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Regional probabilistic fertility forecasting by modeling between-country correlations

Author

Listed:
  • Bailey Fosdick

    (Duke University)

  • Adrian E. Raftery

    (University of Washington)

Abstract

Background: The United Nations (UN) Population Division constructs probabilistic projections for the total fertility rate (TFR) using the Bayesian hierarchical model of Alkema et al. (2011), which produces predictive distributions of the TFR for individual countries. The UN is interested in publishing probabilistic projections for aggregates of countries, such as regions and trading blocs. This requires joint probabilistic projections of future countryspecific TFRs, taking account of the correlations between them. Objective: We propose an extension of the Bayesian hierarchical model that allows for probabilistic projection of aggregate TFR for any set of countries. Methods: We model the correlation between country forecast errors as a linear function of time invariant covariates, namely whether the countries are contiguous, whether they had a common colonizer after 1945, and whether they are in the same UN region. The resulting correlation model is incorporated into the Bayesian hierarchical model’s error distribution. Results: We produce predictive distributions of TFR for 1990-2010 for each of the UN's primary regions. We find that the proportions of the observed values that fall within the prediction intervals from our method are closer to their nominal levels than those produced by the current model. Conclusions: Our results suggest that a substantial proportion of the correlation between forecast errors for TFR in different countries is due to the countries' geographic proximity to one another, and that if this correlation is accounted for, the quality of probabilistic projections of TFR for regions and other aggregates is improved.

Suggested Citation

  • Bailey Fosdick & Adrian E. Raftery, 2014. "Regional probabilistic fertility forecasting by modeling between-country correlations," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(35), pages 1011-1034.
    • Handle: RePEc:dem:demres:v:30:y:2014:i:35
    DOI: 10.4054/DemRes.2014.30.35
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    References listed on IDEAS

    as
    1. 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.
    2. Wolfgang Lutz & Warren Sanderson & Sergei Scherbov, 2001. "The end of world population growth," Nature, Nature, vol. 412(6846), pages 543-545, August.
    3. Mayer, Thierry & Zignago, Soledad, 2006. "Notes on CEPII’s distances measures," MPRA Paper 26469, University Library of Munich, Germany.
    4. Alho, Juha, 2008. "Aggregation across countries in stochastic population forecasts," International Journal of Forecasting, Elsevier, vol. 24(3), pages 343-353.
    5. Ševčíková, Hana & Alkema, Leontine & Raftery, Adrian, 2011. "bayesTFR: An R package for Probabilistic Projections of the Total Fertility Rate," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i01).
    6. Bailey K. Fosdick & Adrian E. Raftery, 2012. "Estimating the Correlation in Bivariate Normal Data With Known Variances and Small Sample Sizes," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 34-41, February.
    7. Leontine Alkema & Adrian Raftery & Patrick Gerland & Samuel Clark & François Pelletier & Thomas Buettner & Gerhard Heilig, 2011. "Probabilistic Projections of the Total Fertility Rate for All Countries," Demography, Springer;Population Association of America (PAA), vol. 48(3), pages 815-839, August.
    8. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
    9. Adrian Raftery & Jennifer Chunn & Patrick Gerland & Hana Ševčíková, 2013. "Bayesian Probabilistic Projections of Life Expectancy for All Countries," Demography, Springer;Population Association of America (PAA), vol. 50(3), pages 777-801, June.
    10. Wolfgang Lutz & Warren Sanderson & Sergei Scherbov, 1997. "Doubling of world population unlikely," Nature, Nature, vol. 387(6635), pages 803-805, June.
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    Cited by:

    1. Daphne H. Liu & Adrian E. Raftery, 2020. "How Do Education and Family Planning Accelerate Fertility Decline?," Population and Development Review, The Population Council, Inc., vol. 46(3), pages 409-441, September.
    2. Kevin Rennert & Brian C. Prest & William A. Pizer & Richard G. Newell & David Anthoff & Cora Kingdon & Lisa Rennels & Roger Cooke & Adrian E. Raftery & Hana Sevcikova & Frank Errickson, 2021. "The Social Cost of Carbon: Advances in Long-Term Probabilistic Projections of Population, GDP, Emissions, and Discount Rates," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 52(2 (Fall)), pages 223-305.
    3. Raftery, Adrian E. & Ševčíková, Hana, 2023. "Probabilistic population forecasting: Short to very long-term," International Journal of Forecasting, Elsevier, vol. 39(1), pages 73-97.
    4. Lin Ma & Manhua Wu & Xiujuan Tian & Guanheng Zheng & Qinchuan Du & Tian Wu, 2019. "China’s Provincial Vehicle Ownership Forecast and Analysis of the Causes Influencing the Trend," Sustainability, MDPI, vol. 11(14), pages 1-26, July.
    5. Michael Pearce & Adrian E. Raftery, 2021. "Probabilistic forecasting of maximum human lifespan by 2100 using Bayesian population projections," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 44(52), pages 1271-1294.
    6. Hana Sevcikova & Patrick Gerland & Adrian E. Raftery, 2018. "Probabilistic projection of subnational total fertility rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 38(60), pages 1843-1884.

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    More about this item

    Keywords

    forecasting; probabilistic projection; total fertility rate (TFR); correlation; aggregation; pseudolikelihood;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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