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Stochastic population forecasts using functional data models for mortality, fertility and migration

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  • Rob J Hyndman
  • Heather Booth

Abstract

Age-sex-specific population forecasts are derived through stochastic population renewal using forecasts of mortality, fertility and net migration. Functional data models with time series coefficients are used to model age-specific mortality and fertility rates. As detailed migration data are lacking, net migration by age and sex is estimated as the difference between historic annual population data and successive populations one year ahead derived from a projection using fertility and mortality data. This estimate, which includes error, is also modeled using a functional data model. The three models involve different strengths of the general Box-Cox transformation chosen to minimise out-of-sample forecast error. Uncertainty is estimated from the model, with an adjustment to ensure the one-step-forecast variances are equal to those obtained with historical data. The three models are then used in the Monte Carlo simulation of future fertility, mortality and net migration, which are combined using the cohort-component method to obtain age-specific forecasts of the population by sex. The distribution of forecasts provides probabilistic prediction intervals. The method is demonstrated by making 20-year forecasts using Australian data for the period 1921-2003.

Suggested Citation

  • Rob J Hyndman & Heather Booth, 2006. "Stochastic population forecasts using functional data models for mortality, fertility and migration," Monash Econometrics and Business Statistics Working Papers 14/06, Monash University, Department of Econometrics and Business Statistics.
  • Handle: RePEc:msh:ebswps:2006-14
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    1. Ortega, Jose Antonio & Poncela, Pilar, 2005. "Joint forecasts of Southern European fertility rates with non-stationary dynamic factor models," International Journal of Forecasting, Elsevier, vol. 21(3), pages 539-550.
    2. Lee, Sang-Hyop & Mason, Andrew, 2007. "Who gains from the demographic dividend? Forecasting income by age," International Journal of Forecasting, Elsevier, vol. 23(4), pages 603-619.
    3. Nan Li & Ronald Lee, 2005. "Coherent mortality forecasts for a group of populations: An extension of the lee-carter method," Demography, Springer;Population Association of America (PAA), vol. 42(3), pages 575-594, August.
    4. Andrei Rogers & Luis Castro & Megan Lea, 2005. "Model Migration Schedules: Three Alternative Linear Parameter Estimation Methods," Mathematical Population Studies, Taylor & Francis Journals, vol. 12(1), pages 17-38.
    5. Renshaw, A. E. & Haberman, S., 2003. "On the forecasting of mortality reduction factors," Insurance: Mathematics and Economics, Elsevier, vol. 32(3), pages 379-401, July.
    6. Peter Congdon, 1993. "Statistical Graduation in Local Demographic Analysis and Projection," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 156(2), pages 237-270, March.
    7. Lee, Ronald D., 1992. "Stochastic demographic forecasting," International Journal of Forecasting, Elsevier, vol. 8(3), pages 315-327, November.
    8. Ronald Lee & Timothy Miller & Michael Anderson, 2004. "Stochastic Infinite Horizon Forecasts for Social Security and Related Studies," NBER Working Papers 10917, National Bureau of Economic Research, Inc.
    9. Miller, Robert B., 1986. "A bivariate model for total fertility rate and mean age of childbearing," Insurance: Mathematics and Economics, Elsevier, vol. 5(2), pages 133-140, April.
    10. Ronald Lee & Timothy Miller, 2001. "Evaluating the performance of the lee-carter method for forecasting mortality," Demography, Springer;Population Association of America (PAA), vol. 38(4), pages 537-549, November.
    11. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
    12. Shripad Tuljapurkar & Nan Li & Carl Boe, 2000. "A universal pattern of mortality decline in the G7 countries," Nature, Nature, vol. 405(6788), pages 789-792, June.
    13. Nico Keilman & Dinh Quang Pham, 2004. "Empirical errors and predicted errors in fertility, mortality and migration forecasts in the European Economic Area," Discussion Papers 386, Statistics Norway, Research Department.
    14. Arthur Renshaw & Steven Haberman, 2003. "Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 52(1), pages 119-137, January.
    15. Booth, Heather, 2006. "Demographic forecasting: 1980 to 2005 in review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 547-581.
    16. Oliver Lipps & Frank Betz, 2004. "Stochastic Population Projection for Germany," MEA discussion paper series 04059, Munich Center for the Economics of Aging (MEA) at the Max Planck Institute for Social Law and Social Policy.
    17. Robert McNown & Andrei Rogers, 1989. "Forecasting Mortality: A Parameterized Time Series Approach," Demography, Springer;Population Association of America (PAA), vol. 26(4), pages 645-660, November.
    18. Heather Booth & Rob Hyndman & Leonie Tickle & Piet de Jong, 2006. "Lee-Carter mortality forecasting: a multi-country comparison of variants and extensions," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 15(9), pages 289-310.
    19. Jan Hoem & Dan Madien & Jørgen Nielsen & Else-Marie Ohlsen & Hans Hansen & Bo Rennermalm, 1981. "Experiments in modelling recent Danish fertility curves," Demography, Springer;Population Association of America (PAA), vol. 18(2), pages 231-244, May.
    20. Bircan Erbas & Rob J. Hyndman & Dorota M. Gertig, 2005. "Forecasting age-specific breast cancer mortality using functional data models," Monash Econometrics and Business Statistics Working Papers 3/05, Monash University, Department of Econometrics and Business Statistics.
    21. Lee, Ronald D., 1993. "Modeling and forecasting the time series of US fertility: Age distribution, range, and ultimate level," International Journal of Forecasting, Elsevier, vol. 9(2), pages 187-202, August.
    22. Alho, Juha M., 1992. "The magnitude of error due to different vital processes in population forecasts," International Journal of Forecasting, Elsevier, vol. 8(3), pages 301-314, November.
    23. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    24. Tom Wilson & Martin Bell, 2004. "Australia's uncertain demographic future," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 11(8), pages 195-234.
    25. Renshaw, A. E. & Haberman, S., 2003. "Lee-Carter mortality forecasting with age-specific enhancement," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 255-272, October.
    26. Nico Keilman, 2001. "Uncertain population forecasts," Nature, Nature, vol. 412(6846), pages 490-491, August.
    27. Carter, Lawrence R. & Lee, Ronald D., 1992. "Modeling and forecasting US sex differentials in mortality," International Journal of Forecasting, Elsevier, vol. 8(3), pages 393-411, November.
    28. Brouhns, Natacha & Denuit, Michel & Vermunt, Jeroen K., 2002. "A Poisson log-bilinear regression approach to the construction of projected lifetables," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 373-393, December.
    29. Nico Keilman & Dinh Quang Pham & Arve Hetland, 2002. "Why population forecasts should be probabilistic - illustrated by the case of Norway," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 6(15), pages 409-454.
    30. Nico Keilman & Dinh Quang Pham, 2000. "Predictive Intervals for Age-Specific Fertility," European Journal of Population, Springer;European Association for Population Studies, vol. 16(1), pages 41-65, March.
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    More about this item

    Keywords

    Fertility forecasting; functional data; mortality forecasting; net migration; nonparametric smoothing; population forecasting; principal components; simulation.;
    All these keywords.

    JEL classification:

    • J11 - Labor and Demographic Economics - - Demographic Economics - - - Demographic Trends, Macroeconomic Effects, and Forecasts
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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