthood Macro-level dynamics

Update of birth probabilities at the macro level according to the average social influence multiplier

) , ( * ) , ( ) , (

1

p x si p x bpr p x bpr

t t t

=

+

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Transition to Parenthood Network typology

distance among agents i and j

ε parameter to adjust for possible differences in age and education

probability of choosing a certain distance d Agent chooses d with respect to pr1(d) and then picks a friend uniformly among all individuals with distance d

ε

j i j i ij

e e x x d − + − =

( )

d c d pr α − = exp ) (

1

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Transition to Parenthood Social influence

      − π − π β + π − π β ξ + = 2 1 1 1 *)) ( * exp( *)) ( exp( si

β ξ ,

intensity of social influence share of members of the peer group with parity ≥ p share of agents with parity ≥ p in the whole population

π * π

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Transition to Parenthood Sensitivity w.r.t. parameters

Plot of sum of absolute differences between simulated and observed age specific fertility rates in 2004. N=50000, average over 25 simulation runs

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Transition to Parenthood Simulation without Social Interaction

Simulation results for simulating 20 years starting from 1984

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Transition to Parenthood Simulation with Social Interaction

Simulation results for simulating 20 years starting from 1984

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Transition to Parenthood Simulation with Social Interaction – Forecasting

Simulation results for simulating 20 years starting from 1984 causal model instead

• f continuing existing

trends !

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Family Policies

Effectiveness of family policies in the context of social structure Direct effect of family policy: alleviation of resource constraint Indirect effect of family policy: diffusion of fertility intentions via social ties Result: family policies can only be successful if they are designed to take into account the characteristics of the society in which they are implemented!

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Family Policies

budget disposable n consumptio childrens' n consumptio individual

, , , , , , , , , n t i t i t i t i t i t i n t i t i t i

c c w y w n c w c − − = = = τ σ

consumption (of time and money) c is a concave function of household budget w

• Consumption and disposable budget

i,t

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Family Policies

• Necessary conditions for having an additional

child ( )

child additional an

• f

n consumptio exceeds budget disposable 1 parity actual exceeds fertility intended

, , , , , ,

τ σ τ + + ≥ ⇔ ≥ >

t i t i t i t i t i t i

n w w y p f

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Family Policies

• Impact of family policies

( ) ( )

( )

        − − + + ≥ − − − − = − − =

t i v t i f t i t i t i v f t i t i t i t i t i t i v f t i t i n t i t i v f

w b w b n w w b b w n w w y w b b w n c w b b

, , , , , , , , , , , , , , ,

1 budget household to al proportion policies family policies family fixed τ σ τ σ τ

i,t

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Family Policies

• Endogenous Social Network

Tendency of individuals to associate with other individuals who have similar characteristics. social distance:

Choose distance with probability:

pick up an agent with distance d as new friend

( ) ( )

homphily

• f

intensity parameter ion normalisat agents

• between tw

distance social exp

1

α α c d d c d pr − =

fertility intended income age

2 1 i i i j i j i j i ij

f z x f f z z x x d − + − + − = ε ε

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Family Policies

high level of transitivity low level of transitivity

In our model network transitivity is varied via pr2 determining the probability of choosing a new friend only among those individuals who are linked to at least one of the agent’s friends.

Network transitivity

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Family Policies

( )

( ) ( ) ( )

parameters numerical ies, probabilit , 1 1 1 1 fertility intended parity s.t. network social s ' within agents

• f

number

4 3 4 , 3 ,

  pr pr pr p pr p f p i j

i i

t i t i i,t j i i

− +

− − = − − = < >

− + − + π π

π π

Probability of being positive (negative) influenced by at least

• ne agent from the peer group

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Family Policies

Probability of increasing, decreasing or keeping the intended fertility constant:

where κ determines the fraction of individuals who increase (decrease) their intended fertility in the case of a mixed influence.

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Family Policies

• initial population: 5000 female agents
• 6 random initial populations
• 88 different sets of family policies
• 1404 different sets of parameters

determining social structure (homophily, social distance, social effects)

• 741312 (=6*88*1404) simulation runs
• Simulations

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Family Policies

Cohort fertility - Policy mix

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Family Policies

Intended fertility - Policy mix

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Family Policies

Fertility Gap - Policy mix

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Family Policies

• positive and significant impact of fixed and proportional

family policies on intended fertility and completed cohort fertility negative and significant impact on fertility gap

• Proportional family policies contribute more to indirect

effect Fixed family policies contribute equally to direct and indirect effect

• Conclusions

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Family Policies

• Homophily increases cohort fertility / intended fertility

and reduces fertility gap, HOWEVER family policies are less effective the higher the homophily

• Network transitivity – not strongly significant
• Impact of fixed and proportional family policies

depends on parameter range investigated. Family policies can only be successful if they explicitly take into account the characteristics of the society to which they are applied.

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• 4. The potential role of ABC

⇒ Simulation has been used in demography,

e.g. micro-simulation ⇒ The focus is on the impact of rates/probabilities (or changes of them) on population dynamics. ⇒ ABCD would include the traditional rate- based approach but also (and especially) the ‘new’ rule-based approach, and mixture of rate-based and rule-based approaches. ⇒Aim: understanding processes, theorizing via simulation (as complementary to theorizing via statistical modeling).

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• 4. The potential role of ABC

Characteristics and good features of ABCD: ⇒ Micro-based demography: agents have a central role (as in the life course approach), but they can interact with other agents and levels. ⇒ Focus on mechanisms: ‘how’ helps us to understand ‘why’. ⇒ Emergent phenomena: some of the demographic ‘laws’ can be seen as emerging from the bottom-up. ⇒ Artificial situation: we may easily study complex societies.

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• 4. The potential role of ABC

⇒ Agent-based modeling can be used as a demographic

laboratory to test the consistence of theories before embarking in expensive surveys (including ‘difficult’ concepts such as values…). Demography studies populations, and agent-based models are always population models. It is a sort of a natural field for applying agent-based modeling and embedding them in a solid empirical and mathematical modeling tradition.

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