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Probabilistic Forecasting Using Stochastic Diffusion Models, With Applications to Cohort Processes of Marriage and Fertility

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  • Mikko Myrskylä
  • Joshua Goldstein

Abstract

In this article, we show how stochastic diffusion models can be used to forecast demographic cohort processes using the Hernes, Gompertz, and logistic models. Such models have been used deterministically in the past, but both behavioral theory and forecast utility are improved by introducing randomness and uncertainty into the standard differential equations governing population processes. Our approach is to add time-series stochasticity to linearized versions of each process. We derive both Monte Carlo and analytic methods for estimating forecast uncertainty. We apply our methods to several examples of marriage and fertility, extending them to simultaneous forecasting of multiple cohorts and to processes restricted by factors such as declining fecundity. Copyright Population Association of America 2013

Suggested Citation

  • Mikko Myrskylä & Joshua Goldstein, 2013. "Probabilistic Forecasting Using Stochastic Diffusion Models, With Applications to Cohort Processes of Marriage and Fertility," Demography, Springer;Population Association of America (PAA), vol. 50(1), pages 237-260, February.
    • Handle: RePEc:spr:demogr:v:50:y:2013:i:1:p:237-260
    DOI: 10.1007/s13524-012-0154-4
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    References listed on IDEAS

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    2. Joshua R. Goldstein, 2010. "A behavioral Gompertz model for cohort fertility schedules in low and moderate fertility populations," MPIDR Working Papers WP-2010-021, Max Planck Institute for Demographic Research, Rostock, Germany.
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    Cited by:

    1. Rachel Margolis & Mikko Myrskylä, 2015. "Parental Well-being Surrounding First Birth as a Determinant of Further Parity Progression," Demography, Springer;Population Association of America (PAA), vol. 52(4), pages 1147-1166, August.
    2. Dănuţ-Vasile Jemna & Mihaela David, 2018. "Post-transitional regional fertility in Romania," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(57), pages 1733-1776.
    3. Jonathan F. Fox & Sebastian Klüsener & Mikko Myrskylä, 2015. "Is a positive relationship between fertility and economic development emerging at the sub-national regional level? Theoretical considerations and evidence from Europe," MPIDR Working Papers WP-2015-006, Max Planck Institute for Demographic Research, Rostock, Germany.
    4. Jonathan Fox & Sebastian Klüsener & Mikko Myrskylä, 2019. "Is a Positive Relationship Between Fertility and Economic Development Emerging at the Sub-National Regional Level? Theoretical Considerations and Evidence from Europe," European Journal of Population, Springer;European Association for Population Studies, vol. 35(3), pages 487-518, July.
    5. Arun S. Hendi, 2019. "Proximate Sources of Change in Trajectories of First Marriage in the United States, 1960–2010," Demography, Springer;Population Association of America (PAA), vol. 56(3), pages 835-862, June.

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