Including Feedback Mechanisms in Micro-simulation Demographic Models Mike Murphy, Department of Social Policy, London School of Economics, Houghton Street, London WC2A 2AE

Micro-simulation Micro-simulation used to estimate the numbers and types of kin that people are likely to have under various demographic conditions. We start with known or assumed population of many individuals, and then simulate individual demographic events. This produces a set of individual records, with a statistical pattern of individual demographic events similar to what would be observed in a real population with fertility, mortality, nuptiality, migration etc..

WORKSHOP ON MODELLING AND SIMULATIONS Woodhouse Rooms, University of Leeds Monday, 17 March 2003

The discipline of demography Demographers …use the term population to refer to a … collectivity that persists through time even though its members are continuously changing through attrition and accession. This collectivity persists even though … a virtually complete turnover of its members occurs at least once a century. Demographic analysis focuses on this enduring collectivity. Preston, Heuvaline and Guillot (2001, p1)

Micro-simulation in Demography Black Box eg reproduction Entry to risk -> Pregnant -> Outcome -> Re- entry to risk Complex systems eg kinship Interest in variability as well as averages

The SOCSIM Model An initial population of individuals sub-divided by sex and age is fed to the computer, and these individuals age month by month; Some will marry (or cohabit) with each other, give birth, divorce or remarry, and finally they die The occurrence of these events for each person at a given age, sex, marital status etc is determined by random numbers in accordance with probabilities of occurrence specified by the user's choice of governing demographic rates

The SOCSIM Model Over time, full sets of links between kin are generated, such as grandparents/grandchildren and cousins as the population evolves and these are available for analysis SOCSIM is a 'closed model' simulation, in which spouses are chosen from within the simulated population list rather than created with some profile of characteristics from outside it, as is the case with an 'open model'

Research Questions What level of variability is intrinsic? How can it be reduced? What actions are important in maintaining Population size Lineages What are the long-term patterns?

Behavioural underpinnings While macro-level analyses have emphasised macro-level outcomes such as overall population size, individuals and families have different objectives, such as maintaining lineages, which are constrained by the inherent stochastic nature of demographic processes such as the sex of a child or the death of a spouse. Stem family preferences which gives greater emphasis to the nuptiality of one sib appears to provide little difference in perpetuating lineages compared with an unconstrained

Alternative scenarios considered (1) Standard Monte Carlo simulation with approximate stationary values of fertility, mortality and nuptiality (2) Nuptiality depends on the population size according to the formula Nuptiality_adjusted = Target_population / Nuptiality_original (3) Nuptiality_adjusted = 2.5 * Nuptiality_original for first-born sons (4) Migration possible for single adults

Simulation population Population dynamics for small populations with the demographic characteristics of the population of England and Wales around 1751 (Wrigley and Schofield, 1989). I use these empirical rates as inputs to the simulation for periods of up to 600 years (nominally 1250 to 1850). The initial populations are of size 200 to 8,000.

Summary of demographic parameters used PeriodTFR (per 1,000) e 0 (males) Age at first marriage (males) ,

Results Standard Monte Carlo micro-simulation models tend to show greater variability than is observed in the dynamics of human populations. Alternative negative feedback mechanisms may lead to more realistic patterns of growth within an agent-based framework. Nuptiality adjustment is sufficient to maintain population homeostasis in most cases Parity-specific adjustment does not lead to major differences from the unconstrained model

Population sizes: 250 simulations of initial population size 2000

Variance of population size distributions

Population sizes: 250 simulations of initial population size 2000 with nuptiality constrained

Population with Fixed Target Proportion with offspring after & Migration/No Migration 150years

Number of ancestors (non-distinct) GenerationsYearsPopulation size , , ,048, ,554, ,073,741, ,359,738,368

Number of descendants

Sum of degree of relatedness

References Murphy, M. (2001) Family and kinship networks in the context of aging societies. Paper prepared for the Conference on Population Ageing in the Industrialized Countries: Challenges and Responses organised by the Committee on Population Age Structures and Public Policy of the International Union for the Scientific Study of Population (IUSSP) and the Nihon University Population Research Institute (NUPRI), Tokyo, Japan, March Murphy, M. and D. Wang. (2002) The impact of intergenerationally-transmitted fertility and nuptiality on population dynamics in contemporary populations, in J. Rodgers and H-P. Kohler (eds.), Biodemography of Human Reproduction and Fertility. Boston: Kluwer Academic Publishers, pp Murphy, M. (2003, forthcoming) Tracing Very Long-Term Kinship Networks Using SOCSIM. To appear in Demographic Research. Murphy, M. (2003, forthcoming) Bringing behaviour back into micro-simulation: Feedback mechanisms in demographic models. To appear in Alexia Fürnkranz- Prskawetz and Francesco Billari (eds) Agent-Based Computational Demography. Physica Verlag.