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Probabilistic Projections of the Total Fertility Rate for All Countries

Abstract

We describe a Bayesian projection model to produce country-specific projections of the total fertility rate (TFR) for all countries. The model decomposes the evolution of TFR into three phases: pre-transition high fertility, the fertility transition, and post-transition low fertility. The model for the fertility decline builds on the United Nations Population Division’s current deterministic projection methodology, which assumes that fertility will eventually fall below replacement level. It models the decline in TFR as the sum of two logistic functions that depend on the current TFR level, and a random term. A Bayesian hierarchical model is used to project future TFR based on both the country’s TFR history and the pattern of all countries. It is estimated from United Nations estimates of past TFR in all countries using a Markov chain Monte Carlo algorithm. The post-transition low fertility phase is modeled using an autoregressive model, in which long-term TFR projections converge toward and oscillate around replacement level. The method is evaluated using out-of-sample projections for the period since 1980 and the period since 1995, and is found to be well calibrated.

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Acknowledgements

The project described was partially supported by Grant Numbers R01 HD054511 (Adrian E. Raftery, Principal Investigator) and HD057246 (Samuel J. Clark, Principal Investigator) from the National Institute of Child Health and Human Development (NICHD). The views and opinions expressed in this article are those of the authors and do not necessarily represent the official views of the NICHD or those of the United Nations. The authors are grateful to Kirill Andreev, John Bongaarts, Jennifer Chunn, Joel Cohen, Timothy Dyson, Taeke Gjaltema, Peter Johnson, Vladimira Kantorova, Nico Keilman, Pablo Lattes, Nan Li, Peter Way, Hania Zlotnik, and three anonymous reviewers for helpful discussions and insightful comments, and to Hana Ševčíková for software development. Alkema thanks the United Nations Population Division for hospitality.

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Correspondence to Leontine Alkema.

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Alkema, L., Raftery, A.E., Gerland, P. et al. Probabilistic Projections of the Total Fertility Rate for All Countries. Demography 48, 815–839 (2011). https://doi.org/10.1007/s13524-011-0040-5

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  • DOI: https://doi.org/10.1007/s13524-011-0040-5

Keywords

  • Autoregressive model
  • Bayesian hierarchical model
  • Fertility projection methodology
  • Markov chain Monte Carlo
  • United Nations World Population Prospects